DEVELOPMENT OF A HIGH-BRIGHTNESS ELECTRON BEAM SYSTEM
TOWARDS FEMTOSECOND MICRODIFFRACTION AND IMAGING AND ITS
APPLICATIONS
By
Kiseok Chang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics - Doctor of Philosophy
2014

ABSTRACT
DEVELOPMENT OF A HIGH-BRIGHTNESS ELECTRON BEAM
SYSTEM TOWARDS FEMTOSECOND MICRODIFFRACTION AND
IMAGING AND ITS APPLICATIONS
By
Kiseok Chang
To make a ‘molecular movie’, an ‘ultrafast camera’ with simultaneously very high spatial
and temporal resolution to match the atomic dynamics is required. The ultrafast electron
diffraction (UED) technique based on femtosecond laser technology can provide a basic
framework for realizing such an ‘ultrafast camera’ although this technology has not achieved its
full utility as a universal imaging and spectroscopy tool, due to limitations in generation and
preservation of a high–brightness electron beam in the ultrafast regime.
With moderate electron pulse intensity (103-104 electrons per pulse), UED experiments
have been successfully applied to investigate photo-induced non-thermal melting processes,
structural phase transitions, and transient surface charge dynamics. Based on the previous
development of ultrafast electron diffractive voltammetry (UEDV), we extend the UEDV with
an aim to identify the different constituents of the measured transient surface voltage (TSV) and
discuss their respective roles in Coulomb refraction. From applying this methodology on Si/SiO2
interface and surfaces decorated with nano-structures, we are able to elucidate localized charge
injection, dielectric relaxation, carrier diffusion, and enhancements on such processes through
surface plasmon resonances, with direct resolution in the charge state and possibly correlated
structural dynamics at these interfaces. These new results highlight the high sensitivity of the
interfacial charge transfer to the nanoscale modification, environment, and surface plasmonics

enhancement and demonstrate the diffraction-based ultrafast surface voltage probe as a unique
method to resolve the nanometer scale charge carrier dynamics.
The future applications of the UED and UEDV techniques lie in the direct visualization
and site-selected studies such as nano-structured interfaces, a single nanoparticle or domain,
which can be enabled by the development of high-brightness ultrafast electron beam system for
ultrafast electron diffraction. To realize the high-brightness beam, we have developed a highbrightness ultrafast electron beam column equipped with a 100 keV Pierce photoelectron gun
and an RF compressor. We are able to generate up to ~5!106 electron per pulse, and, more
importantly with the capability of micro-focusing, we have achieved a high dose delivery to the
sample by three orders of magnitude (up to ~2000 electron/"m2) higher than those of
conventional UED electron systems. In this high intensity pulsed electron beam system, the
major challenge is overcoming strong Coulomb repulsion among electrons (space–charge effect)
in the pulse, because the space–charge effect causes the electron pulse expansion in transverse
and longitudinal direction. To correct the space–charge effect, we have implemented the
magnetic lenses for transverse focusing of the electron pulse, and radio frequency (RF) cavity for
longitudinal recompression of the pulse. Such a system will provide enough flexibility to
manipulate electron pulse phase space, so various experiments that require high spatial and
temporal coherence and/or high-density beam optimized for microdiffraction can be achieved.

To Soyeon, Damian, and Gabriel ....

iv

ACKNOWLEDGMENTS

First and foremost I would like to acknowledge my advisor Prof. Chong-Yu Ruan for
his guidance and exceptional support, and our lab colleagues, Dr. Kihyun Kim, Tzong-Ru
Terry Han, Zhensheng Tao, Nan Du, Faran Zhou and Didi Luo. All the works presented
here would not have been possible to be achieved without their help. Especially, I can not
imagine my PhD degree without the help of Tzong-Ru Terry Han and Zhensheng Tao both
inside and outside of the lab.
I would also like to emphasize my deep appreciation to my previous advisor Prof. David
Tomanek, my first graduate chair Prof. Bhanu Mahanti, theoretical colleagues Savas Berber
and Teng Yang, my classmates and friends in Physics, Kyaw Zin Latt, Kritsada Kittimanpan and Tony Sunghun Ahn. I deeply appreciate all the MSU staffs, especially, Tom
Palazzolo, Tom Hudson, Jim Muns and Rob Bennett in Machine Shop helping us to build
our new ultrafast electron beam system and Reza Lolee to maintain and characterize our
vacuum systems.
I would like to acknowledge specific contributions to the work presented here, Dr. Kihyun Kim and Tzong-Ru Terry Han for performing the surface plasmon project with Au
nanoparticles; Zhensheng Tao, Austin Lo and Travis Salzillo for development of the new
generation ultrafast high–brightness electron beam system; Zhensheng Tao and Nan Du for
characterizing the high–brightness electron beam system; Ryan Murdick for initial development of the transient surface voltammetry technique; lastly, Prof. Chong-Yu Ruan for
his energetic involvement in all the works mentioned above.
Finally, I deeply appreciate my wife Soyeon Kim, my sons Damian Hyunjun Chang and
Gabriel Hyunsoo Chang, and my parents for their love and unconditional supports.
v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

Chapter 1 Introduction . . . . . . . . . . . .
1.1 Ultrafast Camera: Pump-Probe Technique
1.2 Ultrafast X-ray Diffraction . . . . . . . . .
1.3 Ultrafast Electron Diffraction . . . . . . .
Chapter 2
2.1

2.2

2.3

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Current Status of Ultrashort Pulse Development:
Electron . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ultrashort X-ray Pulse Generation . . . . . . . . . . . . . . .
2.1.1 High Harmonics Generation (HHG) . . . . . . . . . . .
2.1.2 Laser Driven Plasma (LDP) . . . . . . . . . . . . . . .
2.1.3 Free Electron Laser . . . . . . . . . . . . . . . . . . . .
Ultrashort Electron Pulse Generation . . . . . . . . . . . . . .
2.2.1 Compact Electron Gun . . . . . . . . . . . . . . . . . .
2.2.2 Single-Electron Pulses . . . . . . . . . . . . . . . . . .
2.2.3 MeV Ultrafast Electron Microscope . . . . . . . . . . .
2.2.4 KeV Ultrafast Electron Microscope . . . . . . . . . . .
Radiation effects induced by X-rays and electrons . . . . . . .

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X-ray and
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Chapter 3 Beam Dynamics in High-Brightness Pulsed Electron Beam-line
3.1 Electron Beam Phase Space Evolution . . . . . . . . . . . . . . . . . . . . .
3.1.1 Brightness and Emittance . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Phase Space Evolution along Electron Optics Systems . . . . . . . . .
3.1.3 Imaging and Aberrations . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Phase Space Evolution in High-Brightness Pulsed Electron Beam System . .
Chapter 4
4.1
4.2
4.3

4.4
4.5

Design of High-Brightness UEM Electron Beam Line at Michigan State University . . . . . . . . . . . . . . . . . . . . . . . . . .
Electron Source: Pierce Geometry DC Photoelectron Gun . . . . . . . . .
Magnetic Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radio-frequency (RF) Cavity . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 RF Field in Pillbox Cavity . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 RF Cavity in High-Brightness Electron Beam Line . . . . . . . . .
4.3.3 RF Station for RF Field and Electron Pulse Synchronization . . . .
Charge-coupled Device (CCD) Camera . . . . . . . . . . . . . . . . . . . .
Other Components for Optical and Electron Beam Delivery . . . . . . . . .
4.5.1 266 nm Excitation Mirror Holder and Electron Beam Shield . . . .

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4.6

4.5.2 Electron Beam Deflector . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5.3 Aperture Manipulator . . . . . . . . . . . . . . . . . . . . . . . . . . 71
The Ultra High Vacuum(UHV) Chamber . . . . . . . . . . . . . . . . . . . 74

Chapter 5 Characterization of The Electron Beam System
5.1 100 kV Pierce Geometry Electron Source . . . . . . . . . . .
5.1.1 Measurement Procedure for Electron Beam Current .
5.1.2 Electron Beam Current Measurement Results . . . .
5.1.3 Pepper Pot Technique for Emittance Measurement .
5.1.4 Beam Emittance Measurement . . . . . . . . . . . .
5.2 Magnetic Lens Focusing Characterization . . . . . . . . . . .
5.3 Phase Jitter of RF Compression . . . . . . . . . . . . . . . .
5.4 Performance Projection for UED Experiment . . . . . . . . .

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Chapter 6
6.1
6.2
6.3
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6.5
6.6
6.7
6.8
6.9

Further Development of Ultrafast Electron Diffractive Voltammetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Origins of Transient Photoinduced Surface Voltage . . . . . . . . . . . . . . 109
Surface Diffraction and Rocking Map Characterization . . . . . . . . . . . . 111
The General Formalism of Electron Diffractive Voltammetry . . . . . . . . . 115
Ultrafast Electron Diffractive Voltammetry Experiment: Photoemission Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Near Surface Field Induced by Photoemission . . . . . . . . . . . . . . . . . 124
Modeling of The Surface Photovoltammetry . . . . . . . . . . . . . . . . . . 127
Surface Photovoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Chapter 7
7.1
7.2
7.3

7.4

Photo-Induced Charge Carrier Dynamics at Nanostructured
Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface Charging of Pure SiO2 /Si Interface . . . . . . . . . . . . . . . . . .
Surface Charging of Au Nanoparticle Decorated Si/SiO2 Surface . . . . . .
Photo-induced Field Enhancement with Localized Surface Plasmon of Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 Localized Surface Plasmon of Gold Nanoparticles . . . . . . . . . .
7.3.2 Localized Surface Plasmon of Hollow Gold Nano-shell . . . . . . . .
7.3.3 Surface Plasmon Mediated Charge Dynamics of Au Nanoparticle Decorated SiO2 /Si Interface . . . . . . . . . . . . . . . . . . . . . . . .
7.3.4 Plasmon Mediated Spectral Hole Burning of Hollow Gold Nano-shell
on Si/SiO2 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 8
8.1

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Preliminary Experiment with High-Brightness Electron Beam
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Shadow Imaging and Beam Alignment . . . . . . . . . . . . . . . . . . . . . 167
vii

8.2 Convergent Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.3 RF Compression of High-Brightness Electron Beam: VO2 . . . . . . . . . . . 172
Chapter 9

Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . 182

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
Appendix A Diffraction Theory for Ultrafast Electron Diffraction . . . . . .185
Appendix B Experiment Setup of Ultrafast Electron Diffraction . . . . . . .197
Appendix C Formalism of diffracted voltammetry under small angle condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .209
Appendix D Magnetic Annealing Procedure . . . . . . . . . . . . . . . . . . . . . . .213
Appendix E Optimization of Pierce Geometry Electron Gun. . . . . . . . . . .214
Appendix F List of Initials and Acronyms . . . . . . . . . . . . . . . . . . . . . . . .217
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219

!

"###!

LIST OF TABLES

Table 2.1

Comparison among X-ray sources [23, 24]
† High average power mode with 10 W driving lasers, e.g., 2 mJ, 5
kHz
‡ Linac Coherent Light Source at Stanford Linear Accelerator Center

9

Table 2.2

Energy deposited in biological specimens [27] . . . . . . . . . . . . . 15

Table 4.1

The location of the optical components in the high-brightness UED
column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Table 4.2

Aperture Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Table 5.1

Electron dose D = Ne /A with CML1=1.0 A and Obj.ML=1.3 A . . 104

Table 5.2

Comparison of the electron dose among different high-flux UED
source
a Michigan State University
b University of Toronto/University of Hamburg Group
c McGill University
d Brookhaven National Laboratory
e Michigan State University (preliminary results) . . . . . . . . . . 106

Table 8.1

The electron beam properties with different conditions
N is the number of electrons per pulse.
2
D=N
A is the electron dose, A = π(HWHM) .
∆θ is a half divergence angle.
σ is the σ-width of the electron spot on the sample, not FWHM.
εx,n is the normalized transverse emittance.
Lt is the coherence length.
B4D = 2N is the 4D brightness. . . . . . . . . . . . . . . . . . . 170
εx,n

ix

LIST OF FIGURES

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 3.1

Schematic diagram of the pump-probe experiment setup. The relative time delay between pump(red) and probe(blue) pulses is controlled by the translational delay stage. . . . . . . . . . . . . . . . .

2

(a) Time-dependent diffracted intensity for (220) reflections. Red
curves are Gaussian fits to the data, corresponding to 10 to 90%
fall times of 280 fs [17] (b) X-ray diffraction efficiency of the (222)
Bragg peak as a function of time delay between the optical pump
pulse (fluence 6 mJ/cm2 ) and the X-ray probe pulse. The solid line
is fitted to the experimental data. The decrease of the mean value
of the X-ray signal (dotted line) is explained by the DebyeWaller
effect, and reflects the increasing random component of the atomic
motion [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Angular shift of (111) gold Bragg peak as a function of delay time
from the same nanocrystal. (a) and (b) are from different individual
nanocrystals. The blue dots are the experimental data and the solid
red line is the modeled peak shift [19]. . . . . . . . . . . . . . . . .

5

The melting dynamics of 2 nm Au nanoparticles. (Left) mRDF
map constructed by stacking mRDFs of UEC patterns at a sequence of delays between 5 and 2300 ps at irradiation fluence F=31
mJ/cm2 . Surface melting (enclosed by the dashed white line) is visible. (Right) mRDF map for F=75 mJ/cm2 . Full scale melting is
observed. The liquid state (enclosed by dashed white line) is characterized by the drop of second nearest density (at 5 ˚
A) to (1 - 1/e)
of the static value (at negative time) [29]. . . . . . . . . . . . . . .

6

Schematic illustration of a transfer matrix in a trace space: Left side
is an initial trace space (xi , xi ) and right side is a final trace space
(xf , xf ). Transfer matrix R maps an object in the initial trace space
into the final trace space: a line → a line, a point → a point, ellipse
→ ellipse, a curve → a curve. . . . . . . . . . . . . . . . . . . . . . 22

x

Figure 3.2

Schematic illustration of electron beam dynamics in drift / magnetic
lens / drift system: (a) the beam line structure illustration in real
space, (b) the emittance of the electron pulse at Z0 , (c) the emittance of the electron pulse at Z1 (drift region). Dashed line is the
emittance at Z0 , and the blue arrow indicates the electron motion in
the trace space, (d) the emittance of the electron pulse at Z2 (after
magnetic lens focusing). Dashed line is the emittance at Z1 , and
the blue arrow indicates the electron motion in the trace space, (e),
(f) the emittance of the electron pulse at Z3 , Z4 respectively. . . . 23

Figure 3.3

Schemtic illustration of an image system with one lens. . . . . . . . 26

Figure 3.4

The 6D emittance εx εy εz vs. the number of emitted electrons
N emit for the extended electron sources with sizes σr (100 µm,
1 mm), thermionic guns [69], Schottky, cold field-emission guns
(CFEG), and heated field emission guns (HFEG).[63] . . . . . . . . 33

Figure 4.1

RF-enabled high-brightness ultrafast electron beam system at Michigan State University . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 4.2

(a) Photoelectron pulse trajectory along an ultrafast electron beam
column equipped with RF compression. The shaded regions represent the locations of the electron optical elements. (b) A scale-up
view of the pulse profiles near the sample plane for nano-area diffractive imaging containing 105 electrons/pulse. An aperture with a
radius of 15 µm is employed to thin out the peripheral electrons to
achieve a divergence angle α ≤ 1.7 mrad. The minimum transverse
radius σT is 0.64 µm, and the minimum longitudinal pulse length
σL is 0.80 µm. (c) A scale-up view of the pulse profiles near the
sample plane for an ultrafast single-shot UED containing 108 electrons/pulse. The minimum transverse radius σT is 51 µm, and the
minimum longitudinal pulse length σL is 0.88 µm [68]. . . . . . . . 38

Figure 4.3

Cathode and anode of Pierce geometry photoelectron gun: (a) electric field calculation using Field Precision [74]. (b) Pierce geometry
photoelectron gun design in the high-brightness UED electron gun
chamber. Cathode and anode are electrically isolated through four
10 inch MACOR insulation rods. Right below the anode, there is
first condenser magnetic lens to focus the electron beam after the
anode. (c),(d) are the electric potential and field profile along the
electron pulse propagation direction. The profiles at different radial
locations are almost identical. This indicates that the field distribution is uniform along the beam propagation direction. . . . . . . . . 40
xi

Figure 4.4

Pierce geometry photoelectron gun head assembly: (a) Fully assembled Pierce gun head, (b) The assembly procedure and the design of
all parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 4.5

Pierce geometry photoelectron gun: (a) the whole Pierce photoelectron gun housed in a UHV chamber, (b) the zoom-in view of the
cathode and high voltage isolation using a ceramic disk as the base,
(c) triple point shielding geometry design at the junction of MACOR
rods and anode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 4.6

Current stability monitor (a) after the electron gun conditioning,
(b) before the conditioning . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 4.7

Schematic illustration of non-uniform magnetic field (red lines) at
the center of the magnetic lens pole-piece. The hole through the
pole-piece is called bore and the disconnected region inside of the
bore is called a gap. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 4.8

Condenser magnetic lens No. 1: (a) The geometry of the lens. The
yellow box region is filled with coils. (b) The magnetic field map
near the pole-piece (region highlighted by the red box in (a)) of the
condenser lens No. 1.: The black arrow indicates the electron pulse
propagation direction and the the plot has the cylindrical symmetry
along the beam propagation direction. (c) Magnetic field strength
profile along the different radial coordinates, R= 0.0, 0.5, 1.0, 1.5,
2.0 (mm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Figure 4.9

Condenser magnetic lens No. 2: (a) The geometry of the lens. The
yellow box region is filled with coils. (b) The magnetic field map
near the pole-piece (region highlighted by the red box in (a)) of the
condenser lens No. 2: the black arrow indicates the electron pulse
propagation direction and the the plot has the cylindrical symmetry
along the beam propagation direction. (c) Magnetic field strength
profile along the different radial coordinates, R= 0.0, 0.5, 1.0, 1.5,
2.0 (mm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

xii

Figure 4.10

Objective magnetic lens: (a) The geometry of the lens. The yellow box region is filled with coils. (b) The magnetic field map near
the pole-piece (region highlighted by the red box in (a)) of the objective magnetic lens: the black arrow indicates the electron pulse
propagation direction and the the plot has the cylindrical symmetry
along the beam propagation direction. (c) Magnetic field strength
profile along the different radial coordinates, R= 0.0, 0.5, 1.0, 1.5,
2.0 (mm). The kinks at R=1.5, 2.0 mm profiles are artifact because
the objective lens exit hole radius is 1.5 mm. . . . . . . . . . . . . . 50

Figure 4.11

(a) Magnetic lens current calibration simulation: Solid lines are
AGM simulation without space–charge effect, and the dashed lines
are Field Precision [74] simulation of non-interacting single electrons,
calculated with the relative permeability shown in (b). The initial
transverse size of the Gaussian electron pulse in AGM simulation is
100 µm and 50 µm with angular spread 0.1 mrad. In Field Precision simulation, the initial position of single electrons is at R=100
µm and 50 µm, and each line represents different initial ray angles,
±0.1, 0 mrad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 4.12

Field Precision simulation of an electron trajectory with non-interacting
particles (Red line) sheme and with space–charge effect induced by
the self-generated electric field of a continuous high current electron beam (blue line). Red and blue solid lines are calculated with
the same focusing condition with CML1=550 A, CML2=450 A,
and Obj.ML=750 A, and the dashed line is calculated with with
CML1=0 A, CML2=450 A, and Obj.ML=750 A. The black dashed
vertical lines indicates electron optics components: (1) the photocathode surface, (2) CML1, (3) CML2, (4) RF cavity, (5) Obj.ML,
(6) the sample, and (7) CCD screen. The shaded region shows where
the electron beam is focused by the Pierce geometry gun. . . . . . . 55

Figure 4.13

Pillbox cavity with radius R and length d: (a) illustration of the
pillbox geometry, (b) top view and side view of transverse magnetic
mode electromagnetic field in pillbox cavity, (c) top view and side
view of the transverse electric mode electromagnetic field in pillbox
cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 4.14

RF cavity: (a) The actual design of geometry optimized RF cavity
and the TM010 mode RF field in the RF cavity (The red ring is a
magnetic field and the black line is an electric field), (b) Phase space
volume evolution with RF compression. . . . . . . . . . . . . . . . 62

xiii

Figure 4.15

Block diagram of the Phase lock loop.

Figure 4.16

Structure of charge coupled device (CCD) camera mount. (a) Schematic
illustration of image acquisition optics in front of CCD camera main
body: Al film and phosphor screen are coated on the optical faceplate surface, and an optical taper focuses a signal with 2:1 ratio
onto an intensifier input window. The Al film screens the background photon from room light and pump laser, and the phosphor
film converts the electron signal to photons which is amplified by the
intensity. The red box indicated the intensifier. (b) a schematic diagram of the micro-channel plate (MCP) in the intensifier. The MCP
is composed of more than 106 micro-channels which are individual
miniature electron multipliers. (c) design of the fully assembled
CCD camera. All the components are made of glass, so, using the
optical grease, we make smooth contacts between parts to minimize
the signal loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure 4.17

266 nm excitation mirror holder and electron beam shield. . . . . . . 69

Figure 4.18

Electron beam deflector. (a) The design of the electron beam deflector: the electron pulse propagates from the bottom to the top (blue
arrow), and two pairs of stainless steel rods generate two orthogonal
directions electric fields which are perpendicular to the electron pulse
propagating direction. Eight MACOR insulation cylinders electrically isolate the high voltage applied rods from the stainless steel
deflector body. The MACOR cylinders are secured with 2-56 setscrews. (b) The electron beam deflection angle as a function of
applied voltage between the stainless steel rods in two orthogonal
directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 4.19

Aperture manipulator. (a) Stereoscan 360 scanning electron microscope aperture manipulator. The red circle in (a) shows where four
apertures are mounted at the same time. We can manipulate the position of each aperture with two micrometers shown at the end of the
aperture manipulator, x, y axis. (b) Actual design of the SEM aperture manipulator assembly with the second electron beam deflector.
The gap between two O-ring seals (white dot) is pumped down with
a dry pump to make the gap region pressure down to 10−3 torr.
Then, two O-ring seals can hold the UHV pressure difference. . . . 73

Figure 4.20

Schematic diagram of the high-brightness UED chambers: (1) the
100 kV electron gun chamber, (2) 266 nm laser mirror chamber, (3)
RF cavity, (4) main specimen chamber. . . . . . . . . . . . . . . . . 75
xiv

. . . . . . . . . . . . . . . . 64

Figure 5.1

Schematic illustration of Faraday cup: To prevent the escape of an
elastic scattered electron, there is an aperture at the entrance hole.
Picoammeter directly measures the current produced by the charged
particles in a vacuum. Typical size of the aperture is a few hundreds
micrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Figure 5.2

Single electron count events of attenuated electron beam on CCD
camera. The yellow square boxes indicates the regions of interest
(ROI) 5 × 5 in pixels. . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 5.3

(a) The probability profile of the integrated intensity of single–
electron events. The square is the experimental measurement and a
blue line is the fitting with Poisson distribution function. The ADU
is 4500 with image intensifier gain 9 V. (b) ADU under different image intensifier gain voltage, after considering the factor 2.1 following
the calibration of electron counts through a Woods horn beam trap.

83

Figure 5.4

(a) The design of the beam trap. The copper tubing outer diameter
is 2.0 mm and the inner diameter is 1.6 mm. The copper tube is held
by a MACOR insulation cylinder, and the end of the copper tube
is connected to a UHV compatible electrical wire which is Kepton–
insulated silver–plated copper wire. (b) Schematic illustration of
the copper tube cross-sectional view. Copper tube can trap the
electrons that enter the copper tube, and the curvature reduces the
probability for the elastically scattered electrons to escape from the
tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Figure 5.5

The number of emitted electrons per pulse. (a) Simulation results of
the number of emitted electrons per pulse Neemit plot as a function
of the number of generated electrons Ne0 , which is proportional to
the input power of 266 nm pulse laser, at various surface extraction
field Fa . This plot shows evidence of virtual cathode (VC) formation [63]. (b) Experimental measurement of the number of emitted
electrons Neemit as a function of input power of 266 nm pulse laser.
The experimental measurement shows consistent linear dependence
on input power below the VC limit, and 1/3 power dependence above
the VC limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Figure 5.6

Illustration of the emittance measurement sheme

xv

. . . . . . . . . . 90

Figure 5.7

Electron beam image and profile on the CCD camera. (a) is a image
of the full electron beam of 106 electron per pulse, and (b) is one
beamlet image after going through the 50 µm aperture. (c) and (d)
are the beam profiles along the horizontal direction. With the acquired intensity and divergence angle of each pixel, we can construct
the phase space distribution and the emittance at the aperture location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 5.8

Electron beam trace space plot (x,x ) of 10 electron per pulse and
106 electron per pulse. Each data point represents the position
and the transverse momentum of each beamlet, and error bar is the
momentum spread of the each beamlet. . . . . . . . . . . . . . . . . 94

Figure 5.9

Dependence of the transverse emittance εx on the number of emitted
electrons (Neemit ) and the extraction field Fa . The inset shows the
temporal evolutions of εx at Fa = 0.32 and 1.0 MV/m (all with 107
electrons), where generally εx reaches a steady state after 40 ps. The
red dot indicates our transverse emittance measurement εx =0.167
µm at a location right after the RF cavity [63]. . . . . . . . . . . . 95

Figure 5.10

(a) Schematic illustration for the beam propagation along the electron column with CML1 and CML2 focusing. The distance shown
in the figure is the actual distance of our electron beam line (see
Fig. 4.1), (b) Focal length of three magnetic lenses as a function of
the applied current. Each focal length measurement is with nonfocused electron beam directly from the electron gun, except the
objective lens. The focal length measurement of the objective lens
is with CML1 and CML2 focusing. . . . . . . . . . . . . . . . . . . 98

Figure 5.11

Comparison between Field Precision trajectory simulation and experiment. (a) The non-interacting single–electron trajectories from
Field Precision simulation. Green, blue, red, black vertical lines indicate the optical components along the high-brightness UED column:
photocathode, CML1, CML2, CCD camera. Each horizontal line is
a single–electron trajectory generated at different initial locations
R. Initial condition of the electron is a completely zero energy particle and it is accelerated only by 100 kV acceleration voltage. The
numbers right next to CCD position are the initial emitting location
R on the photocathode. (b) Ray angle vs. location R on the CCD
screen. The red squares are the experimental measurement of the
ray angles with 10 electron per pulse shown in Fig. 5.8, and black
squares are the simulation. . . . . . . . . . . . . . . . . . . . . . . . 99

xvi

Figure 5.12

Schematic illustration of the phase jitter. (a) Perfect phase match
between RF field and the electron pulse arrival time: the COM
velocity of the electron pulse has no change. The relative phase
mismatch causes (b) decelerating the COM velocity of the electron
pulse, and (c) accelerating the COM velocity. . . . . . . . . . . . . 101

Figure 5.13

Beam size and energy variation of electron pulse with different relative phase between electron pulse and RF field. (a) Beam size
variation with the relative phase: the shaded areas are the compression regions and the unshaded ones are stretch regions where the
faster electrons are accelerated and the slower electrons are decelerated. The top red sine curve illustrates the corresponding RF field
oscillation at ∼1 GHz. Time zero is set at the exact timing for the
perfect pulse compression. The beam size oscillates with the pulse
compression: strong compression induces the transverse expansion
and strong stretch suppresses the transverse expansion. At t =0.75
ps, the beam size is consistent with the beam size without RF compression. (b) Electron energy variation with different relative phase
at 420 W RF power. t =0 ps is the perfect in-phase, 100 keV. Inset
plot is the electron pulse arrival time on the sample as a function
of the relative phase (-0.2∼0.2 ps range). (c),(d) the electron pulse
images on CCD at completely out of phase (stretch (c)), and the
perfect in-phase (compression (d)). . . . . . . . . . . . . . . . . . . 103

Figure 6.1

Transient photoinduced charge redistribution near surface. (a) The
three mechanisms of photoexcitation that cause redistribution of
charges at the surface, bulk, and vacuum levels near Si/SiO2 surface. (b) Transient surface potential diagram caused by various photoinduced charge redistribution. (c) The refraction of the electron
beam in each field region can be modeled by an index of refraction
with n = (∆V + V0 )/V0 , where eV0 is the electron beam energy.

xvii

109

Figure 6.2

Surface electron diffraction pattern in different conditions. (a) Ewald
sphere construction in the grazing incidence angle geometry. By tilting (rocking) the angle of incidence between the electron beam and
the sample, the Ewald sphere intercepts the reciprocal lattice rods
(relrods) at different heights. The in-phase condition is satisfied
when the intercept is at the reciprocal lattice node. The inset shows
the reciprocal node structure, which is effectively determined from
a Fourier Transform (FT) of the crystalline region in the sample
defined by its persistence lengths. (b) Expected rocking map of a
smooth, pristine surface in RHEED. (c) Experimental rocking map
taken from a smooth Si/SiO2 surface. The dashed line shows where
the diffraction pattern in the inset is taken. (d) Expected rocking map of a nanostructured surface. (e) Experimental rocking map
pattern taken from a highly oriented pyrolytic graphite (HOPG) surface. (f) Experimental rocking map taken from a Si/SiO2 surface
sample along a Kikuchi-enhanced diffraction peak. (g) Diffraction
pattern of the Si/SiO2 surface, showing visible Kikuchi pattern. . . 112

Figure 6.3

The idealized slab model for considering the transient surface voltage. The top trajectory is the electron scattering from the crystal
planes with the presence of a surface field. The electron beam, incident at θi , is Bragg scattered at θB , exiting the surface at θo .
Introducing an attractive surface potential Vs will cause the electron beam to be ’refracted’ deeper into the crystal(θi ) and the same
for the Bragg diffracted beam that would ultimately exit the crystal
at θo ” with a net shift ∆B relative to θo . . . . . . . . . . . . . . . 116

Figure 6.4

The refraction-induced shift(∆B ) for diffraction peak located at θo
at Vs =1 volt calculated for difference surface diffraction condition
characterized by a = 0, 1, 2 (see Fig. 6.2). The solid lines are exact
solution from voltammetry formalism. The dashed lines are calculated employing small angle approximation (see text). The incidence
angle (θi ) is set at 2.01◦ . . . . . . . . . . . . . . . . . . . . . . . . . 118

xviii

Figure 6.5

Shadow imaging experiment to characterize the properties of photoemission. (a) Schematic experiment setup of the experiment, in which
the incident electron beam is displaced by x0 from the photoinduced
region by 800nm pump laser. The surface scattered electrons form
a shadow image of the electron cloud on the CCD screen as they are
scattered away from the collective field associated with photoelectrons. In parallel, the surface diffracted beam experiences the electric field associated with photoemitted electron cloud, and deflects
according to its location relative to the cloud. (b) The diffraction
pattern from Si/SiO2 surface is shown with the striped regions selected for extracting the shadow image evolution (yellow) and the
diffracted beam reflection (cyan). (c) & (d) show the snap-shot
shadow images of the photoemitted electron cloud at different time
delays. (e) The respective Gaussian fitting of the shadow images. (f)
Results extracted from fitting the shadow image of the photoemitted
electron cloud, showing the evolution of the CoM position and the
cloud width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Figure 6.6

N-particle shadow projection imaging simulation at two different
time delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Figure 6.7

Experiments to characterize photoelectron dynamics and surface
photovoltage performed at F=65 mJ/cm2 . (a) Data (symbols, colored in red) show the deflection of a selected diffracted beam by the
electric field associated with photoelectrons and the image charges
on the surface acquired in the shadow imaging experiment setup.
N-particle simulations with surface dielectric relaxation times (τr )
ranging from 0, 16, 21 ps, and ∞ are used to fit the data. (b) The
voltammetry results (symbols, colored in red) obtained from the
same diffracted beam, but at the overlapped voltammetry geometry. An N-particle simulation to estimate the refraction contribution
associated with photoemission is shown (solid line, colored in blue)
for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Figure 6.8

(a) An effective circuit model depicting the transient surface voltage
Vs (t) measurement via the refraction shift across SiO2 /Si interface
with 20 nm Au nanopartilce decoration. The electromotive potential
ε(t) comes from the hot carriers generated at the Si substrate. (b)
Example showing the photovoltage Vs (t) measured at the interface
as a function of ε(t). The relationship can be seen as a convolution
with kernel function h(t) characteristic of the RC circuit. . . . . . . 128

xix

Figure 6.9

Theoretical modeling of transient surface voltage Vs (t). Using RC
time of 30.8ps, the corresponding electromotive force emf is deduced,
showing a spontaneous rise and a long decay. . . . . . . . . . . . . 131

Figure 6.10

Transient surface voltage caused purely by ∆DP . ∆P E contribution is subtracted from total TSV, and the surface voltage is calculated by Eq. (6.16). The surface voltage is fitted by an RC charging
and discharging model with τc =30.84 (ps), and τd =296.47 (ps). Inset: Charging/discharging dynamics in a log time scale. . . . . . . . 133

Figure 7.1

Charge redistribution at nanomaterials interfaces subject to photoexcitation. (a) Dielectric realignment; (b) carrier diffusion; (c)
interfacial charge transfer . . . . . . . . . . . . . . . . . . . . . . . . 138

Figure 7.2

Trasient voltammetry from three diffracted beams from Si/SiO2 interface. (a) The angular shift of (0,3,24), (0,1,21), and (0,1,24)
beams excited at F=65mJ/cm2 . (b) The rocking map characterization of (0,3)-relrod, showing a surface diffraction condition a = 1.
(c) The photo voltage deduced from (0,3,24), (0,1,21), and (0,1,24)
beams based on Eq. (6.10) using a = 1. . . . . . . . . . . . . . . . . 142

Figure 7.3

(a) A sample of Au nanoparticles (NPs) immobilized on a functionalized Si substrate. (b) The chemical form of the AEAPTMS
linker molecule. (c) Schematic of an electron beam scattering from
the ordered self-assembled monolayer chain and the corresponding
diffraction pattern [25] . . . . . . . . . . . . . . . . . . . . . . . . . 146

Figure 7.4

(a) An effective circuit model depicting the transient surface voltage
Vs (t) measurement via the refraction shift of the diffracted beams
through SAM. The RS , CS , RM , CM are the effective resistance
and capacitance of the substrate (S) and the SAM (M). The electromotive potential that can drive the photocurrent through the SiO2
layer (iS ) and further through SAM (iM ) is mainly from the hot
carriers generated from the Si (ε1 (t)); whereas the short-lived photoexcited hot carriers generated within the Au nanoparticle (NP)
can also drive the charge transfer in the opposite direction (ε2 (t)).
(b) The overall refraction shift determined by SAM diffracted beam
(labeled Vs ), the background (labeled VB ) obtained from SiO2 /Si
interface, and the molecular charge transport contribution, obtained
by subtracting VB from Vs . . . . . . . . . . . . . . . . . . . . . . 147

xx

Figure 7.5

Schematic illustration of localized surface plasmon oscillation induced by an oscillating electric field in a metal nanoparticle. The
displacement of conduction electron cloud relative to the nuclei is
shown. The frequency of the localized surface plasmon resonance is
denoted ωp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Figure 7.6

Hollow gold nanoshell (HGN) surface plasmon resonance. (a) Schematic
illustration of localized surface plasmon oscillation induced by an oscillating electric field in a hollow gold nanoshell(HGN). The displacement of conduction electron cloud relative to the nuclei is shown.
The frequency of the localized surface plasmon resonance is denoted
ωp .(b) a UV-visible absorption spectra of nine HGN samples varing
diameter and wall thickness.[177] . . . . . . . . . . . . . . . . . . . . 155

Figure 7.7

An energy diagram of plasmon hybridization in a HGN describes the
interaction between the metal sphere plasmon and cavity plasmon
in bulk metal. Two HGN plasmon modes are an antisymmetrically
coupled (antibonding) ω+ plasmon and a symmetrically coupled
(bonding) ω− plasmon. . . . . . . . . . . . . . . . . . . . . . . . . . 157

Figure 7.8

Ultrafast transport at gold nanoparticle (NP)/SAM/silicon interface
near surface plasmon resonance (SPR) excitation. (a) The maximum
transient photovoltage response near SPR excitation, as compared
to the absorption of the similar nanoparticles in water, bulk gold,
and silicon substrate. It is evident that while both show characteristic SPR peak at ∼525 nm the nanoparticles Vs spectrum at surface
(colored in green) lacks the background seen in the optical absorption spectrum of similar nanoparticles in water (colored in red). (b)
The enhancement of hot carrier generation at Si surface (channel II)
can be achieved via SPR evanescent field within the Si surface or
charge carrier injection from highly excited Au nanoparticle (channel
I). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Figure 7.9

(a) The statistics of HGNs diameter before fs laser irradiation and
after irradiation (the number of HGN sampling is ∼700 individual
HGNs in each case), (b) SEM image of the morphology of HGNs
distribution on the SiO2 /Si substrate and the scale bar corresponds
to 1µm, (c) and (d) are the SEM image of HGNs before and after
irradiation, respectively, and the scale bar corresponds to 100 nm. . 160

xxi

Figure 7.10

(a) Debye-Waller factor(DWF) analysis of the diffraction intensity
drop. This indicates the lattice temperature as a function of the
irradiation fluence. (b) DWF profiles of different wavelength pump
laser are fitted with power function, y = axb . (c) Transient surface
voltage (Vs ) generation as a function of different laser wavelength. . 164

Figure 8.1

CeTe3 sample image on 1000 mesh TEM grid: (a) optical microscope image, (b) Projection Shadow image of a full grid with highbrightness UED, (c) Projection shadow image with 50 µm aperture
selected area, a white square shown in (b). . . . . . . . . . . . . . . 168

Figure 8.2

Convergent beam test to maximize the electron dose Ne /A. With
the constant current of CML1=1.0 A and CML2=2.7 A and 170 µm
aperture, the electron beam is focused on the sample position with
adjusting Obj. ML current shown in the each image. Minimum
beam size is smaller than 7 µm which is the limitation of our measurement resolution. This gives us D > 2000 electron/µm2 . (The
whole image is the same size region, 505×620 pixels.) . . . . . . . . 171

Figure 8.3

(a) Convergent beam diffraction of TaS2 with 50 µm aperture (exposure time 500 ms). Hexagon indicates the charge density wave
(CDW) diffraction peak. (b) Parallel beam diffraction of TaS2 with
170 µm aperture (exposure time 2 s). Upper right panel is zoom-in
image of the lower left red square showing CDW diffraction peak. (c)
Convergent beam diffraction of CeTe3 with 50 µm aperture (exposure time 4 s) after the implementation with the beam trap extension
and Teflon spacer to minimize the sample column vibration. . . . . 173

Figure 8.4

(a) Crystal structure of VO2 in metallic rutile phase: the gray ball
is the V atoms and red ball is O atoms. The arrows are the dimerization direction of V atoms in V chain along c axis. (b) and (c) are
the schematic illustration of VO2 density of state of VO2 in metallic
and insulator phase, respectively. . . . . . . . . . . . . . . . . . . . 174

xxii

Figure 8.5

(a) Optical microscope image of VO2 film sample which is grown on
the 5 nm thickness amorphous silicon membrane. The eight square
windows are the VO2 film with 5 nm thickness Si membrane and a
long black rectangle is a broken window. Each square window size is
100 µm × 100 µm, and the displacement between windows is 200 µm,
(b) Diffraction pattern of poly-crystalline VO2 film, (c) Integrate
diffraction intensity profile along the wave vector corresponding to
the radial direction in real space image. The arrows indicate the
V-V dimerization symmetry peaks in a monoclinic insulation phase
(¯30¯2, 31¯3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Figure 8.6

The photo-induced phase transition measurement with VO2 with
different RF power compression of ∼7×104 electrons per pulse: the
measurements are relative diffraction peak intensity change as a
function of the time. . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Figure 8.7

Pulse duration measurement from VO2 phase transition: VO2 phase
transition experiment is performed with ∼7×104 electrons per pulse. 179

Figure 8.8

(a) Electron pulse arriving time fluctuation during the experiment.
Zero fluctuation means the electron energy is exactly 100 keV, and
due to the phase mismatch, the COM velocity of electron pulse is
fluctuated. (b) RF phase stability monitor. The red line shows the
phase fluctuation before temperature instability correction and blue
line shows the phase fluctuation after the correction. . . . . . . . . 181

Figure A.1

Different kinds of electrons scattering from the specimen

Figure A.2

Derivation of Bragg equation 2d sin θ = nλ . . . . . . . . . . . . . . 188

Figure A.3

The phase angle difference of incident beam is k r = 2π sin ϕ/λ and
the path difference at O and r is r sin ϕ. For diffracted beam, the
phase angle difference is −k r. The total phase angle difference
is (k − k ) r, and the beam scattered from dV at r has the phase
factor exp[i(k − k ) r] relative to the beam scattered from a volume
element at the origin O. . . . . . . . . . . . . . . . . . . . . . . . . 191

xxiii

. . . . . . 186

Figure A.4

Ewald sphere construction: The points are reciprocal lattice points
of the crystal. The vector k is drawn in the direction of the incident
beam, and the origin is chosen such that k terminates at any reciprocal lattice points. We draw a Ewald sphere of radius k = 2π/λ about
the origin of k. A diffracted beam will be formed if Ewald sphere
intersects any other reciprocal lattice points. The Ewald sphere as
drawn intercepts a point connected with the end of k by a reciprocal
lattice vector G. The diffracted beam is in the direction k = k + G.
The angle θ is the Bragg angle of Fig. A.2. . . . . . . . . . . . . . . 193

Figure B.1

Ultrafast electron diffraction experiment geometry with ultrafast
electron microscope system. (a) A schemetic diagram of the UEC
optics setup. Both 400 and 800 nm beam lines are shown entering
the delay line, but one of them is blocked based on the choice of excitation. The time delay between pump laser pulse and electron probe
is controlled by delay stage adjusting traveling path length. Also,
pulse shaper is shown in the diagram, but it has not been tested yet.
(b) In UHV specimen chamber, the 100 kV UEM column beam goes
from top down, and 40 kV UED electron beam goes horizontally.
The pump laser lands on the sample with 45o tilting. . . . . . . . . 198

Figure B.2

Schematic picture of the femtosecond laser source: (1) femtosecond
seed pulse (Mai-Tai), (2) amplifier for femtosecond pulse (Spitfire),
(3) continuous wave pump laser for amplification (Empower) . . . . 199

Figure B.3

Universal electron gun design. (a) Zoom-in of the electron gun head
part, (b) actual image of the fully assembled universal electron gun
before installation into the chamber, (c) overall layout of the electron
gun including the gun chamber with 6” conflat flange . . . . . . . . 202

Figure B.4

Performance characterization of the 40 kV universal electron gun.
(a) Analog-to-digital unit (ADU) measurement: CCD camera response of a single electron event is about 175 intensity of one pixel.
(b) the number of electron per pulse with the measured ADU as a
function of a different magnetic lens focusing strength. The reason
for the increase in the number of electron with stronger focusing is
more electrons able to pass through the 100 µm aperture because
of stronger focusing. (c) the beam size at the sample location and
the CCD camera as a function of a different magnetic lens focusing.
(d) divergence angle of the electron beam with different focusing
strength. The divergence angle is calculated by the beam sizes at
the sample and CCD camera with the camera distance between the
sample and CCD camera. . . . . . . . . . . . . . . . . . . . . . . . 204

xxiv

Figure B.5

Structure of charge coupled device (CCD) camera design. (a) Schematic
illustration of CCD camera structure: in front of CCD camera, we
have the optical taper to focus a signal in large area into small CCD
camera input window (2:1 ratio). On the optical taper face, we have
an optical face-plate, and the 60 nm aluminum film and phosphor
film are coated on the face-plate surface. The Al film screens the
background photon from room light and pump laser. The phosphor
film converts the electron signal to photon to amplify the intensity.
Red box indicates the intensifier. (b) the schematic diagram of the
MCP in intensifier. MCP is composed of more than 106 microchannels which are individual miniature electron multipliers. (c)
design of the fully assembled CCD camera. . . . . . . . . . . . . . . 207

Figure E.1

(a) Schematic illustration of a non-interacting photoemission electron generation on a cathode: R is the initial location where the
electron is generated and θ is the divergence angle caused by the
focusing field of Pierce gun geometry. (b) Field Precision simulation
result of the electron divergence angle at different initial position (R)
at various gap distances between the cathode and anode: a gap distance of the current design is 20 mm and the surface extraction field
is 2.2 MV/m field, and 20% smaller gap distance, 16 mm, generates
45% higher extraction field, 3.2 MV/m. . . . . . . . . . . . . . . . 215

xxv

Chapter 1
Introduction

1.1 Ultrafast Camera: Pump-Probe Technique
Making a ‘molecular movie’ to unravel the atomic processes in complex materials is one
of the greatest dreams in condensed matter physics and material science. To make this
dream come true, an ‘ultrafast camera’ with simultaneously very high spatial and temporal
resolution on the scales matching the atomic dynamics is required. The ultrafast pumpprobe scheme based on femtosecond laser technology can provide the basic framework for
realizing such an ‘ultrafast camera’ thanks to significant advancements in photonics and
electronics, and more recently with accelerator technologies [1]. In a pump-probe experiment station as illustrated in Fig. 1.1, two pulses are employed: one acting as a pump and
the other as a probe. The pump pulse initiates an ultrafast process in a target by providing
an impulsive excitation, whereas a second probe pulse, which can be an optical, electron,
X-ray pulse or other ultrafast detection scheme, is employed to characterize the ensuing
ultrafast dynamics. A well defined time delay (∆t) is required to provide the time stamps
of individual events. A series of responses at various ∆t can be used to construct a full
temporal evolution of a process induced within the optically excited target.
The diversity in pump-probe schemes arises from the varied nature of the probe. For example, using optical detection (transmission and reflectance), the optical constant changes
1

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Figure 1.1 Schematic diagram of the pump-probe experiment setup. The relative time delay
between pump(red) and probe(blue) pulses is controlled by the translational delay stage.
over different spectroscopic regimes which manifest the photoexcited electronic properties
[2, 3, 4, 5, 6, 7, 8, 9] and even their coupling to the lattice dynamics [10, 11, 12, 13] can
be deduced. The latest development of ultrafast angular resolved photoemission technique
zooms in on the momentum space of the electron dynamics and offers specific information
on the perturbation and reconstruction of Fermi surface, which is particularly important
to understand the electronic phase transitions [14] and surface electron dynamics [15, 16].
To directly visualize the structural dynamics, the probe also requires the atomic scale
resolution and only hard X-ray and high energy (∼keV) electron probes with sub-angstrom
de Broglie wavelength fulfill this requirement through either diffraction or imaging. In the
following sections, some of the recent ultrafast X-ray/electron diffraction experiments will
be discussed.

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Figure 1.2 (a) Time-dependent diffracted intensity for (220) reflections. Red curves are
Gaussian fits to the data, corresponding to 10 to 90% fall times of 280 fs [17] (b) X-ray
diffraction efficiency of the (222) Bragg peak as a function of time delay between the optical
pump pulse (fluence 6 mJ/cm2 ) and the X-ray probe pulse. The solid line is fitted to the
experimental data. The decrease of the mean value of the X-ray signal (dotted line) is
explained by the DebyeWaller effect, and reflects the increasing random component of the
atomic motion [18].

1.2 Ultrafast X-ray Diffraction
Diffraction of X-rays from crystalline materials is a standard tool for determining equilibrium atomic structures. Using modern development of ultrashort X-ray pulse (see Chapter
2), the time evolution of photoinduced structural changes can be studied in a direct way
by using ultrafast X-ray diffraction techniques.
Earlier ultrafast X-ray studies focused on the optically induced phase transitions and
the selected modes that are crucial for the events. After photoexcitation with high intensity
of ultrashort laser pulse, a substantial fraction of electrons is excited from bonding valence
band to anti-bonding conduction band orbitals. This causes the solid to melt and lose the
long-range order. If the melting occurs before the electronic and lattice temperatures are
in thermal equilibrium, then this process is called non-thermal. A. M. Lindenberg and
3

his colleagues have observed non-thermal melting in a semiconductor InSb with ultrashort
X-ray probe [17]. Femtosecond pump laser changes the interatomic potential energy surfaces and thus induces atomic displacements, eventually leading to the transition from a
crystalline solid to a disordered liquid (Fig. 1.2(a)). Sokolowski-Tinten and colleague have
succeeded in directly measuring the coherent atomic displacement of the lattice atoms close
to a phase transition in photoexcited bismuth [18]. Excitation of large-amplitude coherent optical phonons gives rise to a periodic modulation of the X-ray diffraction efficiency
(Fig. 1.2(b)). Stronger excitation corresponding to atomic displacements exceeding 10 %
of the nearest-neighbor distance leads to a subsequent loss of long-range order, which is
most probably due to melting of the material. Recently, Clark and his colleagues have
achieved the characterization of lattice displacements in individual nanoparticles over 10100 ps scales with atomic sensitivity [19]. Fig. 1.3 shows the Bragg peak position changes of
two different individual nanocrystals (∼400 nm) with 800 nm femtosecond laser excitation,
and measure the subsequent ps evolution of acoustic phonons in single gold nanocrystals
using ultrafast X-ray pulses generated by the Linac Coherent Light Source (X-ray Free
Electron Laser).

1.3 Ultrafast Electron Diffraction
Ultrafast electron diffraction (UED) has a lot in common with ultrafast X-ray diffraction
in the applications, and the achieved spatiotemporal resolution of the two techniques in
current development are quite comparable [20, 21, 22, 23, 24, 25, 26]. However, electrons
have significantly higher scattering cross-section (105 -106 times) than that of X-rays [27],
and ultrafast electron sources with sufficient signal-to-noise ratio for UED experiments are
4

!%#$

!"#$

Figure 1.3 Angular shift of (111) gold Bragg peak as a function of delay time from the same
nanocrystal. (a) and (b) are from different individual nanocrystals. The blue dots are the
experimental data and the solid red line is the modeled peak shift [19].
available in a table-top setup. In comparison, similar studies using X-rays usually are
facility-based. Pros and cons in various electron and X-ray developments will be discussed
in section 2.3.
UED experiment has been successfully applied to investigate photoinduced non-thermal
melting processes [28, 29, 30, 31, 32, 33], structural phase transitions [34, 35, 36, 37, 38],
and transient surface charge dynamics [39, 40, 41], as summarized in a recent monograph
on this subject [42]. Photoinduced crystalline-liquid (or amorphous) phase transformation
of gold nanoparticles has been directly studied [29]. In this nanoparticle study conducted at
MSU’s ultrafast electron crystallography laboratory, the real space atomic bond distribution
is extracted using a modified radial distribution functions (mRDF) method [29]. Fig. 1.4
shows the photoinduced melting process of 2 nm gold nanoparticles with two different
fluences, 31 mJ/cm2 and 75 mJ/cm2 . During the process, the depletion of the major bond
density at ∼5, 8 ˚
A is coupled to the enhancement of slightly longer bond density around
the neighboring region, and this indicates that photoinduced nanoparticle melting process
5

Figure 1.4 The melting dynamics of 2 nm Au nanoparticles. (Left) mRDF map constructed
by stacking mRDFs of UEC patterns at a sequence of delays between 5 and 2300 ps at
irradiation fluence F=31 mJ/cm2 . Surface melting (enclosed by the dashed white line) is
visible. (Right) mRDF map for F=75 mJ/cm2 . Full scale melting is observed. The liquid
state (enclosed by dashed white line) is characterized by the drop of second nearest density
(at 5 ˚
A) to (1 - 1/e) of the static value (at negative time) [29].
resembles a conformation change between selected minimum energy structures on the free
energy landscape, rather than random dissociation in thermal melting. However, to pin
down the exact pathway for size-dependent melting, ultrafast diffraction investigation on
the single-particle level is required and this investigation is not possible with the current
UED setups.
Using UED, phase transitions in solid crystals of strongly correlated materials [43, 37,
44, 35, 45, 46] and nano-materials [47, 34, 48, 49, 50] have also been investigated with
sub-ps resolution. Moreover, exploiting the charge sensitivity of the electron probe, ultrafast electron diffraction voltammetry (UEDV) has been developed to directly measure the
transient surface charge dynamics [40, 51, 41].
6

As shown in this chapter, UED has been successfully demonstrated with the capability
to resolve ultrafast dynamics with atomic and sub-picosecond spatiotemporal resolution
while, in various developments of UED, the electron pulses with 103 -105 electrons per
pulse are also available. Nonetheless, for studying molecular processes on the nanometer
scale such as a single nanoparticle and a single domain of crystals, a figure of merit is the
electron dose, which is still limited to ∼1 electron/µm2 , per pulse. Therefore, the highbrightness ultrafast electron source development which is one of the major topics in this
thesis, is required to overcome this limitation for pushing ultrafast electron diffraction and
imaging into nanoscale domains. The main contributions to the development described in
this thesis are the design and construction of the electron gun, and the complete electron
beam line, including the various electron optical components, the diffraction chamber, and
the detector systems, and the work on RF cavity and characterization of the electron beam
system performance are results of collaboration with Zhensheng Tao and Nan Du. The rest
of the thesis is organized as the following. In Chapter 2, the current status of developing
ultrashort electron and ultrashort X-ray source will be introduced. In Chapter 3, relevant
beam dynamics associated with a high-brightness electron beam system will be discussed.
In Chapter 4 and Chapter 5, the design and the characterization of a Radio-Frequency (RF)
enabled high-brightness electron beam system at MSU will be covered. Work in further
development of UEDV for studying ultrafast charge dynamics in nanostructure interfaces
will be also presented in Chapter 6 and 7. In Chapter 8, the preliminary experiments with
the high-brightness ultrafast electron beam system under development will be shown.

7

Chapter 2
Current Status of Ultrashort Pulse
Development: X-ray and Electron
Both ultrafast X-ray and electron beams can achieve high combined spatial-temporal resolution, but both have faced some fundamental limits, such as the limitation in the source
strength and parasitic effects including radiation damage, loss of coherence, etc.. In this
chapter, the current state of development of ultrashort X-ray and electron sources will be
introduced, which will serve as a baseline in evaluating the development of a high-brightness
ultrafast electron diffraction and imaging system at MSU.

2.1 Ultrashort X-ray Pulse Generation
X-ray sources are one of the strongest candidates to probe ultrafast atomic scale processes.
Different types of X-ray sources have been developed for several decades: (1) table-top
tunable extreme ultraviolet (EUV, 10 - 120 eV) source with high harmonic generation
(HHG), (2) table-top soft X-ray (0.1 - 5 keV) source with laser driven plasma (LDP), (3)
high intensity tunable X-ray source with free electron laser (FEL), from EUV to hard X-ray
(1 - 10 keV). A comparison among the X-ray sources is summarized in Table 2.1.

8

Parameter
Photon Energy

HHG†
20 - 100 eV

LDP
0.1 - 5 keV

FEL ‡
1 - 10 keV

Energy per pulse

20 nJ (at 30 eV)

0.01 - 0.1 µJ

2 mJ (at 150 fs)

Repetition Rate

1 - 10 kHz

1 - 10 Hz

30 - 60 Hz

Pulse Duration

10 attosec - 30 fs

200 fs - 1 ps

5 - 150 fs

Focused Intensity

∼1014 W/cm2

∼1014 W/cm2

5 × 1016 W/cm2

Average Power

0.5 µW (at 50 eV)

100 mW (at 150 fs)

Polarization

Linear

Linear

Linear

Table 2.1 Comparison among X-ray sources [23, 24]
† High average power mode with 10 W driving lasers, e.g., 2 mJ, 5 kHz
‡ Linac Coherent Light Source at Stanford Linear Accelerator Center

2.1.1 High Harmonics Generation (HHG)
Employing gas phase targets, intense femtosecond lasers can generate photons in tabletop scale tunable EUV source with high spatial and temporal coherence through HHG.
The strong electromagnetic field of a femtosecond-laser enables the electrons in atoms to
tunnel through the potential barrier of ions. The liberated electrons are subsequently
accelerated by the strong laser field up to ∼10 eV, and the kinetic energy gained can be
released in the form of coherent radiation at the harmonics of the driving femtosecond-laser
as the electrons decelerate and recombine with the ions. The photons emerge in such a
cooperative interacting region as a burst of broadband coherent radiation with a duration
in the femtosecond-to-attosecond regime. The major advantage of this HHG technique is
low cost and table-top scale compared to accelerator-based X-ray sources.

9

2.1.2 Laser Driven Plasma (LDP)
LDP X-ray source is also a table-top system generating a large number of photons per
pulse and high average power in the soft X-ray regime. When a high intensity ultrashort
laser pulse impinges a solid target, such as a metal surface, photo-induced ionization turns
the surface into a high density plasma. In the dense plasma, energetic hot electrons are
accelerated by the incident laser field, and the X-rays are generated by impingement of the
accelerated electrons into the target material [23]. The compact and bright plasma-based
soft X-ray source can operate in the 10-50 nm wavelength region [52].

2.1.3 Free Electron Laser
X-ray free electron laser (X-FEL) is distinguished by their extremely high intensity (higher
than 1010 photons/pulse), high coherence, and short pulse duration (∼ 100 fs), typically
with a repetition rate of ∼100 Hz. The X-FEL radiation is achieved by the self-amplification
of spontaneous emission of high-energy, high-peak current, and ultrashort pulsed electron
bunches [23]. For hard X-ray generation, X-FEL uses an undulator, which is a periodic
arrangement of magnets with alternating poles generating a magnetic field across the beam
path. As a relativistic electron beam passes through the undulator, the transverse acceleration of the electron beam by the undulator results in synchrotron radiation which is
monochromatic, but incoherent. However, when the synchrotron radiation becomes sufficiently strong, the transverse electric field of the radiation interacts with the transverse
electron beam. This interaction causes some electrons to gain and others to lose energy to
the optical field via the ponderomotive force. This energy modulation evolves into electron
density modulations with a period of one optical wavelength. The modulated electrons are
10

called microbunches, separated by one optical wavelength along the axis. Whereas conventional undulators would cause the electrons to radiate independently, the radiation emitted
by the bunched electrons are in phase, and the emitted field adds together coherently.
Therefore, the X-ray free electron laser can generate up to a 10 fs X-ray pulse containing
up to 1013 photons per pulse in a narrow spectral bandwidth [53].

2.2 Ultrashort Electron Pulse Generation
In the electron source development, the generation of a high density electron pulse is relatively straightforward, but preserving the time resolution of the electron pulse after generation is challenging due to the space–charge effect. The space–charge–led transverse
expansion effecting the focusing power may be compensated by various types of electron
optics, but space–charge–led longitudinal expansion, which degrades the time resolution, is
quite difficult to handle. To overcome such the space–charge effect, four different approaches
have been developed: (1) minimization of the propagation distance with a compact electron beam system, (2) elimination of the space–charge effect with single-electron pulses,
(3) minimization of the space–charge effect with relativistic electrons, (4) reversal of the
electron pulse expansion with radio-frequency (RF) pulse compression.

2.2.1 Compact Electron Gun
One of the simplest ways to minimize the space-charge broadening is reducing the source-tosample distance. Such compact electron beam systems have been successfully demonstrated
by several groups [54, 55, 20, 25]. Most recently, the Baumert group at University of
Kassel has developed a compact UED system with a 8.5 mm cathode-to-sample distance
11

(cathode-to-anode distance ∼3.5 mm and anode-to-sample distance ∼5.0 mm [54]). To
reduce the cathode-to-sample distance, a magnetic lens is mounted after a sample. While
this arrangement does not allow focusing the electron pulse, it may be operated in a lensless
imaging mode, such as projection imaging. This system has achieved a ∼200 fs time
resolution with 5000 electrons per pulse. The Dwayne Miller group has also developed a
compact electron diffraction system having a ≤ 3 cm cathode-to-sample distance [55]. This
system structure is similar to the UED system at MSU, but, to reduce the cathode-tosample distance, a cathode and an anode are inside of the magnetic lens, and the anode
is located directly front of the magnetic lens pole. This system has achieved ∼300 fs time
resolution with ∼104 electrons per pulse [20]. These compact electron guns have achieved
good temporal resolution, however, they typically lack sufficient flexibility to meet different
applications in pulse characteristics. For example, the compact setup does not allow for
front illumination of the photocathode, whereas the back illumination has a low threshold
for the onset of virtual cathode effects, which limits the emitted electron density. It is also
difficult to reach sub-µm scale focusing for microdiffraction applications.

2.2.2 Single-Electron Pulses
Using single-electron pulses, the space–charge effects can be significantly reduced, but increasing the repetition rate by ∼100 MHz is required to maintain a sufficient signal-to-noise
ratio. The Zewail group at Caltech has built the first ultrafast electron microscope (UEM)
with single-electron pulses [56]. The major advantage of this scheme is that a conventional
transmission electron microscope (TEM) can be modified without introducing major components to handle the associated space–charge effects in the intense short-pulsed beam.

12

The time resolution of such a UEM is fundamentally limited by the timing jitter associated
with photoelectron generation, and a temporal resolution of ∼70 fs has been achieved by
optimizing the excitation photon energy [56]. However, the applications to material studies
are limited because the MHz repetition rate requires a robust reversible process to occur.

2.2.3 MeV Ultrafast Electron Microscope
It is known that the space–charge effect can be significantly reduced when charged particles
are accelerated to the relativistic energy regime [57]. For example, when the electron pulse
2
propagates in free space, the acceleration in the longitudinal pulse broadening, d 2l , caused
dt
by Coulomb repulsion, is inversely proportional to γ 3 (γ: Lorentz factor) with a negligible
transverse motion [57]. Therefore, the space–charge–led broadening of an intense electron
pulse can be overcome by accelerating the electron pulse to ∼MeV energies. Using a radiofrequency (RF) photogun, a 1-3 MeV electron pulse is easily achievable with up to ∼107
electrons per pulse. The incorporation of an RF photogun for UED experiment has been
demonstrated by several groups [58, 59], achieving ∼100 fs pulse generation. MeV ultrafast
electron beam systems, however, face other challenges. One challenge is knock-on damage
[27]. The energy deposited in materials by elastic and inelastic scattering of ∼MeV electrons
can be ∼100 eV, whereas the displacement energy associated with light atoms, such as, C,
N, O, is typically ∼25 eV. This means that atoms in such samples can be knocked out by the
MeV electron probe. The second limitation is that the relatively lower elastic scattering
cross-section at higher energy reduces the effective scattering signal strength. The last
challenge is that MeV electron beams require non-standard electron optics and detectors:
especially the corresponding angle for a given momentum transfer is significantly reduced

13

at high energies leading to the requirement of long baseline and increased construction cost.

2.2.4 KeV Ultrafast Electron Microscope
With electron energies on the order of 100 keV (80 - 500 keV; 0.017 - 0.043 ˚
A), the energy
deposited by an electron pulse is moderate (< 20 eV), and the ∼keV energy electron
beam can be controlled by standard electron optics. However, in this energy range, the
space–charge–led pulse broadening is severe. The broadening can be understood from the
accelerated development of a momentum-space correlation in the longitudinal phase space
led by the Coulomb repulsion between electrons. The high-energy electrons at the front of
the pulse are propelled to gain further momentum, whereas the lower-energy electrons at
the tail are further pushed back and decelerated by the Coulomb repulsion [60]. With a well
synchronized RF field, one can flip such a correlation by decelerating the electrons at the
front and accelerating electrons at the tail, leading to a recompressing of the electron pulse
downstream (see section 4.4.3). This RF compression scheme has been widely employed in
accelerator design and has recently been demonstrated in a sub-relativistic beam (∼95 keV)
by the Luiten group at Eindhoven University of Technology [60, 21]. Near 100 fs electron
pulses with ∼106 electrons per pulse have been generated. A high-brightness electron
beamline feeding a UEM system at MSU is also equipped with an RF compression scheme,
which will be detailed in Chapter 4 and Chapter 5.

2.3 Radiation effects induced by X-rays and electrons
High intensity X-ray and electron pulse irradiation can liberate electrons from atoms in
a material, thereby ionizing the material. The ionization leads to formation of highly
14

reactive sites, which disrupt crystal lattices and, eventually, cause structural deformation.
This process is called radiation damage.
Electrons
0.02 ˚
A

X-ray
1.5 ˚
A

X-ray
30 ˚
A

Ratio
(inelastic/elastic)
scattering events

3

10

103 -104

Mechanism of
radiation damage

Secondary
e− emission

Photoelectric
e− emission

Photoelectric
e− emission

Energy deposited
per inelastic event

20 eV

8 keV

400 eV

Energy deposited
per elastic event

60 eV

80 keV

400 keV

1
1

400
∼1000

20
∼10000

1

105 - 106

102 - 103

Energy deposited
relative to electrons:
inelastic
elastic
Elastic mean free path
relative to electrons

Table 2.2 Energy deposited in biological specimens [27]

Minimizing the unexpected radiation damage from incident probing X-rays and electrons
is a key issue for implementing ultrafast diffraction experiments. The radiation damage is
generally caused by two different types of interaction between the probe and a sample:
elastic scattering and inelastic scattering. To compare the radiation damage, we define the
amount of the energy deposited by inelastic scattering per elastic scattering [27]. Fundamentally, when a photon interacts with objects (atoms or molecules), the electromagnetic
field of the photon oscillates valence electrons of the objects and the induced oscillating
dipole of the objects radiates (1) the identical energy photon (Reyleigh scattering, elastic
15

scattering), and the lower energy photon (Compton scattering, inelastic scattering). Similarly, the incident electrons in the objects experience a static electric field generated by
the ion and electron cloud, and the propagation direction is bent (1) without energy loss
(Rutherford scattering, elastic scattering), and with energy loss (inelastic scattering). Two
distinct ways of the interactions lead to different energy deposition on the sample, summarized in Table 2.2 [27]. According to the ratio of inelastic to elastic events for electron and
X-ray shown in Table 2.2 [61], the amount of the energy deposited per elastic event by 0.02
˚
A electrons is much less than than the deposited energies of 1.5 ˚
A and 30 ˚
A X-ray, by 1000
times and 10000 times, respectively.
The different radiation effects and the scattering cross-section associated with the Xray and electron beams give us two complementary perspectives to enable atomic level
probing ultrafast dynamics. For example, the extremely high scattering cross-section of
electrons (105 -106 higher than X-ray) makes electron sources best for studying nanoscale or
mesoscale systems, surfaces, and gas phase dynamics, whereas the smaller scattering crosssection and greater penetration depth make X-ray sources best for the study of solution
phase, biological, and macro-systems. From a technical perspective, the penetration depth
of a keV electron beam naturally matches that of the optical excitation (typically 10100 nm), whereas an X-ray beam has a longer penetration depth (10-100 µm) and must
be implemented using a grazing angle or using very thin samples compared to static Xray experiments. High-brightness electron sources are also easier and less expensive to
implement than the equivalent X-ray source.

16

Chapter 3
Beam Dynamics in High-Brightness
Pulsed Electron Beam-line
In the development of high-brightness electron beamlines for ultrafast electron diffraction
(UED) and imaging (UEM) experiment, one of the most critical components is the electron
source. The definition of the brightness in the acceleration community is εx εNy εz (see
Eq. 3.5), where N is the number of electrons per pulse and εx εy εz is the phase space
volume [62]. The phase space evolution along the beam propagation is directly related
to the electron beam quality such as spatial and temporal resolution: coherence length
hσx , and ε = ∆t∆E (see Eq. 3.35, Eq. 3.37) [63]. In the accelerator community,
Lt = 2m
z
me cγ
e cεx
the technique and theory for high-brightness electron beam generation and evolution have
been studied for several decades. To understand and develop a new generation of UED and
UEM with high-brightness electron sources, the fundamental theory of beam physics and
the concept of phase space are introduced in the following section, followed by a discussion
of the phase space evolution of the electron beam along the high-brightness UED system.

17

3.1 Electron Beam Phase Space Evolution
The basic physical principles of electron beam dynamics can be represented by the Cartesian
coordinate system (x, y, z), where x and y refer to the transverse coordinate while z is
the longitudinal coordinate along the beam propagation direction. Each electron in the
full beam pulse is represented by position and momentum (x, px ; y, py ; z, pz ) in a sixdimensional phase space. A detailed understanding of the motion of the charged particle
requires the study of the center of mass motion (COM) of the electron beam as well as
the motion of the relative coordinates with respect to the COM. The assumption about
the relative motion is that all the charged particles in a pulse are confined within a finite
region, hence the motion is bounded within a finite volume of the phase space. Study of
this relative motion is key to understanding the beam dynamics.

3.1.1 Brightness and Emittance
By definition, a beam such as our electron pulse, is an ensemble of particles that are
defined by 6-dimensional (6D) phase space coordinates, P(x, px ; y, py ; z, pz ). During
the electron pulse propagation, we can define two distinct locations: the initial position
f
f
f
Pi (xi , pix ; yi , piy ; zi , piz ) and the final position Pf (xf , px ; yf , py ; zf , pz ), and
construct a relation between the two locations with a transfer matrix Rp :

P f = Rp P i ,

(3.1)

where Rp is a 6 × 6 matrix that maps the 6D coordinates of an electron within the electron
18

pulse from Pi to Pf under the condition det(Rp )=1 in a beam system governed by Liouville’s theorem. This transfer matrix Rp can be established for the various regions/optical
components between the two locations, such as the drift regions, the magnetic lenses, and
the RF cavity.
In a high energy beam, the longitudinal z-component of the momentum pz is generally
much larger than the other two components px and py (pz

px , py ), and it is often

possible to decouple the four dimensional transverse phase space (x, px ; y, py ) from the
longitudinal phase space (z, pz ). For reasons that will become obvious later, the transverse
phase space is often reconstructed as the trace space with the unitless momentum component
py
p
corresponding to the divergence angle: (x, x ; y, y ), where x ≡ px
z , y ≡ pz . The
p −<p >
longitudinal phase space is reconstructed as (z, δ), where δ ≡ z<pz >z . Therefore, a
particle coordinate in the 6D trace space can be represented as

XT = (x, x , y, y , z, δ),

(3.2)

where XT is the transpose vector of X.
Because the variables in the 6D trace space may be correlated, we define the beam
matrix Σ using a covariance matrix:

19



2
< x >


< x x >



 < yx >

T
Σ ≡< XX >= 

< y x >



 < zx >


< δx >

< xx >

< xy >

< xy >

< xz >



< xδ > 


< x 2 > < x y > < x y > < x z > < x δ >



< yx > < y 2 > < yy > < yz > < yδ > 

 . (3.3)

2
< y x > < y y > < y > < y z > < y δ >



< zx > < zy > < zy > < z 2 > < zδ > 


< δx > < δy > < δy > < δz > < δ 2 >

The elements of the beam matrix are the centered second-order moments associated to
the beam trace space distribution with the mean vector < XT >= 0. The beam matrix of
the propagating electron pulse Σf can be calculated with the initial beam matrix Σi and
the transfer matrix R (cf .Rp is in phase space, and R is in trace space.), which represents
the optical components in high-brightness UED:

Σf = RΣi RT

(3.4)

Statistically, a 6D Gaussian beam ρ(X) in trace space can be represented with a beam
matrix:

ρ(X) =

1
N
exp(− XT Σ−1 X),
2
(2π)3 εx εy εz
1

(3.5)

where N is the number of electrons per pulse and εx εy εz is the volume in trace space. The
6D beam brightness B6D ≡ εx εNy εz corresponds to the electron density in trace space.
The emittance, εx , εy , εz , in trace space are defined as
20

εq ≡

< q 2 >< q 2 > − < qq >2 ,

(3.6)

where q represents x, y, z spatial coordinates. The emittance is statistically a quantity
of the covariance between x and x , and, geometrically, an area in trace space (x, x ): the
emittance is an occupied area where the electrons of one pulse are distributed in the trace
space.
The emittance εx , εy , εz defined in trace space. (x, x , y, y , z, δ) is not conserved
during acceleration because the variables (x, x ) in trace space are not canonical conjugates.
Instead, one defines the normalized emittance εxn :

εxn = βγεx ,

where β = v/c, γ = 1/

(3.7)

1 − β 2 are relativistic factors. This normalized emittance εxn

refers to the area in the canonical phase space, and is conserved during acceleration.
In the following section, the transfer matrix representing various electron optic components, such as a drift region, magnetic lens, and radio-frequency cavity, will be introduced.

3.1.2 Phase Space Evolution along Electron Optics Systems
When the electron pulse travels through a beam column, the evolution in phase space can
be represented by the action of a transfer matrix. The transfer matrix in the linear phase
space motion has the following properties, as illustrated in Fig. 3.1:

21

!" !

!

"! !

!"

!!

Figure 3.1 Schematic illustration of a transfer matrix in a trace space: Left side is an initial
trace space (xi , xi ) and right side is a final trace space (xf , xf ). Transfer matrix R maps
an object in the initial trace space into the final trace space: a line → a line, a point → a
point, ellipse → ellipse, a curve → a curve.
1. Transfer matrix R preserves area. (Liouville‘s Theorem)
2. Different initial points have different final points.
3. Continuous curves stay as continuous curves.
4. Closed curves stay as closed curves.
5. A point inside of a closed curve stays inside of a closed curve.
Also, if the transfer matrix is linear, then we also have:
1. Straight lines stay as straight lines.
2. Ellipses stay as ellipses.
In our high-brightness electron beam column (as to be introduced in Fig. ??), the
major optical components are the magnetic lenses and the radio-frequency (RF) cavity.
22

#$%&"'&'"
./012-+3"4215"

6/7"
#$"

)*+,-"

#&"

#%"

)*+,-"

#("

#'"

#"
!"
#$"

697"

!"

687"

6,7"
627"

!! ! !" " " ! !" #
!! # ! !" #

637"

!! ! !"
!! # ! !

"
"" " "" #
!

Figure 3.2 Schematic illustration of electron beam dynamics in drift / magnetic lens / drift
system: (a) the beam line structure illustration in real space, (b) the emittance of the
electron pulse at Z0 , (c) the emittance of the electron pulse at Z1 (drift region). Dashed
line is the emittance at Z0 , and the blue arrow indicates the electron motion in the trace
space, (d) the emittance of the electron pulse at Z2 (after magnetic lens focusing). Dashed
line is the emittance at Z1 , and the blue arrow indicates the electron motion in the trace
space, (e), (f) the emittance of the electron pulse at Z3 , Z4 respectively.

23

The propagating electron pulse is focused by the magnetic lenses in the transverse direction
and focused by the RF cavity in the longitudinal direction. We can treat our column as two
types of sections, one as the drift region, where the pulse propagates without any external
force, and the other as the focusing region, where the momentum of the electron pulse is
controlled along the transverse or the longitudinal direction. In the drift region without the
space-charge effects, the electrons in the pulse travel with the conserved (x, y, z) momenta,
and, in the focusing region, the momenta of the electrons are changed by electron optics.
Fig. 3.2 shows a schematic illustration of the pulse envelope evolution in trace space when
the electron pulse propagates along the drift and the focusing regions.
When the electron pulse travels in the drift region, from z0 ∼ z1 , we can define the
transverse coordinates x0 , x0 , x1 , x1 with the following relations:

x1 = x0 + l · x0

(3.8)

x1 = x0

(3.9)

where l is the flight time of the electron pulse from z0 to z1 . Therefore we can construct
the transfer matrix as




1 l 
RDrif t = 
.
0 1

(3.10)

This transfer matrix of the drift region has x constant, shown in Eq. 3.8 and Eq. 3.9,
and moves x by an amount proportional to x . Therefore, the trace space envelope is
horizontally sheared, as shown in the Fig. 3.2(c).

24

As the electron pulse passes an ideal, infinitesimally thin magnetic lens (the magnetic
lens shown in Fig. 3.2), its trace space envelopes (x1 , x1 ) right before the magnetic lens
and (x2 , x2 ) right after the magnetic lens are related by the relations:

x2 = x1

(3.11)

1
x2 = − x1 + x1 ,
f

(3.12)

and we can construct the transfer matrix as following:




 1 0
RM L = 
,
1
1
−
f

(3.13)

where f is the focal length of the magnetic lens. This transfer matrix flips the trace space
of the electron pulse with respect to the x axis. After this magnetic lens, the pulse travels
in the drift region again and the trace space envelope starts a horizontal shearing motion.
When the electron pulse reaches the focal point (beam waist), the trace space envelope is
aligned along the x axis as shown in Fig. 3.2(e).

3.1.3 Imaging and Aberrations
The transfer matrix of each optical component shown in Fig. 3.2 can be combined as one
transfer matrix Rtot . Fig. 3.3 shows the simplest example of an imaging system consisting
of drift(l1 )-lens-drift(l2 ). The transfer matrix of this system can be constructed:

25

!!

!!

Figure 3.3 Schemtic illustration of an image system with one lens.

Xf = RDrif t RM L RDrif t Xi

(3.14)

= Rtot Xi ,
where Rtot is




1 l2   1 0 1 l1 
Rtot = 



1
1
−
0 1
0 1
f


l2
l1 l2
1 − f l1 + l2 − f 
=
.
l1
1
1−
−
f
f

(3.15)

(3.16)

To form an image as shown in Fig. 3.3, the various rays from the initial positions have to
be reunited at the final position on the imaging plane. In other words, the final position of
a ray is independent of its initial angle and only depends on the initial position. Therefore,

26

we can construct a boundary condition of the transfer matrix:




 

 
 xf 
 xi 
 (x|x) (x|x )  xi 
  = Rtot   = 
 ,
xi
xf
(x |x) (x |x )
xi

(3.17)

where (x|x )=0 and (x|x) represents the magnification. Using these conditions, Eq. 3.16
can be rewritten into the conventional form of imaging equations based on focal length f
and the magnification of a lens:

l l
1
1
1
l1 + l2 − 1 2 = 0 →
+
= ,
f
l1 l2
f

(3.18)

and the magnification can be deduced:

l
l
1 − 2 = − 2.
f
l1

(3.19)

In full 6D trace space, we can represent the transfer matrix with initial and final vector
coordinates:

27







xf 
 (x|x)
 

 

x 
(x |x)
 f

 

 

y 
 (y|x)
 f

  = 
 

y 
(y |x)
 f

 

 

 zf 
 (z|x)
 

 

zf
(z |x)

(x|x )

(x|y)

(x|y )

(x|z)

 

(x|z )  xi 
 
 
 
(x |x ) (x |y) (x |y ) (x |z) (x |z )
 xi 
 
 
 
(y|x ) (y|y) (y|y ) (y|z) (y|z ) 
  yi 
 .
 
 
(y |x ) (y |y) (y |y ) (y |z) (y |z )
  yi 
 
 
(z|x ) (z|y) (z|y ) (z|z) (z|z )   zi 
 
 
(z |x ) (z |y) (z |y ) (z |z) (z |z )
zi

(3.20)

This linear mapping with the transfer matrix between the initial and the final vector coordinates describes the major part of the beam motion, but to study the effects of the motion
more precisely, it is necessary to consider higher order effects and the higher order terms
can be expressed with the following equations [64]:

i
i
i
i
i
i
xf = Σ(x|xix x x y iy y y z iz z z )xix x x y iy y y z iz z z

(3.21)

i
i
i
i
i
i
xf = Σ(x |xix x x y iy y y z iz z z )xix x x y iy y y z iz z z

(3.22)

i
i
i
i
i
i
yf = Σ(y|xix x x y iy y y z iz z z )xix x x y iy y y z iz z z

(3.23)

i
i
i
i
i
i
yf = Σ(y |xix x x y iy y y z iz z z )xix x x y iy y y z iz z z

(3.24)

i
i
i
i
i
i
zf = Σ(z|xix x x y iy y y z iz z z )xix x x y iy y y z iz z z

(3.25)

i
i
i
i
i
i
zf = Σ(z |xix x x y iy y y z iz z z )xix x x y iy y y z iz z z ,

(3.26)

28

where the sums go over all six-tuples (ix , ix , iy , iy , iz , iz ). The coefficients
i
i
i
(k|xix x x y iy y y z iz z z ), where k = x, x , y, y , z, z , of second or higher order terms
are called aberrations. In an imaging system, (x|x), (y|y) are the magnifications as shown in
Eq. 3.19, and the ideal image, namely without any distortion present, has no higher order
matrix elements:

(x|xx) = 0, (y|yy) = 0, (x|xy) = 0, (x|xxx) = 0, .....

(3.27)

In a real imaging system such as an electron microscope or a camera, the higher order effects are often not negligible, and the image will be distorted. For example, when
rectangluar images are distorted into the shape of pincushions or barrels, it is caused by
non-vanishing of (x|xyy) and (y|yxx) terms. Also, ideally, there should be no effects of
i
i
i
i
initial angles on positions in higher order terms, i.e. (x|x x y y ) = (y|x x y y ) = 0,
but if any of these terms prevails, then they will cause spherical aberration. Similarly, the
positions should not depend on the longitudinal energy of the beam, i.e. (x|z ) = 0 and
(y|z ) = 0, but, if these terms are not negligible, then chromatic aberration will be caused.

3.2 Phase Space Evolution in High-Brightness Pulsed Electron Beam
System
To develop a high brightness pulsed electron source, the biggest challenge is overcoming
the space-charge effects caused by Coulomb interactions among electrons within the high–
density electron pulse. The focused high density beam results in degrading beam quality, in
terms of spatial, temporal, and spectroscopic resolutions, in particular, the stochastic space29

charge effects, such as Boersch effect [65, 66, 63], which manifests as stochastic processes
causing uncorrectable defocusing of the beam. The stochastic space-charge effect leads to
(1) in the transverse direction, an increased beam divergence angle causing image blurring
that differs from the blurring induced by the linear portion of space-charge effect, and
(2) in the longitudinal direction, an increase in energy spread that also affects the time
resolution [66]. To achieve combined atomic and sub-ps spatiotemporal resoultion, careful
understanding of the coherence and phase space evolution of the high–density electron pulse
is required and we can start from the uncertainty principle to understand the intrinsic limit
of the resolution in a high–density electron pulse.
The photons in the femtosecond laser pulse can occupy the same state in the phase
space of a confined coherent pulse because of the bosonic property of photons. However,
the phase space volume of electrons in the pulse is limited by the Pauli exclusion principle.
As discussed in the previous section, the phase space volume is defined as the emittance.
The emittance can be divided into the minimum unit cell as determined by the uncertainty
principle:

[∆x∆y∆z] · [∆px ∆py ∆pz ]cell ∼ h3 .

(3.28)

The energy state of one electron in the unit volume is quantized, and if the probability
is closed to one in the unit volume, then we have to consider the statistics with the states
of electron population and the correlation of electrons. To consider this, the degeneracy
parameter η is introduced [67]. The degeneracy parameter η is very small if the number
of electrons per pulse is small, which is the case for Caltech‘s UEM systems with a single–
electron per pulse being deployed, while in our high-brightness system η is significantly

30

larger because the targeted number of electrons per pulse is ≥ 106 . Generally, the degeneracy η is defined by the number of electrons per unit cell in the phase space, and we can
define the number of electrons per pulse, N , as:

N = η · ζ,

(3.29)

where the number of the occupied unit cells ζ can be defined as

ζ=

εx εy εz
.
h3

(3.30)

The highest achievable η is two, because of the Pauli‘s exclusion principle, considering
up and down spins. At the emittance–limited (to be contrasted to the aberration–limited)
beam waist, the emittance in Eq. 3.6 can be simplified as

εx,n =

1
me c

< x2 >< p2x >,

(3.31)

εy,n =

1
me c

< y 2 >< p2y >,

(3.32)

εz,n =

1
me c

< z 2 >< p2z >,

(3.33)

where me is the mass of an electron, and c is the speed of light. Then we can represent
the transverse beam coherence length Lt with the transverse emittance. For the coherent
diffraction perspective, the transverse beam coherence length is defined as [68]

Lt ≡

λ
,
2α

(3.34)

where λ is the wavelength of the electron pulse and α is the half divergence angle. We
31

can rewrite Lt with transverse emittance under two conditions: (1) symmetric transverse
σx σp
emittance εx = εy and (2) the beam emittance at the beam waist εx,n = me cx (from
< x2 > is the pulse width and σpx =
< p2x > is the rms
Eq. 3.31), where σx =
transverse momentum spread:

Lt =

hσx
.
2me cεx,n

(3.35)

Also, the longitudinal emittance can be represented by the energy spread ∆E and
temporal uncertainty ∆t. In Eq. 3.28, we can decompose

εz,n =

1
σz σp z ,
me c

(3.36)

under similar considerations mentioned above, and, using the relation σpz = ∆E
γvz (E =
p2z
2me ), we can rewrite Eq. 3.36 as

εz,n =

1 ∆t∆E
,
me c γ

(3.37)

where γ is the relativistic Lorentz factor and ∆t = σz /vz . If we generalize Eq. 3.37 beyond
the two conditions, then the longitudinal emittance εz,n must be smaller than m1e c ∆t∆E
γ
because the general definition of εz shown in Eq. 3.6 is εz,n = m1e c < z 2 >< p2z > − < zpz >2
[63].
To characterize the density of an electron beam in 6D phase space, we can use the
N
N h3
3
brightness B6D = εx,n εy,n
εz,n or the degeneracy η = εx,n εy,n εz,n = B6D h . Fig. 3.4
shows the degeneracy η for different operational regimes of conventional transmission electron microscope (TEM) electron guns and the simulation of a flat metallic photocathode

32

Figure 3.4 The 6D emittance εx εy εz vs. the number of emitted electrons N emit for the
extended electron sources with sizes σr (100 µm, 1 mm), thermionic guns [69], Schottky,
cold field-emission guns (CFEG), and heated field emission guns (HFEG).[63]

33

gun [63]. In conventional TEM, the lowest emittance is established with a cold field emission gun (FEG) having a 6D emittance volume of 10−11 µm3 or η ∼ 10−5 [εx ∼ 1 nm
and εz ∼ 10 pm (statistical)] [69]. In contrast, a flat metallic photocathode widely used
in ultrafast electron diffraction has a degraded εx ∼ 20 - 200 nm [63]. In Fig. 3.4, however,
the extended sources of flat metallic photocathode have the emittance volume εx,n εy,n εz,n
scale favorably, leading to a gain in η for electron bunches up to N emit = 106 for a typical
laser pulse size (100 µm ∼ 1 mm). The highest acceleration fields, e.g. Fa = 10 MV/m
in DC guns or Fa = 100 MV/m in RF guns, do not improve η significantly. In the high
charge limits (105 ∼ 106 electrons per pulse), the degeneracy figures are comparable to
FEGs, implying that similar performance (with proper phase space manipulation) could be
reached using a portion of the transverse emittance volume, for example by using apertures,
whereas in the single-shot limit, the emittance volume is expected to be equivalent to those
of thermionic guns.

34

Chapter 4
Design of High-Brightness UEM
Electron Beam Line at Michigan
State University
Ultrafast electron diffraction (UED) with 103 -104 electrons per pulse has achieved subpicosecond temporal resolution and atomic resolution, but the current development of UED
has not achieved direct imaging or coherent diffractive imaging due to insufficient beam density within the sampled volume in the specimen. High-brightness ultrafast electron sources
and optical systems maintaining highly compact beam delivery to the sample will ultimately allow us to realize sub-micron scale coherent diffractive imaging and direct space
ultrafast electron microscope (UEM), which will be a revolutionary technique to visualize
atomic and sub-picosceond processes in nanoscale materials. At Michigan State University,
we have developed a new UED system with an RF-enable high-brightness ultrafast electron source and delivery system (Fig. 4.1). Such a system is already an ultrafast electron
microdiffraction system targeting atomic and sub-picosecond processes within micron or
submicron scale materials. The ultimate target with the continuing development of projection imaging optics is the direct imaging of photo-induced ultrafast atomic dynamics,
energy, and charge transfer.
35

!""#$%#&'()*(#+(,-(.)/#01.2,3(#
!""#$%#&'()*(#+(,-(.)/#45,3(#
0,53(56()#78#!#
9:(*.),5#;(1-#<2'(:3#
=>>#-')),)#-,?5.#@##!6.#1A().?)(#####
!6.#B(C:(*.,)##
0,53(56()#78#=#
M(::,N#
DE#01F'./#
4A().?)(#-15'A?:1.,)#
=53#B(C:(*.,)#&:1.(#
G;H(*.'F(#71I5(.'*#8(56#
00B#*1-()1#C,)#J9B#
K"#$%#9LI?5#C,)#J9B#
00B#*1-()1#C,)#J97#

Figure 4.1 RF-enabled high-brightness ultrafast electron beam system at Michigan State
University

36

A crucial factor to characterize the high-brightness ultrafast microdiffraction or imaging
systems is a six-dimensional normalized beam brightness B6D , which is defined by the number of electrons per pulse N with normalized transverse emittance εx,n (under assumption,
εx,n = εy,n ) and normalized longitudinal emittance εz,n :

B6D =

N
ε2x,n εz,n

.

(4.1)

The first requirement for the number of electrons per pulse N can be established by the
Rose criterion [70]: for adequate gray scaling, an average detector signal for a pixel requires
∼100 electrons for imaging. Therefore, a 1k × 1k CCD camera requires ∼108 electrons for
one image with a single pulse, and, with a single electron detectable CCD, one diffraction
pattern requires ∼106 electrons per pulse. The second requirement for the transverse
emittance εx,n can be established with a coherence length Lt . To obtain a sufficient signal,
the coherence length Lt needs to be long enough to cover a couple of unit cells of a crystal
x at the beam waist,
lattice: Lt ≥ 1 nm. Then, using the coherence length Lt = 2mh c εσx,n
e
the transverse emittance εx,n has to be smaller than ∼0.12 µm if the electron beam size
σx at the sample is ∼100 µm.
Considering the requirements, we carefully designed the high-brightness UED system
consisting of a 100 kV Pierce geometry photoelectron gun, a series of magnetic lenses, and
an RF cavity to deliver the high intensity electron pulse to a specimen. Using an idealized
analytical Gaussian model (AGM) [71, 71, 72], we evaluated the best configuration of our
column arrangement to achieve the atomic and sub-picosecond spatiotemporal resolution
(shown in Fig. 4.2) [68]. In this chapter, we present actual designs of components of our high37

Figure 4.2 (a) Photoelectron pulse trajectory along an ultrafast electron beam column
equipped with RF compression. The shaded regions represent the locations of the electron
optical elements. (b) A scale-up view of the pulse profiles near the sample plane for nanoarea diffractive imaging containing 105 electrons/pulse. An aperture with a radius of 15
µm is employed to thin out the peripheral electrons to achieve a divergence angle α ≤ 1.7
mrad. The minimum transverse radius σT is 0.64 µm, and the minimum longitudinal pulse
length σL is 0.80 µm. (c) A scale-up view of the pulse profiles near the sample plane for an
ultrafast single-shot UED containing 108 electrons/pulse. The minimum transverse radius
σT is 51 µm, and the minimum longitudinal pulse length σL is 0.88 µm [68].

38

brightness ultrafast electron beam system: our home-built Pierce geometry photoelectron
gun, magnetic lenses, RF cavity, charge-coupled device (CCD) camera, deflectors, and
chambers.

4.1 Electron Source: Pierce Geometry DC Photoelectron Gun
As discussed in Chapter 2, we adopt the 100 keV energy electron source for the highbrightness ultrafast electron microdiffraction with the following features: (1) cost-efficient
table-top high intensity source, (2) the low knock-on energy caused by the probe, (3) better
matched inelastic scattering length to the optical penetration depth of the pump laser.
The development of the electron beam source has a long history and a variety of electron
sources have been designed and utilized in diverse beam applications. The Pierce gun was
originally suggested by J. R. Pierce in 1940 [73] and has been widely used to generate a
high intensity electron beam for various applications. We implement this Pierce geometry
in our photoelectron gun design with a cone-shaped anode with a flat cathode to achieve
weakly self-focusing and to accommodate a relatively large operable beam emitting area up
to 1 mm in diameter at ∼100 keV range for high intensity beam generation.
In the Pierce geometry photoelectron gun (shown in Fig. 4.3), the photoemission electron
pulse is generated on a silver photocathode surface by 266 nm pulse laser irradiation, and
the photoelectron pulse is accelerated by 100 kV DC bias between anode and cathode. The
Pierce geometry provides a weakly converging electric equipotential to counter the beam
divergence caused by the space–charge effects. Using Field Precision code [74], we optimized
the cathode and anode geometry to achieve three aspects:
1. A sufficiently large diameter hole on the anode for 266 nm excitation laser to be able
39

-(.&
'()*#$%&

-+.&

'()*#$%&+#$,&

5(66*78%&
97"$#9&

'()*#$%&*%($&

>=&<<&

:;;&"<&
!"#$%&

!"#$%&
=&<<&

0(1"%2/&
3%"4&

-$.&

-/.&

Figure 4.3 Cathode and anode of Pierce geometry photoelectron gun: (a) electric field calculation using Field Precision [74]. (b) Pierce geometry photoelectron gun design in the
high-brightness UED electron gun chamber. Cathode and anode are electrically isolated
through four 10 inch MACOR insulation rods. Right below the anode, there is first condenser magnetic lens to focus the electron beam after the anode. (c),(d) are the electric
potential and field profile along the electron pulse propagation direction. The profiles at
different radial locations are almost identical. This indicates that the field distribution is
uniform along the beam propagation direction.

40

2"3(

243(
-"..$/,'(
0/1&%0(

!"#$%&'(
$'"&(

!"#$%&'(
$'"&(

)$%#%*"#$%&'(
$%+&',(
Figure 4.4 Pierce geometry photoelectron gun head assembly: (a) Fully assembled Pierce
gun head, (b) The assembly procedure and the design of all parts.
to access the photocathode surface.
2. High extraction field to suppress the virtual cathode effect causing beam current
saturation.
3. Low non-linearity of the field to reduce turbulent flow causing irreversible beam emittance growth.
As shown in Fig. 4.3(b), the anode design allows the front-illuminating 266 nm laser
to access the photocathode at up to ∼ 1◦ tilt angle. The simulated electric potential
and field profiles shown in Fig. 4.3(c) and Fig. 4.3(d) are highly homogeneous, despite the
opening hole, so that emission from a relatively large radial position (∼1 mm) experiences
a similar accelerating field along the propagation direction as does emission from the center
of the cathode. The extraction field strength on the surface is about 2.5 MeV/m, which
is sufficient to generate more than 106 electrons per pulse according to a theoretical study
on the short-pulse virtual cathode effect [63]. The maximum field strength is more than 5
MV/m along the optical axis.
We consider a flexible photocathode design to accommodate various technical circum41

stances. The first consideration is for accommodating two different illumination schemes:
front-illumination and back-illumination. The front-illumination has to be implemented
to generate a sufficient number of electrons per pulse (>106 electrons), and the backillumination is required for beam and column alignment in an initial setup of the system.
The second consideration is for different types of photocathode: bulk and thin film. A bulk
type photocathode is easier to prepare and can afford higher quantum efficiency materials
than the thin film type, but the bulk type does not allow us to implement a back-illumination
scheme. This flexibility also allows us to experiment with different types of materials for
photoemission experiments. For example, to minimize the initial transverse emittance, the
work function of the photocathode material has to match the 266 nm laser pulse energy (4.66
eV) because excess photon energy can cause larger initial transverse momentum spread of
the photoemitted electrons [68]. In our first experiment, we adopt 40 nm thick silver film
(the work function is 4.26-4.74 eV [75, 76, 77]) as the photocathode operable both with the
back- and front-illumination schemes for our high-brightness electron beam system.
The switchable photocathode is shown in Fig. 4.4. The cathode head assembly can be
dismounted easily from the cathode body (see Fig. 4.3(b)), and we can take the part out
through a 6” port of the cathode chamber. The full cathode assembly consists of the stainless steel cathode head, the stainless steel photcathode holder, and the sapphire window.
To prepare the photocathode, the sapphire window is first secured on the photocathode
holder with UHV comparable silver-paste. The photocathode holder is then mounted at
the center of the stainless steel cathode head through the 3/4-20 thread. After assembling
all the parts, we deposit the 40 nm thickness silver film on the sapphire window surface
using a thermal evaporator. If we need to change the photocathode material or the type,

42

!"#$%&'$

()*$

-./)0",$1"23$

67$8"9$

(+*$

4),5/$/51$
(,*$

Figure 4.5 Pierce geometry photoelectron gun: (a) the whole Pierce photoelectron gun
housed in a UHV chamber, (b) the zoom-in view of the cathode and high voltage isolation
using a ceramic disk as the base, (c) triple point shielding geometry design at the junction
of MACOR rods and anode.
then we can simply replace the silver coated sapphire window with a differently prepared
one.
One of the most critical issues in 100 kV electron gun design (shown in Fig. 4.5) is the
stability of the high voltage, because, if the local electric field strength at the surface is too
high, then a vacuum breakdown may occur due to the ionization of the residual gas between
the cathode (-100 kV) and ground (0 V). Furthermore, the gas discharge may also lead to
surface breakdown of the insulating materials between the cathode and the anode, creating
a conducting path. These breakdowns lead to electrical arcs inside of a chamber that might
cause damage to other parts or electronics. Although a generic microscopic mechanism
for triggering the vacuum breakdown is not yet established in practical implementation

43

of a high voltage device, the rule of thumb is to avoid creating sharp edges or rough
surfaces. Generally, the ionized charged particles around the cathode can be accelerated
to high energy, and subsequent collisions of the accelerated particles with residual gas lead
to further ionization, and ultimately an avalanche. According to Paschen’s law [78], this
dielectric breakdown voltage depends on the product p · d, where p is pressure and d is the
distance between cathode and anode. While the breakdown voltage at ∼10−5 torr may
be as high as 25 MV/m between two flat electrodes [79], the practical breakdown limit
is around 8 MV/m at 10−8 torr. Our acceleration field strength is below this practical
vacuum breakdown limit. A lower breakdown threshold may be due to local curvature of
the surface. The sharp edge of the surface causes an order of magnitude higher local field,
and this field enhancement might initiate the vacuum breakdown. Therefore, all the parts
near the high voltage are electro-polished to smooth the microscale sharp edges. As shown
in Fig. 4.5(b), the high voltage feedthough pin has the sharp edge directly buried in the
cathode body without any additional connectors. Thus, we completely eliminate the sharp
edges around the high voltage region.
A conducting path can also be established along the surface of an insulator, and this
dielectric breakdown is called a dielectric flash-over or surface tracking. Especially when
the field lines are parallel to the surface of the insulator, the released electrons that gain
energy hop toward the anode through the insulator surface and establish a conducting
path on the surface. To minimize the energetic electron hopping rate, we designed two
insulation stages with two orthogonal surface directions (shown in Fig. 4.5): (1) the high
voltage cathode is mounted at the center of the ceramic disk, and the field direction is along
the radial direction of the chamber, (2) four MACOR rods connect the ceramic disk and

44

the anode, and the field direction is along the electron pulse propagation direction. Also,
triple points, which are junctions of three different media, have to be avoided or shielded
properly because the electric field strength at the triple points can be enhanced, and the
enhanced field causes the dielectric breakdown through the locally charged insulator [80].
Triple points arise naturally at the location where a conductor connects to an insulator in
a vacuum chamber. To minimize the local field enhancement, the rods are mounted on the
counter sink of an anode surface, shown in Fig. 4.5(c).
Given these precautionary measures, it is still extremely hard to completely eliminate
dielectric breakdown, due to microscale whiskers and fragments on the surfaces of the chamber or various parts. Microscale whiskers and fragments can be removed by conditioning the
high voltage photoelectron gun. The conditioning can be simply done by gradually increasing the high voltage until breakdown occurs and then quickly lowering the high voltage.
With this iterative conditioning procedure, the spontaneous but short-lived breakdowns will
clean up the microscale whiskers and fragments gradually. Through constantly monitoring
the high voltage current, we can decide how much the photoelectron gun surface is cleaned
up with the current fluctuation. If the current fluctuation level is within ∼10 nA, then it
is stable enough to operate the system (see Fig. 4.6).

4.2 Magnetic Lenses
In designing the magnetic lens, we need to consider two key aspects: (1) the gap geometry
inside of the bore of a pole-piece and (2) wound coils to apply the current. The pole-piece is
a cylindrically symmetric structure made by a soft magnetic material such as soft-iron (our
magnetic lens material is described in Appendix D.) with a hole drilled through it, called
45

!"##$%&'(!)*'

!"#$

+,-$'(.$/*'

!"##$%&'(!)*'

!%#$

+,-$'(.$/*'
Figure 4.6 Current stability monitor (a) after the electron gun conditioning, (b) before the
conditioning

46

!"
("

.)(%"

#$%&'()*"+,$-%"
.!"

.("
12+"
/)$%+0%&%"

Figure 4.7 Schematic illustration of non-uniform magnetic field (red lines) at the center
of the magnetic lens pole-piece. The hole through the pole-piece is called bore and the
disconnected region inside of the bore is called a gap.

47

!"#$

!%#$

!&#$

Figure 4.8 Condenser magnetic lens No. 1: (a) The geometry of the lens. The yellow
box region is filled with coils. (b) The magnetic field map near the pole-piece (region
highlighted by the red box in (a)) of the condenser lens No. 1.: The black arrow indicates
the electron pulse propagation direction and the the plot has the cylindrical symmetry along
the beam propagation direction. (c) Magnetic field strength profile along the different radial
coordinates, R= 0.0, 0.5, 1.0, 1.5, 2.0 (mm).

48

!"#$

!%#$

!&#$

Figure 4.9 Condenser magnetic lens No. 2: (a) The geometry of the lens. The yellow
box region is filled with coils. (b) The magnetic field map near the pole-piece (region
highlighted by the red box in (a)) of the condenser lens No. 2: the black arrow indicates
the electron pulse propagation direction and the the plot has the cylindrical symmetry along
the beam propagation direction. (c) Magnetic field strength profile along the different radial
coordinates, R= 0.0, 0.5, 1.0, 1.5, 2.0 (mm).
49

!"#$

!%#$
!&#$

Figure 4.10 Objective magnetic lens: (a) The geometry of the lens. The yellow box region
is filled with coils. (b) The magnetic field map near the pole-piece (region highlighted by
the red box in (a)) of the objective magnetic lens: the black arrow indicates the electron
pulse propagation direction and the the plot has the cylindrical symmetry along the beam
propagation direction. (c) Magnetic field strength profile along the different radial coordinates, R= 0.0, 0.5, 1.0, 1.5, 2.0 (mm). The kinks at R=1.5, 2.0 mm profiles are artifact
because the objective lens exit hole radius is 1.5 mm.

50

the bore of the pole-piece. Inside the bore of the pole-piece, there is a gap in the middle
of the bore (shown in Fig. 4.7), and this gap geometry determines the magnetic focusing
strength. Using a finite element numerical method (Field Precision (Commercial Software)
[74]), we optimize the gap geometry and the bore diameter of three magnetic lenses: (1)
condenser magnetic lens No.1 (CML1) right after the Pierce geometry photoelectron gun,
(2) condenser magnetic lens No.2 (CML2) before the RF cavity, and (3) objective magnetic
lens (Obj.ML) right before the sample. The location of the three magnetic lenses are shown
in (a) of Fig. 4.8 (CML1), Fig. 4.9 (CML2) and Fig. 4.10 (objective magnetic lens). The
panel (b) in Fig. 4.8, Fig. 4.9 and Fig. 4.10 shows the magnetic field calculation near the
bore gap, where the vector fields have cylindrical symmetry along the black arrow indicating
the electron pulse propagation direction. The panel (c) shows the magnetic field profiles
along the propagation direction at different radial coordinates. The non-uniform field with
cylindrical symmetry along the optical axis transversely focuses the propagating electron
pulse.
The second issue of the magnetic lens design concerns how much current is required to
focus the electron beam at the desired locations, because the applied current on magnetic
lens determines the focal length. Based on a previous theoretical study with the analytical
Gaussian model (AGM) [68], we establish the lower limit of the required current for each
magnetic lens design. In AGM, the evolution of an electron pulse described by Gaussian
distribution in the phase space is governed by following differential equations [72]:

dσi
2
=
γ,
dt
me i

51

(4.2)

dγi
1
=
dt
me

ηi +

γi2
σi

+

1 N e2
L + Mi σ i ,
√
4π 0 6 σi π i

(4.3)

2γ η
dηi
= − i i,
dt
m e σi

(4.4)

where σi is the spatial beam variance, ηi is the local momentum variance, γi is the momentum chirp and Li is the parametrized function to quantify the ellipticity (more details are
in Ref.[72]) in the transverse and longitudinal directions, that is i = {T, z}, respectively. N
is the number of electrons in the Gaussian pulse, and 0 , e, and me are the vacuum permittivity, and the charge and rest mass of the electron, respectively. The last Mi , (i = T, z)
is the parameter specifying the strength of a magnetic lens for transverse focusing and RF
cavity for longitudinal focusing, respectively. (Note: the emittance,

√

σi ηi , is conserved in

the dynamic equation.) The MT parameter that determines the magnetic focusing strength
corresponds to the magnetic lens focusing with a certain applied current.
To calibrate the required lens current with the parameter MT , we compare the AGM
simulation [68] with ray tracing calculation using Field Precision. Fig. 4.11 shows the
results of AGM simulation and Field Precision simulation. The blue solid line is the AGM
simulation without space–charge effect (N =0). The initial transverse width is 100 µm
and 50 µm, and the initial transverse momentum spread is 2×104 (m/s) corresponding
to 0.1 mrad divergence angle of a 100 keV electron beam entering the lens. The dashed
lines are the non-interacting electron trajectories calculated by Field Precision. To match
the prescribed magnetic lens focusing by AGM, we adjust the current of the lens, so the
resulted focal distance is the same as the AGM. Fig. 4.11 shows that the 100 keV electrons
at R=100 µm and 50 µm with ray angle, ±0.1 and 0 mrad, travel through the magnetic
52

*%,)

02-)

*C,)
5(:%?@()A(B+(%C":"$D)

01-)
5)*6+,)

0--)
4-)
3-)
2-)
1-)

0---)

0--)

0-)

-)

-)
-)

-.-/)

-.0) -.0/)
!"#$%&'()*+,)

-.1)

-)

-.1/)
!

0)

1)

=)
2)
/)
789(:;)*<(#:%,)

3)

>)

4)

Figure 4.11 (a) Magnetic lens current calibration simulation: Solid lines are AGM simulation
without space–charge effect, and the dashed lines are Field Precision [74] simulation of noninteracting single electrons, calculated with the relative permeability shown in (b). The
initial transverse size of the Gaussian electron pulse in AGM simulation is 100 µm and 50
µm with angular spread 0.1 mrad. In Field Precision simulation, the initial position of
single electrons is at R=100 µm and 50 µm, and each line represents different initial ray
angles, ±0.1, 0 mrad.
lens with an applied total current 550 A. The electron trajectories starting at ±1 mrad, and
R=100 µm and 50 µm are crossing at the same focal point of the AGM simulation and the
electrons with 0 mrad are focused at the same focal length at R=0. The ray tracing results
replicate the AGM results in terms of the focal distance and beam waist under similar initial
conditions. We note that the magnetic field is calculated based on the relative permeability
described in Fig. 4.11(b).
Based on this lens focusing simulation, CML1, CML2 and Obj.ML require 550 A, 450
A and 750 A total currents, respectively. In the magnetic lens fabrication, we have to be
concerned about the the relative permeability used in magnetic field calculation because
the actual permeability of the materials strongly depends on the post-processing such as
annealing process (Appendix D). Re-machining after annealing process may also change the
permeability. In the design stage, we used the generic relative permeability of the soft iron

53

shown in Fig. 4.11(b), but we need to calibrate the relative permeability by comparing the
performance of the fabricated lenses with the predictions (to be discussed in Chapter 5).
Due to the uncertainty of the relative permeability, we set the projected lens currents as the
lower limit for the magnetic lenses and allocate the space for coils to achieve ∼5 time higher
desired currents than the projected values. We use the UHV comparable electrical wires
(22 AWG Kepton insulated wire with 5.5 A current rating from Accu-Glass Products, Inc.
(Part number: 112615)) for the CML1 and the Obj.ML coils because the CML1 and the
objective lens are installed inside the UHV chamber (see Fig. 4.1), while a normal magnetic
coil (18 AWG, 10 A current rating) is used for the CML2, which is mounted externally
under the atmosphere. To generate the required currents considering the current rating of
electrical wires and the applied current for the lenses, CML1, CML2, and Obj.ML have 550
(1 A applied current), 150 (3 A applid current), 750 (1 A applied current) coil windings,
respectively.
To characterize the beam path along the whole electron beam column, we simulate
electron beam trajectories under the exact column geometry using two different simulation
methods implemented in Field Precision. The first simulation is ray tracing calculation
based on non-interacting electrons, without space–charge effects. The second simulation is
with space–charge effects induced by the self-generated electric field of a continuous electron
beam, shown in Fig. 4.12. The non-interacting ray tracing calculates the single–electron
trajectories only considering the external field generated by the optical components, while
the simulation with space–charge effects considers both the external field and the selfgenerated electric field to calculate the trajectory where the space–charge contribution is
adjusted at each time step. The vertical lines in Fig. 4.12 indicate the optical component

54

Figure 4.12 Field Precision simulation of an electron trajectory with non-interacting particles (Red line) sheme and with space–charge effect induced by the self-generated electric
field of a continuous high current electron beam (blue line). Red and blue solid lines
are calculated with the same focusing condition with CML1=550 A, CML2=450 A, and
Obj.ML=750 A, and the dashed line is calculated with with CML1=0 A, CML2=450 A,
and Obj.ML=750 A. The black dashed vertical lines indicates electron optics components:
(1) the photocathode surface, (2) CML1, (3) CML2, (4) RF cavity, (5) Obj.ML, (6) the
sample, and (7) CCD screen. The shaded region shows where the electron beam is focused
by the Pierce geometry gun.

55

locations, summarized in table 4.1: (1) the photocathode surface, (2) CML1, (3) CML2, (4)
RF cavity, (5) Obj.ML, (6) the sample, and (7) CCD screen. The trajectorys are calculated
under the same focusing condition with CML1=550 A, CML2=450 A, and Obj.ML=750 A.
In the non-interacting electron simulation, the electron initial energy is zero and accelerated
by the 100 kV acceleration field, and, in the simulation considering space–charge effects, the
initial beam current is defined as 8 mA, which corresponds to 5×106 electrons per 100 ps, a
density relevant to our elongated pulsed electron beam. The solid red line is the convoluted
trajectory of non-interacting electrons emitted from five different initial positions: R= 10,
20, 30, 40 ,50 µm, and the solid blue line is the electron trajectory under the influence
of the space–charge effects at the continuous high-current beam limit. Fig. 4.12 shows
that the electron beam without space–charge effects is strongly focused by the Pierce gun,
and, due to this tight focusing occuring at CML1, CML1 does not further focus the beam
significantly, shown in the comparison between the solid red line and the dashed red line.
The latter is the result with CML1=0 A, CML2=450 A, and Obj.ML=750 A. With spacecharge effects, the Pierce geometry provides a central focusing role to reduce the initial
divergence of the electron beam (divergence angle changes from 40 mrad to 10 mrad),
shown in the shaded region (Fig. 4.12), to bring the beam to convergance at 1 mrad. The
CML2 can further focus the electron beam to travel through RF cavity, and the Obj.ML
can control the electron beam focusing for a nearly parallel beam focused at CCD screen
or a convergent beam focused at the sample. In the microdiffraction mode, which requires
focusing the electron beam on the sample as shown in Fig. 4.12, the coherence length at
the sample (the beam waist) can be calculated by Lt = λe , where λe is the 100 keV
2∆θ
electron wavelength, and ∆θ is the divergence angle. From the Field Precision simulation

56

considering the space–charge effect, Lt is ≥ 1 nm with the 100 keV electron wavelength
λe =0.0037 nm, and the divergence angle ∆θ=1.6 mrad. Therefore, in the design stage, the
optical components fulfill the appropriate functionality to deliver a high density electron
pulse to the sample with the expected requirement of the coherence length, In Chapter 5,
the actual high-brightness electron pulse characterization will be discussed.

Optical Components

Position (m)

Photocathode surface

0.000

CML1

0.070

CML2

0.360

RF cavity

0.640

Obj. ML

1.090

Sample plane

1.110

CCD screen

1.441

Table 4.1 The location of the optical components in the high-brightness UED column

4.3 Radio-frequency (RF) Cavity
With a high-intensity electron pulse (≥106 electron/pulse), pulse compression is required
to overcome the collective space–charge effects, causing pulse broadening. We implemented
the RF cavity to compress the longitudinally broadened electron pulse. In the following
sub-sections, for conceptual understanding the performance of RF cavity, the simplest RF
57

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$%&"

!"

#"

!"
#"

',."/0-1"
#"

!"

30#-"/0-1"

#"

!"

',."/0-1"
!"

#"

30#-"/0-1"

Figure 4.13 Pillbox cavity with radius R and length d: (a) illustration of the pillbox geometry, (b) top view and side view of transverse magnetic mode electromagnetic field in
pillbox cavity, (c) top view and side view of the transverse electric mode electromagnetic
field in pillbox cavity.
cavity, a pillbox is first introduced, followed by an introduction of actual RF cavity and RF
synchronization scheme.

4.3.1 RF Field in Pillbox Cavity
The pillbox cavity, a simple cylinder with radius R and length d as shown in Fig. 4.13(a),
is the simplest geometry for generating an resonant RF field. To derive the RF resonance
of pillbox cavity, we can start from the general wave equation for the radiation field Ψ:
∂ 2Ψ
1 ∂ 2Ψ
−
= 0.
∂R2 c2 ∂t2

58

(4.5)

Using cylindrical coordinates, we can rewrite Eq. 4.5 as

{

∂
1 ∂2
1 ∂
∂
1 ∂2
+
−
}Ψ = 0.
(r ) +
r ∂r ∂r
r2 ∂ϕ2 ∂z 2 c2 ∂t2

(4.6)

If we define the Ψ(r, ϕ, z, t) = Ψr (r)Ψϕ (ϕ)Ψz (z)Ψt (t) with Ψz (z) = cos(kz z) and
Ψt (t) = cos(ωt), then Eq. 4.6 can be derived as

{

1 ∂
∂
1 ∂2
1
(r ) +
− kz2 + ω 2 }Ψ = 0.
2
2
r ∂r ∂r
r ∂ϕ
c2

(4.7)

Now, we can derive the RF field of the pillbox cavity from the following solution of the
general wave equation:

Ψ(r, ϕ, z, t) = Ψ0 Jm (kr) cos(mϕ) cos(kz z) cos(ωt),

(4.8)

where Jm is the m − th Bessel function of the first kind and k 2 = ω 2 /c2 + kz2 with angular
frequency ω = 2πf . If the pillbox wall is perfectly conducting and contains a lossless
medium characterized by a permittivity and a permeability µ, then we can construct two
boundary conditions:
Ψ(R, ϕ, z, t) = 0,

(4.9)

Ψ(r, ϕ, 0, t) = Ψ(r, ϕ, d, t) = 0.

(4.10)

The solution of the general wave equation, Eq. 4.8, imposes two different kinds of resonance modes, transverse electric (TE) modes and a transverse magnetic (TM) modes,
shown in Fig. 4.13 (b), (c). The longitudinal (ˆ
z ) component of the electric field of TM
modes Ez is the pulse compression component. With the boundary conditions, Eq. 4.9 and
59

Eq. 4.10, we can derive the longitudinal component of TM modes as

Ez (r, ϕ, z, t) = E0 Jm (kr) cos(mϕ) cos(kz z) cos(ωt),

(4.11)

k = ζmn /R,

(4.12)

kz = πl/d,

(4.13)

where ζmn is the n − th root of Jm (kr) = 0 (m, n, l ∈ N). The resonance frequency of
TMmnl in the pillbox cavity is given by
2
π 2 l2
ζmn
+
.
R2
d2

1
ωmnl = √
µ

(4.14)

The mode numbers m, n, l are the number of nodes in the rˆ, ϕ,
ˆ and zˆ direction respectively.
With Ez (r, ϕ, z, t), we can evaluate the electromagnetic field of the simplest TM mode,
TM010 which dominantly affects the pulse compression:
ζ
Ez (r, z, t) = E0 J0 ( 01 r) cos(ω010 t),
R

Bϕ (r, ϕ, t) =

√

ζ
µE0 J1 ( 01 r) sin(ω010 t).
R

(4.15)

(4.16)

Other components of TM010 mode are zero, and the resonance frequency is ω010 = ω0 =
√
ζ01 /(R µ). If the cavity wall conductivity is not perfect, then it causes energy loss,
Ploss . The ratio between the time-averaged energy gain Ugain and the energy loss, Ploss ,

60

per cycle is defined as the quality factor (Q-factor) Q:

Q = ω0

Ugain
.
Ploss

(4.17)

This Q-factor represents the quality of the RF cavity power conversion efficiency. The
gap d of the actual RF cavity is 22.5 mm, and the resonance frequency is ∼1 GHz. For
Eq. 4.14 with ω010 , the required radius R of pillbox cavity is ∼12.8 mm, and the Q-factor
is ∼ 4.6 × 103 .

4.3.2 RF Cavity in High-Brightness Electron Beam Line
The RF cavity implemented in our high-brightness electron beam line is more efficient
than the pillbox cavity because the cavity geometry is optimized to improve the Q-factor of
TM010 mode at ∼ 1 GHz resonance frequency. The Q-factor of the RF cavity is ∼ 2.2×104 ,
and the peak electric field on the optical axis is 1∼3 MV/m. The actual RF cavity design
is shown in Fig. 4.14 (a). The optimized geometry RF cavity has a torus shape, and the
magnetic field of the TM010 mode in Eq. 4.16 has cylindrical symmetry and the electric
field is along the optical axis where the electron pulse propagates (shown in Fig. 4.14 (a)).
When the electron pulse passes through the RF cavity, the faster electrons at the front of
the electron pulse are decelerated by the negative direction of the RF field and the slower
electrons at the tail are accelerated. In the phase space shown in Fig. 4.14 (b), the faster
electrons are distributed in the upper-right area and the slower electrons are in the lowerleft area before RF compression. After passing through the RF field region, the momenta
of upper-right area electrons are flipped down to negative due to the deceleration, and the
momenta of the slower electrons are flipped up. During the electron pulse drifting in free
61

345#
#"
!"

365#

!"##

$%&'(%#)*#+',-(%../'0#
"#
12%(#)*#+',-(%../'0#

Figure 4.14 RF cavity: (a) The actual design of geometry optimized RF cavity and the
TM010 mode RF field in the RF cavity (The red ring is a magnetic field and the black line
is an electric field), (b) Phase space volume evolution with RF compression.

62

space, the positive momentum leads electrons to move in the positive direction, and the
negative momentum leads the electrons to move in the negative direction. At the focal
point, the phase space volume is aligned along the momentum axis. The focal length fL is
determined by [81]
eE0 ω0 d
1
≈
sin φ0 ,
fL
me γ 3 vc3

(4.18)

where E0 is electric field amplitude, ω0 is RF cavity resonance frequency, d is gap distance
in RF cavity, me is electron mass, γ is the Lorentz factor of the center of mass velocity of
the electron pulse, and φ0 is the relative phase between electron pulse and the RF field.
Therefore, we can control the RF compression focal length with control of the RF power.

4.3.3 RF Station for RF Field and Electron Pulse Synchronization
As mentioned before, the basic concept of the pulse compression is that the faster electrons
at the front of the pulse are decelerated while the slower electrons at the tail of the pulse
are accelerated with a fast oscillating electric field generated by the RF cavity. Then,
during the subsequent drift region, the pulse starts to be compressed and reaches the
minimum longitudinal length at the sample location. The oscillating electric field in the
TM010 mode of the RF cavity resonates at ∼1 GHz, and the polarity switching time of
the oscillating electric field has to be precisely synchronized with the arriving time of the
electron pulse at the RF cavity. The synchronization between the RF electric field and the
electron pulse is achieved by synchronization between the femto-second laser pulse train of
the laser source and the RF field because the electron pulse in our high-brightness UED is
originally generated by the femto-second laser. This RF synchronization station has been
developed by my colleague Zhensheng Tao, and the more technical details can be found in
63

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!! ! " !

!"#$%&
'%(%)(*+&

/%%:=#)>&

2?&

!! ! " # "! #!$
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/01(%+&

2@&

!! ! ! " !#" "#"$ #
!!! " !
234&

/+%56%7)8&
'090:%+&

Figure 4.15 Block diagram of the Phase lock loop.
his thesis [82]. In this section, the basic concepts and the key factors of RF compression
synchronization will be briefly introduced.
The synchronization means tightly lock the RF electrical signal inside the RF cavity
with the fs laser pulse train, and, in order to achieve the synchronization, we developed a
phase-locked Loop (PLL) [82] with our high-brightness UED independently. Basically, a
PLL is an electrical circuit to lock the phase of output onto the input, and a PLL can be
considered an oscillator whose phase is locked onto the phase of the reference (fs laser pulse
train) input signal. Fig. 7.10 shows a block diagram of a general PLL. The phase detector
compares the phase of feedback and the reference signals, and it develops the output voltage
(V1 ) proportional to the phase difference (∆ϕ) between the two signals with the following
relation:

v1 = Kp ∆ϕ + Vpo ,

(4.19)

where Kp is the phase detector gain, and Vpo is the inherent free running offset voltage.

64

When the loop is locked, the two input frequencies, reference and feedback signals (ωi = ωo )
are the same, and the signals are represented by the following wave equations:

ΨRef = A cos(ωi t + ϕi ),

(4.20)

ΨF eedback = B cos(ωi t + ϕo ),

(4.21)

and, if we apply the mixer as a phase detector, the output, V1 , of the phase detector is
propotional to two frequencies:

AB
v1 ∝ ΨRef · ΨF eedback =
[cos(2ωi t + ϕi + ϕo ) + cos(∆ϕ)].
2

(4.22)

The low-pass filter removes the high frequency component 2ωi , and this filtering range
is determined by the loop filter gain KF (ω). The output voltage V2 of the low-pass filter
is applied to a voltage-controlled oscillator (VCO) as a control voltage in order to adjust
the output signal phase with the following relation:

∆ω = Kc (V2 − Vco ),

(4.23)

where the Kc is VCO gain, and Vco is the control voltage when PLL is locked (ωo = ωi ).

65

4.4 Charge-coupled Device (CCD) Camera
The first requirement for the image acquisition system of high-brightness UED is the high
sensitivity to detect a single electron event. To achieve single electron sensitivity, we implement PIXIS-XF charge-coupled device (CCD) camera from Princeton Instruments with
a HAMAMATSU image intensifier (V7670U-04) for signal amplification. To suppress the
background noise level, we operate the CCD camera at a -35o C set temperature.
Fig. 4.16 shows the design of the image acquisition system consisting of a CCD camera
main body and image acquisition optics (Optical face-plate, Optical taper, and intensifier).
A 60 nm thick aluminum film is coated on the optical face-plate of the image acquisition
optics to block the background photon signals which come from the pump laser or room
light. The penetration depth of visible wavelength photon in Al is ∼15 nm, while that of
100 keV electron beam is ∼ µm range. Therefore, most of the ambient background photons
are blocked by this Al film. The electrons passing through the Al film strike a phosphor
screen and generate a burst of photons in the visible range. These photons are focused by
a 2:1 ratio optical taper on the image intensifier input window. When the photon enters
the intensifier, the photons are converted back into electrons at the front of the image
intensifier by a photocathode. The generated photo-electrons are accelerated and enter
the micro channel plate (MCP). The MCP is composed of more than 106 micro-channels
that are 6 µm diameter individual miniature electron multipliers. Each MCP can provide
an amplification of up to 1000 times with the accurate spatial resolution, and the image
intensifier consists of 3 MCPs, thus allowing a gain of up to 109 . The amplified electrons
strike another phosphor screen to convert the electrons to much a larger number of photons

66

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556'

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Figure 4.16 Structure of charge coupled device (CCD) camera mount. (a) Schematic illustration of image acquisition optics in front of CCD camera main body: Al film and
phosphor screen are coated on the optical face-plate surface, and an optical taper focuses a
signal with 2:1 ratio onto an intensifier input window. The Al film screens the background
photon from room light and pump laser, and the phosphor film converts the electron signal
to photons which is amplified by the intensity. The red box indicated the intensifier. (b) a
schematic diagram of the micro-channel plate (MCP) in the intensifier. The MCP is composed of more than 106 micro-channels which are individual miniature electron multipliers.
(c) design of the fully assembled CCD camera. All the components are made of glass, so,
using the optical grease, we make smooth contacts between parts to minimize the signal
loss.

67

(see Fig. 4.16(a)). This amplified signal in the form of photons is incident on the CCD
camera.
The major issue in the CCD camera mount design is the UHV components and non-UHV
components: the phosphor screen on the optical face-plate has to be in the UHV chamber
and the image intensifier is a UHV non-compatible part. Using an O-ring, which can hold
the high vacuum level only, we mount the optical face-plate as shown in Fig. 4.16(c) (Oring black circle). To achieve chamber pressure down to the UHV level, we implement the
differential pumping scheme. As shown in Fig. 4.16(c), a gap in the image acquisition optics
is sealed by three O-rings: the 1st and 2nd O-ring are at the boundary between UHV and
the gap region and the 3rd O-ring is at the boundary between the gap and the atmosphere.
Pumping down this gap region using a dry pump, the UHV chamber pressure can be held
by a series of O-ring seals because the pressure difference at each O-ring seal is not at UHV
level, but at a high vacuum level. Another technical concern for the design is that all of the
parts in CCD mount assembly are made of glass, so we cannot easily compress them, but
we have to compress them sufficiently to avoid a leak between components. To achieve this,
we have to have perfect dimensions for the stainless steel housing, but practically we cannot
avoid machining error. For this issue, we design another O-ring that can compensate for
the machining tolerance at the adjustable disk (blue color in Fig. 4.16), which is easy to
modify.

4.5 Other Components for Optical and Electron Beam Delivery
In the previous sections, we introduced the major parts of the high-brightness beam system,
the Pierce geometry photoelectron gun, the magnetic lenses, the RF cavity, and the CCD
68

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011$23$)"**+*$
011$23$

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'>6$?</*6=*/$,+-./*$
'>6$B/C/56+*$D+.>$

Figure 4.17 266 nm excitation mirror holder and electron beam shield.
camera. As shown in Fig. 4.1, there are additional parts that also have critical functions
to operate the UED experiments in an optimum condition. In this section, function and
design of the other key components are briefly introduced.

4.5.1 266 nm Excitation Mirror Holder and Electron Beam Shield
To generate the electron pulse in the Pierce geometry DC photoelectron gun, access is
required for the 266 nm laser pulse. For back-illumination, the photocathode back-side
has a pin hole for the 266 nm laser to be able to access the photocathode directly, but,
for front-illumination, a 266 nm UV grade mirror is required because it is not possible for

69

the laser to access the photocathode directly from the front-side. The first design issue is
with the 266 nm UV mirror mount. The 266 nm mirror has to be mounted very close to
the center of the chamber where the electron beam propagates because of the extremely
limited space of the bore of CML1 and the anode hole. Fig. 4.17 shows the mirror mount
structure with an electron beam shield. To make the space large enough for an electron
pulse to go through, the mirror mount holder is mounted ∼17 cm away from the CML1.
Another issue is charge accumulation on the mirror substrate (quartz) because the 266
nm mirror edge is only ∼3 mm away from the electron pulse beam axis. The static field
caused by the accumulated charges can disturb electron pulse propagation. To minimize
charge accumulation, we designed the electron beam shield on top of the mirror as shown
in Fig. 4.17.

4.5.2 Electron Beam Deflector
In principle, if all of the parts in the high-brightness UED system are perfectly fabricated
without any errors and the electron pulse travels through the exact center of the highbrightness UED column, then an electron beam deflector is not required. However, it is
not possible to fabricate the exact dimension and perfectly symmetric components. All of
the machined parts have a tolerance of ∼0.001”, and the accumulated machining tolerance
in each part might not be negligible in a whole assembly. To compensate for this inherent
systematic error, a beam control mechanism is required. In the high–brightness UED
system, we implement two electron beam deflectors that control the electron beam direction
with a static electric field, as shown in Fig. 4.1. The detailed design of the first deflector
is shown in Fig. 4.18(a). It consists of two pairs of stainless steel rods which generate an

70

electric potential difference and the MACOR cylinder which electrically isolates the rods
from the stainless steel deflector body. Electron pulse propagation is from the bottom to
the top in the figure (blue arrow). Each pair of rods generates an electric field in two
orthogonal directions, which are perpendicular to the electron pulse propagation. Using
this electron beam deflector, we can control the beam direction to align it to travel through
the center of the major components such as the magnetic lens and RF cavity.

4.5.3 Aperture Manipulator
To align the electron beam along the high-brightness UED column and reduce the beam
emittance, we need several different sizes of apertures, but it is technically too expansive
to fabricate them from scratch because a customized aperture manipulator has to be designed and a UHV compatible precise motion manipulator is extremly expansive. Therefore,
we use the aperture manipulator that was used for our old scanning electron microscope
(Steroscan 360, Cambridge Instrument), shown in Fig. 4.19 (a). We designed the adapter
to mount the SEM aperture manipulator (shown in Fig. 4.19 (b)). The manipulator is able
to mount four different sizes of apertures, 30 µm, 50 µm, 170 µm, and 3 mm. However, this
manipulator was used for the SEM high vacuum chamber, not for UHV. We applied the
differential pump scheme with two O-ring seals in order to use the SEM aperture holder
in the UHV chamber of our high-brightness UED system (shown Fig. 4.19). Fig. 4.19 also
shows the second electron beam deflector which is right below the aperture.

71

=#?)

6789)!'")!./':)

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6789)!'")!./':)

-#.+/)0%(1&#"+/)

=>?)

;7<1&(')

!"#$%&'(()!"''&)
2'3'."+/)4+,5)

Figure 4.18 Electron beam deflector. (a) The design of the electron beam deflector: the
electron pulse propagates from the bottom to the top (blue arrow), and two pairs of stainless
steel rods generate two orthogonal directions electric fields which are perpendicular to the
electron pulse propagating direction. Eight MACOR insulation cylinders electrically isolate
the high voltage applied rods from the stainless steel deflector body. The MACOR cylinders
are secured with 2-56 set-screws. (b) The electron beam deflection angle as a function of
applied voltage between the stainless steel rods in two orthogonal directions.
72

),+(

)*+(

!"#$%&'"()*&+",&
-&./),%#,)*&

!"#$%&'(
01!&./),%#,)&
!2$3/#(2%",&

78,3$9&0)2(&
43:),)$;2(&
<#=/&,)93"$&
4)5)6%",&

Figure 4.19 Aperture manipulator. (a) Stereoscan 360 scanning electron microscope aperture manipulator. The red circle in (a) shows where four apertures are mounted at the
same time. We can manipulate the position of each aperture with two micrometers shown
at the end of the aperture manipulator, x, y axis. (b) Actual design of the SEM aperture
manipulator assembly with the second electron beam deflector. The gap between two Oring seals (white dot) is pumped down with a dry pump to make the gap region pressure
down to 10−3 torr. Then, two O-ring seals can hold the UHV pressure difference.

73

Aperture Diameter (µm)

x (mm)

y (mm)

3000

4.11

2.75

170

4.30

9.85

50

4.30

17.85

30

4.30

25.65

Table 4.2 Aperture Position

4.6 The Ultra High Vacuum(UHV) Chamber
The UHV chambers of our high-brightness electron beam system consists of an electron gun
chamber, a 266 nm laser mirror chamber, an electron beam column, and a main specimen
chamber. Although all the chambers are connected to each other, in order to achieve and
maintain low enough pressure for the specific function of each chamber, the connection
scheme among the chambers has to be carefully considered because each chamber’s base
pressure requirement is different due to the vacuum components in the chambers.
The lowest pressure chamber is the electron gun chamber because of the 100 kV high
voltage. The electron gun chamber pressure can reach down to ∼10−10 torr with careful
baking of the chamber, but the usual operational pressure is ∼ 2.0 × 10−8 torr because the
main specimen chamber can reach down to ∼10−8 torr and RF cavity pressure is higher
than 10−8 torr. Fig. 4.20 shows the schematic diagram of the UED chamber. When we designed the chambers, we expected that the main chamber base pressure would not actually
be UHV level because of the O-ring seal door which we intentionally implemented to switch

74

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Figure 4.20 Schematic diagram of the high-brightness UED chambers: (1) the 100 kV
electron gun chamber, (2) 266 nm laser mirror chamber, (3) RF cavity, (4) main specimen
chamber.

75

the sample conveniently, nor would the RF cavity pressure be at the UHV level due to outgassing. Therefore, we had to carefully consider the high pressure of the adjacent chambers
to design the low–pressure electron gun chamber. The electron gun chamber is primarily
pumped down by an ion pump (Ion SEM 45, Agilent T echnologies), of which the pumping speed is 45 l/s for nitrogen, and it is connected to the 266 nm laser mirror chamber
through a 50 mm length, 6 mm ID hole, but completely isolated from the main chamber by
closing a 6” CF gate valve (6” GV). Through 50 mm ID bypass, the 266 nm laser mirror
chamber is directly pumped down by a 8” CF turbo pump (Hipace700, P f eif f er V acuum:
Pumping speed 700 l/s) mounted at the main specimen chamber because the RF cavity,
which has the highest pressure, is located between the 266 nm laser mirror chamber and
the main specimen chamber. To minimize the direct contamination of the electron gun
chamber from the RF cavity, we implement 190 mm length and 10 mm ID copper tube
which is enclosed by the CML2. To pump down the RF cavity efficiently, we add another
35 mm ID pump path between the main chamber and RF cavity.

76

Chapter 5
Characterization of The Electron
Beam System
Achieving atomic and sub-picosecond spatiotemporal resolution is a challenging problem
due to the space–charge effects [83, 84, 68]. Generally, there are two types of space–charge–
led phase–space degradation. The first type is caused by the collective space–charge effect
manifested in the electron pulse elongation and expansion from the development of the
phase space correlation (chirping). This space–charge effect is significantly accelerated by
the internal Coulomb fields of the electron pulse [83], but it can be corrected by the RF
compression and electron optics, which are able to reverse the momentum distribution of
electrons in the phase space, as explained in Chapter 3. The second type is caused by
the stochastic space–charge effect [63], which is correlated with an irreversible growth in
phase space volume (the beam emittance), due to fluctuating components of nonlinear
electron dynamics. Moreover, in the high–density femtosecond electron beam generation,
the stochastic space–charge effect is often coupled to formation of a the virtual cathode (VC)
[63]. In this chapter, we will discuss the systematic measurement of the high–brightness
electron beam intensity and the emittance and show beam characteristics of the highbrightness electron beam system based on the comparison with previous theoretical study
of the stochastic space–charge effect and the virtual cathode limit [63].
77

5.1 100 kV Pierce Geometry Electron Source
As we discussed in Chapter 4, 106 electrons per pulse are required to get a sufficient contrast
ratio in the diffraction pattern with a single electron pulse [70], and the coherence length
Lt needs to be longer than 1 nm to cover a sufficient number of unit cells in a crystal lattice. This coherence length Lt requirement constrains the normalized transverse emittance
εx,n ≤0.12 µm with σx ∼100 µm, which is a typical sample size. Under these conditions,
the collective and stochastic space–charge effects are severe in the phase space evolution
of the electron pulse [63]: the electron pulse is not only expanding dramatically (collective
space–charge effect), but the emittance also increases (stochastic space–charge effect), which
reduces the coherence length Lt . The projected lengthening of the pulse envelop caused
by the collective space–charge effects is reversible using magnetic lens focusing and RF
compression [60]. We investigate the feasibility of the focusing and compression methods
for the high–intensity electron pulse and quantify the performance of our high-brightness
electron beam system: electron beam intensity (the number of electrons per cross-sectional
area), the transverse emittance and the electron pulse length. In the following sections, we
introduce the measurement techniques and characterization results.

5.1.1 Measurement Procedure for Electron Beam Current
To count the number of electrons per pulse, there are two independent methods. The
simplest one uses a Faraday cup and a picoammeter, shown in Fig. 5.1. The Faraday cup
is a metal cup designed to catch charged particles in a vacuum, as shown in Fig. 7.1. When
an electron pulse hits the interior of a Faraday cup, the Faraday cup gains a net charge

78

782#)6'
!"#$%&$#'
#8''
#8''

,&"'-.'#/#0%$-1'
)23-$2415'6#%)/'
940-)66#%#$'

()$)*)+',&"'

Figure 5.1 Schematic illustration of Faraday cup: To prevent the escape of an elastic scattered electron, there is an aperture at the entrance hole. Picoammeter directly measures
the current produced by the charged particles in a vacuum. Typical size of the aperture is
a few hundreds micrometer.
due to the electron absorption. The metal cup produces a current that is equivalent to
the number of impinging electrons N = Ie ∆t. Basically, the Faraday cup is a collector
for electrons in a vacuum. The Faraday cup is not as sensitive as an electron multiplier
detector, but it is highly regarded for accuracy because of the direct relation between the
measured current and the number of electrons. This is the reason why a picoammeter
is required. The advantage of this method is that the Faraday cup is a universal charge
detector, independent of energy, mass, chemistry, etc. of the charged particles, and is
limited primarily by the ability to measure a very small beam current.
The second method that we applied is counting the number of electrons using our
charge-coupled device (CCD) camera coupled with an image intensifier, which is capable
of detecting single–electron events. Basically, the CCD consists of a two-dimensional array

79

of pixels. In our set up, when a photon burst generated by the phosphor screen under an
electron impinging event, is received by the image intensifier (see Fig. 4.16), the intensifier
amplifies the signals by adjusting a biasing voltage. The amplification follows power-law
growth with respect to the biasing field, which is directly proportional to the gain voltage,
a control parameter in our experiment. The amplified optical signals then are recorded
by the CCD below. The CCD stores such information as the charges in each pixel, which
accumulate over a finite acquisition time. Afterwards, the charges are read out from pixels
by means of a clocked transfer of the charges along the rows of the CCD. The CCD controller
converts the analog signal (electric charge) into a digital signal (bits), and stores the image.
The acquisition time must be controlled properly to prevent the potential wells associated
with the pixels from overflowing (saturation). Our CCD has 2048 × 2048 pixels, each of
which is 13.5 µm × 13.5 µm in size.
As we discussed in Chapter 4, the amplification through the image intensifier is up
to 109 , which allows us to detect single–electron events. We can quantify the number
of electrons per pulse by measuring the Analog-to-Digital conversion unit (ADU), which
corresponds to the single–electron signals recorded by the CCD. In general, 216 (=65536,
maximum value of a 16-bit integer) counts correspond to the saturation level of the potential
well of the CCD pixels. One of the most powerful properties of the CCD detector is its
linearity. If the saturation is ∼ 65K counts, then the linearity is generally assured for the
counts from the background level (typically 800) to ∼50K. When the counts are close to
saturation, the detector sensitivity diminishes.
To determine the ADU, single–electron events are established by reducing the intensity
of the main electron beam, so the random arrival of single electrons is recorded on the

80

Figure 5.2 Single electron count events of attenuated electron beam on CCD camera. The
yellow square boxes indicates the regions of interest (ROI) 5 × 5 in pixels.

81

CCD camera, as shown in Fig. 5.2. Each single–electron event shown as a dot in Fig. 5.2
is counted with its integrated intensity over the nearby pixels and the statistics of such
an integrated intensity for the single–electron events is constructed. The procedure is as
follows:
1. Select the single–electron event with a certain size of the region of interest (ROI).
2. Count the integrated intensity of the selected ROI after background subtraction.
3. Construct the probability distribution that represents the number of single–electron
events as a function of integrated intensity of ROI.
This procedure is repeated for a sufficient number of single–electron events, which is
usually ∼ 600 events in total. Fig. 5.3 (a) shows the probability profile of single–electron
events with the Poisson distribution fitting (blue line). To determine the ADU, we have to
use the maximum gain (9V) for the image intensifier in order to have a sufficient signal of the
single–electron events, while we need to use a low gain (4V) to measure the electron beam
current because the number of electrons per pulse is too high to measure at the high gain.
Fig. 5.3 (b) shows the ADU as a function of the image intensifier gain, indicating that the
image intensifier amplification is ×4.6 on 1 V gain control voltage increment. It is important
to note here that at low gain the detector doesn’t have enough sensitivity to count single–
electron events, so there is a calibration factor to correlate the partially counted electron
events to the total electron events. In the data presented in Fig. 5.3(b), we calibrate the
ADU by the number of electrons per pulse determined by the direct measurement of the
electron beam current using a Woods horn beam trap to serve as the Faraday cup (shown
in Fig. 5.4) to measure electron current. The advantage of the Woods horn beam trap is
82

!"#$

%"&'()"*+,$-./$!"010#$

!(#$

Figure 5.3 (a) The probability profile of the integrated intensity of single–electron events.
The square is the experimental measurement and a blue line is the fitting with Poisson
distribution function. The ADU is 4500 with image intensifier gain 9 V. (b) ADU under different image intensifier gain voltage, after considering the factor 2.1 following the
calibration of electron counts through a Woods horn beam trap.

83

6,7#
+,-%'#./0)1,2%'#

31!-2'4-,1#54'!#

$%&&!'#()*!#

6*7#

!"##

Figure 5.4 (a) The design of the beam trap. The copper tubing outer diameter is 2.0 mm
and the inner diameter is 1.6 mm. The copper tube is held by a MACOR insulation cylinder,
and the end of the copper tube is connected to a UHV compatible electrical wire which is
Kepton–insulated silver–plated copper wire. (b) Schematic illustration of the copper tube
cross-sectional view. Copper tube can trap the electrons that enter the copper tube, and
the curvature reduces the probability for the elastically scattered electrons to escape from
the tube.

84

the compactness and ease of implementation. The implemented Woods horn beam trap is
designed as an arc shaped copper tube (shown in Fig. 5.4). The copper tube geometry can
trap the electrons when they enter the tube, and an arc curvature reduces the possibility
for the elastically scattered electrons to escape from the tube.
If we assume the ADU events recorded at gain of 9V represent all of the single-electron
events, we determine that the electron current recorded by the picoammeter is a factor
of 2.1 higher than the counting experiment. Correspondingly, the ADU factor shown in
Fig. 5.3(b) has considered this factor.

5.1.2 Electron Beam Current Measurement Results
To characterize the space–charge effect in the electron pulse dynamics along the highbrightness electron beam column, we measure the number of electrons per pulse using
the ADU counting method. According to a photoemission beam dynamics study [63], the
stochastic space–charge effect is strongly coupled to virtual cathode (VC) formation at
the limit of intense ultrashort photoelectron pulse generation. The analytical model [85]
of the VC effect in the short pulse limit showed that a higher current density may be
generated than anticipated by the Child-Langmuir current limit [63, 86]. The onset of the
VC suppresses the photocurrent from its linear growth with increasing incident photon-flux.
A fast multiple method (FMM) simulation considering stochastic scattering and imaging
charge effects shows that the exponent of the photocurrent growth is reduced to 1/3 after
the onset of a VC using a Gaussian pulse profile [63].
Fig. 5.5 shows the comparison between FMM theoretical calculation [63] and the experimental measurement of the actual number of electrons per pulse which travel from the

85

electron gun down to the CCD camera. In our experimental measurement, we directly measure the number of emitted electrons Neemit at the CCD camera, based on the calibrated
ADU value presented in Fig. 5.3(b). We may compare our measurements directly with the
simulation results presented in Fig. 5.5(a), where the initially photoexcited electrons Ne0 ,
are proportional to the incident laser power P : Ne0 = P A/(hν)/f , where the illuminated
area A = πR2 , R is the laser beam radius, and f is the laser repetition rate. The experimental value of Neemit is a factor of ∼4 lower than the simulation data, whereas the incident
area is also different (simulation R = 100 µm and experiment R ∼ 50 µm). Furthermore,
the threshold value Neemit , defined as the Neemit observed at the onset of VC, has a linear
dependence on bias voltage (inset in Fig. 5.5 (b)) in agreement with the simulation. As
observed experimentally, low incident laser flux prior to VC onset (orange line) shown in
Fig. 5.5 (b) are consistent with simulation data. We note that the suppression of this linear
growth after the onset of the VC in our experiments also shows initially (at 70 kV bias)
to 1/3 power exponent, as indicated from the simulation. A decrease of this exponent at a
higher bias V seems to appear, which awaits further studies. For a quantitative comparison,
we conduct the extraction field (Fa ) calculation for our Pierce gun geometry using Field
Precision code [74]. We obtain the conversion factor k = Fa /V to be 22 m−1 . Given this,
we can directly compare the Necrit at the onset of VC. From the experiment, Necrit at 100
keV (corresponding to Fa =2.2 MV/m) is 6×106 , whereas from interpolating the simulated
data, it is ∼1×107 .
This comparison provides us with a handle to evaluate the feasibility for conducting
UED and UEM experiments. The observed Necrit of 6×106 per pulse at 100 keV is still
slightly low compared to the 107 -108 estimate for single-shot UEM imaging, but is sufficient

86

!"#$

%&$&'()$

!*#$

Figure 5.5 The number of emitted electrons per pulse. (a) Simulation results of the number
of emitted electrons per pulse Neemit plot as a function of the number of generated electrons
Ne0 , which is proportional to the input power of 266 nm pulse laser, at various surface
extraction field Fa . This plot shows evidence of virtual cathode (VC) formation [63]. (b)
Experimental measurement of the number of emitted electrons Neemit as a function of
input power of 266 nm pulse laser. The experimental measurement shows consistent linear
dependence on input power below the VC limit, and 1/3 power dependence above the VC
limit.
87

for single-shot UED, which requires 105 -106 electrons per pulse (depending on sample scattering strength). However, perhaps the most challenging issue for imaging is the stochastic
blurring effect at high density limit. In principle, we can increase the surface field strength
by reducing the gap distance between the cathode and the anode, but, in a Pierce geometry
photoelectron gun, the highest field (established around the edge of the cathode and the
anode as shown in Fig. 4.4) has already reached ∼10 MV/m which is close to the practical
break down limit. We may easily develop a gun with slightly different geometry to ameliorate this high edge field strength so the Necrit can be improved (see Appendix E). Another
solution is to push the VC limit up by using longer pulses by shaping the 266 nm laser
pulse. Since the VC effect is largely controlled by the instantaneous electron density at the
cathode surface, longer pulses reduce the instantaneous current. Nonetheless, this is at the
expense of temporal resolution, which may not be recoverable using RF compression if the
initial pulse is too long.

5.1.3 Pepper Pot Technique for Emittance Measurement
In the accelerator community, there are three general techniques to measure the emittance:(1) quadrupole magnet scan method, (2) lens drift scan method, and (3) Pepper Pot
method. The quadrupole magnet scan and the lens drift scan require sufficient drift space
to perform the measurements, so these two methods are practically very hard to implement in our system. However, the Pepper Pot method can be easily applied in our system,
as the relevant aperture and imaging systems are readily available. Moreover, while the
quadrupole magnet scan and the lens drift scan are good for high energy beams (∼ MeV),
the Pepper Pot method is more suitable for high space–charge densities and beams with

88

high energy spread beam in the keV energy range [87]. For a space–charge–dominated
high–intensity beam, the small aperture collimation of the beam into beamlets reduces the
space–charge effects sufficiently to allow the beamlets to expand under the influence of
emittance, instead of space charges.
The emittance of the electron beam is obtained by measuring the electron beam’s spatial
and angular distribution sampled along the cross-sectional area of the incident beam. While
this is typically done with a mask with small aperture arrays (hence the name Pepper Pot),
we can achieve the same result by adjusting an aperture to various locations within the
full beam envelope, as shown in Fig. 5.6, given that the beam is stable and reproducible
in our set up. Each beamlet reveals the local transverse momentum spread, which is
recorded at the CCD with single–electron sensitivity, allowing us to fully reconstruct the
electron pulse phase space, x, px . The adjustable apertures (30 µm, 50µm) and the CCD
camera are depicted in Fig. 4.1 along the electron beam line. The electron beam is sampled
by the aperture, producing a beamlet that is allowed to drift freely before striking the
CCD pixels. While drifting, the beamlet disperses according to its transverse velocity
distribution. Therefore, the spatial profile of the beamlet at the CCD plane is a direct
measurement of the angular divergence of the beamlet. By scanning the aperture across
the full beam, the spatial and angular distribution of the beam in the trace space (x, x )
can be constructed.
The emittance data are stored as an array of beam intensity I(xi , xi,j ) measured at
different aperture positions xi and the different divergence angle xi,j of the j-th CCD pixel.
With the drift length L between the aperture and CCD plane, the measured trace space
distribution is constructed by a series xi (i-th beamlet) of distinct angular distribution, xi,j

89

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001'

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001',)4$56'

Figure 5.6 Illustration of the emittance measurement sheme

90

(j-th pixel within i-th beamlet) defined as

xi,j =

xij − xij,c
,
L

(5.1)

where xij is a coordinate of the j-th pixel of i-th beamlet, and xij,c is the center location
of CCD image of the i-th beamlet.
As with the rms emittance definition shown in Eq. 3.6, we can define the transverse
emittance as

εx ≡

< x2 >< x 2 > − < xx >2 ,

(5.2)

and we can measure the < x2 >, < x 2 >, and < xx > with the following equations:

< x2 >=

i

range
2
j=1 (xi − xc ) I(xi , xi,j )
,
Itot

(5.3)

< x 2 >=

i

range
2
j=1 (xi,j − xc ) I(xi , xi,j )
,
Itot

(5.4)

range
j=1 (xi − xc )(xi,j − xc )I(xi , xi,j )
,
Itot

(5.5)

range
j=1 xi I(xi , xi,j )
,
Itot

(5.6)

< xx >=

i

< xc >=

i

91

< xc >=

range
j=1 xj I(xi , xi,j )
,
Itot

i

(5.7)

range
Itot =
i

j=1

I(xi , xi,j ).

(5.8)

The normalized emittance is defined by

εn,x = βγεx ,

where β = vz /c and γ = 1/

(5.9)

1 − β 2 . Using this formula, we will show the transverse

emittance measurement of our electron pulse in the following sub-section.

5.1.4 Beam Emittance Measurement
To construct the phase space of an electron pulse, sufficient precision of the spatial resolution
of the CCD camera is required. As introduced in Chapter 4, our CCD camera window size
is 2048×2048 pixels, and each pixel is able to detect single–electron events in a 27×27
(µm2 ) area. Each pixel has a well defined location and the high spatial resolution of the
CCD camera allows us to measure the divergence angle with sufficient precision. Fig. 5.7(a)
shows direct images of the full beam consisting of the ∼106 electron pulse. From the beam
profile recorded on the CCD as shown in Fig. 5.7(c), the FWHM of the beam is determined
to be 59 pixels, which corresponds to ∼1.6 mm. Fig. 5.7(b) and Fig. 5.7(d) show the image
and the beam profile of the beamlet after going through the 50 µm aperture. With a series
of such images after aperture scanning across the full beam, we can clearly define the center
92

!"#$%&%$

'()$

'*)$

'+)$

',)$

Figure 5.7 Electron beam image and profile on the CCD camera. (a) is a image of the full
electron beam of 106 electron per pulse, and (b) is one beamlet image after going through
the 50 µm aperture. (c) and (d) are the beam profiles along the horizontal direction. With
the acquired intensity and divergence angle of each pixel, we can construct the phase space
distribution and the emittance at the aperture location.
of each beamlet and calculate the divergence angle for each individual beamlet.
According to the FMM theoretical study [63], above the VC limit, the strong image–
charge field and the stochastic space–charge effects lead to an irreversible emittance growth.
To avoid this irreversible emittance growth, we keep the laser power right below the VC
limit, which is shown in Fig. 5.5. Fig. 5.8 shows the measurements of the transverse phase
space distribution for low electron density (∼10 electron/pulse), and high electron density
(∼5×106 electron/pulse), both below the VC limit. As expected, the phase space distribution has a linear distribution in both cases. This indicates that the electron pulse has no

93

Figure 5.8 Electron beam trace space plot (x,x ) of 10 electron per pulse and 106 electron
per pulse. Each data point represents the position and the transverse momentum of each
beamlet, and error bar is the momentum spread of the each beamlet.
severe non-linear dynamics during the propagation. With this phase space reconstruction
and the intensity profiles of each beamlet shown in Fig. 5.7, we can calculate the transverse
emittance with the equations shown in the previous sub-section.
Fig. 5.9 shows a theoretical study of normalized transverse emittance (Neemit ) as a
function of the extraction field and the number of electrons emitted based on the fast
multiple method [63]. This theoretical study considers two different scenarios with image–
charge dynamics: (1) the image–charges are pinned on the surface, (2) the image–charges are
fully responsive to the motion of the emitted electron pulse. In Fig. 5.9, we can clearly see
a strong increase of transverse emittance εx around the VC limit. When the image charges
are pinned, such as on a rough surface where the image charge dynamics are restricted, the
94

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! ""#$%

!"'$

Figure 5.9 Dependence of the transverse emittance εx on the number of emitted electrons
(Neemit ) and the extraction field Fa . The inset shows the temporal evolutions of εx at
Fa = 0.32 and 1.0 MV/m (all with 107 electrons), where generally εx reaches a steady state
after 40 ps. The red dot indicates our transverse emittance measurement εx =0.167 µm at
a location right after the RF cavity [63].

95

increase of the transverse emittance with Ne is nearly double that in the absence of the
pinning, while the VC limit is the same for both cases. The inset of Fig. 5.9 shows that
the transverse emittance generally reaches a steady state after 40 ps. In the simulation [63]
with the experiment condition, 2.2 MV/m extraction field, the transverse emittances of 106
and 107 electrons per pulse with initial R=100 µm are calculated as 0.0745 µm and 0.208
µm (Note: these data are not shown in Fig. 5.9.), respectively, which agree well with the
measured value of 0.167 µm at 5×106 electrons per pulse. In comparison, at 10 electrons
per pulse, the transverse emittance is 0.053 µm, which is nearly a factor of 2 larger than
the simulation. However, we note that the minimum measurable emittance based on our
approach is limited by the signal-to-noise ratio of a beamlet of the low–density electron
pulse because the emittance measurement from the relatively low signal of the 10 electrons
per pulse is highly affected by how we subtract the background level. On the theoretical
side, at 10 electrons per pulse, the emittance is predominantly in the space–charge–free limit
given by the three–step model [88], which is subject to the accuracy of the work function.
In the current setup of the high-brightness electron beam system, the direct measurement of the longitudinal emittance is not straightforward, but we can establish an upperbound of the longitudinal emittance in the following way. As defined in Eq. 3.37, the
longitudinal emittance εz is directly proportional to ∆t∆E for an optimally compressed
beam, where ∆t is the electron–pulse duration, and ∆E is the energy spread of the pulse.
We might be able to determine ∆E and ∆t simultaneously by monitoring how the Bragg
angle variation ∆θ corresponding to the diffraction peak width is affected by ∆E (see
Eq. 8.1, and Eq. 8.2):

96

∆E = 2

∆θ
E,
θ

(5.10)

and the pulse duration of the electron pulse from the temporal response in an UED experiment.
It is important to note that the diffraction peak width is determined not only by ∆E,
but also by the variations in the structure such as those due to thermal vibration. We can
determine ∆E by deconvoluting from the space–charge–led angular broadening based on
δθsc =

2 − δθ2
δθN
N =0 . We can extract the energy spread-induced angular broadening by

comparing the Bragg angle variation of a high-density electron pulse to that of a low-density
electron pulse. So far, we have not yet consistently implemented such experiments.

5.2 Magnetic Lens Focusing Characterization
To characterize the performance of each magnetic lens, we measure the focal length of the
magnetic lens under different applied current shown in Fig. 5.10(b). As targeted, the CML1
focuses the high density electron pulse to avoid beam divergence induced by strong space–
charge effect, and, with 1.0 A applied loop current (corresponding to 550 A total current
in the simulation because of 550 times coil winding), CML1 focuses the diverging beam
at the CML2 level. CML2 can focus the pulse at the RF cavity or the sample position
with different applied loop currents, ∼3.0 A [3.0×150(coil winding)=450 A] and ∼1.8 A
[1.8×150(coil winding)=270 A], respectively. (Note: the number of coil winding in each
magnetic lens is shown in Chapter 4.) With CML1= 1 A and CML2=2.7 A to establish the

97

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Figure 5.10 (a) Schematic illustration for the beam propagation along the electron column
with CML1 and CML2 focusing. The distance shown in the figure is the actual distance of
our electron beam line (see Fig. 4.1), (b) Focal length of three magnetic lenses as a function
of the applied current. Each focal length measurement is with non-focused electron beam
directly from the electron gun, except the objective lens. The focal length measurement of
the objective lens is with CML1 and CML2 focusing.
initial beam condition, Obj.ML can further control the electron beam convergence to make
a nearly parallel beam for diffraction experiments (Obj.ML = 0.5 A), and a convergent
beam for shadow images or a microdiffraction experiments (Obj.ML ≈ 2.0 A).
As discussed in Chapter 4, the actual magnetic lens current to generate a certain field in
an experiment can be different from the current set by the simulation because of the difference in permeability in the actual magnetic materials used. To calibrate the permeability,
we search for those conditions in the non-interacting single–electron simulation that can
reproduce the experimental measurements. Under the assumption that the dynamics of 10
electrons per pulse is close enough to the dynamics of a non-interacting electron, we directly
compare the simulated trajectories to the emittance measurement conducted at 10 electrons
per pulse (shown in Fig. 5.8). Fig. 5.11(b) shows the comparison of the ray–angle between

98

1'2!
9*:!678!
450!678!

;'<!=*>&.!1$/':2!

132!
!!!!!"#$%&'()*!
!!!!!+,-./#$.*0!

Figure 5.11 Comparison between Field Precision trajectory simulation and experiment. (a)
The non-interacting single–electron trajectories from Field Precision simulation. Green,
blue, red, black vertical lines indicate the optical components along the high-brightness
UED column: photocathode, CML1, CML2, CCD camera. Each horizontal line is a single–
electron trajectory generated at different initial locations R. Initial condition of the electron
is a completely zero energy particle and it is accelerated only by 100 kV acceleration voltage. The numbers right next to CCD position are the initial emitting location R on the
photocathode. (b) Ray angle vs. location R on the CCD screen. The red squares are the
experimental measurement of the ray angles with 10 electron per pulse shown in Fig. 5.8,
and black squares are the simulation.

99

the experiment (red square) and the simulation (black square) as a function of the position
on the CCD screen. The agreement in the ray–angle comparison indicates that the field
distributions in the experiment and the simulation are consistent, while the applied current
of CML2 (275 A) in the simulation is inconsistent with the actual applied current (405 A)
in the experiment. This inconsistency of CML2 is corrected by the calibration factor for the
permeability, 1.47, and we applied this calibration factor to all further simulations. (Note:
the calibration factor of CML2 is 1.47 while the factor of the CML1 and the objective lens
are 1 because CML2 has been re-machined after the annealing process, and it might cause
a change in permeability.)

5.3 Phase Jitter of RF Compression
In the RF synchronization, the most important issue is the precision of the relative phase
stability between the fs laser pulse train and the RF field, especially the phase jitter caused
by environmental fluctuations, such as temperature and humidity, impacting the performance of the electronics (VCO, photodiode, etc.). These fluctuations are a major challenge
to optimization of the pulse compression. As shown in Fig. 5.12, when the electron pulse
arrival time and the node of RF field do not match at the center of the cavity, the center of
mass (COM) velocity of the electron pulse can be accelerated or decelerated. Then the zero
of time (ZoT), defined as the time when an electron pulse and a pump laser pulse arrive at
the sample plane at the same time, fluctuates, and the fluctuation limits the time resolution
of the high-brightness UED. (Note: This limit on the temporal resolution is independent of
the pulse duration.) If we define (1) t0 to be the electron pulse arrival time at the sample,
namely zero energy change (perfect synchronization between the RF field and the electron
100

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Figure 5.12 Schematic illustration of the phase jitter. (a) Perfect phase match between
RF field and the electron pulse arrival time: the COM velocity of the electron pulse has
no change. The relative phase mismatch causes (b) decelerating the COM velocity of the
electron pulse, and (c) accelerating the COM velocity.

101

pulse phase, φe = (t − t0 ) · ω=0, shown in Fig. 5.12(a)), and (2) td and ta to be the decelerated or accelerated electron pulse arrival times (caused by phase mismatch, φe = 0, shown
in Fig. 5.12(b),(c)), then the dispersion-limited time resolution of the high-brightness UED
experiment is limited by |td -ta |. As described below, this phase-jitter-led dispersion could
easily become the limiting factor of the time resolution.
Fig. 5.13 is an experimental measurement of the electron pulse transverse size and energy
variation for controlled phase differences between the electron pulse and the RF field. In
this experiment, the applied RF power is 420 W and, while maintaining the RF power
and the phase, we adjusted the electron pulse arrival time by changing the 266 nm laser
path length using a delay stage. In Fig. 5.13, at t = 0 (perfect phase match for pulse
compression), the electron pulse energy is 100 keV and we observe that the electron beam
transverse size is at a maximum (Fig. 5.13(d)), while at t=500 ps (completely out of phase;
pulse stretched) the electron beam size is at a minimum (Fig. 5.13(c)). This indicates
that the pulse compression induces additional transverse expansion and pulse stretching
suppresses the preexisting expansion. Fig. 5.13(b) shows the energy of the electron pulse as
a function of electron arrival time. Note here, that the electron energy is determined based
on the electron crystallographic pattern changes by mounting a VO2 sample at the sample
plane. The energy shifts of the impinging electrons at the sample cause a shift in the Bragg
angle (see section 8.2). We can clearly see that the electron energy is well correlated with
φe as described above. Since the electron pulse is short compared to the RF period, we
can assume that during cavity gap crossing the electron pulse sees a constant accelerating
field. Given that we can extract the RF field: ERF =

|U −U0 |
, where U0 =100 kV, U is
d

the electron pulse energy, and d is the RF cavity gap distance d=22.5 mm. We determine

102

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Figure 5.13 Beam size and energy variation of electron pulse with different relative phase
between electron pulse and RF field. (a) Beam size variation with the relative phase: the
shaded areas are the compression regions and the unshaded ones are stretch regions where
the faster electrons are accelerated and the slower electrons are decelerated. The top red
sine curve illustrates the corresponding RF field oscillation at ∼1 GHz. Time zero is set
at the exact timing for the perfect pulse compression. The beam size oscillates with the
pulse compression: strong compression induces the transverse expansion and strong stretch
suppresses the transverse expansion. At t =0.75 ps, the beam size is consistent with the
beam size without RF compression. (b) Electron energy variation with different relative
phase at 420 W RF power. t =0 ps is the perfect in-phase, 100 keV. Inset plot is the
electron pulse arrival time on the sample as a function of the relative phase (-0.2∼0.2 ps
range). (c),(d) the electron pulse images on CCD at completely out of phase (stretch (c)),
and the perfect in-phase (compression (d)).

103

that at 420 W, the RF field amplitude is 2.4 MV/m.
From the energy gain, we can extract the arrival time of the electron at the sample
plane: t = l/[c

1−

1
], where c is the speed of light, me is electron mass
(U/(me c2 )+1)2

and l is the distance from the RF cavity to the sample. Then we can compare the arrival
time to the phase jitter, here controlled via φe and expressed in terms of tjitter . The inset
of Fig. 5.13(b) shows this result: 1 ps arrival time variation (-0.5 ps - 0.5 ps) corresponds
to ∼300 fs (-0.15 ps - 0.15 ps) variation of the relative phase, φe = (t − t0 ) · f . This can be
quantified from the slope α =

dt
of the inset, which shows the electron pulse arrival
dtjitter

time vs. the relative phase. At 420 W RF power, 343 fs (α = 343) at the level of RF field
phase jitter is minimally required to achieve 1 ps time resolution. With higher RF power
generating higher RF field, the energy variation is also higher, as shown in Fig. 5.13(b),
and hence the requirements on the phase jitter needed to achieve sub-picosecond temporal
resolution become more stringent.

5.4 Performance Projection for UED Experiment

CML2 (A)

2.51

2.61

2.71

2.81

2.9

D(e/µm2 )

4.87

5.13

5.33

3.90

3.97

Table 5.1 Electron dose D = Ne /A with CML1=1.0 A and Obj.ML=1.3 A
We have demonstrated the performance of our high-brightness ultrafast electron beam
line to be within a factor of 2 of the theoretical source emittance and the capability of
generating in excess of 106 electrons per pulse. Here, we will further evaluate its feasibility
104

for ultrafast electron diffraction implementation by quantifying electron dose and coherence
length. First, on the electron dose, based on the transverse emittance of 0.167 µm at
Ne =5×106 electrons per pulse, to achieve 1 nm coherence length (Lt in Eq. 3.35), the
electron beam diameter needs to be 150 µm in σ–width, according to Eq. 3.35. Another
figure of merit for studying nanomaterials is the electron dose D = Ne /A (A: area of the
beam spot on the sample). D is closely related to the 4D brightness of the beam B4D =
Dxy (factors related to transverse emittance). By using a selected–area aperture, we can
reduce the beam diameter, and hence Ne , but not necessarily the dose. Table 5.1 shows
the characterizations of D based on the shadow imaging under the following conditions:
CML1=1.0 A and Obj.ML=1.3 A, and for different CML2 currents with a 170 µm beam
slicing aperture (Ne of the full beam is ∼2×106 ). Table 5.2 shows the comparison among
the Ds achieved from different UED systems worldwide.
For parallel beam generation (CML1=1.0 A, CML2= 2.7 A, Obj.ML=1.3 A), we obtain
an envelope beam divergence angle of 2 mrad, for a sliced beam with 170 µm aperture and
Ne ≈105 , based on beam size at the sample and at the CCD camera. This value sets a

σx σp
lower limit of the coherence length Lt with εx,n = me cx (from Eq. 3.31):

εn,x =

Pz
σx ∆θ,
me c

(5.11)

where Pz is the momentum along the propagation, σx is the σ–width of the beam spot
σp
on the sample, and ∆θ = P x is the divergence angle. Then the lower limit of coherence
z
length Lt is ∼1.2 nm. We show that reducing the beam size with an aperture, while also
reducing Ne , can improve the Lt while maintaining D up to 5 e/µm2 per pulse. Using a
105

Microbeam
UEDa

High-flux
UEDb [20]

RF
UEDc [81]

MeV RF
UEDd [45]

High-Brightness
UEDe

Ve (kV)

30

60

80

2.8 MV

100

D(e/µm2 )

0.5

0.5

1.0

1.0

5.3

Ne

500

104

105

105

105

FWHM (µm)

30

150

300

300

130

∆t (fs)

300

250

300

300

–

Table 5.2 Comparison of the electron dose among different high-flux UED source
a Michigan State University
b University of Toronto/University of Hamburg Group
c McGill University
d Brookhaven National Laboratory
e Michigan State University (preliminary results)
smaller aperture, further reduction of beam size can be achieved, without decreasing Lt or
D, or by using a higher Obj.ML to increase D, but with some compromise for Lt . The
microdiffraction implementation will be discussed in Chapter 8.
Our results indicate that at 420 W RF power, the achievable RF field strength is 2.4
MV/m. Using Eq. 4.18, the focal length with 420 W RF compression is ∼680 mm using
our experimental parameters, ω0 =1 GHz, d= 22.5 mm. To achieve the sub-picosecond time
resolution, ∼520 W RF compression power is required to focus the pulse on the sample (the
sample distance is ∼440 mm), and the phase jitter stability within the 200 fs level must be
accomplished. Such a phase jitter stability (< 100 fs) has been achieved in our RF system
over a short period (∼2 hours) [82]. Long term operation is subject to the temperature
stability of the laboratory. The specified power from our RF station is 3 kW, but currently

106

the thermal dissipation of the RF connector seems to be limited by the temperature stability
at a lower power level when running in continuous mode. Pulse mode operation could easily
match the required RF power for full compression at the sample plane.

107

Chapter 6
Further Development of Ultrafast
Electron Diffractive Voltammetry

6.1 Introduction
The ultrafast electron diffraction technique is shown to be able to investigate the charge
transfer dynamics at an interfaces due to the sensitivity of the probing electrons to the transient electric field distribution [89, 90, 91], causing a modification of the surface diffraction
pattern [40, 39], which is loosely characterized as the ‘refraction effect’. The methodology
of measuring the interfacial photovoltage via monitoring changes in the Bragg diffracted
electron beams can be characterized as a ultrafast electron diffractive voltammetry (UEDV)
[40, 51]. In this chapter, we extend the prior work on UEDV, by Ryan Murdick [40, 51]
with the aim to identify the different constituents of the measured transient surface voltage
(TSV) and discuss their respective roles in Coulomb refraction. We also develop a general
formalism that can quantitatively describe these phenomena based on surface diffraction
features.

108

Figure 6.1 Transient photoinduced charge redistribution near surface. (a) The three mechanisms of photoexcitation that cause redistribution of charges at the surface, bulk, and
vacuum levels near Si/SiO2 surface. (b) Transient surface potential diagram caused by
various photoinduced charge redistribution. (c) The refraction of the electron beam in each
field region can be modeled by an index of refraction with n = (∆V + V0 )/V0 , where
eV0 is the electron beam energy.

6.2 Origins of Transient Photoinduced Surface Voltage
The photoinduced transient surface charge redistribution can appear in the sub-surface
level (carrier separation, electronic excitation), at interfaces (charge transfer), and above
the surface (photoemission), as exemplified in Fig. 6.1. The magnitude of the surface voltage
(Vs ) can be described generally from the sum of these components [40, 51]:

Vs =

z1
z0

Ez (z)dz,

(6.1)

where z1 is the position at which the probing electron beam enters the field region and z0
is the position of the diffractively probed region. The effects of the these charge redistribution channels are categorized into respective photovoltages. Firstly, on the bulk level, the
inner potential change ∆IP resulting from the adjustment of valence electronic distribution

109

can cause an abrupt refraction shift at the interface, whereas the adjustment/creation of a
space charge region defines a transient voltage ∆SC within the dielectric screening length.
Secondly, on the surface level, the photoinduced interfacial charge transfer over a thin insulating barrier can create a dipole field region, which defines a voltage component ∆DP
on a nm length scale. Thirdly, photoemission can occur into the vacuum region, particularly for high intensity excitations. Subsequently subsurface charge dynamics are induced
to screen the field associated with photoelectron from penetrating into the bulk materials.
Together, they create a near surface field imparting a potential difference ∆PE on a timedependent length-scale defined by the recovery of the photoelectrons to the surface. These
four different mechanisms of surface voltage generation have characteristic time and length
scales, their influences on the probing electron beam ultimately vary with incidence and
exit angles and the interfacial structure. Generally, these photovoltages are linearly superposable, which allows them to be treated independently, and the overall surface voltage can
be expressed as:
Vs = ∆IP + ∆SC + ∆DP + ∆P E.

(6.2)

As a prototype example, photoinduced charge redistribution at a Si/SiO2 interface
(Fig. 6.1) is examined here, in which the voltammetry is contributed significantly from
∆DP as the probing electron beam fully penetrate the top SiO2 layer, whereas the electron
beam has only a short penetration depth (≈ 1 nm) into the Si underlayer. Since the
screening length in a semiconductor is relatively large(≈ 1 µm), the short penetration of
the probing electron beam picks up only a small fraction of the voltage drop along the top SC
region, whereas the surface dipole voltage across the SiO2 layer is fully sampled. Thus, for a
scenario where interfacial charge transfer occurs, ∆DP can dominate over ∆SC. Meanwhile,

110

∆IP is generally small if a phase transition is not involved. The contribution of ∆PE is
more difficult to assess. In the case of Si, the hot carriers are created with a high transient
temperature, which can induce thermionic emission, and under an strong photofield from
an intense laser irradiation the multiphoton photoemission is also possible [92], leading to
a non-negligible photoelectron contribution to the overall photovoltage. Nonetheless, due
to the very different length scales involved in interfacial charge transfer and photoemission,
we expect the dynamics to be rather different, which will be investigated with controlled
experiments.

6.3 Surface Diffraction and Rocking Map Characterization
Since diffractive voltammetry employs diffracted beams, it is necessary to link the photoinduced distortion of diffraction pattern with the surface voltage generation. First, we
examine the formalism of electron diffraction from different types of surfaces, which has
been a source of confusion to properly understand the ultrafast surface electron diffraction
process and a central topic to elucidate for deducing Vs . Fig. 6.2(a) describes the production of the diffraction pattern from a grazing incident electron beam. The Ewald sphere is
constructed to predict the diffraction pattern based on the intercept regions between the
Ewald sphere and the reciprocal lattice network. This methodology is founded on a kinematic (Fourier) theory and can be extended to understand nanoscale diffraction, in which
the size of the reciprocal lattice nodes, as depicted in the inset of Fig. 6.2(a), is determined
by the persistent length of the lattice probed by the electrons. For a long-range-ordered
smooth surface, the in-plane persistent length is very large (La in the inset of Fig. 6.2(a)) as
compared to the penetration depth of the electron (Lc ), producing very thin reciprocal rods
111

Figure 6.2 Surface electron diffraction pattern in different conditions. (a) Ewald sphere
construction in the grazing incidence angle geometry. By tilting (rocking) the angle of
incidence between the electron beam and the sample, the Ewald sphere intercepts the
reciprocal lattice rods (relrods) at different heights. The in-phase condition is satisfied
when the intercept is at the reciprocal lattice node. The inset shows the reciprocal node
structure, which is effectively determined from a Fourier Transform (FT) of the crystalline
region in the sample defined by its persistence lengths. (b) Expected rocking map of a
smooth, pristine surface in RHEED. (c) Experimental rocking map taken from a smooth
Si/SiO2 surface. The dashed line shows where the diffraction pattern in the inset is taken.
(d) Expected rocking map of a nanostructured surface. (e) Experimental rocking map
pattern taken from a highly oriented pyrolytic graphite (HOPG) surface. (f) Experimental
rocking map taken from a Si/SiO2 surface sample along a Kikuchi-enhanced diffraction
peak. (g) Diffraction pattern of the Si/SiO2 surface, showing visible Kikuchi pattern.
112

(relrods). In the limit of Lc =0 (single layer), the reciprocal lattice becomes two-dimensional
(2D) array of relrods, and the diffracted beam is defined by the intercept between the Ewald
sphere and the relrod network, rendering circular diffraction patterns, generally described as
the Laue zones in reflective high-energy electron diffraction (RHEED). For nanostructured
surfaces, Lc ≈ La , the relrods widen significantly, and the diffraction pattern can deviate
significantly from circular Laue patterns. Therefore, observing more than one diffraction
peaks along a single relrod is possible.
To examine the relrod structure, we use rocking map characterization, which is conducted by rocking the sample plane against electron incidence, so Ewald sphere intercept
rolls along the relrod. The rocking map is constructed by slicing a reflection stripe showing
a relrod normal to the shadow edge in the diffraction image and stitching these stripes
together as a function of incidence angle (θi ). A diagonal line with slope (a) equal to 2
in the rocking map exposes the relrod structure in terms of θtot vs. θi , as depicted in
Fig. 6.2(b). The reciprocal node, which is a Fourier transform of a probed crystalline region defined by the persistence lengths of the samples as depicted in the inset of Fig. 6.2(a),
can be examined from the out-of-phase to in-phase conditions in the rocking map. Near
θi =0, the relrod structure is continuous. As θi increases the relrod becomes spotty, due to
the increase of persistent length (Lc ) with the increasing electron penetration depth as a
function of θi . This trend is evidenced in an experimental rocking map produced from a
relatively flat Si surface, as shown in Fig. 6.2(c). For the sake of clarity in discussion, we
will refer to RHEED pattern only when dealing with a smooth surface that produces sharp
circular Laue patterns, which is especially useful for monitoring the layer-by-layer growth
in molecular beam epitaxy [93]. In so speaking, RHEED experiment is not well suited

113

for studying structural dynamics study as neither does the position of the RHEED peak
indicate the respective position of the reciprocal lattice node, nor does RHEED intensity
directly inform lattice fluctuations, such as Debye Waller factor. Only through the inspection of the rocking map can the reciprocal lattice be exposed for structural investigation,
nonetheless, such experiments are tedious to perform for dynamics study [94].
Fortunately, more informative results can be obtained for nanostructured surfaces and
interfaces where the diffraction mechanism differs from ‘RHEED’. In fact, typical ultrafast
electron crystallography (UEC) studies [95, 36, 37, 47, 34], rely on transmitted surface
diffraction features produced with the grazing incidence electrons to determine structural
dynamics. When the transverse persistent length (La in the inset of Fig. 6.2(a)) is short,
such as steps and nanostructure-decorated surfaces, the widened relrods can extend several
periods of the interferences (Bragg reflections), taking advantage of the high energy electron having a large Ewald sphere radius (≈90˚
A−1 at 30 keV) for extensive overlap with
reciprocal lattice. As a result, the slope of the in-phase diffraction in the rocking map
changes from 2 to 0, as it is now possible to penetrate the samples and produce transmission patterns. A simulated rocking map (Fig. 6.2(d)) shows this trend, which is verified
by a study of highly oriented pyrolytic graphite (HOPG) [34], shown in Fig. 6.2(e). This
type of features differ from ‘RHEED’ in that the transmitted diffraction spots carry the
symmetry of the lattice and can be used for structural determination. With UEC operated
in such circumstances, the intensity of transmitted Bragg peaks have been used to monitor
the integrity of the lattice structure, including laser-induced thermal fluctuations and phase
transition [34], and have been exploited to investigate the surface-supported nanoparticles
[29, 96]. What’s essential here for formulating the surface diffractive voltammetry is that

114

the diffraction condition under a = 0 has: θi + θo = θtot = nλ/c, where λ is the electron
wavelength, n is the diffraction order, and c is the lattice constant, can be used to formulate
the diffracted beam trajectory under the presence of transient surface field, as described in
Fig. 6.3. Details of the general formalism of UEDV for a=0 or 2 under different surface
diffraction conditions will be described in detail in section 6.4. We also like to point out
it is generally difficult to know the circumstances of surface diffraction without examining
rocking map. For example, when employing resonance diffraction peaks appearing along
a Kikuchi line [97] for UEDV, the surface diffraction must be characterized according to
a = 1, as shown in Fig. 6.2(f)(map) and (g) (Kikuchi pattern). For this reason, it is critical to identify the surface diffraction circumstance from the rocking map characterization
before a proper interpretation of the data can be established.

6.4 The General Formalism of Electron Diffractive Voltammetry
We derive the general formalism for describing the TSV-induced distortion of the diffraction
pattern under different surface diffraction circumstances. We firstly generalize the problem
in a simplified infinite long slab geometry, as depicted in Fig. 6.3, where a field region
exists near the surface, caused by a photoinduced redistribution of charges. We consider
the ‘refraction’ effect separately for the incident and outgoing beams. As the electron beam
enters the slab, the incidence angle is changed from θi into θi due to the refraction effect
imposed by the surface field region. A similar refraction effect occurs as the diffracted
beams cross the same region to reach the detector screen, which changes the exit angle
from θo in the diffraction region to θo ” as the diffracted beam leaves the field region. The
degree of change depends on the strength of field integrated along the incident and exit
115

e
∆B
Z1

θ''ο

θο

π−θΒ
π−θΒ
θ'ο

Z0

θi
θ' i

Vs

Surface field
region
Crystal

Figure 6.3 The idealized slab model for considering the transient surface voltage. The top
trajectory is the electron scattering from the crystal planes with the presence of a surface
field. The electron beam, incident at θi , is Bragg scattered at θB , exiting the surface
at θo . Introducing an attractive surface potential Vs will cause the electron beam to be
’refracted’ deeper into the crystal(θi ) and the same for the Bragg diffracted beam that
would ultimately exit the crystal at θo ” with a net shift ∆B relative to θo .
paths. Due to the grazing incidence geometry the change in θ is dominated by the field
normal to the surface, we can relate the change in θ to Vs based on momentum–energy
relationship along z direction for the incoming beam:

piz

2
− piz = 2me eVs ,
0
1
2

(6.3)

where piz and piz are the momenta of the incident beam projected along z at z0 and z1 .
1
0
Expressed in terms of angle θ, Eq. (6.3) can be rewritten as:

tan2 θi = tan2 θi +

χ
,
cos2 θi

(6.4)

where χ = Vs /Vo , by utilizing tanθi = piz /px , tanθi = piz /px , and eV0 is the beam
1
0
energy prior entering the field region. Similarly for the outgoing beams, we have:

116

tan2 θo = tan2 θo +

χ
.
cos2 θo

(6.5)

Since the electric field integration is linear, different components of the surface potential
can be superposed on each other, thus the details of Vs composition are not important here.
The voltammetry is established when Vs can be deduced as a function of the observable ∆B ,
which is defined as the angular shift of the diffracted beam (∆B ≡ θo ”−θo ). The derivation
of χ(∆B ) requires the knowledge of surface diffraction. To make the voltammetry generally
applicable to different type of interfaces, we consider all scenarios discussed in Fig. 6.2 by
relating θo and θi with
∆θo = (a − 1)∆θi ,

(6.6)

where a is the slope along the in-phase diffracted beams in the rocking map. For example,
a = 2 belongs to the case of RHEED (Fig. 6.2(b)), a = 0 is associated with the transmitted Bragg diffraction (Fig. 6.2(d)), and a = 1 can be attributed to Kikuchi diffraction
(Fig. 6.2(f)). Following the notation in Fig. 6.3, at the diffracted region:

θo = (a − 1)(θi − θi ) + θo ,

(6.7)

which allows us to rewrite tan θo in Eq. (6.5), which we define as D, in terms of θi and θo :

tan θo =

where θi = tan−1 (

tan[θo + (1 − a)θi ] − tan[(1 − a)θi ]

1 + tan[θo + (1 − a)θi ] tan[(1 − a)θi ]

≡ D,

(6.8)

sin2 θi +χ
) according to Eq. (6.4). From Eq. (6.5) at given Vs , θi and
1−sin2 θi

θo :

117

0.00

a=2
a=1

-0.04

∆B (º)

a=0

-0.08
a=0, exact
a=0, small angle approx.
a=1, exact
a=1, small angle approx.

-0.12
-0.16

1

2

3

4

5

6

7

θO(º)
Figure 6.4 The refraction-induced shift(∆B ) for diffraction peak located at θo at Vs =1
volt calculated for difference surface diffraction condition characterized by a = 0, 1, 2 (see
Fig. 6.2). The solid lines are exact solution from voltammetry formalism. The dashed lines
are calculated employing small angle approximation (see text). The incidence angle (θi ) is
set at 2.01◦ .

D2 − χ
.
1 + D2

θo = sin−1

(6.9)

To get Vs -induced angular shift in the diffraction pattern:

∆B = sin−1

D2 − χ
− θo .
1 + D2

(6.10)

Since D is a function of χ, it is difficult to deduce χ(∆B , θi , θo ) directly from Eq. (6.10).
Small angle approximation allows inverting Eq. (6.10) to obtain χ(∆B ) for different a,
which is presented in the Appendix C. One salient feature of the refraction-induced shift
is that the magnitude of ∆B increases as θo decreases. This is easily seen in Fig. 6.4,
118

where ∆B is calculated for a = 0, 1, 2 at Vs = 1V , following the exact solution based on
Eq. (6.10). We note that the corresponding change in ∆B at a = 0 is nearly twice the value
at a = 1, whereas at a = 2, ∆B remains to be 0 for all θo . We also calculate ∆B using
small–angle solutions (Eqs. (C.7) & (C.10)) in the Appendix C. The difference between
the two is barely noticeable. These results show that voltammetry is best performed using
nanostructured materials where transmitted Bragg diffraction is possible (i.e. a = 0),
whereas UEDV would be impossible under strictly RHEED condition. Nonetheless, in real
circumstances, even for a relatively flat surface, a is usually not exactly equal to 2, as shown
in Fig. 6.2(c). Deviation from a = 2 results in a small, but non-negligible sensitivity to Vs .
Generally, the angular dependence of Vs -induced shift is opposite to the structure-related
one, as the Fourier relationship: dθ/θ ∼ −dr/r demands that if only the structural change
is present ∆B would increase as θo increases. In contrast, the refraction-induced shift
responds to Vs oppositely, resulting in non-uniform cancellation of structure-induced shift.
This nonreciprocal feature is the basis of a Fourier phasing method [25], used to correct the
Vs -induced distortion in the diffraction pattern in order to accurately assess the structural
dynamics.

6.5 Ultrafast Electron Diffractive Voltammetry Experiment: Photoemission Contribution
As discussed in section 6.2, the photoemission contribution in UEDV measurement is hard
to assess, but we expect the dynamics to be different because the length scales involved in
interfacial charge transfer and photoemission are very different. To isolate the photoemis-

119

sion contribution in the vacuum region, i.e. ∆P E, we conduct a controlled study in which
the photoelectron dynamics and the surface photovoltage are characterized simultaneously.
This is achieved by using ultrafast electron shadow projection imaging, which has been reported previously for studying photoemission from an HOPG surface [98]. The advantage
of electron projection imaging is that it can be implemented in situ with the voltammetry
experiment by simply displacing the electron beam from the pump-probe overlap position
by a distance (x0 ) (Fig. 6.5(a)), thereby investigating the photoelectron dynamics under
the same excitation condition as the voltammetry experiment. In addition, the diffracted
beams, which are also visible in the shadow images, are affected only by photoemitted electrons above the surface generated by the pump laser, but not affected by the subsurface
fields probed in the voltammetry geometry, thus establishing a clean way to evaluate the
effect of ∆P E in voltammetry.
In principle all the relevant information pertaining to photoemission for creating the
transient near-surface field can be obtained from the projection imaging study. Fig. 6.5(c),
(d) show two selected snap-shots of the shadow images of the photoemitted electron cloud
obtained at t=42 ps and 62 ps under a laser fluence of 65 mJ/cm2 . The initial lateral dimension of the electron cloud is determined by our pump laser incident at 45o to the surface
normal. As a result, the laser footprint is elliptical with σx = 330µm and σy = 233µm,
which are determined by the cross-correlation response by scanning the probe beam across
the laser–illuminated region [25]. The projection distance (source-to-camera) employed in
this study is 16.5 cm and the offset distance x0 = 2.23mm, giving a magnification factor
∼ 74. The linescan of the shadow images (integrated vertically along the yellow stripe
depicted in Fig. 6.5(b)) contains the respective temporal evolution of Gaussian-like elec-

120

tron cloud together with a near-surface build-up (lines colored in red in Fig. 6.5(c), (d),
and from fitting the linescans [98] (Fig. 6.5(e)) at different times the temporal evolution
of cloud width (σz ) and center-of-mass position (zCoM ) can be determined, as depicted
in Fig. 6.5(f) for t = 0 ∼ 100 ps. From these temporal profile changes, we observe a
linear increase of position and width, and extract an electron cloud expansion velocity
vσz = 0.336µm/ps and an initial CoM velocity vCoM = 1.02µm/ps.
The creation of shadow images can be understood based on scattering of the probing
electrons from the collective field established by the photoelectrons:

1
EP E =
4π 0

N
i=1

e
.
(r − ri )2

(6.11)

The deflection from the collective field reduces the numbers of originally forward-going
electrons reaching the CCD camera, thus effectively creating a shadow of the electron
cloud. This process can be directly simulated by an N-particle simulation employing Monte
Carlo sampling of a 3D Gaussian electron distribution, which is parameterized based on
σ’s obtained from fitting the shadow images. We then send rays of electrons representing
the probing electron beam across the 3D electron cloud whose collective field is calculated
first by summing the pair-wise fields from individual electrons within the cloud. To speed
up the calculation, we establish a mean-field model to match the results calculated from
the multi-particle calculation based on the impact parameter to the electron cloud. We
note that the deflection caused by the collective field is linear with respect to the electron
density in the regime of interest here, which warrants the usefulness of the mean-field
approach. To simulate the shadow formation, 107 electron rays are used along the line of
sight to establish the shadow line scans and the electron counts on the CCD screen are

121

Figure 6.5 Shadow imaging experiment to characterize the properties of photoemission. (a)
Schematic experiment setup of the experiment, in which the incident electron beam is displaced by x0 from the photoinduced region by 800nm pump laser. The surface scattered
electrons form a shadow image of the electron cloud on the CCD screen as they are scattered away from the collective field associated with photoelectrons. In parallel, the surface
diffracted beam experiences the electric field associated with photoemitted electron cloud,
and deflects according to its location relative to the cloud. (b) The diffraction pattern from
Si/SiO2 surface is shown with the striped regions selected for extracting the shadow image
evolution (yellow) and the diffracted beam reflection (cyan). (c) & (d) show the snap-shot
shadow images of the photoemitted electron cloud at different time delays. (e) The respective Gaussian fitting of the shadow images. (f) Results extracted from fitting the shadow
image of the photoemitted electron cloud, showing the evolution of the CoM position and
the cloud width.
122

0.02

Normalized Intensity

(b)

Simulation
Experiment

0.01

Normalized Intensity

(a)

0.00
-0.01
-0.02
-0.03

+42 ps

-0.04
-0.05
2000

3000

4000

5000

6000

7000

8000

Position on Screen( µm)

0.02

Simulation

0.01

Experiment

0.00
-0.01
-0.02
-0.03

+62 ps

-0.04
-0.05
2000

3000

4000

5000

6000

7000

8000

Position on Screen( µm)

Figure 6.6 N-particle shadow projection imaging simulation at two different time delays.
calculated with and without intervening by the 3D electron cloud. The shadow profiles
are constructed by dividing the electron counts along the line scans with the rays being
intersected by the 3D cloud in the path and the line scans without intersection and compared
with the experimental results. Fig. 6.6 shows the comparison at two different delay times at
t=42 and 62 ps (solid lines are N-particle simulation results and dashed lines are the fitted
Gaussian profiles obtained from experimental shadow images). The agreement between the
N-particle simulations and the shadow imaging results are excellent. Since the depth of
the shadow is proportional to the photoemitted electron density, the agreement between
the experiment and simulation not only indicates the robustness of the shadow imaging
technique in profiling the photoemission, but also offers a measurement of the photoelectron
density created by the photo-illumination.
An independent approach to deduce the photo-electron density is through a singlebeam deflection experiment across the photo-emitted electron cloud [99]. Importantly, the
3D cloud geometry established by the shadow imaging technique can be confirmed by the
deflection of a diffracted beam from Si(111) surface diffraction, as it traverse through the
collective field associated with photoelectrons. Single-beam deflection experiment has the
advantage of being highly sensitive to the field and so is applicable even at very long times
123

(ns) when the electron cloud becomes too diffusive to monitor by the shadow imaging approach. To extend the field characterization to longer time, we analyze the Si-111 beam
deflection data contained in the diffraction images obtained from shadow imaging experiment. The analysis is of a Kikuchi diffraction enhanced peak (with θi =2.01◦ & θo =5.76◦ )
along the central stripe region circled by the dashed line in cyan in Fig. 6.5(b)). Fig. 6.7(a)
shows the temporal evolution of the angular shift. The up and down swings of the beam
can be associated with the beam crossing from above and under the 3D electron cloud
[99]. Importantly, the electron density required to correctly simulate the shadow profile can
now be directly confirmed by simulating the specific electron trajectory using an N-particle
calculation as described earlier. Furthermore, the absolute downward shift of the diffracted
beam is also affected by the counter image force associated with the image charges that are
created on the surface responding to the photoemission, which is also modeled numerically
as described below.

6.6 Near Surface Field Induced by Photoemission
To fully simulate the diffracted beam trajectory, which extends to 2 ns, we need to know the
projectile motion of the 3D electron cloud and the corresponding image charge dynamics
that provide additional field component. To comply with the rate and the magnitude of
beam deflection, a metal-like dielectric response with a very large at early times due to the
excessive amount of charges initially built up on surface is considered.

decays exponentially

to the equilibrium value of 3.9 for SiO2 [100], and can be described by SiO =3.9 + A
2
−t/τ
r . The field model for image charges is included with the dielectric relaxation process
e
and is described by [101]:
124

(a) 8.0x10-5
∆B(radian)

6.0x10
4.0x10
2.0x10

0.0048º

Experiment
N-particle simulation
τr=16 ps
τr= 0 ps
τr= 21 ps
τr= Infinity

-5
-5
-5

0.0

0º

-5

-2.0x10

-5

-4.0x10

-5

-6.0x10

-5

-0.0048º

-8.0x10

-4

-1.0x10

0

400

800

1200

1600

2000

Time (ps)

(b)
∆B(radian)

0.0000

0º

-0.0001
-0.0002

Experiment

-0.0003

N-particle simulation

-0.0004

0.03º

-0.0005
0

400

800

1200 1600 2000 2400

Time (ps)
Figure 6.7 Experiments to characterize photoelectron dynamics and surface photovoltage
performed at F=65 mJ/cm2 . (a) Data (symbols, colored in red) show the deflection of
a selected diffracted beam by the electric field associated with photoelectrons and the
image charges on the surface acquired in the shadow imaging experiment setup. N-particle
simulations with surface dielectric relaxation times (τr ) ranging from 0, 16, 21 ps, and ∞
are used to fit the data. (b) The voltammetry results (symbols, colored in red) obtained
from the same diffracted beam, but at the overlapped voltammetry geometry. An N-particle
simulation to estimate the refraction contribution associated with photoemission is shown
(solid line, colored in blue) for comparison.
125

N
1 SiO2 − 1
e
.
EImg = −
4π 0 SiO + 1
(r − ri )2
2
i=1

(6.12)

The time-dependent angular shift of the diffracted beam is calculated using:

∆θ =

Edl
,
2V0 cos2 θ

(6.13)

where V0 =30kV and E in the path integral contains contributions from photoelectrons
(Eq. (6.11)) and image charges (Eq. (6.12)). The integration takes place over 3×FWHM
across the Gaussian cloud. Previously, an analytical model [99] and N-particle simulation
[39] of the transient field associated with photoelectron cloud and image charges has been
implemented to account for deflection of a probing electron beam. The dielectric response
of the surface has not been explicitly included. The necessity of incorporating the surface
dielectric relaxation to account for the change in

is evident from comparing the models

with different dielectric relaxation times and the experimental data, which are shown in
Fig. 6.7(a). We find A=104 and τr =16 ps provide a reasonable agreement to the experimental data. To comply with the deflection data at long times, the knowledge of the
photoelectron cloud beyond the initial linear trajectory is needed. The return rate of the
photoelectrons to the surface is determined by the strength of the image force, which is
gradually weakened as the expansion of the photoelectron cloud into the surface will lead
to cancellation of the image charges even before the CoM trajectory reaches the turning
point and weakens the image force. We apply an additional 3rd order term to account
for this effect. The deflection of the diffracted beam can be calculated self-consistently by
varying the coefficients of the 2nd and 3rd order polynomials to fit the deflection data. We
note that the fitting is based on a fixed initial condition (electron density and CoM and
126

expansion velocity) determined by shadow imaging, but the results from fitting deflection
data extend our knowledge of the surface field development beyond the timescale (0-150 ps)
obtainable from the shadow imaging, and serve as the basis for estimating the long time
behavior for the voltammetry measurement.

6.7 Modeling of The Surface Photovoltammetry
The transient electron diffractive approach can be used to investigate electron transport
in molecular contacts [102, 103, 104, 105, 106]. In a nanoparticle decorated interface,
Au NP/SiO2 /Si, a transient charging of the nanoparticle is caused by photoinduced charge
transfer between the substrate and the nanoparticle through insulating buffer layers (SiO2 ).
The transient charging establishes a voltage determined by the charging energy of the
nanoparticles with respect to the driving surface potential and the resistance of the buffer
layers, which can be conceptualized as an effective RC circuit as depicted in Fig. 6.8(a).
The diffracted beams are employed to investigate the charge transfer dynamics between the
nanoparticles and the substrate. The capacitance C can be calculated directly from the
geometry of the interface using a finite element method. When C is known, the resistance
of the buffer layer can be directly deduced by the RC time in the charging and discharging
of the nanoparticle decorated interface.
To simulate the photovoltammetry dynamics driven by the emf of the photoexcited carriers, we can construct equivalent circuit models. As an example, we examine the interfacial
charge transfer from semiconductor photoreceptor (Si) across the insulating tunnel junction
(SiO2 ) layer to the surface with metallic (Au) nanoparticles or with just the surface states.
The schematic layout of such a nanocircuit is depicted in Fig. 6.8. The photoexcitation of
127

(a)

(b)
R
E

Si

i

E(t)

h(t)

Vs(t)

RC=500 ps

Vs

C

SiO2
Au NP

0

Time (ns)

4

0

Time (ns)

4

0

Time (ns)

4

Figure 6.8 (a) An effective circuit model depicting the transient surface voltage Vs (t) measurement via the refraction shift across SiO2 /Si interface with 20 nm Au nanopartilce
decoration. The electromotive potential ε(t) comes from the hot carriers generated at the
Si substrate. (b) Example showing the photovoltage Vs (t) measured at the interface as a
function of ε(t). The relationship can be seen as a convolution with kernel function h(t)
characteristic of the RC circuit.

128

the semiconductor substrate generates electron/hole pairs that elevate the electrochemical
potential at semiconductor surface, which can be a source of emf driving carriers across the
insulating junction. The injection of hot carriers into the metal surface results in charge
separation, which forms a photovoltage Vs between the semiconductor and metal surface.
Such a photovoltage generation is fundamentally limited by the charging time, τ = RJ CJ ,
of the junction, where RJ and CJ are the junction resistance and capacitance. The photovoltage Vs (t) determined here can be used to derive the emf if the response time τ is
known, based on the linear response of the nanocircuit model:

Vs (t) =

∞
−∞

ε(τ ) · h(t − τ )dτ,

(6.14)

where h(t) = 1/RCe−(t−t0 )/RC u(t), u(t) is the heaviside step function, and t0 is the zeroof-time. In this formulation, the transient surface voltage Vs (t) is the convoluted response
of the electromotive potential ε(t) by the kernel function h(t). h(t) is inherent to the circuit
setup and can be obtained by the inverse Laplace transformation of the effective reactance
ratio γ, which, in the case of the RC circuit describe in Fig 6.8 (a), is ZC /(ZR + ZC ),
where ZC = 1/Cs is the reactance of capacitor, and ZR = R is the reactance of the resistor
in the complex frequency (s) domain. Applying Laplace transformation on both sides of
Eq. (6.14), we establish the relationship between Vs and ε in the s-domain:

1/RC
V˜s (t) = ε˜(s)
,
s + 1/RC

(6.15)

from which we can derive ε˜(s), based on V˜s (s), and use it to deduce ε(t) through inverse
129

Laplace transform. Fig. 6.8 (b) depicts three examples of Vs (t) driven by different ε(t).
For an impulse ε(t), the Vs (t) is simply the kernel function h(t), an exponential decay
with τ = RJ CJ . For a square pulse, the Vs (t) rises exponentially with τ = RJ CJ . In
practice, the carriers electromotive potential will likely have a form of nonexponential rise
and decay, as depicted in the bottom panel of Fig. 6.8 (b). Given a typical nanodevice
dimension, such as 10nm nanoparticle next to a gold electrode with a ≈ 2nm tunneling
gap, the effective RC time is on the order of 10 ps. This timescale is fundamentally much
shorter than the contemporary integrated device with a typical switching time ≥ 50ps. On
the other hand, the RC time is on the upper end of the interfacial charge transfer timescale
reported by optical and photoemission techniques, which is at the limit of state-to-state
population dynamics, and fundamentally different from the tunneling time [107]. Using
Eq. (6.15), we can deduce the effective emf dynamics based on photovoltammetry data,
which shows rise and decay times of τc = 30.84ps, and τd = 296.47ps, respectively, for
surface charging and discharging. Using τ of 30.8ps, we can deduce the ε(t) as depicted
in Fig. 6.9, where a spontaneous rise and long decay is seen which is consistent with the
carrier density dynamics calculated using the Boltzmann transport coupled TTM [51].

6.8 Surface Photovoltage
Having obtained the near surface field associated with the photoelectrons from the shadow
imaging and diffracted beam deflection measurements in the offset geometry, we can now
evaluate the contribution associated with photoemission in the voltammetry experiment
conducted by shifting the beam from the offset geometry to the overlap geometry, as reported in Fig. 6.7(b) (line and symbols, colored in red). The diffracted beam used in the
130

2.0
1.8
1.6
1.4

Vs

1.2
1.0
0.8
0.6
0.4

Experimental V s(t)
Theoretical V s(t)
emf

0.2
0.0
-0.2
0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

Time (ns)
Figure 6.9 Theoretical modeling of transient surface voltage Vs (t). Using RC time of 30.8ps,
the corresponding electromotive force emf is deduced, showing a spontaneous rise and a long
decay.

131

voltammetry experiment appears at the intercept of a Kikuchi line and a 2D reciprocal lattice rod (Fig. 6.2(g)). We characterize the diffraction being a two-step process, where the
incident beam is first scattered randomly to form an isotropic source, and then scattered
into surface Laue Zones. This is consistent with a = 1 observed in the θtot vs θi relationship obtained from the rocking map analysis presented in Fig. 6.2(f), implying that only
the refraction along the exit path contributes to ∆B , and so we can simplify the generalized
TSV formula accordingly, and deduce the photovoltage based on: χ = −∆B (∆B + 2θo )
(see Appendix C, Eq. (C.11)).
We evaluate the contribution ∆PE in the overall photovoltage measurement by building on the knowledge of near surface fields induced by photo-emission characterized by
the shadow imaging and deflection experiments. The ∆B associated with ∆PE can be
calculated by an N particle simulation of ∆B along the exit beam path at θo , similar to
that in evaluating the deflection experiment, but under an overlap geometry used in the
voltammetry experiment. The simulated ∆B is depicted in Fig. 6.7(b) (solid line, colored
in blue) to represent the ∆PE contribution, and compared to the overall ∆B measured
experimentally. Remarkably, the photoemission-associated ∆B matches very well with the
long-time tail of the voltammetry measurement, but contributes maximally about 25-30%
of the total angular shift at the early times. This indicates that the slow dynamics of TSV
at the long time are controlled by the return of the photoemitted electrons to the surface,
whereas interfacial charge transfer across the SiO2 layer is more relevant at the short times.
By excluding the ∆PE contribution from the overall ∆B , we deduce a Vs (t) relevant to
the surface charging dynamics, as depicted in Fig. 6.10.

132

∆DP (Volt)

2.0

Experiment
Fit 2.0

1.5

1.5
1.0

1.0

0.5
0.0

0.5

-0.5
10

100

1000

0.0
-0.5
0

400

800

1200

1600

2000

Time (ps)
Figure 6.10 Transient surface voltage caused purely by ∆DP . ∆P E contribution is subtracted from total TSV, and the surface voltage is calculated by Eq. (6.16). The surface voltage is fitted by an RC charging and discharging model with τc =30.84 (ps), and
τd =296.47 (ps). Inset: Charging/discharging dynamics in a log time scale.

133

By fitting the ∆PE subtracted Vs (t) with an effective RC-charging/discharging model:

Vs = Vf it (1 − e−t/τc )e−t/τd ,

(6.16)

we determined the RC time constants: τc =30.84 ps, and τd =296.47 ps respectively for
surface charging and discharging. We attribute the difference between the two to the
change of hot electron photoconductivity across the SiO2 interface. The photo-generated
hot electrons facilitate the surface charging through access to the excited states, leading
to a much shorter RC time than the discharging, which involves a cooler interface with a
reduced photoconductivity, leaving the SiO2 surface to stay charged for a longer period of
time.
We compare the TSV results reported here for a smooth Si/SiO2 interface with one
reported previously for a step Si/SiO2 interface [40]. We find that the timescales in charging
and discharging the interface in the two studies are similar, whereas the TSV induced in
the smooth interface (maximum 1.7V at 65 mJ/cm2 ) is smaller than the stepped interface
(maximum 3V at 72 mJ/cm2 ). By applying the shadow imaging technique under the
same conditions (electron incidence/exit angles and laser fluences) as the voltammetry
experiment, we are able to quantitatively identify the contribution of photoemission on
the overall voltammetry result, where photoemission is mainly responsible for the slow
decay, but does not contribute significantly to the short time dynamics, which clarifies the
origin of the diffracted beam movement [99]. For cases where photoexcitation can cause
significant structural changes, a correction on the refraction-induced shift in diffraction
pattern is needed. We point to the first ultrafast electron crystallography investigation of
134

Si(111) surface, which was performed using 266 nm laser pulse [94]. Because of the much
shorter laser penetration depth (4nm), the absorbed optical density is concentrated near
the surface, propelling not only hot electron dynamics, but also surface structural changes.
From examining the reported time-dependent rocking curve (Fig.4(a) in the paper [94]), the
movement of the ‘in-phase’ Bragg peak at small angle (∼ 3.1◦ ) is slightly larger than that of
a peak at higher angle(∼ 3.9◦ ), which is consistent with a surface refraction phenomenon
being present. But the surface charging is not the full story, as the ‘surface’ structural
dynamics was also examined in the ‘out-of-phase’ condition(Fig.4(b) in the paper [94]),
where the presence of multiple interference peaks is a signature of transmitted diffraction
from surface nanostructure. Such a pattern was modeled using a slab model that identified
the changes are from the top surface layer and the sub-surface (111) layers, contributing
the contrasting movements of the two different peaks separated in ≈ 30ps. The surface
dynamics could be mediated by the impulsive strain induced by ultrafast laser pulse heating
and/or surface charges. Further controlled study is needed to clarify the nature of the
surface dynamics on surface charging, photo-emission and the corresponding structural
dynamics, which can be achieved using the methodologies provided here.

6.9 Summary
We have established a general formalism for the UEDV concept, which is applied to investigate the photoinduced charge migration from the substrate to nanostructured interfaces.
We show that the surface diffraction and boundary conditions need to be accounted to correctly formulate the ultrafast voltammetry based on Coulomb refraction-induced diffracted
beam dynamics. We identify that the voltammetry appears on the surface, subsurface,
135

and vacuum levels, associated with interfacial charge transfer, carrier diffusion, and photoemission respectively, under intense laser irradiation. From quantitative shadow imaging
techniques performed at the same condition as voltammetry and N-particle simulations, we
are able to assess the voltammetry contribution associated with photoemission, and quantitatively deduce the surface charging dynamics from the overall voltammetry. We find that
the photoemission impacts the voltammetry most in the long time, whereas the interfacial
charge dynamics dominates the voltammetry at the ultrafast (0-100 ps) timescale. The
surface photovoltage, the capacitance of the nanointerface, and the resistance of the buffer
layers can be conceptualized as an effective RC circuit and, using the RC time of the effective RC circuit, we can deduce a corresponding electromotive force. A spontaneous rise
and long decay of the electromotive force is consistent with the carrier density dynamics of
the Boltzmann transport coupled two-temperature model calculation [51].

136

Chapter 7
Photo-Induced Charge Carrier
Dynamics at Nanostructured
Interfaces
In previous chapter, we presented an ultrafast electron diffractive voltammetry technique
to investigate the surface charge carrier dynamics at the nanometer scale. This diffractionbased method utilizes the feature-gated nanomaterial diffraction pattern to identify the
scattering sites and to deduce the associated charge dynamics from the nanocrystallographic
refraction-shift observed in the ultrafast electron diffraction patterns. By applying this
methodology on Si/SiO2 interface and surfaces decorated with nanostructures, we are able
to elucidate the localized charge injection, dielectric relaxation, and carrier diffusion, with
direct resolution of the charge state and possibly correlated structural dynamics at these
interfaces, which are central to nanoelectronics [108], photovoltaics, and photocatalysis
[109, 110] development.
Through the sensitivity of the diffracted electron beams to the local electric fields, three
prominent charge redistribution processes induced by photoexcitation can be observed as
described in Fig. 7.1: (1) Dielectric realignment: The alignment of the dipolar elements
within the dielectrics changes, resulting in displacement fields even though there is no ac137

(a)

P

(b)
-

+

(c)

E

+
+

+
+

+

-

E

Figure 7.1 Charge redistribution at nanomaterials interfaces subject to photoexcitation. (a)
Dielectric realignment; (b) carrier diffusion; (c) interfacial charge transfer
tual carrier current in the materials. (2) Carriers diffusion: The photocarriers in the excited
region diffuse to the unexcited region, inducing internal photocurrent. (3) Interfacial charge
transfer: The photoexcitation changes the balance of chemical potential at the interface,
resulting in charge transfer to counteract the shift in free energy. Decay of these photovoltages might involve drift and dipolar relaxation, in addition to carrier recombination,
diffusion, and radiative decays.
To demonstrate the proof of principle, systematic investigations were conducted at interfaces with progressively grown complexities. First, a planar Si/SiO2 surface was investigated with infrared laser pulse to drive the hot carriers through the SiO2 layer. In the
sub-10 nm dielectric SiO2 layer, ultrafast surface charge dynamics is shown to strongly
couple to the sub-surface carrier dynamics, exhibiting drift-diffusion relaxation behavior.
Second, gold nanoparticles decoration was incorporated with molecular linkers connecting
the nanoparticles to the surface. The large curvature of the nanoparticle surface facilitates the field focusing effect, which can enhance the carrier dynamics across the interface
through the field-assisted tunneling. Third, surface plasmon enhancement effects were investigated. Strong dielectric-induced spectral shift in the response function highlights the
mode-selective optical antenna effects between the nanostructures and their surroundings.
138

These studies elucidate the key features of light-driven charge transfer dynamics around
these interfaces, which help to understand the fundamental processes relevant to nanoelectronics, photovoltaics, and photocatalysis.

7.1 Surface Charging of Pure SiO2/Si Interface
The SiO2 /Si interface is the fundamental building block of CMOS devices. The nature
of charge transfer, trapping, and detrapping at the SiO2 /Si interface has gained notable
interest as the dielectric oxide layer necessarily becomes thinner as the elemental feature
size continues to shrink. Moreover, this interface has also been tapped as the electronic
grade interface to grow molecular electronic devices, with increasing effort exploring different avenues of fabricating interfaces using self-assembled monolayers (SAMs) [104] and
nanoparticles [102, 104, 111, 105, 106]. For validating the diffractive photovoltammetry
methodology, the SiO2 /Si interface provides a simplest test ground. Under ultrafast laser
irradiation, a fraction of the valence band (VB) electrons in Si are promoted to the conduction band (CB), followed by charge rearrangement at the interface, depending on the
nature of the excitation (laser intensity, energy, etc.). The very large band gap of SiO2 (8.9
eV) ensures that the SiO2 layer is transparent to the incident visible light. The field arises
from charge separation at the interface as carriers are transported from the bulk to the
surface. In ultrathin SiO2 layers (1−10 nm), the charge transport across the SiO2 layer is
predominantly via tunneling, which makes both surface charging and discharging relatively
efficient processes. However, the details of the dynamics remain nontrivial for photocarriers as both direct or field-induced (FowlerNordheim) tunneling [112, 113, 114] are driven
by the increase of the quasi-Fermi level of hot electrons (holes) above the conduction (va139

lence) band offset. The possibility of dielectric enhancement of the interface dipole, as well
as thermionic and multiphoton-mediated photoemission, can also add to this near-surface
field [99, 98, 39].
Several techniques have been employed to examine charge transfer mechanisms associated with this interface, most notably, EFISH (electric field-induced second harmonic
generation), which has been applied to characterize leakage currents through oxide layers,
long-lived trap states, and band offsets [115, 116]. Photoelectron spectroscopic methods
have been effective in elucidating the interfacial electronic structures [117, 118], as well as
monitoring the surface state populations directly [119, 120, 121]. Bulk carrier dynamics in
Si have been studied extensively at the pico- to femtosecond time scales with a variety of
time-resolved techniques [120, 49, 122, 123, 124, 38]. Many of the surface-sensitive experiments were performed with high repetition rate lasers, on the order of 80 MHz, implying
that the system is pumped every ≈ 13 ns, which is before trapped charges can relax, such
that the residual charge level is continuously pumped. The amount of the residual charge
depends on the integrity of the interface, or, more directly, the density of interface states.
Using standard RCA cleaning protocols, a thin (2−5 nm) insulating SiO2 layer can be
reliably grown on single crystalline Si substrate. Because the penetration depth (l) of the
infrared pump laser (800 nm) for Si is significantly longer (1 µm) [125] than that of the
electron beam (≈ 5 nm, incident angle 6.8o ), characteristic carrier lifetime (τi ) probed at the
surface (≈ 700 ps), which can be estimated based on τi = l2 /D, where D ≈15 cm2 /s [126] is
the diffusivity of the electrons, is significantly longer than the electronphonon coupling time
(≈ 5 ps), thus allowing the stored photon energy to be maintained within the photoexcited
region. Meanwhile, due to the large disparity in the electronic and lattice heat capacities,

140

even at a relatively high fluence of 65 mJcm2 , the lattice temperature rise is very small
(≈ 40 K) [40]. This is in sharp contrast to the more than three orders of magnitude
increase of the carrier density in the surface excited region from the intrinsic level [126]
by photoexcitation, thereby creating a favorable condition for studying hot electron-driven
interfacial charge transfer across the SiO2 layer without worrying too much of lattice effect.
Using the formalism from Sect. 6.4, the changes in diffraction angle are converted to
surface voltage, which is presented in Fig. 7.2. The objective here is to analyze the Bragg
peak dynamics from multiple peaks. This was to see if the agreement is robust as incidence
angle and diffraction order are varied. In principle, the transient surface voltage Vs should
remain the same as different relrods are examined. We choose to investigate (0,3,24),
(0,1,21), (0,1,24) on the (0,3) and (0,1) relrods with N = 7 and 8 (crystallographic notation
for diffraction order is multiplied by a factor of 3 due to the ABC layering of the Si(111)
surface), corresponding to θi of 6.24o , 4.15o , and 4.70o , and θo of 3.50o , 4.02o , and 4.63o ,
respectively. The excitation fluence is fixed at 65 mJ/cm2 . Under photoillumination, the
transient movement of the three diffracted beams, depicted in Fig. 7.2(a), indeed exhibits
nonreciprocal signatures as described previously, i.e. the higher order Bragg peak shifts
less than the lower order one, which is characteristic of the surface voltage-induced effect
[40]. Closer examination of the shifts shows that nonreciprocity applies only to θo , but not
to θi , as the maximally shifted beam is (0,3,24), which has a θi = 6.24o larger than the
rest, whereas its corresponding θo is 3.50o , which is smaller than the rest. This angular
dependence is confirmed by the rocking map analysis for the relrods exhibiting a = 1 near
the in-phase diffraction, as shown in Fig. 7.2(b) for (0,3) relrod. By applying a = 1 in Eq.
(6.10), we deduce Vs for the three diffracted beams and successfully reproduce Vs largely

141

Figure 7.2 Trasient voltammetry from three diffracted beams from Si/SiO2 interface. (a)
The angular shift of (0,3,24), (0,1,21), and (0,1,24) beams excited at F=65mJ/cm2 . (b)
The rocking map characterization of (0,3)-relrod, showing a surface diffraction condition
a = 1. (c) The photo voltage deduced from (0,3,24), (0,1,21), and (0,1,24) beams based on
Eq. (6.10) using a = 1.

142

independent of θi , indicating the slab model description is a good model for describing the
essential photovoltage response observed by diffraction.
Our diffractive voltammetry results contain sufficient information to understand the
origin of the photovoltage, which might include fields along the surface dielectric SiO2
layer, the subsurface bulk space charge region, and even the near-surface vacuum region.
In the case of the band photovoltage induced in the bulk space charge region, the limit is
the flat-band value of approximately 300 mV [127, 128]. As our Vs exceeds such a limit,
we rule out that the band bending induced by the space-charge layer is responsible for the
Vs observed here. This is further evidenced by the fact that the space-charge layer in Si
is rather thick (≈ 1 µm) as compared to the penetration depth of the electron probe (≤
10 nm). We turn our attention to the surface charging across SiO2 dielectric layer, where
the surface field is fully probed by the electron beam. The subsurface carrier dynamics is
strongly coupled to the net surface charges, which, through the elevated carrier screening,
defines a dynamical space charge region. In the previous investigation of surface charging
processes by EFISH [129, 115, 130, 131, 132, 133], the sub-surface electric field is deduced
based on modeling the field-enhancement of optical second harmonic generation signal as
well as photoemission [119]. We find that the field strength E

1V /nm obtained in our

study is very similar to what was found in EFISH studies under similar excitation conditions
[129, 115], but because of a lower laser repetition rate applied here (1 kHz, compared to

80

MHz in EFISH) cyclic residual charge accumulation from deep trap states [11, 134, 135, 136]
is avoided, allowing ps interfacial charging dynamics to be resolved directly.

143

7.2 Surface Charging of Au Nanoparticle Decorated Si/SiO2 Surface
The scope of nanoparticle research spans many disciplines with vast possibilities of incorporation into practical use, including nanoelectronics [137, 138], photovoltaics [109, 139,
140, 141, 142] and even quantum-dot-based lasers [143, 144]. On the biological/life sciences
side, it has recently been shown that gold and silver nanoparticles, when delivered to siteselective cancerous cells, can destroy them upon exposure to a pulsed-laser source, without
damaging surrounding tissue [145, 146]. Noble metal nanoparticle also serves as electron
trap that enhances charge separation in the near junction region. Of recent interest is
the concept of using a nanoparticle as an optical antenna by exploiting the plasmon-based
near-field enhancement, which is capable of surpassing the diffraction limit for spatial resolution [147]. It has been observed that the same near-field optical-enhancement effect
improves the carrier generation in the nearby semiconductor substrate and boosts the efficiency of the solar cell [148] or photocatalyst. At a fundamental level, the photoinduced
carrier dynamics and possible plasmonic enhancement effects at the contact region can
be investigated via diffractive voltammetry by monitoring the photovoltage between the
nanoparticles and the substrate, which in this case is directly related to the charge state
of the nanoparticle: Vs = Q/C, where Q is the surface charge of the nanoparticle and C
is the capacitance of the nanoparticle/SAM/Si interface. Because of the large curvature of
nanoparticle surface, the surface charges on SiO2 /Si surface can strongly interact with the
injected charges in the nanoparticle through field focusing at the contact region, leading
to enhanced carrier transport and charge separation. Two different mechanisms should be
144

considered, namely: (I) The hot electron-driven process, where the strong light sensitization at metallic nanoparticles generates high-temperature carriers with higher efficiency to
tunnel through the SAM energy barrier, creating a photoelectron current from nanoparticle
to the substrate; and (II) The photovoltage-driven dynamics initiated by electrons at Si CB
edge, created by photoexcitation. While the net effect of enhancing the hot carriers concentration at metal-semiconductor interface is the same, the net photo-current flow in the
two cases is opposite, which can be measured directly with diffractive photovoltammetry.
When channel (I) is dominant, it leads to a positive charging of the nanoparticle, thereby
causing the diffracted beam to shift upward. If channel (II) is dominant, the nanoparticle
will be negatively charged, and consequently the diffraction peaks will move downward in
addition to the movement induced by the surface charging of the SiO2 .
Monodisperse metallic nanoparticles (Fig. 7.3) can be deposited on Si substrates by way
of SAM of aminosilanes AEAPTMS [25, 149]. The aminosilane chains, which are anchored
to the Si substrate, immobilize the nanoparticles through the formation of strong van der
Waals bonds. When an ensemble of nanoparticles is sampled by the electron beam, a
powder diffraction pattern results [25], which is constituted from the many different crystal
faces that the beam samples in its footprint on the surface. In addition, the linker molecules
that take part in the anchoring of nanoparticles tend to orient themselves in a manner that
is sufficiently ordered, such that very clear diffraction spots from the linker molecules are
present in the patterns (Fig. 7.3(c)). Here, the charging dynamics will be examined for
an interfacial structure consisting of the interconnected nanoparticle/SAM/semiconductor
geometry discussed here, shown in Fig. 7.4(a). The fortuitous discovery of SAM diffraction
peaks in conjunction with the extension of diffractive voltammetry to arbitrary geome-

145

Si
O

2.472 A

q

N
2.474 A

C
H

(a)

E-bea

m

Phot
o

q = 28.8

(b)

100 nm

(c)

s (A-1)

2.866 A

Au NP

5.27

n trig

ger

7.98

2.75
Si-111

Shadow Edge

Figure 7.3 (a) A sample of Au nanoparticles (NPs) immobilized on a functionalized Si
substrate. (b) The chemical form of the AEAPTMS linker molecule. (c) Schematic of an
electron beam scattering from the ordered self-assembled monolayer chain and the corresponding diffraction pattern [25]

146

!"
!!"

Figure 7.4 (a) An effective circuit model depicting the transient surface voltage Vs (t) measurement via the refraction shift of the diffracted beams through SAM. The RS , CS , RM ,
CM are the effective resistance and capacitance of the substrate (S) and the SAM (M). The
electromotive potential that can drive the photocurrent through the SiO2 layer (iS ) and
further through SAM (iM ) is mainly from the hot carriers generated from the Si (ε1 (t));
whereas the short-lived photoexcited hot carriers generated within the Au nanoparticle
(NP) can also drive the charge transfer in the opposite direction (ε2 (t)). (b) The overall
refraction shift determined by SAM diffracted beam (labeled Vs ), the background (labeled
VB ) obtained from SiO2 /Si interface, and the molecular charge transport contribution,
obtained by subtracting VB from Vs
tries, fuels an ongoing effort toward using the SAM dynamics for uncovering the charge
transport (forward or backward) across the interface from semiconductor to nanoparticle,
or vice versa. Following photoexcitation, hot electrons are generated in the substrate and
nanoparticles, from which a charge transfer process will ensue depending on the relative
offset between the transient electrochemical potentials of the two systems. Quantifying this
process would provide an additional technique for the investigation of molecular transport,
an area of notable interest [103, 150].
In our first experiment studying the molecular transport, 20 nm gold nanoparticles were
used, and the interface is illuminated with 800 nm near-infrared laser pulse [25]. This ar-

147

rangement avoids the surface plasmon excitation of the nanoparticles (≈ 500 nm), and
we expect the interfacial charge dynamics between the nanoparticle and the SiO2 /Si is
determined by two competing processes as described in Fig. 7.4(a). Specifically, the transient voltage induced by charge transfer between the substrate and the nanoparticle can be
monitored by analyzing the SAM diffraction peaks corresponding to momentum transfers,
s = 2.75, 5.27, 7.98˚
A−1 (orders N = 13), as depicted in Fig. 7.3(c). The total transient shift
∆B includes two serial voltage drops: one across the SiO2 /Si surface (VB ), and the other
across the SAM (VM ), as depicted by the effective RC-circuit in Fig. 7.4(a). To isolate
the voltage across the linker molecule, the contribution from VB must be subtracted out.
Typically, the ∆B associated with a bare SiO2 /Si surface has an exponential down turn
followed by a ≈200 ps recovery. The presence of an additional upward swing followed by
a downward swing to recovery can be discerned with careful analysis, which is shown in
Fig. 7.4(b). These additional components sampled by diffraction through SAM suggest a
new channel of photo-current emerges between the silicon substrate and the nanoparticles,
which creates a more positive potential at the interface to account for the initial upswing
of the diffracted beams [25].
These results strongly indicate that both processes (I) and (II) are at play. Process (I)
is a key player at 1-40 ps due to the hot electrons generated within the strongly sensitized
gold nanoparticle. However, because of the lifetime of the hot electrons in gold nanoparticle
is limited by the electronphonon coupling on the few ps timescale, the emf ε2 (t) is shortlived. Meanwhile the photoexcited CB carriers at silicon surface is very long-lived, limited
mainly by the drift-diffusion carrier recombination at ≥ 200ps timescale [40]. The ε(t)
is persistent and ultimately dominant at long times driving the photocurrent across the

148

interface.
Examining the data in Fig. 7.4(b) shows a charging and discharging time of 8 ± 1ps.
Based on the effective RC model, we obtain a resistance RM = 2.74M Ω using C = 2.92 ×
10−18 Farad, deduced from finite element modeling of the interface. It is rather interesting
to compare this molecular resistance with the steady-state value of 12.5M Ω obtained by
applying a bias voltage across the molecular interface [149] using 10 nm (thus a covered area
by the functional molecules is ∼4 times smaller than that of 20 nm Au NP) Au nanoparticle.
The RM obtained using ultrafast voltammetry is four times smaller than the steady-state
measurement for 10 nm particle, which shows the molecular resistivity obtained from two
different methods are nearly identical.

7.3 Photo-induced Field Enhancement with Localized Surface Plasmon of Nanostructures
The photo-induced surface charge transfer shown in bare SiO2 /Si interface and gold nanoparticle decorated SiO2 /Si interfacehas is excited by 800 nm pump laser which is out of the
resonance of a gold nanoparticle surface plasmon frequency. In novel metal, the conduction
electrons can be excited into collective oscillatory motion about the heavy ionic core. This
occurs when the frequency of light photons matches the natural frequency of surface electrons oscillating against the restoring force of positive nuclei. The surface plasmon resonance
in nanometer-sized structures is called localized surface plasmon resonance (LSPR) shown
in Fig. 7.5. LSPR exhibits enhanced near-field amplitude at the resonance frequency. This
field is highly localized at the nanostructures and enhances surface charge transfer at the

149

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0+*12/.+*"%(%/&-+*"/(+21"
Figure 7.5 Schematic illustration of localized surface plasmon oscillation induced by an oscillating electric field in a metal nanoparticle. The displacement of conduction electron cloud
relative to the nuclei is shown. The frequency of the localized surface plasmon resonance is
denoted ωp .
interface between a nanostructure and a surface. In this section, we present photo-induced
charge transfer enhancement due to LSPR.

7.3.1 Localized Surface Plasmon of Gold Nanoparticles
The conduction band electrons in a metal nanoparticle can collectively oscillate with the
incident external field of which the wavelength is much larger than the nanoparticle size, and
this collective motion can be described by the dipole approximation of Mie theory.[151, 152]
In this approximation the wavelength-dependent extinction cross-section of a single particle,
Cext (ω), which defines the energy losses in the direction of propagation of the incident light
due to both scattering and absorption by the particle, is described in terms of the dielectric
function of the metal, ε(ω) = ε1 (ω) + iε2 (ω), and the dielectric constant of the medium,
εm , as shown below:
150

3/2
ε2 (ω)
12πR3 εm ω
,
Cext (ω) =
c
[ε1 (ω) + 2εm ]2 + ε2 (ω)2

(7.1)

where ω is incident light frequency, and R is the nanoparticle radius.
As can be seen from Eq. (7.1), the extinction cross-section of a particle depends on the
dielectric function of the metal of which the particle is composed. This gives rise to very
different absorption and scattering characteristics for different metal nanoparticles. The
maximum of Cext (ω), the resonance condition, will take place when the denominator of
the right-hand side of the equation becomes minimal. This is fulfilled approximately at
the frequency, ωp for which ε1 (ωp ) = −2εm , if the imaginary part of the metal dielectric
function, ε2 (ωp ) is small. The frequency of the surface plasmon resonance, ωp , is depicted
in Fig.7.5 in terms of the period of the oscillation of the electric field and the conduction
electrons within a metal nanoparticle.
The large absorption cross-section values of the surface plasmon resonance band imply
that a NP is able to efficiently acquire a vast amount of energy when irradiated with light at
the appropriate wavelength. Thus, it is interesting to ask questions about the excited state
deactivation pathways and their corresponding dynamics in gold nanoparticles. In other
words, how efficient is the deactivation of a photoexcited gold nanoparticle? It is useful to
clarify what is meant by excited state deactivation in the context of the surface plasmon
resonance in metal nanoparticles. Because the surface plasmon resonance is a manifestation
of a coherent oscillation of the conduction band electrons, the loss of coherence is a form of
deactivation of the excited state and it may have observable effects. However, this loss of
coherence does not involve any energy redistribution, but merely the change of the plane

151

in which each electron oscillates (i.e. the change of the plasmon wave vector), thus leading
to the loss in coherence. This process is very fast, on the order of a few femtoseconds. We
are instead interested in the deactivation of the NP excited state via energy dissipation
through a charge transfer and the discussion in this section focuses on this process only.
The charge transfer for the equilibration of the photoexcited electrons in the Au NP
after photoexcitation is electron-electron relaxation. The high energy electrons after the
photoexcitation can undergo collisions with other electrons present in the volume of the
nanoparticle, leading to the partition of the energy between the electrons. This process
leads to a change in the energetic distribution of electrons from the highly non-thermal
distribution present immediately after the photoexcitation to a statistical Fermi-Dirac distribution with a high temperature Fermi level. These hot electrons further lose their kinetic
energy due to collisions with the ionic crystal lattice of the NP. This process, usually referred
to as electron-phonon relaxation, leads to the lowering of the Fermi level and thermalization
of the crystal lattice of the nanoparticle.[153] Hodak et al. showed that the electron-phononrelaxation time constant in gold NPs did not depend on the size of nanoparticles for samples
within the 2.5 nm to 120 nm size range,[8] and that its value (0.7 ps) was very similar to
that measured for bulk gold films.[154] Since higher laser power causes a higher temperature jump of the electrons after electron-electron relaxation, the electron-phonon-relaxation
time constant depends on the power of the excitation beam, as shown experimentally by
various researchers.[153, 8, 155] A spectacular phenomenon related to the heating of the
crystal lattice of gold NPs due to the electron-phonon relaxation has been demonstrated by
Hodak et al..[156] The researchers observed coherent oscillations in the signal of the surface
plasmon resonance band bleach in a femtosecond transient absorption experiment.

152

The induced collective electron oscillations associated with the surface plasmon resonance give rise to induced local electric fields near the nanoparticle surface. The induced
electric field originating from the charge separation in the nanoparticle during the plasmon
resonance oscillations is very large at very small distances from the surface. For silver
nanoparticles the values of the induced field can be tens of times larger than the incident
electric field values. Hao and Schatz performed calculations for a silver sphere with a 20
nm diameter and found that due to the surface plasmon resonance the incident electric
field is enhanced by 13 times at the immediate particle surface.[157] This enhancement
factor quickly drops to smaller values as the distance from the surface increases.[157, 158]
These enhanced local fields are responsible for increased rates of field-dependent processes
at surfaces of nanostructured metals.
While phenomena in which the local field effect plays a crucial role include surfaceenhanced photochemistry and second-harmonic generation perhaps the most celebrated analytical technique based on the local electric-field enhancement by metal surfaces is SurfaceEnhanced Raman Spectroscopy. Jeanmaire and Van Duyne found in the late 1970s that
pyridine molecules physisorbed onto a rough silver electrode exhibit an unusually strong
Raman signal.[159] It is agreed today that the enhanced intensity of the Raman scattering
signal of molecules adsorbed on rough metal surfaces is largely due to the enhanced local
field effects in the close proximity of the nanostructured metal surface. These signal enhancements can be as large as 1014 , of which a factor of 107 − 108 is attributed to the
local field effects.[160] The large improvement in the detectability afforded by the signal
enhancement resulted in a number of analytical techniques, including methods allowing one
to probe single molecules.[160]

153

7.3.2 Localized Surface Plasmon of Hollow Gold Nano-shell
The surface plasmon resonance absorption of the nonspherical nanostructures strongly depends on the shape or the size of the nanomaterial [161, 162, 163, 164, 165, 166, 167, 168,
169, 170, 171], and the surface plasmon resonance of various metal nanostructures has been
successfully demonstrated: nanorods, nanowires, nanocages, nanospheres, nanoprisms, and
nanoplates or sheets [172, 173, 174, 175, 176]. A hollow gold nano-shells (HGNs) is another
example having a unique capability for the surface plasmon applications because HGNs
have a broadly tunable surface plasmon resonance in the entire visible to near infrared
depending on both their core diameter as well as the shell thickness. Fig. 7.6 illustrates
the resonance mode of electrons in HGNs and the UV-visible adsorption spectra of nine
HGN samples with varying diameters and shell thickness.[177] The diverse surface plasmon
resonance absorption of HGNs is the result of multiple resonances in the structure, and the
mechanism of the diverse surface plasmon resonance generation can be understood by a
plasmon hybridization model [178, 179, 180, 181].
The highly geometry-dependent plasmon response of HGNs can be seen as an interaction between the essentially fixed-frequency plasmon response of a nanosphere and that of
a nano-cavity (Fig. 7.7). The sphere and cavity plasmons are electromagnetic excitations
that induce surface charges at the inner and outer interfaces of the metal shell. Because
of the finite thickness of the shell layer, the sphere and cavity plasmons interact with each
other. The strength of the interaction between the sphere and cavity plasmons is controlled
by the thickness of the metal shell layer. This interaction results in the splitting of the plasmon resonances into two new resonances: the lower energy symmetric or bonding plasmon
and the higher energy antisymmetric or antibonding plasmon (Fig. 7.7). The different com154

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Figure 7.6 Hollow gold nanoshell (HGN) surface plasmon resonance. (a) Schematic illustration of localized surface plasmon oscillation induced by an oscillating electric field in
a hollow gold nanoshell(HGN). The displacement of conduction electron cloud relative to
the nuclei is shown. The frequency of the localized surface plasmon resonance is denoted
ωp .(b) a UV-visible absorption spectra of nine HGN samples varing diameter and wall
thickness.[177]
155

binations of the nanosphere and the nano-cavity geometries generate the diverse plasmon
responses at different energies.

7.3.3 Surface Plasmon Mediated Charge Dynamics of Au Nanoparticle
Decorated SiO2 /Si Interface
From section 7.3, it is shown that there are two non-mutually exclusive channels of charge
transfer between the nanoparticle/semiconductor interface. In this section, we investigate
how these channels will be enhanced by the SPR excitation. To evaluate the SPR enhancement effect, we monitor the correlation between the SPR intensity and the transient surface
voltage (Vs ) on nearby silicon substrate using UEDV technique.
The wavelength λ of the incident laser pulses is varied from 400 to 800 nm using an
optical parametric amplifier (OPA), while keeping the fluence F at a constant value of 4
mJ/cm2 . The spectrum of maximum Vs obtained at different λ exhibits a Gaussian-like
function centered at 525 nm, as depicted in Fig. 7.8(a) (green curve). This excitation
spectroscopy of Vs has a peak similar in position and bandwidth to that of the light absorption spectrum measured in water (red curve in Fig. 7.6(a)) [155]. The strong resonance
at λ ∼525 nm is identified as the dipolar resonance mode - a dominant extinction mode for
particle smaller than 50 nm.
On the other hand, the photovoltage spectrum does not contain the background seen in
the optical measurement. The lack of non-SPR background in photovoltage measurement
is a strong indication that surface charge dynamics is driven by dipolar resonance structure
highly localized at the interface between Si and the nanoparticle. In contrast, the farfield absorption response obtained in optical spectroscopy has components not necessarily

156

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Figure 7.7 An energy diagram of plasmon hybridization in a HGN describes the interaction
between the metal sphere plasmon and cavity plasmon in bulk metal. Two HGN plasmon
modes are an antisymmetrically coupled (antibonding) ω+ plasmon and a symmetrically
coupled (bonding) ω− plasmon.

157

(b)

Absorption, A.U.

(a)
Bulk Si
Bulk Au

SPR

(I)

(II) - - - -Near-field
induced

Au NP+water
SPR

Au
valence band

Au
NP
Si

Vs, A.U.

Si
conduction band

Si
valence band

AuNP+Si 115 K
AuNP+Si 300 K

400 450 500 550 600 650 700 750 800

Au NP
SPR field

Si

Wavelength (nm)
Figure 7.8 Ultrafast transport at gold nanoparticle (NP)/SAM/silicon interface near surface
plasmon resonance (SPR) excitation. (a) The maximum transient photovoltage response
near SPR excitation, as compared to the absorption of the similar nanoparticles in water,
bulk gold, and silicon substrate. It is evident that while both show characteristic SPR peak
at ∼525 nm the nanoparticles Vs spectrum at surface (colored in green) lacks the background seen in the optical absorption spectrum of similar nanoparticles in water (colored
in red). (b) The enhancement of hot carrier generation at Si surface (channel II) can be
achieved via SPR evanescent field within the Si surface or charge carrier injection from
highly excited Au nanoparticle (channel I).

158

localized at the interface. The photovoltage measurements at 400 and 800 nm, both of
which are far off from the dipolar resonance spectral range, are nearly an order of magnitude
smaller than that at dipolar resonance (at 525 nm). Therefore, the near-field enhancement
factor of photocarrier generation at Si surface by dipolar resonance excitation is at least a
factor of 10.

7.3.4 Plasmon Mediated Spectral Hole Burning of Hollow Gold Nano-shell
on Si/SiO2 Surface
Potential application of HGNs is a drug delivery agent. HGNs encapsulate a drug inside of
the shell or HGNs carry a drug attached on the outer surface. In 2010, Lu et al. successfully
bioconjugated HGNs with siRNA on the outer surface and triggered a photothermally
induced siRNA release via pulsed laser irradiation [182]. If drug molecules are encapsulated
inside the HGNs, then the triggering mechanism to release the drug molecules on the target
location is required. One possible triggering method is laser-induced fragmentation of the
HGNs. In the research reported by Lu et al. [182], the pulsed laser irradiation can lead to
fragmentation of the HGNs. There were indications of solid AuNP formation due to HGN
fragmentation, but the detailed fragmentation mechanism is still not well understood.
Using ultrafast electron diffraction (UED) and scanning electron microscope (SEM),
we investigate the photo-induced structural changes of HGNs. The HGNs samples were
prepared by Damon Wheeler in Jin Zhang‘s group at University of California–Santa Cruz:
using size controlled cobalt nanoparticle templates, the gold nanoshell is grew on the surface
of the cobalt nanoparticle template, and the core cobalt template can be removed with the
a chemical reaction [183, 184]. The HGN diameter is controlled by the size of the cobalt

159

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Figure 7.9 (a) The statistics of HGNs diameter before fs laser irradiation and after irradiation (the number of HGN sampling is ∼700 individual HGNs in each case), (b) SEM
image of the morphology of HGNs distribution on the SiO2 /Si substrate and the scale bar
corresponds to 1µm, (c) and (d) are the SEM image of HGNs before and after irradiation,
respectively, and the scale bar corresponds to 100 nm.
160

nanoparticle templates and the shell thickness is controlled by the gold solution concentration. In UED experiment, which is a collaboration between myself and Dr. Kihyun Kim
and Terry Han in our group, HGNs are deposited on the functionalized silicon substrate,
and the deposited HGNs are secured by the van der Waals force between the HGN and the
substrate (the sample preparation procedure will be presented in the next paragraph.). This
secured HGN structure on the substrate allows us define the irradiated and non-irradiated
area for UED experiments. Using SEM, we directly image and compare the irradiated and
non-irradiated samples after UED experiment. Also, using UED experiment, we quantify
the nonlinear response of lattice temperature and surface charge dynamics with different
wavelength fs-laser pump irradiation (600 - 800 nm).
The sample preparation procedure has been adapted from wet chemistry methods [185]
that are now commonly employed in fabricating ordered 2D assembly of nanoparticles on
substrates [186, 149, 187, 188, 189]. The process can be broken down into 3 steps as
described below.
1. Surface pre-treatment: Silicon wafers are cleaned by ultrasonic agitation in acetone
and then in methanol to remove macroscopic contaminants. Thereafter, they are carried
through a modified RCA-like process [190, 191] to throughly clean the surface of all organic
and inorganic residues. This involves immersion in the following solutions for 10 min each:
1. H2 SO4 /H2 O2 (7:3), at 90◦ C to remove organic residues.
2. 40% NH4 F solution in deionized (DI) water at room temperature, to remove the
native oxide layer on silicon.
3. NH4 OH/H2 O2 /H2 O (1:1:6) at 90◦ C to remove metallic contaminants and establish
a fresh, thin (1-2 nm) oxide layer with hydroxyl (-OH) coating.
161

4. HCl/H2 O2 /H2 O (1:1:5) at 90◦ C to remove final trace metal & ionic contaminants
introduced in the steps above.
The substrate is throughly rinsed in copious amounts of DI water in between each of the
above mentioned steps, which finally results in a clean, hydroxyl (-OH) terminated silicon
substrate.
2. Surface functionalization: The organic molecule used in this study for surface functionalization (creation of the SAM layer) is (3-Aminopropyl) trimethoxysilane
[H2 N(CH2 )3 Si(OCH3 )3 ] abbreviated as APTMS. Other organosilane molecules with differing alkane chain lengths may also be employed. The clean substrate is immersed for
60 min in a dilute solution (≈ 9mM) of APTMS in DI water, with some acetic acid to
enhance functionalization. (APTMS:Acetic Acid:DI water = 1:5:480). This is followed by
a thorough rinse in DI water and drying under dry-nitrogen gas. It is then heated to 120◦ C
to strengthen the siloxane (Si-O) bond between the terminal silane group of the SAM and
the Silicon substrate [186].
3. HGN deposition: Finally, the surface functionalized substrate is immersed in a citrate
stabilized colloidal HGN solution for a period of 1-2 hours to allow the HGNs to anchor
onto the SAM surface. Immersion of the substrate in the solution protonates the terminal
amine (NH2 ) groups of the SAM molecules to form positively charged NH+
3 end groups
[188]. The HGNs, on the other hand, are covered by negatively charged citrate ligands
that stabilize them against agglomeration via mutual repulsion. These negatively charged
ligands bind electrostatically to the protonated NH+
3 groups of the SAM, thus immobilizing
the HGNs on the surface [189]. There would of course be a large number of SAM molecules
underneath a single HGN to help anchor the nanocrystal firmly onto the substrate. Any

162

loosely bound nanocrystals are removed by a final rinse and dry cycle. Figure 7.9 shows
the sample morphology obtained by this procedure.
The SPR frequency of the HGNs used in our experiment is 654 nm which is red-shifted
into NIR from the ∼520 nm resonance of typical solid Au NPs. The statistics of irradiated and non-irradiated HGNs from SEM images (∼700 HGNs sampling in each case)
in Fig. 7.9(a) clearly shows that ∼35 nm outer diameter of non-irradiated HGNs on the
silicon substrate are transformed into ∼25 nm diameter HGNs after irradiation. The SEM
images in Fig. 7.9(c) and Fig. 7.9(d) also show that the HGNs’ outer diameter is reduced
and appearance of larger clusters may be formed through melting of aggregated HGNs.
Due to the structure transformation of HGNs under irradiation, the UED results indicate
the new state achieved after the systems undergoing transformation. Using UED, we could
quantify a non-linear response as a result of these changes, via lattice temperature change
and the transient surface voltage change as a function of applied excitation wavelengths
and fluences.
The lattice temperature microscopically corresponds to the random atomic vibration,
and the random vibration diminishes the intensity of the diffraction spectra by a Debye2 2
Waller factor (DWF), e−2M , where M = s 4u¯ , u¯2 is the mean-square atomic displacement
perpendicular to the reflecting planes, and s = 4π sin( 2θ ) is the momentum transfer associλe
ated with the maxima located at the scattering angle. Thus, the change in the mean-square
atomic displacement, ∆¯
u2 , measured relative to the unperturbed state at negative times,
determines the rise in lattice temperature and can be calculated from the diffraction intensities as ln[I(t)/I0 ] = −s2 ∆u2 /4.
With HGNs structure dynamics induced by off-resonance pump, 800nm, we observe

163

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Figure 7.10 (a) Debye-Waller factor(DWF) analysis of the diffraction intensity drop. This
indicates the lattice temperature as a function of the irradiation fluence. (b) DWF profiles
of different wavelength pump laser are fitted with power function, y = axb . (c) Transient
surface voltage (Vs ) generation as a function of different laser wavelength.
164

that ∼15 ps after irradiation, photoexcited HGNs have the maximum change in lattice
temperature and transient surface voltage. We fix the 15 ps time delay from the irradiation
moment, and observe the lattice temperature and transient surface voltage with different
pump laser wavelength and the fluence, shown in Fig. 7.10. In Fig. 7.10(a) and (b), we
can see that lattice temperature with on-resonance pump, 654 nm, is not linear response
(2.7±0.8 power dependence) in the fluence scan whereas, with off-resonance, it is linear
response. This non-linearity indicates that the lattice heating and restructuring of HGN
are mediated by surface plasmon resonance. In Fig. 7.10(a), the lattice temperature change
with off-resonance pump laser irradiation at low fluence is higher than that of on-resonance
pump laser irradiation, and this measurement shows the similarity to the spectral hole
burning. Moreover, the transient surface voltage (Fig. 7.10(c)) induced by different pump
wavelength also shows the spectral hole burning feature. The drastic decrease in transient
surface voltage at 654 nm indicates disappearance of HGNs absorbing at the surface plasmon
resonance frequency.
The persistent spectral hole burning characteristics of HGNs induced by fs laser pulse
has been proposed to account for melting of HGNs [183]. Although we could not observe the
structure dynamics directly, based on ultrafast electron diffraction responses and scanning
electron microscope data, we have shown that HGNs structure is modified by fs laser, and
the shrinking of the size caused thickening in shell wall and the blue shift of surface plasmon
resonance frequency.

165

7.4 Summary
We successfully extend the UEDV methodology to investigate ultrafast charge transfer process induced by fs-laser at various nanostructures/molecule/Silicon interfaces. We have
identified two non-mutually exclusive channels of charge transfer at the interfaces, and the
measured molecular resistivity is consistent with the steady-state measurement at the moderate laser irradiation. A factor of 10 SPR enhancement of the surface charge transfer is directly measured and the low non-SPR background in the surface photovoltage measurement
indicates that the surface charge dynamics is driven by dipolar resonance structure highly
localized at the interface between Si and the nanoparticle. While the current applications
of UEDV are concentrated in cases where the charge transfers are driven in an ensemble of
nanosturctures, the mechanisms associated with different microscopic processes can still be
discerned through examining the fine voltammetry features, such as the ultrafast charging
dynamics in an individual nanoparticle interface. The future application of this methodology lies in a more definitive, site-selected voltammetry study on a single nanostructured
interface, which can be enabled by the development of nanometer scale high-brightness
ultrafast electron beam system for ultrafast electron microscope [56, 192, 68].

166

Chapter 8
Preliminary Experiment with
High-Brightness Electron Beam
System
In this chapter, we discuss the latest progress in implementing experiment protocols for
achieving high spatial and temporal focusing for ultrafast electron microdiffraction experiments.

8.1 Shadow Imaging and Beam Alignment
An important target of our high-brightness electron beam system is to achieve microscale
high–dose beam delivery to investigate structural dynamics at selected particles or domain
sites. First, we have established an experimental protocol for identifying such particles or
domains using the flexible electron optical arrangement, in order to optimize our beam for
conducting ultrafast measurements of the precise sites. The shadow imaging of microscale
samples can be readily implemented by adjusting the focal plane of the beam relative to
the sample plane. Fig. 8.1 shows that, by using an objective lens, we can directly monitor
the sample in situ by projection shadow imaging. Fig. 8.1(a) and Fig. 8.1(b) show the

167

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Figure 8.1 CeTe3 sample image on 1000 mesh TEM grid: (a) optical microscope image, (b)
Projection Shadow image of a full grid with high-brightness UED, (c) Projection shadow
image with 50 µm aperture selected area, a white square shown in (b).
optical image and the corresponding shadow image of the sample on a 1000 mesh full TEM
grid using the projection imaging with a full beam crossing between the sample and CCD
camera. Fig. 8.1(c) shows the shadow image with a 50 µm aperture to select a single sample
for diffraction investigation: the location of the sample is marked as the white square inside
the full image of Fig. 8.1(b). The TEM grid bar thickness is 6 µm, and the square opening
is 19 µm, which provides a measurement of the actual sample size. From the contrast, a
calibration can also be established to provide a thickness map of the sample. The shadow
image capability thus provides a convenient way to identify the sample for a pump-probe
overlap and to characterize the beam properties at the sample plane.
Shadow imaging can also serve to diagnose the beam properties. We note that, from

168

Fig. 8.1(b), we can observe image distortion of the TEM grid at four edges: the TEM grid
shadow image is shown as an arc, not a straight line (pincushion). This image distortion
is from the field distortion caused by the first deflector rods– an artifact to be corrected in
the future. However, the distortion occurs only at the edges of the full scale view, whereas
in practice only a small region is inspected. How much the image distortion can affect our
experiment is still under investigation. In the design of the deflector, there is a 2.5 mm
diameter beam alignment pinhole centered around the two pairs of deflector rods, separated
by 2.0 mm each. The rods are mounted 30 mm below the aperture. Although the beam
size at the deflector level is ∼300µm, it is possible for the electron pulse to travel close
to the deflector rod, breaking the symmetry (1o tilt causes ∼450µm shift at the deflector
location). Therefore, it might be necessary to increase the deflector rod gap and/or reduce
the distance between the aperture and the deflector rods.

8.2 Convergent Beam
To evaluate the feasibility for ultrafast electron microdiffraction, the electron pulse is tightly
focused on the sample level with different applied currents of Obj. ML. Fig. 8.2 shows the
direct beam images with the 1000 mesh TEM grid on the CCD screen. With the 170 µm
aperture, the electron beam can be focused down to ∼7 µm (FWHM, Obj.ML=3.4 A) on
the sample, and the electron dose D is 2042 electrons/µm2 which is 3 order higher than
other ultrafast electron diffraction systems (see Table 5.2) with the compromise for 50%
reduction of Lt , 0.474 nm, as shown in Table 8.1. Furthermore, we can fully manipulate
the beam properties with different Obj.ML currents and different aperture sizes. As shown
in Table 8.1, using an Obj.ML=2.9 A, we can focus the electron beam down to ∼15 µm
169

on the sample. With this condition, the electron dose D is still 449 electron/µm2 and the
coherence length Lt is 0.568 nm with the divergence angle ∆θ= 4.0 mrad, calculated by
Lt =

h
derived from Eq. 3.31 and Eq. 5.11. Also, with different size of the aperture,
2Pz ∆θ

50 µm aperture offers us the longer coherence length 0.689 nm with maintaining the electron
does 260 electron/µm2 as shown in Table 8.1. With the adjustment of Obj.ML focusing
(divergence angle), the diffracted electron beam signal can be enhanced by a factor of ∼50
while maintaining the coherence length ∼1 nm. This is enough flexibility to manipulate
electron pulse phase space, which enables us to investigate various materials using different experiments requiring high spatial and temporal coherence and/or high-density beam
optimized for microdiffraction.
Aperture Obj.ML
(µm)
(A)

N

D
(e/µm2 )

∆θ
(mrad)

σ
(µm)

εx,n
(nm)

Lt
(nm)

B4D
(e/nm2 )

50

2.9

5000

260

3.3

2.1

3.673

0.689

370.640

170

2.9

80000

449

4.0

6.4

13.568

0.568

434.569

170

3.4

80000

2042

4.8

3.0

7.632

0.474

1373.451

Table 8.1 The electron beam properties with different conditions
N is the number of electrons per pulse.
2
D=N
A is the electron dose, A = π(HWHM) .
∆θ is a half divergence angle.
σ is the σ-width of the electron spot on the sample, not FWHM.
εx,n is the normalized transverse emittance.
Lt is the coherence length.
B4D = 2N is the 4D brightness.
εx,n
Fig. 8.3 shows the convergent beam diffraction of TaS2 and CeTe3 samples with 50
µm aperture. The convergent beam diffraction pattern shown in Fig. 8.3(a) is not clear
170

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Figure 8.2 Convergent beam test to maximize the electron dose Ne /A. With the constant
current of CML1=1.0 A and CML2=2.7 A and 170 µm aperture, the electron beam is
focused on the sample position with adjusting Obj. ML current shown in the each image.
Minimum beam size is smaller than 7 µm which is the limitation of our measurement
resolution. This gives us D > 2000 electron/µm2 . (The whole image is the same size
region, 505×620 pixels.)

171

enough due to insufficient exposure time (500 ms) which is limited by the strong main beam
intensity and a sample stage instability (random vibration). In this first setup, the main
beam cannot be fully blocked by the beam trap because of the limitation of the beam trap
motion range. Also, because the beam size of the focused electron beam has reached ∼1
µm scale, the sample holder and electron beam stability become central for the diffraction
pattern quality. To achieve convergent beam diffraction, we temporarily implement a beam
trap extension to block the beam and a Teflon spacer underneath the sample transfer
arm to minimize the vibration. With the implementation, the convergent beam diffraction
pattern of CeTe3 shown in Fig. 8.3(c) is significantly improved. Currently, we have not fully
achieved the convergent beam diffraction dynamics yet, but we have seen the feasibility of
the high-brightness electron beam system for convergent beam microdiffraction to study
micron or sub-micron scale materials. To ultimately resolve these problems for the ultrafast
microdiffraction experiments, we may consider implementing the following setup: (1) a new
beam trap considering with the convergent main beam position, (2) a more stable Obj. ML
with a fine feedback to provide stable lens focusing at high magnification (or focusing), (3)
a retractable fork to stabilize the stage.

8.3 RF Compression of High-Brightness Electron Beam: VO2
We have implemented our first characterization of RF compression of a high-brightness
electron beam based on measuring the temporal response of a well-defined ultrafast structural phase transition. While indirect, this measurements allow us to understand the limit
of electron beam performance in a diffraction experiment. Our ultimate diagnosis is based
on the shadow imaging technique [98] employing a diagnostic imaging electron gun at the
172

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Figure 8.3 (a) Convergent beam diffraction of TaS2 with 50 µm aperture (exposure time 500
ms). Hexagon indicates the charge density wave (CDW) diffraction peak. (b) Parallel beam
diffraction of TaS2 with 170 µm aperture (exposure time 2 s). Upper right panel is zoom-in
image of the lower left red square showing CDW diffraction peak. (c) Convergent beam
diffraction of CeTe3 with 50 µm aperture (exposure time 4 s) after the implementation with
the beam trap extension and Teflon spacer to minimize the sample column vibration.
perpendicular direction of the high-brightness electron beamline direction (see Appendix
B.2). The shadow imaging technique will allow direct characterization of beam transverse
and longitudinal profiles under RF compression. In the following, we report the results of
temporal characteristics based on UED experiments on optical response of a VO2 , of which
the phase transition time is within hundreds of femtoseconds [193, 194]. According to the
reported phase transition time of the VO2 sample, we can deconvolute the time resolution
of the high-brightness electron pulse with a different level of RF compression.
Vanadium dioxide VO2 is one of the prototypical systems which has the metal-insulator
transition (MIT), from a metallic rutile structure into an insulator monoclinic structure at
a critical temperature (Tc ≈ 340K). There has been extensive debate over whether the
origin of the VO2 MIT is Pierls [195, 196] or Mott-Hubbard [197] physics. However, the
MIT in VO2 is clearly a structural transition from the rutile structure (> 340K) to a
monoclinic structure (< 340K), in which two V atoms in each V chain are dimerized along
the c-axis with a twisting of V-V pairs due to an anti-ferroelectric shift toward the oxygens
173

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Figure 8.4 (a) Crystal structure of VO2 in metallic rutile phase: the gray ball is the V
atoms and red ball is O atoms. The arrows are the dimerization direction of V atoms in
V chain along c axis. (b) and (c) are the schematic illustration of VO2 density of state of
VO2 in metallic and insulator phase, respectively.

174

lying along an axis perpendicular to the c-axis, as shown in Fig. 8.4(a). The answer to the
argument about the MIT microscopic pathway is how we discriminate between two types
of orbitals and corresponding bands: (1) lower energy π ∗ (dxy ) orbitals in t2g orbitals with
direct overlap between the neighboring V in V chain, and (2) d|| (dxz , dyz ) orbitals in

t2g orbitals. In the rutile phase, the d|| band overlaps with the π ∗ band, resulting in an
isotropic metallic state shown in Fig. 8.4(b). The twisting in the monoclinic phase increases
the V-O hybridization and moves the π ∗ band up above the Fermi level. Therefore, only
the d|| band is partially occupied, and the band is split by the dimerization, leading to
insulating state, shown in Fig 8.4(c). The V-V dimerization can be directly monitored by
the diffraction peak after photoexcitation, and this phase transition time is short enough
to measure the time resolution of the current setup of high-brightness UED.
Fig. 8.5 shows the optical image of VO2 film sample and a diffraction pattern of the
ground state of the VO2 . The 50 nm thickness VO2 film is grown on the 5 nm thickness
amorphous silicon membrane using pulsed laser deposition, and the VO2 film on the silicon
membrane is poly-crystaline, so the diffraction pattern corresponds to a powder diffraction
image as shown in Fig. 8.5(b). We integrated the diffraction ring as a function of the
wave vector, which corresponds to the ring radius in the real space image of Fig. 8.5(b), to
produce the profile shown in Fig. 8.5(c). The two small peaks at ∼3.35 ˚
A−1 and ∼4.11
˚
A−1 correspond to the V-V dimerization symmetries, ¯30¯2, 31¯3, respectively. After photoexcitation, the dimerization in monoclinic insulator phase is instantaneously dissociated
completely due to perturbation in electron-electron and electron-phonon coupling initiated
by photon energy. Then we can directly monitor the phase transition dynamics with the
variation of diffraction peak intensity.

175

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Figure 8.5 (a) Optical microscope image of VO2 film sample which is grown on the 5 nm
thickness amorphous silicon membrane. The eight square windows are the VO2 film with
5 nm thickness Si membrane and a long black rectangle is a broken window. Each square
window size is 100 µm × 100 µm, and the displacement between windows is 200 µm, (b)
Diffraction pattern of poly-crystalline VO2 film, (c) Integrate diffraction intensity profile
along the wave vector corresponding to the radial direction in real space image. The arrows
indicate the V-V dimerization symmetry peaks in a monoclinic insulation phase (¯30¯2, 31¯3).

176

To run the experiment with RF compression, the first requirement is the synchronization
of the electron pulse and RF field as discussed in Chapter 4 and 5. The phase mismatch
between electron pulse arriving time and RF field causes the COM mass velocity change of
the electron pulse, and this COM velocity can be accurately measured with the diffraction
peak position in real space image because the COM velocity determines the kinetic energy
of an electron pulse and the kinetic energy determines the scattering angle:

λ= √

h
,
2me E

1
sin θB = |K|λ,
2

(8.1)
(8.2)

where me , E are electron mass and the kinetic energy of electron pulse, respectively, K is
the change of the wave vector due to diffraction from the certain symmetry lattice plane,
and θB is Bragg angle. In other words, if the electron kinetic energy is changed, then
the diffraction ring radius in Fig. 8.5(b) is changed. In order to synchronize the phase
between an electron pulse and RF field, we adjust the 266 nm laser path length to perfectly
match the diffraction patterns with RF compression and without RF compression. With
the optimized phase condition of the RF compression, a longitudinal length of the electron
pulse has to be focused on the sample position, and the focal length fL of RF compression
[81] shown in Eq. 4.18 can be controlled by the RF field E0 .
Fig. 8.6 shows the phase transition dynamics of VO2 induced by 800 nm, 45 fs laser
pulses and measured with electron pulses compressed by different RF power. To avoid
damaging the sample, which is only a few tens of nanometer thick, we maintained a pump
laser fluence of 3 mJ/cm2 (the damage threshold ∼5 mJ/cm2 ). The phase transition
177

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!"#$#'%$&$
!"#$(%%$&$

Figure 8.6 The photo-induced phase transition measurement with VO2 with different RF
power compression of ∼7×104 electrons per pulse: the measurements are relative diffraction
peak intensity change as a function of the time.

178

Figure 8.7 Pulse duration measurement from VO2 phase transition: VO2 phase transition
experiment is performed with ∼7×104 electrons per pulse.
response is determined by a fit using an Error function:
x−x
√ 0
2
2A
2σ e−t dt,
f (x) =
π 0

(8.3)

where A, x0 , σ are fitting parameters. Time resolution of the high-brightness electron pulse
is extracted based on the response time σ and deconvoluted it from the reported transient
response of VO2 samples, which is on ≤ 1 ps timescale [193, 194]. As shown in Fig. 8.6,
the timescale of transient response is reduced with increasing RF power, indicating the
compression of the probing electron pulses.
Fig. 8.7 shows the results of RF compression using the values of σ extracted from the
179

Error function fitting. Without RF field, the electron beam (with ∼7×104 electrons per
pulse) has developed a pulse duration of 33 ±12 ps (in σ–width) from the source to the
sample plane. At an RF power of 210 W, the electron pulse is compressed to 10 ± 4 ps,
and at 316 W, the pulse is further reduced to 5 ±2 ps.
In Fig. 8.7, it is not clear to tell whether the RF compression has reached optimal
temporal focusing at 316 W RF power. We note that, according to the analytical Gaussian
model prediction [68], 520W RF power is required for optimal temporal focusing at the
sample plane with a pulse duration below 1 ps, limited by the phase jitter between the
electron pulse and RF field (see Chapter 5). The lowest pulse duration achieved is primarily
limited by system instability which we have identified. A periodic breathing motion (∆θ)
of the diffraction pattern was observed, and we correlated the electron pulse arriving time
fluctuation at the sample plane to the periodic motion (∆θ) of the diffraction pattern.
According to Eq. 5.10, the observed diffraction pattern position shift (∆θ) is directly related
to the electron pulse energy fluctuation ∆E which can be translated to an electron arriving
time fluctuation (as shown in Fig. 5.13(b)). The results of the electron pulse arriving time
fluctuation are depicted in Fig. 8.8(a), where there is a periodic oscillation with a period
of 2.5 minutes. The standard deviation σ= 3.5 ps of the oscillation is quite consistent
with our pulse duration measurement. The oscillation is caused by active temperature
regulation of the RF station (the red line in Fig. 8.8(b) is before correction). We improved
the temperature stability by adjusting the gain of the temperature control unit (the blue
line in Fig. 8.8(b) is after correction). We are currently performing another pulse duration
measurement to check the improvement.

180

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Figure 8.8 (a) Electron pulse arriving time fluctuation during the experiment. Zero fluctuation means the electron energy is exactly 100 keV, and due to the phase mismatch, the
COM velocity of electron pulse is fluctuated. (b) RF phase stability monitor. The red line
shows the phase fluctuation before temperature instability correction and blue line shows
the phase fluctuation after the correction.

181

Chapter 9
Summary and Outlook
To achieve the direct visualization of the ultrafast dynamics, we have developed the RFenabled high-brightness ultrafast electron microdiffraction system as the first step. The
high-brightness electron beam system with a sub-relativistic 100 keV electron beam has successfully achieved a beam intensity ∼5×106 electron pulse achieving a transverse emittance
εt ∼ 0.167µm. The high-brightness electron beam system is fully capable to manipulate the
electron pulse phase space. With a parallel electron beam, we have achieved Lt = 1.2 nm,
at Ne =105 and an electron dose D= 5 electron/µm2 . With a convergent electron beam, we
have achieved that, (1) at σ ∼3 µm, an electron does D ∼2000 electron/µm2 and Lt ∼0.5
nm, and, (2) at σ ∼5 µm, D ∼250 electron/µm2 and Lt ∼1.0 nm (cf. D of conventional
UED systems is ∼1 electron/µm2 at σ ∼300 µm.). This flexibility of the high-brightness
electron beam system enables us to investigate various materials using operational modes
emphasizing high spatial and temporal coherence and/or high-density beam optimized for
ultrafast electron microdiffraction. Although further optimization for RF compression is
required, we have demonstrated the ∼105 electron pulse can be compressed down to ≤5 ps
pulse duration in our first test. A further RF compression experiment is ongoing to achieve
the target of ≈200 fs, set by the RF station stability in our system.
Furthermore, we are able to extend the diffractive voltammetry methodology to investigate molecular charge transport process under a strong field induced by laser at a gold
182

nanopaticle/molecule/Silicon interface. At the moderate field circumstance, we obtain similar molecular resistivity as the steady-state measurement. While the current applications
of diffractive voltammetry are concentrated in cases where the charge transfers are driven in
an ensemble of nanosturctures, the mechanisms associated with different microscopic processes can still be discerned through examining the fine voltammetry features, such as the
ultrafast charge dynamics in an individual nanoparticle interface. The future application of
this methodology lies in a more definitive, site-selected voltammetry study on an individual
nanostructured interface, which can be enabled by the development of a high-brightness
electron beam system in an ultrafast electron microscope setup capable of zooming in on
such features.
The work presented here represents the first step in realizing a high-brightness ultrafast
electron microscope. Key steps that are still needed to reach this ultimate goal include
further characterizing the correlated beam dynamics in full 6D phase space, and identifying the factors such as aberration and focusability limits in different operation regimes.
Interdisciplinary collaboration that pushes the boundaries of ultrafast science, acceleration
physics, and beam dynamics toward a more precise and flexible control of beam dynamics
is central for furthering the ultrafast imaging technologies using electrons.

183

APPENDICES

184

Appendix A
Diffraction Theory for Ultrafast
Electron Diffraction
Electron diffraction is one of the most powerful experiment tools for determining the structures. The electron is a low-mass, negatively charged particle, so it can easily be deflected
by passing close to other electrons or the positive nucleus of an atom. These Coulomb
interaction causes electron scattering, which is the process that makes electron microscope
feasible. The wave nature of electrons gives rise to diffraction effect, and this diffraction
effect creates electron microscope images or diffraction patterns. Therefore, it is essential
to understand both the particle approach and wave approach to electron scattering in order
to interpret all the information that comes from electron microscope. Electron scattering
from materials is a reasonably complex area of physics, but several references provide a detailed and rigorous treatment of the subject [198, 199, 200, 201, 202]. In following section,
a conceptual introduction to the phenomena of diffraction will be introduced.
A.1 Diffration and Reciprocal Lattice
In the electron microscope, we are mostly interested in scattered electrons which do
not deviate far from the incident-electron direction because these electrons includes the
information which we seek about the internal structure of the specimen. Other forms of
scattering, such as electrons which are scattered through large angle and electrons ejected
185

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Figure A.1 Different kinds of electrons scattering from the specimen
from specimen, such as secondary electrons, are also of interest although they are much
greater interest in the scanning electron microscope (SEM).
We represent incident and scattered electrons as beams of electrons, which are confined
to well-defined paths in the microscope. So the electrons that hit the specimen are called
incident beam and electrons scattered by the specimen are diffracted or scattered beams.
Electrons going through the specimen are separated into electrons without angular deviation and with measurable angular deviation. In the electron-scattering phenomena, there
are the most important terms elastic and inelastic scattering, describing scattering without
energy loss and with some measurable energy loss. We can also separate scattered electrons into coherent and incoherent. These distinctions are related since elastically scattered
186

electrons are usually coherent and inelastically scattered electron are usually incoherent.
Let‘s assume that the incident electron waves are coherent, that is, they are essentially in
phase with one another and of a fixed wavelength, governed by the accelerating voltage.
Then, coherently scattered electrons are in-phase and incoherently scattered electrons have
no phase relationship after interacting with the specimen. The various terms are defined
by the following general principles (Fig. A.1) :
1. Elastic scattering is usually coherent, if the specimen is thin and crystalline.
2. Elastic scattering usually occurs at relatively low angle(1◦ ∼ 10◦ ), i.e., it is strongly
peaked in the forward direction.
3. At higher angles(≥ 10◦ ) elastic scattering becomes more incoherent.
4. Inelastic scattering is almost always incoherent and is very low angle(< 1◦ ) scattering.
A.1.1 Diffraction of Waves and Reciprocal Lattice
The diffraction depends on the crystal structure and on the wavelength. At wavelengths
of incident electron beam, the superposition of the waves scattered elastically by the individual atoms of a crystal results in ordinary refraction. When the wavelength of the electron
beam is comparable with or smaller than the lattice constant, we may find diffracted beams
in directions quite different from the incident direction.
Consider parallel lattice planes spaced d apart (Fig.A.2). The electron beam is incident
in the plane of the paper. The toal path difference for the beams reflected from adjacent
planes is 2d sin θ, where θ is measured from the plane (Fig. A.2). Constructive interference
of the electron beam from successive planes occures when the path difference is an integer
number n of wavelength λ, so that
187

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Figure A.2 Derivation of Bragg equation 2d sin θ = nλ

2d sin θ = nλ

BraggLaw.

(A.1)

According to Bragg law, only certain angle θ of reflection from all periodic parallel
planes will add up in phase to give a strong reflected beam, and this is a consequence of
the periodicity of the lattice. Notice that the law does not refer to the composite of the
basis of atoms associated with every lattice point. However, the composition of the basis
determines the relative intensity of the various orders of diffraction from a given set of
parallel planes. We will discuss about this in section 4.1.3.
The Bragg derivation of the diffraction condition Eq. (A.1) gives a neat statement of
the condition for the constructive interference of waves scattered from the lattice points.
We need a deeper analysis to determine the scattering intensity from the basis of atoms,
which means from the spatial distribution of electrons within each cell. We know that a

188

crystal is invariant under any translation, T = u1 a1 + u2 a2 + u3 a3 , where u1 , u2 , u3 are
integers and a1 , a2 , a3 are the crystal axes. Local physical property of the crystal, such as
electron distribution (electron density), n(r), is invariant under T, n(r) = n(r + T). This
periodicity creates an ideal situation for Fourier analysis. The most interesting properties of
crystals are directly related to the Fourier components of electron density. We can represent
the periodic electron density n(r) in three dimensions:

n(r) =

nG exp(iG r),

(A.2)

G
where G is a set of vectors which makes n(r) is invariant under all crystal translation
T. The set of Fourier coefficients nG determines the scattering amplitude.
To proceed further with the Fourier analysis of the electron density, we must find the
vectors G of the Fourier sum n(r) =

nG exp(iG r). There is a powerful way to find

a set of vectors G with constructing a Reciprocal Space. Reciprocal lattice axis vecotors,
b1 , b2 , b3 are defined as :

a2 × a3
a3 × a1
a1 × a2
b1 = 2π
, b2 = 2π
, b3 = 2π
a1 a2 × a3
a1 a2 × a3
a1 a2 × a3

(A.3)

If a1 , a2 , a3 are primitive vectors of the crystal lattice, then b1 , b2 , b3 are the primitive
vectors of the reciprocal lattice. Each vector is orthogonal to two axis vectors of the crystal
lattice. Thus, b1 , b2 , b3 have the property

bi aj = 2πδij

(A.4)

where δij is Kronecker delta. Points in the reciprocal lattice are mapped by the set of

189

vectors

G = v1 b1 + v2 b2 + v3 b3 ,

(A.5)

where v1 , v2 , v3 are integers. A vector G of this form is a reciprocal lattice vector.
Every crystal structure has two lattices associated with it: the crystal lattice and the
reciprocal lattice. A diffraction pattern of a crystal is a map of the reciprocal lattice of the
crystal. A microscope image is a map of the crystal structure in real space. Two lattices
are related by the definitions Eq. A.3. Thus when we rotate a crystal in a sample holder,
we rotate both the direct lattice and the reciprocal lattice.
A.1.2 The Ewald Construction in Reciprocal Space
The set of reciprocal lattice vectors G determines the possible reflection of incident
waves. In Fig. A.3, the difference in phase factors is exp[i(k − k ) r] between beams
scattered from volume elements r apart. The wavevectors of the incident and outgoing
beams are k and k , respectively. We suppose that the amplitude of the wave scattered from
a volume element is proportional to the local electron density n(r). The total amplitude of
the scattered wave in the direction of k is proportional to the integral over the crystal of
n(r)dV times the phase factor exp[i(k − k ) r].
In other word, the amplitude of the electric or magnetic field vectors in the scattered
electromagnetic wave is proportional to the following integral which defines the quantify F
that we call the scattering amplitude:

F =

dV n(r)exp[i(k − k ) r] =

dV n(r)exp[−i∆k r],

(A.6)

where k − k = −∆k, or k + ∆k = k . ∆k is scattered vector which is the change in
190

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Figure A.3 The phase angle difference of incident beam is k r = 2π sin ϕ/λ and the path
difference at O and r is r sin ϕ. For diffracted beam, the phase angle difference is −k r.
The total phase angle difference is (k − k ) r, and the beam scattered from dV at r has
the phase factor exp[i(k − k ) r] relative to the beam scattered from a volume element at
the origin O.

191

wavevector.
When we put Eq. A.2 of n(r) into Eq. A.6, then we can get the scattering amplitude

F =
G

dV nG exp[i(G − ∆k) r].

(A.7)

When ∆k = G, the exponential in Eq. A.7 vanishes and F = V nG . This means that
scattering amplitude F is negligible when ∆k differs significantly from any reciprocal lattice
vector G.
In elastic scattering process, the magnitudes of k and k are equal with energy conservation law, and two conditions, k 2 = k 2 and ∆k = G gives us diffraction condition (If G
is a reciprocal lattice vector, then -G is also a reciprocal lattice vector.):

2k G = G2 .

(A.8)

The condition ∆k = G of diffraction theory can be expressed in another way called Laue
equations. This different representation is important because it gives us the geometrical
information. Take the scalar product of both ∆k and G with a1 , a2 , a3 . Then we get

a1 ∆k = 2πv1 ,

a2 ∆k = 2πv2 ,

a3 ∆k = 2πv3 ,

(A.9)

These equations imply a geometrical interpretation: the first equation represents that
∆k lies on a certain cone about the direction of a1 , second lies about a2 and third one lies
about a3 . Therefore, ∆k must satisfy all three equations, and it must lie at the common
line of intersection of three cones. Ewald construction helps us visulize the nature of the
accident that must occur in order to satisfy the diffraction condition in three dimension,

192

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Figure A.4 Ewald sphere construction: The points are reciprocal lattice points of the crystal.
The vector k is drawn in the direction of the incident beam, and the origin is chosen such
that k terminates at any reciprocal lattice points. We draw a Ewald sphere of radius
k = 2π/λ about the origin of k. A diffracted beam will be formed if Ewald sphere intersects
any other reciprocal lattice points. The Ewald sphere as drawn intercepts a point connected
with the end of k by a reciprocal lattice vector G. The diffracted beam is in the direction
k = k + G. The angle θ is the Bragg angle of Fig. A.2.

193

∆k = G.
We now construct the sphere of radius k. The sphere is known as the sphere of reflection so called Ewald sphere. The key point is that when the Ewald sphere intersects the
reciprocal lattice points, the diffraction condition, ∆k = G in Eq. A.8,is satisfied. ehen
combine the concepts of the reciprocal lattice, and Ewald construction to picture how the
intensity of each diffracted beam varies as we tilt the specimen or the electron beam. We
can see the position of a diffraction peaks move when the Ewald sphere is moved relative
to the reciprocal lattice. Also, if any points in the reciprocal lattice intersect the surface of
the Ewald sphere, the set of planes corresponding to the points must satisfy the diffraction
condition, Eq. A.8, and hence that the planes will diffract strongly.
A.1.3 Frouier Analysis of The Basis: Structure Factor and Atomic Form
Factor
When the diffraction condition 2k G = G2 , Eq. A.8 is satisfied, the scattering amplitude
Eq. A.6 for a crystal of N cells can be written as

FG = N

cell

dV n(r)exp[−iG r] = N SG .

(A.10)

The quantity SG is called the structure factor and is defined as an integral over a single cell,
with r = 0 at one corner. It is useful to write the electron density n(r) as the superposition
of electron density function nj associated with each atom j of the cell. If rj is the vector
to the center of atom j, then the function nj (r − rj ) defines the contribution of that atom
to the electron density at r. The total electron density at r due to all atoms in the single

194

cell is the sum
s
n(r) =
j=1

nj (r − rj )

(A.11)

over the s atoms of the basis. The decomposition of n(r) is not unique because we can not
always say how much charge density is associated with each atom.
The structure factor defined by Eq. A.10 can be written as integral over the s atoms of
a cell:

SG =

dV nj (r − rj )exp(−iG r)

j
=

(A.12)
exp(−iG rj )

dV nj (ρ)exp(−iG ρ),

j
where ρ = r − rj . Now we can define the atomic form factor as
fj =

dV nj (ρ)exp(−iG ρ),

(A.13)

integrated over all space. If nj (ρ) is an atomic property, fj is an atomic property. We
combine Eq. A.12 and Eq. A.13 to obtain the structure factor of the basis in the form

SG =

fj exp(−iG rj ).

(A.14)

j
Using the definition, rj = xj a1 + yj a2 + zj a3 of j-th atom, Eq. A.14 can be transformed
into
SG (hkl) =

fj exp(−2πi(hxj + kyj + lzj )).

(A.15)

j
The fj is physical quantity of the scattering power of the jth atom in the unit cell. The
195

value of fj involves the number and distribution of jth atomic electrons, and the wavelength
and angle of scattering of the incident beam. The scattered electrons from a single atom
takes account of interference effects within the atom. We defined the atomic form factor
in Eq. A.13 (rj = 0; a single atom). If we assume that electron distribution is spherically
symmetric, then we can derive a single atomic form factor:

fj = 2π
= 2π
= 4π

drr2 d(cos α)nj (r)exp(−iGr cos α)
eiGr − e−iGr
iGr
sin Gr
drnj (r)r2
,
Gr
drr2 nj (r)

The electron density is uniformly concentrated at the center, then fj = 4π

(A.16)

drnj (r)r2

is equal to the number of atomic electrons, Z. Therefore, fj is the ratio of the scattered
amplitude of actual electron distribution.

196

Appendix B
Experiment Setup of Ultrafast
Electron Diffraction
Ultrafast electron diffraction (UED) technique is pump-probe methode which is the most
appropriate experiment to study photo-induced ultrafast dynamics of atomic structure and
charge transfer. [28, 203, 40, 96, 34, 30, 95, 29, 25, 204] UED employs timed sequences of
femtosecond laser pulse to initiate the reaction and ultrashort electron pulse generated by
the femtosecond laser pulse to probe the transient dynamics of atomic structure and charge
carriers. This sequence of pulse is repeated, timing the electron pulse to arrive before and
after irradiation. A series of the snapshots of diffraction patterns at different time delay
can be inverted to reveal the four-dimensional transient structure dynamics.
With ultrafast electron microscope system, I have also built the UED system in the
same chamber shown in Fig. B.1(b). Two systems driven by the same femtosecond laser
can be operated independently. Moreover, the 40 kV electron pulse relative timing to 100
kV UEM electron probe can be controlled with another delay stage of 266 nm laser. So 40
kV electron beam can be used for the pump to excite the sample.
In the UED experiment setup, the pump laser is focused onto the sample at the center
of the UHV chamber. The pulsed electron source is generated through photoemission from
a 40 nm thickness silver cathode, accelerated to 40 keV, collimated and focused onto the
197

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Figure B.1 Ultrafast electron diffraction experiment geometry with ultrafast electron microscope system. (a) A schemetic diagram of the UEC optics setup. Both 400 and 800 nm
beam lines are shown entering the delay line, but one of them is blocked based on the choice
of excitation. The time delay between pump laser pulse and electron probe is controlled
by delay stage adjusting traveling path length. Also, pulse shaper is shown in the diagram,
but it has not been tested yet. (b) In UHV specimen chamber, the 100 kV UEM column
beam goes from top down, and 40 kV UED electron beam goes horizontally. The pump
laser lands on the sample with 45o tilting.

198

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Figure B.2 Schematic picture of the femtosecond laser source: (1) femtosecond seed pulse
(Mai-Tai), (2) amplifier for femtosecond pulse (Spitfire), (3) continuous wave pump laser
for amplification (Empower)
sample. The probe is scattered from the sample and the signal is collected at the other end
of the UHV chamber using an intensified CCD camera which is capable of single-electron
detection.
B.1 The Femtosecond Laser System
The femtosecond laser source is composed of 3 separated sub-systems shown in Fig. B.2:
Mai-Tai, Spitfire, and Empower. These three units operate together to generate the final
amplified pulsed laser. To genearte high power femtosecond pulse laser, there are two separated stages; (1) pulse generation in Mai-Tai, (2) amplification with Spitfire and Empower.
The low power (∼ nJ/pulse) seed pulse laser output is generated by two lasers, continuous
wave (CW) diode-pumped Nd:YVO4 laser and a mode-locked Ti:Sapphire pulsed laser,
which are enclosed in two separate chambers.
The Nd:YVO4 gain medium in CW pump chamber lases at 1024 nm which is frequencydoubled to 532 nm in a non-critically phase matched Lanthanum Triborate (LBO) crystal

199

in order to match the absorption spectrum of Ti:Sapphire in the pulsed output chamber.
The Ti:Sapphire gain medium which is pumped by the CW diode-pumped laser generates
femtosecond pulse which is active mode–locked to produce 45 fs laser pulse with 600 mW
average power at the pulse repetition rate of 84 MHz. This corresponds to ∼ 7 nJ/pulse.
These seed pulses enter the Spitfire where they are first stretched in time using a 4-pass
stretcher grating. This is done to avoid non-linear effects, such as self-focusing that can set
in at high laser peak-power and possibly damage the optical components. The stretched
pulse is then allowed to enter the amplifier cavity consisting of a Ti:Sapphire gain medium
which is pumped by a Q-switched Nd:YLF laser (Empower) that provides ∼ 20 W pulsed
output at 10 kHz repetition rate. Since Nd:YLF lases at 1053 nm, the output is upconverted
to 527 nm in an LBO crystal to match Ti:Sapphire absorption peak. This intense 20 W
laser sets up the population inversion in the Ti:Sapphire crystal, following which, the seed
femtosecond laser pulses from the Mai-Tai are allowed to enter the amplifier cavity. The
seed laser picks up gain each time it passes through the pumped Ti:Sapphire gain medium
and builds up in strength over multiple cavity round trips. Once the population inversion
in Ti:Sapphire has been completely consumed and no further amplification is possible, the
amplified pulse is directed out of the cavity into a pulse compressor where it is compressed
back to femtosecond duration. The final pulse train exiting the system posses the following
characteristics: 45 fs, 800 nm center wavelength, 0.4 mJ/pulse and 10 kHz pulse repetition
rate.
B.2 40 kV Pulsed DC Elecron-Gun
The pulsed electron source for a probe in UED experiment is shown in Fig. B.3. Ultrafast
electron pulse is generated by irradiation of 266 nm (4.6 eV) femtosecond laser pulse on a

200

semi-transparent silver film (∼ 40 nm thickness, work function of silver: ∼ 4.4 eV). The
film is thermally evaporated onto a transparent sapphire substrate. Photoemission electron
pulse generated by femtosecond laser pulse preserves the ultrashort time duration of the
incident laser pulse. This electron pulse is accelerated to 40 kV in the gap between the
cathode and the anode (gap distance ∼ 6 mm), and it enters the central bore of a magnetic
pole pieces through 100µm aperture to make th beam align into the optical axis of the
magnetic lens. 1500 Au mesh is mounted in front of the anode hole, in order to prevent the
field penetration through the anode hole which might cause irreversible beam emittance
growing. The magnetic lens pole piece is made of soft-iron with solenoidal current carrying
coils in its interior. The magnetic lens pole generates the non-uniform magnetic field and
the electron pulse is spatially focused by this non-uniform field. The fouced electron pulse
exits the pole piece through 2nd aperture which can be changed, 50 ∼ 200µm. After
magnetic lens, two pairs of deflector rods controls the electron pulse direction towards the
sample at the center of the chamber.
To develop a short-pulse electron gun, the challenge is how we can overcome the inherent
repulsion among electrons in a pulse, by the collective space-charge effect. This space charge
effect tends to broaden the temporal resolution of the electron pulse in the drift region as it
propagates to the sample. There are several approaches to overcome the space charge effect:
(1) short flight distance [84], (2) radio-frequency compression of electron pulse [205, 60],
(3) high acceleration voltage in relativistic regime [58], (4) single-electron mode [56] where
the space charge effect is eliminated, (4) electron pulse self compression [206]. We use the
second approach for our UEM system, but, for UED system, use the first approach, a short
flight distance gun by designing a universal electron gun in which the distance is ≤ 7 cm.

201

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Figure B.3 Universal electron gun design. (a) Zoom-in of the electron gun head part,
(b) actual image of the fully assembled universal electron gun before installation into the
chamber, (c) overall layout of the electron gun including the gun chamber with 6” conflat
flange

202

Moreover, 40 kV universal electron gun is fully independent unit which can be mounted in
any chamber having the 6” conflat flange port (shown in Fig. B.3).

The major purpose

of the new 40 kV electron gun is constructing the universal electron gun as a complete
unit, which can be mounted into any type of chambers. So practical challenge for designing
the electron gun is how we can install all the parts, high voltage (HV), electrical wires for
deflectors, and the water cooling line for a magnetic lens, into one complete unit, and at the
same time, how can we make a short distance from the electron gun cathode to a sample,
in order to minimize the space charge effect of the electron pulse. As shown in Fig. B.3,
the gun head part (a blue box in Fig. B.3(a)), including cathode head, anode, magnetic
lens, deflectors is outside of the electron gun chamber because it will be inside of the target
chamber where the electron gun and a sample are mounted (shown in Fig. B.1(b)). The
electron gun chamber is mounted to the target chamber through the 6” CF flange, and the
electrical wires for deflector rods and thermocouple to monitor magnetic lens temperature,
and the water cooling tubes are installed through six of the 1.33 inch CF flanges at the side
ports of specially designed 6 inch CF flange. Also, high voltage feedthrough is mounted
at one of 4 ports (three 4.5 inch ports and one 2.75 inch port) in a gun chamber (shown
Fig. B.3(c)), and the high voltage pin is directly connected to the cathode body without
any additional connector. So we can avoid the arcing problem because all the sharp edges
are berried completely. Another technical issue is the potential problem of arcing in a
silver film on cathode and the MACOR rods to isolate cathode from the ground. This
arcing problem can be easily solved with recoating the 40 nm silver film on the cathode and
replace the MACOR rods, so we have to implement the way to replace them easily, instead
of unmounting a whole electron gun. So the cathode and MACOR rods are designed easily

203

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Figure B.4 Performance characterization of the 40 kV universal electron gun. (a) Analog-todigital unit (ADU) measurement: CCD camera response of a single electron event is about
175 intensity of one pixel. (b) the number of electron per pulse with the measured ADU as
a function of a different magnetic lens focusing strength. The reason for the increase in the
number of electron with stronger focusing is more electrons able to pass through the 100
µm aperture because of stronger focusing. (c) the beam size at the sample location and
the CCD camera as a function of a different magnetic lens focusing. (d) divergence angle
of the electron beam with different focusing strength. The divergence angle is calculated
by the beam sizes at the sample and CCD camera with the camera distance between the
sample and CCD camera.

204

disassembled through the 8 inch CF flange at the bottom, shown in Fig. B.3(c).
The performance of the universal 40 kV electron gun is comparable with our old system,
and the number of electrons per pulse is even higher up to a factor of five. To characterize
the electron pulse of this 40 kV electron gun, we quantify the number of electrons per
pulse and magnetic lens focusing strength with measuring the electron beam size (shown
Fig. B.4). To count the number of electron, we operate the electron gun in a single electron
mode by reducing the 266 nm laser intensity to extremely low levels. This enabled the
detection of isolated single electron events at the CCD. Measuring the detector response over
multitude of such recorded events allowed us to determine the average detector response
per single electron event, and, as shown in Fig. B.4(a), a single electron signal of CCD
camera corresponds to ∼ 175 of signal intensity. Based on this estimate, we obtained a
maximum probe pulse intensity of 5 × 103 electrons per pulse, though normal operating
conditions range in the 4 × 103 ∼ 5 × 103 range. While this is not sufficient for single shot
diffraction acquisition, which typically requires ∼ 106 electrons per pulse, it is sufficient
for multi-shot diffraction investigations. The beam size is also critical from experimental
point of view because it significantly reduces the detrimental effects of velocity mismatch
[206] which causes the reduction in the temporal resolution. The electron beam size in our
old system is about 30 µm and the electron beam size of new universal electron gun is
also about 30 µm in experimental condition, where the electron beam is close to parallel
beam. Therefore, new universal electron performance is sufficient for independant UED
experiment, and the UED experiment with the electron gun can be run in any types of
chambers.
B.3 Image Acquisition System: Charge Coupled Device(CCD) Camera

205

For a diffraction acquisition system, a highly sensitive device capability to detect a single
electron event is necessary to detect weak diffraction signals. To achieve the high sensitivity,
we are using PI-MAX from Princeton instrument operating at -20o C which is implemented
with image intensifier from Hamamatsu. The image intensifier is composed more than 106
individual miniature electron multipliers with an excellent input to output spatial geometric
accuracy, in order to amplify weak diffraction signals with a high spatial resolution. The
construction of the system is shown in Fig. B.5. There are several stages through which the
signal represented by the incident electron proceeds to achieve amplification, and eventual
detection.
As shown in Fig. B.5, 60 nm thickness aluminum film to block the background photon
signals which come from the pump laser or room light is coated on the optical face-plate of
the image acquisition system, CCD camera. The penetration depth of visible wavelength
photon in Al is ∼ 15 nm, while that of 40 kV electron beam is about several µm range.
Therefore, most of the ambient background photon are blocked by this Al film. The electrons penetrating through the Al film strike a phosphor screen and generates the visible
range photon. These photons are focused by a 2:1 ratio optical taper which is a bundle of
optical fibers on the CCD camera intensifier window. Then the photons are converted back
into electrons at the front of image intensifier by photo-cathode. The generated photoelectrons are accelerated and enters the micro channel plate (MCP). The MCP is composed
more than 106 micro-channels which are individual miniature electron multipliers. The
electron amplification is achieved by sequential secondary electron generation. The amplified electrons strike another phosphor to convert the electrons to much larger number of
photons. These amplified photons are detected by CCD camera. A special absorptive layer

206

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Figure B.5 Structure of charge coupled device (CCD) camera design. (a) Schematic illustration of CCD camera structure: in front of CCD camera, we have the optical taper to
focus a signal in large area into small CCD camera input window (2:1 ratio). On the optical
taper face, we have an optical face-plate, and the 60 nm aluminum film and phosphor film
are coated on the face-plate surface. The Al film screens the background photon from room
light and pump laser. The phosphor film converts the electron signal to photon to amplify
the intensity. Red box indicates the intensifier. (b) the schematic diagram of the MCP
in intensifier. MCP is composed of more than 106 micro-channels which are individual
miniature electron multipliers. (c) design of the fully assembled CCD camera.

207

absorbs any of the light that might leak through the semi-transparent photocathode, while
the aluminum reflection layer seeks to block any light generated near the phosphor screen
from returning to the photocathode. Each MCP can provide an amplification of up to 1000
times, and an image intensifier can have up to 3 MCPs between the photocathode and the
phosphor screen, thus allowing a gain of up to 109 . Finally, the amplified signal, in the
form of light photons is incident on the CCD screen, where it is detected in the usual way.
Moreover, each MCP which is 6 µm diameter independent electron multiplier allows the
accurate spatial resolution of the amplified signals.

208

Appendix C
Formalism of diffracted voltammetry
under small angle condition
C.1 Slab model UEDV formalism can simplified by applying small angle approximation:
θi & θo

D=

1, and χ

1. Under these conditions, Eq. (6.8) is reduced to:

[θo + (1 − a)θi ] − [(1 − a)

θi2 + χ]

1 + [θo + (1 − a)θi ][(1 − a)

θi2 + χ]

∼ [θo + (1 − a)θi ] − [(1 − a)

θi2 + χ]. (C.1)

Also, ∆B is modified as
(∆B + θo )2 ∼ D2 − χ.

(C.2)

By combining Eq. (C.1) & Eq. (C.2), we can get the following equation:

(∆B +θo )2 = [θo +(1−a)θi ]2 +(1−a)2 θi2 +a(a−2)χ−2(1−a)[θo +(1−a)θi ]

θi2 + χ. (C.3)

Solving Eq. (C.3) for χ, we arrive at the following relationship:

χ=

B
±
2
2a (a − 2)2

[

C
B
]2 −
,
2
2
2
2a (a − 2)
a (a − 2)2

209

(C.4)

where

B = 4(a − 1)2 (θi2 + θo2 ) + 4(a2 − 2a + 2)(1 − a)θi θo + 2a(a − 2)(∆2B + 2∆B θo ), (C.5)
C = [(θo + (1 − a)θi )2 − (∆B + θo )2 ]2 + (1 − a)2 θi2 [(1 − a)2 θi2 − 2(θo + (1 − a)θi )2 ]. (C.6)
Simplification can be made for different a value. For a = 0, Eq. (C.3) can be simplified
as:
(∆B + θo )2 = [θo + θi ]2 + θi2 − 2[θo + θi ]

θi2 + χ,

(C.7)

so the inversion can be made analytically:
( 1 ∆2 + ∆B θo − θo θi )2 − θi2 (∆B + θo )2
.
χ= 2 B
(θo + θi )2

(C.8)

which is equivalent to Eq. (1) in the previous study.[40]
If ∆B

θi & θo , Eq. (C.8) can be further linearized:

χ = −2

θo2 θi

∆ .
(θo + θi )2 B

(C.9)

For a = 1, Eq. (C.3) can be simplified as:

(∆B + θo )2 = θo2 − χ,

(C.10)

χ = −∆B (∆B + 2θo ).

(C.11)

yielding a TSV formalism:

210

If ∆B

θi & θo ,
χ = −2θo ∆B .

(C.12)

For a = 2, implying θi = θo in RHEED geometry, we can reduce the general formalism
to
(∆B + θo )2 = θi2 .

(C.13)

Therefore, the surface scattered diffraction change, ∆B , is independent of χ. In other
words, the measured ∆B in experiments is not affected by TSV.
C.2 Beyond slab model Small angle approximation can also be made for TSV determination beyond the slab model, formulated in Eqs. (??) to (??). For Θo (θo , α) = Θi (θi , α),
the surface potential, Vs from ∆B , can be written for small angles as

χ=

[(c + 2)Θi (θi , α) − cΘo (θo , α)]

±

[(c + 2)Θi (θi , α) − cΘo (θo , α)]2 − 4ab[Θo (θo , α) − Θi (θi , α)]2

b[Θo (θo , α) − Θi (θi , α)]2 ,
where

2
θo ∆B − θi θo + ∆2B /2 − θi2 θo + ∆B 2
a=
,
θi + θo 2
b=

1
θi + θo 2

211

,

(C.14)

(C.15)

(C.16)

and
2θi2 + 2θi θo − 2∆B θo − ∆2B
c=
.
θi + θo 2

212

(C.17)

Appendix D
Magnetic Annealing Procedure
The magnetic lens material is low carbon soft-iron including chemical composition
(C/Mn/P/S/Si/Al/N: 0.01/0/18/0.005/0.005/0.1/0.004 %) from CMI Specialty Producs,
Inc.. After fabricating the magnetic lenses, the parts are annealed with following procedure
to maximize the magnetic property which is recommanded by the company:
1. Anneal the fabricated parts up to 1544o F.
2. Hold at 1450 - 1550o F for 1-2 hours.
3. Cool to 1450o F in 1 hour in vacuum.
4. Cool to 1350o F in 1 hour in vacuum.
5. Cool to 1250o F in 1 hour in vacuum.
6. Cool to 1150o F in 1 hour in vacuum.
7. Cool to 900o F in 1 hour in vacuum.
8. Cool 200o F/hr to 300o F in atmosphere to prevent warpage of thin complicated parts.
9. Air cool to ambient.

213

Appendix E
Optimization of Pierce Geometry
Electron Gun
As discussed in section 4.2, the combination of Pierce gun and CML1 provides the initial
convergence of photoemitted electron beam, which is then subject to the space–charge–
driven expansion of the photoelectron pulse. The performance of the prescribed Pierce
geometry will depend on the electron density present. The conventional Pierce geometry
has the highest field present at the edge of the cone–shaped anode, which limits the achievable extraction field at the cathode surface. Based on the experimental feedback, we may
consider different cathode and anode geometry for providing higher extraction field at the
cathode surface while maintaining the necessary self–focusing effect for compensating the
space–charge–driven beam divergence. Fig. E.1 shows ray tracing simulation using different gap distances to compare the self–focusing power based on non-interacting electrons.
We found that if we reduce the gap distance by 20%, we can increase the extraction field
strength by 45%, whereas the self–focusing power, as measured by the divergence angel
at crossover, can be reduced by more than a factor of 2. In comparison, increasing the
gap distance by 20% leads to a 20% increase of self-focusing power, and a 20% decrease
of extraction field. The self-focusing power should be tuned to the strength of the space–
charge–driven expansion associated with high–intensity beam. Since the cathode is easily
214

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-.$//$
0$

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!

!1#$

Figure E.1 (a) Schematic illustration of a non-interacting photoemission electron generation on a cathode: R is the initial location where the electron is generated and θ is the
divergence angle caused by the focusing field of Pierce gun geometry. (b) Field Precision
simulation result of the electron divergence angle at different initial position (R) at various
gap distances between the cathode and anode: a gap distance of the current design is 20
mm and the surface extraction field is 2.2 MV/m field, and 20% smaller gap distance, 16
mm, generates 45% higher extraction field, 3.2 MV/m.

215

changeable in our set up, we may use different cathode geometry for generating different
density beams.

216

Appendix F
List of Initials and Acronyms
ADU

Analog-to-Digital
Unit

AGM

Analytical Gaussian
Model

CB

Conduction Band

CCD

Charge Coupled Device

CML

Condenser Magnetic
Lens

CFEG

Cold Field Emission
Gun

COM

Center Of Mass

DWF

Debye–Waller Factor

EUV

Extreme Ultra Violet

FEG

Field Emission Gun

FEL

Free Electron Laser

FMM

Fast Multiple Method

HFEG

Hot Field Emission Electron Gun

HGN

Hollow Gold Nano–shell

HHG

High Harmonics Generation

HOPG

Highly Oriented
Pyrolytic Graphite

LDP

Laser Driven Plasma

LSPR

Localized Surface
Plasmon Resonance

MCP

Micro Channel Plate

mRDF

modified Radial
Distribution Functions

NP

Nano–Particle

Obj.ML

Objective Magnetic lens

PE

Photo–Emission

REED

Reflective High-energy
Electron Diffraction

217

RF

Radio–Frequency

ROI

Region OF Interest

SAM

Self-Assembly Monolayer

SEM

Scanning Electron Microscope

SPR

Surface Plasmon Resonance

TEM

Transmission Electron Microscope

TTM

Two Temperature Model

TSV

Transient Surface Voltage

UED

Ultrafast Electron Diffraction

UEM

Ultrafast Electron Microscope

VC

Valence Band

VC

Virtual Cathode

VCO

Voltage Control Oscillator

X–FEL

X-ray Free Electron Laser

ZOT

Zero Of Time

6D

Six Dimension

218

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219

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