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dissertation entitled

INVESTIGATIONS ON INTERFACIAL DYNAMICS WITH
ULTRAFAST ELECTRON DIFFRACTION

presented by

Ryan A. Murdick

has been accepted towards fulfillment
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5/08 KzlProleccaPresIClRC/Dateoueindd

INVESTIGATIONS ON INTERFACIAL DYNAMICS WITH ULTRAFAST
ELECTRON DIFFRACTION

By
Ryan A. Murdick

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Physics & Astronomy

2009

ABSTRACT

INVESTIGATIONS ON INTERFACIAL DYNAMICS WITH
ULTRAFAST ELECTRON DIFFRACTION

By
Ryan A. Murdick

An ultrafast electron diffractive voltammetry (UEDV) technique is introduced, ex-
tended from ultrafast electron diffraction, to investigate the ultrafast charge transport
dynamics at interfaces and in nanostructures. Rooted in Coulomb-induced refrac-
tion, formalisms are presented to quantitatively deduce the transient surface volt-
ages (TSVs), caused by photoinduced charge redistributions at interfaces, and are
applied to examine a prototypical Si/SiOg interface, known to be susceptible to pho-
toinduced interfacial charging. The ultrafast time resolution and high sensitivity to
surface charges of this electron diffractive approach allows direct elucidation of the
transient effects of photoinduced hot electron transport at nanometer (~2 nm) in-
terfaces. Two distinctive regimes are uncovered, characterized by the time scales
associated with charge separation. At the low fluence regime, the charge transfer is
described by a thermally-mediated process with linear dependence on the excitation
fluence. Theoretical analysis of the transient thermal properties of the carriers show
that it is well-described by a direct tunneling of the laser heated electrons through the
dielectric oxide layer to surface states. At higher fluences, a coherent multiphoton
absorption process is invoked to directly inject electrons into the conduction band
of SiOg, leading to a more efficient surface charge accumulation. A quadratic flu—
ence dependence on this coherent, 3-photon lead electron injection is characterized
by the rapid dephasing of the intermediately generated hot electrons from 2-photon
absorption, limiting the yield of the consecutive 1-photon absorption by free carriers.

The TSV formalism is extended beyond the simple slab geometry associated

with planar surfaces (Si/SiOg), to interfaces with arbitrary geometrical features,

by imposing a corrective scheme to the slab model. The validity of this treat-
ment is demonstrated in an investigation of the charge transfer dynamics at a metal
nanoparticle/self-assembled monolayer (SAM)/ semiconductor interconnected struc-
ture, allowing for the elucidation of the photo-initiated charging processes (forward
and backward) through the SAM, by monitoring the deflection of the associated
Bragg peaks in conjunction with the UEDV extended formalism to interpret the sur-
face voltage.

The design, calibration, and implementation of a molecular beam doser (MBD),
capable of layer-by-layer coverage is also presented, with preliminary investigations
on interfacial ice.

With the development of UEDV and implementation of the MBD, continued in-
vestigations of charge transfer in more complex interfaces can be explored, such as
those pertinent to novel solar-cell device technology, as their quantum efficiencies
are usually strongly dependent on an interfacial charge transfer process. As UEDV
is inherently capable of probing charge and atomic motion simultaneously, systems
that exhibit phenomena that are attributable to strong coupling of the atomic and
electronic degrees of freedom are of particular interest for future investigations with
UEDV, such as optically induced electronic phase transitions and colossal field switch-

ing in functional oxides.

To my family, Aaron, Carrie, John, and Marcia

iv

ACKNOWLEDGMENT

First and foremost I would like to acknowledge Dr. Chong-Yu Ruan, Ramanikalyan
Raman, and Dr. Yoshie Murooka. I will always think of the four of us as a team, of
which I feel very proud to have had a place. Their hard work and dedication with
Professor Ruan’s energy and leadership allowed for this beautiful lab to be built.

My various mentors along the way: Drs. Bradley Roth, Andrew Goldberg, Nor-
man Birge, Bhanu Mahanti, Ned Jackson, Martin Berz, Andrei Slavin, Ken Elder,
Alberto Rojo, and Uma Venkateswaran.

My friends and colleagues from condensed matter: Tzong-Ru Terry Han, Rick
Worhatch, Dr. Chris Farrow,'Zhensheng Tao, Pampa Devi, Luke Granlund, and Josh
Veazey.

I would also like to acknowledge Jim Muns, Torn Palazzollo, and Tom Hudson of
the MSU Machine Shop, along with Drs. Reza Loloee, Baokang Bi, Ronald Mickens,
and Merlin Bruening for allowing our group to use his ellipsometer.

There are several components to our lab and to this work, from which I would
like to acknowledge specific contributions, beginning with R.K. Raman and Aric Pell
for the development of the electron guns in our lab; Dr. Yoshie Murooka and R.K.
Raman for designing and overseeing the first (Yoshie) and second (Raman) generation
sample holders. I would also like to acknowledge Zhensheng Tao for his development
and implementation of portions of the formalism in Chapter 5, specifically Section
5.3.2, as well as Richard Worhatch for his contribution to the ‘RC—circuit’ portion
of Chapter 6, and Tzong—Ru Terry Han for his efforts in sample preparation and
stage temperature calibrations, and of course, Professor Ruan for his involvement in
everything mentioned here, and throughout the entire work.

Finally, my wife Amy, who has loved and supported me, unconditionally, through
these trying years.

I am very humbled and grateful to have worked along side of all of you.

TABLE OF CONTENTS

List of Tables ................................. ix
List of Figures ................................ xi
Introduction ........................... 1
1.1 Charge Transfer .............................. 1
1.2 History: Shutters to Short Pulses .................... 2
Ultrafast Electron Crystallography Laboratory at MSU ..... 8
2.1 Introduction ................................ 8
2.2 Optical Pump - Diffraction Probe Setup ................ 11
2.2.1 Pump-Probe Alignment ..................... 13
2.3 Experimental Measurements and Calibrations ............. 19
2.3.1 Laser Fluence ........................... 19
2. 3. 2 Pulse Width- Interferometric Autocorrelation ......... 21
2.3.3 Electron Beam Spot Size ..................... 24
2.3.4 Rocking Curve .......................... 25
Electron Phonon Interaction ................... 28
3.1 Two-Temperature Model ......................... 28
3.1.1 Numerical Solution ........................ 31
3.1.2 Extensions to the Two-Temperature Model ........... 32
3.1.3 Thermal Transport in N anoparticles .............. 38
3.2 Boltzmann Transport in Semiconductors ................ 41
3.2.1 Numerical Scheme ........................ 43
3.2.2 Non-thermal Regime ....................... 49
3.2.3 Quasi-Fermi Levels ........................ 52
3.3 Discussion ................................. 56
Ultrafast Electron Diffractive Voltammetry ........... 57
4.1 Introduction ................................ 57
4.2 Coulomb Refraction ............................ 59
4.2.1 Slab Model ............................ 61
4.3 Generation of Near-Surface Fields .................... 64
4.3.1 Field Constituents ........................ 64
4.4 Quasi-3D Structure ............................ 67
4.4.1 Robustness of the TSV Formalism ................ 69
4.5 Coulomb Refraction vs. Lattice Expansion ............... 78
4.6 Beyond the Slab Model .......................... 78

4.6.1 Correction for Finite-Slab Geometry .............. 82
4.6.2 Correction at the N anoparticle/ SAM/ Semiconductor Interface 85

4.7 Discussion ................................. 86
5 Carrier Transport at the Si/Si02 Interface ............ 88
5.1 Introduction ................................ 88
5.2 Experimental Methods .......................... 90
5.2.1 Surface Preparation ........................ 90
5.2.2 Pump-Probe Alignment ..................... 91
5.2.3 Data Analysis ........................... 91
5.3 Photoinduced Surface Charging (Injection) ............... 95
5.3.1 Direct Tunneling ......................... 95
5.3.2 Coherent (2+1) Absorption (2-Photon + Free Carrier) . . . . 103
5.4 Surface-Bulk Coupling (Relaxation) ................... 107
5.5 Discussion ................................. 112
5.5.1 Thermionic and Photoinduced Emission ............ 112
5.5.2 Dielectric Enhancement of the Interface Dipole ........ 114
5.5.3 thure Investigations / Open Questions ............. 116
6 Charge Transfer in Surface-Supported N anoparticles ....... 120
6.1 Introduction ................................ 120
6.2 Sample Preparation ............................ 123
6.3 Surface Plasmon Resonance / Mie Theory ............... 127
6.3.1 Example Calculations of Mie Scattering with TTM ...... 132

6.4 UEDV Investigations on Molecular Transport at the Nanoparticle /
Molecules / Substrate Interface ..................... 135
6.5 Near-Field Lensing: Nano-cavity Patterning .............. 139
6.5.1 Near-Field Enhancement ..................... 139
7 Molecular Beam Doser ..................... 145
7.1 Introduction ................................ 145
7.2 Design Methodology ........................... 147
7.3 Pinhole Orifice .............................. 147
7.4 Microcapillary Array ........................... 150
7.5 Operation ................................. 155
7.6 Tests with H20 .............................. 158
7.6.1 Thermal Desorption Test ..................... 158
7.6.2 Preliminary Testing of H20 on Si ................ 160
7.7 Discussion ................................. 165
8 Summaries 8: Discussion ..................... 166
Appendices 169

"IIHUO

Principles of Electron Diffraction ................ 169

A.O.l Bragg’s Law ............................ 169
A.O.2 The Reciprocal Lattice ...................... 170
A.O.3 Ewald Construction ........................ 172
Femtosecond Laser Pulse Generation .............. 176
8.0.4 Modelocking ............................ 176
3.0.5 Regenerative Amplification .................... 179
Thermophysica] Properties of Selected Metals .......... 182
Complex Index of Refraction for Au and Ag ........... 183
Riccati-Bessel Functions ..................... 187
Two-Temperature Model Computer Program .......... 189
E1 Non-Thermal Electrons Subroutine ................... 194
References .......................... 198

viii

2.1

3.1

5.1

5.2

7.1

CI

LIST OF TABLES

Relationships between the widths, Atp and Ata, of a signal and its
autocorrelation function, respectively ...................

Silicon input parameters for the Boltzmann Transport Model.

Some of the measurements of the 2-photon absorption coefficient (B)
for Si found in the literature. Few studies exist that have measured
this parameter. Wavelength varies between 625-1064 nm for the studies
listed and pulse duration from 28 £5 to 100 ps, possibly explaining the
wide range of values for B. .......................

The underlying processes associated with 2+1 absorption, all of which
are occurring within the duration of the optical excitation pulse. For an
arbitrary fluence (column 1), the 2-photon yield will increase quadrati-
cally (column 2), but this population will experience a loss from electron-
electron scattering (column 3), which has linear dependence on fluence.
The probability of absorbing a third photon is linear with the photon
flux, still illuminating the surface (column 4). The net effect is the

2+1 yield, which goes as N2+1 oc (F2 x F71 x F = F2) - quadratic

(column 5). ................................

A comparison of the various conditions that can be used to dose. Either
of the scenarios in the first two rows works fine, but the bottom line
scenario is optimal. ............................

The thermophysical properties for gold, silver, copper, platinum, alu-
minium, and nickel. The values of 63 and R are given at 800 nm (1.55
eV). Acquiring them for other wavelengths is quite simple by just gath-
ering the complex index of refraction values (n and n) from the various
physical and chemistry handbooks [195], and using 63 = /\/47rrs. Ex-
perimentally gathered reflectivities are available in Reference [195].

22

44

108

157

182

D.1

D2

D3

D4

The complex index of refraction ii = n + in for Au and Ag at various
wavelengths, from Johnson and Christy (1972) [370] (continues on next
page). ................................... 183
Au and Ag complex index of refraction (continued from previous page). 184

An and Ag complex index of refraction (continued from previous page). 185

Au and Ag complex index of refraction (continued from previous page). 186

1.1

2.1

2.2

2.3

LIST OF FIGURES

Images in this dissertation are presented in color

The fast camera invented by Muybridge allowed the question to be
answered: do all four hooves of a horse leave the ground at the same
instant during a gallup? The answer is no. All four legs are off the
ground, but not with full extension, which was presumed by many at
the time. This sequence was taken 6/ 19 / 1878 at a track in Palo Alto,
CA. This photograph is property of the Library of Congress Prints and
Photographs, Washington, DC 20540 ...................

Ultrafast electron diffraction geometry at MSU. (a) A schematic of the
UEC optical setup. For completeness, both 400 and 800 nm beam
lines are shown entering the delay line. In practice one of them will
be blocked based on the choice of excitation energy [190]. (b) In the
UHV chamber, an optical pulse (of 400 or 800 nm) excites the sample
(red), followed by subsequent probing in the form of electron diffraction
(blue). The electron pulse is generated from an ultrashort laser pulse
striking a silver photocathode (not depicted), negatively biased at -30
kV, which is focused onto the sample. Diffracted electrons are captured

on an image intensified phosphor screen and recorded by a CCD camera.

The group velocity mismatch problem is demonstrated in parts (a)
and (b), the synchronization of the two is inherently confounded by
their differing propagation speeds. In (c)-(e), the electron beam sees
the same pump for all spatial probing points, because of the wavefront
tilting of the pump. [191] .........................

The UHV chamber and tools for surface preparation and characteriza-
tion [190]. .................................

9

10

12

2.4

2.5

2.6

2.7

2.8

2.9

Coarse alignment. The electron beam and diode lasers from two dif-
ferent vantage points are passed through the needle. This means that
the diodes overlap at a point in space corresponding to a known point
through which the e-beam will pass ....................

Pump-probe fine alignment. (a) The pump laser (red), incident at
45°, incrementally moves vertically (2) along the stage (motion not
depicted), with a probe shot (blue) taken at each stop. The maximum
change in the diffraction pattern corresponds to improving the rough
alignment shown in (b) to the partially aligned in (c). The stage go-
niometer is then adjusted incrementally along the :r-direction, at each
stop taking diffraction images from the pumped and unpumped sample
by varying the delay before and after the zero of time. The x-position
where maximum change was observed corresponds to the fully aligned
position in (d). ..............................

Alignment scans. (a) The first scan of the fine alignment process,
showing the Bragg peak position change on the CCD screen (inset
shows the intensity drop) as the laser spot is displaced in increments
of 50 pm. (b) The second scan of fine alignment, where the stage
is stopped every 10 am to take diffraction shots at delays of 500 ps
(circles) and 700 ps (triangles), and the ZoT is 540 ps. The lens and

15

stage positions were chosen here to be -0.65 and 12.70 mm, respectively. 18

As the laser spot is brought into the probe area, the response of the
Bragg peak increases until it reaches a maximum. At this point, the
pump and probe are perfectly concentric, followed by the gradual de
crease in Bragg peak response as the laser is dragged out of the probe
region. The FWHM of this curve is the laser spot size. ........

Two beams of frequency w enter the doubling crystal at an angle of 26,
relative to one another. In the crystal, they overlap spatially and tem-
porally, so that each instant in time represents a different intersection
point of the two wavefronts. The SH emission from the crystal (2w)
corresponds to different ‘delays’ from these intersections, which are in-
tegrated in time to make up the autocorrelation signal (red). A filter
prevents the two fundamental beams (w) from entering the detector
(not shown) .................................

Signal time axis calibration. The oscilloscope profile of the autocor-
relation signal has a spread AS, which is proportional to the pulse
width. When the autocorrelation function is spatially displaced by L,
the oscilloscope profile moves by AT. Moving L and observing AT is
the essence of the calibration (see text) ..................

23

25

2.10 The intensity of the direct beam recorded on the CCD as the knife—

2.11

3.1

3.2

3.3

3.4

3.5

3.6

edge is incrementally moved in from -15 to +15 ,um. Inset: Schematic
of the knife-edge encroaching the electron beam path [190]. .....

A compiled rocking curve map, revealing the reciprocal space for an
Si(111) surface. (a) An example of one of the full diffraction images
that are collected at varying incidence angles. A region of interest
is selected from each full image, shown by the white boxes. (b) The
rocking curve map, compiled along the (0, 1) reciprocal lattice rod, over
incidences of 0.70 < 0, < 82°; 9 S is the scattering angle. .......

The energy coupling scheme assumed by the TTM. First, the laser
pulse is absorbed by the free electrons in the metal, which evolve into
a Fermi-Dirac distribution in the first z 50 fs. The thermal electrons
dump energy into the lattice, causing them to equilibrate after z 1 ps
(depending on the metal). Both electrons and lattice undergo thermal
losses from heat diffusion, the rates of which are largely governed by
the thermal conductivity, K. (and strictly speaking the heat capacity
and sound speed too). ..........................

An example TTM calculation of the electronic (Te) and lattice (T2)
temperatures on the top surface (2 = 0) of a 100 nm Au thin film irra-
diated with a 50 fs laser pulse of 50 mJ/cm2. Inset: depth dependence
when the pulse is at maximum inside the film (150 fs). ........

The combined atomistic approach at the surface with the TTM for
bulk, formulated by Zhigilei et al [259]. Electron-phonon coupling in
the atomistic region is expressed through the term, gmnvg, where of,
is the thermal velocity of the nth cell and 6 represents the temperature
dependent electron-phonon coupling frequency [259]. .........

The spatial discretization mesh used for the Boltzmann Transport
model calculation prescribed by Chen et al [264]. ...........

The depth dependence of the electronic temperature, Te, plotted at
50, 250, 500, and 1000 fs. Here, the thickness L = 60 pm, the pulse
duration tp = 45 fs, and the fluence F = 35 mJ/cm2. .........

The depth dependence of the lattice temperature, T,, plotted at 50 fs
(red), 250 fs (green), 500 fs (blue), and 1 ps (orange), for L = 60 um,
tp = 45 fs, and F = 35 mJ/cmz. Inset: Carrier density, n, plotted as a
function of depth (y—axis is log); n reaches maximum at @140 fs, which
is 5 fs after the laser pulse is at maximum amplitude (tp set to 45 fs;
initiated 3 pulse widths before time zero, shown in Equation 3.36).

xiii

26

27

29

33

38

45

47

48

3.7

3.8

3.9

4.1

4.2

4.3

4.4

An example calculation for the nt-BTM performed on silicon. The
fluence, wavelength, pulse width, and thickness are 35 mJ/cmz, 800
nm, 45 fs, and 50 pm, respectively. Inset: Zoomed-in view of the first
500 fs. ...................................

A comparison of the BTM and nt—BTM. The fluence, wavelength, pulse
width, and thickness are 35 mJ/cmz, 800 nm, 45 fs, and 50 pm, respec-
tively. Inset: Zoomed-in view of the first 500 fs. The laser temporal
profile is shown in orange. For the thermal case, Te reaches 1800 K
with the laser at only 6% of its maximum. Inset: Lattice temperature,

The quasi-Fermi level is plotted for both the BTM (green) and nt-
BTM (blue). Compared to all other quantities, ,ae exhibits the largest
difference between the two models because it depends on both Te and
ne. The nt-BTM is more physical as the Fermi gas should be nearly
degenerate before electron scattering commences, which the nt-BTM
closely resembles. The BTM curve actually drops below the valence
band edge, which is non-physical. Inset: The carrier density, plotted
for both models with the laser temporal profile shown in orange. . . .

Two different electron trajectories shown; one with no surface potential
present (light-gray) and the augmentation of the trajectory due to a
surface potential, V3 (black). The magnitude of the surface potential
can be deduced from the vertical displacement of the peak on the CCD
screen. ...................................

The parameter space of Equation 4.9 for V3 = 3.0 V. Small values of
both 0,- and 90 imply a small momentum component normal to the
surface, which means the effect from the field is more pronounced, as
reflected in the larger peak shifts, AB. .................

Mechanisms associated with vacuum emission. (a) Multiphoton ab-
sorption can supply sufficient energy for an electron to overcome the
work function. (b) With thermionic emission, the quasi-Fermi level
need not be above the work function, as the width of the Fermi distri-
bution is sufficiently broad because the electrons are hot. As the tail
rises above the work function, electrons are emitted into the vacuum.

Transient surface potential diagram introduced by various sources of
photoinduced charge separations (see text) near the Si/ SiOg / OH in-
terface. The transient surface voltage (TSV) determined using the
electron diffractive approach comes from the electric field integration

50

51

55

61

63

65

over the region traversed by the incident and diffracted electron beams. 68

 

 

4.5

4.6

4.7

4.8

The Ewald construction in the reflection geometry. The incident beam
8,- impinges the crystal at a glancing angle, 0,. A finite sub-surface
periodicity is sampled by the beam, causing a vertical interference pat-
tern to form on the reciprocal lattice rods (the white spots on the rods
and grey spots on screen), illustrating the potentially quasi-3D nature
of the diffraction pattern (see text). The bright peaks on the screen
(white) represent the points where the reciprocal lattice interference
spots intersect the Ewald sphere. If 0,- is increased (or decreased), the
Ewald sphere rocks about point 0 while the rods remain stationary,
causing the Laue circles to cross different parts of the reciprocal lat-
tice for examination with diffraction. The dashed circle represents the
zeroth order Laue zone (ZOLZ). ....................

Diffraction patterns from (a) a smooth Si (111) surface, (b) a Si(111)

surface with prominent step edges, (c) metallic nanoparticles, (d) HOPG.

The patterns shown in (b)-(d) exhibit quasi-3D features, while (a) does
not. Determining the plausibility of Coulomb refraction-based shifting
can be bolstered when several peaks from the same reciprocal lattice
are co—present on a single diffraction pattern, as this allows for a direct
comparison in a single shot, rather than rocking the sample to find the
next order on the rod. ..........................

Compiled rocking map for Si(111) (a), Au nanoparticles of size 2 nm
(b), and HOPG (c). These maps are obtained by stitching together
scattered intensity patterns along the normal direction over a range of
incident angles (02-). The corresponding scattering angle (05) for the
intensity pattern is also shown. In (a), the Ewald sphere cut from the
(0,3) rod is traced out in the diagonal, as each Bragg peak is present
for only a small angular range, while in (b) and (c) the diffraction is
powder-like, in which multiple peaks are co—present over an extended
range of electron incidence .........................

(a) The momentum transfer As as a function of time for the (0,0,24)
(red) and (0,0,27) (blue) peaks. As expected, the lower order peaks
shift more than those of higher order, consistent with the TSV formal-
ism. Inset: the diffraction pattern from the fixed crystal orientation
used throughout this pump-probe experiment. The (0,0,30) peak is
present in this pattern, shown by the top-most peak. The signal-to-
noise for this peak was rather weak to follow dynamically, so it was
excluded. (b) The transient surface voltage (TSV) for the listed flu-
ences. The two different orders are in close agreement for all fluences.
[107] ....................................

71

72

74

 

 

4.9

4.10

4.11

4.12

4.13

4.14

Schematic experimental geometry of ultrafast electron crystallography,
showing the different angles of rotation, 9 and 45, the former associated
with a rocking curve, the latter with an in-plane rotation (a). In part
(b), the Ewald sphere intersects the (0,3) rod. An in-plane rotation
(Art) about the (0,0) rod causes the (0,3) rod to move away out of the
intersection and the (0,1) rod to move in. ...............

The TSV deduced from examining the (0,1) and (0,3) reciprocal rods
for the Si(111) / Si02 / OH interface, with a fixed laser fluence of 64.3
mJ/cm2. The incidence angles for the (0,3,24), (0,1,21), and (0,1,24)
peaks are 6.240, 4.700, and 4.150, respectively ..............

The total peak shift, A B, calculated for varying degrees of lattice ex-
pansion (blue) and surface voltage. For a fixed voltage, the associated
shift is less prominent for higher orders of diffraction (00). This is in
contrast to the structural based shift, 63, where the higher orders are
more strongly affected. .........................

The electron beam diameter being much smaller than that of the laser
is an underlying assumption for the validity of the formalism presented
in Section 4.2.1, where the TSV is not affected by the tangential com-
ponents of the field, because the electron beam enters and exits from
the top of the ‘capacitor.’ The aspect ratio of the capacitor is exagger-
ated for clarity. Realistically, the height and width are of the orders of
1 nm and 100 pm, respectively. .....................

General refraction geometry for a grazing incidence electron beam.
The effective bending of the incident(exiting) beam, caused by the local
field associated with V3 in the nanostructures, differs depending on the
entry(exit) point zi(zf). Since the relative change of the transverse
momentum remains small, the slab model can be extended to treat
arbitrary geometries through a correction factor, 9(a, 0), that depends
on position (through oz) and angle (see text) ...............

Correcting the TSV for a finite slab. (a) The potential is calculated
for the mesh, followed by launching an electron at an angle 6 from the
origin (at = y = 0), and using the change in kinetic energy, deduced
from 9’ to get the probed voltage, V3*. The aspect ratio, a = h/ a, is
varied to examine different exit points. (b) Simulation results for the
correction factor, 6(0, (1), as a function of aspect ratio, 0:, show that
for smaller launch angles, the correction factor is well-approximated by
Equation 4.23 ................................

75

76

79

79

80

83

 

4.15 (a) The calculated potential for the case of a 20 nm metallic nanopar-

5.1

5.2

5.3

5.4

5.5

ticle, charged to -5 V, with a 1 nm thick, dielectric layer (6 = 2.5) atop
the Si substrate. (b) The correction factor as a function of aspect ratio
(SAM to nanoparticle) is calculated by resolving the trajectory from
the electric forces. The solid points are the simulated data; the lines
are from the approximation 8 = h / D (see text). Inset: The correc—
tion factor as a function of launch angle 0 for three different launch
positions along the SAM ..........................

(a) The diffraction peak is fit at each delay scan with a Gaussian (blue),
followed by converting the camera pixel coordinates to s-coordinates
(b) using the unit cell, lattice constant, camera distance, etc. (see
text). The momentum transfer (3) at each delay is then converted to
transient surface voltage using Equation 4.11. The orange lines in (a)
are intensity line scans from within the guided area (magenta). . . . .

UEDV data with fitting curves given by Equation 5.1, zoomed in to
early times to show the contrasting r,- as fluence increases. The panels
that have insets are showing the full time scale. ............

Injection time (top) and the maximum amplitude voltage (bottom),
both as a function of fluence. Both plots show the onset of a faster and
stronger source of voltage after ~ 20 mJ/cmz. The fluence—dependent
TSV can be fitted with a quadratic equation (aF + bF2), in which
the quadratic component (bF2) overtakes the linear one (aF) near 20

86

93

93

mJ/cm2, coinciding with the crossover behavior in r,- at the same fluence. 97

(a) A band diagram depicting the Si/SiOg/vacuum interface. (b)
Schematic of the energy diagram with relevant quantities used for the
tunneling calculations. Electrons that tunnel through the oxide to the
SiOg / vac interface, cause the quasi-Fermi level p2 to raise, making the
barrier take on a trapezoidal shape. The electronic density of states
is shown in light-grey for the silicon (D1) and the SiOg / vac interface
(D2). The difference between the two levels, An (dark grey band) is
the primary factor in determining the tunneling current. For a given
energy (a), when Au, D1(e), and D2(€) are all 74 0, then there will
be a tunneling current through the 3102. (c) Probability amplitude
schematic; the wave functions with amplitudes (A, B, C, D, G) are used
to compute the tunneling matrix elements, M (a). ...........

The characteristic time associated with surface charging, 11,-, as a func-
tion of excitation fluence. The simulated 7',- assumes that the TSV
is constituted solely from the voltage drop across the oxide barrier,
calculated from Equation 5.21. .....................

xvii

101

 

5.6

5.7

5.8

5.9

5.10

5.11

5.12

6.1

Coherent absorption, characterized by a consecutive 2- and 1-photon
absorption with electron scattering dephasing. .............

Results from the 2+1 photon calculations using the formalism above,
showing a quadratic dependence in the internal photoemitted yield. .

'Ifansient surface state population measured by photoemission [126]
(diamonds) compared with the measured TSV (triangles) (rescaled;
F =72 mJ/cmz), demonstrating very similar decay rates. .......

(a) Log-log plot of the TSV with a linear fit to the long time data. (b)
A schematic of the space—charge region. (c) A schematic of the bipolar
(two-slab) drift model in (c) is implemented to describe the recombi-
nation. (d) Carrier drift causes the surface charge, 00 to diminish with
a characteristic time 70, after which, 00 falls as t‘1 obtained from the
slab model. ................................

Thermionic emission at an Si/Si02 interface. The work function is
exceeded by the fraction of electrons occupying states in the upper
tail of the Fermi-Dirac distribution (shaded region). As the excitation
pulse is absorbed by the surface, the accumulated yield from the tail
can lead to a non-negligible charge density cloud above the surface.

UEDV data at 400 nm excitation. (a) The TSV response at different
fluences. The ZoT was determined to be 540 ps. (b) Fit results for
800 nm (red) and 400 nm (blue) data (800 is the same as in Section
5.3; shown here for a baseline). Parameters Ti and TSV (inset) are
plotted against laser fluence. Both 400 and 800 nm experiments show
distinctive fast (TH) and slow (TL) injection times for high and low
fluence regimes, respectively, yet the TSV dependence on F is linear
for 400, and quadratic for 800 nm excitations, respectively. ......

A pulse width dependence was observed for the transient surface volt-
age. Blue, green, and red correspond to ~41, 72, and 90 fs, respectively.
The fluence dropped slightly as the pulse width was made shorter
(F = 44.6 mJ/cm2 for the 41 fs pulse and 49.0 mJ/cm2 for the 90
fs pulse) ...................................

(a) A sample of Au nanoparticles immobilized on a functionalized Si
substrate. (b) The chemical form of the APTMS linker molecule.
(c) Schematic of an electron beam scattering from the ordered self-
assembled monolayer chain and the corresponding diffraction pattern.
[190, 194]. .................................

xviii

105

107

109

111

114

118

119

121

 

6.2

6.3

6.4

6.5

6.6

Small-angle diffraction pattern obtained from the Au nanoparticle /
SAM / semiconductor interface. (a) The raw diffraction image shows
powder diffraction from the Au nanoparticles as well as a vertical array
of spots at the center (arrows), corresponding to the self-assembled
linker molecules. (b) Scattering intensity as a function of momentum
transfer (s), where radial averaging has been performed around each
ring perimeter, followed by a subtraction of the diffractive background
(incoherent scattering), yielding the peaks shown in the plot. The
peaks identified are consistent with fcc polycrystalline structure with
a lattice constant equal to that of Au (a =4.080 A). .........

The stages of sample preparation. (a) A modified RCA process leaves
a clean, hydroxylated Si surface. (b) Immersion of wafers in APTMS
and acetic acid, dissolved in deionized water functionalizes the surface,
followed by a rinse/ dry cycle (0), and subsequent immersion in colloid
solution (d) (described in text), and a final rinse/ dry step (e) [190]. .

The effect of varying the ethanol / water ratio on surface coverage. All
panels have 1 mL of colloid solution. The ratios of H20 to ethanol
are given in the upper-right comer of each panel. The hydrophobicity
is reduced as the ethanol concentration is increased, which effectively
enhances the mobility of the nanoparticles in solution [190] .......

The effect of varying the pH of the solution during arninosilane func-
tionalization. Adding small amounts of acetic acid increases the den-
sity of anchoring sites (N H?) for the negatively charged nanoparticles,
hence the increased coverage. Panels (a) and (b) have areal densities
of 70 and 300 rim—2, respectively. Note, sample (b) would give convo-
luted signal, as the nanoparticles are overly dense, scattered electrons
would be intercepted by adjacent nanoparticles before arriving to the
CCD. [190] ................................

A 20 ml bottle of Au nanoparticles with average diameter of 9.6 um i
10%. The red color has to do with the way light is scattered and ab-
sorbed by the nanoparticles. The nanoparticles are monodisperse (non-
aggragated) due to surface functionalization with citrates. A sharp
change in pH (toward basic) would cause them to agglomerate and the
solution would turn blue because of the new average nanoparticle size.

122

125

126

126

The scattering and absorption properties are strongly dependent on size. 127

 

6.7

6.8

6.9

6.10

6.11

The oscillating dipolar mode of a metallic nanoparticle. The incoming
wavefront has an electric field E that induces a collective oscillation of
the free electron gas about the positive ionic core. Polarization arises
because of the net charge difference created near the surface, which
causes the restoring force for the polarization to flip. Here, the period
of oscillation is T. This figure was re-drawn from Reference [364]. . .

Example Mie Scattering calculations. (a) Absorption factor for 20
nm Au and Ag nanoparticles. The inset shows the scattering factor
(A = 1 and nm = 1.33). (b) The electron and lattice temperature
of Ag (solid) and Ag (dashed) irradiated by a 400 nm, 50 fs, pulse
at 5 mJ/cm , where ”abs was used instead of R and 63 (see Section
3.1.3). (c) Absorption factor for 40 nm Ag nanoparticle as a function
of the refractive index of the surrounding. Shown are vacuum (1.0),
water (1.33), and common value for nanoparticle ligands (2.5), clearly
indicating the strong dependence of the SPR position. ((1) Surface
scattering factor A is varied for Qabs, which mostly affects the SPR
width. ...................................

The normalized scattering factor for Au nanoparticles of 10 nm diam-
eter, showing a strong peak near 650 nm, which will appear red in the
visible spectrum. .............................

UEDV applied to the Semiconductor / SAM / Nanoparticle interface. (a)
A ground state diffraction pattern of this system, which exhibits the
characteristic Debye—Scherrer rings for the polycrystalline Au nanopar-
ticles, co—present with the diffraction peaks associated with the linker
molecules. The latter, extracted from the full pattern, are also shown
in part (b) (inset). (b) The total transient shift, A B, observed from
the (001) diffracted beam (circled), which is that of N = 1 (s = 2.75
A’l) from the aminosilane linker molecule (chemical structure shown
in inset) ...................................

The equivalent circuit diagram to describe the charging and discharg-
ing dynamics in the semiconductor/ SAM / nanoparticle interconnected
geometry. Subscripts ‘M’ and ‘8’ describe the linker molecule and
Si/ 8102 surface, respectively. Their associated resistances, capaci-
tances, and voltage drops are denoted by R, C, and V, respectively.
The resistances of the bulk (Rbulk) and vacuum gap (Ii/vac) are con—
siderably larger than RM and RS, such that both --) oo. .......

128

133

135

137

137

 

6.12

6.13

6.14

6.15

6.16

7.1

7.2

(a) The refraction shift observed by following the (001) diffracted beam
(at s = 2.75 A) from the SAM described in Fig. 6.1. The solid points
represent the raw diffraction shifts arising from the SAM (VM) and
the Si/SiOg surface (Vs) (continuous line) (see text). The inset shows
the early time evolution of the TSV shift that has a significant VM
contribution, deviating from the smooth transition of VS described by
Equation 5.1. (b) The voltage drop across the SAM, VM, which was
determined by first subtracting the contribution V3 from A 3, followed
by applying Equation 4.19. The fit shows a rise time T,- = 5.6 ps and
a biexponential decay with time scales 13.1 and 77.7 ps .........

Femtosecond laser induced nano—cavity formation. (a)-(b) are from one
sample, (c)-(d) from another. ......................

A schematic of near-field lensing under the assumption of UEC geom-
etry (pump laser incident at 45°. The lens that is shown is fictitious,
but captures the essence of the near-field antenna. The extinction cross
section ”east is the ratio of the incident power to the total intensity
scattered and absorbed. .........................

The efficiency factors, Qabs (blue), Qsca(green), and an (red), for 40
nm Ag (a) and Au (b) embedded in a dielectric medium with index of
refraction nm=1.5 .............................

Shown are the effects of particle size on the scattered near—field [181].
The UEC geometry is similar (in polarization), but tilted to 45° inci-
dence. ...................................

Schematic view of the doser reservoirs. Gas is admitted into the system
to a pressure P0. The pinhole orifice prevents the intra—doser pressure,
PD from rising significantly, from its original pressure prior to dosing,
P. Here, P is the pressure of the main chamber and S is the pumping
speed ....................................

A laser-drilled, stainless steel gasket, deformed between a VCR double-
female and double-male operates as a flow restrictor. The clearance
hole has a 2 am diameter and was drilled at the center of the gasket.

139

140

141

143

143

147

148

 

 

7.3

7.4

7.5

7.6

7.7

7.8

7.9

7.10

Dry nitrogen gas is pumped through the pinhole. (a) The left volume
is purged with N 2 until it reaches P0. The right volume (load-lock)
is continuously pumped by a turbo molecular pump (pumping speed
S), such that it is maintained at z mid-10’8 torr. The time taken for
P0 —) P is used to measure the conductance, along with the gas and
geometric properties (P0, V, T, m). The pressure rise in the load—lock
from the influx of N2 is negligible. (b) The measured pressure in time
during the pumping shows that under these conditions, it takes z 20
hours for the pressures to equilibrate to the load—lock base pressure. .

Scanning electron micrograph images of the microcapillary array. The
resulting holes from laser drilling were z25-40 ,am in diameter, spaced
500 pm apart, and conical through the thickness. ...........

Holding mechanism for the microcapillary array. The microcapillary
array is simply pressed between the two pieces shown that are fastened
by 4 # 0—80 machine screws, leaving the possibility of gas leaking
through the sides. However, flow through the array holes is unimpeded,
so should be favored ...........................

Schematic of the two setups used to investigate the rate of side leak.
(a) With no holes drilled (blind), the shim-stock only permits passage
through the sides. (b) This configuration permits gas through the
MCA holes and the sides (parallel conductances). The time associated
with pumping gas through each configuration allows for the side leak
rate to be determined (see text) ......................

A direct comparison of the ‘pump-through’ times associated with a
blank piece of shim-stock and the drilled piece. Their difference gives
the leak rate through the sides, which is found to be ~ 4% (see text).

A full schematic view of the molecular beam doser. ..........

UHV chamber pressure as a function of sample-holder temperature. As
the sample—holder warms, various species desorb from the Si surface,
hence the rise in global pressure. The bifurcated peak at z150 K is
water desorption. ............................

The final CAD drawings of the MBD and GHS. Upper right: motion-
feedthrough in the form of a push-pull is connected to a rigid copper
piece, on which the MBD sits. The flexible stainless steel tubing is
seen dangling from the MBD head. Bottom center: a snapshot of the
actual GHS (the ballast is not shown). The CAD drawing (blue) does
not depict the flexible tubing. ......................

)otii

149

150

151

152

154

155

160

161

 

7.11 Ground state diffraction patterns of an ice layer adsorbed to Si(lll) / 3102.
The cryo-chiller for the stage was turned off after the pattern in the 118
K shot was taken. Repeated shots were taken as the stage warmed to
160 K, where all remaining water had clearly sublimated. At 145-150
K, it can be seen that the Debye-Scherrer rings become substantially
sharper, signifying that the water has sublimated down to the last bilayer. 162

7.12 Laser annealing water on Si. (a) The usual water structure near 118
K, the rings are rather broad. (b) The ice structure following laser
irradiation with 66 mJ/cm2 for 15 mins at 1 kHz with 45 fs pulses. . 163

7.13 The Debye-Scherrer rings are identified for the annealed water struc-
ture. The maximum intensity from the gated region (red dashed box)
is plotted as a function of the ambient temperature during the warm-
ing cycle (inset), where the ‘M’ shape can be seen as the water goes
through sublimation. .......................... 164

 

A.1 Bragg Scattering. The path difference between two adjacent lattice
planes is (1 sin 0. .............................. 169

A2 The Ewald construction. A 2D cross-section of the Ewald sphere is
shown, representing all possible momentum transfer candidates, 8.
Constructive interference occurs only when 3 lies in the reciprocal lat-
tice, shown by the black dots. ...................... 173

A3 The Ewald construction as periodicity is suppressed in the longitudi-
nal direction. Panel (a): the Ewald sphere intersecting a 3D array of
reciprocal lattice points. Long range order is present in all directions.
Panel (b): when the electron beam samples only superficial (surface)
layers, the reciprocal lattice points are elongated in the direction nor-
mal to the surface, resulting several families of planes of reciprocal
lattice rods. Panel (c): the area of the Ewald sphere intersected by
a reciprocal lattice plane. Constructive interference will occur when 3
passes through one of the rods. ..................... 173

AA Typical Ewald constructions (not to scale) for the cases of LEED (a),
transmission geometries such as TEM (b), and reflection mode geome-
tries, such as RHEED (c). The size of the respective Ewald spheres will
be much different for these three cases, depending on the accelerating
voltage. Generally speaking, LEED would have the smallest, followed
by RHEED, followed by TEM. Ensemble wave vectors sf are drawn
opaque. All interior angles here are 05 .................. 175

xxiii

B.1 Panel (a) The frequency range (bandwidth) for an arbitrary lasing
medium, (b) standing waves created in an optical cavity, (c) the super-
position of (a) and (b), which is the laser output. The lasing medium
selects only those cavity modes that fall within its bandwidth. . . . . 177

B2 The normalized absorption and emission spectra for Ti:Sapphire. Ab-
sorption occurs from about 400 to 650 nm; emission from 600 to 1050
nm [438]. ................................. 178

B3 The seed pulses are stretched (in time) prior to amplification as to
not damage the Ti:Sapphire crystal, followed by amplification in the
Ti:Sapphire crystal. Finally they compressed back down after amplifi-
cation. [440] ................................ 181

 

xxiv

Chapter 1

Introduction

1. 1 Charge Transfer

The need for a clean energy economy for tomorrow has ushered in a mandate to
develop practical solar (carbon neutral) energy capture technologies [1—4]. Charge
transfer mechanisms [5—14] and their elucidation lie at the root of novel solar cell
technological development [4, 6, 15—51]. An efficient conversion mechanism that re-
liably competes with internal recombination is the essence of next generation solar
cell technology, including dye- [6, 16, 34, 39—43, 43, 44, 48, 52] and quantum dot-
sensitized [18, 35] nanoparticles and films, often in conjunction with nanowires for
enhanced transport [4, 23, 33, 34, 38], surface plasmon-enhanced harvesting capa-
bilities [20, 23, 25, 30—32, 45, 51, 53], and multiple exciton generation capability
[17, 21, 27—29, 33, 47].

Charge transfer is also inherent to semiconductor technology, with steady-state
probes at semiconductor/ oxide interfaces including conventional steady-state mea-
surement techniques, such as capacitance-voltage (C-V) measurements, Kelvin probes,

and X-ray photoelectron spectroscopy [54—59].

The nature of charge transfer, trapping, and detrapping at the Si/SiOg interface
has gained notable interest as CMOS devices are further integrated in accordance
with Moore’s law. While the mechanisms associated with tunneling have been stud-
ied for years [60—65], it is in the more recent past that gate dielectric oxides have
approached the sub-micron to nanometer length scales, which has initiated interest
in comparing the various mechanisms associated with leakage currents and tunneling,
often concerning the roles of Fowler-Nordheim (FN) and direct tunneling [56, 66—77].

Time-resolved investigations on the Si / SiOg interface are commonly done through
a contactless approach called electric field induced second harmonic generation (EFISH)
[78—100], which is effective in probing the interfacial field as it is a point of broken
symmetry; a necessity for SHG. In general, these studies are performed with high
repetition rate lasers, on the order of 80 MHz, implying that the system is pumped
every ~13 us, which is before trapped charge can relax, such that the residual charge
level is continuously pumped. This of course depends on the integrity of the interface,
or, more directly, the density of interface states.

One of the focal points of this work is a contactless, time-resolved voltage probing
technique that has been implemented at MSU, extended from ultrafast electron crys-
tallography (UEC) [101—104] and ultrafast electron diffraction (UED) [102, 105—110].

1.2 History: Shutters to Short Pulses

It was predicted in 1931 that the fundamental time scale associated with chemical
reactions should be on the order of femtoseconds [111]. Short-pulsed energy excita-
tions had already become a tool used to characterize the lifetime of chemical reactions
on the milli- to microsecond time scales by the 1960’s, owing to the efforts of Eigen,
Porter, and Norrish, who were recipients of the 1967 Nobel Prize in Chemistry [112—
116].

The interest in resolving chemical nonequilibrium and transition states continued
through the work of Femtochemistry, a technique pioneered by Nobel Laureate Ahmed
H. Zewail (1999, Chemistry) [37, 117—121]. In the ‘pump-probe’ method used by
Zewail, a short-duration energy perturbation (usually in the form of an optical pulse)
is first introduced to a system of interest. Before the system can return to its original
(ground) state, a measurement is taken on the system with another short-duration
probe pulse, so as to capture the effects from the pump. Probe pulses can be timed
very precisely to arrive at fixed intervals after the pump has initiated the reaction.
In the studies of the transient molecular processes, femtosecond pump and probe
time resolutions are required. Pump-probe methodology of this general description
has been applied to various systems, from gas phase molecular reactions [121], to
condensed matter material processes recently, and encompasses many different forms
that lead the frontier of time-resolved research today.

The spirit of a fs pump-probe arrangement is to acquire information on matter
when it is displaced from equilibrium by electronic excitations. It is thus common
for the pump to be an ultrashort laser pulse to initiate various states of excitation
(nonequilibrium), while variations come into play with ultrafast probes, depending
on applications. One form of probe is a subsequent optical pulse that photoejects
electrons from the system, which are then detected in an energy analyzer, known as
time-resolved two photon photoemission (TR—TPP) [122—126], which is often coupled
with angle-resolved photoemission spectroscopy (ARPES) [127] to examine the carrier
energy-momentum relationship (Fermi-surface) in materials. Another form is that of
a probing laser pulse that is used to study the reflective or absorptive properties of
the system, (transient absorption or reflective spectroscopy) [16, 39, 47, 128—136].
The transient optical responses of the reflected light, (or lack there of) are used
to characterize the electronic properties of the photoexcited states. There are also

several interesting nonlinear optical techniques that exploit broken symmetries, which

can be used as an ultrafast probe. Examples include second-harmonic generation
(SHG) and sum-frequency generation (SFG) [80, 85, 90, 92, 97, 137—156], which is
highly sensitive to surfaces and interfaces. Another form of probe is that of a low
energy infrared (terahertz) pulse that is detected after passing through the excited
sample, with the changes in frequency and phase giving a complete measurement of
the complex dielectric function, permitting simultaneous studies of carrier relaxation
and transport, without the necessity of an electrical contact point with the sample
[21,157,158]

The essence of pump-probe, which is to function as an effective ‘fast camera’
to capture these ultrafast events, dates all the way back to the late 1800’s and the
invention of the first camera to implement a fast shutter speed. Specifically, it was
used to answer a question as to whether all four hooves of a horse left the ground at
the same time in an individual gallup. Eadweard Muybridge settled this controversy
by constructing a camera with a shutter that could open and close approximately
1000 times per second, which was capable of resolving the various stages of a horse’s
locomotive cycle (Figure 1.1), while it galloped approximately 20 miles per hour (10
m/s). He did this by arranging triggers at various points on the race track that would
snap the photo as the horse passed.

A more modern example of a fast detector is that of a streak camera [159—168],
which can be employed to measure the temporal profile of an optical pulse, provided
the pulse width is longer than a: 100 fs (lasers are well-below this today). Essentially,
a streak camera converts the temporal characteristics of an optical pulse into a spatial
profile on a CCD detector, by applying a time varying field to the incoming pulse.
Specifically, incoming photons are directed onto a photocathode (preferably with low
work function). The electronic emission is accelerated through deflector plates that
have a time varying electric field, causing the electron bunch to spray across the CCD

detector. The temporal characteristics of the pulse can be deduced from the dispersion

 

 

 

 

 

  

 

 

 

 

 

 

 

Figure 1.1: The fast camera invented by Muybridge allowed the question to be an-
swered: do all four hooves of a horse leave the ground at the same instant during a
gallup? The answer is no. All four legs are off the ground, but not with full extension,
which was presumed by many at the time. This sequence was taken 6 / 19 / 1878 at a
track in Palo Alto, CA. This photograph is property of the Library of Congress Prints
and Photographs, Washington, DC 20540.

relationship of detected electrons, which depends on the accelerating voltage, work
function of the photocathode, and electric field applied to the deflectors [161]. The
time resolution of a streak camera is limited (mostly) by the temporal dispersion of
the photoelectron bunch as it is accelerated from the photocathode to the deflection
plates. Accordingly, contemporary designs attempt to minimize this distance [161].
Streak cameras have also been implemented for measurement of ultrashort electron
pulses [169].

The streak camera, which is literally a fast camera, has not enjoyed the same rapid
growth [166, 170] over the past decade as its counterpart, the ultrafast probe, which
is more of a figurative fast camera. A fast probe relieves the necessity of having
a fast detector, some of which will be discussed in the next section, including the
cornerstone technique of this work, ultrafast electron diffraction [102-105, 171—174].

Ultrafast electron diffraction (UED) is an optical pump - diffraction probe tech-
nique, spear-headed initially at the California Institute of Technology (Ahmed H.
Zewail’s group) [102—105, 171—174]. A femtosecond laser pulse excites the sample,
while an ultrashort electron pulse serves as the diffractive probe of the crystal struc-
ture, at a fixed delay time after the pump arrival. Unlike optical techniques, the
diffractive probe is directly sensitive to the atomic configuration of the materials,
thus providing crucial information on the nonequilibrium structures of the transient
states.

Since its implementation, UED has had numerous accomplishments and remains
a robust tool for investigations requiring high spatio—temporal resolution [102—104,
172, 173, 175-177]. Similar developments of ultrafast diffraction techniques using
X—rays rather than electrons to probe structure [178—185] have also undergone signifi-
cant progress, especially with the recent development of femtosecond high brightness

coherent X—ray sources from free electron lasers [186—189].

The work here is on the multi—faceted development and expansion of UED at
MSU since 2004; specifically, the spawning and development of measuring tran-
sient interfacial electron dynamics. The technique, ultrafast electron diffractive

voltammetry (UEDV), will be presented in Chapter 4.

 

Chapter 2

Ultrafast Electron Crystallography
Laboratory at MSU

2.1 Introduction

The development of ultrafast electron crystallography (UEC) at MSU aims to combine
surface sensitivity, atomic scale spatial resolution, and ultrafast temporal resolution,
in order to investigate the ultrafast processes that proceed at nanometer scale surfaces
and interfaces. Surface sensitivity is a consequence of the grazing incidence geometry,
which, by definition, implies a large transverse momentum component relative to the
one normal to the surface. With only ~1% of kinetic energy directed into the depth
of the crystal, the beam penetrates only a few sub-surface atomic layers (~ 1 — 2 nm,
depending on incidence angle), thus lending to the surface sensitivity.
Note that surface sensitivity and spatial resolution do not refer to the same thing.
High surface sensitivity, indirectly, refers to the level of signal-to—noise (S / N) of scat-
tered electrons arising from their interaction with the surface layer. It is bolstered
by a small probe beam cross-section. Spatial resolution, on the other hand, is de-

fined by the Compton wavelength (A8), which is the intrinsic size property of the

probing electron, and thus needs not relate to the surface. Consider for example a
transmission electron microscope (TEM), which is operated at high accelerating volt-
ages (~ 200 kV) affording high spatial resolution, but the beam can be transmitted
throtngh hundreds of atomic layers, and would not be considered surface-sensitive.

Optics Bench
266 nm

      

UHV
Chamber

 

 

 

 

 

Figure 2- 1: Ultrafast electron diffraction geometry at MSU. (a) A schematic of the

UEC optical setup. For completeness, both 400 and 800 nm beam lines are shown

entering the delay line. In practice one of them will be blocked based on the choice

of excitation energy [190]. (b) In the UHV chamber, an optical pulse (of 400 or 800
nm) Excites the sample (red), followed by subsequent probing in the form of electron
diffraction (blue). The electron pulse is generated from an ultrashort laser pulse
striking a. silver photocathode (not depicted), negatively biased at —30 kV, which is
focused onto the sample. Diffracted electrons are captured on an image intensified
phosphor screen and recorded by a CCD camera.

One Of the difficulties encountered with the surface sensitive probe is that of the
‘velocity mismatch’ between the pump and probe, as the former travels at the speed of
light (C) and is incident at 45°; the latter at z 0.34c (depending on the accelerating
voltage) is incident at a grazing incidence angle. As a result, the ultimate time
resolution is limited by the convolution of the two pulses, since their respective arrival

times on the surface are different at different points (Figure 2.2) [191]. Baum and

9

Zewail demonstrated a method using optics, where the wavefront of the pump pulse
was tilted relative to the propagation direction, effectively forcing the pump arrival

to be consistent with that of the probe at all points [191].

A B 2:17.:
:éi fl/AL’ Eff—5.42:2:
v‘ Sample

 

Figure 2.2: The group velocity mismatch problem is demonstrated in parts (a) and
(b), the synchronization of the two is inherently confounded by their differing propap
gation speeds. In (c)-(e), the electron beam sees the same pump for all spatial probing
points, because of the wavefront tilting of the pump. [191]

To overcome the velocity mismatch problem, the approach taken at MSU is to
significantly reduce the probe size, which limits the spatial area of pump-probe overlap
on the surface, thus achieving a high temporal resolution. Through implementation
of a short—focal distance electron lens and a set of properly positioned apertures, an
electron probe as small as 5 pm has been demonstrated in studying nanostructures and
nanointerfaces [190, 192—194]. Future generation electron guns, which will naturally
strive towards even smaller beam cross-sections, will very likely possess the capability
0f probing a single nanoparticle.
In addition to the importance of the probe characteristics, some of the more techni—
cal aspects of UEC, pertaining to instrumentation, pump-probe geometry, frequently

occurring measurements and calibrations, and various measures that can be taken to

10

reduce sources of error will be outlined in this chapter. It can be thought of as a

‘behind-the-scenes’ look at what goes into a UEC experiment.

2.2 Optical Pump - Diffraction Probe Setup

At MSU, the pumpprobe scheme, depicted in Figure 2.1, has a fs-laser pump pulse
coupled to an electron beam (or e-beam) that probes the crystal structure near the
surface via diffraction, as discussed above.

Diffracted electrons are collected in a micro-channel plate amplification medium
(capable of 10,000 e/ e gain), proximity focused onto a phosphor screen, and a CCD
camera records the image. Experiments are carried out in an ultra-high vacuum
(UHV) system, possessing experimental tools such as a quadrupole mass spectrom-
eter (QMS), detectors for low-energy electron diffraction (LEED), Auger electron
spectroscopy, and a spherical energy analyzer, along with several tools for surface
Preparation, including an argon sputtering gun, a molecular beam doser (design and
calibration in Chapter 7), and a load-lock to allow fast sample transfer with no dis-
ruption to UHV, all of which is depicted in Figure 2.3. The stage has cryo-cooling
capability (down to below 20 K) and five degrees of spatial motion.

A commercial femtosecond laser system (purchased from Spectra Physics), em-
ploys a Ti:Sapphire lasing medium to generate ultrashort pulses, at a repetition rate
of of ~80 MHz and pulse energy of 2.5 nJ (Figure 2.1). This seed laser is fed into a
regenerative amplifier (‘Spitfire’), which is pumped by an external laser (‘Empower’),
’60 reach a. significantly higher pulse energy (up to 2.5 mJ / pulse), with pulse dura-
tions 0f ~ 45 fs and repetition rate of 1 kHz. The principles of femtosecond laser
pulse generation, including modelocking and regenerative amplification are presented

in Appendix B.

11

UHV Chamber

  

Level 2 Quadrupole Mass

Spectrometer

     
 
 

Photoelectron

D/Auger
CCD

a Loadlock LeveL3 Camera Spherical
- mm

Figure 2 -3: The UHV chamber and tools for surface preparation and characterization
[190].

Upon exiting the Spitfire, the laser is split into two beam lines (50/50), where
one is directed through the delay stage and subsequently to pump the sample, and
the other is run through a frequency triplerl, such that a 267 nm (4.65 eV) beam
is emitted. It is then directed into the UHV chamber where it strikes the electron

gun photocathode), held at -30 kV. The photocathode is a thin Ag film of thickness
(~ 40 nm), which has a work function ~ 4.5 eV [195], just below the frequency-tripled
exciting pulse energy, to generate photoelectrons with relatively low energy spread. In
this arrangement, an ultrashort pulse of electrons of similar duration as the exciting
laser pulse [196—199] can be generated at the photocathode, and are accelerated to 30
keV in just 5 mm. A proximity-coupled magnetic lens focuses the electron beam onto
the sample. The overall photocathode-to—sample distance is ~5 cm, allowing only a

moderate space-charge broadening spread to develop, so as to reach the sub-ps time

resolution.

2.2. 1 Pump-Probe Alignment

Concentric pump-probe spatial overlap is essential prior to beginning an experiment.
A stainless-steel shaft with a needle point (z 75 pm) was built onto the stage (Figure
2.4) for the purpose of pump-probe alignment. The stage position is adjusted such
that it can be determined that the electron beam is passing through the needle tip,
as shown in Figure 2.4 where an actual image from the CCD of an unfocused beam
is displayed. As the electron beam is focused, the beam waist (full-width at half
maximum) is smaller than the needle tip size, so the integrated transmission intensity
(through the needle) is used to judge the position of the electron beam relative to the
needle tip.
Having ensured the passage of the probe beam through the needle tip, the second

step is to bring the pump beam through the needle tip as well, thus creating ‘pump-

 

1The TPH Tripler model was purchased from Minioptic.

13

probe overlap.’ However, allowing the pump laser to directly focus onto the needle

tip could actually damage it. For this reason, two diode lasers (adjustable), each
with a different vantage point, are used instead to simultaneously pass through the
needle tip. Now, the diode lasers overlap at a point in free space, corresponding to a
point through which the electron beam is known to pass. The stage is then moved
and oriented in such a way that the diode laser spots overlap on some metallic flat
surface of the stage. The pump laser is then admitted into the chamber with high
attenuation (to avoid the possibility of damaging anything inside), and displaced with
adjustment mirrors such that it overlaps with the diode spots. This roughly aligns
the pump and probe in space. Thus, when the stage is subsequently moved to a point
where a diffraction pattern is observed, it can be assumed that the influence of the
pump laser is present to some extent.

At this point, the fine adjustments can be made by examining the actual diffrac-
tion responses on the sample surface as feedback following additional fine steps of
controlling the beams on the surface, as described in Figure 2.5. The first step is to
bring the excitation laser beam to a more precise vertical (7. in Figure 2.5) alignment
position with respect to the probing electron spot on the surface, by way of an ad-
justment lens to displace the laser spot. By monitoring the corresponding changes in
the diffraction pattern as the laser beam is moved through the region (here the laser

pulse is timed to arrive before the electron probe pulse), a ‘maximum change point’
can be identified and the corresponding z-position of the adjustment lens is fixed for
the experiment. This results in vertical alignment of the beam spots, as shown in
Figure 2.5 (c)

Note, the maximum change in the diffraction pattern could be ascertained from
various diffraction signatures, such as displacement of spot positions, or drop in Bragg
peak intensity; ultimately, depending on the characteristics of the system on which

alignment is being executed. Silicon peaks, for example, exhibit very little intensity

14

 

 

  

Ill," needle

Sample

 

Figure 2.4: Coarse alignment. The electron beam and diode lasers from two different
vantage points are passed through the needle. This means that the diodes overlap at
a point in space corresponding to a known point through which the e—beam will pass.

15

drop, so the position changes are used to align. Also note that aligning the horizontal

axes of the two beam spots could also have been done by moving the electron beam
instead of the laser beam, but this would necessitate the use of another set of beam
deflectors to shift the spot in that direction (which are installed on the gun). The lens
here is under planar 2D motor control, which allows for efficient automation of the
process. Moreover, deflecting a strongly focused electron beam would cause a change
of the crossover size of the beam on the surface and shift the point of interception
with the laser beam in the y—direction. Modifications like these introduce undesirable
changes to the pump-probe overlap.

The second step of fine adjustment targets alignment of the pump and probe spots
horizontally (y) on the surface, by displacing the sample stage in the :r-direction. By
inspection of the hypothetical example in Figure 2.5(c), the stage would need to move
along positive a: to compensate the offset. Similar to achieving vertical alignment,
the diffraction changes are recorded as a function of the stage position, which is
incrementally displaced (every 10—20 pm) in the as-direction. However, varying the
stage position relative to the electron beam modifies the diffraction pattern. For this
reason, at each stage position (ac-increment), both ground and excited state patterns
are recorded for self-referencing, shown in Figure 2.6(b). The :r-position where the
maximum difference is observed corresponds to the fully aligned position.

Because of the grazing incidence, motion of the .r-goniometer (stage) causes the e-
beam footprint to move ~10-fold larger on the surface in the y-direction, or Aysmf =
Axstage/ tan0i, where the incidence angle, 02-, is very small. This is in contrast to
the Pump laser, which has lzx/2 correspondence because of the 45° incidence. Taking
note of the two alignment steps, the first step moves the laser in free space, while
the second step moves the electron footprint on the sample, as it is the stage that is

moved.

16

 

 

Figure 2.5: Pump-probe fine alignment. (a) The pump laser (red), incident at 45°,

lllcrementally moves vertically (2) along the stage (motion not depicted), with a
probe shot (blue) taken at each stop. The maximum change in the diffraction pattern
Foflesponds to improving the rough alignment shown in (b) to the partially aligned
11:. (C)- The stage goniometer is then adjusted incrementally along the x-direction,
at each stop taking diffraction images from the pumped and unpumped sample by
Varying the delay before and after the zero of time. The z-position where maximum
Ch ange was observed corresponds to the fully aligned position in (d).

Alignment Scans

 

 

 

 

 

 

 

 

 

‘x‘ 1795 V I V I V I V I V I I V I V 1 V I V I V I
o ‘ V o D I l
V 179.0 - av.v v e ay 500 ps .
5 . 3"" 1
IE 1 78.5 J . Gog .
3 l 00 ,
a 1 7800 ‘ V \ F
g . ’ W l
g 1 77.5 . V7 v v l
a 1 V 00 q
5’ ‘77-0 ‘ Q50 -1 2 -o.s -04 ‘ K ’ V '
2 ' (3) Vertical Lens Position (mm) (b) VVDela 700 s '

m 176's V I V I V I V I V I V I V I V I V I yV f F i
-1.25 -1.00 -0.75 -0.50 -0.25 0.00 12.80 12.76 12.72 12.68 12.64 12.60

Vertical Lens Position (mm) X - Goniometer Position (mm)

Figure 2.6: Alignment scans. (a) The first scan of the fine alignment process, showing
the Bragg peak position change on the CCD screen (inset shows the intensity drop)
as the laser spot is displaced in increments of 50 pm. (b) The second scan of fine
alignment, where the stage is stopped every 10 pm to take diffraction shots at delays
of 500 ps (circles) and 700 ps (triangles), and the ZoT is 540 ps. The lens and stage
positions were chosen here to be -O.65 and 12.70 mm, respectively.

Why not displace the lens horizontally for the second step to find the overlap? In
principle, this can be done (and sometimes is). There are several reasons why it is not
advisable. One reason is that it changes the camera distance and thus, the ZoT, as
the pump and probe will be overlapped at a different point in free space than before,
Which is necessarily nearer or further from the camera. Note that vertically displacing
the pump laser does not change the ZoT, because the camera distance remains the
Same, which is why it is safe to do in the first alignment step.

MOVing the z-goniometer changes the point where the pump and probe strike
the surface, but in free space the point of overlap is unchanged. In the event that
the a“lignrnent needs to be adjusted during an experiment, as most experiments will

SQmetimes go on for 1-10 weeks, some data sets could have different zeroes of time,
EU hiCh makes it impossible to be unequivocal when correlating them.

A recent study was conducted by the UEC group where the pump laser induced

a. PhOtoemission yield from a graphite surface, and the background scattering from

18

the diffracted beams could actually be used to ‘image’ this cloud [200]. There, the
pump and probe were intentionally misaligned so that the pump laser would strike
the surface to the right of the probe pulse. As a result, scattered electrons would be
forced to traverse the photoemitted cloud in transit to the CCD. See Reference [200]
for details pertaining to the technique and quantification of the photoemission yield.
Another noteworthy point is that of pump-probe interaction, which could happen

as the two pulses are engaging the sample. For a post-ZoT delay time, the pump laser
pulse could very well encroach the probe pulse in transit to the surface, and exert
a ponderomotive force on the electrons in the pulse. Generally speaking, this is not
a practical concern as these fields tend to be rather weak, though at high fluences
there are sometimes some effects. In fact, Hebeisen et al. devised a technique to

characterize the electron pulse width from these effects [201].

2.3 Experimental Measurements and Calibrations

2.3.1 Laser Fluence

F luence is formally defined as the single pulse energy divided by the laser beam cross-
Sectional area, striking the surface. The pulse energy is measured with a power meter2
at a position in front of the port where the excitation laser enters the UHV chamber.

Intom the power measurement (P), the corresponding pulse energy (Ep) is given by

Ep (J/pulse) - P (W) (2.1)

T frep (HZ),

Where frep = 1 kHz is the repetition rate of the laser.
All that remains is to know the laser irradiated area on the sample surface, Al-

If the PI‘Obe spot size is small compared to that of the pump laser spot, this can

 

2SPeCl'Il‘ar-Physics, Model 407 A

19

be deduced by performing the first of the two alignment scans described in Section
2.2, above. As the pump laser is dragged across the surface, the static electron
probe (in position) will record increasing dynamical effects as the laser approaches
concentricity with the probe, and conversely the dynamics will be quenched as the
pump laser continues on its path away from the probe. The probe saw a Gaussian
excitation over the motion according to the diffraction patterns recorded along the
way; the full-width at half-maximum (FWHM), corresponding to the laser spot size,

as shown in Figure 2.7.

 

 

 

 

02 l V I V I fi I ' f
l .
g oo- 00 <> 0‘” 000
I? ‘ °° o o ‘
a -0.2- o -
x 1 ‘
§ 414- FWHM <> ,
O: 4 O ‘
5’ -0.6- o ..
m ‘ o ,
-0.8- o -
q o ‘
’1.0‘ u
-1'.o ' -o'.5 ' 0T0 ' 0T5 ' 1T0

Laser Spot Coordinate (mm)

IFigure 2.7: As the laser spot is brought into the probe area, the response of the Bragg
peak Increases until it reaches a maximum. At this point, the pump and probe are
perfectly concentric, followed by the gradual decrease in Bragg peak response as the

ééser is dragged out of the probe region. The FWHM of this curve is the laser spot
lzae

The laser strikes the sample at an angle of 45 0, so the horizontal component
of the Spot, size is flu) (w is FWHM). For the elliptically—shaped laser spot, the

real, 15 A1 = 7rw2/x/é. The v1ewport WlndOW introduces a slight attenuation factor

20

to the laser as it enters the UHV chamber, which has been measured to be 0.806

(transmittance). So the laser fluence is

F = 0.806 (%) = (0.806) (figfié) (2.2)

2.3.2 Pulse Width - Interferometric Autocorrelation

3 mea-

Several different techniques have been developed for sub-ps pulse duration
surement, including (but not limited to) interferometric autocorrelation, frequency-
resolved optical gating (FROG) [202], and spectral phase interferometry for direct
electric field reconstruction (SPIDER) [203]. The technique employed here is the for-

mer [204]. The autocorrelation function is the cross-correlation of a signal with itself,

01'

A(T) = /00 E(t)E(t — 7')dt, (2.3)

—oo
where E (t) represents the signal of the fs laser pulse.

Within the framework of autocorrelation, there is more than one method. Essen-
tially, the idea is to find the autocorrelation function, A(7'), measure its width, Ata,
and then relate it to the pulse width, Atp. Very simple relationships, can be derived
(trivially) that relate Ata to Atp, depending on the shape of the pulse (Gaussian,

Sech2, Lorentzian, etc.); some examples are given in Table 2.1.
Conventionally, measuring A(T) is as follows: the pulsed input beam (fundamen-
tal) is Split (50/50), followed by delaying the twin with respect to the original and
then 13888ng them through a doubling crystal, where a second harmonic will be gen-

el‘ ated (SHG). In other words, the two input signals, with fundamental frequency wl,
\

 

3 . . . .
8 Throughout this work, pulse duration and pulse Width Will be used synonymously. There are
I he M where it is more intuitive to use one over the other, but they mean the same thing.

21

 

Pulse Shape Signal Widths

 

 

E(t) Atp/Ata
Gaussian exp [—2.77 (t/Atp)2] 0.707
Lorentzian (1 + 2t / Atp) _2 0.500
Hyperbolic Sec sech2 (1.76 t / Atp) 0.648

 

Table 2.1: Relationships between the widths, Atp and Ata, of a signal and its auto-
correlation function, respectively.

enter the crystal and a frequency-doubled signal exits,
wl + wl => Log. (24)

The amplitude of the SHG signal is oc E2, which is the integrand of Equation 2.3,
thus demonstrating the necessity of the doubling crystal. The intensity output can
be recorded at various delay times (demonstrating the necessity of a variable delay
stage), thereby tracing out the temporal profile of the autocorrelation function, A(7').
Once acquired, its width, Ata, is used to deduce Atp.

A second way, which is the one employed in the UEC lab at MSU, is to use

a. Single-shot autocorrelator4, which eliminates the need for a variable delay stage
[205, 206]- Again the fundamental is split into two pulsed beams, with one delayed
relative to the other. Here though, the two pulses will enter the nonlinear crystal
a-‘I: an angle 6, with respect to the z-axis, causing them to cross inside at an angle
( Figure 2.8). As the pulsed-beams cross each other, they overlap both spatially and

temPOMIly, provided the beam diameter is much larger than the spatial length of

 

4The A Single Shot Autocorrelator was purchased from Minioptic Technology, Inc.

22

the pulse, cAtp. As shown in Figure 2.8, the SH signal is generated by the crystal
and emitted along the bisecting axis of the two beams (the z—axis in the figure). The
signal is proportional to the intensity product of the beams. Since the beams cross at
an angle, each overlapping point corresponds to a different ‘delay’ between the pulses.
The signal is summed in time as it reaches the detector (a CCD camera), such that

the final shape is Gaussian in space along the y-axis, as depicted in Figure 2.8.

 

 

 

 

 

 

“‘~~ Nonlinear y
‘~~.\ Crystal . I
Z
79
xx”, 1 "\ V Autocorrelation
, ' cl> P ,
_,-—' Signal

 

 

 

Figure 2.8: Two beams of frequency to enter the doubling crystal at an angle of 20,
relative to one another. In the crystal, they overlap spatially and temporally, so that
each instant in time represents a difierent intersection point of the two wavefronts.
:I'he SH emission from the crystal (2w) corresponds to different ‘delays’ from these
Intersections, which are integrated in time to make up the autocorrelation signal
(red), A filter prevents the two fundamental beams (to) from entering the detector

(not shown),

But from this spatial profile, how is the pulse-width deduced? The autocorrelation
Signal is fed into an oscilloscope, which displays the Gaussian-like profile, with a
F “HM, AS (Figure 2.9) in oscilloscope time units. It is important to note that AS

18 “Ct the pulse-width itself, though it is proportional to it. The time axis of the

23

oscilloscope cannot be true for this input5, and therefore must be calibrated. This

is done by displacing the mean position of the autocorrelation signal by a known
distance, L, with a micrometer inside the device, which rotates the doubling crystal.
The micrometer reading has been pre—calibrated against rotation angle, so L can
be trusted as the true spatial displacement of the Gaussian. On the oscilloscope,
the pulse will move by some time interval, AT (Figure 2.9). But it is indisputable
that the time displacement was L/c, meaning that AT in osciIIOSCOpe time units
equals L/c in reality. Thus a calibration factor has been deduced, which is‘L / CAT.
This calibration must be done every time pulse width is to be measured. The final

expression for the (Gaussian) pulse width is

Atp = 0.707 7 (3:7) AS, (2.5)

where the factor '7 is to correct for group velocity dispersion ('y = 1.8 for the one used

here) .

2.3.3 Electron Beam Spot Size

Measuring the cross-sectional area of the electron beam is carried out using a standard
technique called the knife-edge method. With a calibrated and trusted goniometer
for stage motion, a knife-edge is clipped on to the stage. Direct beam is a term
llsed to describe the incident electron beam as it flies directly to the CCD, without
g«(:atteiing off of the sample (the stage must be moved out of the way prior). Direct
beam images are continuously acquired as the knife edge is incrementally brought
i linto its trajectory. As the knife-edge eclipses the beam, the intensity of the direct
7%

earn drops, The profile begins at some steady value and then slowly drops to zero,

I%3’Ppihg Out a complementary error function (erfc(x)) as shown in Figure 2.10. The

 

5 .
If It were true, then the oscilloscope could be used to measure the pulse width and autocorrelation
“<0 I
u d not be necessary!

24

 

 

 

 

KAT—K

Oscilloscope

 

 

 

Figure 2.9: Signal time axis calibration. The oscilloscope profile of the autocorre-
lation signal has a spread AS, which is proportional to the pulse width. When the
autocorrelation function is spatially displaced by L, the oscilloscope profile moves by
AT. Moving L and observing AT is the essence of the calibration (see text).

half-Width of this function corresponds to the size of the electron beam. Note, the
curve in Figure 2.10 is not a universal for the lab. The beam size can vary due to a
number of factors, including changing the current in the magnetic lens that focuses
the beam, or the iris diameter for the laser beam as it enters the photocathode. It

is very typical to change one or both of these, depending on the requirements of the

experiment. Consequently, knife-edge scans are commonly done for each experiment.

32.3.4 Rocking Curve

jhe rocking curve is a standard technique for reflection mode diffraction [207]. Es-
§entially, a rocking curve is a series of diffraction images recorded over some range of
imcidence angle, 0,. In UEC, it is frequently used as a way to survey the landscape of
t he CI’l’st a] prior to beginning the time-resolved experiment [194]. Figure 2.11 shows
§ typical rocking curve, this one performed on a rough Si(111) surface. Full images
W

ere reeOI‘ded over a range of incidence angles, followed by cropping out a region of

i
:titerest (ROI) from the each image [Figure 2.11(a)], corresponding to a particular

25

 

l
l

 

 

 

 

 

 

 

-1
1.2 _, - r
g _ knife g
m ’13 1.0 —. edge 2
C Q) d)
93s 08 ‘ X
E To ' _
E E 0.6—.
a o —
.9 5 0.4 __
‘D 0.2-
0.0 Ls, -. 7 ,
'02 ITIII—IIITIT ‘ ‘
-15 -1O -5 0 5 10 15
X (m)

Figure 2.10: The intensity of the direct beam recorded on the CCD as the knife-edge
is incrementally moved in from -15 to +15 am. Inset: Schematic of the knife-edge
encroaching the electron beam path [190].
rod in reciprocal space. These cropped portions from each 0i are stitched together
in order to synthesize a new image, which is a map of the region as a function of 6,,
shown in Figure 2.11(b). The rocking curve map in Figure 2.11(b) was synthesized
by cropping a rectangle around the region in each diffraction image corresponding to
Where the (0,1) is, or would be.
Note that not all peaks appearing in the white boxes in Figure 2.11(a) necessarily
must be from the same rod (though these are). As the images are scanned through,
aPots may pop up in that region that are from a different rod. Careful analysis of
the SPaCing between adjacent peaks appearing on the rocking curve maps provides a

bobust feedback for identifying the corresponding rods.

26

 

   

82°: 6,- : o.7°

 

Figure 2.11: A compiled rocking curve map, revealing the reciprocal space fc
Si(111) surface. (a) An example of one of the full diffraction images that are 00114
at varying incidence angles. A region of interest is selected from each full image, s]
by the white boxes. (b) The rocking curve map, compiled along the (0,1) recip
lattice rod, over incidences of 07" < 9i < 82°; 6 S is the scattering angle.

27

Chapter 3

Electron Phonon Interaction

3.1 Two-Temperature Model

Moving to the theoretical side of UEC, when an ultrafast optical pulse impinges the
surface of a metal, the energy is absorbed by the free electrons. If the width of the
excitation pulse is shorter than the electron-phonon coupling time, a nonequilibrium
is established between the electrons and lattice [208]. The Two-Temperature Model

(TTM) [209—213] describes such processes for metallic thin films, given by

BTe 3 (16

 

Came)? = ‘E — (Te — Ti) + Stat). (3-1)
.aTz' _ 897$ _ ,
c, at _ 82 + C(Te 7“,), (3.2)
8g ' 8T -
qe,z' = _Te,i?:,3 — Ne,i(T€9Ti) 8:1, (3'3)

\Where the laser heating source term, S (2, t), can be described by a Gaussian in time

§nd an exponential spatial decay into the metal:

2
t-t
—4l 2
4ln2(I—R)Fe_z/5se n (752) .

S(Z, t) = 7r tpds

 

(3.4)

28

In the above equations, subscripts e and 2' represent the electron and lattice subsys-

 

Gon-Thermal ElectronD

 

 

 

 

T~503
1' ~ 1 ps
C Thermal Electrons Phonons )
Ke Ki

 

 

( ............ j ( .............. )

Figure 3.1: The energy coupling scheme assumed by the TTM. First, the laser pulse
is absorbed by the free electrons in the metal, which evolve into a Fermi-Dirac dis-
tribution in the first z 50 £3. The thermal electrons dump energy into the lattice,
causing them to equilibrate after z 1 ps (depending on the metal). Both electrons
and lattice undergo thermal losses from heat diffusion, the rates of which are largely
governed by the thermal conductivity, K. (and strictly speaking the heat capacity and
sound speed too).

terns, respectively; T is temperature, q is heat flux, C is heat capacity, It is thermal
conductivity, 7' is relaxation time, and G is the electron-phonon coupling factor. The
Optical pulse interacts with the film through parameters F, tp, R, and 63, which repre-
Sent the fluence, pulse width, reflectivity, and optical penetration depth, respectively.
Parameters R and 63 depend on wavelength. The electronic heat capacity and phonon

relaxation time are given by [208, 214]

 

Ce=7Te (3-5)
$1M
3Kz'
= 3.6
2 Cw? ( )

29

respectively, where '7 is the linear coefficient of heat capacity for the metal and vs the
speed of sound through the metal.

The TTM is nonlinear (through the temperature dependences of Ce and He) and
coupled through the term G (Te — T,), which describes electron-phonon interaction.
Parameter G is inversely proportional to the electron-phonon coupling time, rep, or
the mean time for electron-phonon scattering. In noble metals, such as Au or Ag,

the electron-phonon coupling is quite weak compared to transition metals like Pt or

Ni because of the unfilled d-bands associated with the latter. When electrons are

excited in a metal with core—level vacancies, it is energetically favorable to try to fill

them, which is why the electron-phonon scattering rate will be quite fast relative to

that of a noble metal. In a noble metal, electron scattering from atomic sites is more

‘random,’ since they do not possess the attractive vacancy sites for electrons to rush

to fill- This is manifested in smaller values of G for Au/ Ag than Pt / Ni (or larger rep);

0,4,, = 2.60x 1016, (3,4,, = 2.80x 1016,01), = 1.09x 1018, and 0N, = 1.05x1018, all

in units of W III-3 K-1 [215]. In principle, G has dependence on electron temperature

[216] , though it is frequently neglected. For a comprehensive study on the band-

structure and temperature dependence of the various thermophysical properties in
the TTM, see Reference [215].

Since the advent of the short-pulsed laser (even beforel), the TTM has been ubiq-

liitous in its employment because of its time-tested robustness in explaining experi-

I‘nental observables. Examples include melting and ablation [141, 192, 212, 217—224],

laser-ind uced desorption of species from surfaces [225-227], electron-phonon coupling

£133, 134, 157, 222, 224, 228—241], nanometer-sized particles [129—135, 192, 230, 231,

Q33 242, 243], and general thin-film transport and thermo—mechanical properties

C 142’ 2227 223, 233, 236, 237, 244—247]. It is particularly handy for studying ultra-

 

.1 The inaugural publication of the TTM in 1957 predates the invention of the laser [209]. Inter-
§ stingly, the authors have a passage where they state: “If the lattice temperature is much less than
«he tempera-tare of the electrons ( hardly a practical case), then ”, today it is very much a practical

e “nth Short-pulsed lasers!

30

fast laser-induced thermionic emission from metals, as the emission fundamentally

depends on the electronic temperature [198, 247, 248].

3.1. 1 Numerical Solution

Equations 3.1-3.4 are numerically solvable by discretizing them in accordance with the
MacCormack method, which, simply stated is a predictor-corrector scheme with pre-
dictor gradients reaching forward (upwind) and corrector gradients backward (down-
wind). Quantities Te, Ti, and 9e,z' are marched forward in time by first calculating
an auxiliary value (superscript *) using a forward difference, with upwind spatial gra-
dients. Assigning n and k to be indices of time and space, respectively, the predictor

step is given by

 

 

 

(n) (n)
* (n+1) _ (n) At (‘16 k+1 " ‘16 k ) (n) _(n)
Tek —Tek +_(71—) -— Az —G(Tek —T,k)+S(z,t) ,
7Te k
(3.7)
,(n) ,(n)
_*(n+1) _ ,(n) At ((12 k+1 _ q‘ k ) (n) ,(n) .
ink .41},c +5 — AZ +G(Tek —T,k) , (3.8)
dropping the subscripts on the heat flux, both qe and q, are discretized as
To») _T(n)
+1 At k+1 k
q*k(n ) = q gen) _ _T_ q in) + K( AZ ) (39)

The corrected values of T 6, Ti: and q€,i are given by

* (n+1) (n)
T (n+1) (T6 k + Te 1: ) At
‘9 k = 2 + * (n+1)

31

 

( =1: (n+1) =1: (n+1)

Qe k — (1e k—l ) * (n+1) * (n+1)
x - AZ — G (Te k — T,- k )+ S(z,t) , (3.10)

 

(Ti*(n+1) +72%») M

 

 

 

 

(n+1) _ __
T‘ k — 2 + 2C,-

(qi*k(n+1) _ qi*k(niI—l)) ( 1) ( 1)

— a: n+ :1: 71+
x - AZ + G (Te k — T,- k ) , (3.11)
and
at: +1 n =1: +1 :1: +1
(n+1) _ (q km )+ q(k)) _ 9}: =1: (n+1) + (Tk(n )- Thinl ))
q k — 2 27' q k K A2

(3.12)

By inspection, the final values are the average between prediction steps, and the re-

evaluated functions, in terms of the predictions, this time with ‘downwind’ spatial
gradients.

Figure 3.2 shows an example calculation for a thin Au film of 100 nm, irradiated

by a 50 mJ/cm2 pulse at 50 fs, calculated using the numerical scheme presented above

with original Fortran source code (Appendix F).

3.1.2 Extensions to the Two-Temperature Model

There have been numerous extensions to the conventional TTM. The form presented
above in Equations 3.1-3.3 is actually the dual-hyperbolic form proposed by Chen

[212]; dual because both electrons and lattice employ the non-Fourier variant for heat

flux. This, in and of itself, is an extension from the original parabolic form, where

the electron heat flux was taken to be Fourier, qe = -8Te/8z, and q, was neglected

a1 together [211]. The non-Fourier heat flux has the form of Equation 3.3, which is

32

 

 

 

 

 

 

   

3 8
53 EB
A‘Ll-.Aj4-4LL.

Depth (nm)

Temperature (K)
‘6’
23

§

 

 

 

 

 

O
I

q

1
q

q

10 20 30
Time (ps)

Figure 3.2: An example TTM calculation of the electronic (Te) and lattice (Ti) tem-
peratures: on the top surface (z = 0) of a 100 nm Au thin film irradiated with a 50 fs
laser pulse of 50 mJ/cmz. Inset: depth dependence when the pulse is at maximum
inside the film (150 fs). '
more physical because it assumes a finite propagation speed for heat diffusion, arising
from the first term on the RHS2.
Recent theoretical efforts in comparing Boltzmann Transport (BT) to the TTM
have shown that the former is more accurate when comparing with experiments [249,
250]. Particularly, when the electron mean free path exceeds the material dimension
or the excitation pulse is shorter than the electron thermalization time. In these
cases, the TTM will have a tendency to over-estimate the electron temperature. This
is largely due to ballistic transport of electrons, which is absent from the TTM.
Ballistic transport carries electrons away from the surface much more quickly than a
diffusional process. Usually ballistic transport is negligible, but, it must be considered
when the excitation fluence is relatively high on a material with weak electron-phonon
Coupling [228, 229]. An example case would be irradiating a thin film of Au or Ag with

a sub-100 fs pulse at >50 mJ/cm2 (by no means is this example all-encompassing).

2RHS/LHs: right-hand side / left-hand side

33

In cases such as these, the transport of heat carriers through the film proceeds much
more rapidly than what is predicted from strictly diffusional terms. One way around
this, without resorting to BT calculations, is to augment the laser source term such

that it accounts for ballistic transport [212]. Namely, Equation 3.4 becomes

u-w e—z/(a.+a.>.-w(t-?£B)2

S z,t - a , 3.13
( ) fl tp(6s + 6b) [1 _ e—L/(53+5b)] ( )

where 6b is the ballistic range of hot electrons and L is the film thickness.

As emphasized by Wellershoff and colleagues in 1999 [229], an electron tempera-
ture is only established when thermalization is reached within the electron gas (though
electrons and lattice may still be under strong nonequilibrium at this point). One
of the inherent short-comings of the TTM is the assumption of an instantaneously
thermal electron distribution. In reality, the optical pulse creates a non-thermal popu-
lation, which degenerates into a Fermi-Dirac (thermal) distribution through electron-
electron collisions and, to a lesser extent, electron-phonon scattering.

In 2006, Carpene devised a simple, but effective fix for the treatment of the initial,
non-thermal, regime [251]. Without rigorous derivation, the author implemented a
phenomenological formalism for calculating the initial non-thermal electron distribu-
tion, based on a laser-induced, infinitesimal perturbation to the Fermi-Dirac distri-
bution, which is integrated over the time that the laser pulse interacts with the film.

The thermal electron distribution no longer interacts with the laser directly. Instead,
the laser heating source term is removed from the rate equation for Te and replaced
With a term representing the relaxation rate between the non-thermal and thermal

electron populations, BUee/Bt. Equation(3.1) becomes

8T 8
Gem—5,3 = —£ — (Te — T.) +

aUee
8t '

 

(3.14)

34

 

Euthermore, there is no reason to preclude the process of non-thermal electron scat-
tering from phonons. Accounting for this process results in a heating source term for

the lattice as well, BUep/Bt, making the new rate equation for the lattice

,aTz'_ 3% ,
C“ at _ az +G(Te TZH

aUep

(9t , (3.15)

with the relaxation rates given by

 

 

t’—t 2
__ —az t ——w(—t—B)
BUee = g“ (1 R)F ae / e p Hee(t-t') dt’, (3.16)

at tp (1,1,)? 00

 

 

2
t —t
_ —az t —w(—£—2)

at 15,, (1,1,)? 00
where a is the linear absorption coefficient, which is equivalent to 1/63 in Equa-

tion(3.4), and

e— (“1+w2) (t—t’)

 

H86“ — ti) = — (t t’)2 [h2V2(t - t’) + 5%7860 — 8—w1(t_tl))l (3-18)
— that;2 t—t’
Hepa — t’) = f ( )( )e%rree(1 — e-w1(t_t,)) (3.19)

 

(t — ti) Tep

where wl E (hu/eFK/E)2 and wz E l/Tep.
When integrated3, the physical representation of H 33 is the accumulated propor-
tion of absorbed photon energy that has made the transition from the non-thermal to
the thermal electron bath; Hep for non-thermal electrons energy transitioned to the
phonon bath. In the limit of an instantaneously thermal electron distribution (the

conventional TTM), both H66 and Hep —-> (hu)2 6 (t —- t').

 

 

3Strictly speaking, H88 and Hep are integral kernels. More physical meaning can be ascribed to

their integration rather than the quantities themselves.

35

 

This formulation by Carpene is termed here the non-thermal Two-Temperature
Model (nt-TTM). The additional source term to the lattice means it can be heated
sooner, and possibly at a faster rate than with the conventional TTM, depending on
the magnitude of G. Consequently, the maximum lattice temperature is routinely
calculated higher (and occurs sooner) in the nt-TTM than the TTM. Conversely,
the maximum electron temperature is calculated lower and occurs later. This is not
surprising, since at any given instant during laser pulse absorption, in the thermal
model, Te receives 100% of the energy, while in the non-thermal model, the energy
is subdivided between the two populations. The non-thermal population will not be
entirely depleted of its energy until the pulse has passed. By this time, electron-
phonon losses are under way and some energy was dumped into the lattice already
by the non-thermal electron collisions with phonons, thus precluding any possibility
of reaching the same temperature as the maximum predicted in the thermal model.

Carpene’s method has been integrated here with the TTM in the form of a sub-
routine call (Appendix F.1) and has since proven to be well worth the effort, as will
be shown in Chapter 5, where non-physical results from calculations are predicted for
semiconductors in the sub-50 fs time regime.

At this point, inaccuracies in the conventional TTM have been shown for two
major cases, and in both, temperatures were over-estimated. In the first case, a strong
ballistic transport regime was activated by the laser because of a high fluence applied
to a film with weak electron-phonon coupling. In such a case, the non-physically slow

transport of heat carriers (electrons) from the surface, in the form of diffusion, leads
to the large T e that is calculated near the surface.

The second instance arises when an instantaneous Fermi-Dirac distribution is as-

Sllrned prior to the electron-electron relaxation time period. Treating this non-thermal
distribution as a thermal one is increasingly problematic as photon energy and elec-

tron collision frequency increase, and also with decreasing pulse width. The electron

36

 

collision frequency is, itself, a transient quantity that increases with temperature. It
can be generally inferred that higher fiuences increase the likelihood of the TTM de-
scription breaking down, as the possibility of under-estimating Te based on the laser
energy would violate energy conservation, since the TTM already assumes that all
laser energy is instantly dumped into the free electron system. In other words, if the
laser energr is to be re—partitioned in any way, Te cannot possibly receive any more of
it than what is already ‘assigned’ to it in the TTM. In that sense, the TTM provides
an upper limit on T6, and possesses greater accuracy at lower fluences.

Perhaps the largest upgrade of the TTM was performed by Leonid Zhigilei and
co-workers [215, 252—258], where a model was formulated that combined the TTM
with molecular dynamics. The TTM was used to describe the bulk continuum and
an atomistic approach for the surface layers, based on an embedded atom method
(EAM) of molecular dynamics (MD). In this model, the TTM is used to calculate
the electron temperature for both regions, and the lattice temperature in the sub—
surface continuum region. The surface layer lattice temperature is calculated for each

simulation cell with the expression

Ncell 2
T299”: 2 mn (21,5) /3kBNceu, (3.20)

n=1

where 22$, is the thermal velocity of the nth cell and the forces on the cells are calculated

from
a2rn

 

mn

Where 5 represents the temperature dependent electron-phonon coupling frequency.

A schematic of the methodology is given in Figure 3.3 [259].

37

 

Two-Temperature Model
Electron Temperature

l—+-|—°+*-l-'-1L+i+l—°—l-*+°-l-°-l-'—l-°—l—>

 

 

Z
t t t t t t l 1 t l
Two-Temperature Model ‘ ':?;::‘. ' _ Z 3
Lattice Temperature (— E
.. " z <—

 

    

 

pressure - transmitting / heat - conducting boundary condition

Figure 3.3: The combined atomistic approach at the surface with the TTM for bulk,
formulated by Zhigilei et al [259]. Electron-phonon coupling in the atomistic region
is expressed through the term, émnvg, where 12$, is the thermal velocity of the nth

cell and 5 represents the temperature dependent electron—phonon coupling frequency
[259].

3.1.3 Thermal Transport in Nanoparticles

An alternative TTM is employed for nanoparticles under ultrafast laser irradiation.
Modeling nanoparticle heat transport differs from the bulk in several ways, such that
the fundamental physics of the problem must be reformulated, deviating slightly from
the conventional T TM for thin films. In addition, some of the various thermophysical
parameters are different, such as G’ due to the reduced electron—phonon coupling time
because of increased scattering with the surface.

When considering optical excitation of a thin film, the area of the film is assumed
to be larger than laser spot-size. In addition, the optical penetration depth (typically
1 0—20 nm) is smaller than the film thickness for most cases, which necessitates the

inclusion of thermal gradients into the model. As an example, consider a 2 nm Au
nanoparticle, which has an optical penetration depth of 15.3 nm. Laser heating of the
11anoparticle is uniform through the particle. Instead of using the form of an expo-

Ijelitial decay over the skin depth, like Equation 3.4, the source term is reformulated

38

in terms of the absorption cross-section,

t-t 2
Se) = fig (Me) {47513) , (3.22)
where V is the nanoparticle volume and Jabs is the absorption cross-section of the
nanoparticle, which must be calculated from the Mie Theory (see Section 6.3).

For a spherical particle, the surface-to-volume ratio increases as 1 / R with decreas-
ing particle size. With the large surface-to—volume ratio, an additional cooling channel
for the lattice is activated, as heat can be transferred to its surroundings through the
surface. This is particularly true when the nanoparticle colloid is immersed in a sol—
vent, as is commonly the case in optical studies [135, 260]. An additional term can

be added to the TTM to describe this cooling, such that Equation 3.2 becomes

0% = C(Te _ Ti) _ W,

, at T8 (3.23)

where 7'3 represents the characteristic time for lattice cooling. The physics of the
energy exchange between the nanoparticle and its surroundings are are buried in 7'3.
Notice that the diffusion term, qu/Bz has been dropped. Neglecting the electronic
diffusion term gives

8T6 _

Cefi‘ —G(Te — 71",) + 30:). (3.24)

Equations 3.22-3.24 give the TTM for nanoparticles. To re—cap, the changes are:

(1 — R) Jabs 892' (Ti — 300K) age
63 —+ V 82 —-> T8 62 —> O. (3.25)

Before proceeding, a few notes are considered on the lattice cooling rate. The
dependence of 7's on nanoparticle radius, R, can vary based on the nature of the

Cooling. Namely, the cooling is controlled either by the dissipation rate through

39

the interface or through heat-diffusion in the aqueous environment, surrounding the
nanoparticle [261]. To examine the diffusion-limited cooling, consider a spherical
nanoparticle at some elevated temperature Tp, cooling through heat-diffusion:
87}, D a2
__ = _ __ T , 3.26
Where D is the diffusion coefficient of the solvent. After reducing to 1D form via

change of variable, this can be solved analytically with a Laplace transform [262]; the

solution being of the form

7.2
Tp(r, t) oc f(t)exp (—-52), (3.27)

which yields the characteristic decay time associated with a diffusional process, T ~
7'2 / D. So if a series of size-dependent measurements of lattice cooling found that
t he decay time were proportional to R2, it could be concluded that the decay was
(:1 iflusion-controlled. Conversely, if the decay rate of the nanoparticle ensued through

interfacial heat transfer, the temperature is described by [260]

BT
§1TT3CP3£E = —47r’r2FTp, ' (3-28)

; U here I‘ is defined as the interfacial heat conductance. The solution is an exponential
decay with characteristic decay time, T3 = rC’p / 31"; in other words, linear dependence

f - .
or Interface-controlled decay. Re—cappmg:

7'3 oc R2 => diffusion-controlled

73 cc R => interface-controlled.

40

Hu and Hartland found quadratic dependence for colloidal Au nanoparticles of 4-50
nm in an aqueous solution [135]; linear dependence was found for various metals (Au

and Pt) and metal alloys (AuPd) in Reference [260].

3.2 Boltzmann Transport in Semiconductors

Ultrafast pulsed laser irradiation is an industry standard for processing silicon-based
dexrices; be it micro-machining, annealing, removal of adsorbates (cleaning), etc. [263].
Consequently, there has been a recent flux of theoretical models to describe the en-
ergy transport in semiconductors. The more recent work (since 2005) will be briefly
outlined.
In 2005, Chen and colleagues formulated a self-consistent model for transport dy-
namics in semiconductors subjected to ultrafast laser irradiation, using the relaxation-
t ime approximation of the Boltzmann equation [264]. Model simulations on Si and
G e demonstrated strong accuracy in predicting damage thresholds for varying pulse-
Width and fluence, when the lattice temperature was below the melting point (carrier-
in duced damage).
With a similar model, in 2007, Korfiatis and colleagues performed a study on
d a—1'11age thresholds in Si, with emphasis on differentiating thermal from non-thermal
ba‘Sed damage, and also the dependence of melting threshold characteristics on wave-
length [265]. In 2009, they again simulated damage characteristics associated with Si
Wi t 11 an expanded model to account for ablation depth, this time with emphasis on
Or '6‘th formation and morphology [266].
«Also in 2009, Qi and Sub developed an extensive model for Si transport with
sevefital key expansions: (1) the inclusion of thermo-mechanical coupling, (2) multi-
dith ensionality, (3) long time scale integration without compromising short time scale

prQ . .
ceases. In other words, full treatment of each valid time scale, from electron-

41

phonon coupling (~ 1 ps) to the necessary integration times to examine thermo-
mechanical processes of about 1 ns. The model and its results are published as two

parts [267, 268].
Here, the model by Chen and colleagues [264] will be given and solved, as it
is frequently invoked in ultrafast laser heating of Si, which is one of the primary
topics of this work. It is similar to the Two-Temperature Model (TTM) for metals,
presented in Section 3.1, though it involves a third rate equation, in addition to
electron and phonon temperature, which is governing equation for carrier generation
and recombination. In metals, the carrier density is assumed constant in the TTM.
I n one-dimensional form, the coupled system of partial differential equations, termed

here as the Boltzmann—Transport Model (BTM), is given by

 

 

an _ aI(z,t) (”(2.02 3 31
(3t _ hu 2hz/ 771. +6” 82’ (3'29)
8T3 _ 2 2 a”! Cell .
Ce}, 8t — (a + Gn)1(z, t) + 5 [(z, t) 82 Tep (Te T,)

 

 

6n BEG 8n BEG BTZ'

8t (EC + 3kBTe) n ( an at + 8T,- 5) , (3.30)

an _ _8_ .@ Ceh _ .
CZ at — 82 (“’2 82) + 78]) (T8 T2), (3°31)

_ 8n n BEG n 8T8

8T6

W = (EG' + 4kBTe) J — (Ice + Ith) (72:) , (3.33)
W
1:) ere carrier heat capacity is given by
BB

Ce), = 3nkB + n—a—Tg, (3.34)

42

and the laser source term is described by

(a + 6n)10(t)e—(a+en)z 7
(a + en) + .6103) '1 _ el—<a+en>z] ’

(3.35)

 

1(z, t) =

 

Where 10(t) represents the temporal dependence of the laser source, which is given by

the Gaussian fimction

“—0 _ RlFe-wl(t*3tp)/tpl2, (3.36)

I0(15) = —
7T tp
a and )6 represent the 1- and 2-photon absorption coefficients respectively; '7, (9, EC,
and 6 are the Auger recombination coefficient, impact ionization coefficient, band gap
energy, and free carrier absorption cross-section, respectively. Constitutive Equations
3 - :32 and 3.33 represent the carrier current (J) and ambipolar energy current (W),

respectively. Parameters are given in Table 3.1, with their empirical functional de-

p endences, if applicable.

3 - 2.1 Numerical Scheme

The Boltzmann Transport Model (Equations 3.30-3.33) is solved using a staggered
mesh (Figure 3.4) [264] with spatial gradients given by central difference. Forward
ti 1116 marching is carried out through a 3rd order Runge—Kutta scheme with total

val-Ti ation diminishing (TVD) implemented [279—281], with sealed boundaries:

J(O,L; t) = W(O, L; t) = q(0, L; t) = 0, (3.37)

and. initialization given by

n(z,0) = 1012 cm—3 Te(z,

0) = T,(z,0) = 300 K. (3.38)

43

 

/ Property

 

 

 

Expression
n,- (W/cm K) [269] 1585 T,-1'23
C,- (J/cm3) [269] 1.978 + 3.54 x 10—4T, — 3.68/T,-2
158,}, (eV/sAK) [270] —3.47 x 108 + 4.45 x 106 Te
’76,, (fs) [128] 240 [1+ (n/6.0 x 1020 cm-3)2]
’7 (cm6/s) [271] 3.8 x 10—31
t9 (s-l) [272] 3.6 x 1010 exp(—1.5EG/kBTe)
1) (cmZ/s) [273] 18(300 K/T,)
130 (eV) [274] 1.16 — 7.02 x 10—4 T,+12108 — 1.5 x 10—8n1/3
12 (800 nm) [275] 0.370 + 5 x 10’5(T,- — 300 K)
12 (400 nm) [275] 0.541 + 5 x 10-5(T, — 300 K)
Q (cm-1) (800 nm) [265] 5.02 x 103 exp(T,-/430)
Q (cm—1) (400 nm) [276] 5.51 x 104 exp(T,-/420)
B (cm/GW) (800 mn) [277] 1.8
6 (cm/GW) (400 nm) [128] 10.0
6 (cm2) [278] 5.1 x 10‘18(T,-/3OO K)
772.5" 0.19

 

Table 3.1: Silicon input parameters for the Boltzmann Transport Model.

44

 

 

 

 

 

 

i: l 2 3 n-2 n-l n
j: l 2 3 n-2 n-1 n n+1
0 Te, 1}, n
O W, L Q

 

 

 

Figure 3.4: The spatial discretization mesh used for the Boltzmann Transport model
calculation prescribed by Chen et al [264].
Rather than discretizing the entire model, only the essentials of the TVD scheme
are presented for an arbitrary equation, 8gb/Bt = L[ct, d); z, t]. Using time and space
indices, 77. and 11:, respectively, the TVD scheme is given by computing two auxiliary

steps and then the updated value in terms of the auxiliary values:

¢(1) = ¢(n) + Amati), 101)), (3.39)

45(2) = 26W + :30) + Emma“), A”) + At), (3.40)
(n+1)=1-<n> Z (2) E (2) (n) a

ct 3gb + 345 -+- 3AtL (d) , t + 2 . (3.41)

This method for the time-stepping is different than the one prescribed by Chen

3 t al. for this model, which was a forward difference. The reason for this is that the
J51"~1~3Q1erical ‘stiffness’ of this system was found to increase as the excitation pulse was
h ade shorter, more intense, or more energetic (tp l, F T, A .L). In general, the
Si lhdation requirements here exceed those used in Reference [264], which is likely why

131:1

I
Q addition, the 3rd order RK scheme allows for the choice of a slightly larger time

Q method they prescribed did not hold up for most of the cases considered here.

45

step than used by Chen and colleagues (5 x 10‘20 s), which cuts down computation
time.
An example calculation is given in Figure 3.5, depicting the depth dependence of
the electronic temperature, Te, for several selected times prior to 1 ps. In general, the
Spatial gradients are only steep enough to be active in the early times (31 ps), when
the laser pulse is being absorbed by the film. The 45 fs pulse is completely absorbed
into the film by 250 fs. In other words, the laser source term given in Equation
3 - 35 has zero amplitude by this time. The depth dependences of lattice temperature
and carrier density are given in Figure 3.6. Example calculations depicting temporal
dependences are presented in Section 3.2.2.
The carrier density, n, reaches its maximum concurrently with the laser pulse
( near z135 fs) and changes very slowly compared to Te. This is why only 45 fs
and 1 ps curves are plotted for n in Figure 3.6; those of 250 and 500 fs are nearly
identical to 1 ps. It is not a surprise because the carrier density speed should be less
1: han that of the electron thermal energy. The thermal energy propagates through
(I: arrier collisions, which is more efficient than actually displacing carriers, as they will
1 i l{ely collide before traveling very far. A simple calculation confirms this (in addition
to the BTM calculations in Figures 3.5 and 3.6). A rough estimate of the carrier
d ensity speed is given by vn ~ aD z 450 m/s. A similar estimate can be made for
the electronic thermal propagation speed, ’UT ~ 0(Ke/Ceh) z 2500 m/s, nearly an
or der of magnitude higher than that of the carrier density. Simply put, these example
Cal inations show the difference between chemical and heat diffusion speeds.
1N ote, the lattice temperature was not mentioned (because it is still ramping up),
bu 1:- its speed is much slower than that of the electrons because the heat capacity of
“lg lattice is more than 1000 times greater than that of the electrons, while their

1:
1‘TQITJnal conductivities rarely differ by more than a factor of 10 (both are functions

0F
t emperature).

46

 

 

 

I
O 1 S 30 45 60
Depth (um)
F i sure 3.5: The depth dependence of the electronic temperature, Te, plotted at 50,

2 5 0, 500, and 1000 fs. Here, the thickness L = 60 pm, the pulse duration tp = 45 fs,
agild the fluence F = 35 mJ/cm2.

47

 

 

 

 

 

lllllllll

 

310q 6 1'5 3'0 4'5 so

‘ Depth (11m)

 

 

 

 

0 1o 20 30
Depth (M)

F igure 3. 6: The depth dependence of the lattice temperature T,, plotted at 50 fs
< red), 250 fs (green), 500 fs (blue), and 1 ps (orange), for L— —— 60 pm, tp— — 45 fs,
and F = 35 mJ/cm2. Inset: Carrier density, n, plotted as a function of depth (y-
a‘DC—‘ls is log); 71 reaches maximum at ~140 fs, which is 5 fs after the laser pulse IS at
Q31 83nmum amplitude (73,, set to 45 fs; initiated 3 pulse widths before time zero, shown
i 11 Equation 3. 36).

48

3.2.2 Non-thermal Regime

The nonequilibrium regime associated with the internal relaxation of the electron gas

to a Fermi-Dirac distribution was treated by implementing the formalism of Carpene
[251], as was done in Section 3.1.2 for the TTM. The formalism is essentially the same;
the laser source term is removed from Equation 3.30, and replaced by BUee/Bt, which
is identical to Equation 3.16, and a source term is added to the lattice (Equation 3.31),
which is BUep/Bt from Equation 3.17. An additional step, beyond Carpene’s model
must also be taken with the BTM. Namely, that is to subdivide the carrier density
into thermal and non-thermal populations. To do this, a dimensionless quantity rep-

resenting the proportion of carriers that have made the transition from non-thermal

to the thermal population is defined, P(t), given by4

_ f3 Hee(t-ét’)dt’
P(t)= (ht/)2 . (3.42)

As a matter of convenience, the RHS of Equation 3.29 is defined as F(n,t). The

t hermal population of electrons, fi(t), is given as

if}; = Pa) Fin. mm, (343)

Wi th Equation 3.29 now representing the non-thermal population. Furthermore, in
t: he last two terms in Equation 3.30, the n and ("in/(9t parts are replaced by their
C h ermal counterparts, ft and aft/8t. This formulation is termed here the non-thermal
B 0113sz Transport Model (nt-BTM). An example calculation is given in Figure
.3 - ‘7-

"To appreciate the importance of proper treatment of the non-thermal regime, it

1 . . . . .
S useful to examine it along-side the conventional model, wh1ch is done in Flgure

 

re‘ 1:. ‘ Note that the units of H“ are [Energy]2 / [time], so P(t) can be thought of as the square energy
1% of incident photons to the converted-thermal energy, at time t.

49

 

 

 

 

 

 

2.5
f L

w ‘2.0 O
I- - A m
= 3a” ‘ x -1
a 42 _1.5 _‘ 2.
h 1500 ' O“ (“D
8. 1 .1,0 0° C
E c - ° - 31.. (3D
11’ ° % 5°° -o.5 f4.-
t <

0.0

 

 

 

 

 

Time (ps)

 

F i gure 3.7: An example calculation for the nt—BTM performed on silicon. The fluence,
W8Velength, pulse width, and thickness are 35 mJ/cm2, 800 nm, 45 fs, and 50 pm,
respectively. Inset: Zoomed-in View of the first 500 fs.

50

3.8. Focusing on the thermal case for a moment, it is striking that the electronic
temperature ramps up dramatically (to z 1800 K) in Figure 3.8 when only the front
tail of the laser has entered the film (6% of maximum). The reason for this is that
the carrier heat capacity, Ceh’ increases approximately linearly with 71 (see Equation
3.34), and the temporal profile of the carrier density follows that of the laser (see
Figure 3.9, inset). When the electrons receive just a small portion of laser energy, the
temperature is drastically raised because the heat capacity is still ‘waiting’ for n to
ramp up. At this instant, it is still 8 orders of magnitude lower than what it will be

when n reaches maximum5.

4000

 

 

    
   

Thermal

 

 

lloclron Temperature (K)

 

 

0* Non-Thermal

 

 

 

 

I '

o 160 200 300
Time (fs)

P“:ig'ure 3.8: A comparison of the BTM and nt-BTM. The fiuence, wavelength, pulse
W5- (ith, and thickness are 35 mJ/cm2, 800 nm, 45 fs, and 50 pm, respectively. Inset:
,LZ Q Glued-in view of the first 500 fs. The laser temporal profile is shown in orange. For
If) e thermal case, Te reaches 1800 K with the laser at only 6% of its maximum. Inset:
at tice temperature, Ti-

 

(x) The early rise of Te was noted by Chen and colleagues in Reference [264], however they did not
mnent on the physical validity of the observation.

51

But is this physically valid? The answer is no, because it occurs over a time
period that precedes the electron-electron scattering time. The temperature could not
exhibit such changes in the absence of electron scattering events. Strictly speaking,
even the use of the word ‘temperature’ is incorrect, since it is an ill-conceived quantity

prior to electron thermalization. Notice that the nt-BTM result has not yet responded
during this time. Furthermore the BTM over-estimates temperature by 37% for the
case considered in Figure 3.8. The importance of properly treating this small window

of time is abundantly clear, as accuracy is sacrificed otherwise.

3 .2.3 Quasi-Fermi Levels

Under nonequilibrium conditions in a semiconductor, the electron and hole concen-
trations require separate descriptions for their . respective occupation levels, termed
quasi-Fermi levels, (150 (subscript 0, carrier, means it could be electron or hole). With

the carrier temperature, Tc, and density, nc, evaluated, ch can be calculated by im-

 

p licitly solving
2 0° fl
= N T — d , 3.44
nc C( afi/g 1+exp(:r—nc) a: ( )
where NC(TC), the effective density of states, is expressed as
:1: 3/2
mc kBTC
N T = 2 —— , 3.45
c( c) [ 2.2-.2 l < )

a--1:I.d the scaled reduced Fermi level, 770, is expressed for electrons (e) and holes (h) (in

units of kBTC) as
(fie - EC

778 = kBTe 1 (3'46)
and
_ (f’h — EV
77h — kB Te . (3.47)

52

In principle, it is straight-forward to supplement the Boltzmann Transport algo—
rithm with the calculation of the quasi-Fermi level. However, since (be cannot be
isolated in Equation 3.44, it must be determined numerically. It is convenient to
define a quantity representing the quasi-Fermi level relative to the conduction band

edge6 since it is more intuitive (termed the reduced Fermi level):

Solving Equation 3.44 for 776 is performed via the N ewton-Raphson method [282],

which has the general form

$l+1 = ml “131)

 

 

_ _, 3.49
marl) ( )

Where f (at) = 0 (it is the RHS minus the LHS of the equation to be solved).

For the case here, it is convenient to begin with the following definitions:

716“)
A E , 3.50
Ne(Te) ( )
1 00 fl
F E —— d 3.51
V076) F(V +1) /0 1 + exp(:c — Tie) :13, ( )
and

f(77€) E A — F1/2(7Ie)- (3-52)

Equation 3.51 are the familiar Fermi integrals; exploiting their simple differentia-

t i On rules, the derivative of Equation 3.52 is

I I
f (716) = —F1/2(77€) = -F_1/2(TI€)- (3-53)
\
6 .At this point, the subscript c is dropped and only the quasi-Fermi level associated with electrons

i
s QQnsidered (holes are discarded).

53

By inspection of Equations 3.44 and 3.52, any 77e such that, f (776) aé 0, must
be incorrect. While not correct, evaluating the function and its derivative at this
value produces a new value that is closer to to the correct one (the essence of the

Newton—Raphson method). The correct 716 can be found by successive iteration:

778‘” 1) = 776m - M. (3.54)
f [(776m)

While simple, this method is quite powerful. Calculation of 713 is performed at
each time step within the Boltzmann Transport PDE7 solving program. Since He
does not change significantly from one time step to the next8, the initial guess of 176
on successive time steps is fairly close to the converged value. Mathematically, that is
to say that the losses incurred in calculation speed from adding this iterative section

to the BT solver are minimal because At is chosen, such that

Ine(t + At) - 77e(t)|
Ine(t)|

 

<< 1. (3.55)

Thus faster converging methods, which would require higher order derivatives,
are unnecessary here. The transient behavior of the quasi-Fermi level displays large
differences between the cases when the non-thermal regime is treated correctly and

when it is assumed thermal (Figure 3.9).

\_
> PDE: partial differential equation.
Convergence requires that time steps are chosen small, such that no quantities change too rapidly

“‘2‘
gr the course of one step.

54

 

 

 

    

 

 

 

% I
i 0. SF I
g s; ' Band Gap ‘
|+ V .1. a
g . «pg 2.0 .
a _2. 8° 1 0 -
E 0.0 ._
1 E o on zoo 300 i
Q Time(fs)
EU I ' I '
0 250 500
T1me(fs)

Figure 3.9: The quasi-Fermi level is plotted for both the BTM (green) and nt—BTM
C blue). Compared to all other quantities, 116 exhibits the largest difference between
t be two models because it depends on both Te and mg. The nt-BTM is more physical
as the Fermi gas should be nearly degenerate before electron scattering commences,
which the nt—BTM closely resembles. The BTM curve actually drops below the
VE-lence band edge, which is non-physical. Inset: The carrier density, plotted for both
m Odels with the laser temporal profile shown in orange.

55

3.3 Discussion

A comprehensive introduction to the Two-Temperature Model, which is frequently

inVOked for data analysis, has been presented. For example, the thermal expansion

coefficient for most materials is well-established [195, 283]. With Debye-Waller anal-
ySiS of the Bragg peak motion, the lattice temperature of the system can be measured
with UEC. The TTM provides a convenient secondary check on the value.

The model for nanoparticles has been used in conjunction with the Mie scattering
formalism to explain recent UEC experimental observations pertaining to Ag nanopar-
ticles, which is not included in this work, but can be found in Reference [193]. The full
Mie scattering formalism shall be presented in Section 6.3 with example temperature
calculations for Ag and Au.

The Boltzmann Transport model for silicon is the most frequently employed of

all the models presented in this work. Results from the nt—BTM will be invoked in

Chapters 4 and 5.

56

Chapter 4

Ultrafast Electron Diffractive

Voltammetry

4.1 Introduction

To most scientists, the word ‘diffraction’ carries with it the connotation of resolving
Structures. Rightfully so, since diffraction, in its various forms, has been the work
hOrse for resolving crystal structures and lattice constants for most of the last century.
When a coherent electron beam is scattered off the crystal planes, such as with
UEC, a natural question that arises is, should one be concerned with electrostatic
interactions with local fields near the surface; specifically, those not having to do with
the inner (crystal) potential. As will be demonstrated in this chapter, the answer is
yes; particularly in RHEED1 or LEED2 geometries, where the incident beams have
Small momentum components normal to the crystal. In general, electric fields near
surfaces have their strongest components normal to the surface, since this is where
the Symmetry is broken (there is no reason for charge to separate in-plane unless

there is a boundary, crack, defect, etc.).

—\
1
RHEED: reflective high energy electron diffraction.

2
LEED: low energy electron diffraction.

57

Traditionally, the charge-based deflection of the electron beam has been regarded
as an artifact or source of systematic error for electron crystallography measure-
ments [284]. However, with careful analysis, the electron beam can be used as a
charge-sensitive probe, and it is generalizable to complex geometries and interfa-
cial structures. Furthermore, since it is the pump laser pulse that is responsible for
generating the near-surface field(s) (more on this later), the technique is inherently
time-resolved. Over the past two years, Ultrafast Electron Diffractive Voltammetry
(UEDV) has emerged as a formidable technique for measuring phenomena associated
with charge separation near surfaces [107, 194, 285]. In addition, there have been sim-
ilar efforts to use an electron beam to measure charge-based phenomena, though not
diffractive. Miller and colleagues conducted a pump-probe study where an optically
ablated plume was probed with an electron beam. The electric field was quantified
based on the deflection of the direct beam spot on the CCD screen [286]. In 2009,
Park and Zuo conducted a similar experiment, where they flew the direct beam over
the sample and monitored the deflection arising from pump-induced surface charging
[287].

Historically, the available measurement techniques for surface potentials have been
sparse. Cowley proposed a novel method for surface potential measurement using a
nanometer-sized probe in a STEM [288]. With this, the central spot of the microd-
iffraction pattern will stretch and warp, which can be analyzed to determine some
properties of the surface potential. Sufficiently large, flat crystal faces are neces-
sary. Gold, being inert, was a model system, on which the technique was employed
successfully for the (111) surface [289]. It is not a direct measurement of surface
potential, since it requires careful analysis of the streaking lengths (associated with
the central spot) calculated from a modified image barrier model, and also an a-p'r‘z'orz'

preemption of the functional form of the potential.

58

More recently, Spence and colleagues considered the possibility of Convergent-
Beam Low Energy Electron Diffraction (CBLEED) to map the potential associated
with a. surface dipole layer. There, a nanometer-sized probe was proposed in con-
junction with CBLEED rocking curve measurements to deduce the surface potential
[290]. With the convergent-beam geometry, many orders can be recorded at once in
the reflection rocking curve due to the small probe (nm). The associated intensity
variations are sufficiently sensitive to surface dipole layer parameters, such that the
surface potential could be accurately deduced from multiple scattering calculations.
Calculation of the LEED patterns with the inclusion of a surface potential (super-
imposed on the crystal inner potential), would allow for simulation of an observed
CBLEED pattern. It is important to note that this was a proposal for a developing
a CBLEED apparatus, accompanied with multiple scattering calculations. The mea-
surements for the surface dipole layer depend on accurate knowledge of the imaginary
part of the inner potential (pertaining to multiple scattering and other electron ex-
tinctions [207]). Due to contemporary advances in items such as energy filters, cooling
stages, CCD detectors, and most notably, convergent-beam geometry, determination
of the multiple scattering effects from raw diffraction patterns has become realizable3
[291]. Spence and colleagues concluded that CBLEED was worthy of further develop-
ment based on measurements of multiple scattering phenomena, formerly unavailable,

coupled with calculation of the patterns.

4.2 Coulomb Refraction

The term ‘surface potential’ has a long standing history in semiconductor physics as
pertaining to a space-charge region (SCR), arising from depletion (majority carrier
concentration at the surface is less than the bulk level), accumulation (majority carrier

near surface is greater than in bulk) , or inversion (minority carrier concentration

 

3In Reference [290], these advances were termed as a ‘minor revolution.’

59

exceeds that of the majority carrier). The fields measured by UEDV can and do
pertain to an SCR, but it is not the only constituent when the system is driven far
from its equilibrium with the pump laser. The primary sources of the pump-induced
field near the surface will be discussed in detail, but for now, note that the potential
measured by UEDV is not limited to that associated with an SCR. Before exploring
the field sources, the measurement technique will first be detailed along with the
formalism for quantifying the ‘Coulomb refraction’ of the scattered beams.
Refraction, a term typically reserved for photons as they propagate through dif-
ferent media, can be used analogously to describe electron propagation through crys-

talline media, where the index of refraction is given by [292, 293]

”(2 = V —_V0 :Oev'ia (41)

with V0 and V3 being the accelerating and surface voltages, respectively. The case
of an incident electron beam with kinetic energy K = eVO impinging a crystal at an
angle 6,; with respect to the surface plane is depicted in Figure 4.1. Under normal
conditions, where there is no field near the surface, it scatters from the crystal planes
and exits the surface at an angle 60. The addition of a constant electric field in the
probe volume augments the trajectory. The incident electron is refracted deeper into
the crystal than it otherwise would have been; the diffracted electron traveling to the
surface (exiting) is impeded by the electrostatic forces (from Vs), such that it exits at
an angle 6’0, which is shallower than 00. The surface potential, V3, is generally small
compared to the inner potential, U I p, such that both the refracted and unrefracted
beam paths scatter through the same Bragg angle, 03. In other words, the intrinsic
momentum transfer that the crystal exerts on the beam is conserved. Accordingly,

the Bragg condition remains intact, regardless of the presence of a field, which implies

60

sin 00 + sin 9,- = sin 0:, + sin a; = Nhkli. (4.2)
dhkl

 

 

.. - u= u,P (No Field) cc.”

—-h— U = U“, + cV, (Field Present)

 

 

    

 

 

 

 

 

 

 

 

Figure 4.1: Two different electron trajectories shown; one with no surface potential
present (light—gray) and the augmentation of the trajectory due to a surface potential,
Vs (black). The magnitude of the surface potential can be deduced from the vertical
displacement of the peak on the CCD screen.

From the characteristics of the trajectory with and Without a field present, a
relationship can be formulated between the shift in the trajectory and the surface

potential, effectively quantifying the Bragg peak shifts.

4.2.1 Slab Model

Using Equation 4.2, and invoking all of its assumptions, a relationship can be formu-
lated for V3 in terms of experimentally known quantities, 9i and 00, as is done here
for a simple slab geometry like the one depicted in Figure 4.1. Assuming a constant
electric field with no tangential components, the energy gained or lost by propagating

through V3 should be solely reflected in the vertical momentum, such that

1921 _ P2,; = 2me(K, ’ K) = 2meVs (4-3)
2

61

and

p3, — pi” = 2me(K’ '— K) = 2meV3, (4.4)
0 0
where K ’ = 6(V0 + V3) and the vertical momenta are given by
p?! = pa; tan 6;, (4.5)
2

and

p27: = pm tan 97:, (4.6)

with analogous relationships for 6:, and Hg. Using p2/2me = 8V0, Equation 4.3

 

becomes
X
tan2 6] = tan2 6,- + c052 9., (4.7)
2
where X E Vs/VO, and Equation 4.4 becomes
2 I 2 ll X
tan 6 =tan 9 +——, 4.8
0 0 cos2 98’ ( )

Using the Bragg condition (Equation 4.2), from Equations 4.7 and 4.8, the quantities

0; and 6:, can be suppressed in favor of 0,; and 62', to give

D2 _
AB = sin"1 \/ X 60, (4.9)

 

 

1+D2 -

where

 

_ tan(60 + 6,) — \/tan2 6, + x/ 0082 9i
1 + tan(60 + 6,)\/tan2 9,- + x/ 0082 6i,

 

(4.10)

 

and the shift in the outgoing angle, A B E 60 - 93’. A useful exercise for investigating
the parameter space is to calculate the Bragg peak shift, AB, over a series of varying
angles 6, and 190, which is shown in Figure 4.2. By inspection, it is immediately clear

that the larger shifts are expected for small 6,- and 00. In other words, the maximum

62

shifts are expected for the lowest order peaks observed, at the shallowest incidence
angles. This is consistent with expectations, as the electrons that are propagating
nearly parallel to the surface will spend more time in the field, and should be deflected

more as a result.

Vs = 3 Volts

90 (deg)

NW-hU'IONm

 

—|

12345678
0,-(deg)

Figure 4.2: The parameter space of Equation 4.9 for V3 = 3.0 V. Small values of both
0,- and (90 imply a small momentum component normal to the surface, which means
the effect from the field is more pronounced, as reflected in the larger peak shifts,
AB-

With additional algebra, and substituting back in for x, an expression can also be
formulated that gives the surface potential, V3, as a function of V0, 6,, 00, and the

observable Bragg peak shift, AB, by inverting Equation 4.9, which is

2 2 2
fi_ (aOAB—o,90+AB/2) —6, (90+AB) (411)
V0 (fa-+190)2 ' '

 

This expression has several assumptions: (1) The electric field at the surface is

homogeneous, has negligible tangential components, and spans the entire depth of the

63

probe region. (2) The spot size of the probing electron beam is much smaller than
that of the excitation laser, such that there are no edge effects from the field as the
beam enters or exits the crystal. Accordingly, the transverse momentum components
remain unchanged for all cases considered. (3) The effect of V3, does not interfere
with the inner potential (VIP) from which usual electron scattering commences, such
that the Bragg angle, 63, is conserved in the presence of V3. In other words, the

intrinsic manner of the diffraction is unchanged.

4.3 Generation of Near-Surface Fields

The electric field, which is responsible for Coulomb refraction, arises from a photoin-
duced charge separation from the pump laser. However, this description is still rather
vague when considering the possible ways in which charge can separate. In this sec-
tion, the aim is to clearly identify the different constituents of the measured transient

surface voltage (TSV) and discuss their respective roles in Coulomb refraction.

4.3.1 Field Constituents

A qualitative assessment of the various field sources shall be outlined first. The work
function for most materials is ~4-5 eV, and the excitation laser employed here can
be Operated at energies of 1.55 (800 nm) or 3.10 eV (400 nm)4. For both energies,
the 2-photon absorption cross-section is non-negligible (longer wavelengths result in
increased multiphoton absorption events [277, 278, 294, 295]). Clearly, the 3.1 eV
excitation pulse is capable of directly ejecting electrons through multiphoton emission.
While 3—photon processes have rather small cross-sections at 800 nm [294, 295], which

would be necessary to directly overcome the work function in most materials, 2-photon

 

4In principle, the frequency-tripled 267 Hz beam could also be used to pump the sample, though,
to date, it has only been used for photo-electron generation with the electron gun

64

processes with an 800 nm excitation are quite common, especially with moderate to
high laser intensities [277].

Multiphoton absorption in conjunction with the wide Fermi distribution associated
with a hot electron distribution makes thermionic emission also quite plausible [247,
248, 296—298]. Generally speaking, a photoemitted charge distribution, denoted here
as 0113c, should be considered in the TSV measurement [200]. Its contribution can be
suppressed (or enhanced), depending on the system, excitation fluence, pulse—energy,
and pulse-width. The effect of vacuum emission is depicted schematically in Figure

4.3.

VSC

 

(a) (b)

Figure 4.3: Mechanisms associated with vacuum emission. (a) Multiphoton absorp-
tion can supply sufficient energy for an electron to overcome the work fimction. (b)
With thermionic emission, the quasi-Fermi level need not be above the work ftmction,
as the width of the Fermi distribution is sufficiently broad because the electrons are
hot. As the tail rises above the work fimction, electrons are emitted into the vacuum.

Another possibility is that of a space-charge region established in the bulk due
to the electronic occupation of surface states [81, 126, 299]. When a semiconductor,
such as silicon, is irradiated with an ultrafast laser, electron-hole pairs are generated
in the bulk. Under normal circumstances, these electrons and holes will relax to their
respective band edges (conduction or valence) and recombine [300]. Should there be

an abundance of available surface states in the system (e.g. because the surface is

65

oxidized [107, 122, 301] or due to a reconstruction [126, 302]), it is plausible that a
portion of the highly excited electrons may find a lower energy cost in occupying these
states than relaxing to the conduction band minimum, thus establishing a potential
gradient, as the bulk responds to the lost charge. The lifetime of surface or trap
states [87, 107, 126] plays a crucial role in determining the bulk response. This
lifetime is affected by the coupling strength between surface and bulk evanescent
states, tunneling (or leakage) currents [87, 90, 303], etc. This sub-surface field should
be considered in TSV measurements, particularly in a system with poor screening.
Another possible contribution to the field is that of the surface dipole layer.
[36, 54, 194, 290, 304—310], which arises from the charge relaxation associated with
the termination of crystal structure at surfaces. The surface dipole layer is central
to the fundamental mechanisms in processes such as chemisorption of self-assembled
monolayers on metals and semiconductors [49, 54, 311], charge transfer at metal-
semiconductor heterojunctions [312], dye-sensitized solar cells [313], organic light
emitting diodes (OLEDs) [314], and even molecular patterning [315]. A static dipole
is known to form at the Si/SiOg interface due to charge transfer induced by a dif-
ference in electronegativity between Si atoms and Si02 molecules [306]. The surface
dipolar field region can be enhanced by further charge separation from photoexcita—
tion, where an upper surface sheet is occupied by one charge and the lower by the
counter charge [194]. A summary of the TSV that the incident electron beam sees as
it scatters from the crystal is shown in Figure 4.4. The Coulomb force is proportional
to the strength of the electric field, so the measured TSV comes from field-integration

along its trajectory through the photo-induced field region (laser excited region), or

21
TSV =/ Ez(z)dz, (4.12)
20

where 21 is the position at which the electron beam enters the field region, and 2.0 the

position of the diffractively probed region (both are shown in Figure 4.4). The TSV

66

could be expressed more generally by summing from each constituent, the changes of

the net potential near the surface, or

TSV = AVIP + AVdp + AVsc(62) + AVvsc(6i, 00, avsc), (4.13)

where the aspect ratio of the vacuum space charge region, avsc = (szc - zo) / L,
changes as the photoemitted electron disk moves away from the surface [194, 200, 287],
AVIP describes the change in the inner potential, AVdp, the change in potential
arising from a change in the strength of the interfacial dipole, AVsc, the sub-surface
bulk space-charge region, AVvsc, the potential associated with emitted charge density,

adp, and L the associated length of the laser spot on the surface.

4.4 Quasi-3D Structure

As mentioned in Appendix A.O.3, suppression of the spatial coordinate normal to
the surface that the electron beam samples (e.g., RHEED or LEED geometry) will
result in the elongation of the reciprocal lattice. To fully illustrate the point, con-
sider the limiting case of an infinitesimally thin surface, where a 2D array of vertical
rods extending from —00 to 00 would result. Elongation of the reciprocal lattice
can be understood through the standard relationship between Fourier complements:
Asz2 = 27r, which gives rise to the Scherrer criterion for estimating the length
scales of crystallites [316]. In practicality, it is inevitable that a finite sub—surface
periodicity will be sampled by the electron beam. A possible ramification of which
is that the reciprocal lattice degenerates into modulated rods, as shown in Figure
4.5. This is particularly common when the surface is rough, giving a finite, in-plane
persistence length for diffraction [207], or if the surface has steps or ripples, which

effectively results in a spread of 0,- over the electron footprint on the surface.

67

 

Surface Potential Diagram

\
\

e—beam‘
\

    
  

0 Volts

 

 

 

 

A

 

 

 

3- 81-02 81 (Bulk)

 

 

 

 

Figure 4.4: Transient surface potential diagram introduced by various sources of pho-
toinduced charge separations (see text) near the Si / S102 / OH interface. The transient
surface voltage (TSV) determined using the electron diflractive approach comes from
the electric field integration over the region traversed by the incident and diffracted
electron beams.

Convergent beams also have a spread in the incidence angle over the beam spot
(by definition, since the impinging beam is conical) in addition to the small spot size,
which paradoxically yields more information than a larger spot size [207, 290, 317,
318]. In fact, for any diffraction-limited probe, the size of the angle-resolved cone of
scattering generated for each Bragg order increases as the probe size is reduced [290].

In Figure 4.5, the dark grey spots on the CCD screen represent the modulated
spot pattern on the reciprocal lattice rods, with the pattern corresponding to the
true lattice spacing. In fact, when the surface is sufficiently rough or when the crys-
tallographic orientation of the sample is randomized, such as the powder diffraction
from nanoparticles or quasi-polycrystalline diffraction from highly-oriented pyrolytic
graphite (HOPG), more than one Bragg peak can appear simultaneously at a fired 6,,
as shown in Figure 4.6(b)-(d). The reliable appearance of the 3D Bragg diffraction
over a finite A0,- ensures persistent tracking of the 3D crystalline property (lattice
parameters and associated potential) as laser-induced perturbations arise within the

crystal.

4.4.1 Robustness of the TSV Formalism

To experimentally examine the interference along the reciprocal lattice rods, a rock-
ing curve is acquired, which is the measured diffraction intensity over a range of 0,-
(introduced in Section 2.3.4). This is carried out in the ultrafast electron crystallog-
raphy (UEC) experimental setup [190] by tilting the sample plane while the direct
beam remains fixed, which defines s = so — s,- = 0, at position C in the diffraction
image (Figure 4.5). Here, rocking analysis over three types of crystal is presented:
a smooth silicon (111) surface [107, 194], 2 nm gold nanoparticles [192], and HOPG
[108, 194], as described in Figure 4.7 [194]. The periodicity of the (111) modula-
tion in the reciprocal lattice rods was examined by collecting the intensities frame

by frame in the Oi-scan over the (0,3) reciprocal lattice rod. By stitching together

69

 

Figure 4.5: The Ewald construction in the reflection geometry. The incident beam 3,-
impinges the crystal at a glancing angle, 02-. A finite sub-surface periodicity is sampled
by the beam, causing a vertical interference pattern to form on the reciprocal lattice
rods (the white spots on the rods and grey spots on screen), illustrating the potentially
quasi-3D nature of the diffraction pattern (see text). The bright peaks on the screen
(white) represent the points where the reciprocal lattice interference spots intersect
the Ewald sphere. If 9,- is increased (or decreased), the Ewald sphere rocks about
point 0 while the rods remain stationary, causing the Laue circles to cross different
parts of the reciprocal lattice for examination with diffraction. The dashed circle
represents the zeroth order Laue zone (ZOLZ).

70

 

Figure 4.6: Diffraction patterns from (a) a smooth Si (111) surface, (b) a Si(111)
surface with prominent step edges, (0) metallic nanoparticles, (d) HOPG. The pat-
terns shown in (b)—(d) exhibit quasi-3D features, while (a) does not. Determining the
plausibility of Coulomb refraction-based shifting can be bolstered when several peaks
from the same reciprocal lattice are co—present on a single diffraction pattern, as this
allows for a direct comparison in a single shot, rather than rocking the sample to find
the next order on the rod.

the intensity scan along the rod over the given range, shown as a compiled rocking
map in Figure 4.7(a), the evolution of the projected Bragg peaks in the diffraction
image with changing 6, as the Ewald sphere cuts across different sections of the rod,
could be elucidated. For the (0,3) rod, the trajectory of the Ewald sphere cut evolves
diagonally across the compiled rocking map, with the periodic intensity increasing

over nearly evenly spaced 6,(60), which obeys the Bragg relationship,

/\e
d111’

 

sin 6i + sin 60 = N111 (4.14)

where N111 denotes the diffraction order and dlll is the interlayer separation (3.135
A for Si). As 6, increases, so does the sub-surface periodicity sampled by the beam,
as it penetrates deeper with an increased momentum component perpendicular to
the surface. This reduces the range A6, for which the Bragg peaks can be observed,

thus reflecting the complementary (Fourier) relationship. For a stepped surface, the

71

domain structures produce 3D features, yielding multiple Bragg peaks to appear at
one crystal orientation, as shown in Figure 4.6(b). In the diffraction obtained from
HOPG (singleshot pattern in part (d) of Figure 4.6), this extension becomes nearly
continuous, as shown in the rocking curve map in Figure 4.7(c). Following this quasi-
3D extension, shown in the rocking curve maps, the associated changes introduced

in the atomic and electronic degrees of freedom caused by photoexcitation can be

monitored.

(C)

56° 10.2°

95

 

 

O

1.4° 4.0

           

4.7° e, 3.50 91'

23°

0.10 5.69 e, 2.00

 

 

 

 

Figure 4.7: Compiled rocking map for Si(111) (a), Au nanoparticles of size 2 nm (b),
and HOPG (c). These maps are obtained by stitching together scattered intensity
patterns along the normal direction over a range of incident angles (6,). The cor-
responding scattering angle (6 S) for the intensity pattern is also shown. In (a), the
Ewald sphere cut from the (0,3) rod is traced out in the diagonal, as each Bragg
peak is present for only a small angular range, while in (b) and (c) the diffraction is
powder-like, in which multiple peaks are co-present over an extended range of electron
incidence.

The first case chosen to demonstrate robustness is that of a single incidence angle
with multiple peaks on the same rod, exhibited here by a Si(111) surface with a
chemically grown oxide layer (see Section 5.2.1), with prominent step edges [107, 194].
Here, three peaks along the (0,0) rod were clearly visible at an incidence angle of
6, = 6.80 (Figure 4.8 inset). Using the formalism from Section 4.2.1, the changes in
momentum transfer were converted to surface voltage, which is presented in Figure
4.8. Note that the (0,0,24) and (0,0,27) peaks agree on the value of the maximum

transient surface voltage for the fluences presented. The incidence angle for these two

72

peaks was, of course, the same, since they were co-present on the same diffraction
image. The (0,0,24) peak shifted more than the (0,0,27) as is shown in Figure 4.8(a),
which is expected from Equation 4.11, where smaller values of 60 (and 6,) predict
larger shifts (A3) for a given voltage (Figure 4.2).

At this point, the focus is shifted to investigating the TSVs obtained from different
points on different Laue circles. Various reciprocal lattice rods can be examined in an
experiment by rotating the sample in-plane (denoted by angle 45), shown schematically
in Figure 4.9. Combining the ab and 6, operations, it is possible, in principle, to
determine the 3D atomic lattice structure. The rocking curve for a smooth Si(111)
surface is shown in Figure 4.7(a). Unlike the case above with the stepped-surface, the
higher orders are present only as incidence angle 6, is also increased, which is also an
indication of the superior surface integrity.

The objective here was to analyze the Bragg peak motion from multiple peaks on
this rod, compare them to each other, as well as another peak from a different rod.
This was to see if the agreement is robust as incidence angle and diffraction order are
varied (previously only the variations associated with the latter were examined). In
principle, the TSV formalism should remain equally valid as different rods than the
(0,0) are examined.

Peaks (0,1,24), (0,1,24), and (0,3,24) were found at incidence angles of 624°,
470°, and 415°, respectively. The dynamics of each were elucidated by performing
pump-probe experiments under a fluence of 64.3 mJ/cmz, pulse width 45 fs, with a
near infrared pump wavelength of 800 nm. Figure 4.10 compares the transient surface
potential delay scans for the three peaks. The two peaks from the (0,1) rod show
strong agreement, with a small deviation from the (0,3,24) peak. The deviation could
come from other sources of TSV that cannot be described by the idealized dipolar

slab model, which may possess an angular dependence.

73

 

0.00 ~ '
0.05 ~
0.10 ‘
0.15 ‘
0.20 ‘

As (A4)

 

 

 

   
    

 

—E-— (0,0,24)
+ (0,0,27) _

 

 

 

72 mJ/cm2

TSV (VoltS)

 

22 mJ/cm2 (b)

 

 

 

o 500 1000 1500 2000 2500 3000
Time (ps)

Figure 4.8: (a) The momentum transfer As as a function of time for the (0,0,24) (red)
and (0,0,27) (blue) peaks. As expected, the lower order peaks shift more than those
of higher order, consistent with the TSV formalism. Inset: the diffraction pattern
from the fixed crystal orientation used throughout this pump-probe experiment. The
(0,0,30) peak is present in this pattern, shown by the top-most peak. The signal-to-
noise for this peak was rather weak to follow dynamically, so it was excluded. (b)
The transient surface voltage (TSV) for the listed fluences. The two different orders
are in close agreement for all fluences. [107]

74

 

(a) (b) (C)

Diffraction Image X—stal rot.

Shadow
Camera Edge

Distance

  
   

lefracted
Beams

¢ 17 ————— +2
Sample

Deflector

 

 

  

Ewald Sphere
(fixed)

 

 

0 Bright Peak
0 No Peak

Incldent
Electron Beam

 

 

 

 

 

 

Figure 4.9: Schematic experimental geometry of ultrafast electron crystallography,
showing the different angles of rotation, 6 and (1), the former associated with a rocking
curve, the latter with an in—plane rotation (a). In part (b), the Ewald sphere intersects
the (0,3) rod. An in—plane rotation (A¢) about the (0,0) rod causes the (0,3) rod to
move away out of the intersection and the (0,1) rod to move in.

75

An area worthy of future consideration would be the examination of a TSV correc-
tion factor based on the position of the Bragg peak along the ‘perimeter’ of the Laue
circle. The agreement for the two very different 6, suggests that the TSV change is
largely caused by the finite-depth potential drop across the SiOg dipolar layer as the
electron beam crosses it, en route to the diffracting Si(111) planes. At this fluence,
the Si(111) lattice spacing is expected to change at most 0.011% (m 3.4 x 10‘4 A),
corresponding to a maximum temperature rise of 40 K, calculated from a Boltzmann
transport model [264] (Section 3.2), and the linear thermal expansion coefficient [283],

thus oflering less than 1% contribution to the observed A 3'

 

1 .2 n -
J . (or 3! 24) '

"0‘ A (0.1.24)
(0,1,21)

  
 
 
 

L

l

0.8 .
0.6 d

TS V (Volts)

 

 

 

 

 

 

0.4-
0.2: 621.. Ill—1E SK):
4 +++ so .I
l
0.0-e— __________________
'0-2 *I'IrT'I'I'I‘I

 

 

-100 0 100 200 300 400 500 600 700

Time (ps)

Figure 4.10: The TSV deduced from examining the (0,1) and (0,3) reciprocal rods
for the Si(111) / 8102 / OH interface, with a fixed laser fluence of 64.3 mJ/cmz. The
incidence angles for the (0,3,24), (0,1,21), and (0,1,24) peaks are 624°, 470°, and
415°, respectively.

76

A relatively high fluence was chosen for these experiments so the delay scan for
each of the three peaks could be carried out quickly. Lower fluences require more
acquisitions at each delay so the change in peak position can be resolved from the
noise level, which is not the case for high fluences, where the dynamical effects are
easily discernible, thus requiring fewer delay cycles as fewer frames are necessary to
average out the noise.

Here, each experiment required a 3-frame average for each delay, where each frame
consisted of approximately 4000 shots (pumped and probed 4000 times per frame,
implying a 4 second acquisition time with the 1 kHz repetition rate), meaning that the
experiment on each peak lasted about 30—40 minutes. Over the course of several hours,
the laser is quite reliable, making it very safe to presume that the three experiments
were performed under identical pump conditions. As an additional check, the pump
fluence was checked before and after the experiment, as was the alignment condition;
neither exhibited any change.

The situation becomes increasingly complicated as the fluence decreases, as the
peak shifting is generally on the order of tenths of pixels, sometimes less (the highest
experimental resolution achievable by the author is a 0.06 pixel change in peak posi-
tion, on Si at a fluence of as 12.5 mJ/cm2). The ‘dynamical coordinates’ for nearly
all other systems, respond considerably stronger to pump excitation than silicon. For
example, with HOPG, peaks will shift ~ 20 pixels under moderate to high fluences.
Even low fluences respond with 5—10 pixels. It is not unusual over the course of ~8-
12 hours, for the laser, electron beam, or stage to drift slightly, thereby changing
the alignment condition. If present, these artifacts must be carefully monitored and

extracted.

77

4.5 Coulomb Refraction vs. Lattice Expansion

Based on Equations 4.9 and 4.11, the field-induced shifts can be evaluated to under-
stand the trend of A B under different incidence angles, diffraction orders, and surface
potentials, and a comparison can be made for the dependence of the structure-related
shifts, 63. At a given V3, |AB| generally decreases more rapidly for larger diffraction
orders (60 values), as demonstrated in Figure 4.11.

The opposite is true for thermal expansion, where the shift, 6 B = —6B - 6a/ a, is
proportionally magnified for the higher orders (6 3). Indeed, larger diffraction cones5
respond more strongly to a lattice expansion, 6a. Further comparison of the relative
changes of A B and 5 B in two contrasting regimes shows that for smaller 6, and N,
A B tends to dominate over 53, as shown in Figure 4.11(a), simulated for 6, = 125°
and N N 2 over a nominal V3 range of ~ 1 V.

For larger 6, and N, the trend will reverse, as demonstrated in Figure 4.11(b),
where 6, = 505° and N ~ 8, comparing to a nominal structural change at the level
of 0.5%, which corresponds to lattice heating of the order of 500 K for solids. To
separate A B from 6 B experimentally, it is thus beneficial to examine both high and
low angle regimes, i.e. low 6, and N for TSV determination, and high 6, and N
for structural changes [194]. In fact, this is another reason why peak (0,0,30) was
not presented in Figure 4.8, as it was not an ideal candidate for TSV measurement.
An additional method (not presented here) involves a Fourier phasing algorithm for

isolating the TSV effects from structural changes in graphite [108, 190, 194].

4.6 Beyond the Slab Model

Recall from Section 4.2.1 that one of the underlying assumptions of the slab model

is that the field has negligible tangential components. The large laser spot size com-

 

5A diffraction cone is described by joining the vertices of vectors 3,- and so.

78

(a)

 

 

   

 

 

 

 

 

 

10 « ,
melting melting
8
«I
n:
E 1 -structural 1. , structural
2 change change
<
I tti ] lattice
0.1 l - 1;.an 0'1 heating
0 2' 4 6 a 10 0 i 1: 6 a 10
90(deg) 90(deg,

Figure 4.11: The total peak shift, A 3, calculated for varying degrees of lattice ex-
pansion (blue) and surface voltage. For a fixed voltage, the associated shift is less
prominent for higher orders of diffraction (60). This is in contrast to the structural
based shift, 63, where the higher orders are more strongly affected.

pared to that of the electron beam validates the assumption of a homogeneous field
perpendicular to the surface, since this is what the e—beam sees. Essentially, the elec-
tron beam enters and exits from the top surface of the charged capacitor slab, and
knows nothing of the edge effects (Figure 4.12).

Probe Region

C((iil‘liiLl)

+++++++++++++

Figure 4.12: The electron beam diameter being much smaller than that of the laser is
an underlying assumption for the validity of the formalism presented in Section 4.2.1,
where the TSV is not affected by the tangential components of the field, because the
electron beam enters and exits from the top of the ‘capacitor.’ The aspect ratio of
the capacitor is exaggerated for clarity. Realistically, the height and width are of the
orders of 1 nm and 100 pm, respectively.

 

In principle, extending the UEDV technique to less ‘friendly’ field geometries
should be possible, as the charged probe will respond to the fields through which
it propagates. The question lies in the interpretation of the resulting diffraction

patterns.

79

To quantitatively evaluate the various systematic factors that may affect proper
deduction of the TSV, and to treat the TSV beyond simple geometries, the formalism
described in Equations 4.9 and 4.11 can be extended to consider Coulomb reflection
in various, non-planar geometries. It will be demonstrated that extension to an
arbitrary shaped potential (depicted in Figure 4.13), is realizable with the surface-
sensitive probe.

The primary justification of this approach hinges on the fact that the effect of
a surface potential, whatever its shape may be, is to contribute much less change
(proportionally) to the tangential momentum components than those perpendicular
to the surface. This is plausible because the electron beam has nearly 100% of the
accelerating voltage (30 kV) in its horizontal momentum. As a result, any tangential
field components (which tend to be rather weak compared to the longitudinal one)
are expected to have only marginal effects on the high energy momentum components

in that direction.

 
 

_________ l

|~———L————-l

 

Figure 4.13: General refraction geometry for a grazing incidence electron beam. The
effective bending of the incident(exiting) beam, caused by the local field associated
with V3 in the nanostructures, differs depending on the entry(exit) point 2:] (23’). Since
the relative change of the transverse momentum remains small, the slab model can
be extended to treat arbitrary geometries through a correction factor, 6(a, 6), that
depends on position (through a) and angle (see text).

80

Rather than constructing a new formalism from first principles, a correction factor
is imposed onto the slab model for both the incoming and outgoing electron wave

vectors, given by 9,(6,, or) and 90(60, (1), such that Equations 4.7 and 4.8 become

X

 

 

 

tan2 6; = tan2 6, + 6),-(6,, COT, (4.15)
- cos 6,
and
tan2 6:, = tan2 6:; + 90(60, a)—%. (4.16)
cos 60
Analogously, Equation 4.9 becomes
AB = sin‘1 [/D2 130%; COX — 60. (4.17)
where -
D _ tan (6, + 60) — \/tan2 6, + 8,(6,, a)X/ cos2 6, (4.18)

 

 

_ 1 + tan(6, + 60)\/tan2 6, + 8,(6,, a)x/ cos2 6,.
For 90(60, oz) 76 8,(6,, a), the surface potential, V3 from A B, can be written for

small angles as

x = { [<c+ “new, a) — c6000. 001

 

d: \/[(c + 2)@,(6,, a) — 060(60, 01)]2 — 4ab[60(60, a) — 8,(6,, 01)]2 }

/ weapon) — 6),-(9,0012,

(4.19)

where

81

2
(60A,; - 9,00 + 2123/2) — 0,? (00 + A B)2

 

a = , 4.20
(6.- + as)? ‘ ’
b = —1——2, (4.21)
(92' + 60)
and 2 2
26. +266 —2A 9 -A
C: 2 ’ 0 B 0 B. (4.22)

 

(0.- + as)?
If 80(60, (1) = 6,(6,, a), then X = a. The + or - is chosen in Equation 4.19 based

on the sign of (c + 2)9, —— Leo; + is used if the quantity is g 0, - is used if it is > 0.

4.6.1 Correction for Finite-Slab Geometry

With the general formalism laid out, the attention is turned to non-planar geometries.
The first example is similar to the slab geometry, but with the e-beam propagating
out the side of the ‘capacitor,’ rather than exiting from the top. This could occur ex-
perimentally if the electron beam diameter were as large, or larger than the laser spot.
In this scenario, ‘surely some of the incoming electrons would sample the tangential
field components from the capacitor.

To investigate the deviation from the slab model, a simulation is performed where
the electron is propagated through a parallel plate capacitor with a fixed nominal
voltage, and then analyzed in the far field to determine the ‘measured’ voltage when
it is no longer under the influence of the capacitor. Comparing the far-field voltage
to the nominal one gives the correction factor. Of particular interest here, are the
cases where the electron exits the capacitor from the side, rather than the top. An

approximation can be made a — priorz' that the correction factor is

6/a if6 < a,

22

6(6, (1) (4.23)

1 if62cr.

82

If this simple approximation for the correction is assumed to be true, it can imme—
diately be noted that the divergence of A B as the diffracted electron beam approaches
the shadow edge (60 approaches 0) is suppressed by this correction factor. Note, in
Equation 4.9, A B diverges as 60 —> 1, whereas A B —) sin—1 W in Equa-
tion 4.17 because 60 —> 0 as 60 —> 0.

The real correction factor is obtained through the following procedure. A parallel-
plate capacitor is simulated with vacuum dielectric between the plates (6 = 60), which
are 2h apart and 2a wide, and charged such that there is a 10 V potential difference
between the plates. The plate at y = h is held at a voltage, Vplate = —5 V, and
the bottom plate (y = —h) is held at +5 V. The top-right quadrant is depicted in
Figure 4.14(a), which by symmetry, is actually sufficient to solve the problem (y = 0

is grounded).

 

 

 

    

(I.

Figure 4.14: Correcting the TSV for a finite slab. (a) The potential is calculated for
the mesh, followed by launching an electron at an angle 6 from the origin (2 = y = 0),
and using the change in kinetic energy, deduced from 6’ to get the probed voltage, Vs’“.
The aspect ratio, a = h/a, is varied to examine different exit points. (b) Simulation
results for the correction factor, 6(6, a), as a function of aspect ratio, a, show that for
smaller launch angles, the correction factor is well-approximated by Equation 4.23.

83

Using the figure as a guide, the electron is launched at an angle 6 from the capacitor
center (a: = y = 0), with kinetic energy eVO = 30 keV, thus defining the momentum
components as pa; = m 0036 and py = m sin 6.

A 5 x 5 mm2 mesh with variable spacing (finest near the edges of the capacitor)
is constructed to resolve the field. Dirichlet boundary conditions are set at the mesh
limits y = 0 and 5 mm, and :1: = 5 mm, where the potential is fixed at 0 V. The
solution is symmetric about the y—axis (the a: = 0 boundary is reflective). The upper
limits of the mesh were found to be sufficiently large compared to the capacitor
dimensions (for all capacitor sizes considered) such that the potential could be set to
0 V at the right and top limits of the mesh, with no loss of accuracy.

With all boundaries defined and the nominal capacitor voltage set, the potential
at all a: and y node points was calculated (uniquely) by iteratively solving Laplace’s
equation at each node point until convergence was reached [319]. Once the electro—
static potential had been determined, the equations of motion were solved for an
electron propagating through the field6. When the electron reached so = 5 mm, the
calculation was stopped and the hypothetical ‘measured’ voltage, V63“, is determined

from the ratio of momentum components in the far field, or

*

‘V/—3 = tan2 6’ — tan2 6 z 6'2 — 62, (4.24)
0

where 6’ is the arctangent of the momentum components in the far-field, and a small-
angle approximation was assumed. Any difference between V; and Vplate is an indi-
cation of a source of error in the TSV measurement. The correction factor can now

be properly defined from the simulation results, as

v;

6(9‘0‘) = vplate-

 

(4.25)

 

6These calculations were carried out using the Trak Charged Particle Toolkit from Field Precision.

84

The results are shown in Figure 4.14(b), where the aspect ratio of the capacitor,
a = h/ L, is varied so that the effects associated with the different exit points can
be analyzed. The edge-effects are increasingly important for the smaller angles and
larger aspect ratios. This makes sense, since an electron launched at a shallow angle,
in a capacitor where the top plate is rather far away (large a), will ride along the
symmetry boundary of the capacitor until it exits, which means that it would have
flown through a region of very small potential. The closer it gets to the top plate,
the more potential, close to the nominal value, it would have experienced.

Conversely, the higher orders (large 6) will have a greater likelihood of flying out
the top of the capacitor, even when a is large, which is why 8 deviates from 1.0 much
more slowly at 6 = 35° than at 6 = 15° or 25°. As expected, edge effects, or those
associated with a field possessing a non-negligible tangential component, are expected
to be more pronounced with larger diffraction cones. This is consistent with phys-
ical intuition, since the larger diffraction cones have smaller horizontal momentum

components.

4.6.2 Correction at the Nanoparticle/ SAM/ Semiconductor

Interface

The second scenario is that of an array of metallic nanoparticles, immobilized on a
semiconductor substrate via self-assembled molecular (SAM) chains. This nanopar-
ticle/ SAM / semiconductor interconnect occurs frequently in UEC [190, 192—194], and
is addressed in greater detail in Chapter 6. Here, the emphasis is on determining
the accuracy of TSVs in measuring the associated fields with charge that has been
transferred to the nanoparticle, such that it is fixed at a nominal voltage. Since this
chapter is on the topic of the measurement technique, the nanoparticle data on charg-
ing and discharging are withheld until Chapter 6. Only the measurement correction

factors shall be derived here.

85

Similar analysis is performed for this geometry to that of the slab correction, this
time setting the potential of the nanoparticle to the nominal voltage of —5 V. The
nanoparticle sits on a 1 nm dielectric slab (er = 2.5), representing the self-assembled
linker chain. Beneath it is a grounded metal slab representing photoexcited silicon.
The equations of motion were solved for various nanoparticle sizes, and at different
launch points along the height of the linker molecule. The results are shown in
Figure 4.15. Here, the aspect ratio is redefined as the ratio of SAM thickness (h) to

the nanoparticle diameter (D), a = h/D; h = 1 nm for all cases simulated.

Metal
Nanoparticle

(b)

(5V)

(-2 V)
0 (deg)

 

X

 

0.00 0.25 0.50 0.75 1.00
0:

Figure 4.15: (a) The calculated potential for the case of a 20 nm metallic nanoparticle,
charged to -5 V, with a 1 nm thick, dielectric layer (6 = 2.5) atop the Si substrate. (b)
The correction factor as a function of aspect ratio (SAM to nanoparticle) is calculated
by resolving the trajectory from the electric forces. The solid points are the simulated
data; the lines are from the approximation 6 = h / D (see text). Inset: The correction
factor as a function of launch angle 6 for three different launch positions along the
SAM.

4.7 Discussion ,

A general formalism of electron diffractive voltammetry has been constructed, that is

suitable to deduce surface potentials for arbitrary geometries. This chapter empha-

86

sized the measurement technique, with a general description of the various field con-
stituents near the surface, including vacuum emission, surface charging, bulk space-
charge, and surface dipole layers. In addition, their effects were contrasted with those
associated with lattice expansion, which are also buried in the Bragg peak motion.
Notable differences were identified in their respective behaviors, which were quanti-
fied in various experimental regimes, such as deep/ shallow incidence and low/high
diffraction orders.

When operated in proper regimes, UEDV possesses the unique capability of moni-
toring ‘site—specific7’ charge dynamics with ultrafast time resolution, thereby making
the determination of electrical conductance possible from the transient I-V charac-
teristics associated with various nanoscale materials and interfaces, evidenced here
from the studies of charging dynamics at the semiconductor/ oxide interface, and
on a semiconductor/ molecule / metal nanoparticle interconnect. In contrast to opti-
cal spectroscopic techniques [5, 6, 320], whose lifetime measurements of the charge
transfer states provide a quantitative measurement of the electronic coupling matrix
elements, the time scale determined with the voltammetry methodology is a transport
time scale integrated over all possible channels of charge transfer, with both forward
and backward channels considered. Therefore, these two approaches provide a strong

complement to one another.

 

7Here, the term site-specific is used to imply a characteristic length scale for nanostructures,
which can be as small as a few nm.

87

Chapter 5

Carrier Transport at the Si / SiOg

Interface

5.1 Introduction

The nature of charge transfer, trapping, and detrapping at the Si/SiOg interface
has gained notable interest as CMOS devices are further integrated in accordance
with Moore’s law. As the dielectric oxide layer necessarily becomes thinner, leakage
currents become a non-negligible hindrance in transistor performance, an effect that
was formerly not present with thicker oxides. Leakage currents commonly lead to
interfacial fields as carriers occupy defect and surface states. These fields, measurable
with UEDV, provide additional insights into the intricacies associated with interfacial
charge transfer.

On the most basic level, the field arises from charge separation at the interface
as carriers are transported from the bulk to the surface. The nature of the field
is influenced by many variables, including, but not limited to, dopant (type and
concentration), defect state density, surface roughness, oxide thickness, the strength of

surfacebulk coupling, etc. In addition, the charge rearrangement mechanisms remain

88

non-trivial, be it via direct or field-induced (Fowler-Nordheim) tunneling [303, 321,
322], internal photoemission (IPE) as the quasi-Fermi level of hot electrons (holes) is
raised above the conduction (valence) band offset, which usually involves some sort
of multiphoton absorption effects. 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.

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 [78—100].

Photoelectron spectroscopic methods have been effective in elucidating the inter-
facial electronic structures [323, 324], as well as monitoring the surface state popula-
tions directly [122, 126, 299]. Bulk carrier dynamics in Si have been studied exten-
sively on the pico— to femtosecond time scales with a variety time-resolved techniques
[104, 126, 128, 136, 286, 300, 325].

The focus here is to investigate the charge injection processes during charge re-
arrangement (field generation), and in doing so, provide additiOnal clarity to the
source(s) of the field, using the recently developed technique of ultrafast electron
diffractive voltammetry (UEDV) [107, 194, 285], discussed in Chapter 4. Under ul-
trafast laser irradiation, a fraction of the valence band (VB) electrons are promoted
to the conduction band (CB), followed by charge rearrangement at the interface, de-
pending the nature of the excitation (laser intensity, energy, duration, etc.), as will
be demonstrated in this chapter. This chapter will summarize the general results on
interfacial hot carrier transport that have been ascertained from Si / SiOg experimen-

tation, specifically UEDV.

89

5.2 Experimental Methods

5.2.1 Surface Preparation

Preparation of silicon wafers follows a modified RCA procedure [326]. Si(111) wafers1
of p— and n—type are cleaned in H2804/H202 (7:3) for 10 min at 90°C, followed by
immersion in room temperature N H4F (40% in H20 for 6 min) to remove the native
oxide. An ultrathin oxide layer is deposited by immersion in HCl/ H202 /H20 (1:1:5)
for 10 min at 90°C, followed by further cleaning in NH4OH/ H202/H20 (1:1:6)
for 10 min at 90 °C. Oxide thicknesses are measured with an ellipsometer. For the
experiment here, an n-type wafer was chosen with thickness 19.8 :l: 2.0 A.

The sample was immediately transferred to the UHV chamber via load-lock. The
optical pulse width was measured prior to beginning the experiment to be 40.8:l:3.2 fs,
using the autocorrelation method described in Section 2.3.2. The laser spot footprint
on the surface, which is elliptical, was measured to be 6.96:l:0.63 x 105 pm2, using the
method in Section 2.3.1. Laser fluences were measured before and after each delay
scan, as the laser power can slightly fluctuate over the course of a day. When they
were different, an assessment was made as to when the laser power had dropped (or
risen) based on the electron counts. A weighted average was computed between the
before and after fluences, according to the proportion that the scan was deemed to
have spent at each fluence.

These experiments were carried out at ~ 6.0 x 10’9 torr. The sample stage
was brought to within ~1 mm of the electron gun, as to minimize space-charge
broadening effects (a camera is positioned to look directly at the sample surface
through a con-fiat viewport flange, which allows visible verification of the alignment).
The direct electron beam was measured using the knife-edge method (Section 2.3.3) to

be 22.1 :l: 1.3 pm, corresponding to an e-beam footprint on the sample with elliptical

 

1Silicon wafers, purchased from Silicon Inc., Boise, ID

90

area of 5.29 x 103 ,um2, which is about a factor of 13 smaller than the pump laser

footprint.

5.2.2 Pump-Probe Alignment

After most delay scans, the pump-probe alignment was re-checked with the alignment
scans described in Figures 2.5 and 2.6, from Section 2.2.1, which is standard practice
for pump-probe investigations of Si when applying the laser energy and fluences used
here, as it does not exhibit a large response to the pump laser since the optical
penetration depth at 800 nm is m 4 pm.

Realignment is imperative if an overall drift in the position of Bragg peaks was
observed, which happens approximately 20% of the time when a delay scan exceeds
10 hours (most likely to occur with low fluences). It may also be necessary to discard
the data if an assessment cannot be made as to when the alignment was lost. An
alignment check usually takes about 40 minutes, and if possible, is performed at
the desired fluence of the next experiment. However, in the interest of conserving
laser run time, if the dynamical changes at the next fluence are known to be quite
small, a higher fluence may be chosen to align the pump and probe so that the next
experiment can begin swiftly. For example, F = 64.3 mJ/cm2 was used to align the
scans for fluences of 13.6, 17.1, and 17.4 mJ/cmz, as the changes in the spot position

are quickly resolvable at that fluence.

5.2.3 Data Analysis

The diffraction patterns for each delay are fit according to the intrinsic properties
of the crystal (lattice constant, crystal orientation), and the physical geometry of
the UHV chamber (camera distance, incidence angle, beam angles, crystal rotation,
accelerating voltage, etc.), such that the theoretical spot pattern matches well with

the observed one. This is essentially a geometry problem of first calculating the

91

Ewald sphere intersections with the reciprocal lattice, which can be deduced from
the accelerating voltage and incidence angle (which give the radius and orientation
of the Ewald sphere) and the unit cell with the corresponding lattice constant of the
material to calculate the reciprocal lattice. The intersections are projected in space
by the camera distance to give the calculated spot pattern on the screen, which was
all programmed in a home-built crystal fitting program. Fitting each pattern with
a Gaussian for the diffraction peak at each delay, a plot is generated of momentum
transfer 3 vs. time, each of which is converted to a TSV delay scan using the formalism
from Chapter 4, specifically Equation 4.11. The process is illustrated in Figure 5.1,
where the Gaussian peak fit is shown on a raw diffraction image in panel (a). The
spot position in pixels (the mean of the Gaussian) can be directly converted into
momentum transfer coordinates using the fit parameters of the ground (pre—excited)
state, leading to the plot in panel (b). Finally, using the UEDV formalism, s(t) is
converted to TSV (inset).

Each TSV plot is fitted with an empirical function describing charge injection and

decay, given as

Vs = Vfitl1_ eXP(—t/Ti)l /(1 + t/Tc), (5-1)

such that the charge injection (7,), relaxation (Tc), and maximum amplitude voltage
(Vfit) characteristics can be extracted. The results are shown in Figure 5.3.

The two main features of the TSV results are: (1) The time scale for charge
separation (7,) here is characterized by charge injection into the surface states of
SiOg, has two separate time scales. At the lower fluences (F < 20 mJ/cm2), the
injection time, TL z 100 ps, while the higher fluences (F > 20 mJ/cm2) the injection
time is significantly shorter, as TH z 65 ps. (2) The fluence dependence of the TSV
can be very well described by a quadratic relationship, TSV = aF + bF2, where
a = 1.016 X 10"2 (mJ/cm2)_1 and b = 8.803 x 10‘4 (mJ/cm2)-2. The crossover

from TL to TH as F increases is very consistent with the corresponding TSV rise

92

Convert Pixel to s - coordinate

Fit Gaussian at each Delay
15054 1* " j 'i '7‘f I I ' I ' U

 

y
t l v v
virillax ( g v V V V V V 1
rim/LS.
V
‘ r-x‘15.53-(v .— 0‘ .gOO" '
GuidesforFlt , , oI< V 3 2-200 0 .
——-—!——1 v . (7% no. ‘
V >
v, m

      

 

15.52 A V "' '6°° ' -
500 1500 2500
(b) Delay Time (ps)

 

 

 

Dela = '50 [SI 7 i W 15.51 I - I . I v I - I ' I ' I
y p (a) 500 1500 2500 3500
Delay Time (ps)

Figure 5.1: (a) The diffraction peak is fit at each delay scan with a Gaussian (blue),
followed by converting the camera pixel coordinates to s—coordinates (b) using the
unit cell, lattice constant, camera distance, etc. (see text). The momentum transfer
(5) at each delay is then converted to transient surface voltage using Equation 4.11.
The orange lines in (a) are intensity line scans from within the guided area (magenta).

 

   

 

 

    

 

 

 

 

 

 

: l r - 0.4
0.06. I : e
1 I ' 0.3
0.04. ' '
E 5 ° t“
E 0.02. 1 - t I .0.1 a:
:3 0,00 F: 17.1 mJ/cmz, F=28.7 mJ/cnn2 .no <
| . A
V ; I I I I I I I I 1.2 <
O
a 0.6. : . o . l : 1.0 a
'- l l ~03 V
0.4- I b
1 ~0.6
02, , ~0.4
I I02
- . F: 43.4 mJ/cm2 F: 64.3 mJ/cmz M
-s'o 0 so 100 1&0 -5'0 0 5'0 100 150 200

 

Time (ps)
Figure 5.2: UEDV data with fitting curves given by Equation 5.1, zoomed in to early

times to show the contrasting r, as fluence increases. The panels that have insets are
showing the full time scale.

93

observed here. The crossover from linear (aF) to quadratic (bF2) contributions as
the main source of the TSV appears near F m 20 mJ/cm2, as shown in Figure 5.3.
This crossover behavior in the fluence dependence in Ti and the maximum ampli-
tude TSV near 20 mJ/cm2 can be explained through the following simple analysis of
the respective proportions of the total TSV mediated by the 1- and 2—photon absorp-
tions. Consider the simple picture of electron-hole pair generation through optical
excitation, with 1- and 2-photon absorption present (neglecting Auger recombination,

diffusion, and depth dependence):

5" hu + 2h1/

 

5" _ 010(1) 510002

Integrating over time gives

if: e) i=1: (WM: (5205:?»

which is equivalent to

 

 

 

ntotal=
, F o. -41n2(:;.t2)2
3-‘/4n2-(1—R) / e P dt+ (5.4)
hu 7r tp —oo

 

 

3

e
2hu 7r t?) -00

_ 2
B .4ln2.(1—R)2F2/°° $111207?) dt

where the first and second lines are the 1- and 2-photon yields, respectively. Simpli-

fying Equation 5.5, the ratio of 2- to l-photon yields can be expressed as

ln2 B (1 — R)F

R(2:1) = 3; - 3 ° ——tp , (5.5)

94

or a: 0.332 - fll—gtggg thus revealing the pulse width dependence. Additionally, a
dependence on fluence and the ratio of 2- to 1- photon absorption coefficients, fl/a is
revealed.

Using the parameters for Si of a = 2.27 x 103 cm‘1 and R = 0.37, with the pulse-
width measured during the experiment of tp = 40.8, assuming that R(2:1) = 1 when
the 2-photon overtakes linear absorption processes, a measured value of the 2-photon
absorption coefficient, ,8, can be deduced from the fluence threshold observed in these
experiments. Assuming the measured fluence threshold here could lie between 18-22
mJ/cm2, this corresponds to 5 = 7.5 — 9.1 cm/GW, which is within the range of

values found in the literature, as is shown in Table 5.1.

As will be discussed in the following sections, the linear dependence of T,- on F

at lower fluences can be explained based on a thermally-mediated electron tunneling
process across the SiOg layer, in which the rise of the quasi-Fermi level in Si is linearly
proportional to F. However, as the 2-photon absorption overtakes the l-photon as the
primary mechanism in generating carriers in Si, a coherent (2+1) photo-absorption
process will lead to photoinjection of electrons into the Si02 the conduction band,

1: hus leading to a more efficient way of injecting charges to the surface of Si02.

5 .3 Photoinduced Surface Charging (Injection)

5 -3.1 Direct Tunneling

1‘3 this seCtion, direct tunneling of electrons from Si through the oxide is considered
[Q01 61, 67, 68, 303, 329]. The oxide acts as a tunneling barrier for the excited plasma
‘1‘ the Silicon sub—surface region. From the frame of reference of a standard hetero-

iunction investigation of ultrathin oxide tunneling, the situation here is atypical, in

95

 

 

 

(arm/GW) (mJ/cmz) (nm) (ps)
50.0 3.3 625 0.1 Sokolowski-Tinten et al. (2000)

 

pump-probe reflectivity [136]

 

 

1.5 109.4 1064 4-100 Boggess et al. (1986)

pump-probe transmissivity [278]

 

1.8 91.1 850 0.2 Bristow et al. (2007)

pump-probe transmissivity [27 7]

 

4.3 625 0.08 Esser et al. (1990)

pump-probe transmis. /reflectiv. [327]

 

18.2 800 0.130 Korfiatis et al. (2007)
imposed theoretically [265]

 

24.1 800 0.028 Sabbah & Riffe (2002)

pump—probe reflectivity [328]

 

20.0 800 0.045 Murdick et al. (2009)
UEDV

 

 

 

 

g§ble 5.1: Some of the measurements of the 2-photon absorption coefficient ([3) for
1

W found in the literature. Few studies exist that have measured this parameter.
f1: ayelength varies between 625-1064 nm for the studies listed and pulse duration
Qm 28 fs to 100 ps, possibly explaining the wide range of values for 6.

96

 

 

110w
7,7100.
0.
v
P
o

 

 

4d
’0? ‘ -(,
.4: 3- , '0
£2 ' i 066)
v 2- ‘ 0° '
a '
1- .
H l
0- . Linear

 

 

 

-10 O 10 20 30 40 50 60 70
Figure 5.3: Injection time (top) and the maximum amplitude voltage (bottom), both
as a function of fluence. Both plots show the onset of a faster and stronger source
of voltage after N 20 mJ/cm2. The fluence-dependent TSV can be fitted with a
quadratic equation (aF + bF2), in which the quadratic component (bF2) overtakes

the linear one (aF) near 20 mJ/cm2, coinciding with the crossover behavior in T,- at
the same fluence.

97

that there is no applied voltage, contacts, or measured current. Rather, the voltage
is the result of optical excitation.

Optical voltage generation occurs because the quasi-Fermi level of the substrate
is raised due to the photoexcitation of (hot) carriers, in conjunction with a finite
tunneling probability, which is directly attributable to its nanoscale thickness. While
electronic injection to deep trap states at the interface will contribute to the overall
TSV, as revealed from optical pump-probe studies [81, 85], its contribution is negli-
gible on shorter time scales (hundreds of ps) due to the relatively low density of deep
trap states compared to the surface charge density accumulated through tunneling.
Deep trap states tend to have longer lifetimes (2 us) which are not observed here.

Note that Fowler-Nordheim tunneling is not applicable here because the quasi-
Fermi level of Si would have to rise by at least the conduction band offset between
Si and 3102 (m 3.2 eV), such that it would lie in the triangular part of the barrier.
An excitation like this would cause carrier-induced damage before this could occur.
Moreover, the tunneling is the source of the voltage here, whereas with FN tunneling,
an applied field induces the tunneling.

An approximation can be made assuming a parallel-plate capacitor, with the volt-
age drop across the dielectric oxide Vb = eaL/ 50601;, which confirms the order of
magnitude to be 10—100 mV, using a surface state density, 6‘ = 1012-1013 cm.2 [330],
L = 1 nm, and 60:2: = 2.1.

With the calculation of the quasi-Fermi level (pa) and electronic temperature (Te)

from the models introduced in Section 3.2, the tunneling current through the oxide

can be calculated from [60, 61, 67, 68, 303]

47re

«0:718/ 01(5) 02(5) [1.7112(5)]? [f1(€,m)-f2(€,u2)l as, (5.6)

98

by»-
.1. A“

are?

17 ‘I
)5 .Li

W295

where D1(5) represents the 3D density of states in the Si bulk, D2(e) is the 2D density
of states at the Si/SiOg interface, I is the wave function decay length into Si, 5' is
the sample area excited by the pump laser, f1 and f2 are the Fermi functions at
the Si/Si02 and 3102 /vacuum interfaces, respectively, and M1203) are the matrix
elements of the transmission, given by [60, 67, 68]

~ 75.2 L
M12 = —— (44*sz - dew/11042, (5-7)

2m 0
where «#1 and $2 are the wave functions on the left (z 3 0) and right sides (2 2 L)
of the barrier, respectively (see Figure 5.4).
For a trapezoidal barrier, the wave function in each region is given by [70] (as-

suming no incident wave from the right)

Aexp (iklz) + Bexp (—2'k1z) for 2 S O,
Cexp (foz kb(z’)dz’)

 

 

 

 

$0?) = (5-8)
+Dexp(— [OZ kb(z')dz') for 0 < z < L,
Gexp(ik3z) for z 2 L,
Where
k1 = [/ 24:13 (5.9)
kb(z) = [Final/[522) — 5], (5.10)
k3 = Wm“; evb], (5.11)
L
u = / kb(z)dz, (5.12)
0
D1(s) = ;%§‘/2m15, (5.13)
02(5) = fie—(E—EFF/wg, (5.14)

V(z) = (1)0 — 6E2, (130 is the conduction band level offset between the Si and Si02,
m1 and m2 are the effective masses of the silicon and oxide, respectively (m* is
approximated as ml for tunneled electrons). The electric field in the barrier is E =
‘Vb / L, where L is the oxide thickness. The simple picture in Figure 5.4(c) depicts the
stationary states associated with Equation 5.8. The transmission matrix elements can

be found by inserting Equation 5.8 into 5.7. After applying the boundary conditions

 

0+

 

 

_ 1 dip 1 do
_ + _ _ = _ _
212(L )-w(L >, m (d) [L_ m1(d) H. (5.15)
and properly normalizing, the matrix elements are found to be
|M (e)|2 — h4 k1 + k3 2sin2 M T(e) (516)
12 _ m212 k1 - kg 2 ’ '

Where T(e) is the transmission probability (IGI2/ |A|2 in Eq. 5.8), given by [70]

 

_ b
T(5) _ L 2 L 2. (5.17)
k klk h m k k mlkb 'nh
3+—kgb- cosu + W— mL 31 u
The total accumulation of tunneled charge at time t,
t
QtunU) =/ i(t’) dt’. (5.18)
0

allows the voltage drop across the barrier, Vb to be deduced from the total capacitance,
Ctot, which consists of two series capacitors: electrostatic (C E) and quantum (Cq)

[331], given by

100

 

 

 

 

 

 

 

l/]
3.2 eV MAW, D G
c3 — :
B C
VB 1.1 eV
4.6 eV Si (111) : Si02 [Vac
l |

 

 

 

 

 

. . , 2:0 z=L
Si(111) S102 Vac Si(111) $102 Vac

(a) (b) (C)

 

 

 

 

Figure 5.4: (a) A band diagram depicting the Si/SiOz/vacuum interface. (b)
SChematic of the energy diagram with relevant quantities used for the tunneling cal-
culations. Electrons that turmel through the oxide to the SiOz/vac interface, cause
the quasi-Fermi level p2 to raise, making the barrier take on a trapezoidal shape. The
electronic density of states is shown in light-grey for the silicon (D1) and the Si02 / vac
interface (Dz). The difference between the two levels, An (dark grey band) is the
primary factor in determining the tmmeling current. For a. given energy (5), when
Au, D1(e), and D2(e) are all aé 0, then there will be a tunneling current through
the Si02. (c) Probability amplitude schematic; the wave functions with amplitudes
(A, B, C, D, G) are used to compute the tunneling matrix elements, M (e).

101

66 S
CE: 00:1:

L (5.19)

and

Cq = 62020517) (5.20)

respectively, where 603; is the relative permittivity of SiOg, and D2(EF) is given by
Equation 5.14.

Note that Cq becomes particularly important as the length scale of the insulating
dielectric decreases, such as the case here. With the thicker oxides of the past,
quantum capacitance effects could be neglected since Cq >> C E, and thus the voltage
drop across the ‘quantum capacitor’ was negligible. The voltage drop across the

barrier due to optically-induced tunneling is then

V50) = 9377252 (5.21)

Where Ctot = CQCE/(CQ + CE).

The goal is to investigate the role of tunneling on the slow 7', observed for low
fluences. Accordingly, the charge relaxation (long time) portion of the experimen-
tal Curves, which is deemed to be due to a different mechanism, is maintained
by imposing the relaxation factor from Eq. 4.3 onto the simulated Vb, such that
Vs == Vb (11:71:) The simulated V3 is fitted with the injection factor from Eq. 4.3,
sz’t [1 — exp (—%)], the results of which are shown in Figure 5.5, for parameters
5' = 6.96 X 10‘7 m2, m1 = 0.19me, m2 = 0.5me, L = 1.0 nm, (1)0 = 3.125 eV,
5 = 2.75 x 1013 cm_2, w = 0.35 eV,sF = —0.373 eV, and z = 1.0 A; [84]. The
density of states at the SiOg / vacuum interface and the barrier thickness and height
were used as fitting parameters. The tunneling current was most sensitive to L and

(PO, which enter through the transmission probability, T(s).

102

 

    

 

 

 

110« 0.“
A l
m 100..
Q 4
V 90.,
(S 80
m: j
‘ U
60: GO
SOI'I'I'I'I'I'I-
010203040506070

F (mJ/cmz)

Figure 5.5: The characteristic time associated with surface charging, Ti, as a function
of excitation fluence. The simulated 7', assumes that the TSV is constituted solely
from the voltage drop across the oxide barrier, calculated from Equation 5.21.

Note, one of the assumptions of the calculation is that the relaxation of tunneled
electrons to lower lying levels on the right side of the barrier is assumed to occur
faster than the time scales associated with the tunneling events through the barrier.

From the results of this calculation, shown in Figure 5.5, it seems plausible that

direct tunneling is a dominant mechanism for voltage generation at low fluences.
Moreover, the role of tunneling rapidly diminishes as fluence is increased to moderate
or high levels, indicating that another mechanism seemingly over—powers the tunneling
as the primary source of the TSV generation, which will be investigated in the next

section.

5.3.2 Coherent (2+1) Absorption (2—Photon + Free Carrier)

The quadratic dependence of T,- on fluence is interpreted as a coherent absorption
process, where a significant fraction of the population lying at the 2-photon level
(~ 1.5 eV above the CB edge) begins to dephase through scattering with other

electrons that have been elevated to that level.

103

The ability to promote an electron to the SiOg conduction band depends on the
dephasing time of the hot electrons generated by 2-photon absorption and the initial
point in momentum space in the non-thermal regime, as will be detailed later, the
electron dephasing time (T58) is inversely proportional to the hot electron density.

Presented below is self-consistent analysis of 1- and 2-photon absorption, with a
‘lossy’ term for electron-electron scattering, Tee. From this fraction, the probability of
an additional photon absorption is calculated, thus arriving at the effective absorption
cross-section describing the ‘2+1’ yield. Note that it is not the same as 3—photon
absorption, where three coherent photons would be absorbed simultaneously, and a
cubic dependence would be expected in the TSV (3—photon absorption is negligible
at wavelengths this short).

From the 2+1 population, the net charge transfer to the surface is quantified via
injection of photoelectrons into the conduction band of SiOg, leading to surface charg-
ing. This process of electron transport from Si to SiOg is called internal photoemission
(IPE) (internal because the electrons are not at the vacuum level). A schematic of the
process is shown in Figure 5.6. This process is found to have quadratic dependence

and a sufficiently high yield to describe the TSV magnitudes observed here.
Recall from Equation 3.36, the Gaussian expression describing the temporal char-
acter of laser interaction with Si,

41n2 (1 — R)F e
71' tp

 

 

100) = XI)

 

—4ln2 (213%)2] . (5.22)

P

The spatial dependence assumes an exponential decay into the substrate

[(2, t) = 10(t)e_z/6€ff (5.23)

104

Internal Photoemission
(2+1 Coherent Absorption)

 

 

     
   

 

- - - Vac ---------------------
+ f-ph >
abs. Injection
C B
2-ph ........
abs. ' \ifee
SiOz

 

Figure 5.6: Coherent absorption, characterized by a consecutive 2- and l-photon
absorption with electron scattering dephasing.

105

_ a

1"“

‘4

~..r

P A

where the effective optical penetration depth is given by

 

 

1 6((1 + 8n) + ,310
= . . 4
(leff a+8nln[ a+8n+510] (52)
The 2-photon absorbed population is described by
3N2 h 51(2 t)2 N2 MA”
__1’_ = __’_ _ __P____
a, (z, t) 251/ Tee , (5.25)

where B is the 2-photon absorption coefficient, just as in Section 3.2, and the second

term on the RHS describes the ensuing electron-electron relaxation, Tee, given by

[332]

1 ne4

—— — L
Tee 71'62 8m*E m"‘1/2

 

(Ek, (10), (5.26)

where

 

87'rl.*Ek7 1
L E , =10 1 + —— —
( f ‘10) g( n2qg ) 1+h2q3/8m*Ek

(h2qg/2m*Ek) (1+h2q3/8m* Eh)
—g {1 — 1+(52qg/2m*Ek) (1+h2q8/8m*E;j} , (5.27)

and ‘10 == l/AD, where ’\D is the Debye length, given by )‘D = VckBTe/nefi.
The free-carrier absorption N fca, which is the 2+1 absorbed population, is cal-

culated from

aNfca [(2, t)

 

where 6 is the free-carrier absorption cross-section [278].
Of the electron population that has gained sufficient energy to overcome the barrier

for IPE, the total accumulation is given by,

t 00
N,,,e(t)= f0 f0 Nfca(z,t’)n(z,t’)dzdt', (5.29)

106

1 0.0

 

 

 

 

 

 

 

'm'a'a'aTa'a'a
Fluence (mJ/cmz)

Figure 5.7: Results from the 2+1 photon calculations using the formalism above,
showing a quadratic dependence in the internal photoemitted yield.

where the transport efficiency, 17(z, t), represents the fraction of the ‘eligible’ popula-
tion, N fad, that can be transported and satisfy momentum conservation.

As can be seen in the above figures, the dependence is indeed quadratic. The
processes involved in the 2+1 transport are outlined in Table 5.2. At this point,
the characteristic length associated with this charge separation cannot be determined
with certainty, however, at densities on the order of 1014 cm-z, the magnitude of
the IPE yield is certainly suflicient to generate the TSV magnitudes observed in the

experiments here.

5.4 Surface-Bulk Coupling (Relaxation)

It was previously shown [107] that the decay behavior of the TSV at the Si(111)/Si02
interface compares well with the surface state dynamics on a vacuum-cleaved Si(111)-

(2 x 1) surface, revealed by a photoemission study [126] (Figure 5.8), where the surface

107

 

,F; .W.

.0. J. L

J.. -
| “T, ‘1’.“
A _.A s

C

no» 1
H' l I ’
‘h‘.i-‘

.1.

3“!

-It

I

 

 

Fluence (a.u.) 2-photon Tee Photon Flux 2+1 Yield

 

 

1 1 1 1 1
2 4 1/2 2 4
3 9 1/3 3 9

 

Table 5.2: The underlying processes associated with 2+1 absorption, all of which
are occurring within the duration of the optical excitation pulse. For an arbitrary
fluence (column 1), the 2-photon yield will increase quadratically (column 2), but
this population will experience a loss from electron-electron scattering (column 3),
which has linear dependence on fluence. The probability of absorbing a third photon
is linear with the photon flux, still illuminating the surface (column 4). The net effect

is the 2+1 yield, which goes as N2+1 oc (F2 x F-1 x F = F2) — quadratic (column
5).

recombination observed was said to be due to a strong coupling between the surface
states and bulk evanescent states.

In Figure 5.8, the TSV has been rescaled to match with the amplitude of the data
extracted from Reference [126]. A striking similarity in the relaxation rates is clear.
If the observed field here were because of charge transfer to deep trap states, the
time scale for the TSV to decay would be on the order of ns-ps or possibly longer,
and the observed 100 ps would not make sense. There would also be a residual
charging effect since deep trap state occupation is largely irreversible. No residual
effect was observed. Since it is known that the generated TSV involves the surface
(bulk Dember fields are far too weak to deflect the beam to this extent), it is very
reasonable to presume the same strong surface-bulk coupling as in Reference [126],
ultimately dictating the decay rate of the field.

Further evidence of the strong role played by carrier dynamics on the surface re-

combination is revealed by the power-law decay of the TSV, shown in Figure 5.9(a),

108

 

 

1.5 ., l ' l ' l ' 1 fl 1 ' I _,
0 Surface State Population
A -A— Rescaled TSV
{-3 1 o -
r: .
3
.o'
t-
5; 0.5 -
0.0 - ’ 4

 

 

 

0 '200 ' 400 ' 600 ' 800 '1000
Time (ps)

Figure 5.8: Transient surface state p0pulation measured by photoemission [126] (di-
amonds) compared with the measured TSV (triangles) (rescaled; F=72 mJ/cmz),
demonstrating very similar decay rates. ~

where an exponent near -1 (-0.93 i 0.03) is ascribed to the characteristic decay of
surface charges, with a time constant of 100 ps. If the field decayed because 1D
diffusion the power would be -1 / 2. The -1 power arises from a phenomenological
model for bipolar drift recombination, which is illustrated in Figure 5.9(b)-(d). The
relaxation of electrons occupying surface states is rate-limited by the bulk carrier dy-
namics. The nonequilibrium space-charge layer, with initial separated charge density
00, is modeled as two separate slabs, separated by a distance le_ h in a dielectric
medium (65.,- = 11.8 for Si), shown in Fig. 59(0). The power-law characteristics are

manifested in the simple rate equation

100-012,

dt Tr (5.30)

with the space-charge recombination time T1- = l/pE depending on the transient
field E, which is directly related to the surface charge a(t). Its solution a(t) =

(To/(t/Tc + 1) has a characteristic time scale Tc = le/pao, which is the time for

109

the TSV to drop by 50% from its initial value, and corresponds to the induction
period in the log-log plot of the solution, as described in Figure 5.9(d). For t >> Tc,
the t‘1 behavior emerges, similar to what is observed experimentally (Figure 5.9).
To compare with the experimental results, a linear decay of the surface potential
barrier (V3) is assumed over the space-charge layer le—h: and determine the size of
the induced space-charge regime to be l m 400 nm (using carrier mobility, p=100
cmz/V-s according to Reference [264], the measured Tc of ~100 ps, and V3 of 2 V),

which is in agreement with the laser penetration depth in Si.

110

 

 

 

 

 

 

10 h... s-....... . ......, .
I \ :
* x -0.93 i 0.03 :
E \ '
=3 1‘:
o 2
2.
>"’
<1 01.
0.01 . ..... . .
1 10 -100 1000

 

 

 

 

 

 

 

 

 

 

 

 

time

Figure 5.9: (a) Log-log plot of the TSV with a linear fit to the long time data. (b) A
schematic of the space-charge region. (0) A schematic of the bipolar (two-slab) drift
model in (c) is implemented to describe the recombination. ((1) Carrier drift causes
the surface charge, 00 to diminish with a characteristic time 7'0, after which, 00 falls
as t"1 obtained from the slab model.

111

5.5 Discussion

Using UEDV, the fundamental nature of the mechanisms associated with surface
voltage generation at the Si / Si02 interface have been investigated. With careful
analysis of the charge transfer processes, the UEDV data clearly separate two dis-
tinctive regimes of charge rearrangement. The first is associated with a low intensity
excitation regime, showing a linear dependence on fluence. In Section 5.3.1, analysis
on the direct tunneling of electrons through the oxide correlated well with the UEDV
observations, thereby providing strong evidence that it is the underlying mechanism
of TSV generation in this regime. The primary charge transfer process occurring in
this regime involves electron tunneling from Si to the surface states of SiOz.

The second mechanism involves charge transfer to unoccupied states in the Si02
conduction band, through an absorption process that relies on a coherent, 2+1 optical
absorption. Note that the energy offset from the valence band edge of Si to the CB
edge of Si02 is z 4.3-4.5 eV, indicating that 2-ph0ton absorption alone is insufficient
for significant electron transport to SiOg (in the form of IPE). The analysis of a
coherent, 2+1 photon absorption process was demonstrated here to constitute a sig-
nificantly high yield and shorter injection time, consistent with observations. More
importantly, the 2+1 absorption (with electron dephasing) explains the quadratic

trend observed experimentally, rather than a cubic one.

5.5.1 Thermionic and Photoinduced Emission

As discussed in Section 4, when performing UEDV experiments, one of the most
essential features that must be extracted from the data is the source of the electric
field. The robustness of TSV determination in Si / SiOg, which is mostly independent
of electron penetration depth (controlled by the incidence angle, 92‘; see Figure 4.10),

indicates that the main source of TSV comes from the fixed length voltage drop

112

across the SiOg barrier. However, a weak 6,- dependence is found at short times,
which contributes approximately 10% of the TSV.

Sources of Oi—dependent TSVs include the vacuum and bulk space charge regions,
AVvsc and AVsc, respectively. In the case of AVsc, the threshold is the flatband pho-
tovoltage of approximately 300 mV [310]. The vacuum space charge region, AVvsc,
established by the formation of a vacuum emitted electron cloud above the surface,
stems from several possible emission pathways, such as thermionic, direct photoe—
mission, or field-induced, which leads to a time-dependent electric field above the
surface.

Thermionic emission occurs when the tail of the Fermi-Dirac distribution rises
above the vacuum level (Figure 5.10). As the process evolves, a space-charge cloud
develops, which serves as a hindrance to further electron emission. Riffe and colleagues
formulated a simple addition to the Richardson-Dushman equation to account for the
space-charge effect [248]. The expression gives the number of emitted electrons, Nesc,

per unit time that will fly outward from the surface,

dNesc
dt

 

 

_ 2
= 7rR1R2C'1k%3Te2 exp (_5F H+ W+ae Nesc/Rl) ,

kBTe (5.31)

where 01 = 47rm/h3, R1 and R2 represent the semi-major and minor radii of the
(elliptical) excitation laser, respectively. The Fermi energy, chemical potentialz, and
work function are represented by 5F, 11, and W, respectively. The last term in the
numerator of the exponential in Equation 5.31 was introduced by Riffe and colleagues
to account for the space-charge effect [248]. The factor, a, is a geometrical factor
characterizing the emitted electron distribution (in units of [47mm] '1). For a spheroid,

thin-disc, or thin ellipsoid, a = 1.2, 1.7, and 1.95, respectively.

 

1’For a metal the chemical potential should be used, whereas with semiconductors the quasi-Fermi
level should be used for both electrons and holes, such as here with Si.

113

 

 

 

 

Figure 5.10: Thermionic emission at an Si / Si02 interface. The work function is
exceeded by the fraction of electrons occupying states in the upper tail of the Fermi-
Dirac distribution (shaded region). As the excitation pulse is absorbed by the surface,
the accumulated yield from the tail can lead to a non-negligible charge density cloud
above the surface.

Here, the thermionic emission source is neglected because of the low photon energy
(1.55 eV) resulting in a low theoretical yield of photoelectrons, and more so because of
the crystallographic probe used to measure the TSV, which has been shown previously
to be most strongly affected by sub-surface fields [194]. For non-crystallographic
methods where the direct electron beam has been used to probe photoelectrons, see

References [200, 286, 287].

5.5.2 Dielectric Enhancement of the Interface Dipole

Prior to photo-excitation, a static dipole forms at the Si/SiOg interface because of
an abrupt difference in the electronegativity in the Si and SiOg atoms,[36, 306, 333]

inducing an interface potential given by

ep*ldN3
V = ,
dp (652' + 60x) /2

 

(5.32)

where p* is the amount of partial charge transfer from Si to Si02 (depending on the

electronegativity offset), ld = 1.67 A is the distance of transition associated with

114

the interface[324, 333] (the Si-O bond length), N3 is the planar density of Si atoms
(7.833 x 1014 bonds/cm2 for Si-111), and 63,- and 603; are the relative permittivities
of the Si and Si02, equal to 11.8 and 2.1, respectively. Taking p* = 0.22 electrons
per bond,[333] the potential of the static surface dipole is estimated to be Vdp = 749
mV.

The hot carrier plasma initiated by photo-excitation causes a sharp change to
the dielectric properties of silicon as the free carrier response acts to lower the
permittivity.[136] In 2000, Sokolowski—Tinten and von der Linde demonstrated with
pump-probe reflectivity measurements that the effect is well-described by the Drude
model for a damped plasma. Under photo-excitation, the dielectric function takes

the form

6* = 65,; + Affcrv (5.33)

where the free carrier permittivity change, efcr(w, n), is expressed according to the

Drude model

_ (Up 2 1

 

TD is the Drude damping time[136] of 1.1 fs, cop is the plasma frequency, given by

 

*

top = ‘ /62n/50€S,-m;pt, where n is the carrier density, and m 0p

t is the optical effective
mass, measured to be[136] z 0.18 me.

In Eq. 5.32, the permittivity of the interface is represented by the average of Si
and SiOg, implying that for a sufficiently dense plasma generation, the free carrier
response can enhance the interfacial potential. The carrier density, n, will rise non-
linearly with increasing fluence, as the generation due to multiphoton absorption

0: F2, which means the TSV should also, since Affcr oc (.012, or n.

115

 

~\~

0}
.L

riu

.h '-

To calculate the effect of the free carrier response on surface dipole enhancement
(SDE), the transport model from Section 3.2 is invoked to calculate the plasma fre-
quency, which, in turn gives Acfcr, and thus the effect of SDE. The SDE factor is
estimated by substituting Equations 5.33 and 5.34 into Equation 5.32, simulated over
the course of the plasma generation. Results from the SDE calculations could not
account for the magnitude of the TSV observed here, nor the trend. For the highest
fiuences, the estimated SDE is ~100 mV. Thus, it is concluded that SDE effects are

negligible here.

5.5.3 Future Investigations / Open Questions

In addition to the UEDV experiments described in this chapter, experiments were
also performed for a series of 400 nm excitation fluences, as shown in Figure 5.11,
with fluences ranging from 1.7 to 20.4 mJ/cm2. While similar injection times as
the 800 nm experiments were found, with distinctive TH (~50 ps) and TL (~100
ps) at high and low fluences, respectively, the corresponding TSV is much higher
in the case of 400 nm, which could be due to the increased abundance of direct
band gap transitions. Furthermore, unlike the quadratic fluence dependence found
at 800 nm, the dependence at 400 nm is approximately linear, as the initial creation
of free carriers can be achieved now by 1-photon absorption, rather than 2-photon
absorption.

As UEDV continues to evolve in the coming years, specifically with data pertaining
to vacuum space charge by applying the new charge-imaging probe geometry from
Reference [200], it is likely that the hot electron dynamics within the materials that
lead to TSVs as well as photoemission can be fully elucidated. Another interesting
experiment might be to test both pump energies on a direct band gap semiconductor

like gallium arsenide, or a wide band gap like TiOg, and compare the injection times.

116

Additional experiments were also performed on p-type Si(111) and a Si(100) sam-
ple with heavy doping (p ~ 0.01 Q-cm). Neither showed major differences in the
TSV dynamics. As expected, the TSVs observed by UEDV are not affected by the
majority carrier concentration at the ground state because the bulk of the TSV is
due to photoexcitation from a high intensity optical source. Regardless of where the
Fermi level lies in the gap, both are going to respond the same way to femtosecond
laser excitation. However, additional insights pertaining to tunneling could possibly
be gained by examining the low fluence regimes of n— and p—types with heavy d0ping
in both, such that the Fermi level is pinned near CB or VB edge. There, it would be
expected that the p—type would show a lesser TSV from tunneling, as the quasi-Fermi
level would start from ~ 1 eV below that of the n-type.

Performing the same experiments at low temperatures (5, 100 K) would be ben-
eficial in that it would suppress the linear absorption, allowing only the effects from
2-photon absorption to contribute to the TSV, due to the depletion of the phonon
p0pulation which is necessary to assist indirect transitions. Such experiments were
carried out, but inconclusive as the diffraction signal dropped unexpectedly after the
stage was cooled, rendering any conclusions ambiguous.

A preliminary pulse-width dependence experiment was conducted for a n—type
Si(111)/Si02 sample, shown in Figure 5.12. As the pulse width of the excitation
laser is shortened, the TSV response increases. While this is consistent with the
interpretation of the (2+1)-induced process, in which an enhanced transient optical
field at shorter pulse duration promotes 2—photon absorption (see Equation 5.5), the
degree to which consecutive 1-photon absorption is affected by electron-electron re
laxation (also enhanced), is not yet fully resolved. A full experiment where both
fluence and pulse width are varied should serve to provide additional insights to the

relationship between multiphoton absorption and the TSV.

117

 

- ' - fi—o—EOA '
200 (a) Fluence +14] +
(mJ/cn12) :13” +

     
    
    

 

 

 

 

 

 

 

o n n ‘
9 1
é-zoo 1
a -400
l~ .
.500 1 ‘10 600 700 .'
500 ' 10'00 ' 15'00 ' 20'00 ' 2500
Time (ps)

 

 

-

A

O-‘NW-bkn

 

TS V (Volts)

 

 

 

0 2'0 4'0 6'0 80
F(mJ/cm2)

 

 

 

 

F (mJ/cmz)

Figure 5.11: UEDV data at 400 nm excitation. (a) The TSV response at different
fluences. The ZoT was determined to be 540 ps. (b) Fit results for 800 nm (red) and
400 nm (blue) data (800 is the same as in Section 5.3; shown here for a baseline).
Parameters 1',- and TSV (inset) are plotted against laser fluence. Both 400 and 800
nm experiments show distinctive fast (TH) and slow (TL) injection times for high and
low fluence regimes, respectively, yet the TSV dependence on F is linear for 400, and
quadratic for 800 nm excitations, respectively.

118

Pulse Width Dependence
005 I ' I v I v fi I

 

 

   
 

 

 

 

-50 0 50 10015021F250 '

Time (ps) #

0 ' 500 '10'00'15'00'2000
Time (ps)

 

 

 

Figure 5.12: A pulse width dependence was observed for the transient surface voltage.
Blue, green, and red correspond to ~41, 72, and 90 fs, respectively. The fluence
dropped slightly as the pulse width was made shorter (F = 44.6 mJ/cm2 for the 41
fs pulse and 49.0 mJ/cm2 for the 90 fs pulse).

119

Chapter 6

Charge Transfer in

Surface-Supported Nanoparticles ‘

6.1 Introduction

The scope of nanoparticle research spans many disciplines with vast possibilities of
incorporation into practical use, including nanoelectronics [334—340], photovoltaics
[15, 17—19, 22, 26, 29, 33—35, 40—43, 46, 48, 50], and even quantum-dot based lasers
[341—346]. On the biological/ life sciences side, it has recently been shown that gold
and silver nanoparticles, when delivered to site-selective cancerous cells, can destroy
them upon exposure to a pulsed-laser source, without damaging surrounding tissue
[347—349]. Metallic nanoparticles have also been invoked in biomedical imaging [350,
351]. 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 beating the
diffraction limit for spatial resolution [352-355]. It has been observed that the same
near-field optical-enhancement (‘lensing’) effect can be used for creating nano—sized

features on substrates [356—358].

120

Monodisperse metallic nanoparticles (Figure 6.1) can be deposited on Si substrates
(8.) by way of self-assembled aminosilanes (b) [190, 359, 360]. The aminosilane chains,

which are anchored to the Si substrate, immobilize the nanoparticles through the

formation of van der Waals bonds.

 

 

 

 

 

 

Figure 6.1: (a) A sample of Au nanoparticles immobilized on a functionalized Si
substrate. (b) The chemical form of the APTMS linker molecule. (0) Schematic of
an electron beam scattering from the ordered self—assembled monolayer chain and the
corresponding diffraction pattern. [190, 194].

The 2D nanoparticle ensemble shown in Figure 6.1(a) is an ideal prototype for
UEC [192, 193]. In fact, a special implementation of UEC, called ultrafast electron
nanocrystallography (UEnC) has recently emerged, where the technique has been
optimized for the study of nanoscale structures (e.g. metallic nanoparticles, quantum
dots, nanointerfaces, etc.) [190, 192]. When an ensemble of nanoparticles is sampled
by the electron beam, a powder diffraction pattern results, as is shown in Figure
6.2(a), which is constituted from the many different crystal faces (b) that the beam.

samples in its footprint on the surface. In addtion, the linker molecules that take part

121

in the anchoring of nanoparticles tend to orient themselves in a manner that that is
sufficiently ordered, such that very clear diffraction spots from the linker molecules

are present in the patterns [Figure 6.2(a)].

 

//////
Si (1 11)

Intensity (a.u.)

Linker « \ "

 

 

 

 

 

Figure 6.2: Small-angle diffraction pattern obtained from the Au nanoparticle / SAM
/ semiconductor interface. (a) The raw diffraction image shows powder diffraction
from the Au nanoparticles as well as a vertical array of spots at the center (ar-
rows), corresponding to the self—assembled linker molecules. (b) Scattering intensity
as a function of momentum transfer (3), where radial averaging has been performed
around each ring perimeter, followed by a subtraction of the diffractive background
(incoherent scattering), yielding the peaks shown in the plot. The peaks identified
are consistent with fcc polycrystalline structure with a lattice constant equal to that
of Au (a =4.080 A).

Here, the charging dynamics will be examined for an interfacial structure con—
sisting of the interconnected nanoparticle/SAM/semiconductor geometry discussed
here, shown in Figure 6.1. Observations of the near-field lensing effect will also be
presented briefly. First, the sample preparation procedures will be covered, followed
by a brief overview of the Mie theory, which is central to the topic of photoinduced

charge transfer and near-field effects in nanoparticles.

122

35

L’;

(’7‘

6.2 Sample Preparation

The nanoparticles that have been studied by the UEC group at MSU are always ad-
sorbed on a substrate, never in solution, because the experiments are done in UHV.
The particles must be well isolated on the surface, to avoid multiple scattering effects,
as scattered electrons from one nanoparticle could interact with another nanoparticle
en route to the CCD, ultimately destroying the signal to noise. Au and Ag solutions
are purchased in monodisperse colloidal form. Individual nanoparticles are negativley
charged via citrate ligation, such that they tend to remain monodisperse if the pH is
not altered. Spin-coating this solution onto Si wafers is one option, though from ex-
perience, it tends to give a very low yield of nanoparticle coverage. Furthermore, with
the nanoparticles in direct contact with the Si, the long-term stability of the samples
might be affected by the atomic diffusion between the nanoparticles and the sub—
strate. Moreover, the strong diffraction signal from the crystalline Si substrate might
overwhelm the overall signal, rendering the diffraction signal from the nanoparticle
undetectable.

Functionalization of the Si substrate with a self-assembled aminosilane layer is
used to effectively control the areal densities of adsorption, as well as to provide a
buffer layer that is sufficiently thick, to suppress the diffraction signal from the under-
lying substrate. Depending on the aminosilane that is chosen, the nanoparticles will
be raised from the substrate by approximately 1 nm. Specifically, the linker molecules
implemented in the UEC lab include [3-(2-Aminoethylamino)propyl]trimethoxysilane
(APTMS), (3-Aminopropyl)trimethoxysilane (APTES) and 2-[2-(3—Trimethoxysilyl -
propylamino)ethylamino]ethylamine (APES), which self-assemble to about 0.8, 1.0,
and 1.2 nm in thickness, respectively. The inclusion (or omission) of N H-groups along
the chain allow its length to be adjusted; from shortest to longest, there are zero, one,

and two NH-groups on the chains of APTES, APTMS, and APES, respectivelyl.

 

1Aminosilanes are ordered from Sigma-Aldrich.

123

Preparation of wafers follows similar recipes to those in References [338, 359,
360], which is schematically outlined in Figure 6.3. Silicon wafers are first cleaned
using traditional acid / peroxide based cleaning techniques [326]. The usual cycle is
immersion in HgSO4/H202 (‘pirahna’) (7:3) for 10 min at 90 °C, NH4F (40% in H20
for 6 min), NH4OH/ H202/H2O (‘base piranha’) (1:1:6) for 10 min at 90 °C, and
HCl/ H202/H2O (1:1:5) for 10 min at 90 OC. Between each step wafers are rinsed in
deionized water for 10 min. After the cleaning, a hydroxylated surface results, shown
in Figure 6.3(a).

Surface functionalization with the arninosilanes is the next step. In this step, the
silane head attaches to the -OH groups on the Si surface. The general procedure for
APTMS is to immerse all wafers into a solution containing 5 mL of APTMS and 1 mL
of acetic acid, dissolved in 480 mL of H20 [Figure 6.3(b)], for 60 minutes, followed
by a rinse and dry N 2 cycle [Figure 6.3(c)], then baking at 120° in an oven with pure
N2 gas to complete Si-O bond formation. Upon immersion in the Au nanoparticle
solution (Au colloid, ethanol, H20 at 1:1:2), individual Au nanoparticles become
immobilized as they form van der Waals bonds with the protonated N H; sites. A
rinse and dry cycle follows, and the sample is ready to be imaged in an SEM. Note
the 1:1:2 ratio for colloid/ ethanol / water can be varied and different surface coverage
densities will result, which is shown in Figure 6.4.

Further control of dispersion is achieved by altering the pH of the APTMS solution
in the functionalization step, which varies the density of -NH2 anchoring sites [361].
For example, raising the amount of acetic acid from 1 mL will indirectly result in an
increased surface coverage density [362], which is demonstrated in Figure 6.4, where
the pH of 7.0 and 2.0 result in nanoparticle areal densities of 70 and 300 rim—2,

respectively.

124

 

(a) (b) (c)
1:11:11:
oooooooo Dry N2
1111111: —> .. APTMS k/
I a f‘ :1:N IN :N
z ¢ 2 z z z
a <5 X? 571 9.

M00
Meo>
M90
090“, ‘
“so
MeO\
M907
Mao
i I

H
H

 

 

 

 

 

 

 

Figure 6.3: The stages of sample preparation. (a) A modified RCA process leaves a
clean, hydroxylated Si surface. (b) Immersion of wafers in APTMS and acetic acid,
dissolved in deionized water functionalizes the surface, followed by a rinse/ dry cycle
(0), and subsequent immersion in colloid solution (d) (described in text), and a final

rinse/dry step (e) [190].

125

 

Figure 6.4: The effect of varying the ethanol/water ratio on surface coverage. All
panels have 1 mL of colloid solution. The ratios of H20 to ethanol are given in
the upper-right corner of each panel. The hydrophobicity is reduced as the ethanol
concentration is increased, which effectively enhances the mobility of the nanoparticles
in solution [190].

 

Figure 6.5: The effect of varying the pH of the solution during aminosilane func-
tionalization. Adding small amounts of acetic acid increases the density of anchoring
sites (NHél') for the negatively charged nanoparticles, hence the increased coverage.
Panels (a) and (b) have areal densities of 70 and 300 rim—2, respectively. Note, sam-
ple (b) would give convoluted signal, as the nanoparticles are overly dense, scattered
electrons would be intercepted by adjacent nanoparticles before arriving to the CCD.
[190]

126

6.3 Surface Plasmon Resonance / Mie Theory

A gold colloid solution is red (Figure 6.6). Why? In 1908, German physicist Gustav
Mie aimed to answer this question and did. The answer lies in the way that the
nanoparticles scatter light. Mie proved this by solving Maxwell’s equations for elec-
tromagnetic radiation interacting with small metal spheres (assuming bulk dielectric

functions), subject to the appropriate boundary conditions [363].

 

Figure 6.6: A 20 ml bottle of Au nanoparticles with average diameter of 9.6 nm :E
10%. The red color has to do with the way light is scattered and absorbed by the
nanoparticles. The nanoparticles are monodisperse (non-aggregated) due to surface
fimctionalization with citrates. A sharp change in pH (toward basic) would cause
them to agglomerate and the solution would turn blue because of the new average
nanoparticle size. The scattering and absorption properties are strongly dependent
on size.

When light impinges a metal, the free electrons can be excited into collective
oscillatory motion about the heavy ionic core. This occurs when the conditions are
met for surface plasmon resonance (SPR), which depends on the dielectric properties
of the metal as well as the size. Usually these oscillations are found in the deep
ultraviolet spectral region, but for some materials, particularly noble metals, the
absorption properties are strongly influenced by interband transitions, the sum effects
of which lead to a red-shifting of the SPR. Figure 6.7 shows an example of excitation

of the'dipolar mode of of a metallic nanoparticle. The term ‘surface’ in SPR can be

made clear from this figure; while the electrons are oscillating about the positive ionic

127

core, the restoring force arises from the surface polarization, which flips every half

oscillation.

 

 

1‘ (+172

 

 

 

Figure 6.7: The oscillating dipolar mode of a metallic nanoparticle. The incoming
wavefront has an electric field E that induces a collective oscillation of the free elec-
tron gas about the positive ionic core. Polarization arises because of the net charge
difference created near the surface, which causes the restoring force for the polar-
ization to flip. Here, the period of oscillation is T. This figure was re-drawn from
Reference [364].

The intensity losses of the wavefront due to absorption and scattering from a

volume of nanoparticles with number density N, are given by
_ — Na 2
Nate) — 100 — e abs ) (6.1)

and

AIsca(Z) = IO (1 -- e—Nasca'z) , (6.2)

respectively [364].

The absorption cross-section, ”abs! accounts for heat generation within the nanopar-
ticle. The scattering cross-section, 03m, describes scattering from the nanoparticles,
or changes in the propagation direction. A third quantity lmown as the extinction
cross-section is defined as

out = as“; + ”abs (6.3)

128

The results from Mie’s calculations are [364, 365],

27r 00
(Text- — ——2 231(21 + 1) Re( (al + bl), (6.4)
00
27r
Usca = ‘l—k'lfi 291+ 1)(lall2 + lbll2): (6-5)

I

ll
p—A

with
I I
W = mT/Jlfmw)¢](f€) - ¢](m$)¢l(3), (6.6)
mil); (W077) (33) - 1/1) (m$)m($)

 

bl : iblfmxld’flx) " m¢l(mx)1,bl(:c), (6.7)

manic) — mwfimxmrm)

 

where m = ri/nm is the ratio of the complex index of refraction, ii, to the real
refractive index of the surrounding medium, nm. The prime indicates differentiation
with respect to the argument. The dimensionless parameter as, defined as 2: = |k|R,
characterizes the size, with R being the nanoparticle radius, and k = 27r/A, where A
is the wavelength of the incoming light. Emctions 2,01 and 17) are the Riccati-Bessel
functions, which are presented in Appendix E. Each 1 value in the sum gives a different
order of multipole excitation within the nanoparticle.

When the wavelength of incoming light is reasonably large compared to the
nanoparticle (A 2, 20B), only the dipolar, l = 2 term is significant, and the ex-

tinction cross-section reduces to

3/2V 52(w)
[51(w) + 2Eml2 + 5201)?

 

am— _ 9— gem (6.8)

where V = (47r/3)R3 is the nanoparticle volume. Notice that in Equation 6.8, the
spectral features (6) of the extinction cross-section do not depend on particle size,
though clearly the amplitude does through V. But the width and position of the

plasmon are unaffected. Does this mean that the spectral features become indepen-

129

dent of size as nanoparticles shrink? The answer is no. Not only because there exists
ample experimental evidence to the contrary [242, 364, 366—368], but also because the
assumption of bulk dielectric function becomes invalid at sizes this small (3 20 nm).
Essentially, this would be equivalent to saying that the band structure is the same
for nanoparticles and bulk, which is, of course, not true. Apart from this, the Mie
formulation has been extremely successful in describing the optical spectra. Rather
than abandoning it all together, remedying this short-coming is considerably simpler
than some of the alternatives.

One possible remedy is to start from the beginning, as Mie did, solving Maxwell’s
equations, but this time properly accounting for all of the possible fields and excita-
tions at the retarded (or advanced) times and construct a non-local dielectric response
function. In general, this option is quite difficult and not analytically solvable. For an
in depth discussion, see pp. 72-75 of Reference [364]. Another option, which is widely
invoked, is to formulate an effective, size—dependent dielectric function in terms of the
bulk function, and stick with the Mie formulation. In other words, modify the bulk
dielectric function to reflect the necessary size-dependence.

Before formulating the phenomenological size-dependent dielectric fimction, it
is worthwhile to pause and examine the key differences between bulk metals and
nanoparticles. Naturally, the surface—to-volume ratio is greatly enhanced in the lat-
ter. If the electron mean free path2, loo, exceeds the particle size, surface scattering
becomes a limiting factor for electron relaxation, meaning that proper treatment of
the surface scattering must be implemented. Given that, plasmons in a nanoparticle
generally dephase more quickly than in bulk.

The Drude dielectric response of free electrons in a metal is given by [369],

 

2Subscript oo refers to bulk.

130

where 7 represents the phenomenological damping constant and the plasma frequency

/ 2
as
01p = w, (6.10)

where n is the volume density of electrons in the metal and m* their effective mass.

is,

For bulk, '7 = 700, and 700 is the sum of electron-electron and electron-phonon
scattering rates, as those are the two primary processes that provide damping for
the excited free electron gas. The finite size effect enters the formalism through
the damping parameter, 7. Specifically, the damping will now have two terms, one
comprising bulk scattering events (700), and an additional term for surface scattering,

such that the net damping factor (now size-dependent) becomes

7(3) = 100(0) + 14%, (6.11)

where A is essentially a fitting parameter that will depend on the metal and v F is the

Fermi velocity. This means the net dielectric function, now size-dependent, becomes

[364]

5(w,R) = Eoof’ )+ “123(m— w2+;(R)2)+

7:21.)

(6 (12)
Since the bulk dielectric functions for noble metals are rather well-tabulated [370—
372], parameter A from Equation 6.11 is frequently used as an experimental fitting
parameter, allowing for the formalism presented here for the dielectric function mod-

ifications to be used in conjunction with the Mie theory [242, 368, 373—389].
Recently, the importance of parameter A has been recognized and expanded in
the literature, due to past experimental observations of its dependence on the sur-

rounding medium, em, [390, 391]. Pinchuk and colleagues have expanded A into

131

two parts, noting that it encompasses an elastic scattering component from the sur-

face, ASize, and an interfacial damping component from adsorbate—induced resonance

states, Ainterface, such that A = ASize + Ainterf ace [392—395].

6.3.1 Example Calculations of Mie Scattering with TTM

A program was written to convert the material dielectric functions to the size-dependent
one and solve the corresponding scattering cross-sections, which couples nicely to the
TTM presented in Section 3.1.3. The logical steps will be briefly laid out here.

The nanoparticle size R and bulk material index of refraction, ii = n + in, are
read in along with the corresponding wavelength (A), bulk mean free path (loo), Fermi
velocity (up), plasma frequency (top), empirical scattering parameter (A), and sur-
rounding medium index of refraction (Tim). The bulk damping constant is calculated
from 700 = v F / Zoo, and the size-dependent damping function from Equation 6.11.
Using the FIesnel reltationships, the real and imaginary parts of the dielectric func-

tion are constructed from 51 = n2 — n2 and 52 = 2am, respectively. The corrected

- - - 2 2 2 ’1 2 2 ‘1
function, 5(a), R) 13 evaluated by adding top (w + 700) — (to + 7(R) ) to

2
'92 7 R — 00 t th ' ' art.
the real part, and z w (fly—(1%)? w—z'LT) o e imaginary p

 

 

 

 

+700
Now, size-dependent n and is can be computed from
2 2 1/2
5 + s + s
n = \/( 1 2: 1, (6.13)
and
2 2 1/2 _
5 +5 5
n = \/( 1 2’2 1, (6.14)

followed by a call to a subroutine that takes the new 11 and is, along with nm and A,
and returns amt, Jabs, and 036a [365]. Using the indices of refraction for Au and Ag

from Johnson and Christy (1972) [370], Figure 6.8 shows several example calculations,

132

where efficiency factors are defined as Qabs = “abs/”R2, and analogously for osca

and dext.

 

 

25000

 

 

 

 

 

 

 

‘-=----------I

Temperature (K)
_| .3 N

01 01
9 § §.§ 3

 

 

 

 

 

' v ' v f vvvvvv

0 20 40 60 80 100
Time(ps)

‘ r

 

 

 

l A J m—. A

 

 

 

Qabs
019th

 

 

 

 

 

 

300'400'500'6001700 350 ' 400 ' 450
A (nm) 21. (nm)

Figure 6.8: Example Mie Scattering calculations. (a) Absorption factor for 20 11111 An
and Ag nanoparticles. The inset shows the scattering factor (A = 1 and am = 1.33).
(b) The electron and lattice temperature of Ag (solid) and Ag (dashed) irradiated
by a 400 nm, 50 fs, pulse at 5 mJ/cmz, where ”abs was used instead of R and 63
(see Section 3.1.3). (0) Absorption factor for 40 nm Ag nanoparticle as a function of
the refractive index of the surrounding. Shown are vacuum (1.0), water (1.33), and
common value for nanoparticle ligands (2.5), clearly indicating the strong dependence
of the SPR position. ((1) Surface scattering factor A is varied for Qabs, which mostly
affects the SPR width.

It is interesting to see how Au and Ag, both of which are fcc noble metals with
similar bulk electric and chemical properties, behave so differently because of SPR
excitation. For example, in Figure 6.8(a), Ag will absorb much more than Au at

wavelengths near 400 nm, which is reflected in the temperature rises, as shown in the

133

TTM calculation in part (b). Had the excitation been closer to the SPR for Au (z
525 nm), the trend would reverse and Au would become hotter.

Electron ‘spill-out,’ which is due to the extension of the electronic wavefunction
beyond the surface, can also be an important effect [364, 396—398]. In classical elec-
trodynamics, the nanoparticle surface, r = R, is treated as a ‘hard boundary’. That
is to say that the electron charge density abruptly changes from —en inside the metal,
where n is the volume density of electrons, to zero outside the nanoparticle (r -—> RT).
This is usually valid, but in reality, the change in electron density is not abrupt, it
decays outside the metal over a distance comparable to the Fermi wavelength [399].
If the metal is large in dimension, hard boundary treatment is valid. However, the
spill out distance can be as high as tenths of nanometers, which in some cases, is not
much smaller than the nanoparticle itself. Material property changes associated with
electron spill out can include reduced screening effects leading to stronger electron-
phonon coupling [400], and changes in SPR position and width [401, 402].

In the beginning of this section it was asked why Au nanoparticles are red. Figure
6.9 has the answer.

The Mie formalism presented here with the TTM from Section 3.1.3 has been
successfully implemented as secondary checks on lattice temperature for UEnC stud-
ies, most notably, Ag nanoparticles [193], where it assisted to preclude a thermally-
mediated channel for fragmentation at low fluence (not presented here). With the
general Mie picture in mind, some of the interesting observations associated with

nanoparticle charging will be presented.

134

 

 

 

g 1.0
,5 0.8
E
g 0.6
3
5 0.4
3 0.2
VI
0' 0.0

 

 

 

500 '550 ' 600 '650 ' 700 "750 '800
A (nm)

Figure 6.9: The normalized scattering factor for Au nanoparticles of 10 nm diameter,
showing a strong peak near 650 nm, which will appear red in the visible spectrum.

6.4 UEDV Investigations on Molecular Transport
at the Nanoparticle / Molecules / Substrate
Interface

As mentioned, the molecular wires that take part in the immobilization (aminosilanes)
tend to order very well beneath the nanoparticles. So much so, that their structures
are clearly resolvable from electron diffraction [190, 192], as was shown in Figure 6.2.

The fortuitous discovery of SAM diffraction peaks3 in conjunction with the exten-
sion of UEDV to arbitrary geometries (Section 4.6.2), 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

 

3It actually came as a surprise to see the diffraction peaks from the SAM in the first studies of
Au nanopartices in the UEC lab.

135

 

which, a charge transfer process will ensue depending on the relative offset between
the transient Fermi levels of the two systems. Quantifying this process would pro-
vide an additional technique for the investigation of molecular transport, an area of
notable interest [403~408]. The diffraction peaks associated with the SAM are the
most suitable for studying the charge transfer process, as the powder diffraction pat-
tern (Debye—Scherrer rings) from the Au can exhibit strong Debye-Waller changes
[182, 185, 192] in intensity and position due to the formidable structural changes,
which only serve to complicate the isolation of the TSV. The potential associated
with these nanostructures can be determined from an extended slab model, with
an angular-dependent correction factor (8 from Section 4.6.2) to model the relevant
angular shifts observed in the diffraction.

Specifically, the transient voltage of a 20 nm gold nanoparticle, caused by pho-
toinduced charge transfer between the substrate and the nanoparticle, can be moni-
tored by analyzing the SAM diffraction peaks corresponding to momentum transfers,
3:275, 5.27, 7.98 13:1 (orders N = 1 to 3), which is depicted in Figure 6.10. For
small-angle diffraction (0 S 2°), the dispersion in 9 due to the position-dependent
refraction effect can be ignored, as shown in the inset of Fig. 4.15(b). In other words,
the same correction factor, 8, can be applied to all three of the diffraction orders
from the SAM.

The total transient shift A B in Figure 6.10(b) includes two charging mechanisms:
one is due to the voltage drop across the Si/SiOg surface (V3), and the other is the
drop across the SAM (VM), (recall the TSV ‘voltmeter’ in the Figure 4.4). A simple
RC—circuit is adopted to conceptualize the transport properties associated with this
interface (Figure 6.11). To isolate the voltage drop across the linker molecule, the
contribution to A B from Vs must be subtracted out. Typically, the A B associated

with a bare Si/SiOg surface has an exponential down turn followed by a power-law

136

 

//////
Si (1 11)

 

 

 

 

 

0 500 1000 1500 2000 2500
Time(ps)

Figure 6.10: UEDV applied to the Semiconductor/ SAM/ N anoparticle interface. (a)
A ground state diffraction pattern of this system, which exhibits the characteristic
Debye—Scherrer rings for the polycrystalline Au nanoparticles, co—present with the
diffraction peaks associated with the linker molecules. The latter, extracted from the
full pattern, are also shown in part (b) (inset). (b) The total transient shift, AB,
observed from the (001) diffracted beam (circled), which is that of N = 1 (s = 2.75
A‘l) from the aminosilane linker molecule (chemical structure shown in inset).

recovery (recall from Chapter 5). The temporal evolution of the TSV for Si/SiOg is

well-fit by the empirical functional form given by Equation 5.1.

 

 

SAM Vacuum

Bulk Surface

 

 

 

Figure 6.11: The equivalent circuit diagram to describe the charging and discharging
dylf‘a-m'lcs in the semiconductor/SAM/nanoparticle interconnected geometry. Sub-
scrlPt-S ‘M’ and ‘5’ describe the linker molecule and Si/Si02 surface, respectively.
The“ associated resistances, capacitances, and voltage drops are denoted by R, C,
::d V, respectively. The resistances of the bulk (Rbulk) and vacuum gap (If/vac) are
nslderably larger than RM and R 5', such that both —> 00.

137

The presence of an additional upward swing followed by a fast exponential down-

ward swing can be discerned with careful analysis, which is shown in Figure 6.12.

Whatever the relaxation mechanism of VM, it does not appear to be a power-law

decay like that associated with V3, which is governed by the long carrier relaxation in

the silicon bulk. This is useful in separating the two contributions, which is done by
fitting with Equation 5.1 in the long-time relaxation regime and also with the data
near the ZoT. From this well-constrained fit, TC is found to be 33.5 ps, similar to
that in Si(111)/Si02-only substrate, while 7,- is significantly shorter (22.6 ps), reflect-
ing the abundance of new acceptor states provided by SAM / Au functionalization,
enhancing the rate of surface charge transfer. Subtracting out V3, the voltage drop
across 1: he SAM, VM, shows distinctive exponential charging and discharging charac-
teristics , associated with the hot electron transport through the SAM, which can be
analyzed to yield the respective molecular RC time (7720), as shown in Fig.6.12(b).
Upon fitting VM(t), it is found that the transient resistance, RM = 1.92 M9 for
the Charging stroke, followed by 4.5 M0 at the onset of the discharging stroke, and
then riSing to 26.6 M52 over the slower arm of the discharging stroke, with C M set
to 2-92 X 10"18 F for all. The capacitance was determined from the field modeling of
the interface described in Section 4.6.2.

It is rather interesting to compare the molecular resistance, RM values above,
to the St eady—state values determined by Sato and colleagues, for the same linker
“10190118 [360]. They reported R = 12.5 M9, obtained by applying a bias voltage

across ttlle molecular interface, using a 10 nm Au nanOparticle (implying a SAM
coverage area ~ 4 times smaller). The smaller injection resistance obtained using
the ultIafast photo-initiated voltammetry setting, as compared to the recovery R S or
the Stearly-state data, can be understood from the hot electron transport picture, in
Which the hot carriers initiated by photoexcitation are given more access to a broader

r
ange of unoccupied acceptor states and a reduced interfacial potential barrier (hence

138

 

 

 

    

 

 

 

 

 

 

 

 

 

 

(a) (b)
r . . 7‘. . . . . . a . .
0.0000-
-00005 3 6‘ ' V”
._ 4" ‘ g 5- —-Fit
'0 .0010« a 4. _
00 u
v — 13.1.77]
’— -o.0015« g 3- . PS 1
a“ .. 2_ 5.6ps .
-0.0020~ E 1
« :+
'0.0025 ‘ 4“ MIA "m. (P') E n
""" 0 so 150 25.0 g V
.0030 . . . . . l- . . . . . . . . . .
0 500 10001500 2000 2500 0 20 40 60 80 130
Time (ps) Time (ps)

Figure 6.12: (a) The refraction shift observed by following the (001) diffracted beam
(at s = 2.75 A) from the SAM described in Fig. 6.1. The solid points represent
the raw diffraction shifts arising from the SAM (VM) and the Si/Si02 surface (V3)
(continuous line) (see text). The inset shows the early time evolution of the TSV
shift that has a significant VM contribution, deviating from the smooth transition of
VS described by Equation 5.1. (b) The voltage drop across the SAM, VM, which was
determined by first subtracting the contribution V3 from A3, followed by applying
Equation 4.19. The fit shows a rise time 7',- = 5.6 ps and a biexponential decay with
time scales 13.1 and 77.7 ps.

the lower resistance to transport of 1.92 M0). As the carriers cool, these channels

are leSS active, reflected by the higher resistance of 26.6 M9.

6-5 Near-Field Lensing: Nano—cavity Patterning

6-5-1 Near-Field Enhancement

What is near-field enhancement? Perhaps a better question is why? In fact, a glance
at “Me 6.7 may help clarify. As the nanoparticle has a strong proclivity to absorb
near SPR wavelengths, the incident light begins driving the conduction electrons into
OSCillamien about the ion core, such that surface charge piles up on the poles (equal and
Opposite), oscillating sign every 7r/w. In other words, it is acting like an antenna.
This Oscillation interacts with the peripheral electromagnetic radiation, drawing it

to the nanoparticle. By peripheral radiation, this means photons that were on a

139

course to fly by the nanoparticle in the absence of this interaction. This is why it is
sometimes referred to as a lensing effect.
N ear-field ablation of Si was observed by surprise in the UEC lab in 2006. Upon
SEM imaging some over-exposed samples of surface-supported Au nanoparticles from
UEC experiments, Dr. Yoshie Murooka found a surprisingly strong presence of nano—

cavities on the Si substrate, shown in Figure 6.13. Interestingly, this cavity formation

occurred at laser fiuences that were below the damage threshold of the Si.

 

Figure 6 - 13: Femtosecond laser induced nano—cavity formation. (3)-(b) are from one
831111318, (c)—(d) from another.

R€5Clently, Obara and colleagues have shown that near-field focusing is responsible
for these effects, and can be used to selectively ablate portions of the substrate lying
beneath the nanoparticles. The process is depicted schematically in Figure 6.14.

The mechanisms behind the near-field focusing effect are well-understood on a

thee
1"Estical level, and the technique has been demonstrated for nano—cavity formation

140

‘Lens’Area ~ 0'“,

 

636% flQb Abged SI

Figure 6 .14: A schematic of near-field lensing under the assumption of UEC geometry
(pump laser incident at 45°. The lens that is shown is fictitious, but captures the
essence of the near-field antenna. The extinction cross section amt is the ratio of the
incident power to the total intensity scattered and absorbed.
to depths as small as tens of nanometers [181, 409], though the widths of the nanocav-
ities produced from this method are usually quite large (~ 1 — 1.5 x D, D 2, 100
nm)- Driven by the interests in making sub-10 rim nano—cavities, options are being
explored in the UEC lab to exploit the near-field effect in 2—5 nm nanoparticles. First,
the Properties that make a good ‘lens’ are briefly highlighted, through simple analysis,
follwed by a proposed experimental direction.

Briefly, the formalism of the field enhancement is examined. Conversion of incident

far-field radiation to the near-field is characterized by the near-field efficiency, an,
given by

an = 2202.12 [a + wage)? + zlh§i’1(x)12] + (2: + 1)Ibzu2lh§2)(2)l2}
l=1

(6.15)

141

Where hi2) (x) denotes Hankel functions of the second kind, at and bl have the same
definitions as in Equations 6.6 and 6.7, respectively, and cc = kR, with k = 27rnm/A
[410] . The dielectric properties of the material enter through a1 and bl- Note that

Equation 6.15 is not the field enhancement factor itself, however it is proportional to
it.

Consider the following comparison between Ag and Au 40 nm diameter particles,

in a dielectric medium with index of refraction nm = 1.5, and parameter A from
Equation 6.11 is given as 1 for both cases. Figure 6.15 shows the near-field efficiency
With scattering and absorption efficiencies also depicted for each. While the silver
has a much stronger effect, to attribute it to the SPR absorption alone would be
incorrect. The near-field effect is present with particles that are strong absorbers
(for the antenna ‘lensing’ effect) and strong scatterers. Strong absorption alone is
insuffici ent (if the particle absorbed everything and scattered nothing, there would
be no field outside to do the ablating). The ‘E2-power’ that is doing the drilling
is actually scattered radiation from the incident field (pump laser), the amount of
which, is greatly enhanced because of the dipole oscillation antenna effect. In fact,
because the surface plasmons in silver are damped so quickly (~ 5 fs), Au is actually
considered to be a more ideal candidate for near-field ablation [356, 409, 411], if the
wavelength is near infrared, where the scattering properties are 600 times larger than
the ebSOrption in the near-field [409].

Plech and colleagues recently reviewed the field of femtosecond laser effects on
plasmonic structures [181]. In Figure 6.16 (reproduced from Reference [181]), they
showed that as particle size is reduced such that it is /\ >> R, the scattered fields
resemble those depicted. ).

Interestingly, Eversole and colleagues showed that by tilting the angle of incident

radiation by 45°, much stronger ablation effects were observed, namely, in the thresh-

142

Near Field Results

 

 

 

 

 

 

 

 

 

 

14 f - 4 . - d 3*
- 12.‘ a Silver ,
g" 10: ( ) abs .‘
.2 1 .
g 8? nf '.
a: 6'. l
a 4 q d
2 1 l
O - sca - _1 _ f f
360 460 560 500 200 400 600 800
Wavelength (nm)

Figure 6.15: The efficiency factors, Qabs (blue), Qsca(green), and an (red), for
40 nm Ag (a) and Au (b) embedded in a dielectric medium with index of refraction

nm=1 .5 -

 

O

D<<A Dgl

 

gigure 6.16: Shown are the effects of particle size on the scattered near-field [181].
he UEC geometry is similar (in polarization), but tilted to 45° incidence.

143

 

old [409]. This is actually the same geometry as the UEC system, with the pump
laser incident at 45°.

An interesting, yet simple experiment would be to test on small nanoparticles (2—5
nm) with the pump laser at nearly planar incidence, which would tilt the direction of
scattered radiation in the small particle limit in Figure 6.16, such that it is directed
normal to surface. One hindrance is that near-field effects are smaller with smaller
nanoparticles. But a size-selective study could be carried out, beginning with 10—20
nin sizes to observe the effects. Moreover, while the near-field enhancement may
be smaller, the lightning rod effect will be larger since it only has to do with small
features (specifically potential gradients near small features) and is not a resonance
phenomenon. The nanoparticles would ideally be spin-coated onto the surface to

minimize the distance between nanoparticle and surface.

144

‘v

Chapter 7

Molecular Beam Doser

7. 1 Introduction

Interfacial water plays a crucial role in all of life, as it is involved in a vast array of
biological, chemical, and physical processes [412—415]. Arguably, the most widely-
employed technique to date to characterize the ultrafast processes associated with
interfacial water has been nonlinear vibrational spectroscopy, based on second har-
monic and sum frequency generation (SHG and SFG) [416—418]. The identification
of site-specific spectroscopic responses from these techniques provide very rich infor-
mation on the structural and dynamic behavior of this important substance.

Recently, it has been demonstrated that the transient structural dynamics of
nanometer scale water / ice bilayers on surfaces can be effectively resolved by UEC
[103, 177].

Recent work by Tian et al. reveals that at the water / vacuum interface and wa-
ter/ molecule interface, a strong interfacial field is present, suggesting a significant
charge redistribution at the interface and that the environment is highly basic [419].
The charge transfer mediated by water and ice is central to many photochemically

active processes including ozone depletion and photocatalysis.

145

 

To investigate the charge transfer dynamics across nanometer thick water/ ice
structures adsorbed to substrates, a UHV molecular beam doser (MBD) was devel-
oped that is capable of layer-by-layer growth of interfacial water. This doser system is
coupled to the UEC stage, which has cryo-cooling capabilities, down to ,5 20 K, allow-
ing gas-phase vapor to condense into ice very efficiently upon exposure. This chapter
serves to demonstrate the design, calibration, and implementation of the molecular
beam doser, along with some preliminary data from the inaugural experiments with
interfacial water at MSU.

Dosing, which is a common technique in surface science, is to expose a sample
to a gas in situ and allow the gas to adsorb onto the surface [420, 421]. To do this,
one option is to back-fill the vacuum chamber with the gas the experimenter wishes
to expose, monitoring its partial pressure as a means of quantitative exposure [85].
However, this is not a viable option here for severalhreasons. First, the photocathode,
situated inside the vacuum chamber, is in close proximity to the sample (~5 cm),
is held to an accelerating voltage of -30 kV during experiments, . A sudden influx
of gas molecules could easily be ionized by this voltage, possibly resulting in an arc
discharge, which could be devastating to the multitude of electronics in the vicinity.
Secondly, a sharp increase in pressure can take days to pump out, particularly for the
case of water. Moreover, displacement of impurities on the chamber wall could reduce

the purity of the gas that is to be dosed. There is also a risk of damage to the mass
Spectrometers and ionization gauges, due to the interaction of the back-filled H20
383 with the sensitive thermionic emitters, which are inherent to these devices . To
avoid these problems, it is necessary to expose the sample to the gas in a controlled,

quantitative manner.

146

7 .2 Design Methodology

The MBD, was designed with the following criteria in mind: (1) the effusion rate must
be slow and controlled as to allow for quantitative gas deposition, (2) the dosing must
be uniform over the surface, (3) the dosing head must be in close proximity to the
sample as to minimize the gas not sticking to the sample and it must be retractable
as to not interfere with experiments that do not require dosing, (4) dosing must have
rapid shutoff capability, and (5) it must be all metal construction because of the
presence of a high voltage electron gun, which could otherwise charge it up. Slow
effusion is achieved through the use of a pinhole orifice, which dramatically impedes
the flow, while uniform dosing is ensured via a microcapillary array at the end of
the dosing gun (Figure 7.1). This component was fabricated by drilling micron-sized
holes in a square of copper shim-stock with the femtosecond laser, similar to Reference

[422] (see Section 7.4).

 

Gas E] lntra-Doser a UHV Chamber I

 

 

pa [1 pp i p s—>
. \
2 pm Pinhole Microcapillary Array

Figure 7.1: Schematic View of the doser reservoirs. Gas is admitted into the system to
a pressure 130- The pinhole orifice prevents the intra-doser pressure, PD from rising
significantly, from its original pressure prior to dosing, P. Here, P is the pressure of
the main chamber and S is the pumping speed

7 .3 Pinhole Orifice

Flow restriction is the key to controlled dosing because the gas being introduced to

the system is 9—10 orders of magnitude higher in pressure than UHV. To do this, a

147

pinhole orifice is employed in the form of a 1 / 4” VCRI, deformable, stainless-steel
gasket2, which is compressed between a VCR double-male3 and VCR double-female4

(Figure 7.2).

 

VCR Gasket

VCR Double-Male (2 pm clearance)

   

VCR Double-Female
(1/4")

 

 

 

Figure 7.2: A laser-drilled, stainless steel gasket, deformed between a VCR double-
female and double-male operates as a flow restrictor. The clearance hole has a 2 pm
diameter and was drilled at the center of the gasket.

The conductance of an orifice whose diameter is small compared to its length (as

is the case here, 2:600 pm) is given by the expression [423]

D2 /7rRT
C = L 27", an

1 + 3113
where D is the pinhole diameter, L the orifice length (gasket thickness), R is the ideal
gas constant, and m and T are the molecular weight and temperature, respectively,
of the gas. For D = (2.0 i 0.2) pm, L = (0.6 i 0.1) pm, m = 28 amu, and T = 300
K, the conductance is calculated to be C = (1.7 :l: 0.6) x 10’9 L/s.

To compare this calculated result with a measurement, the pinhole gasket was
calibrated with N2 gas in the load-lock (Figure 7.3), prior to installing it with the
doser (Figure 7.3). To calibrate, on one side of the pinhole a volume, V, was purged
with N 2 gas to a static pressure, P0, and subsequently pumped through the pinhole

until it equilibrated with the load-lock pressure (UHV). The time constant associated

 

lVCR: variable compression ratio.

2Stainless-steel VCR gasket with a 2 pm hole drilled in the center, purchased from Lenox Laser.
3Swagelok, part number SS—4—VCR—6—DM.

4Swagelok, part number SS-4-VCR-6—DF.

148

 

with the decay of N2 pressure, 7', is related to the conductance by

mP V 1
C = ( [)ng ) ;, (7.2)

 

 

 

Purged with N2

%VTm

 

 

 

 

 

in 1
l n- .
o' '560'1600'15'00

Time (s)

 

/ c
2 um pinhole

Figure 7.3: Dry nitrogen gas is pumped through the pinhole. (a) The left volume
is purged with N 2 until it reaches P0. The right volume (load-lock) is continuously
pumped by a turbo molecular pump (pumping speed S), such that it is maintained
at % mid-10"8 torr. The time taken for P0 —) P is used to measure the conductance,
along with the gas and geometric properties (P0, V, T, m). The pressure rise in the
load-lock from the influx of N 2 is negligible. (b) The measured pressure in time during
the pumping shows that under these conditions, it takes 2 20 hours for the pressures
to equilibrate to the load-lock base pressure.

where p is the mass density of the gas (1.251 g/ L). After purging the volume,
V w (6.0 :l: 1.2) x 10’6 m3 with N2 to P0 = (14 :l: 2) Torr, the exponential de-
cay time associated with the pump-down was measured to be m (7.2 i 2.0) x 104 5,
corresponding to a conductance of (1.1i 0.7) x 10'9 L / s, which is depicted in Figure
7.3(b). The calculated result from Equation 7.1 is in agreement with the measure-
ment. Note that the decay is exponential because the gas is in the molecular flow
regime, meaning that the mean free path of the gas molecules is large compared to
the dimensions of its container. Put more simply, the gas molecules rarely collide
with each other, they are much more likely to collide with the surrounding walls. If
the flow were viscous, Equation7.2 would no longer apply. For more on comparing

molecular with laminar flow, see Reference [423].

149

 

7 .4 Microcapillary Array

As mentioned in Section 7.1, the MBD must be of all-metal construction because
of the presence of an electron beam. Microcapillary arrays, conventionally made of
glass, are available for purchase but they are rather expensive and would need to be
Sputter-coated with a metal to not charge up. Rather than doing this, fabricating it
with the femtosecond laser was found to be simpler and more cost-effective. Copper
shim-stock was purchased from McMaster—Carr of thickness 0.002” (m 50.8 nm) and
mounted to a home-built, 2D micrometer controlled stage. The laser was deflected
outside of the UHV chamber and focused onto the shim—stock, then raster-scanned
along the shim-stock, exposing it to pulses of z 200 ml at each stop, resulting in

clearance holes of z 25 — 40 nm diameter, spaced 500 rim apart (Figure 7.2).

(r ‘
l _
d
/ |——1
C 9 /
Tapered
\

Microcapillary \
Array

 

   
 

 

Pinhole

   

 

 

 

 

Figure 7.4: Scanning electron micrograph images of the microcapillary array. The
resulting holes from laser drilling were ~25-40 pin in diameter, spaced 500 pm apart,
and conical through the thickness.

The microcapillary array is held in place by pressing it between two pieces that
comprise the doser head (Figure 7.5). The pieces are fastened by machine screws;
the pressure exerted by the screws dictates the goodness of seal. Ideally, all gas

molecules entering the doser head will exit through the MCA holes. But since the

150

 

locking mechanism for the MCA is a press-fit, the leak through the sides needs to
calibrated beforehand as well.

Press MCA against doser cap

 

Figure 7.5: Holding mechanism for the microcapillary array. The microcapillary array
is simply pressed between the two pieces shown that are fastened by 4 # 0-80 machine
screws, leaving the possibility of gas leaking through the sides. However, flow through
the array holes is unimpeded, so should be favored

To first order, it is conceivable that most of the gas will exit the MCA, since it
is porous. Quantifying the leak rate through the sides involves a similar procedure
to that of the pinhole orifice calibration (Section 7.3). Two tests are run with dry
nitrogen gas: the first is where it is pumped through the MCA (Figure 7.6), the second
through an undrilled ‘blind’ piece of copper shim-stock with the same dimensions as
the MCA. The blind piece only permits gas through the sides, while the MCA has
this channel in parallel with the MCA holes.

With the MCA in place, the total conductance (which encompasses both the sides
and the holes conducting in parallel) is given by

_ _ mPOV 1
Ctot — Cszde + Choles — ( pRT ) T1" (7'3)

151

Blind Shim-Stock
(side leak throu . hput onl )

1V~ (a)

 

Side Leak
If, v T m P<<P

 

 

 

l

 

r_r

Microcapillary Array
(side leak 8: clearance throu . h - ut)

'3

(b)

A

Side Leak

If) V T m P<<PO

-.
.- ~—

 

l I ,

Figure 7 .6: Schematic of the two setups used to investigate the rate of side leak. (a)
With no holes drilled (blind), the shim-stock only permits passage through the sides.
(b) This configuration permits gas through the MCA holes and the sides (parallel
conductances). The time associated with pumping gas through each configuration
allows for the side leak rate to be determined (see text).

152

When the blind piece is in, the total conductance is only that of the gas leaking

from the sides, given by

 

mP V 1
Cside = ( pROT ) '— (7.4)

72’
indicating that the ratio of the side leak to the total conductance with both channels

working in parallel is

 

 

Csz'de = mPOV . pRT . 7'_1 (7 5)
Ctot pRT mPOV 72’ '
such that the proportion escaping through the array holes is

——Csid€ = 1 — 1. (7.6)

The measured values for T1 and r2 were 1.4 and 35.1 seconds, respectively (Figure
77). Inserting these values into Equation 7.6 gives the ratio of 0.96, meaning that

96% of the gas effuses through the holes of the MCA and the doser will work as
intended,

153

 

1O

 

  

Blind vs. Microcapillary Array
E I I
E ‘1. 1.
cu 1 i
h 1 ‘
3 .
a 1
e °-‘1. ._ a
n. 5 p” n 3

0.01

 

 

 

0 100 200 300 400 500
Time (s)
Figure 7-7: A direct comparison of the ‘pump—through’ times associated with a blank

piece Of shim-stock and the drilled piece. Their difference gives the leak rate through
the Sides, which is found to be ~ 4% (see text).

154

7.5 Operation

Extreme caution must be taken when administering a gas at a pressure that is 9—10
orders of magnitude higher than that of the volume into which it is being admitted,
especially when the gas is water. This section describes the dosing procedure and

the steps that must be taken to guard against undesirable — potentially catastrophic

   
  
   

  
 

incidents.
6 ATM : UHV “a
l :
po’flrocb’c E .. ' 1‘9“.“
6’0 OI : Multlport’ ‘00
Fluld ”~96 ' 9“" 3
_ Feedthrotigh a B
. .7 ._. .. -— fl
Steady :5,
State Q : Pinhole
o E Gasket
was“ i
“we“ :

Foreline

Figure 7.8: A full schematic view of the molecular beam doser.

A full schematic of the MBD, with all of its functioning parts is depicted in Figure
7-8- To simplify the explanation of the dosing procedure, the four valves used in dosing
are Ila-med in Figure 7.8 (Evac, Dose, Purge, and Steady-State). The atmosphere
Side Of the MBD is referred to as the gas-handling system (GHS). Using Figure 7.8
as 3 Ellide, operation of the MBD is as follows. First, pump the GHS: with Purge and

D086 Closed, open Evac and Steady-State (this is actually the steady-state condition
for the dosing system). Second, admit water vapor into the GHS by closing Evac and
Steady'State (has no consequence at this step, but it needs to be closed eventually),
and Opening Purge (Dose remains closed). The vapor pressure is monitored on the
manometen When a stable backing pressure is reached, Dose may then be opened

to commence exposure.

155

When the sample is adequately dosed, the flow is quickly stopped by closing

Puma and opening Evac, which evacuates the GHS and any gas that has not yet

passed through the pinhole5. Finally, the non-operational condition is restored once
00.96 is closed and Steady-State is re-opened, with Evac remaining openfi.

As pointed out by Huffstetler and Leavitt, it is necessary to uniformly heat the
outside of the GHS with heating tape to prevent water condensation on the inner
walls , which gives rise to unstable backing pressures and introduces difficulties in
evacuating the GHS [424]. In this case, spatial constraints forced the use of 1/4”
tubing for the GHS (1 / 2” tubing was preferred and is more common). This makes the
issue of heating the GHS more delicate, as the high surface-to-volume ratio increases
the likelihood of gas adsorption on the GHS inner walls.

The tubing on the UHV side of the MBD is necessarily heated to a higher tem-
perature than the GHS to prevent condensation on its inner walls as well as to offset
the Possibility of Joule-Thomson cooling (throttling) as the gas passes through the
Pinhole- Because of the all-metal construction of the closer, conventional heating
methods, such as NiCr wire could not be used unless the wire were sheathed such to
be electrically insulated from the closer. A much simpler solution was found to be
simply passing an electrical current through the stainless steel tubing on the UHV
side 0f the MBD (typical current / voltages z 6—10 A at 1-3 V); the resistance, while
10‘” (m 0.25 Q), is large enough to where resistive heating is sufficient to hold the
walls at a. sufficiently high temperature (5—10° higher than the GHS). A thermocou-

ple is employed to monitor this temperature. The GHS temperature is monitored by
correlating the manometer pressure with the temperature associated with its value
011 the Pressure-temperature diagram for the vapor pressure of water, and also via

pyrometer as a secondary check. Optimal dosing conditions are usually chosen to be

 

W
:A negligible volume of gas on the UHV side of the pinhole will still be dosed.
Typlcal operation is to allow the MBD to be continuously pumped for about an hour, with the
MBD heat-ing slightly raised from the dosing level to minimize wall adsorption.

156

 

With backing pressure near 42-48 Torr, which corresponds to a. water vapor tempera-
ture in the GHS of 35—40°C, though the stainless steel walls of the GHS are routinely
measured with an optical pyrometer to be higher under such conditions (70-80°C),
which is expected as its thermal conductivity is quite low (for a metal), such that the
static condition has the walls hotter than the vapor inside.

The last operational point, which cannot be over-stressed, is that heating of the
reservoir in which the water is contained can be done, but it is crucial that the gas-
handling system walls are warmer than the water container. Heating the water supply
has benefits, as the water vapor will flow out more rapidly upon exposure to vacuum
pressure. However, the GHS has a high surface—to-volume ratio and the flow rate out
of the GHS is governed by the pinhole. Increasing the influx of water vapor, while
resulting in a higher dosing rate, drastically increases the likelihood of condensation
011 the GHS walls, even when they are heated. The point is most easily illustrated

by Considering the various possibilities, given in Table 7.1.

 

 

 

 

 

 

 

supply Temp. GHS Temp. Dosing Rate Risk of Condensation
ambient warm slow low

ambient hot slow low

warm warm fast moderate

hOlS warm faster high

warm hot fast low

 

 

 

 

 

Table 7. 1 : A comparison of the various conditions that can be used to dose. Either of
the scenarios in the first two rows works fine, but the bottom line scenario is optimal.

157

 

7.6 Tests with H20

Calibration of the various conductance and leak rates associated with the pinhole and
MCA are outlined in their respective sections above. Here, the MBD has been moved
to its final working place in the UHV chamber.

During a dosing experiment, the sample stage is cooled to ~20 K. If, for some
reason , the dosing rate were to become much faster than anticipated, the sample stage
would act as a cold trap and it is unlikely that the global pressure of the chamber
would rise considerably, if at all, since the doser is in close proximity to the sample-
holder- This could leave the experimenter with a false sense of security. When the
cooling is stopped and the temperature is rising to ambient, vacuum contamination
could occur as the water sublimates from the sample stage. Furthermore, a sudden
Spike in the pressure introduces the possibility of arc discharge from the high voltage
used by the electron gun, even if the spike is short-lived. These effects, which are con-
sider ed in the next section, serve as the final pre—cautionary test prior to attempting

substrate dosing.

7 .6. 1 Thermal Desorption Test

To test. how well (or unwell) the UHV pressure holds up during dosing conditions, a
‘mock’ dosing experiment was held. A silicon wafer with chemically grown oxide (see
Section 5-2.1) was placed in the UHV chamber. The sample-holder was cooled, such
that the stage read a temperature close to 20 K.

DOSing commenced for 2 hours, at which point the cryo-cooler responsible for
maintaining the low temperature of the sample-holder, was switched off. Pressure was
recorded in real time as the sample-holder warmed to ambient temperature, a plot of
which is shown in Figure 7.9. Water desorption occurred near a stage temperature

Of 150 K. The reason it is bifurcated is most likely that water was dosed onto the

158

 

Various copper surfaces of the stage in addition to the Si wafer. The two will have
difl'erent energies of adsorption. A quadrupole mass spectrometer (QMS) could be
employed to identify the peaks below 100 K, but the focus here was to determine the
net rise in chamber pressure from dosed water desorption. If it were the case that
too much water had been dosed, this would risk damage to the QMS, which is more
costly than the ion-gauge used for the measurements here.

Warming from 55 to 280 K took about 6 hours. Note that within 2 minutes of
switching the cryo-cooler off, the stage warms from 20 to ~40 K. The pressure rose
nearly an order of magnitude from water desorption, which lasted all of 10 minutes,
and was then pumped out very effectively. More importantly, the sublimated water
did not cover a significant amount of surface area in the chamber, since the baseline
Pressure is completely recovered in a matter of hours with no baking. The net result
of this test is that the MBD is safe for UHV use. Arise to mid-10’8 for a few minutes
is non— problematic. Furthermore, it comes at the conclusion of the experiment, when
any dosed water would have been sublimated by then anyway (so the experiment
W0111d be over).

Recall in the introduction of this chapter there were five requirements to be met;
slow Bffusion, uniform coverage, rapid shutoff, metal construction, and retractability.
All have been discussed at this point except for the last one, which is accomplished by
using a. standard linear motion feedthrough, or ‘push-pull.’ Due to spatial constraints
and a limited number of unoccupied chamber flanges, the inlet from the GHS and the
motion feedthrough had to come through two different ports7 (Figure 7.10). Both
P01'ts Were CF-2.75”, which means that the inner diameter is a mere 1.1”, which
W0111d have made it impossibly tight to put the push-pull in the same flange, when
trying to run in a 1 / 4” flexline for the gas, which has a female nut that is nearly an

inch, thermocouple wire, electrical wire for the heating.

 

VAT? ‘two-flange’ problem could have been circumvented if a 0.450” or larger flange had00 been
a a Q-

159

 

 

(x 10‘8 Torr)

 

 

 

Chamber
Pressure

 

' v v i

so 160 150 260
Stage Temperature (K)

250

Figure 7.9: UHV chamber pressure as a function of sample-holder temperature. As
the sample-holder warms, various species desorb from the Si surface, hence the rise
in global pressure. The bifurcated peak at 2150 K is water desorption.

The doser sits at the same height as the sample on the stage in the experimental
Position. The push-pull is fastened to an OFHC copper piece, on which the MBD
sits securely in place, as all parts are rigid. However, this requires that the tubing
inlet from the GHS, responsible for supplying the closer with water, cannot be rigid.

Flexible stainless steel tubing of l/ 4” diameter with VCR terminations was ordered

to custom specs from Finemech Inc. to meet this constraint.

7.6-2 Preliminary Testing of H20 on Si

Prior to dosing, the water in the ballast was taken through three consecutive freeze-
PumP‘thaw cycles to improve the purity of the water. The water supply ballast was
imm€rsed in a liquid nitrogen container to freeze the water inside. The dissolved
333 tends to be expelled from water when it freezes. The Purge valve is then opened

(Figure 7 -8) to allow unoccupied volume inside the ballast to be pumped of impurities.

160

 

 

Figure 7.10: The final CAD drawings of the MBD and GHS. Upper right: motion-
feedthrough in the form of a push-pull is connected to a rigid copper piece, on which
the MBD sits. The flexible stainless steel tubing is seen dangling from the MBD head.
Bottom center: a snapshot of the actual GHS (the ballast is not shown). The CAD
dfeWing (blue) does not depict the flexible tubing.

The Purge valve is closed and the water is allowed to thaw, followed by repeating the
cycle Several times.

The first surface to be dosed was the Si(111)/Si02 (hydrophilic) surface. The
UHV System began at high-10‘9 Torr. The sample stage was cooled down to z 20
K, WhiCh made the pressure drop even lower, to 5.5x 10’9 torr. Water was admitted
to the gas-handling system, which was warmed with heating tape to approximately
35°C, Such that the backing pressure was z 45 torr. The ballast was mildly heated 2-
3°C ebOVe ambient. The stainless steel hosing inside the vacuum chamber was heated
by running a. steady DC current of 9.1 A at 2.4 V. Calibrations have shown that the
point 0f Contact for the thermocouple that reads stage temperature is actually colder
than the sample itself, as it sits in a. well-shielded area. All temperatures from this

point on refer to the calibrated sample temperature rather than the stage.

161

Dosing commenced for 60 minutes when the sample reached 95 K. Diffraction pat-
terns during dosing displayed ring-like signatures, evident of a polycrystalline struc—
ture. After dosing for 60 minutes, the cryo—cooler was switched off, and ground state
diffraction patterns were continuously recorded throughout the warming of the stage,
some of which are shown in Figure 7.11, beginning with 118 K. At approximately 145
K, the ice begins to sublimate and the rings sharpen as the temperature increases,
becoming completely desorbed near 156-158 K. At 150—155 K, the diffraction images

show characteristics of a cubic ice layer [103], before rapidly sublimating, allowing

the silicon peak beneath to show, which can first be seen at ~156 K.

 

Figure 7.11: Ground state diffraction patterns of an ice layer adsorbed to
Si(111)/Si02. The cryo-chiller for the stage was turned off after the pattern in the
118 K shot was taken. Repeated shots were taken as the stage warmed to 160 K,
where all remaining water had clearly sublimated. At 145—150 K, it can be seen that
the Debye-Scherrer rings become substantially sharper, signifying that the water has
sublimated down to the last bilayer.

162

It is tricky to maintain the sharp Debye-Scherrer rings by switching the cryo—
cooler back on once they are visible to reverse the temperature trend, due to the
poor thermal conductance between the crystat and sample holder (it has been found
to take 15—20 minutes to reverse the temperature rise and begin to cool). However,
the structure can be annealed with ample time to chill the stage back down before
sublimation. Figure 7.12(a) shows water at 118 K, with no annealing, while part b
shows the annealed structure on Si following pulsed laser irradiation of 66 mJ/cm2
for 15 mins at 1 kHz with 45 fs pulses. The cryo—cooler was then switched back on,
and the bilayer rings can now be studied however desired. The Debye-Scherrer rings

are identified in Figure 7.13.

Annealed (b)

   

Figure 7.12: Laser annealing water on Si. (a) The usual water structure near 118 K,
the rin s are rather broad. (b) The ice structure following laser irradiation with 66
mJ/cm for 15 mins at 1 kHz with 45 fs pulses.

Also in Figure 7.13 is the intensity from the gated region as a function of the ambi—
ent temperature during stage warming. At each acquisition during the warm-up, the
maximum intensity was chosen from this box and plotted against temperature. Note,
the two downward spikes at 125 and 140 K are artifacts due to the slight adjustments
of the stage that were necessary to account for thermal expansion of the stage itself

as it warmed. In the initial stages of the warm-up, the diffraction pattern has to be

163

 

  
 
  

 

60,000 \f‘ '

40,0001

Gated Intensity

 

 

20,000 ‘
”0130140 150 160 1’0
Temperature (K)

 

  

Figure 7.13: The Debye-Scherrer rings are identified for the annealed water struc-
ture. The maximum intensity from the gated region (red dashed box) is plotted as a
function of the ambient temperature during the warming cycle (inset), where the ‘M’
shape can be seen as the water goes through sublimation.

164

 

 

‘chased’ a bit by adjusting the goniometer to keep the pattern optimal, but it sub-
sides by 140 K, at which point it remains fairly stable throughout, needing only minor
adjustments that actually become quite predictable with experience. The behavior
of the curve from 150—159 K (the‘M’ shape in the curve) is highly reproducible.

At this point, the interpretation of the ‘M’ shape in the intensity/temperature
plot (Figure 7.13) is as follows. The first peak is due to a well-ordered ice bilayer,
from which, the top monolayer begins to desorb, and the diffraction intensity begins
to drop. Prior to desorbing, the remaining monolayer has a reconstruction of sorts as
it relaxes into a commensurate layer, again, resulting in an increase in the diffraction
intensity. This is short-lived as, finally, the last monolayer desorbs and the intensity

drOps to zero from the H20 structure.

7 .7 Discussion

A molecular beam doser was designed, assembled, and installed in the UEC lab at
MSU. Following the dosing procedure recipe outlined here, any substrate that is
loaded into the UHV chamber can be dosed. Silicon was tested as a prototype and in
principle the dynamics of the interfacial water could have been investigated, however
this has already been done for this system [103].

Other experiments that come to mind are single crystal Ti02 films [425], which
have considerable interest in their interaction with water [426, 427] because Ti02 is
a photocatalyst[428]. When placed in water, directing UV light onto TiOg causes
it to cleave impurities that are adsorbed to its surface. The harmless products,
usually C02 and H20, desorb, meaning that TiOg effectively purifies water under
sunlight. Recent studies with time resolved photoemission have elucidated interesting
properties of the interfacial electronic structure at the TlO2/H20 interface[124], and

charge transfer coupled to atomic motion at the TiOg/CHgOH interface [123].

165

 

Chapter 8

Summaries & Discussion

The most important aspect of this work is the development of ultrafast electron
diffractive voltammetry (UEDV) and its successful application in measuring the tran-
sient dynamics of interfacial charge transfer, as demonstrated through the studies of
hot electron processes (generation and surface charging) at the Si / Si02 interface,
and molecular transport across a nanoparticle / molecule / semiconductor interconnect.
Additionally, the transient near-surface field determined by UEDV can be directly
combined with the photoemission dynamics obtained by ultrafast electron projec-
tion imaging [200] to provide a more complete understanding of electron dynamics in
photoexcited materials.

UEDV is complementary to a cohort of other approaches that are sensitive to the
surface electron dynamics, such as photoelectron [123—125] and surface-field enhanced
nonlinear spectroscopy [81, 85, 153]. The site-specific and charge-sensitive character-
istics of electron diffractive approach allows the transient effect of electron transport
to be elucidated, while spectroscopic techniques provide information on the energetics
and rates of electronic relaxation and accumulation in surface charging dynamics.

The ultrafast time resolution and high sensitivity to nanoscale charging of the

UEDV approach, allows the identification of two distinct charge transfer mechanisms

166

 

near the surface of Si / Si02, distinguished by the fluence dependence of their respec—
tive injection times (Figure 5.3) of surface charging. To understand the origins of
these charge transfer behaviors, theoretical modeling of Boltzmann transport near
the Si surface is implemented, with appropriate treatment of the early time non-
thermal regime and calculation of quasi-Fermi levels to take into account the tran-
sient hot electron states, all of which is presented in Chapter 3. This analysis leads
to the conclusion that the observed linear TSV response at lower fluences is due
to a thermally-mediated tunneling process, which ensues as the quasi-Fermi level of
electrons is raised, followed by direct tunneling through the oxide, for which calcu-
lation follows the formalism in Section 5.3.1. Photoexcitation of carriers determines
the quasi-Fermi level, while the electron temperature dictates the width of the Fermi
distribution, both of which are factors in the tunneling calculation (see Equation 5.6).

In contrast, a consecutive 2- and l-photon absorption process (2+1) leading to
a direct injection of charge into the Si02 conduction band is invoked to explain the
more rapid and quadratic rise of the TSV at higher fluences. This picture is supported
by incorporating Boltzmann transport with the (2+ 1) formalism presented in Section
5.3.2, confirming that the rapid dephasing of the 2-photon generated hot carriers limits
the free carrier absorption process, thus leading to the specific quadratic dependence
that was observed.

UEDV holds tremendous potential in the possible application to some of the novel
solar cell designs, such as dye- and/ or quantum dot-sensitized films (or nanocrys-
tals), where the interfacial charge transfer mechanisms are central to the quantum
efficiency, and generally speaking, occur on an ultrafast time scale [39]. Another in-
teresting avenue of application that explores the capability of the ultrafast transient
field determination at interfaces is to investigate the local field switching caused by
electron phase transitions, as a phase shift in the electron wave can be introduced as

it traverses through an extended electric and magnetic field. The correlation between

167

 

the atomic and electronic degrees of freedom has been a long-standing problem in
studying strongly correlated electronic systems [429—431]. The growth of local charge
instability and / or lattice distortion[173, 430, 432, 433] has recently been revealed to
appear prior to its colossal electronic switching (phase transition) into different func-
tional states in these systems. The simultaneous determination of the transient field
and structural dynamics, which are inherently measurable with UEDV, is proposed as
a tool for researching the complex intermediate phases in electronic phase transitions

involving structural changes.

168

 

 

Appendix A

Principles of Electron Diffraction

A.O.l Bragg’s Law

Scattered electrons from adjacent crystallographic planes will interfere constructively
when their path difference is an integer multiple of the electron wavelength, Ac, which

leads to the Bragg condition (Figure A.1),

mAe = 2d sin 6. (A.1)

 

 

Figure A.1: Bragg Scattering. The path difference between two adjacent lattice planes
is d sin 0.

169

 

For a crystal with lattice constant a, and a Bragg plane with Miller indices {h, k, l},

13he lattice spacing for an arbitrary cubic system can be found from the relation

_ a
\/h2+k2+12’

 

(A2)

 

dhkl

WIliCh leads to a relationship between the lattice constant, a, and the Bragg peak

InBJdma
_m_/\ 2 _ sin2(9hkz) (A 3)
2a —h2+k2+12' '

A.O-2 The Reciprocal Lattice

Regardless of the type of diffraction probe (X-ray, neutron, electron, etc.), the recip-
rocal space is the natural coordinate system to describe probe interaction with the
crystal .. Consider the functional form of Equation~ A.3, the measurable quantity, ohkla
is related to the reciprocal of the lattice parameter, a. This point provides merely a
small example of the essence of diffraction: put simply, diffraction measurements are

taken in reciprocal space. For a Bravais lattice described by
R = nlal + 71232 + 71333, (AA)

the Corresponding reciprocal lattice is defined such that the primitive vectors of the

direCt space, {a} and those of the reciprocal space, {b} satisfy the relationship

bj - a.) = 27175211, (A.5)

 

from which, the individual primitive vectors of reciprocal space can be stated as

(a2 X 83)
b = 27r , A.6
1 a1- (a2 x as) ( )

 

170

 

(83 X 8‘1)
b = 27r , A.7
2 32 ' (33 X a1) ( )

and

 

b3 = 271' (a1 X 82) . (A.8)
a3 ' (31 X 32)

The (hkl) plane will be perpendicular to vector Ashkl = hbl + kbg + lb3, with
the Spacing between adjacent (hkl) planes given by

27r

In reflection mode geometry, the probing electrons sample only a few, sub-surface,
atomic planes. Consequently, it is convenient to define a planar geometry in direct

space as

R = nlal + n2a2. (A.10)

N Ote) the primitive vectors here will not necessarily be the same as those in Equation
A-4- They depend on the crystal cut of the surface being investigated. Taking the

direction normal to the surface to be 2, the reciprocal lattice is described by

(A.11)

and

alxfi

b =2 ——.
2 7ra2-(3111Xfi)

(A.12)

Note that a primitive vector 51;; is not present in Equation A.10, meaning that if
a third primitive vector for the reciprocal lattice were to be defined, it would have a
magnitude tending toward 00. This nonetheless corresponds to something physical.

In fact -.. the reciprocal lattice for an infinitesimally thin (ideal) surface is not a 3D

171

array of points, but rather a 2D array of rods, with each rod extending from -oo to

00. This point will be discussed further in Section (A.O.3).

A.O.3 Ewald Construction

The Ewald Construction is a convenient and elegant tool to determine which scat-
tering planes will give rise to constructive interference, based on the incident wave
Vect0r (direction and magnitude), the reciprocal lattice, and the scattered wave vec-
101,3: Consider a coherent electron beam incident on a crystal surface, 8,, which
makes an angle 9,- with the plane of the surface. The diffracted wave vectors, sf,

have magnitude equal to that of Si,

lSil = lel, . (A-13)

that is to say that elastic scattering is one of the underlying assumptions of the
Ewald Construction. The momentum transfer, 5, must lie in the reciprocal lattice for
conStI‘Iictive interference,

s=sf—s,-=Km. (A.14)

Where Km is the a vector of the reciprocal lattice, through which the mth diffracted
b83111 passes. The Ewald sphere, depicted in Figure A.2 can be thought of as an
ensemble of all candidate momentum transfers, such that energy and momentum
are Conserved. Should one of these candidate momentum transfers line up with a
1‘ eCiPI‘Ocal lattice vector, Km, constructive interference will result.
For glancing incidence, the beam penetrates only a few superficial layers. Sup-
preSSing this longitudinal degree—of-freedom in direct space (2:) causes elongation of
its reciI)rocal space conjugate (K z). As a result, the reciprocal lattice goes from a 3D

array Of points to a 2D array of rods, which is depicted in Figure A.3(b).

172

 

 

 

 

 

 

FigU—I'e A2: The Ewald construction. A 2D cross-section of the Ewald sphere is shown,
rePrefienting all possible momentum transfer candidates, 5. Constructive interference
occurs only when 3 lies in the reciprocal lattice, shown by the black dots.

 

   

 

 

Figure
dir-

A.3: The Ewald construction as periodicity is suppressed in the longitudinal
.ectiOn. Panel (a): the Ewald sphere intersecting a 3D array of reciprocal lattice
Pomts - Long range order is present in all directions. Panel (b): when the electron
beam Samples only superficial (surface) layers, the reciprocal lattice points are elon-
gated in the direction normal to the surface, resulting several families of planes of
r"?CII‘)1‘(3Dcal lattice rods. Panel (c): the area of the Ewald sphere intersected by a re-
Ciprocal lattice plane. Constructive interference will occur when s passes through one
Of t e rods.

173

There are several cases where the longitudinal reciprocal lattice dimension be-
COmes elongated. Figure A.4 shows three examples, Low Energy Electron Diffraction
(LEED) [434], Transmission Electron Microscopy (TEM) [435], and Reflection High
Energy Electron Diffraction (RHEED) [207], which is the geometry used in the UEC
lab at MSU. It may be puzzling why the term RHEED is not used to describe the tech-
niQUe employed in this work. Typically, RHEED implicitly carries the connotation of
11101ecular beam epitaxy (MBE), which is not part of UEC. Furthermore, it is quite
COmlnon for a RHEED/MBE group to invoke time-dependent plots in publications,
Were the characteristic time scales are representative of the rate for molecular layer
growth (minutes). A term like ‘Time-Resolved RHEED’ could potentially mislead
readers, since the time—resolved here refers to femtoseconds. The decision to not use
the term RHEED is to avoid this confusion, especially since RHEED/MBE pre—dates
UEC by many years. A
In Figure A.4(b), the reciprocal lattice associated with TEM, or any transmission
geometry, may not necessarily be rods, as it will depend on the sample thickness.
The accelerating voltages used in TEM are typically 100—200 kV, which has the im-
pliciii-tion that thicker samples, of order ~100 nm can be penetrated by the beam.
In transmission mode UEC, accelerating voltages are typically 55-60 kV, with film
thicknesses on the order of 20—50 nm. For example, Harb and colleagues used Si films
of thickness 30 and 50 nm with an accelerating voltage of 55 kV [325]; N ie et al. used
Iised 20 nm films of A1 with 60 kV in Reference [436]. A 20 nm Si(OOl) film will
have @150 lattice planes, which constitutes long—range order. Consequently, the rods
in Figure A.4b would need to be ‘discretized.’ Conversely, it is quite common for
TEM samples to consist of only several atomic layers, in which case the rod picture
is a’cclll‘ate. It is of little consequence, since most sf vectors tend to be parallel to

the rods in transmission geometry.

174

 

LEED TEM RHEED

llllllllllllllllllllllll

H I

ll

mums. llllllll
L (a)

    

 

 

(b) (C)

Figure A.4: Typical Ewald constructions (not to scale) for the cases of LEED (a),
transmission geometries such as TEM (b), and reflection mode geometries, such as
RHEED (c). The size of the respective Ewald spheres will be much different for these
three cases, depending on the accelerating voltage. Generally speaking, LEED would
have the smallest, followed by RHEED, followed by TEM. Ensemble wave vectors Sf
are drawn opaque. All interior angles here are 95.

Figure A.4 demonstrates the convenience and power of using the Ewald construc-
tion. Specifically, robust predictive power regarding the likelihood of satisfying diffrac-
tion COnditions for a given accelerating voltage, lattice, and geometry, is available prior
to rullliing the experiment, simply by drawing a correctly scaled picture. For exam-
ple, the large Ewald sphere in a TEM will have many intersections with the reciprocal

lattice , implying many diffraction spots. For LEED, the Ewald sphere is relatively
Small (because of the low accelerating voltage implying a small magnitude of si),
IIIear-Ling less intersections. However, the low accelerating voltages guarantee only su—
I’erfiCial penetration, meaning that for all intents and purposes, the rods stretch from
(‘00, 00). Furthermore, the cone describing the flux of scattered electrons, Sf, will

Subtend a reasonably large solid angle, thereby sweeping out all intersections within.

175

Appendix B

Femtosecond Laser Pulse

Generation

When the first working laser came into fruition in 1960, it was described as “a solution
lOOking for a problem” [437]. In UEC, it is employed in similar spirit. Namely, it serves
as a lSneans to excite the sample by introducing an intense perturbation that exists only
for only tens of femtoseconds. This is how a system is ‘kicked’ into nonequilibrium in
UEC (and in many other time-resolved techniques). The short duration of the laser
PHIse is achieved through a technique called modelocking, followed by a regenerative

amplification process to make these short burts more intense; both will be described

below -

$0-4 Modelocking

consider two flat mirrors separated by a distance L, with light of wavelength, /\
bouncing back and forth from the mirrors (L >> A). This is a simple example of
an Optical cavity. The waves will interfere in the region between the mirrors such
that St finding modes are created, with each independently oscillating mode separated

from 8.11 adjacent mode by frequency, AV = c/ 2L. This alone represents the cavity

176

 

mode structure. The insertion of a gain or lasing medium (e.g. a crystal such as
Ti:Sapphire, NszAG, LBO, etc.) into the optical cavity, causes the selection of a
r 8~11ge of energies, in the frequency domain to remain, while the rest are annihilated
(Figure B1). In this scenario, the phases of these modes are not coupled or ‘locked’
toSether. In fact, releasing them from the cavity would result in a continuous-wave
(CW) laser, in which frequency fluctuations, would lead to beating effects, resulting

111 a mode-averaging such that the output intensity is nearly constant.

 

 

ll
Gain Medium (a)
5‘
8 Optical Cavity Structure] (b)
Laser Output (c)

 

 

7

Frequency

 

 

 

Flgllre B.1: Panel (a) The frequency range (bandwidth) for an arbitrary lasing
medium, (b) standing waves created in an optical cavity, (c) the superposition of
(a) and (b), which is the laser output. The lasing medium selects only those cavity
InOdes that fall within its bandwidth.

MOdelocking is a technique that enforces a fixed phase between a cavity mode and
its S‘13—‘1‘ounding modes. There is a variety of ways to do this; the case outlined here will
be aCtiwe modelocking with an acousto-optic modulator (AOM). The gain medium,

Ti:Sapphire, has a bandwidth of z 300 nm, centered around 800 nm of (Figure B2)-
The ACM, positioned in the laser cavity, sinusoidally modulates the amplitude of

177

int ref-cavity modes. For a mode with frequency, u, modulating its amplitude with

’ . If the frequency of

a frequency 11’ will result in symmetric sidebands at V :l: u
modulation is chosen such that it coincides with the characteristic AV associated
Wi th the cavity, the central mode and the sidebands, which are driven in phase,
correspond to cavity modes. The result is that the central mode and its sidebands
are phase-locked. This operation is continued on the sidemodes until the entire cavity
consists of modes with a fixed phase relationship, which are separated in the time
domain by T = 2L / c, where T is the time for one round trip through the cavity. The
tem :poral width of each pulse (pulse-width) is inversely proportional to the number

Of modes which are oscillating in phase, N, and the mode separation, Au. Assuming

a. G aussian shape with N modes, the minimum achievable pulse-width is

0.44

 

 

 

 

1 0 Absorption Emission

2"
c
a
E‘
E
.3:
e 0.5
.9.
«E
c
a
E

0

 

 

400.5301600' 760' 860' 950.1600.
Wavelength (nm)

Figure B.2: The normalized absorption and emission spectra for Ti:Sapphire. Ab-
sorption occurs from about 400 to 650 nm; emission from 600 to 1050 nm [438].

178

In the UEC lab at MSU, a continuous wave laser (Spectra-Physics; Millennia®)
outputs a beam at 532 nm, which is used to pump the modelocked Ti:Sapphire laser
(Spectra-Physics; Tsunami®).

The Ti:Sapphire is the most commonly used lasing medium for ultrashort pulse
generation because of its wide gain bandwidth and its broad absorption band in the
blue to green range (Figure 8.2), which has the implication that it can be pumped
by a wider variety of lasers. A wider bandwidth leads to a shorter pulse, but it also
leads to an enhancement in group velocity dispersion (GVD). GVD occurs because
the index of refraction is frequency-dependentl, which results in different frequencies
having different transit times through the cavity. For a positive GVDZ, the lower
frequencies (red) lead the higher ones (blue), and vice-versa for a negative chirp. The
expression given in Equation 8.1 is said to be the transform-limited value of the
pulse—width. In actuality, tp Z 0.44/NAV. GVD is one of the primary reasons why
the pulse-width may be greater than the transform-limited value. However, pulse-
broadening due to GVD can be reversed. In the Tsunami, velocity dispersion is offset

by a series of prisms to compensate the effect.

B.O.5 Regenerative Amplification

The beam outputted from Tsunami has a repetition rate of z 80 MHz, a wavelength
near 800 nm, and is < 80 fs in duration, with each pulse carrying z 2—3 ml. Upon
exiting the Tsunami, the beam, which will be referred to as the seed laser from now
on, enters an amplifier, called the Spitfire®. Like the Tsunami, the Spitfire has
3

a Ti:Sapphire crystal in the optical cavity, however, its purpose is not the same .

The population inversion in the Spitfire is created by an external laser called the

 

1GVD is not solely caused by the Ti:Sapphire rod, but also the intra-cavity optical components.
For all materials, the index of refraction is frequency-dependent.

2This can also be called a positive ‘chirp.’

3The Spitfire can actually operate as a laser instead of a regenerative amplifier. In fact, this is
part of its optimization procedure. The primary purpose is as an amplifier though.

179

2.7!..—

 

Empower® which outputs a 527 nm pulsed4 beam at 1 kHz. The intensity of the
Empower is ultimately what controls the level of amplification.

When a Ti:Sapphire crystal is irradiated with an intense laser beam, the beam
will have a tendency to ‘self-focus’ as it travels through the crystal [439]. Consider
the scenario where the number of photons in a pulsed beam, which is conserved, is
travelling enveloped in a beam whose area is shrinking from the self-focusing effect.
The concentrated energy per unit area, or fluence of the beam will continuously
increase as the beam traverses the crystal, which can quickly overwhelm the crystal
and ultimately damage it. To use the Ti:Sapphire crystal to amplify the pulse, it
is first necessary to decrease the duration of the seed pulse, or stretch it, to avoid
damaging the crystal. When an ultrashort pulse is stretched, its peak intensity is
reduced. This allows for safe passage through the Ti:Sapphire crystal where it is
amplified. Upon passage through the crystal, the amplified pulse is still longer than
what the Tsunami fed in, so the third task for the Spitfire is to compress the pulse back
down to ultrashort, thus completing the regenerative amplification cycle. This process
is called Chirped-Pulse Amplification (CPA) because stretching the pulse in the time
domain is equivalent to introducing a frequency chirp. To reiterate, the three stages
are (Figure BB): (1) stretch the seed laser to keep it from damaging the Ti:Sapphire
crystal, (2) pass it through the Ti:Sapphire crystal and allow amplification (the crystal
being pumped by Empower) (3) compress the pulses back down. The Spitfire output
is what will eventually pump the sample. Its repetition rate is controlled by Empower.

Note, from Tsunami to Spitfire, the conversion was

 

 

Tsunami Spitfire
2 ml per pulse __) 2.5 ml per pulse
80 MHz 1 kHz

 

4The repetition rate of the Empower is user controlled between 50 Hz and 10 kHz. Increasing
the rep. rate will decrease the energy per pulse.

180

 

High repetition rate lasers are frequently (pardon the pun) employed in pump-
probe studies, sometimes putting them at a disadvantage. Consider how often a laser
with repetition rate of 80 MHz will pump a a sample: every 12.5 ns. Some systems
are not completely relaxed in 12.5 us (which will be discussed further in Chapter 5).
For now, just note that 1 kHz is beneficial in that it does not run the risk of pumping
the residual level associated with some effect, unless that effect has not relaxed by 1

ms and it allows for much higher degrees of excitation to a system since it is amplified.

 

 

 

 

 

Stretcher > Amplifier Compressor ——>-

A—p AaA—y

V

 

 

 

 

 

 

 

 

 

 

 

Low Power Reduced Power Amplified High Peak Power
Short Pulse Stretched Pulse Stretched Pulse Compressed Pulse
(Pulses not to scale)

Figure B3: The seed pulses are stretched (in time) prior to amplification as to not
damage the Ti:Sapphire crystal, followed by amplification in the Ti:Sapphire crystal.
Finally they compressed back down after amplification. [440]

181

 

Appendix C

Thermophysical Properties of

Selected Metals

 

 

 

Au Ag Cu Pt Al Ni
C, 2.49 2.47 3.45 2.86 2.42 3.95 (x106 J . m—3 K4)
is,- 317 429 401 716 237 907 (Wm—1K—1)
T,- 36.4 39.2 15.4 70.7 7.1 18.9 (ps)
7 67.6 62.5 71.0 748.1 91.2 1077.4 (Jim-3K-1 )
2.5 2.8 10.0 110.0 31.0 105.0 (x1016 W-m-3K—1)
0.93 0.96 0.96 0.72 0.87 0.69
as 12.7 14.5 12.1 12.8 7.5 14.5 (nm)

 

Table 0.1: The thermophysical properties for gold, silver, copper, platinum, alu-
minium, and nickel. The values of 63 and R are given at 800 nm (1.55 eV). Acquiring
them for other wavelengths is quite simple by just gathering the complex index of
refraction values (n and n) from the various physical and chemistry handbooks [195],
and using 63 = A/47m. Experimentally gathered reflectivities are available in Refer-

ence [195].

182

 

 

Appendix D

Complex Index of Refraction for

Au and Ag

 

 

 

 

Au Ag

A (nm) n n n K
1938 0.240 14.080 0.920 13.780
1610 0.560 11.210 0.150 11.850
1393 0.430 9.519 0.130 10.100
1216 0.350 8.145 0.090 8.828
1088 0.270 7.150 0.040 7.795
984 0.220 6.350 0.040 6.992
892 0.170 5.663 0.040 6.312
821 0.160 5.083 0.040 5.727
756 0.140 4.542 0.030 5.242

105 0.130 4.103 0.040 4.838

 

Table D.1: The complex index of refraction 77. = n + in for Au and Ag at various
Wavelengths, from Johnson and Christy ( 1972) [370] (continues on next page).

183

 

 

 

 

Au Ag
A (nm) n K. n K:
660 0.140 3.697 0.050 4.483
617 0.210 3.272 0.060 4.152
582 0.290 2.863 0.050 3.858
549 0.430 2.455 0.060 3.586
521 0.620 2.081 0.050 3.324
496 1.040 1.833 0.050 3.093
471 1.310 1.849 0.050 2.869
451 1.380 1.914 0.040 2.657
431 1.450 1.948 0.040 2.462
413 1.460 1.958 0.050 2.275
397 1.470 1.952 0.050 2.070
382 1.460 1.933 0.050 1.864
368 1.480 1.895 0.070 1.657

 

Table D.2: Au and Ag complex index of refraction (continued from previous page).

184

 

 

 

 

 

Au Ag
A (nm) n K: n It
354 1.500 1.866 0.100 1.419
343 1.480 1.871 0.140 1.142
332 1.480 1.883 0.170 0.829
320 1.540 1.898 0.810 0.392
311 1.530 1.893 1.130 0.616
301 1.530 1.889 1 .340 0.964
292 1.490 1.878 1.390 1.161
284 1.470 1.869 1.410 1.264
276 1.430 1.847 1.410 1.331
269 1.380 1.803 1.380 1.372
262 1.350 1.749 1.350 1.387
255 1.330 1.688 1.330 1.393

 

Table D3: Au and Ag complex index of refraction (continued from previous page).

185

 

 

 

 

Au Ag
A (nm) 72 I6: n r»:
249 1.330 1.631 1.310 1.389
243 1.320 1.577 1.300 1.378
237 1.320 1.536 1.280 1.367
231 1.300 1.497 1.280 1.357
226 1.310 1.460 1.260 1.344
221 1.300 1.427 1.250 1.342
216 1.300 1.387 1.220 1.336
212 1.300 1.350 1.200 1.325
207 1.300 1.304 1.180 1.312
203 1.330 1.277 1.150 1.296
199 1.330 1.251 1.140 1.277
195 1.340 1.226 1.120 1.255
192 1.320 1.203 1.100 1.232
188 1.280 1.188 1.070 1.212

 

Table D4: Au and Ag complex index of refraction (continued from previous page).

186

 

Appendix E

Riccati—Bessel Functions

The Riccati-Bessel functions 101(2) and X1017) are given in terms of the conventional

Bessel functions of the 1st and 2nd kinds, Ja(:c), and Ya(x), respectively:

iM117) = gain—U203): (E.1)

>46) = —\/§n+1/2<w>, (E2)

and
7”(913) = g (Jl+1/2(~T) —in+1/2(1‘)) = 101(2) + ixz($)o (E3)

The first and second Bessel functions are

(E.4)

 

0° (_1)m g; 2m+a
Ja(l‘) = 20 m!1"(m + a +1) (2)

m:

and
Ja(:c) cos(a77) - J_a(x).
sin(onr)

 

Ya(:z:) =

187

 

Derivatives satisfy the convenient relationship

2.100 = 20.40:) -— 9% (E6)

.7:

where Za could be Ja or Ya. If a is integer, the following relationship is also valid:

Z—a(5’3) = (-1)O‘ Z042). (E7) 71

 

188

 

Appendix F

Two-Temperature Model

Computer Program

 

 

! This program solves the Two-Temperature Model for metals

! with non-Fourier heat transfer for the heat flux.

 

! UNITS: MKS

 

 

! COMPILES: Fortran 90, (f90,f95,gfortran,g95,ifort,etc.)

 

! CALLS: nrtype.f90

 

! CODED BY: Ryan A. Murdick (5/20/2006)

! (rmurdicngmail.com)

 

 

USE nrtype;
IMPLICIT NONE

189

REAL(DP),ALLOCATABLE :: Te(:),Ti(:),Qe(:),Qi(:),
TeStar(:),TiStar(:),QeStar(:),QiStar(:)
REAL(DP) F,1ambda,tp,tm,ds,R,Ki,Ci,Ce,Ke,G,tau_i,tau_e,
gam,gauss,TO,dt,dz,thick,time,t,tt,z,zz,S,C(50)

INTEGER(I4B) n,k,nt,nz

LASER

 

 

F=1000.0_DP
tp=45.0D-15
tm=2.0_DP*tp
ds=15.3D-9
R=O.93_DP

gauss=4.0-DP*DLOG(2.0_DP)

MATERIAL (Au)

 

 

 

Ki=317.0_DP
Ci=2.5D6
tau_i=38.7D-12
tau_e=40.0D-15
G=2.6D16
gam=70.0_DP

DIMENSIONS / RUN TIME

 

 

! (input these)

190

thick=100.0D-9

nz-101

time=5.0D-12

dt=5.0D-17

! (leave these alone)

dz=thick/(nz-1)

nt=NINT(time/dt)+1
ALLOCATE(Te(nz),TeStar(nz),Ti(nz),TiStar(nz),Qe(nz),

Qi(nz),QeStar(nz),QiStar(nz))

INITIALIZE

T0=298.0_DP

DD k=1,nz
Te(k)=TO
TeStar(k)=TO
Ti(k)=T0
TiStar(k)=TO
Qe(k)=0.0_DP
QeStar(k)=0.0_DP
Qi(k)=0.0_DP
QiStar(k)=0.0_DP

ENDDO

SPEED-UP CONSTANTS

C(1)=sqrt(gauss/PI_D)*(1-R)/(tp*ds)*F

191

C(2)=1.0_DP/ds
C(3)=gam/tp**2
C(4)=1.0_DP/dz
C(5)=-dt/dz
C(6)=dt*G
C(7)=dt/dz/Ci
C(8)=dt*G/Ci
C(9)=1.0_DP-dt/tau_i
C(10)=Ki*dt/tau_i/dz
C(11)=dt/tau_i/dz
C(12)=Ki/dz
C(13)=2.0_DP*dt*Ki/dz**2/Ci

IF(C(13) >= 1.0_DP) PRINT*, ’UnStable Courant’

0PEN(unit=20,file=’T_time.dat’)

SOLVE

 

 

! (begin time lOOp)
DO n=1,nt
t-(n-1)*dt
! (begin space loop)
D0 k=2,nz-1
z=(k-1)*dz
S=C(1)*DEXP(-C(2)*z)*DEXP(-C(3)*(t-tm)**2)

! Predictor Step

192

*

 

! _ _____
Cesgam*Te(k)
TeStar(k)=Te(k)+(C(5)*(Qe(k)-Qe(k-1))
-C(6)*(Te(k)-Ti(k))+dt*S)/Ce
TiStar(k)=Ti(k)-C(7)*(Qi(k)-Qi(k-1))
+C(8)*(Te(k)-Ti(k))
QeStar(k)=Qe(k)*(1.0_DP-dt/tau_e)
+C(5)*Ke/tau_e*(Te(k)-Te(k-1))
QiStar(k)=Qi(k)*C(9)-C(10)*(Ti(k)-Ti(k-1))
Ke=Ki*TeStar(k)/TiStar(k)

! Corrector Step

 

Ce=gam*TeStar(k)

Te(k)=0.5_DP*(Te(k)+TeStar(k)
+(C(5)*(QeStar(k+1)-QeStar(k))
-C(6)*(TeStar(k)-TiStar(k))+dt*S)/Ce)

Ti(k)=0.5_DP*(Ti(k)+TiStar(k)
-C(7)*(QiStar(k+1)-QiStar(k))
+C(8)*(TeStar(k)-TiStar(k)))

Qe(k)=0.5_DP*(QeStar(k)*(1.0_DP-dt/tau_e)+Qe(k)
+C(5)*Ke/tau_e*(TeStar(k+1)-TeStar(k)))

Qi(k)=0.5_DP*(QiStar(k)*C(9)+Qi(k)
-C(10)*(TiStar(k+1)-TiStar(k)))

Ke=Ki*Te(k)/Ti(k)

ENDDO

! (spatial loop done)

193

F.1

! Boundary Conditions

 

Te(1)=Te(2)

Ti(1)=Ti(2)
TeStar(1)=TeStar(2)
Te(nz)=Te(nz-1)
TeStar(nz)=TeStar(nz-1)
Tian)=Ti(nz-1)
TiStar(nz)=TiStar(nz-1)
tt't’l‘l .0D12

WRITE(20,*) tt,Te(1),Ti(1)
ENDDD

! (time loop done)
CLOSEC20)

STOP

END

Non-Thermal Electrons Subroutine

 

This subroutine calculates non-thermal electron
scattering channels. Call from a TTM or Boltzman
transport program, just replace your laser source

like in Carpene (2006)

 

194

COMPILES: Fortran 90, (f90,f95,gfortran,g95,ifort,etc.)

 

 

CALLS: nrtype.f90, and your favorite integration
subroutine (Simpson’s rule, etc.)

Replace the calls to INTEGRATE below.

 

CODED BY: Ryan A. Murdick (7/17/2009)

(rmurdicngmail.com)

 

NOTES: Make sure your source heating term has
gaussian shape with max at

three pulse-widths. This is not checked for

 

SUBROUTINE NON_THERM (t,dt,ll,tp,Ef,h_nu,Tau_ep,wp,
NN,Ree,Rep)

USE nrtype;

IMPLICIT NONE

INPUT/OUTPUT DECLARATION (GLOBAL)

 

REAL(DP),INTENT(IN) :: t,tp,Ef,h_nu,Tau_ep,dt
INTEGER(I4B),INTENT(IN) :: NN,11
REAL(DP),INTENT(OUT) :: Ree,Rep

BEGIN LOCAL DECLARAION

 

REAL(DP),ALLOCATABLE :: arg1(:),arg2(:)

195

 

REAL(DP) beta,TauO,wp,tm,Tee,c1,c2,c3,
* c4,c5,c6,tt,P,Hee,Hep,sml,h_nu2

INTEGER<I4B> nt,i

 

Tau0=128.0-DP/(PI_D**2*3.0_DP**O.5_DP*wp)
tm=3.0_DP*tp

beta=4.0_DP*DLOG(2.0_DP)
!h_nu2=h_nu-1.1_DP*e

h_nu2=h_nu

c1=1.0_DP
c2=h_nu2**2/Ef**2/Tau0+1.0_DP/Tau_ep
c3=h_nu2**2/Ef**2/Tau0

c4-Ef**2*Tau0

c5-h_nu2**2

sml=1.0D-2O

 

Since the pulse is only defined from " O to 5*tp,
we can safely integrate Hee(t-tt)*P(tt) from 0 to t,

even though mathematically it should be -infinity to t

Integrate 5 pulse-widths (-2.5:2.5) tp
(Sufficient for Gaussian)

dt=5.0_DP*tp/(1.0_DP*NN)

Set the upper integration limit

"t" was read in by the routine, make sure

196

nt reflects t.
nt=NINT(t/dt+1.0)
PRINT*,ll
ALLOCATE(arg1(ll),arg2(ll))
INTEGRATE {P(tt) H(tt), tt 2 O..t}
(tt is the dummy integration variable)
DO i=1,ll
tt=(i-1)*dt
P=DEXP(-beta*(tt-tm)**2/tp**2)
Hee=-DEXP(-(t-tt)*c2)/(t-tt+sml)**2*(
c5*(t-tt)+c4*(1.0_DP-DEXP(c3*(t-tt))))
arg1(i)=P*Hee
Hepa-DEXP(-(t-tt)*c2)/((t-tt+sm1)*Tau_ep)*
c4*(1.0_DP-DEXP(c3*(t-tt)))
arg2(i)=P*Hep
IF(11<=10) PRINT*,’ll,i,Hee’,ll,i,Hee
ENDDO
CALL INTEGRATE(arg1,ll,dt,Ree)
CALL INTEGRATE(arg2,ll,dt,Rep)

[Ree/(hv)“2] is dimensionless

 

DEALLOCATE(arg1,arg2)

 

END SUBROUTINE NON_THERM

197

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