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Optical studies of alkalides and electrides.

presented by
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OPTICAL STUDIES OF ALKALIDES AND ELECI'RIDES

by

Chin g-Tung Kuo

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1994

ABSTRACT
OPTICAL STUDIES OF ALKALIDES AND ELECTRIDES
b y

Chin g-Tung Kuo

A high vacuum system was built for photoemission
measurements. The system allows one to load alkalides and
electrides under vacuum and at low temperatures with minimum
contact with air or moisture. The vacuum of the measuring system
can reach better than 10'8 torr. The temperature of the sample
holder can be controlled to i 2 °C and cooled down to -l30 °C. The
lOOO-W xenon light source is monochromatized, and light in the
range from 200 to 900 nm is used. The response time of the system
is z 40 ms, and the gain of the preamplifier is 109. A data acquisition
system is employed to control the scanning monochromator and the
electrometer, and to record data with respect to wavelength or time.

The quantum yield spectra of the alkalides, K+(15C5)2-K',
Rb+(15C5)2-Rb', Na+c222-Na-, K+c222-K-, CS+C222°CS‘ and K+C222-Na-
, Show the common features of main emission peak at an energy
higher than 4 eV and a low energy tail, and sometimes the high
energy peak has a shoulder on the low energy side and peaks at

lower energies. The high energy peak is less temperature dependent

and is assigned as the emission from the valence electrons. The low
energy emission strongly depends on temperature and the
experimental conditions, and is presumed to be emission of trapped
electrons. Photoemission threshold energies were determined, and
depend not only on the alkali metal anion but also on the
environment in which the anions reside.

Laser pulses had appreciable effects on polycrystalline
Na+C222-Na' samples. Most samples of Na+C222-Na' contain both
defect sites and defect electrons. As a result, the photoemission
spectrum yields an additional shoulder at 360 nm ( 3.4 eV) and
peaks and shoulders in the range of 500 - 700 nm, besides the main
emission peak of Na‘ at 290 nm (z 4.3 eV). The 6 ns, high intensity
laser pulses result in transient depletion of shallowly trapped
electrons and/or occupancy of defect sites, and also lead to apparent
modifications of the surface layers. Two kinetic models are
developed to explain the mechanisms of the photobleaching effects
and population-depopulation of defect electron traps.

In order to study the anisotropic properties of Na+C222-Na',
nearly-normal incidence reflectivity on various faces of single-
crystal Na+C222~Na' was measured in the photon energy range 0.5-
3.1 eV. The polarization-dependent spectra were determined for the
electric field vector parallel and perpendicular to the C axis, based on
the orientation-dependent results, known structure and the shapes
of the single-crystals. A Kramers-Kronig analysis of the reflectivity
yielded the spectral dependence of the real and imaginary parts of
the complex dielectric constant and refractive index, as well as the

absorption coefficient and the energy loss function. Comparison of

the polarization-dependent spectra permitted identification of the
orientation-dependent interband transitions. A peak with energy
1.64 eV appears irregularly, which is presumably due to trapped
electrons. The polarization dependence of the spectra provide us
with further insight into the nature of anisotropic energy states of

Na+C222-Na'.

ACKNOWIEDGMENTS

I would like to express my appreciation to Dr. James L. Dye for
his constant guidance and support during this course of project. I
would like to thank Dr. William P. Pratt for his advice on many
aspects of this work. I would also like to thank Dr. John L. McCraken
for his help in correction of this thesis.

I would also like to thank all the members in Dr. Dye’s research
group with whom I worked with, in particular Dr. James L.
Hendrickson. I would also like to thank Dr. kuo-Lih Tsai for his help
in beginning of my synthesis.

I would also like to express my appreciation to electronic
specialist Martin Rabb for his help in designing the electronics and in
solving electronic problems. I would also like to thank machinist
Thomas Palazzola for his help in building the vacuum system. I
would like to thank master glassblowers Manfred Langer, Scott
Bancroft and Keki Mistry, who built and repaired numerous glass
cells for this work.

I am grateful to receive financial support from National Science

Foundation grants No. DMR 90-24525.

TABLE OF CONTENTS

 

Bags:
TABLE OF CONTENTS ........................................................................ VI
LIST OF TABLES ........................................................................... VIII
LIST OF FIGURES .............................................................................. IX
CHAPTER I: INTRODUCTION AND BACKGROUND. . . ......................... 1
LA. Introduction to Alkalides and Electrides ..................................... 1
LB. Trapped Electrons in Frozen Glasses and Optical
Photobleaching effects .............................................................. 7
LC. Ultraviolet Photoelectron Emission ............................................ 11
I.Cl. Instruments for Ultraviolet Photoemission
Spectroscopy. ................................................................ 12
I.C2. Quantum Yield Spectra and Energy Distribution
Curves. ......................................................................... 18
I.C3. Work Function ........... ................................. . ........ . ......... 22

I.C4. Direct and Indirect Transitions in Photoemission..............27

CHAPTER II: THE PHOTOEMISSION APPARATUS AND

PHOTOEMISSION STUDIES ................................................................ 32
11A. Introduction ............................................................................ 32
IIB. Description of the System ......................................................... 35

11.81. General Aspects of Design ...................................... . ........ 35
II.B2. The Vacuum System ....................................................... 37
II.B3. Temperature Control ....................................................... 39
11.84. Electronic Systems .......................................................... 42
[1.85. Data Acquisition Methods ............................................... 42
II.B6. Optical System ............................................................... 47
II.C. Experimental ............................................................................ 47
II.Cl. Sample Preparation ........................................................ 47
II.C2. Measurements ................................................................ 48
MD. Results and Discussion .............................................................. 50

vi

CHAPTER III: THE PHOTOELECTRON EMISSION FROM Na+C222-Na‘:

EFFECTS OF LASER PULSES .......................................... 75
III.A. Introduction ........................................................................... 75
III.B. Experimental ........................................................................... 79
III.C. Results ......... . ........................................................................... 82
III.D. Discussion ................................................................................ 90
III.D. Conclusions ........................................................................... 108

CHAPTER IV: REFLECTANCE STUDIES OF SODIUM CRYPTAND [2.2.2]

SODIDE ...................................................................... 1 10
IV.A. Introduction ......................................................................... 111
IV.Al. The Kramers-Kroni g Relations ................................... 115
IV.A2. The Optical Dispersion Theory ................................... 118
IV.A3. Procedure and Approximations for Kramers—Kronig
Applications .............................................................. 1 19
IV.B. Experimental ........................................................................ 120
IV.C. Results and Discussion .......................................................... 126
IV.D. Conclusions .......................................................................... 146
CHAPTER V: CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK.
V.A. Conclusions ............................................................................ 147
V.B. Suggestions for Further Works ............................................... 152
APPEN DIX ...................................................................................... 152
REFERENCES .................................................................................... 166

vii

2-1

4-1

LIST OF TABLES

£3.25

ASCII codes for the monochromator-computer interface. .......45
The photoemission threshold energies of the valence
bands of alkalides and the work functions of the

corresponding alkali metals. ................................................. .62

Important physical parameters and equations for a

medium. ............................................................................. l 1 8
Equations for calculation of the optical constants. ................ 124
Polarized and non—polarized studies of Na+C222-Na'. ........... 144

viii

1-1

1-2.

1-3

2-3

2-4

LIST OF FIGURES

Bass
Representative complexants a) lS-crown-5 (15C5) b)
cryptand[2.2.2] (C222) c) pentamethylpentacyclen
(PMPCY). ............................................................................... .2
Comparison of PE spectra: a) the integral form of a
spectrum generated by retardation, b) the energy
distribution curve spectrum obtained by differentiation
of spectrum in a. .................................................................. l 6
The structures of deflection electron energy analyzers:
(a) 127 ° cylindrical deflector; (b) electrostatic mirror. ........ 18
Schematic representation of the three-step model for
the photoemission process. .................................................. 19

Effect of band bending on the threshold for photoemission. ..21

Correction of the binding energy 55w for metal and
nonmetal samples. ............................................................... 24

Schematic representations of indirect and direct transitions. .29

Schematic view of the photoemission apparatus. .................... 36
Block diagram of the photoemission spectrometer. ................. 38
The structure of the vertical wand. ........................................ 40

The stabilizing rate and precision of temperature
control of the sample holder. ................................................ 41

The circuit of the spectrometer. ............................................. 43

ix

2-6

2-7

2-8

2-9

2-10

2-11

2-12

2-13

2-14

2-15

2-16

2-17

2-18

2-19

Schematic view of sample loading and transportation. ........... 49
Quantum yield spectrum of K+(15C5)2-K' at -60 °C. ................ 51
Quantum yield spectrum of Rb+(15C5)2-Rb‘ at -60 °C. . ........... 52

Photoemission quantum yield spectra of

nearly defect-free crystals of Na+C222-Na' at -60°C .............. 53
Quantum yield spectrum of K+C222.K' at -60 °C. .................. 54
Quantum yield spectrum of Cs+C222-Cs ' at -60 °C. .............. 55
Quantum yield spectrum of K+C222oNa' at -60 °C. ................ 56

Normalized decrease in the photoemission intensity
at various wavelengths with changes in temperature

for K+(15C5)2-K'. ................................................................ 58
Quantum yield spectrum of K+C222-e' at -60 °C. .................. 64
Quantum yield spectrum of K+(15C5)2-e' at -60 °C. .............. 65
Quantum yield spectrum of Cs+(18C6)2-e' at -60 °C. ............. 66

Quantum yield spectrum of Na+C222-Na‘ (with trapped
electrons present) at -60 °C. ............................................... 68

The reduction of the photoemission quantum
yield spectrum of Na+C222-Na' as a function of
the magnetic field. ............................................................. 71

The normalized reduction of the photoemission
intensity of Na+C222-Na' at different wavelengths
as a function of the magnetic field. ....................... . ............ 72

2-20 The time-stability of photoemission from Na+C222-Na'

3-1

3-2

3-3

3-4

3-5

3-6

3-8

at -60 °C. ........................................................................... 73

The photoelectron emission current of Na+C222-Na'
at 400 nm and -60 °C versus imposed bias voltage. ............. 81

Photoemission quantum yield spectra of a Na+C222-
Na" polycrystalline sample at -60 °C. ............. . ................. 84

The response of the photoelectron emission current at -60 °C of
a Na+C222-Na' polycrystalline thin sample to successive 532
nm laser pulses as analyzed with 400 nm xenon light. ......... 86

The response of the photoelectron emission current of a
Na+C222-Na' polycrystalline thin sample to successive 532 nm
laser pulses as analyzed with 600 nm xenon light. .......... 87

Growth of the photoelectron emission current of Na+C222-Na’ at
600 nm after 532 nm laser pulses at three temperatures. ....88

Linear dependence of the photoelectron emission current of Na‘
C222-Na' (open squares) and of the recovery rate constant
(crosses in squares) on the 600 nm xenon light intensity after
532 nm laser pulses. ............................................................ 89

(a) Photoemission from Na+C222-Na' at 500 nm xenon

light and -60 °C after the laser pulse, (b) the

combination of the electron emissions at 400 nm

and 600 nm after the laser pulses. ...................................... 91

Energy diagram of Na+C222-Na‘ related to photoelectron
emission. The solid curve is the excess quantum yield that
results from a number of laser pulses with 600 nm xenon
analyzing light, plotted versus energy, and is obtained

from the data shown in Figure 3-2. ..................................... 93

xi

3-9 Sequence used to determine the thermal decay rate of
Na+C222-Na’ in the absence of laser pulses. ........................ 97

3-10 Decay and growth of the photoelectron emission current of
N a+C222-Na' after a 532 nm laser pulse at ~30 °C with analysis
by 600 nm xenon light. ...................................................... .99

3~11 The least-squares fit of three successive photoelectron
emission growth signals of Na+C222-Na' after 532 nm laser
pulses at ~60 °C by Equation 23-10, a double exponential
function in which the slower rate constant is not adjusted,
but is determined from the growth rate prior to laser
irradiation .......................................................................... 105

3~12 The effect of 1063 nm weak laser pulses (10 Hz) on the
photoelectron emission current of Na+C222-Na‘ at ~60 °C
during and after illumination with 400 nm xenon light. ...107

4~1 Contour for the Cauchy Principle Value integral. ............... .113

4~2 Schematic diagram of the refractive microscope system. ....122

4~3 Reflectance spectra of a single-crystal of Na+C222-Na'
at=s ~60 °C. ...................................................................... .127

4~4 Temperature-dependent reflectance spectra of
Na+C222-Na'. ................................................................... .128

4~5 Reflectance Spectra of single-crystal Na+C222-Na' at =3 ~ 60 °C
with various small tilt angles of the surface plane. ............129

4~6 Near-normal incidence reflectivity of single-crystal
Na+c222-Na- for El/C and he at = - 60 °C. .................... .131

xii

4~7 Absorption spectra of a polycrystalline thin film of

4~8

Na+C222-Na'with a thickness of 930 A at z ~ 60 °C.
(Data of J. E. Hendrickson [86]) ........................................... 132

Spectral dependence of the derived extinction coefficient k of

single-crystal Na+C222-Na' for El/C and EiC
at z - 60 °C. ........................................................................ 133

4~9 Absorption coefficient of single-crystal Na+C222-Na‘ for E/IC

4~10

4-11

4~12

4-13

4~14

4~15

4~16

and Eic at== ~60 °C. ................................. . ....... . ........... ....134

Spectral dependence of the real part of the refractive index n
of single-crystal Na+C222-Na' for El/C and ELC

at = ~ 60 °C. ....................................................................... 136
Spectral dependence of the real part of the dielectric function
a, of single-crystal Na+C222-Na' for E/IC and ELC

at == ~60 °C. ........................................................................ 137
Spectral dependence of the imaginary part of the dielectric
function 82 of single-crystal Na+C222-Na' for El/C and EiC
at --— ~60 °C. ........................................................................ 139
Spectral dependence of the energy loss function, ~Im(e“), of
single-crystal Na+C222-Na' for E/IC and ELC

at as ~ 60 °C. ........................................................................ 140
Spectral dependence of extinction coefficient k of single-crystal
Na+C222-Na‘ at ~ ~ 60 °C. ................................................... 141
The spectral dependence of the extinction coefficient of single-

crystal Na+C222-Na’ at z ~ 60 °C. ....................................... 143

The reflectance spectrum obtained from Kramers-Kronig
conversion of the absorption spectrum in Figure 4~7. .......145

xiii

CHAPTER I
INTRODUCTION AND BACKGROUND

I.A. Introduction to Alkalides and Electrides

Two new classes of compounds, with very special reactions and
properties, have been synthesized in Dye’s laboratory and named
alkalides and electrides. The general formula for alkalides is M+C-M';
the stable alkali metal cations, M+, are complexed and caged in
macrocyclic molecules represented here by C, whereas the counter-
ions, M”. can be stable and exist outside the cage to balance the
charges. The metal cation and “anion in a compound can be the same
element or can be different. If they are different, the electron
affinity of the anionic element and the complexation constant of that
which forms the cation will determine the direction of charge
transfer. Electrides have the general formula M+C-e', where the
electrons serve as anions to balance the positive charges. The
macrocyclic complexants that have been used are cryp[tands, crown
ethers, and more recently, the aza- based cryptands and cyclens.
Examples of these complexants are shown in Fig. 1~1.

The synthesis and study of alkalides and electrides has been
continuing for the past twenty years. Since 1974, more than 30
alkalides and 5 electrides have been synthesized and characterized.
The first crystalline alkalide was Na+C222~Na'~ which was crystallized
from amine solutions that contained sodium and cryptand[2.2.2]

(C222) [1]. Although many alkalides and electrides have been

2

synthesized in Dye’s laboratory, Na+C222-Na' is still the most stable
and the one that has been most thoroughly characterized [2-4]. The
first crystalline electride is Cs+(l8C6)2e' which is formed by
carefully controlling the 1:2 stoichiometric ratio of cesium to crown
ether, 18C6. In this electride, the electron e' apparently resides in
the otherwise empty anion cavity.[5] That is, the electron density is
centered in this cavity although some electron density undoubtedly

spreads onto the surrounding complexant molecules.

Figure l-1. Representative complexants a) 15~crown~5 (15C5) b)
cryptand[2.2.2] (C222) c) pentamethylpentacyclen (PMPCY).

Syntheses of alkalides and electrides are quite Straightforward
because the experiences and procedures have been well established
[8]. The main technique for the synthesis is that the reaction and
crystallization have to be carried out under vacuum at low
temperature. The procedures can be generalized by several steps.

First, a proper ratio of alkali metal and complexant are introduced

3

into the reaction cell in a helium glove box, then the metal is
evaporated to form a mirror to increase the reaction surface. A well
purified solvent such as methylamine or dimethylether is added as
the first solvent. Trimethylamine or diethylether is then used as the
second solvent to reduce the solubility of the complex, M+C-M' or
M+C-e‘. The crystal product can be obtained by precipitation from a
saturated solution by either slow removal of the more volatile and
more polar solvent or slow-cooling of the whole system. The details
for the syntheses have been described in the references [6,7].

The alkalides and electrides are sensitive to decomposition by
air, moisture or elevated temperatures, so they have to be handled
and stored at low temperatures and in an inert or vacuum
environment. In spite of these restrictions, their physical
characteristics have been examined by various methods; among
these are the optical, EPR and NMR spectra, conductivity and
magnetic susceptibility.

The EPR method provides opportunities for detecting both the
existence of trapped electrons and the environment of the trapping
sites. For example, if the cations are well-shielded within a cryptand
cage or a crown ether sandwich, there is no hyperfine splitting in the
EPR spectrum. This results from the weak interactions between the
trapped electrons and many surrounding cations. But when the
cation forms an ion-pair with the anion, then the hyperfine coupling
to a single cation becomes appreciable. For example, the well-
resolved EPR spectra of K+(18C6)-Na' and Rb+(18C6)-Na‘ Show
hyperfine splittings indicating the presence of ion-pairs, M+-Na', in

these compounds [8].

4

In early studies of alkalides, the NMR method was used to
identify the presence of the species M+ and M', based on the
interpretation of the chemical shift behavior. For example, the 23Na
NMR spectrum of Na+(C222)-Na' in solution has the same chemical
shifts of Na+ and Na' as the MAS solid state spectrum of the
polycrystalline sample [9,10]. The spectrum of Cs+(18C6)2-Na' only
shows the peaks of C84” and Na', which means that this is the right
formula instead of a mixture of ceside and sodide [11]. Later, the
NMR method was extended to Study the nature of electron-trapping
in electrides and the temperature effects of phase transitions and
Structural disorder [12].

The electrical conductivities of all alkalides have an exponential
dependence on 1/T that makes the alkalides behave as apparent
semiconductors, where T is the temperature. However, the band gap
obtained is generally too low and is dependent on the preparation,
meaning that the conductivity is extrinsic instead of intrinsic, and is
due to the presence of trapped electrons with energy states in the
gap [13]. The only alkalide which can be crystallized nearly free of
defect electrons is Na+C222~Na', which has a band gap of 2.4 eV,
obtained from both powder and two-probe single crystal
measurements [2]. Conductivity measurements of the electrides,
Cs+(18C6)2-e‘ and Cs+(15C5)2-e', showed that, in addition to defect
electronic conductivity, cationic conductivity is present. The
transport process is referred as a Cs-Cs+ exchange, and the cesium
cation was apparently reduced to metal and deposited on the cathode

[14]. The electride K+C222-e‘ has a much higher conductivity (a: 1010

5
times higher) which may be due to the “chained” dimer electrons
along with the channel vacancies [l6].

Temperature-dependent magnetic susceptibility
measurements provide very useful information regarding the inter-
electron interactions. For example, both the electrides CS+(15C5)2-e‘
and Cs+(18C6)2~e' have antiferromagnetic properties whose Neel
temperatures are dependent on the annealing history. The
phenomenon was interpreted as being due to the movement of the
complexant molecules to block the channels, or to the presence of CS',
which decreases the electron-electron interactions [15]. The
magnetic susceptibility of K+(C222)-K' changed with an increase in
temperature from essentially diamagnetic to partially paramagnetic,
which was interpreted as due to a thermally populated triplet state
lying 0.03 to 0.05 eV above the ground state at 200 K [16].

The most extensive studies applied to the alkalides and
electrides are optical methods. In the earlier studies only the
absorption spectra of thin films was measured; later, other optical
techniques, such as photoluminescence [4,17], photoemission [18],
and reflectance [19] were adopted to study solid samples. The
absorption spectra revealed information on the energies of band-
band and/or band-continuum transitions for the metal anions, M‘,
which led to the identification of the absorbing species by comparing
the absorption spectra of both solutions and polycrystalline films.
The ground state of the metal anion, M', is ns2,which constitutes the
valence band. The band-band and the band-continuum transitions
are presumed to be us2 —> nsnp and n52 —> continuum, respectively.

The n52 -9 nsnp transitions of M' in M+C222-M‘ films are at 650 ,

6

840, 860 and 950 nm for Na‘, K", Rb' and CS', respectively [3]. The
nsZ—) continuum transition of Na+C222-Na' polycrystalline films
appears as a shoulder in the spectrum at 500 ~550 nm (~23 eV). A
small high energy peak is also present at 400 nm (3.1 eV) with a
fixed intensity ratio with respect to the main peak, and it has the
same direction of shifts as the main peak following a change of
temperature. The species has not been identified, but may be due to
the transition from the valence band to the vacuum level. The
optical absorption of electride films showed the presence of two
classes, which are called “localized” and “delocalized”. Most electrides
have a distinct absorption peak in the near infrared region that
results from the localization of trapped electrons. However, the
absorption spectrum of K+C222-e' has a characteristic “plasma edge”,
which is similar to that of concentrated liquid solutions of Na in
ammonia. In such spectra, the absorbance increases throughout the
visible towards the infrared and remains high in the infrared. The
electrons in K+C222-e' are suggested to be somewhat delocalized, due
to the overlap of the wave functions of trapped electrons with
adjacent trapped electrons. But the presence of partial localization or
grain-boundary effects could be the source of activated conductivity
rather than true metallic behavior.

A short laser pulse on the alkalides is able to produce
luminescence [17]. The luminescence spectra were temperature
dependent, giving red shifts with an increase in the temperature;
also, the intensities dramatically decreased as the temperature
increased. The quantum yields were affected by the amount of

defect trapped electrons in the samples; samples with fewer defects

7

had higher yields. For Na+C222-Na'~ the fluorescence peak position
varied with temperature from 1.854 eV at 7 K to 1.828 eV at 80 K
[4], when it was illuminated by a 50 picosecond dye laser with
energies between 2.2 and 2.0 eV. The time-resolved spectra were
deconvoluted by fitting with a double exponential, and a simple
picture of the emission suggested that the emissions were from at
least two closely spaced levels. The short-time emission was from
the bottom of the p-band, where electrons could further relax with
the surrounding charges to a lower excited level, from which there
was long-time emission. However, this simple picture could not
completely describe the time-dependent spectra and short-time rate

constant.

I.B. 111%an Elootrons in Frozen Glassos and Qotioal
h ble chin ffe

Free electrons can be liberated by the impact of high energy
electrons or by ionizing radiation, 'y-rays or x—rays in glassy solids at
various cryogenic temperatures. They can be chemically stabilized in
trapped states in the frozen matrix . Such trapped electrons have
been observed in various frozen organic and aqueous liquids such as
alcohols, ethers, amines, alkenes alkanes and alkali aqueous
solutions. The aqueous ices contain trace amount of solutes, such as
sodium salts or N, N, N', N'~tetramethyl~p~phenylenediamine (TMPD)
[20], and the trapped electrons are formed by photoionization of the
solutes. However, significant yields of trapped electrons have not

been found in pure crystalline samples of the solvent. The frozen

8
liquids are in amorphous states, formed by rapidly quenching the
samples with liquid nitrogen or liquid helium, and apparently
contain defect sites at which the electrons can be trapped.

Electron spin resonance and optical absorption spectrometry
are the most common methods used to detect the trapped electrons
(et'). Other evidence for trapped electrons was found in
luminescence, electrical conductivity, and differential thermal
analysis studies [21]. The optical absorption spectra of the organic
and aqueous ice glasses that contain trapped electrons are broad, and
extend from the visible or near infrared to the IR region. The
absorption peaks have a long high—energy “tail” and a short low~
energy side, and they were suggested 'to have been composed of
individual electrons in different trap depths; where the red end of
the spectrum of each et‘ is the photoionization threshold for the trap
and the blue side of the maximum is the energy required to move
the electron far enough to react with a cation or a radical rather than
being retrapped [22]. The spectra of et' in the frozen glasses are
similar to those in the respective liquids, but the former are
narrowed and blue shifted; this suggests that the nature of trapped
electrons is Similar in liquids and glasses, but that the trapped
electrons in the glasses are more stabilized [23].

The electrons in the trapping sites can be thermalized into
more stable states. The stabilizing mechanisms suggested were that
they are first weakly trapped in the matrix of molecules through
dipole interactions, which then induces a rearrangement of the
molecules around them, and the traps deepen as the arrangements of

molecules achieve equilibrium. This explained the broad absorption

9
bands as due to the electrons occupying a continuum of trap depths.
The above suggestion was verified by the facts that the spectra of er
produced in organic glasses are not stable, but undergo a continual
blue shift with time after production, which can be as long as 380
seconds [24]. This indicates that the electrons deepened in the traps
after a sufficiently long period of time.

A convincing piece of evidence to prove that the trapped
electrons, et' , are distributed in a continuum of trap depths rather
than being in the same depth of traps, is the reversible partial
photobleaching of the blue side of spectra accompanied by the
enhancement of the red side. The most conclusive evidence is the
selective bleaching effects on the absorption spectra of 2-
methyltetrahydrofuran (MTHF), 3~methylpentane (3PM) and C2H50H
glasses at selective wavelengths when monochromatic bleaching light
is used. For example, the bleaching effects of et' occur in MTHF only
in the range from 1200 to 1550 nm when monochromatized light of
1338 nm wavelength is used [25].

Photobleaching effects showed that the trapped electrons in
hydrocarbon glasses can be detrapped by a monophotonic process at
all wavelengths of their absorption spectra, from far on the low
energy side (2500 nm) to far on the high energy side (400 nm)
[25,26]. This implies that the photon energy absorbed by the
trapped electrons can raise the electrons to the quasi-free state in
the glassy matrix. But not every electron that absorbs a photon is
activated enough to react with the radical or cation, Since the
quantum yield of bleaching at wavelengths on the red side is low,

and increases with photon energy. In the slightly more polar matrix,

1 O

MTHF, the absorption maximum is at 1200 nm, and monophotonic
bleaching occurs up to about 1200 nm but not at wavelengths longer
than that. This implies that the energy given to the electrons by the
longer wavelengths is lower than that necessary to reach the quasi-
free state and is insufficient to prevent the subsequent prompt
return to the oriented coulomb well of the parent trap or the
formation of a new trap without appreciable migration. A plot of the
photon energy maximum (1,.) versus the static dielectric constant
(D3) of the matrix compound forms a smooth curve, which suggests
that the trap depths increase with an increase in molecular polarities
[25].

The EPR spectra of trapped electrons is a broad Gaussian line
resulting from hyperfine interactions with a g value near the free
electron value. The line widths of EPR spectra of the trapped
electrons in glasses at 77 K generally broaden with increasing
polarity of the matrix molecules. This indicates increased hyperfine
interactions with the atoms in the walls as the traps become deeper
[23], due to the Structure change or relaxation effect. The EPR
spectrum also contains information about the orientation of
molecules around the trapped electrons. For example, the EPR singlet
in deuterium-substituted alcohol CszOD is narrower than that in
C 2H 50H by the ratio approximately expected if the hyperfine
coupling with deuteriums replaces that with protons. Apparently the
hydroxyl groups in the trapping walls align toward the trapped
electrons [27, 28]. Electron spin echo studies or ENDOR, can be used
to obtain more detailed quantitative information about electron

locales. The spectrum shows a hyperfine splitting pattern which is

1 1
related to the structural information about the solvation shell of a
localized electron. The solvation structure of the electron in a variety
of solvents has been elucidated in this way [29].

The spontaneous removal of trapped electrons occurs by
combination with cations, radicals or the additives of aqueous ices.
Half-lives are on the order of tens of minutes near the glass
transition temperature for organic glasses and alkaline ices. The rate

increases with a rise in temperature. Possible mechanisms of

electron migration include: (1) diffusion of et' coupled with its
surrounding shell molecules ; (2) diffusion of et' without the
movement of surrounding molecules, only the polarity passing to the
new molecules as et'; and (3) quantum tunneling to a radical, cation
or an added scavenger with greater electron affinity than the trap.
In the third suggested mechanism, the thermal detrapping and
movement to a reaction partner by a hopping mechanism seems
improbable, since the detrapping thresholds are larger than 0.5 eV
and the H is only 0.006 eV at 77 K [22].

LC. lrvil Ph el rnEmisin

The first photoelectric effect was observed by Hertz [30] in
1887. He found that a spark between two electrodes occurs more
easily when the negative electrode is illuminated by ultraviolet light.
The effects were interpreted by Einstein [31] in 1905 by quantum
mechanics, which led to the establishment of the foundations of the
quantum theory of radiation. In the 19505, the understanding of the

band structures of solid samples particularly enhanced the

1 2
knowledge about the microscopic basis of photoemission. Many
theories have been developed since then.

Photoelectron emission (PEE) from a solid provides less
ambiguous information about the nature of electron transitions than
does the optical absorption spectrum. The electronic transition in
PEE is absolute, in that only final states whose energies are higher
than the vacuum level contribute to the spectrum. By contrast, the
absorption transition occurs relatively; that is, the electronic
transition takes place only when the energy difference between the
final state and the initial state corresponds to the selection rule.
Therefore, the photoelectron spectrum formed by populating a given
set of final states indicates the absolute energies of the initial
electron states.

The alkalides and electrides have unusual properties as
introduced previously; they would be excellent candidates for
photoemission studies of the energy state of the alkali anion outer
shell (ns2) electrons, and those of any trapped electrons in the
sample.

The nature of the instruments used, and the principles of work
function measurements, optical transitions and the photoemission
spectra will be introduced in this chapter because they include most
of the important background information needed to understand

photoemission.

I.Cl. Instruments for Ultraviolet Photoemission Spectroscopy

1 3

Photoemission spectroscopy can be divided into two categories:
ultraviolet photoemission (UPS) and X—ray photoemission (XPS). The
former is mainly for the study of the energy states of valence
electrons and energy bands in a solid; the latter is primarily for
probing energy levels of core electrons, although it can be used at
lower resolution to study the valence band. For the alkalides and
electrides, only the energies of the valence band and states above it
are of direct interest to us, so this introductory chapter will limit its
scope to ultraviolet photoemission.

An ultraviolet photoemission spectrometer is composed of
three major parts; light sources, vacuum chambers and electron
energy detectors. In the early 19605, conventional light sources,
such as mercury arcs and tungsten lamps, etc., together with a
conventional monochromator, were used [32][33]. The available
photon energies were under 6 eV, which limited the applications
because the work functions of most materials are at least 3 to 5
electron volts [34]. In the late 60s, obtaining higher energy photon
sources became more important. With the development of vacuum
techniques, some higher energy photon sources could be applied.
The vacuum UV photon source was first introduced by Spencer [35],
in which a hydrogen lamp was separated from the vacuum chamber
by an LiF window. Currently, the most common photon sources are
the discrete He(I) line at 21.2 eV and He(II) line at 40.8 eV [36]. The
Hel radiation arises from the transition 2p~2s of the neutral He atom,
and the He(Il) line is from a singly ionized atom. Both line widths
are only a few milli-electron volts (meV). Although the line widths

can be broadened by experimental conditions such as the self-

1 4
absorption effect, the changes usually are quite minor. There are
two other source lines from Ne at 16.8 and 26.9 eV. They are not as
commonly used as the He lines, but sometimes are convenient when
one wants to follow the changes of solid sample cross-sections with
photon energy.

The most common UV lamp is the cold cathode discharge tube,
which has a double differential pumping stage to limit the gas flow
into the sample chamber when a solid sample is measured. When a
gas sample is measured, the double differential pumping is
unnecessary. The discharge chamber is confined by a quartz tube of
~ 1 mm bore which determines the dimensions of the light that is
shone on the sample.

Due to the fact that the cross-sections of different atomic
subshells change as a function of the photon energy [37], synchrotron
radiation has become an ideal light source, since it has the property
of a high intensity monochromatized source of continuously tunable
energy. The synchrotron radiation is polarized in the plane of the
electron orbital, so it is very effective in determining the orientations
of surface states such as surface plasmons, surface-bonded
molecules, etc.. However, only radiation sources from a storage ring,
rather than an ordinary synchrotron, are suitable for this application
because the radiation emitted from the storage ring is continuous,
whereas the pulsed radiation from an ordinary synchrotron can’t be
used as a photon source in photoemission spectroscopy. A storage
ring with a 107 (Hz) r.f. power source can repeatedly top up the
electron beam current to account for losses by radiation emission

[38].

1 5

A good vacuum system in the photoemission spectrometer
fulfills two basic functions. First, emitted electrons can pass from the
surface of samples through the vacuum toward the electron detectors
without making too many collisions with residual gases. A moderate
vacuum of 10'5 torr would satisfy this requirement. Such a pressure
is actually the operating vacuum in an energy analyzer for the
measurement of gas samples. Second, a good vacuum environment
can keep the solid surfaces clean. Theoretically, a solid surface will
be covered by a monolayer of gas every second at a pressure of 10“
torr, assuming a sticking probability of 1 for the solid surface
studied. For routine analysis, a vacuum of 10'9 torr is a compromise
between the pumping time and surface cleanliness. Some
experiments, especially for fundamental surface studies such as the
changes of surface states with the absorption of molecules, require
more restricted conditions in that the vacuum must be 10'10 torr or
even higher [39].

The electron detection systems consist of electron energy
analyzers and detectors. The function of an electron analyzer is to
measure the energy distribution of electrons emitted from a sample.
The energy analyzer is divided into two categories, according to the
methods used to separate electrons with different energies. These
are potential retarding fields and deflection fields. The retarding
field energy analyzer is essentially a high pass energy filter; only
electrons with kinetic energies that surpass the height of the
potential barrier can reach the detector. The spectrum observed is
the current reaching the collector upon scanning decrements of the

retarding potential (Figure 1-2). The energy distribution curve then

1'6
is obtained by either electrical or numerical differentiation of the

Spectrum [40].

 

 

15

a: 15

L-

b C)

: i:

U 3

LIJ U

D. LIJ
O.

p

 

 

E E
(a) (b)

Figure 1-2. Comparison of PEE spectra: a) the integral form of
spectrum generated by retardation, b) the energy distribution curve
spectrum obtained by differentiation of the spectrum in a.

The retarding field analyzers are somewhat limited in
resolution. First, the barrier heights of the retarding potentials are
not actually a measure of the total kinetic energies of the electrons,
but rather of the momenta. If one electron approaches the retarding

grid at the angle, 6, only the velocity component normal to the grid is

effective in surmounting the retarding potential. The electron with
energy E=%mV2 will be retarded when the retarding potential

reaches a value V,=%m(Vsin0)2. The angular spread will result in

energy aberration, which will be greatest when the electrons

approach the grid at grazing incidence. A Spherical retarding grid

17

with a sample in the center minimizes the energy aberration effect.
Second, perfect equipotential is not actually produced when a
retarding potential is applied to a wire mesh grid. The field spills out
into each mesh hole like a meniscus electrostatic lens, which also
degrades the resolution. Third, the increments of stepped signals at
lower retarding potentials also increase the background levels and
the noise associated with the magnitude of the background level.
Background levels are the total current detected instead of just the
signal in each step. Therefore, the result leads to a poor signal-to-
noise ratio on the low kinetic energy side of the spectrum.

Deflection analyzers are subdivided into two different types,
magnetic deflection analyzers and electrostatic deflection analyzers.
Magnetic deflection analyzers are not common, due to the difficulties
in controlling low magnetic fields for low energy electrons (in UPS)
and in canceling external magnetic fields.

Electrostatic analyzers are more easily screened from external
magnetic fields, and are now universally used. The magnetic
shielding is normally made from material of high magnetic
susceptibility, such as mu-metal or the combinations of mu-metal
and current-carrying coils. There are two types of deflection
electron energy analyzers (Figure 1~3). One is usually referred to as
a deflector or condenser, where electrons essentially travel along the
equipotential lines; the other is the electrostatic mirror, in which
electrons move across the equipotential lines where a gradient of
potential is established between two parallel plates. The detectors

for the deflection fields are electron mulitipliers [41].

l8

 

 

Electron

5 0U 1’ C e Detector

(a) (b)

Figure 1~3. The structures of deflection electron energy analyzers:
(a) 127 ° cylindrical deflector; (b) electrostatic mirror.

I.C2. Quantum Yield Spectra and Energy Distribution Curves

The simplest form of photoelectron spectroscopy is the
quantum yield spectrum, in which the total flux of photoelectrons is
measured as a function of the energy of the incident photon. The
sample is held in or on a photo cathode with an applied electric field
which accelerates the electrons toward the anode with a high enough
voltage to give a saturation current. The anode is usually set to
virtual ground potential, and the cathode has a negative bias.

Photoemission normally is a volume process, and the electron

excitation is suggested as a three-step model [42][43]. First, the

1 9
optical excitation of electrons occurs at a distance from the surface,
where the excitation corresponds to the electronic structure of the
solid. Second, the excited electrons must travel through the crystal
to the surface. Scattering occurs during such transport, due to
electron-phonon and/or electron-electron interactions. Third, the
excited electrons finally escape over the surface barrier into the

vacuum (as illustrated in Figure 1~4).

 

 

in vacuum, ‘2' transport '
K1
Excited state, k J.
1 , excitation
3. escape
Initial state, k i

 

Figure 1-4. Schematic representation of the three-step model for the
photoemission process: 1) electrons in the initial state '19); 2)

electrons photoexcited to the final state lkj); and 3) electrons

photoemitted into the vacuum and coupled with some plane wave
state, kj’.

Based on this model, the spectral dependence of the yield per

incident photon for a solid was derived as

2,Cl

{lama} / [a(£>]}

Y(E)=A(E) 1+[l/a(E)L(E)] ’

 

(1-1)

where A(E) is the escape function that describes the probability of an
electron emitted via the surface, and L(E) is the mean free path of an
electron of energy E. The absorption coefficient, 01(5), is divided into
two parts: the absorption coefficients for transitions above the
vacuum level, apt-(E), and below the vacuum level, aC(E) [43].

If the mean free path is large, the major contributions to the
quantum yield spectrum are from electrons that originate in the bulk
because the number of the surface states is small compared to the
total number of participating bulk states. However, the contributions
to the spectrum caused by the electrons excited directly from the
surface states is also important. A theory developed by Kane [44]
shows that the photoemission threshold of a semiconductor can be

characterized by a dependence of the form

Y=A(hv-ET)’, (1-2)

where Y is photoemission quantum yield, A is a constant, T is
predicted by the model of the transition that produces energetic
electrons and the scattering processes. For example, the power order
r is 1 and 5/2 for direct and indirect transitions in bulk processes,
respectively.

The surface barrier is an extension of the electron wave

functions beyond the positive ion cores. Therefore, the barrier

heig
plat

and
stat

dov

Fig
ph<

inc
doi
AE
by

sili

2 1
heights, hence the thresholds, are different for different crystal
planes of a material. The surface electron distribution is so sensitive
to the surface condition that structural change, absorbed molecules
and external fields will cause severe changes. Therefore, surface
states often induce a surface charge that bends the band either up or

down near the surface.

 

 

 

Figure 1~5. Effect of band bending on the threshold for
photoemission: (a) for a n-type semiconductor the bands bend up by
AE, and the photoemission threshold for excitation from the bulk is
increased by AE; (b) for a p-type semiconductor, the bands bend
down by AE, and the threshold emission from the bulk decreases by
AB. The electron affinity at the surface is assumed not to be changed
by the bending.

When Gobeli and Allen studied the photoemission from cleaved

silicon (111) plane [45], they observed that the spectra were

2 2
dependent on the sample dopings, and they interpreted this as being
due to the volume excitation process modified by surface charge
band bending. For a material with p-type degenerate-doping, the
bands bend down, and the surface inversion layer will lower the
photoemission threshold for emission from the bulk. On the
contrary, for a n-type degenerately doped material, the bands bend

up at the surface, which will cause an increase of the photoemission

threshold from the bulk (Figure 1~5) [46].

I.C3. Work Function

Determining the characteristics of various materials is a major
task in a photoemission study. The work function ¢,~ is the strength
of the potential barrier that prevents the valence electrons from
escaping from the surface of the solid. It is defined as the difference
between the potential immediately outside the solid surface (vacuum
level) and the Fermi energy in the solid. In a metal at 0 K, the
highest energy electrons are at the Fermi level; in a semiconductor or
insulator, the Fermi level usually lies within the forbidden gap,
defined as the energy difference between the top of valence band
and the bottom of the conduction band. In general, there are two
types of methods for determination of the work function: one is the
contact potential, which is the energy transfer of electrons from one
metal to another. Another is the escape of electrons from a solid
surface, which includes photoemission, thermionic and field emission.
Different methods and experimental conditions can lead to

widespread difference in the results, which usually depend on the

23

surface conditions. Our research has focused on the photoemission
method.

The determination of the work function of a metal by
photoemission, can be either by the lowest frequency of light at
which photoemission occurs or by the highest electron energy for a
given exciting photon. However, the thresholds are usually not
sharp, which is due to either the spread in the Fermi distribution at
high temperatures which permits photoemission for hv <<Dor to the
measurement of photoemission from polycrystalline materials. The
measurements from polycrystalline sample may yield different
average work functions, and even the results from a single-crystal
surface can be distorted by the presence of exposed patches of other
orientation faces.

In photoemission, when a metal sample is electrically
connected to the collector of the spectrometer, there always exists a
small electric field between them due to the difference in work
function of the sample and the collector, where the sample metal and
spectrometer have the same potential at the Fermi level. If the
spectrometer collector has a higher work function than the metal
sample, then the electrons leaving the sample will be retarded by the
electric field existing between the sample and the spectrometer
collector. In a quantum yield spectrum with no bias voltage, the
measured work function is for the collector instead for the metal
sample. Therefore a compensating bias voltage is needed to extract

the emitted electrons to obtain the correct work function. In an

energy distribution curve (EDC) the measured kinetic energy E”, will

24

be lower than the true kinetic energy by an amount (mp—4),) (Figure

1-6).

PHOTCN SQJRCE
SAMPLE

' ANALYZER

 

 

 

 

 

 

METAL NmMETAL

Figure 1~6. Correction of the binding energy E5“ for metal and

nonmetal samples: (a) if a metal has lower work function than that of
the Spectrometer, the binding energy has to be corrected as
EL=hv-E&—(¢,P—¢,); (b) the binding energy of a nonmetal has to be

corrected with respect to both the work function difference and the
surface charge on the sample, E;=hv-Em—(¢,p-E,)-¢c,.

The binding energy, with respect to the vacuum level, has to

be corrected by the difference

2 5
EL=hv—Em-(¢,p—¢,) (1-3)

where the hv is the photon energyfi

In insulators and semiconductors, the correction term for the
difference of the work function is (AP-5;) where E, is the energy
from Fermi level to the vacuum for the sample. In addition, when
the electrons leave the sample, there is a positive surface charge
existing on the sample due to the lack of good conductance. The
surface charge will decelerate the emitted electrons, and the amount
of energy lost equals the surface charge; therefore, the binding

energy with respect to the vacuum level is
EvBacth—Eh'n-(¢sp_Ef)-¢ch (1-4)

where 4",, is the surface charge. Because it is difficult to determine

the work function or binding energy with respect to the vacuum
level for insulators or semiconductors, an alternative measurement is
the threshold energy E, which is the energy difference from the top
of the valence band to the vacuum level [47][48].

Fowler[49] developed a theory to accurately determine the
work function for metals by fitting the tail into the theory. He
explained that the causes for broadening are the results of the
diminishing number of electrons with sufficient energy to overcome
the work function as the electron approaches the vacuum, and
changes in the band structure resulting from the temperature effect.
The latter factor is not very important to the broadening; the former

is related to the concept of the conservation of linear momentum

26
parallel to the surface. He developed a data analysis method to
extract the work function a from the temperature-dependent
spectral quantum yield and also from the energy distribution curve.

The equation derived from momentum conservation is

 

log(%)=3+logf(h:;¢) (1-5)

where j is the photocurrent, f is a tabulated function, B is a constant
independent of v and T, and 4) is the work function. The plot of
log(%2) vs h%T is called the Fowler plot; the horizontal shift yields
the work function while the vertical shift gives the constant B.
Although these results were derived carefully, they were only rough
approximations when compared to more recent data because of the
poor vacuum conditions used in earlier experiments.
Temperature-dependent studies are usually plagued by
changes in surface condition with temperature. It is nearly
impossible to avoid contamination of the surface as the temperature
is lowered. For a theoretical temperature study, it is customary to

express the temperature dependence of the work function as [50]

fl- 34’ 57$ -
fl-3a(aan)T+[aT)v (1 6)

 

in which a is the expansion coefficient. The first term on the right-
hand side is the volume dependent term, while the second term is
the explicit form of the temperature dependence. The volume

dependent term is a function with dipole moment dependence; the

27

temperature dependent term is related to the change in the ionic
charge induced by vibrational changes. These two terms have
contributions with opposite signs; therefore they almost cancel each
other. For example, Cu has +3k and ~1.6k for the volume and the
temperature dependent terms, respectively, where k is Boltzmann's
constant. This fact adds difficulty to experiments designed to obtain
reasonable information on the change of the work function with
changes in temperature. Considering that the electrical potential
induced by the lattice vibration can be screened by electrons, a more
reliable calculation was performed with the pseudopotential
formalism in which the potential induced by lattice vibrations is

smeared out [51].

I.C4. Direct and Indirect Transitions in Photoemission

Energy distribution curves (EDC) usually Show various features
which are ultimately related to the electronic band structure, and the
features of the spectra Show up in a way relating to the nature of
optical transition. To distinguish between direct and indirect
transitions from the features of spectra provides additional
information for exploring the electronic band structures. The criteria
are based on the variations of the energy distribution features with
different exciting photons in the photoemission.

For a direct transition between discrete levels, the excited
electrons originating in the bulk are excited to the empty states in
the conduction band without phonon assistance. Therefore, the k

vectors in the initial and final states have to be identical. Such a

2 8

constraint usually forces the summation of the initial state energy
and the photon energy to be equal to the final state energy, and
leads to two sorts of features in the experimental EDC: (1) the
structure will appear and disappear abruptly at different photon
energies, and (2) an increase of the photon energy by a certain
amount, Aha), does not result in a peak-Shifting to a higher energy by
AM). The former effect is because the transition probability varies
with photon energy, such that the occurrence of any optical
transition in photoemission is associated with a critical point in the
final state, the critical point is more a saddle point rather than a
maximum or minimum position in the density of states curve. The
latter is because various photon energies will emit electrons from
their corresponding initial states in k-space. The energies of the
initial states depend on the curvature of the valence band [53].
(Figure 1~7b)

For an indirect transition, the probability of an electron excited
to the energy E from a lower energy E -ha) by the photon energy ha)
is proportional to the product of the initial and the final density of

states, and the energy distribution of photoemitted electrons D(E) is
0(5) = CT(E)N,.(E — hw)1v,(z~:) (1-7)

where N, and N, are the initial and final optical density of states, C is
a constant, and T(E) is the escape function which is determined from
the experimental data. Because the indirect photoemission is
determined both by the empty high density of final states and by the

high density of initial states, the emission peak in EDC either (1)

29

remains and is located at a constant energy in the distribution curve
when the energy of photons is changed, and the energy of such a
peak corresponds to the location of a maximum density of the final
states, or (2) moves to a higher energy in an increment exactly equal
to the amount of change of photon energy, corresponding to a peak in
the density of filled valence band states [52]. (Figure 1~7a)

In the direct transition, if the wave functions of the initial state
and the final state are well described by the Bloch wave function,
and the excitation only involves a single electron, then the initial and
final values of k must be the same. In contrast, for the indirect
transition, the excitation does involve more than the single electron,
for example electron-phonon scattering, the overall k may be still
conserved (conservation of momentum) without the k values being
the same in the initial and final states.

For solids with d~state electrons, such as transition metals, the
bands are quite flat, and for such flat bands it sometimes is difficult
to determine whether the transition is direct or indirect. The way to
distinguish the transitions is to measure the temperature
dependence and to compare the absolute quantum yield magnitude,
because indirect transitions have obvious temperature dependence

and lower quantum yield magnitudes [52].

 

 

 

 

 

 

 

 

’3

Z

.2.”

m Vacuum
8 48181.
a

h

“a ”4

3‘ _____
'51

§

Ef
. k
(a) (b)

Figure 1~7. Schematic. representations of indirect and direct

transitions. (a) A photoemission energy distribution for indirect
transitions with constant matrix elements. The low energy peak is
fixed in energy corresponding to a high density of states in the
empty conduction band; the high energy peak that moves in energy
by an amount exactly equal to the change in photon energy,
Ahw=hco'-ha), corresponds to a peak in the density of filled valence
band states. (b) The direct transition processes. Because of the
energy variations in the initial states, the important features in EDC
move to higher energies at a somewhat slower rate than the increase
in photon energy.

Another criterion was proposed by Spicer [43], that a nondirect
transition can take place in the excitation process in the three-step
model. The nondirect transition has a peak with the characteristics
of an indirect transition, and the peak moves to higher energy by an
amount that is exactly equal to the increment of the photon energy,
except that it is temperature independent. The suggestion was based

on the experimental results from the semiconductors CS3Bi and ngSb,

3 1
and the metals Cu and Ag [53][54]. He interpreted the effects as due
to a weak overlap of valence state wave functions on adjacent lattice
sites, and energy conservation instead of momentum conservation
becomes the selection rule for the optical transition.

However, the interpretations are not without controversy. The
transitions in the energy distribution curves for Cu and Ag were
interpreted as nondirect processes by Spicer; whereas the results
obtained by Smith [55] indicate direct transitions. Both model
calculations of the energy distribution of the joint density of states
and experimental spectra of the energy distribution curves were
used to prove that the transition processes are direct. Other
measurements of Cu and Ag with higher photon energy, 10 ~ 27 eV,
also indicated that the transitions are direct rather than nondirect
processes [56]. The discrepancies are due to the fact that the three-
step model is too simple to interpret all the photoemission

phenomena [57].

3 2
CHAPTER II

THE PHOTOEMISSION APPARATUS AND PHOTOEMISSION STUDIES

IIA. lnttooootion

Alkalides and electrides are very sensitive to air, moisture and
temperature. Except for~ a few compounds, most alkalides are usually
highly unstable and will decompose at temperatures higher than ~20
°C, even under inert atmosphere or vacuum conditions; the electrides
are even more unstable and the decomposition temperature is lower,
with decompositions setting in when the temperature is higher than
-40 °c [8,58].

For these materials, the experimental conditions have to be
restrictive. Many measurements of bulk properties can be
performed if the samples are transferred in a glove bag that is filled
with nitrogen gas or in a dry box; however, an even more restrictive
condition is required for the surface measurements, since the
materials are so reactive that their surfaces are easily decomposed,
or can become contaminated, especially at low temperatures. Based
on the above considerations, the present photoemission apparatus
was built to circumvent these difficulties. The design permits the
sample to be loaded under a high vacuum environment at low
temperatures to minimize decomposition.

Two photoemission apparatuses had been built in the past, but
both systems were not without problems in vacuum and sample

loading. The first one was made entirely from Pyrex, except for the

33

metal electrodes. The vessel was pumped by a small ion pump, and
the vacuum was maintained at only 10'4 torr [18]. The second
photoemission apparatus was constructed of stainless steel; however,
most of the O-rings used at the joints were Viton instead of copper
gaskets. Such sealing introduced the possibility of leakage caused
either by the shrinkage of the gaskets at low temperatures or by the
deterioration of the gaskets by organic solvents such as
methylamine. Although the system was pumped by a
turbomolecular pump, the vacuum could reach only 10'5 torr [59].
In both previous systems the loading of samples had to be
performed in a glove bag, so that we could not rule out the
possibility of a trace amount of moisture being condensed on the
surface of sample. As mentioned earlier, the surface quality is so
important for photoemission studies that we decided to design a new
system to decrease the chance of the sample coming in contact with
air or moisture.

Thermionic emissions from the alkalides and electrides had
been observed in the previous system [72]. However, the
phenomena did not show up in this new system. We infer that the
thermionic emissions might be from the surface reactions or the
surface contamination due to the lower vacuum of 10'5 torr, which is
compared to this new system with vacuum of 10'8 torr.

Alkalides and electrides have very unusual properties due to
the presence of weakly bound n32 electrons in anions and as trapped
electrons in electrides. The apparent band gaps of most alkalides are
low (0.8 ~1.5 eV), which probably results from defect electrons

whose energy states lie in the gap. All the alkalides, except

34

Na+C222~Na‘, are therefore considered to be electron-doped extrinsic
semiconductors [13], and electrides are insulators, semiconductors or
near-metals. The photoemission method is a useful way to
characterize the energy states of trapped electrons and the valence
bands of these compounds.

Photoelectron emission spectroscopy (PEE) provides direct
information in exploring the electronic states of materials, especially
solid materials. In our system, the light source spans the region from
the ultraviolet to the near infrared. Ultraviolet incident radiation
probes the electron distribution of valence electrons to provide direct
information about the amount of energy required for the transition
of electrons from the valence band to the vacuum. Visible and
infrared radiation provide information about excitation of the
trapped electrons.

The emitted electrons originate from depths a few hundred
Angstroms below the surface, and electron emission involves both
volume and surface processes [44], so that surface cleanliness is very
critical in PEE for a solid sample. The most common methods of
obtaining a fresh surface are by cleavage of a crystal [73], by ion
Sputtering [60], or by continuous evaporation of a metal to form a
fresh film [61] in an ultra-high vacuum environment. Unfortunately,
none of these methods can be applied to the alkalides and electrides
due to the high instability and reactivity of these compounds.
Therefore, our procedure has to be more complicated than the usual
methods, in that we have to load and dissolve the sample, alkalides

or electrides, in a solvent and then remove the solvent under high

35
vacuum and at a low temperature, so that a fresh film can be
obtained.

There have been a number of apparatuses built for
photoemission measurements with the possibility of study under
UHV conditions and at low temperatures [62,63], but none of these
provide for loading samples which are air and temperature sensitive.
The apparatus which we built has the advantage of loading the
sample while cold with minimum contact with gases, which gives the

best possible way to guarantee the quality of the samples.

IIB. Dosoriotion of tho System

II.Bl. General Aspects of Design

The photoelectron emission apparatus shown in Fig. 2-1 has
four main components. (1) The vacuum system is composed mainly
of the loading chamber, the film-preparation chamber, and the main
chamber where photoelectron emission is measured; (2) The
pumping system which consists of two roughing pumps for pre-
pumping of the sample loading chamber and for pumping the
transition feedthroughs, an 8 inch cryogenic pump (Leybold-
Heraeus) which is isolated from the film preparation chamber by a
high-vacuum valve for efficient condensing of solvent gas from the
sample film, and a turbomolecular pump (Varian 3000) backed by a
high capacity roughing pump (Varian SD-300) to pump out the main
chamber, creating the high vacuum (better than 10'8 torr); (3) The
feedthroughs, which provide the necessary electrical and optical

access, and cooling, sample transportation and temperature control;

36

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WASTE BOTTLE/ /;C))UC: PUMP
TRA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NDSPOHTATION

VERTICAL WAND

SAMPLE LOADIN3
WAND

Figure 2-1. Schematic view of the photoemission apparatus

37
(4) The data collection system, which uses an IBM XT microcomputer
for the collection of data, and an IEEE 488 interface board (from
Metrabite) to talk and listen to a Keithley 617 electrometer. The
computer also communicates with a home-built interface via a RS-
232 serial port to control the scanning speed of the monochromator
and to read data from the controller. The block diagram of the

system is given in Fig. 2~2.

II.B2. The Vacuum System

The vacuum system is composed of a loading chamber, pre~
chamber and main chamber. The materials, including the gate valves,
are stainless steel (MDC Manufacturing Co.); the joint materials are
copper gaskets, with the exception of the loading chamber where
Viton gaskets are used. There are two reasons for the use of Viton
instead of copper gaskets: one is that the vacuum of 10'5 torr will be
good enough for sample loading, and the other is for easy, fast
cleaning and operation.

Before operating the system, the main chamber and
preparation chamber are pumped down to 10'8 and 10'6 torr
respectively, while the gate valve between these two chambers is
closed to assure ultra high vacuum in the main chamber. However,
the gate must be opened momentarily to transport the sample from
the preparation chamber into the main chamber. There is a 3/8"
orifice in the gate when it is open. The effect of the orifice has been
evaluated, and its throughput is only 1x 10‘6 Watt (equal to the
conductance of 1x10'8 L S'1 at atmosphere) if the vacuums in the

preparation chamber and the main chamber are 10‘6 and 10"9 torr,

38

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39

respectively. Thus, opening the gate valve causes little deterioration

of the vacuum in the main chamber.

II.B3. Temperature Control

Temperature control is essential in the experiment. The
vertical wand, for holding the sample during measurement, provided
for temperature control, with the structure shown in Figure 2~3.
There are two inner tubes in the wand, one inside the other, which
have two functions: one is for directing the flow of nitrogen gas, and
the other is to work as a heater to warm the nitrogen gas. The high
resistance of stainless steel tubing allows generation of heat by
passing current through it. House nitrogen, with a pressure of 20 psi,
is circulated through a liquid nitrogen bath and then used to cool
down the sample holder. The temperature of the sample holder,
which can go down to ~l30 °C, is monitored and controlled by an
Omega temperature controller (model No. CN2001T~AT). A Variac
and a converter are added in the circuit between the heater and the
temperature controller for more accurate and efficient controlling.
For example, for a 20 degree change from ~80 to ~60 °C, the
temperature was stabilized in 10 minutes to within :2 °C (see Fig. 2-
4). However, it takes longer to decrease the temperature further; a
30 degree change from ~60 to ~90 °C required 20 minutes to
stabilize. The flow rates of nitrogen are controlled by two flow
meters (manufactured by Cole Parmer Co.) with calibrated scales
from zero to 23 and zero to 11 liters per minute, respectively. The
larger flow meter regulates nitrogen flowing through the

temperature controllable vertical wand, and the other flow meter

40

   
 
   
 
  

Thermocouple

Epoxy

   
 
 
    

electrical
msulator

electrical
insulator

control

Figure 2~3. The structure of the vertical wand. The temperature is
monitored by a thermocouple and stabilized by a temperature
controller which produces an output current to heat up the inner

stainless steel tubing if the temperature is lower than the pre-set
value.

41

  

 

-50 .—
Preset ~60 °C
-60 —.
6‘
L
9 ~70 -
3
£9
8
E -80 -
g Preset ~90 °C
-90 _
~1OO -

 

I 1 l I I I
o 10 20 30 4o 50
Time (minutes)

Figure 2~4. The stabilizing rate and precision of temperature control
of the sample holder.

42

adjusts the nitrogen flow through the sample-holding and the

transportation wands.

II.B4. Electronic Systems

The electronics circuit of the spectrometer is shown in Figure
2~5. The sample holder is the cathode, and the electron collector
works as the anode. For quantum yield measurements, the grid was
connected to a real ground potential to prevent charge capacitance
inside the spectrometer, Since larger capacitance will increase the
response time. In order to eliminate the noise generated from
magnetic and electric field interferences, the preamplifier (109
amplification) was placed inside the vacuum system. When
necessary, the amplification factor can be switched to 9x107. The
output voltage is measured by a Keithley 617 electrometer. Due to
space charge buildup on the surface of the sample film, a bias voltage
(supplied by the same electrometer) was imposed between the
cathode and the anode to extract the emitted electrons. The typical
extraction voltage was 40 V, which corresponds to an electric field of
~ 8 V/cm. The response time of the system is a 40 ms. It was
determined from the fast exponential decay of the “shot-signal”
recorded by an oscilloscope (Tektronix 7313), when an alkali metal

film was illuminated by a laser pulse.

II.B5. Data Acquisition Methods
An IBM XT computer with an IEEE-488 interface board, a
Keithley electrometer and a home-built interface are used for data

acquisition. The computer controls the output of the bias voltage and

43

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44

reads the input signal of the electrometer; in addition, it also controls
the scanning Speeds of the monochromator and records the
corresponding wavelengths through the home-built interface.

The Keithley 617 Programmable Electrometer can be used as a
sensitive voltmeter, ammeter and ohmmeter. When measuring, it
can also act as a voltage source which ranges from ~102 V to +102 V
in 50 mV increments.

The programs were written in Microsoft GW—Basic language.
The IEEE-488 interface board has some software located in ROM for
controllers. In programming, we need only call in the software as
subroutines. The home-built interface for the monochromator
stepper motor is commanded by specific ASCII codes ( see Table 2~1)
that direct the logic executions. The UART unit (Universal
Asynchronous Receiver-Transmitter) in the interface is designed to
operate with a microprocessor, and to incorporate auxiliary logic.
When the interface is energized, the registers in the UART are loaded
automatically to set up for communication: 8 bit word, 9600 baud, no
parity bit, one stop bit. When the set-up is ready, the interface will
send a “2” (00000010) to the computer to signify that it is ready to
receive commands from the computer. Data sent to the interface
should have the interface codes listed in Table 2-1. First, set the
Grating, then sequentially the Step Rate, and Start and Stop digital
numbers. When a READ command is sent, the interface will send the
digit requested and immediately go back into the receive mode to
accept the next command. Such flip-back-and-forth operation
proceeds until the logic matches the Stop command. The program

must be written according to these formats.

Table 2~1.

Decimal

0

LII-huh.)

16

1 7

18
19
20
21
22
23
24
25
32+DIGI'1‘
48+"
64+"
80+"
96+"
112+"
128+"
144+"
160+"

45

ASCII codes for the monochromator-computer interface.

Hex

Ul~hbJN

10
11
12
13
14
15
16
17
18
19
2x
3x
4x
5x

7x
8x
9x
Ax

Command Description

Set the direction to REVERSE

Set the direction to FORWARD

START in the REVERSE direction

START in the FORWARD direction

STOP with direction set to REVERSE

STOP with direction set to FORWARD

set the GRATING to 1 and STEP RATE to 100

" " " " 2 " " " " 1 0 0

" " " " 1 " " " " 50
" " " 2 " " " " 50

" " " " 1 " " " " 20

" " " " 2 " " " " 20

" " " " l " " " " 10

" " " " 2 " " " " 10

" ” " " l " " " " 5

" " " " 2 " " " " 5

enter START DIGIT 0, x=DIGIT:0,l,2,3,4,5,6,7,8,9

.. .. .. 1, ..

.. n .. 2, ..

.. .. .. 0, ..

.. .. .. 1, ..

.. .. .. 2, ..

read COUNTER DIGIT O, x=DIGIT read:1,2,3

.. .. .. 1, ..

H H H 2, H

46

The photoemission data as a function of wavelength were
collected by using the Basic program MONOVOLT.bas which is listed
in the Appendix. This program controls the Keithley 617
electrometer and the monochromator. The program can take
measurements at different bias voltages up to ~102 V. Typically, ~40
V bias gives the saturation emitting current, which is determined by
using the program VOLTSCAN.bas. The monochromator has 5 speed
rates and can scan forward or backward. The parameters for these
functions can be set in the program. As for the other data acquisition
programs used in these experiments, the data collected by
MONOVOLT.bas were stored in ASCII format, which can be used
directly for quantum yield calculations and plotting purposes.

The program VOLTSCAN.bas applies the scanning bias voltage
to the spectrometer when the light source is at a specific wavelength.
The program only needs to communicate with the Keithley 617
electrometer, while the monochromator is preset at a specific
wavelength. This allows us to determine the saturation current from
the emitting intensity as a function of voltage. If a positive bias
were scanned (but not feasible with our sample) the spectrum
obtained could be differentiated with respect to the applied voltage
to obtain the energy distribution curve.

The program PHOLASER.bas was written for measurements
made during photobleaching experiments. This program was derived
from the program VOLTSCAN.bas, and allows one to measure the
photoemission current as a function of time at a specific wavelength
and bias voltage. The time interval between data points can be

preset. This. allows the study of photobleaching effects in

47

photoemission caused by laser pulses. Detailed descriptions of the

bleaching phenomena are given in Chapter 3.

II.B6. Optical System

The light from a 1000~W xenon lamp is focused onto the
entrance slit of the scanning monochromator (Oriel model No. 77250).
Two diffraction gratings are used, and they range from 200-700 and
from 300 ~ 1000 nm, with a resolution of ~13 nm. The
monochromatized light is collimated and directed through a right-
angle mirror, then focused vertically through a quartz window onto
the sample. The output signal is pre-amplified before leaving the

vacuum system, and the dark current is about 2 picoamperes.

II.C. Exoorimontal

II.Cl. Sample Preparation

The electrides and alkalides were synthesized under vacuum
(”310'5 torr) in a low temperature environment [7,8]. When the
synthesis had been completed, the crystalline samples were sealed in
Pyrex ampoules which were sealed to the synthesis cell. The
samples were stored in a liquid nitrogen dewar prior to the
measurements.

The sealed sample was loaded into the tip of the loading wand,
where it was kept cold by blowing cold nitrogen gas through the
inner tubes of the vacuum insulated wand. The loading chamber was
first pumped by a roughing pump until the pressure reached less

than 100 mtorr, then the gate valve between the loading chamber

48

and the preparation chamber was opened to let the cryopump
evacuate both chambers. The sample was then loaded in a vacuum
of == 10'5 torr. The procedures are as follows: (1) first, the
transportation wand is moved forward to break the sample ampoule;
(2) then another wand directly opposite from the loading wand, with
a spatula on the tip, removes the sample and loads it into the sample
cup; (3) finally, the sample is transported to the vertical wand which
had been pre-cooled to a temperature of ~60 °C by blowing cold
nitrogen through it. (Fig. 2~6)

The vertical wand is used for film preparation and spectral
measurements. We prepared a fresh surface film by the “dissolve~
and-dry” procedure. First the solvent, methylamine or
dimethylether, was condensed onto the crystalline sample by cold~
condensation at ~60 °C in the vacuum of the preparation chamber.
When the crystal had been completely dissolved, the solvent was
removed first by condensation into a liquid nitrogen trap, then
pumped by the cryogenic pump immediately for 3 minutes. After
the solvent had been removed, the characteristic color of the sample
reappeared on the film. Thereafter, the vertical wand was pushed
upward slowly, through the opening in the gate valve, into the center

of the spherical spectrometer for the measurements.

II.C2. Measurements

The computer controlled the output bias voltage and the
scanning speed of the monochromator, and simultaneously recorded
the intensity of photoemission (as a voltage) and the corresponding

wavelengths of the exciting photons (in nanometers). The

49

SPATULA

SAMPLE CUP
DISC FOR
7 BFEAKING SAMPLE

TO MAIN CHAMBER f

 

 

 

 

FINCER

 

CHYCPUMP

SAMPLE
HNER

   
  

  
  

LOADING
CHAMBER

FINER HOLDER

  

TOFDUG-l PLMP

Jr PFEPARATION
CHAMBER

 

 

NOTE FOR CLAHTY,

THE CHAIBB‘I S-lClNN IS
mTATED 90 FE_ATIVE TO
THE PFB’ARATION CHAMBER

 

Figure 2-6. Schematic view of sample loading and transportation.
The transportation wand has a level 0.8 cm lower than
the loading and spatula wands.

50

monochromatized light focused on the sample had a trapezoidal
shape and was about 2x3 mm2 in size. The light intensity was on the
order of 1015 photons per second, which generally emitted electrons
to yield photocurrents in the nanoampere range. After 109
amplification, the output was the order of volts. The quantum yield
was calculated by reference to a standard light intensity measured
by a silicon diode detector (EG&G model No. UV44430). The yield is

calculated as follows:

Ys = (Is/Ip)Yp (2-1)

where Is and 1p are the photocurrent measured from sample and the
calibrated standard photocell, and Yp is the quantum efficiency of the

photocell.

II.D. Rosolts and Disoossioo

Because the sample could be loaded in a vacuum environment
and kept cold during film preparation, we were able to measure
photoemission from alkalides. The alkalides, K+(15C5)2-K',
Rb+(15C5)2-Rb', Na+C222-Na', K+C222-K', CS+C222-CS' and K+C222-Na',
were measured (Fig. 2~7 - 2~12). The spectra show the common
characteristics that there is a main peak at greater than 4 eV and a
low energy tail, and sometimes the high energy peak has a shoulder
on the low energy side. The low energy tail may contain another
broad peak whose position varies with respect to the nature of

sample. For example, K+C222-Na', Rb+(15C5)2-Rb' and

51

 

 

 

 

 

 

  

 

 

   

Ioomo'6 -
80-
'2
0)
">1
E 60- '.
a '-
c .
(U '.
3 n
C 401} >-
. . . 2.0 1.0
20-
I I I I
300 400 500 600 700

Wavelength (nm)

Figure 2~7. Quantum yield spectrum of K+(15C5)2-K‘ at ~60 °C. The
photoemission threshold energy for the valence band is as 3.4 :l: 0.1

eV, which is determined by extrapolating the low energy side of the
main emission peak to intercept the X-axis.

52

 

18x10.6 -
16-

14-

 

    

 

'Quantum Yield

 

 

-lliifi11lilllI-'_l-'
40 30 20 L0
eV

 

 

 

0 * I I I I I ‘ I 7%
300 400 500 600 700 800 900
Wavelength (nm)

Figure 2~8. Quantum yield spectrum of Rb+(15C5)2-Rb' at ~60 °C.
The photoemission threshold energy for the valence band is an 2.9 :l:
0.1 eV, which is determined by extrapolating the low energy side of

the high energy peak to intercept the X-axis. The low energy peak,
500 ~ 650 nm, is from trapped electrons.

53

 

 

 

 

 

 

 

 

 

35 l l I l l l
Na+C222-Na' l _l l l
30- .1 _ l-
25- - ‘
'9 25-l 20- " "-
3'2 A . .
c 9 15‘ I. a. .—
3 20— l E .' . -
>5 v 10- g '2 I—
.S. ‘5‘ 5 - - T
3' 10‘ 0 I I I -
5 4 3 2 1
Energy (eV)
5 - _
o I I I I I #‘a'l'
300 400 500 600 700 800 900

Wavelength (nm)

Figure 2~9. The threshold energy for the emission from the valence
band edge to the vacuum level is 3.1:l: 0.05 eV, obtained by the
extrapolation of the low energy straight line behavior versus energy

shown in the inset. The slightly increased spectrum shows the slight
effect of three 532 nm laser pulses.

54

14x10'6 -

12-I

104

m
l

 

Quantum Yield

 

 

 

4x) 110 21) L0
eV

 

 

 

 

0 T I T I F $=u1
300 400 500 600 700 800 900

Wavelength (nm)

Figure 2~10. Quantum yield spectrum of K+C222-K' at ~60 °C. The
photoemission threshold energy for the valence band is s 3.1:l: 0.1

eV, which is determined by extrapolating the low energy side of the
main emission peak to intercept the X-axis.

55

 

8x10- -

4 J '1,
'-

5

0 lrrifij

40 1&0 21) ‘L0

 

 

Quantum yield

 

 

 

 

2—
eV
0 I l l l I I I
300 400 500 600 700 800 900

Wavelength (nm)

Figure 2~11. Quantum yield spectrum of Cs+C222-Cs ' at ~60 °C. The
photoemission threshold energy for the valence band is as 3.4 :l: 0.05
eV, which is determined by extrapolating the low energy side of the
main emission peak to intercept the X-axis.

56

 

 

 

 

 

25x10“ - ‘jf
20—

20-
2 To
.9 g;
>‘ 15- 10+
EE .
a I
E I
<6
:3 10-
O o IIIVUUFITTT

4t) :10 2x) to
5_~ eV

 

 

 

 

0 I I I I — I I I
300 400 500 600 700 800 900
Wavelength (nm)

Figure 2~12. Quantum yield spectrum of K+C222-Na' at ~60 °C. The
photoemission threshold energy for the valence band is as 3.6 :l: 0.05
eV, which is determined by extrapolating the low energy side of the
high energy peak to intercept the X-axis. The low energy peak, 460 ~
570 nm, is from the trapped electrons.

57

Na+C222-Na' (see Figure 2~17) have peaks in the range of 460 ~ 570,

500 ~ 650 and 430 ~ 700 nm, respectively. The low energy peak
doesn’t always appear for a sample in different experimental runs,
and its intensity depends on the experimental conditions which
include the method of sample loading, film preparation and the
temperature. The photoemission quantum yields for these alkalides
vary from ==10'4 to :10". The emission intensity is relevant to the
inherent properties of the compound as well as the experimental
parameters such as thickness of sample film, surface conditions and
temperature. In general, thicker films have lower emission
intensities, which may be due to the higher resistance leading to a
slow charge neutralization. The surface charge indeed reduced the
emission intensity.

Figure 2~13 shows the decrease in the photoemission intensity
of K+(15C5)2-K' with a decrease in temperature. The measurements
were made at ~30, ~60 and ~90 °C in order, and the time intervals
between the measurements were about 30 minutes. The emissions
on the high energy Side apparently show less temperature
dependence than those on the low energy side. Although we also
have to consider the decay of intensity with time, the time effect is
small in this short period compared with the temperature effect.

The same anion in different complexant systems is expected to
have different photoemission threshold energies because the highest
energy bands are formed from contributions of the alkali metal anion
outer-shell electrons whose energies relative to the vacuum level
will be sensitive to the environment. Indeed, the onsets of

photoemission of the high energy peaks from K+(15C5)2-K‘ and

58

 

   
   

100
A 80— -l— 350 nm
°\° —Cl— 450 nm
E -O- 550 nm
‘5 60 -X- 650 nm
2 _
.93
E!
.E’ 4o-
o
3
“o
m
(E
20-
J
o...

 

 

 

I I I I I I I
-30 ~40 ~50 ~60 ~70 ~80 ~90 ~100
Temperature (°C)

Figure 2~l3. Normalized decrease in the photoemission intensity at
various wavelengths with changes in temperature for K+(15C5)2-K'.
The measurements were performed first at ~30 °C, then ~60 °C and

~90 °C in order, and the time intervals between the measurements
were 29 and 34 minutes, respectively.

5 9
K+C222-K' are different (z 3.4 i 0.1 and z 3.1 i 0.1 eV, respectively).

The structure of K+(15C5)2-K‘ is monoclinic [66], and the anion is
isolated, so that the interactions between the anions are very weak.
By contrast, K+C222-K‘ is triclinic [67], and the distance between the
potassium anions (4.90 A) is less than the expected Van der Waals
separation, and there is a considerable amount bonding character in
the K‘ ~ K‘ interaction. Energy differences between the n32 and nsnp
states associated with different alkalides were also observed by M.
Faber [65]. In her optical absorption experiments on polycrystalline
alkalide films, the spectra showed some shifts for the same anion in
different complexant systems, as for example, the transition energy
of 4s2 —9 454p for the potassium anion shifted from 1.47 eV for
K+C222-K' to 1.51 eV for K+(18C6)2-K'. She also found that the
solvents from which the dried films were formed also affected the
transition energies for the same alkalide, but the reason was unclear.

The sodides, Na+C222-Na' and K+C222-Na' have the same
complexant system, but their photoelectron emission spectra show
different threshold energies (z 3.1 i 0.05 and z 3.6 :l: 0.05 eV,
respectively). The reason for this may be due to their different
structures, hexagonal for the Na+C222-Na’ and orthorhombic for the
K+C222-Na‘ [68,69]. Although the sodium anions in both compounds
are rather isolated and with similar Na'~H distances, they are not
exactly in the same environment. The band states are formed from
combinations of the wave functions of many sodium anions and
surrounding molecules, and their energies relative to the vacuum
level would be sensitive to structural differences. Based on these

considerations and the experimental thresholds, we suggest that the

60

binding energy of the valence band electron is not solely determined
either by the anion or by the complexant, but rather is influenced by
the structure of the compound.

The onsets of the high energy peaks are not sharp for two
reasons. One is that the emission from trapped electrons that lie in
the band gap contributes to the onset signal. Another is the
temperature effect, in that [the lattice vibrations assist the lower
energy electrons to transit to the vacuum level. Such phonon-
assisted transitions had been observed in the optical absorption
experiments of Na+C222~Na‘ thin films, in which the increase of
temperature tended to broaden the absorption peak on the low
energy side for the transition from the ground sate to the p~band
state. The characteristics of the trapped electron states will be
elucidated later.

Photoemission is mostly a volume process, in that electrons
excited in the bulk are the main contributors to the emission.
Although surface states also contribute to the photoemission, the
total number of surface states is very small compared to the number
of states in the bulk that can participate in the emission. In this
experiment, the high energy peak was less temperature dependent
than the low energy peaks. This is a characteristic of direct rather
than indirect transitions. At the onsets of photoemission of the
alkalides the photon energies were less than 4 eV and electron~
electron scattering is unlikely at such low electron energies [70].
Therefore, we can suggest that the high energy peak of
photoemission was due to bulk and direct processes, and that the

electrons were unscattered by electron-electron interactions at the

61

onset of the emission. The photoemission theory developed by Kane
[44] concluded that if the photoemission is a bulk process with direct
transitions and unscattered transport, the quantum yield is
proportional to (hm—ET), in which E, is the photoemission threshold
energy. Based on this theory, we could extrapolate the straight line
portion of the of the photoemission to intercept the X-axis in order to
obtain the emission threshold energy for the valence- band.

A comparison between the onset of photoemission of an
alkalide with the work function of the corresponding metal also
provides some useful information. The photoemission threshold
energies, together with the work functions of the corresponding
alkali metals are listed in Table 2~2. The threshold energies are
higher than the. work functions of the corresponding metals.
Apparently, stabilization of the anions in the ionic lattice yields
outer-shell electrons that are more strongly bound than those of the
free electrons of alkali metals, even though the binding energy of the
electrons in M'(g) is much weaker. than in M(g). ‘

An alternative argument suggests that the energy from the top
of the valence band to the vacuum level corresponds to the onset of
the low energy peak instead of the high energy peak. Strong
evidence against this proposal is that for a nearly defect-free
crystalline sample of Na+C222-Na'~ the low energy band is absent,
and only the high energy peak shows up in the spectra. (see Figure
2~9) The low energy bands do not always appear in the spectra of
alkalides. In addition, the gap energy of Na+C222-Na‘was
determined as 2.4 eV by conductivity measurements [2], whereas the

onset of the low energy peak in photoemission is only = 1.77 eV

62

Table 2~2. The photoemission threshold energies of the valence

bands of alkalides and the work functions of the corresponding alkali

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

metals.

Compound Photoemission threshold energy
(eV)

K+(15C5)2.K~ 3.4 i 0.1

Rb+(15C5)2.Rb~ 2.9 i 0.1

Na+C222.Na~ 3.1 i 0.05

K+C222.K~ 3.1 :t 0.1

Cs+C222.Cs~ 3.1 i 0.05

K+C222.Na~ 3.6 i 0.05

Metal Work function (eV)*

Na 2.75

K 2.30

Rb 2.16

Cs 2.14

 

 

* Data from CRC Handbook of Chemistry and Physics, 71st editon

(1991).

 

 

63

(700 nm). If the alternative argument were true, then the energy of
the vacuum level would be below the bottom of conduction band,
which is improbable. These facts provide strong evidence that the
low energy emission peak is from some higher energy states rather
than from the valence band. Due to the facts that the low energy
band is strongly temperature-dependent and is extended to the near
infrared, these high energy states are presumed to be electron-
trapping States whose energies have a broad distribution in the gap.
We tried to measure photoemission from the electrides,
K+(15C5)2-e', K+C222-e' and CS+(18C6)2-e', which are even more
sensitive to the environment, especially to temperature. Although
we could obtain photoemission signals from this class of compounds,
the quantum yields were low (Figure 2~14 ~ 2-16). The spectra do
not Show appreciable photoemission on the low energy sides (IR
range) as we expected for the electrides, which may be due to partial
decomposition of the electrides or the presence of excess metal in the
samples. The photoemission was probably from a mix of metal,
alkalide and complexant instead of from the trapped electrons of the
electride. Alkali metal formed by partial decomposition might react
with the left—over electride to form an alkalide. There might be
some electride left, but the ratio between these components can’t be
known and the surface layers would be most subject to change. We
carefully checked the procedure of sample handling for the
measurement, and tried to find the causes for the decomposition. It
is possible that this occurred during sample loading and transferring,
but it seems unlikely. Because the temperatures of the loading wand

and the transport wand were measured and both were kept colder

64

5x106 -

Quantum yield

 

 

 

0 I I I I W

300 400 soo 600 700 800 900
Wavelength (nm)

Figure 2~14. Quantum yield spectrum of K+C222-e’ at ~60 °C. The
spectrum doesn’t Show significant emission on the low energy side,
which may be due to the decomplexation or decomposition of the

sample or the presence of excess metal.

65

 

 

 

20x10'6-
'0
a; 15—
'3
E
a |
C
CD 10-
3
C
5..
0 I I I I

 

 

300 400 soo 600 700
Wavelength (nm)

Figure 2~15. Quantum yield spectrum of K+(15C5)2-e‘ at ~60 °C. The
spectrum doesn’t show significant emission on the low energy side,
which may be due to the decomplexation or decomposition of the
sample or the presence of excess metal.

66

 

 

 

4x10" -
E 3 "I
.9?
>-
E
3
g 2 "
3
O
1 -l
0 I I I I I ———1’——_==='I
300 400 500 600 700 800 900

Wavelength (nm)

Figure 2~16. Quantum yield spectrum of Cs+(18C6)2-e‘ at ~60 °C. The
spectrum doesn’t show significant emission on the low energy side.

The saw-tooth shape on the high energy Side is due to noise because
the emission signal was weak.

67

than ~60 °C, it is unlikely to be the cause of decomposition. On the
other hand, other factors than temperature such as the presence of
reactive impurities might be the cause. Another possibility for the
decomposition may be the heat released into the sample when the
solvent condensed at the time of film preparation. The heat released
by condensation of dimethylether vapor at ~60 °C is estimated to be
32 KJ/mole. When 0.05 ml was condensed from room temperature
to ~60 °C, it would release z 35 Joules of heat. We can’t say all this
heat released would go to raise the temperature of the sample
because the heat could be absorbed by the sample cup, and the
copper cup was cooled by cold nitrogen gas. However, at the moment
of condensing, the solvent vapor contacted the sample, which might
raise the temperature of the sample momentarily, especially the
surface. It is impossible to estimate how much the temperature
increased, but that might lead to partial decomposition of the
electrides, because they are so temperature-sensitive. In any event,
all attempts to measure the true photoemission spectra of electrides
in this system have been unsuccessful. The conductivity
measurement of Cs+(18C6)2-e' shows that the transition energy from
the ground state to the conduction band is more than one eV, so that
we cannot rule out the possibility that the observed photoemission
spectrum for this compound may be due to a true signal. (Figure 2~
16)

Fig. 2~l7 shows the photoemission quantum yield of
N a+C222-N a', which has an emission peak at 290 nm presumed to be
mainly attributed to the electron emission from the sodium anion

valence electrons, 382, to the vacuum. The polycrystalline film with

68

80x10'6 -

a:
o
1

Quantum yield
8
l

20-

 

 

0 I l I I l I
300 400 soo 600 700 800 900
Wavelength (nm)

Figure 2~17. Quantum yield spectrum of Na+C222-Na' (with trapped
elctrons present) at ~60 °C. The high energy peak is mainly from the
valence band, and the low energy peak (from 430 ~ 700 nm) is from
trapped electrons.

69

defect States yields an additional shoulder at 360 nm and broad
emission at 430 '700 nm. The emission on the low energy side,
presumed to be from trapped electrons [18, 71], is much higher in
intensity than that obtained in previous work, performed under
poorer vacuum conditions (10‘4 torr) and a different loading
procedure. This confirms the strong influence of vacuum
environments and of apprOpriate sample loading. In past
experiments [18], the sample was loaded inside a glove bag filled
with inert gas, in which condensation of some moisture was more or
less inevitable, and subsequently the water might react with trapped
electrons as a scavenger, leading to a decrease in the photoemission
of trapped electrons.

To verify that the photoemission was electronic instead of ionic,
a set of Helmholtz coils 8 inches in diameter and with 150 turns on
each side was set up, with the spectrometer in the center of the coils.
It generated a magnetic field of 14 Gauss when one Ampere of
current passed through the coils. Because the retarding effect is
proportional to the mass of charged particle, smaller mass charged
particles have smaller radii of a circular trajectory. An electron will
be retarded a thousand times more than the lightest atomicion
under the same experimental conditions. Actually, under the
conditions used, emitted electrons would return to the surface from
which they are emitted. This method provides a clear way to
distinguish whether the emission is from electrons or ions. If the
photoelectron emission were from ions instead of electrons, a small
magnetic field applied to the Helmholtz coils wouldn’t have any

obvious effect on the spectrum. If some range of the spectrum is

70

partially from ions, the decrease of the signal would be much smaller
than that of electrons. Figure 2~18 shows the photoemission
quantum yield of Na+C222-Na' at various Strengths of the magnetic
field. The emission intensity decreased to 15 % when a magnetic
field of 42 Gauss was applied, and it further decreased to 6 % in a
magnetic field of 56 Gauss. The radii of the helical trajectories are
estimated that they are 0.4 mm and 15 m for an electron and a
sodium anion, respectively. Assuming that the initial emitting
direction of the electron and the Na' is normal to the sample surface
in a magnetic field of 56 Gauss.

Figure 2-19 shows the normalized decrease of emission
intensities of Na+C222-Na' at various wavelengths in different
magnetic fields. The reducing rates of the emission intensities at
different wavelengths were uniform, and the results strongly verify
that the emission over the whole spectral range is electronic.

Figure 2~20 shows the stability of photoemission from
Na+C222-Na‘ films versus time after the sample films were formed.
Stability of the samples was always a concern, and it was affected
mainly by the vacuum condition. The intense light beam should not
be a problem because the light source was monochromatic, and the
light spot on the sample spread over an area of 2x3 mm2 instead of
being concentrated at a point. For Na+C222-Na", the emission
intensity decreased only 5 % in 10 minutes at ~60 °C at 350 nm;
however, at 600 nm the decrease in the intensity could reach 21 %.
Because the photoemission on the low energy side was presumed to
be from the trapped electrons the more rapid decay is

understandable since trapped electrons would have lower stability

71

 

 

‘l20x‘l0'6 -
1001
'2
g a o -
-Cl- zero magnetic field
E . . -x- 42 Gauss
3 — 56 G
(D 6 0 _. ‘- . auss
c .
I:
O .
40-1
20-
0 - _ w___ ‘_ p .
I I I I l I I

300 400 soo 600 700 800 900
Wavelength (nm)

Figure 2~18. The reduction of the photoemission quantum yield
spectrum of Na+C222-Na' as a function of the magnetic field.

72

 

 

 

 

100%
+ 350nm
80... Cl 450nm
A 550nm
,1. O 650nm
E
O —I
E 60
S"
2:
175 40-
r:
2
E
20- a
u
0..
I I I I I I I
0 10 20 30 40 50 60

Magnetic field (Gauss)

Figure 2~l9. The normalized reduction of the photoemission

intensity of Na+C222~Na‘ at different wavelengths as a function of
the magnetic field.

73

 

   

i3 {'3 {I
80~
60-
-Cl- 350nm
—l—- 600nm

Reduced Intensity % (Norm)

 

 

40 —
20 -
0 A
I I I I I I
20 30 40 50 60 70
Time (min)

Figure 2~20. The time—stability of photoemission from Na+C222-Na'
at ~60 °C.

74

than Na'. The stability was sample dependent, and most alkalides
lasted more than 2 hours without apparent decomposition, which
allowed us enough time to measure the photoemission under
different experimental conditions.

Although the system has been used up to now for only
photoemission studies of air~ and temperature~ sensitive materials, it
could also be used for photoconductivity studies. All that would be
required would be the modification of the vertical wand to one
equipped with conductance patterns on the sample holder. Then the
photoconductance signal would be able to be separated from the
contribution of photoemission. Both the photoemission and
photoconductance methods are very useful in exploring energy states

in semiconductors.

7 5
CHAPTER III

THE PHOTOELECTRON EMISSION FROM Na+C222-Na': EFFECTS OF
LASER PULSES

III.A. Introoootion

It has been known for a long time that when alkali metals are
dissolved in alkylamines or polyethers, an equilibrium is established
between solvated electrons and alkali metal anions. However, the
nature of the solvated electrons, where the electrons reside and in
what form they are present, is still debated. Alkali metal anions had
been reported as existing in metal-ammonia [74], metal-amine and
metal-ether solutions by optical spectra characterizations [75-77],
although later studies showed that they are not present in metal-
ammonia solutions [8]. The presence of alkali metal anions in the
solid state was confirmed by the synthesis of alkalides, ionic salts
that contain alkali metal anions [1, 8]. Among them,
Na+(cryptandl2,2,2])-Na' (Na+C222-Na') was the first compound
crystallized and identified [1].

In Na+C222-Na’~ the sodium cation is encapsulated in the
cryptand, and the macrocyclic cryptand molecule serves to separate
the positive and negative ions in the solid, such that the sodium
anion resides outside of the cage and balances the positive charge.
The crystal structure consists of close-packed cryptated cations with
sodium anions in the pseudo-octahedral holes, and the structure has

considerable anisotropy. Although, as with all alkalides, this sodide

7 6
is thermally unstable and is sensitive to air and moisture, it is the
most stable alkalide synthesized to date and can be stable for several
days at room temperature. In order to insure stability, however, it is
synthesized and studied only in vacuo or in an inert atmosphere and
at low temperatures, usually below ~20 °C.

The physical properties of Na+C222-Na" have been studied most
intensively among all alkalides. The optical absorption spectra of
thin films show a broad absorption peak at 1.91 eV and a shoulder at
as 2.4 eV. The main peak has the same position as for Na' in
ethylenediamine and was assigned to the be sodium anion 382 ->
333p bound-bound transition [3]. The shoulder, which does not
appear .in solution, was assumed to result from electronic excitation
from the valence band 382 to the bottom of conduction band, in
agreement with both powder and two-probe single crystal
conductivity measurements [2]. The conductivity measurements
indicate that Na+C222-Na' behaves as an intrinsic semiconductor with
a band gap of = 2.4 eV. The photoelectron emission spectrum from a
rapidly dried Na+C222-Na' film had been previously measured under
a low vacuum of 10'4 torr [18], and showed two peaks at 3.4 and 2.0
eV. The high-energy peak was less temperature-dependent and was
attributed to direct emission of the electron from the valence band to
the vacuum, while the low-energy peak was strongly broadened and
increased more rapidly in intensity than the high-energy peak when
the temperature increased. This emission peak was attributed to the
photoemission of electrons trapped at lattice defect sites and was

presumed to be an indirect process.

77

Luminescence spectra of crystalline Na+C222-Na' were studied
by using a 50 picosecond pulsed dye laser at wavelengths between
560 and 618 nm (2.2 and 2.0 eV), which resulted in a narrow
fluorescence peak. The peak position varied with temperature from
1.854 eV at 7 K to 1.828 eV at 80 K [4]. The time-resolved emission
spectra, obtained by fitting the spectra with a double exponential
function, showed that emission occurred from at least two closely
spaced levels. On the high energy side of the band, the excitation
occurred by absorption of photons in a 352 -> 3s3p process, which
both emitted radiation and further relaxed to a lower level from
which the longer-time emission was observed. However, this picture
was too simple to completely interpret the time-dependent spectral
shape and the rate of decay on the high energy side. The role of
exciton-polaritons [78, 101] and local exciton trapping [17, 102] have
been recently described in detail.

Flash photolysis of the alkali metal anion, M', in solution has
been studied extensively; however such photolytic studies conducted
in the solid state are more recent. Photolysis of Na' in solution
caused a bleaching of the 650 nm absorption peak of the Na'
absorption and the formation of a new absorption band in the
infrared. The results were interpreted as the detachment of
electrons from Na" to form solvated electrons, with recovery times
that varied from milliseconds to seconds depending on the
temperature and viscosity [79-81].

The laser photolysis of solvent-free Na+C222-Na‘ films showed
[82] that a 15 ns pulsed dye laser at 605 nm with power higher than
1 mJ/mm3Z (peak power 6.6x104 W) could bleach the 650 nm

78

absorbance of Na', and a new absorbing species was created in the
infrared simultaneously. The half-time of partial recovery is as 30 ms
at room temperature. The system did not return completely to its
original State after the bleaching but rather a new set of absorbing
species was established. The photo-bleaching effect was presumed
to be due to the detachment of the electron from the sodium anion
and its trapping at another trapping site, accompanied by partial
decomposition.

Trapped electrons are commonly found in alkali halides and in
frozen glasses, when the defect sites are added deliberately by
irradiation or by “dOping” with alkali metals [83, 84]. Photoemission
studies of doped alkali halides yielded a low energy emission peak in
the quantum yield spectrum whose position depended on the alkali
halide studied [84].

Trapped electrons, et', in frozen organic or aqueous glasses
have being studied thoroughly by various methods, such as electron
spin resonance, optical absorption, luminescence and electrical
conductivity [21]. Suggested stabilization mechanisms for the
trapped electrons are that the mobile electrons produced by
radiation are first thermalized and stabilized through ion-dipole
interactions. Further stabilization in the trap sites results from
molecular orientation at rates that depend on the polarity of the
matrix molecules and the temperature [25].. The absorption spectra
of trapped electrons in glasses Show a shift with time and
temperature that strongly suggests that they are distributed among a
continuum of trap depths rather than all being trapped with the

same energy. The decay of trapped electrons, accompanied by a

79

blue shift, is better interpreted by trap deepening due to molecular
orientation rather than by thermal detrapping and retrapping [24].
The present study focuses on laser photolysis of polycrystalline
films of Na+C222-Na' in which transient surface modifications are
associated with photobleaching effects caused by nanosecond laser
pulses. In this chapter we investigate the effect of laser irradiation
on the photoelectron emission from Na+C222-Na'. The results are
described in terms of possible structural changes and the creation of
trapped electrons. A kinetic model for the redistribution of trapped

electrons is suggested based on the recovery effects.

III.B. Experimental

Crystalline samples of Na+C222-Na' were synthesized by
methods described previously [6, 22], with crystal growth in a pre-
evacuated (10'5 torr) glass cell at low temperatures. The primary
solvent was methylamine and the second solvent was
trimethylamine, which was used to reduce the solubility of the
compound. Before adding the second solvent, the complexation
reaction between a sodium metal film and cryptand C222 was
carried out for at least 12 hours at a temperature of ~30 °C. At this
or a lower temperature, the crystalline samples were grown by
slowly evaporating the solvents starting with a
methylamine/trimethylamine ratio of about 2:1. After removing
primarily the more volatile methylamine, the product crystallized in
the remaining solvent, which was rich in the less polar

trimethylamine. The crystals were then washed five times with pure

8 0
trimethylamine in the same glass cell by condensation and filtration.
After evaporating the remaining solvent, the sample was sealed in
vacuo in small ampoules attached to the synthesis cell and stored in
a liquid nitrogen dewar.

The photoemisson was measured with a 1000 watt xenon light
source before and after irradiation with a pulsed laser. The xenon
light was monochromatized with a scanning monochromator (Oriel
model No. 77250) with gratings (Oriel #77296 and #77298) and a
resolution of z 10 nm. The pulsed YAG laser was frequency-doubled
to 532 nm by a KD*P (potassium dideuterium phosphate) crystal, and
filtered by a pair of dichroic beam splitters (Spectra-Physics DHS-2).
The pulse frequency was set in the manual mode, and the duration
between the pulses was as long as 30 seconds to avoid accumulating
heat on the sample, and to permit observation of the full time-
development of the effect of photo-bleaching. The diameter of laser
beam is about 1 cm2 which can completely cover the whole sample
cup. The light spot of the monochromatic xenon light spot is a
trapezoidal shape with the size about 2x3 mm2. Each laser pulse was
7 ns in duration and had an average energy deposition at the sample
of 0.1 mJ/mmz, as estimated from measurements by a laser power
meter ( Opher with ~N type absorber head) and losses at the
reflective mirrors and beam-Splitter.

The spectrometer had the anode virtually grounded, and the
cathode was biased at - 40 V to assure that the saturation current of
photoemission would be obtained. The emitting current is shown in
Figure 3~l as a function of electric field. To perform quantum yield

measurements, the grid for the retarding field was grounded to

81

1.2- °'

1.0-

P
on
1

Current (M)
1

.°
.3:
l

0.2-

 

l l l I F I I I
o 5 ~10 ~15 ~20 ~25 ~30 ~35 ~40
Bias voltage (V)

Fig. 3-1. The photoelectron emission current of Na+C222-Na' at 400
nm and ~60 °C versus imposed bias voltage. The current reaches
plateau (saturation) when the bias voltage is larger than ~5 V.

8 2

reduce the capacitance in the spectrometer. The response time of the
spectrometer was measured to be a 40 ms. The signal was
preamplified by a factor of 109 with a preamplifier inside of the
vacuum system. It was then measured with an electrometer
(Keithley 617). The noise background was as 2 pA. An IBM XT
computer with an IEEE-488 Interface ( from Metrabite) and a home-
built stepper motor interface were used for the data acquisition. The
former interface was used for the electrometer and the latter was for
controlling the monochromator.

To make a film, the crystalline sample was introduced into the
system under vacuum, placed in a copper cathode cup, and dissolved
in methylamine by condensing the solvent vapor onto the sample at
~60 °C. The solvent was then removed by evaporation into a liquid
nitrogen trap to form a polycrystalline film, followed by evacuation
with a cryogenic pump to remove any residual solvent (p ~ 10‘6
torr). For determining the emission characteristic of nearly defect-
free crystalline Na+C222-Na', the crystals were merely wet with
methylamine to renew the surface, followed by solvent evaporation.
The emission spectra were measured under a vacuum of 10'8 torr,
produced with a turbopump (Varian Model V300). The temperature
was controlled (Omega model No. CN2001T~AT) with an accuracy of
:2 °C. The details of the photoemission system are described in
Chapter 2. The quantum yield was calculated with the reference
light intensity measured by a silicon photodiode detector (EG&G
model NO. UV44430).

III.C. flew

83

Photoemission quantum yield spectra of polycrystalline
Na+C222-Na' films were obtained at wavelengths from 240 ~ 900 nm.
Figure 2~9 shows the spectrum of the photoemission from a
collection of nearly perfect shiny crystals that were only slightly wet
by methylamine prior to the measurement. The spectrum shows an
emission peak at 290 nm and a very low emission on the low energy
side above 400 nm wavelength. The main peak is less temperature
dependent than the low energy peaks described later and is
attributed to direct emission from the sodium anion. The quantum
yield is in the range of 10:5 ~ 104. As shown in Figure 2~9, laser
pulses had practically no effect on the emission spectrum of this
sample. Figure 3-2 shows the emission spectrum at ~60 °C from a
more typical Na+C222-Na' thin polycrystalline sample prepared by
solvent evaporation from completely dissolved samples. The
spectrum shows, in addition to the high energy peak at 290 nm, a
shoulder at 360 nm and a broad emission band in the range 500 ~
700 nm. The lower energy emission bands are presumed to result
from defect electrons, due to their strong temperature dependence
and the absence of such bands in a good crystalline sample. Samples
of this type presumably contained both defect sites and excess defect
electrons produced by the fast solvent evaporation process.

The emission characteristics of these films were easily modified
by the pulsed laser presumably because of the presence of lattice'
defects at which electrons could be trapped. As shown in Figure 3-2,
the nanosecond doubled Nd:YAG laser at 532 nm had no appreciable

effect on the emission below 290 nm. However, after several

84

 

70

 

 

 

 

 
    

\ 4.0 3.0 2.0 1.0
Energy (eV)

 

 

 

 

0 I I I I I I
300 400 500 500 700 800 900

Wavelength (nm)

Figure 3-2. Photoemission quantum yield spectra of a Na+C222-Na‘
polycrystalline sample at ~60 °C. The solid line is the original
emission spectrum; the dashed line is the emission spectrum after
the sample was illuminated by a number of laser pulses. The inset
shows the pre-irradiation quantum yield spectrum as a function of
the photon energy of the xenon light - monochromator system.

succ
pror
of .
regi
live
ord
mo:
40(
Fig
tra'
fol
the
the
an

cf

[I

85

successive laser pulses, with time intervals ~ 30 seconds, there was
pronounced enhancement of the emission at 360 nm and in the range
of 500 - 900 nm. The increase of emission in the lower energy
region is assumed to result from population of initially empty, long-
lived defect sites by electrons that are excited by the laser pulses. In
order to study the photolysis effects in more detail, we set the
monochromator to pass the xenon light at both 600 nm (2.07 eV) and
400 nm (3.1 eV) during the period of consecutive laser pulses.
Figure 3~3a shows that when the xenon light is set at 400 nm the
transient response of electron emission during the laser pulse is
followed by a decay to a steady-state. Figure 3~4b shows that when
the xenon light is set at 600 nm and additional laser pulses are used,
the emission intensity decreases abruptly following the laser pulses,
and then increases slowly to a new Steady-state value. The same
effects were observed when the xenon light was first set at the
wavelength of 600 nm, and then at 400 nm. (Figures 3~4a and 3-3b
which can be compared with Figures 3~3a and 3-4b) A common
characteristic is that the Steady-state emission intensity increased
after each laser pulse until a saturation condition was reached, after
which additional laser pulses had little effect.

Figure 3-5 shows the recovery behavior at different
temperatures, ~95, ~60 and ~30 °C. Note that recovery rate at 600
nm decreases with an increase in temperature. Analyses of the data
by fitting the derived equations will be discussed later. When the
intensity of the xenon light was modified by using neutral density
filters, Figure 3-6 shows that the more intense the light the faster

the recovery to steady-state at 600 nm. The recovery and decay

 

 

 

 

 

 

 

 

 

 

 

 

 

1 4- —> I 3 1
(b) . ‘

1 2- -2.9
2 1'0“ ‘— —2 5 E
5 (a) V
~ 0'8“ 0.86 ‘2-3 E
C d)
0 I-
: 0 6 0 a4 21 '5
:I " - ‘ ‘ °
C.) U

0.4- °°°2“ ~1.9

0.80-
0 2‘_____. I I . I ‘1 7
50 60 70
0‘0 I I I I I I I’m"1 5
0 50 100 150 200 250 300 350

Time (seconds)

Figure 3-3. The response of the photoelectron emission current at

~60 °C of a Na+C222-Na' polycrystalline thin sample to successive 532
nm laser pulses as analyzed with 400 nm xenon light. The lower
curve (a) shows the response of a fresh sample, while the upper
curve (b) shows the response of a separate sample that had been
previously pulsed repeatedly and analyzed with 600 nm xenon light
(curve a in Figure 3-4). The inset shows the decay kinetics of the
fresh sample after the first pulse. The solid line is the least-squares

fit by an exponential with k = 0.36 i 0.03 5'1. The decay after
subsequent laser pulses also showed a slow component (see text).

 

 

 

 

 

 

 

 

 

 

 

I l J l I
30— (a) (01 L . r I L — II— 35
1.551 '-
257 1.50- - " 30..
<
1.45- - 5
220- 140.. _)_ 25“
5 <— ' =
E 1.35 , . . I g
0 1 s- 0 so - 2 ° =
t (b) u
3
o —->‘
1 o - 1.5
0.5- - 1.0
I r- I I
O 100 200 300 400

Time (seconds)

Figure 3~4. The response of the photoelectron emission current of a
Na+C222-Na' polycrystalline thin sample to successive 532 nm laser
pulses as analyzed with 600 nm xenon light (curve a). The drop to
zero after seven pulses Shows the dark current obtained by
interrupting the xenon light. The inset shows the growth upon
illumination with the 600 nm xenon light before laser pulsing. The
solid curve is the least-squares fit by a simple exponential with rate
constant 0.0305 i 0.0006 S'l. The lower curve (b) shows the
behavior of a separate sample that had been previously pulsed
repeatedly and analyzed with 400 nm xenon light (curve a in Figure
3~3). Note the slight relative increase per pulse.

88

2.0 l I l I l

 

-30 °C

1.5-

-60 °C

\

1.0-

Current (nA)

-95 °C

 

 

 

0.0

 

I I I I I
0 20 40 60 80 100

Time (seconds)

Figure 3—5. Growth of the photoelectron emission current of

Na+C222-Na' at 600 nm after 532 nm laser pulses at three

temperatures. Note the increase in current and the decrease in
growth rate as the temperature is increased.

89

 

 

 

 

2.0- a 20
, '3
_ E
21.5 —o.15 3
N g
5 8
‘5 ~. 3
E 1.0- —o.10 E
= .
u t“
2
9 O
O 5- H -0 05 5
I
0.0 I I I I . I ..OoOO
o 20 40 so 80 100

Light Intensity %

Figure 3~6. Linear dependence of the photoelectron emission current

of Na’C222-Na' (open squares) and of the recovery rate constant
(crosses in squares) on the 600 nm xenon light intensity after 532
nm laser pulses. Note that the intercept of the former is zero, while
that of the latter is 0.065 t 0.005 8'], close to the value obtained
from a direct measurement of the thermal decay (see Figure 3-9).

9 0

rates are the result of competition between replenishment of empty
trap sites by the light from the xenon lamp, which populates the
traps by excitation from the valence band, and the thermal decay
toward an equilibrium state. The electron emission from trapped
sites appears to be an indirect process since it is so sensitive to
temperature. When the xenon light was set at other wavelengths
between 500 and 700 nm, we also observed intermediate effects,
including a decrease followed by an increase. (see Figure 3~7)

A magnetic field of - 14 Gauss was applied during a test of the
system to confirm that the emission was from electrons instead of
ions. Effects due to artificial response of the circuits were also ruled
out by studying the photoemission from an evaporated potassium
film and bare copper under the same vacuum condition used with
samples. No time-dependent artifacts were observed from the

metals except for the circuit rise time of 40 ms.

III.D. Diseossion

The experimental facts may be summarized as follows:

(1). [an is proportional to "I where n, is the concentration of trapped
electrons in level i and 1a,, is the emission current.

(2). 1,,” is strongly temperature dependent, with increased emission
at higher temperature (Figure 3~5).

(3). When the xenon light is turned off, a steady-state is reached

after seconds to minutes such that n, decays exponentially with time

to a dark equilibrium value (Figure 3~9).

91

 

 

 

 

 

1.5 -‘
A14 .
<
5 k T—v—
E 1 3 .4 r M
Q) ff
t 4-
: .,"
.9 '
3
'g 1.1-
m
1.0 I I I I I j
0 10 20 30 40 50
Time (Second)
(a)
1.5 -
1.4 I
A
E
v 'I . - '0 “0.” M55-
“ 1 31 . u.-.” ..- ooooooooooooooooooooooooooooooooooooooooo
c a.“"."' ............................
.13 ..~- .
81 2 . ..
g . ° ' ' 400 nm
.7, ‘ 600 nm
E 1.1 H o . combined data
1.1.1 ‘-\
1.0 _
I I I I
0 1° 20 30

(b)

Fig. 3~7. (a) Photoemission from Na+C222-Na' at 500 nm xenon light
and ~60 °C after the laser pulse, (b) the combination of the electron
emissions at 400 nm and 600 nm after the laser pulses. Figure b is

the sum of the photoemission intensities at 400 and 600 nm,

decreased by 2.0. One can see that Figure a and the calculated curve

in b are nearly the same.

92

(4). Depletion of n5 within 530 nm of the vacuum level occurs during
the laser pulse when compared with the steady—state value of n,
(Figure 3-4).

(5). Enhancement of n, within 400 nm of the vacuum level occurs

during the laser pulse when compared with the steady-state value of
n, (Figure 3~3).
(6). Repeated pulses lead to a constant steady-state value of n, after
4 ~ 6 pulses. The biggest jump occurs with the first pulse (Figures 3-
3a and 3~4a).
(7). The rate constant for the growth of n,- after a pulse, monitored at
600 nm is directly proportional to I , the xenon light intensity, when
first-order growth is assumed (Figure 3~6).
(8). The growth rate constant decreases with increasing temperature
when first-order kinetics are used (Figure 3~5).
(9). The decay rate constant from the “full light” value of n‘. in the
dark is 0.06 to 0.07 S'1 at ~60 °C (Figure 3~9). This is also the zero
light intensity intercept of a plot of the rate constant versus [xenon
at ~60 °C (Figure 3~6).
(10). The initial and steady State emission currents are directly
proportional to I (Figures 3~6 and 3~9).
(11). The decay amplitude (400 nm) decreases as we approach
saturation but the growth amplitude is relatively constant (600 nm)
(Figures 3~3a and 3~4b).

We first provide qualitative explanations of the effect of laser
irradiation on the emission characteristics of Na+C222-Na' and then
develop a model to explain the kinetics. The basis for the

explanation is the schematic energy diagram shown in Figure 3~8, in

93

Vacuum
level

 

-0.0 -T_-’T\

Region A

1"

i

Energy (eV)
3
/'~

 

 

 

 

 

 

 

\
~2.0 —
~2.5-
\
~3.0 —
0 113-5 25-5

Quantum Yield

_ -- - - — - — —

 

\

\\ \\ \\\ \ \\ \\\ \\\\\ \ \\\\\\\i\\\\\\\\\\\

)

_—_

 

 

M\\\ \\\\\\\\V\\

l

 

3.0

—2.5

Bottom of
conduction
band

-2.0

Bottom of
p~band

-1.5

“-1.0

*- 0.5

- 0,0 Ground

315-5 state

Figure 3~8. Energy diagram of Na+C222-Na' related to photoelectron
emission. The solid curve is the excess quantum yield that results
from a number of laser pulses with 600 nm xenon analyzing light,
plotted versus energy, and is obtained from the data shown in Figure
3~2. The open arrows represent the energy of 532 nm laser photons,
the solid arrows that of 600 nm photons, and the shaded arrows that
of 400 nm photons. The regions A, B, C represent electron trap
energy regions that have different types of behavior (see text).

94

which the zero of energy is at the top of the 352 valence band. The
bottom of the 3s3p band is at 1.84 eV based on fluorescence studies
[4] while the bottom of the conduction band is at as 2.4 eV based on
conductivity measurements [2].

The vacuum level is a: 3.1 eV above the valence band edge.
This is determined by extrapolating the straight line portion of the
high-energy peak (290 nm) to zero emission. The high-energy peak
is not very temperature dependent, suggesting that the emission is
primarily direct, rather than indirect. According to the theory
developed by Kane [44] for photoemission by bulk, direct processes
without electron-electron scattering, the quantum yield is
proportional to (hm-ET), in which E, is the threshold energy.

The breadth of the photoemission spectrum due to defect
electrons is so large that we presume the existence of defect traps at
various energies as represented by the short solid lines in Figure 3~8.
Furthermore, it is clear that trap-to-trap migration of electrons at
equilibrium is very slow, probably because of the spatial separation
of the traps and low electron mobilities.

It is possible that the laser pulses generate additional trapping
sites or cause chemical or structural changes at the surface. If so,
however, this does not seem to alter the photoemission response of
the compound. The photoemission spectrum of defect-free crystals is
unchanged by the laser pulses, suggesting that new traps are either
not formed or are not involved in subsequent photoemission. Also,
the effect of laser irradiation decreases after 4 ~ 6 pulses, which
again suggests that additional traps are not formed as a result of the

laser pulses.

9 5

The picture that emerges from such considerations is that the
initial samples contain both empty and filled defect sites, distributed
over a wide energy range. Examination of Figure 3~2 shows that the
defect electron concentration after laser irradiation is 3 ~ 4 times as
high as before, with peak positions of spectra lying 3.4 eV and 2.0 eV
below the vacuum level, but distributed over a wide range of
energies.

The laser photon energy is too small for single photon induced
electron emission from the ground state of Na‘ but it is high enough
to transiently populate the p~band. Other studies [82, 86] Show that
high-power laser pulses can alter the absorption spectrum of thin
films of this sodide, so that it is not surprising that the laser pulses
increase the trapped electron concentration. In addition, we
anticipate that the laser pulse will tend to “sweep-out” trapped
electrons that are within 2.33 eV of the vacuum level.

The laser power is critical to the analysis of the effect of laser
pulses. The energy deposited by the 532 nm laser pulses is z 0.1 mJ
mm'2. This is close to, but below, the threshold for photobleaching of
absorbance (z 0.2 mJ mm'z). At much higher power levels, the
photoemission disappeared after a single pulse, presumably because
of photo-decomposition on the surface.

Photons from the xenon lamp at 600 nm (2.07 eV) are not only
able to cause photoemission from trapped electrons that are 1.0 eV
or more above the valence band, but they can also populate states
below 1.84 eV by electron transfer from the p~band to vacant traps.
This results in steady-state photoemission from a higher population

of trapped electrons than are present in the dark. Interrupting the

9 6

light results in thermal decay of these excess electrons with a first—
order rate constant of 0.06 ~ 0.07 8']. (see Figure 3~9) Restoration of
the light causes a slow increase in the photoemission intensity. Both
the rate and the steady-state level achieved are proportional to the
light intensity. It is important to note, however, that the order of 80
% of the final steady-state emission current is obtained immediately
upon illumination. This again provides evidence for the presence of
long-lived trapped electrons.

The temporal behavior after a laser pulse when 600 nm xenon
light is present can be explained on the basis of the observations
described above. Unless saturation has already occurred from
previous laser pulses, the immediate effect of the laser pulse is to
increase the photoemission current by increasing the number of
trapped electrons with energies that are at least 1.0 eV above the
ground state. However, depletion of pre-existing trapped electrons
in this energy range leaves empty traps that can be filled from the
p~band and replenished by the xenon lamp. Thus, the emission
current grows until a steady-state is reached. Competition between
trap-filling and decay of the p~band excited Na' by fluorescence and
radiationless decay causes the return to steady-state to be slower at
higher temperatures where the steady-state p~band population is
smaller.

When the xenon light comes from the monochromator at 400
nm the results are very different. At this wavelength, any trapped
electrons above the ground state can be emitted (indeed even some
emission from Na' is expected). The result is that the laser pulse

causes a net overpopulation of trapped electrons that decay

III II a] ( Cl. C

97

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.9 l 1 1 1
E
v o
08 £10—
. - m _
§20~
G
"'30- D
'6
0.7— §4°" —
2 light 35°“ . I . I
5 off 0 10 20
a light Time (see)
I: 0.5.. on , K’L
: Ki
0
0.5“ I-—
0.4- -
0'3 I I I
0 50 100 150 200
Time (sec)

Figure 3~9. Sequence used to determine the thermal decay rate of

Na+C222-Na‘ in the absence of laser pulses. The decrease in signal
intensity upon turning on the 600 nm xenon light after a variable
dark period is plotted in the inset versus the length of the dark
period. During the dark period the emission current was zero. The
estimated rate constant for exponential thermal decay (dotted line in
the inset) is between 0.06 and 0.07 S'l.

51
ar.

la

en
ele
ICE

the

98

thermally to a lower steady-state population. The competition
between these two effects is particularly clear at intermediate
wavelengths (500 nm) in which decay first occurs to a level below
the steady-state level, followed by slow growth to the steady-state
level (Figure 3~7).

These qualitative explanations can be put into more
quantitative terms with the aid of a few assumptions about relative
rates.

When the xenon light is set at 600 nm, the photons can emit
trapped electrons that lie within 2.07 eV of the vacuum level, and
also pump the laser induced excess electrons in the region within
2.33 eV of the ground state to the higher energy traps. At the same
time this light will excite valence band electrons to replenish
depleted shallow trap sites. Therefore, the concentration of trapped
electrons is a result of the competition process between the thermal
decay of laser induced excess electrons and the population of the
depleted shallow trap sites. The effects can be seen in Figure 3~10,
where the emission first decays and then slowly recovers. The
spectrum can be deconvoluted into two separate processes, decay
and recovery, with the equations derived from the models described
later.

In comparison, when the xenon light is at 400 nm the photon
energy can emit any trapped electrons and even the valence band
electrons to the vacuum. The emission is from an overpopulated
region because of the presence of laser-induced excess electrons in
the deep trap sites. Therefore, the emission intensity is high at first,

then decays to the steady-state value. No obvious recovery growth

99

 

 

 

 

 

1.80- ‘ 1 ' 1 -
1.75-
A I
g 1.70-
E
2
3 1.55~
1.60-
1'55 I i I I '-
10 20 30 40
Time (sec)

Figure 3~10. Decay and growth of the photoelectron emission current
of Na+C222-Na‘ after a 532 nm laser pulse at ~30 °C with analysis by
600 nm xenon light. The solid line is the fit of these data by two
exponentials with rate constants of 0.23 i- 0.01 8'1 (decay) and 0.070
:l: 0.004 s-1 (growth).

1 0 0
is observed, probably because the photon-excited electrons at this
wavelength are effectively quenched because they are in the
conduction band or in a high-energy p~band.

From the previous qualitative observations and presumptions,
two models are suggested to explain the recovery effects. The
photon-excited electrons from higher energy states proceed to relax
into empty trapping sites at lower energies, or else excited Na' states
at the bottom of the p-band, either fill traps or return to the ground
state by fluorescence and radiationless decay.

Based on the first model, the energy states of the trapping site
can be divided into 3 regions (Figure 3-8):

N
(a) Deep trapping sites in“, which are filled with laser-

induced excess electrons, from which the electrons will not be
emitted by 600 nm (2.07 eV) photons to the vacuum, but only to
higher energy (shallow) trapping sites. Since photoemission from
this region is only allowed by the 400 nm light, at this wavelength
only decay of the photoemission current is observed after the 532
nm laser pulse. Such decay is biphasic. The fast component (k as 0.4
5'1) decreases in magnitude with successive pulses while the slower

component (k = 0.09 S’l) remains significant.

(b) The medium trapping sites 2"!» which are depleted by the
b

laser pulse but are filled by laser-excited excess electrons. These
trapped electrons can be emitted to the vacuum by 600 nm xenon
light, and the empty states can also be refilled by electrons that are
excited from deep traps and from the valence band. A net

enhancement of the final trapped electron concentration is observed,

1 0 1
resulting from the laser pulse and 600 nm xenon light repopulation
of traps.
(c) Trapping sites that are 2.33 eV or more above the ground

p
state Eric, which are depleted by the laser pulse, but are not refilled

C

by the laser induced excess electrons. These trapped electrons can
be emitted to the vacuum, and the empty traps will be refilled by
the photon-excited electrons from the deep traps and the valence
band (when 400 nm analyzing light is used). The concentration of
trapped electrons in this region is too low to show long-time
photoemission that is significant on the scale of photoemission
intensities from the other regions.

In the first model the kinetic mechanism for the recovery

from photobleaching by 600 nm xenon light would be

N
(12% N
4;- : Calkg - (1k, + In); n,

m
(12% N

m
2‘ = Cblkg + CblkOZna - (1k, + 19)an
a b

 

(3-1)
I p
(1an N p

c = Gel/:02», — (1k, + 19)an
dt 0 c

 

where Ca and Cb are the coefficients for the excitation of

N m
electrons from the ground state to fill the trap sites of Zn“ and 2n,”
0 b

I is the xenon light intensity, k8 is the quantum yield for the

excitation of electrons from the valence band to higher energy trap

1 0 2
sites, kc is the quantum yield for the emission of trapped electrons to
the vacuum, k, is the rate constant of thermal relaxation of trapped
electrons, k0 is the quantum yield for the emission of deep trapped

electrons to the shallow traps, and C}, and Cc are the coefficients for

N m
the emission of trapped electrons from states 2nd to states 211,, and
a b

p
Eric , respectively.

C

The photoemission intensity 1”,, at 600 nm is the sum of

electron emissions from 2.07 eV below the vacuum level, which

includes region C and part of region B.

I“ = Ik,[cPB(z) + cm], (3-2)

where c, is a constant factor. The total emission can be obtained by

solving the Equation 3-1 (with the assumption kez kg),
1,,” = x + m + 2)exp-<”‘«+"t>'. (3-3)

The analyses of the recovery at 600 nm with this equation will
be discussed later. This model does not explain the anomalous
temperature—dependent recovery rates (slower at higher
temperature). This mechanism also includes too many detailed
processes, some of which may not be important.

In order to interpret the temperature-dependence of the
recovery rate, another model is suggested in which the trapping
states are filled from the bottom of the p-band and the lifetime of

Na' ions in the p-state decreases with an increase in temperature [4]

Cl]

ral

Wh
sir:
pul
C01

1 O 3
(see Figure 3-8). This would decrease the repopulation rate of the
trapping sites as the temperature increases.
The concentration of excited Na' ions in the p-band, up, is an
equilibrium between the promotion rate and the decay rate by

fluorescence and radiationless decay,

d
7;!- = k5] -k,n,, (34)

in which I is the light intensity, kE is related to the cross-section for
photon absorption, and k, represents both fluorescence and

radiationless decay. Thus, in steady-state,

n = 1 (3'5)

If the major cause of trap-emptying is thermal relaxation to lower-

cnergy states (including the ground state) with rate constant k, , the

 

rate of change of trapped electron concentration, (2‘, is given by
5%: 101,01, —n,)-k,n,, (3-6)

where k is the refilling rate constant from the p-band to the trapped

sites, n, is the initial empty trap concentration produced by the laser

pulse and n, is the concentration of electrons in these traps.

Combination of equations (3-5) and (3-6) gives

104

2&— L": _ _ -
dt -[k,]1(n' n,) lorn, (3 7)

The photoemission intensity I”, at 600 nm is proportional to

the density of trapped electrons in the appropriate region. The
solution to Equation 3-7 can be expressed as an exponential function,

-[Ik' +k, ]:

1,, = A + Bexp , (3-8)

where k' is (5515—), A is 1"

I

and B is —(1;-I:).

“9

Neither Equation 3—3 nor Equation 3-8 yields a complete fit of
the recovery of the photoemission at -60 °C. The approximate rate
constants are =—- 0.15 i 0.01 5'1 for the former and = 0.23 i 0.02 5'1
for the latter. The suggested mechanisms do not precisely describe
the photobleaching effects. However, the latter model is preferred
rather than the former one since it can interpret the temperature-
dependence of the recovery rates.

To complete the analysis of the growth rate, a slow growth rate
equal to that obtained with a fresh sample (0.0305 8'1, see the inset
in Figure 3-4) must be included. Thus, the complete expression for

the growth of the emission intensity is

I, = A + Be‘“ + Ce'o'ow‘ (3-10)

The agreement of this equation with the data from repeated

pulses is shown in Figure 3-11.

105

 

 

 

__ w
1.2- _
1.0-' _

A _ . M

< _ _ -

5

‘50 8- _

Q)

I...

I.

=

U
0.6- I—

0.4- h—

 

 

 

I l l l l l
O 1 0 20 30 4O 50
Time (seconds)

Figure 3-11. The least-squares fit of three successive photoelectron
emission growth signals of Na+C222-Na' after 532 nm laser pulses at
-60 °C by Equation 3-10, a double exponential function in which the
slower rate constant is not adjusted, but is determined from the
growth rate prior to laser irradiation. Successive curves are
displaced by 0.4 nA for clarity of presentation.

1 0 6

When the xenon light is set at 400 nm, the energy of the
photons (3.1 eV) is high enough to emit electrons from any of the
trapped sites and also from the valence band. Light of this
wavelength can also pump electrons from the valence band to all
trapped sites, probably through the bottom of the conduction band or
a higher p-state, but the excited electrons may be efficiently
quenched in the conduction band.

If the trapped electrons in Region C had long enough lifetimes,
it was reasoned that two-photon absorption would yield enhanced
photoelectron emission. In Figure 3-12, low intensity IR laser (1064
nm, 1.1 111] mm'2 per pulse with duration 0.2 ms) were
intermittently combined with 400 nm xenon light. After illumination
of the polycrystalline film sample with the 400 nm xenon light ,
turning on the IR laser pulse trains (pulse rate of10 Hz) resulted in
increased emission that continued to grow to a saturation level
during exposure to both beams. When the xenon light was blocked,
the emission abruptly dropped to a lower level and then continued to
decrease slowly toward zero. An exponential fit of the decay data,
assuming no emission at infinite time yielded a rate constant of
0.0044 1 0.0003 5‘1. This indicates that long-lived traps within 1.2
eV of the vacuum level can be populated by 400 nm light.
Illumination of the sample with 600 nm light followed by continuous
IR laser pulses at low intensities had practically no cooperative
effect. This is expected since the 600 nm photons have too low

energies to populate many traps within 1.2 eV of the vacuum level.

107

0.5-

 

.°
h
l

   

.°
to
l

 

 

 

 

Current (nA)

 

{
I

 

 

0.1-

 

 

 

I I I I T I I I
0 100 200 300 400 500 600 700

Time (seconds)

Figure 3-12. The effect of 1063 nm weak laser pulses (10 Hz) on the
photoelectron emission current of Na+C222-Na' at -60 °C during and
after illumination with 400 nm xenon light. The successive vertical
lines represent the effects of : 1) IR + 400 nm on; 2) 400 nm light off
(note the slow decay of the signal with only IR illumination); 3) 400
nm light on again (note the growth to a plateau level); 4) IR laser
light interrupted (note the constant signal representing saturation of
trap occupancy); 5) IR laser light on again (note that saturation has
already been achieved); 6) 400 nm light off (note the exponential
slow decay towards zero signal with only the IR laser on). The solid

line shows the fit of the final decay by a simple exponential having
the value zero at infinite time.

108

III.D. Conclusions

The existence of defect sites in crystalline Na+C222-Na'
depends on the procedure used for sample preparation. For a pure,
nearly perfect crystal there is a low density of defect states in the
energy gap. The photoemission spectrum of a collection of such
"good" crystals shows a high energy emission peak at 290 nm and
very low emission on the low energy side above 400 nm. For a
polycrystalline sample, which contains more grain boundaries, defect
sites and defect electrons, the photoemission spectrum shows, in
addition to the high energy peak at 290 nm, a shoulder at 360 nm
and a broad emission band in the range 500 - 700 nm. The low
energy emission is presumed to be from trapped electrons.

Laser pluses are able to modify the surface of the sample, and
can deplete trapped electrons that lie within 2.33 eV of the vacuum
level. They can also populate trapping sites within 2.33 eV of the
ground‘ state with laser-excited excess electrons. When the
wavelength of the xenon light is longer than 500 nm, the photons
have lower energies than the photoemission threshold energy of the
valence band, and a recovery growth in photoemission is observed.
By contrast, at 400 nm only decay of the laser "shot-peak" occurred.
Two kinetic models are suggested to explain the results based on
competition between trap-filling and thermal decay. The refilling of
empty traps by the photo-excited electrons is probably through the
p-band at 600 nm, and through the conduction band or a higher

energy band at 400 nm.

1 0 9
The nature of the trapped electrons, such as in what
environments they reside or what type of defects are present is still
unclear. The stabilization of the trapped electrons may be similar to
that of trapped electrons in frozen ices. It is not possible to
accurately calculate the density of trapped electrons from this
experiment, but other studies suggest that the concentrations are less

than a few percent of the Na‘ concentration.

l 10
CHAPTER IV

REFLECT AN CE STUDIES OF SODIUM CRYPTAND [2.2.2] SODIDE

IV.A. Introduction

Crystals usually exhibit a wide range of light absorbance when
the frequency is varied. In the spectral region of strong resonances,
the crystal can be opaque even for the thinnest obtainable sample.
Therefore, transmission measurements become impossible and
utilization of reflectance spectroscopy is called for. For example, the
semiconductors Si and GaAs are more suitable for reflectance than
transmission measurements. In our case, the films of Na+C222~Na'
are polycrystalline samples instead of single-crystals, formed either
by solvent evaporation of the sodium sodide solution or by co-
deposition of Na and cryptand[2.2.2] vapors. Hence, it is impossible
to obtain information about orientation-dependent transitional
energies from transmission measurements.

The sodide crystal, Na+C222-Na', has a closest-packed structure
in which cryptated cations form a hexagonal pattern with sodium
anions in the pseudo-octahedral holes. The packing follows an A, B,
C, A...pattern. The distance of Na‘ to Na‘ is 8.83 A in the packing
plane perpendicular to the C axis, and 11 A from Na' to the nearest
Na' in an adjacent plane [1]. As a result, Na+C222-Na' has prominent
anisotropy of its physical properties. As is true of all alkalides, this

sodide is an air- and temperature- sensitive compound.

111

So, for any optical study, the crystalline sample has to be under
vacuum and at low temperatures.

The reflectance spectrum of Na+C222-Na‘ has been measured
previously [19]. However, analysis of the reflectance data was done
by combining the reflectivity and absorption data instead of by a
Kramers-Kronig conversion. Also, this analysis could not provide
information about the anisotropic properties of the sodide, because
the polycrystalline films used for absorbance studies contained
crystals with various orientations In order to obtain further insights
into the orientation-dependence of the excited p-states of the sodium
anion, we applied the Kramers-Kronig method to analyze the
reflectance results for single crystals.

Near-normal incidence reflectivity was measured, with a
reflective microscope. Non-polarized and polarized light was used
for the measurements. For the polarization-dependent
measurements, the electric field vector of the light was aligned both
perpendicular and parallel to the c-axis in the energy range 0.5 to
3.1 eV at z -60 °C. The optical constants were deduced from a
Kramers-Kronig analysis of the reflectivity data. The calculated
results are compared with those from the absorption spectra of thin
polycrystalline vapor-deposited films of Na+C222-Na'.

The principles of Kramers-Kronig analyses, the theory of optical
dispersion relations and the procedures used to make

approximations are included in this introductory section.

IV.Al. Tho Kramers-Kronig Relations

112
The Kramers-Kronig (KK) relations are central to the

analysis of optical experiments [87,88]. They are a pair of relations,

,, _ 2a) 0., d(a)') ,
(4-1)

a (w')=—Pj6°——)2dw

These equations enable us to find the imaginary part in a linear
passive system from the real part of the response function if the
frequency range is large enough, and vice versa. For example, we
can relate the real and imaginary dielectric functions or refractive
indices by the KK relations.

The origin of the KK relations is the Cauchy integral form and
the Cauchy principle value contour [89]. In the Cauchy integral, a

function f(z) is analytic when it is in the interior region, within a

closed contour bounded by C. The integration is

§Ci(-ld =2m’f (.20) (4-2)

If 20 is in the exterior region, the integral is zero.

The Cauchy principle value contour is shown in Fig. 4-1, where

20 is exterior to the contour but unlimitedly close to the real X axis.

The integration of the closed contour i—flQ—dz is zero.

113

 

 

 

Figure 4-1. Contour for the Cauchy Principle Value integral.

The integrations of segments 1 and 2 can be derived

L1)+L2) = 1.797120) = PILM'dx’ (4‘3)

x-zo,

where f(x) is a complex function. Equation 4-3 is the origin of the
Kramers-Kronig relations, which can be split into the real and
imaginary parts of KK dispersion relations (as these in Equation 4-1),
provide the following conditions can be met [90],

(1) The poles of f(x) are all below the real axis X.

(2) The integration of f(x% in the upper half semi-circle
vanishes (a sufficient condition is f(x)—)O uniformly as |x|—>oo).

(3) The real part of f(x) is an even function and the imaginary
part is odd.

The reflectivity 7(a)) is a complex function defined as the ratio
of the incident electric field E to the reflected electric field. The

reflectance R, defined as the intensity ratio,

114

R = [E(ref)). .(E(ref))

E(inc) E(I'nc) (4~4)

is a real quantity, and has is a physically measurable value. The

reflectance can also be expressed and related to the reflectivity, 7(a))

b y
y<w>=Ri<w)e“<°” (4-5)

where 0(0)) is the phase difference (or phase-shift) between the
incident and reflected waves. It is difficult to measure the phase
shift directly in reflectance, but the phase shift can be calculated
when the reflectance is obtainable. Theoretically, if we know the
reflectance at all frequencies we are able calculate the phase-shift

angle through the Kramers-Kronig relations,

1

2 .

«wk—ZEN w

0 (9'2-

where P is the Cauchy principle value, which indicates the process of
integration that a voids the poles at (0'. It is difficult to carry out the
direct integration in Equation 4-6 due to the unknown values at very
high and very low frequencies. In order to proceed with numerical
integration, Equation 4-6 can be converted by partial-integration to

the form

115

1 |a)'+w|dlnR(w') ,
9w =——| l d 4-7
( ) 27: 0 n|c0'-a)l dw‘ a) ( )

 

This integration form permits some approximations that make
the empirical numerical analysis appropriate. When the reflectance
R(w’) becomes a constant in the very low and very high frequency
regions, these regions do not make contributions to the integration

W is zero; and when (0' is much greater

(w' +%. _w)l becomes very

small. These properties allow us to avoid the difficulties of obtaining

because the derivative

or much less than a), the contribution of In

 

experimental data at the extremes of frequency. The reflectance
data at very high and very low frequencies are usually inaccessible
by optical measurements. However, with sufficiently accurate
extrapolations from the available experimental data, the KK

calculations will not yield large deviations from the true spectra

[91,92].

IV.A2. Tho Qotioal Dispersion Thooty

For the optical study of a solid material, it is important to
understand the interaction of photons with the material.
Experimentally, the photon probe should have a larger wavelength
(A) than the dimensions of a unit cell, the roughness of the surface of
the material should be much less than the wavelength of the light
used, and only the bulk properties are considered to contribute.

The optical properties of a solid can be described in term of the

macroscopic properties such as the refractive index n and the

116

extinction coefficient k. With Maxwell's equations, these optical
constants can be further derived to yield relations to other functions
such as the dielectric constants (e' and e"), the optical conductivity (0'
and o") and the energy loss function.

The optical constants are complex functions and any solid
medium can be described by the complex refractive index,
N(E)=n(E)-ik(E), or the complex dielectric function,
e(E)=e,(E)—iez(E). Since all the optical constants can be derived from
n(E) and k(E), and they are functions of the photon energy, these
equations are called the optical dispersion relations.

When an electric field is applied to solids, it will cause the
opposite displacements of positive and negative charge entities. The
polarization is defined as the dipole moment per unit volume, and is

expressed as the integral form

P = V‘,,'1 Z niqiui. (4-8)

The integration is over one primitive cell, where VP is the unit

cell volume, and q is the charge, a is the displacement and n is the
number of electrons in the unit cell. The dipole moment u can be
expressed as a power series of E, uoc 0tE+BE2+yE3+----. When a normal
electric field is applied (< 104 eV/cm), only the linear term needs to
be considered. Polarization then becomes proportional to the electric
field, P = x E, where x is electric susceptibility.

Reflectivity arises from oscillating valence electrons out of
phase with the incident radiation. In the process no absorption of

the induced polarization current occurs, and interference of the

117

incident wave with the reradiated waves from the valence electrons
leads to reflectivity. When a very low frequency electric field is
applied, the polarization is completely adjusted to the applied field,
so x is a real number. However, as the frequency increases some of
the displacements of heavier effective mass that contribute to P will
not be able to follow the frequency. The part of the polarization that
is out of phase by 1t/2 is the imaginary part. Therefore, P is strictly
defined as P = (x1 + ixz) E. This equation relates the magnitude and
phase relations between two physically observable quantities, P and
E

The classical theory of the dispersion relations is mainly due to
the Lorentz and Drude models. The Lorentz model is applicable to
insulators and semiconductors, which assumes that all the interband
transitions are direct (k conservative). The Drude treatment is
applicable to free electron models , in which the interband
transitions include all the transitions not involving a reciprocal
lattice. From the Lorentz oscillator, the dielectric functions for

nonmagnetic materials can be derived as

47zNe2 (a),2 - of)

m ((0,,2 — (02)2 + F2022
_ 47rNe2 Fe)
m (0002 — (02): + 1‘20)2

 

(4-9)

 

in which (00 is the inherent harmonic frequency of the bound

electrons, and F is a viscous damping coefficient. When Equations

4-9 are applied to classical atoms with more than one electron per

atom, the N, a) and 1" terms need only be replaced by N,, a), and I},

118

respectively, and the equations are changed to summation forms.
Equations 4-9 indicate that the real dielectric function is

qualitatively dependent upon the band gap, and 72000 is verified as

corresponding approximately to the band gap, where 8, decreases

with the increase of hwo [93].

Table 4-1 Important physical parameters and equations for a
medium.

 

 

 

 

 

 

 

Parameters Equations
81,11 81 = 1+ 41ml
£2.12 82 = 41rx2
01,12,82 01= 03x2 = cog/41:
0241.81 (’2 =‘(011=-c0(81—1)/4n
8,,n,k €1=n2-k2
£2,n,k £2 =2nk

 

1 l
n,£,,£2 "2 =(5181 +(512 +592]
2 1 2 2 l
[gapgz k = 5 -81+(81+€2)2

 

 

 

 

 

The physically unobservable parameters x, e and o are defined

in complex forms, and are co-related to each other, such that, once

119
one parameter is known the others can be obtained also. They
define the essential optical characteristics of a solid. In Table 4-1,
the equations for the parameters and their relations to the optical

constants n and k are listed [94].

IV.A3. Broooooro and Approximations to: Ktamors-Krooig
Applications

Theoretically, calculating the exact 0 requires the reflectance
spectrum at all the frequencies. Empirically, this is impossible due to
the difficulties of obtaining data at very high and very low
frequencies. However, reasonably accurate calculations can be made
if an appropriate extrapolation of R is applied beyond the range of
measurement.

The extrapolation to zero frequency is easy; there are two ways

to approach the goal. First, if the low-frequency dielectric constant is
(n—1)2+k2

2 2 can be used
(n+1) +k

measured [95], the equations 2;‘,=r12-k2 and R:

 

to calculate the reflectance R at very low frequency, since the
absorption coefficient k of the electron transition is zero at very low
frequency. It should be pointed out that absorption bands from
vibrations at low frequency do not contribute to the electronic
transitions, and can be ignored. Second, for certain crystals, an
accurate index of refraction n at very low frequency can be obtained
from prism measurements [96, 97], so that R can be obtained.

The extrapolation of R beyond the data range to higher
energies does not follow a simple rule, but there are conventions.

Providing that the frequency region does not contain strong bands

120

caused by electronic transitions, the reflectance remains high until
the plasma frequency, then falls rapidly at higher energy. The
plasma frequency for semiconductors can sometimes be roughly
estimated by using the free-electron plasma equation mp=(47‘"ez/n)%,
by substituting the number of valence electrons per atom as free
electrons into the equation. 80, at high energy the value of R can be
deduced from the asymptotic expression for the dielectric constant

[98].
R(w) = ca)", (4-11)

at much higher energies, n and k can be assumed to be a land 0,
respectively.

A more quantitative description of the extrapolation of R can
be evaluated by comparing the known absorption coefficients of a
bulk transmission to the calculated ones at energies near the band
gap.

Original reflectance data are usually affected by noise,
therefore the spectrum does not show a completely smooth curve. If
direct differentiation of the data is carried out for numerical
integration of Equation 4-7, the calculated results would lead to
scattered values. A technique to circumvent this difficulty is to
smooth the data by using the Savitzky-Golay method. The Savitzky-
Golay smoothing is a least-squares procedure that allows the spectra

to have their original shapes after the operation.

IV.B. Exam

121

The sodide crystals were grown by programmed slow cooling, 2
°C per hour, of a solution of Na+C222-Na' in a mixture of solvents
from -10 °C to -60 °C, in which the ratio of the solvents
methylamine/trimethylamine was about 3:1. Crystals of dimensions
up to several mm on an edge were formed, and some of these
crystals were selected and vacuum-sealed in a quartz optical cell that
was attached to the crystal-growing apparatus. They were stored in
a -80 °C freezer and kept at a low temperature during the reflectance
measurements. By never opening the cell after crystal growth, very
shiny single crystals could be studied.

The reflectivity spectrometer had an Ealing-Beck microscope
body with a 15X/ 28 reflecting objective (Figure 4-2). The light
source was a ISO-W tungsten-halogen lamp with the light directed
by a 90° mirror via objective mirrors to the sample. Between the
light source and the semi-transparent mirror a linear polarizer was
installed with its polarization direction perpendicular to the
reflective plane. The light hit the sample at near-normal incidence (a
6°), and the light spot was about 40 um in diameter. The reflected
light was transmitted to and through an optical fiber to the optical
analyzer (Guided Wave model 206), which had resolutions of 6 nm
from 400 nm to 1200 nm and 8 nm from 1200 to 2400 nm. A Si
detector was used for the former optical range and a PbS detector
was employed for the latter. Each of the reflectivity data points was
accumulated 15 times to enhance the signal-to-noise ratio. The
reflectivity of Na+C222-Cl' was used to calibrate that of the
Na+C222-Na'.

122

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ts: m>m>> cm @230

 

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SEE __ _
038.20 _
5.: \. II
it

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.830

 

 

.mNtfloa

 

mam;
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Q83
cmmofiz
c382.

 

 

123

In order to obtain the optical constants, we performed
Kramers-Kronig analyses. In the far infrared, the reflectance was
extrapolated to zero frequency by calculating R from the low
frequency dielectric constant, presuming the absorptivity to be zero
at zero frequency. At high energy, the reflectance was extrapolated
with the asymptotic expression R(w)=cw"4. The complete
reflectance data set was first smoothed by the Savitzky-Golay
method, then was subjected to a Spline fit to expand the data from
about 150 to 2048 points. (The data expansions were used to reduce
the errors in the derivatives required for the calculations.) After the
phase shifts, 6(a)), were calculated, the other orientation-dependent
optical constants were then obtained by using the equations shown
in Table 4-2.

As shown in the Appendix, three programs were written in the
FORTRAN language for the numerical integration. In the integration,
a key step is that in each integration to generate a data point, a
corresponding pole has to be avoided.

The program KKFAB02.FOR is for numerical integration of
Equation 4-7. The input data has to be a text array, and in the form
of three columns with the number of rows less than 2200. The
contents in the columns are R(co), AlnR(co) and E, in order. The
output is in the same form as the input, in that the data of the
columns are R(a)), (0(6) and E, in order. The output data are in the
text form, and can be loaded into Lotus 1-2-3, and the optical
constants can be calculated by using the equations listed in Table

4—2.

124

Table 4-2. Equations for calculation of the optical constants.*

 

Kramers-Kronig conversion

1

 

 

 

 

 

 

 

 

 

 

 

”lnRZ ((0')
0(w)=—P[0:—2—
E ' ' ff' ' t l
xtrnction coe 1c1en k_ 2stin0
- l
1+R-2R2c056
Refractive Index _ l-R
- l
1+R-2R_2cosa
Real part of the dielectric
function 5' =n2-k2
Imaginary part of the dielectric
function 8' = 2nk
Energy loss function -Im(l)= 2nk
e (n’+k2)2
*The applications to anisotropy are restricted.

 

125
Equation 4~7 can be further partially integrated to another

integration form [99]

6(0)) = $101“) — (0)1an — w'|+ (a) + w' )ln|a) + w'|]d(fl%02). (4-12)

The program FORKRON.FOR is for numerical integration of
Equation 4-12. The input and output forms are the same as those of
the program KKFAB02.FOR, except that the contents of columns are
R(a)), AlnR(co), E and 1),, in order, where P, is [A1nR(ar,,,)-AInR(m,)].
The results calculated from this program are nearly identical to those
calculated from the program KKFAB02.FOR. No advantage in the
numerical integration is observed. by using Equation 4-12 instead of
Equation 4-7 , but it provides a mean for comparison.

From Equation 4-1, a reflectance spectrum can be converted to
an absorption spectrum, and vice versa. However, the extrapolation
procedures for an absorption spectrum are different from those of
reflectance. On the low frequency side, the absorptioncan be
extrapolated to zero if one can assure that no electronic transitions
occur below a specific frequency. On the higher energy side, the
absorption can be assumed to be approaching a very low value, and
k approaches zero at very high frequency. The program
KKRFAB02.FOR is for converting the absorption spectrum to
reflectance. The contents of the input columns are the absorption A,
Ak(m) and E, in order, in which k is the extinction coefficient. The
outputs are k, n-1 and E. Note that the integration of Equation 4-13
yields n—l instead of n [100],

126

_ 2 ~ w'k(co') .
"(w)—1_;?0 WC!) . (4-13)

IV.C. Results and Discussion

Fig. 4—3 is a reflectance spectrum of a single crystal of
Na+C222-Na‘ in the range from 0.5 to 3.1 eV (400 - 2400 nm)- The

peak reflectance is at --= 2.1 eV (z 600 nm) and a small shoulder
occurs at z 1.65 eV (z 680 nm). The small shoulder does not always
show up on a given plane of the crystal, and its intensity varies with
a change in the light spot position. We suggest that the shoulder
maybe correspond to an indirect electronic transition of Na“, as
indicated by the strong temperature dependence. The position of the
shoulder shifts to a lower energy when the temperature is increased,
and vice versa. (Figure 4-4) An alternative explanation is that the
shoulder results from defect electrons that are trapped at Na'
vacancies.

As shown in Figure 4-5, the shapes of reflectance spectra do
not change appreciably by rotating the surface plane. This indicates
that the reflectance spectra are true signals despite the fact that the
surface is not exactly perpendicular to the beam path. The reflective
light cone carries real information about the material.

Due to the hexagonal 'structure of Na+C222~Na', anisotropic
properties are expected. However, these properties cannot be
observed in thin film samples because the films are composed of
polycrystals with various orientations. Single crystal reflectance

measurement with polarized light sources would provide abundant

127

 

60-

50-

40—

30-

Reflectance %

20—

.‘O.....
‘0’. "fid. "'0
o ‘0.

 

 

 

1 .0 1 .5 2 .0 2 .5 3 .0
Photon Energy (eV)

Figure 4-3. Reflectance spectra of a single-crystal of Na+C222-Na'
at e - 60 °C. Non-polarized light was used for this measurement.

128

 

60-

40-1

0 °C
3 O _ ........... '60 °C

 

Reflectance °/o

10-

 

 

 

0 I I I I I I
400 500 600 700 800 900 1000

Wavelength (nm)

Figure 4~4. Temperature-dependent ‘ reflectance spectra of
Na+C222-Na‘. The shoulder at = 780 nm shifts from 775 nm to 795

nm when the temperature is increased from - 60 °C to 0 °C.
Polarized light was used for this measurement with Ell C.

129

 

50—

40-

 

—— A, 0° tilt

 

 

o , , . .
o\ ------ B, 0.7° tIlt (nght)
§ 30 4 ;gé;.:\ a. - - - C, 1.4° tilt (right)
3 5"“... \‘z .3. ........... D, 0.70 "It (Iefl)
3 g; y, g - ----- F, 1.4 ° tilt (left)
'5 M \‘t.
a: :' ‘t.
2 0 _ ' 51‘ \‘t .3. .
i ‘\“‘ 0.. . 5.“...1 .......
0’ :I \\\”, I _ ~ ‘ .......................... ”
.é',’ ‘-""°~ ‘ ‘ ~L’ -----
1 O _ ‘-':;"’ “-.~....‘-.‘..~ ;._..0‘:~“ ’. '
‘13, I ’ ’ """"" . ” °“ :')?“~ .
O l l l l

Figure 4-5.

at as - 60 °C with various small tilt angles of the surface plane.

600 800 1 000
Wavelength (nm)

Reflectance spectra of single-crystal Na+C222-Na‘

Non-polarized light was used for this measurement.

130

information to help in understanding the anisotropic properties that
are related to the differences of the Optical dispersion constants
along the a- and b- axes from those along the c-axis.

Typical polarization dependent near-normal incidence
reflectivity spectra at --= -60 °C of single crystal Na+C222.Na' in the
energy range 0.5 - 3.1 eV are shown in Figure 4-6. The spectrum A
has 4 major features at energies of 1.6, 1.95, 2.05 and 3.1 eV. In
addition, there is a shoulder at 2.4 eV. Spectrum B has 3 major
features at energies of 2.05, 2.5 and 3.1 eV and 3 very minor
shoulders at the energies 1.6, 1.9 and 2.3 eV. There is seemingly a
one-to-one correspondence in the peak positions. For example, the
peaks at 1.6 and 1.95 eV for spectrum A correspond to the shoulders
at 1.6 and 1.9 eV for spectra B. However, the peak at 2.5 eV in
spectrum B does not have its counterpart in spectrum A.

The reflectivity spectra shown in Figure 4-6 were measured
from different faces of the single crystal. A number of such
measurements were made with the electric field E of the polarized
light along various directions in the faces. The reflectivity spectra
were related to the structure by examining the characteristic shapes
of the single crystals. For example, spectrum A corresponds to El/C,
and spectrum B is for EIC.

The optical constants shown in Figures 4-8 to 4-13, which are
more relevant to the electronic states under discussion than the
reflectivity spectra, were deduced by means of Kramers-Kronig
analyses of the reflectivity spectra. In Figure 4-9, the absorption
spectra are obtained from the extinction coefficient k (Figure 4-8)

and show that the main peak position is at 1.91 eV. One low energy

131

 

 

Reflectivity °/o

 

 

 

1.0 1.5 2.0 2.5 3.0
Energy (eV)

Figure 4-6. Near-normal incidence reflectivity of single-crystal
Na+C222-Na’ for El/C and EiC at = - 60 °C.

 

132

 

2.0

1.5-4

Absorption

0.5—

 

 

 

 

 

0.0

Figure 4-7.

I l l l l
1.5 2.0 2.5 3.0 3.5
Photon Energy (eV)

Absorption spectra of a polycrystalline thin film of

Na+C222-Na' with a thickness of 930 A at z - 60 °C.
(Data of I. E. Hendrickson [86])

133

 

 

 

 

3.0
ft
3‘.
2.5~ g 1.
f
x l
*5 2.0- /
.9
.2
a:
3 i
O 1.5" i
C
.2 /
‘3
LU ............. E // C axis
0.5— \
«0’
NM
0.0 l l l l l
1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-8. Spectral dependence of the derived extinction
coefficient k of single-crystal Na+C222-Na' for El/C and E_LC

at == - 60 °C. The peaks with tick marks are not real, but are due to
noise on the weak signal.

134

 

 

 

 

500x103 - A
5 400—
E
.9
5.3 — ELCaxis
E 300 — ------- E // C axis
0
C
.9
‘5.
8 200-
(I)
..D
<
100‘ / \ “0/
O l T l l l
1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-9. Absorption coefficient of single-crystal Na+C222-Na' for
E/IC and EIC at z -60 °C. On the high energy side of the main
peak, the spectrum shows an apparent shoulder at == 2.35 eV for
El/C and a peak at 2.5 eV for EIC. The peaks with tick marks are
not real, but are due to noise on the weak signal.

135

peak at 1.65 eV only shows up for E/IC. The shoulder at 2.35 eV for
El/C corresponds to a very small peak for EILC whereas the peak
that appears at 2.5 eV for E.LC is absent for El/C . These results are
compared with the absorption spectrum of thin vapor—deposited
films (Figure 4-7), together with other measurements such as
fluorescence [17], conductivity[18] and photoemission. We identified
the peak at as 1.91 eV as due to the transition from 332 -r 3s3p, the
shoulder at 2.35 or peak at 2.5 eV is the transition from 3s2 ->
conduction band, and the 1.65 eV peak is presumed to be the
absorption peak of trapped defect electrons on the surface.

The refractive index spectrum (Figure 4-10), n, as a function of
photon energy is less affected than the extinction spectra, k, on the
low energy side, by either the accumulated errors or extrapolation
inaccuracy. Therefore, such spectra can be accurate even at low
energies. The refractive index values 1.85 and 1.7 for E/IC and EIC,
respectively, at low frequencies, are presumed to be accurate.
Comparing the main peak of the spectra in k with that in It, shows
that the peak in k occurs at higher energies than that in n, which is
consistent with the theory of interband transitions. Integration of

the extinction coefficient k from very low frequency to very high

frequency yields the oscillator strength, f, which is defined as
4.33x10'9C‘1Jk(V)dV, in which C is the concentration of the absorbing

species in mole per liter [19].

Figure 4-11 gives the real part of the optical dielectric function
of Na+C222-Na'. The plasma energy, (up, is estimated to be about 2.5

eV, where the value of 21 is zero. The real part of the dielectric

function is qualitatively dependent on the band gap. The optical

136

 

 

 

 

 

 

— EiCaxis

c ~--- E //C axis
X
(D
U
E.
o
.2
8
£9
8 a
I 1.0-

0.5—

0.0 I I I I I

1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-10. Spectral dependence of the real part of the refractive
index n of single-crystal Na+C222-Na' for E/IC and EiC at as - 60

°C.

137

 

 

 

  

—— E .LC axis
~~--~~ E // C axis

Real Dielectric Constant e,
O
l

 

 

-6—l

 

 

 

1.0 1.5 2.0 2.5 3.0
Energy (eV)

Figure 4-11. Spectral dependence of the real part of the dielectric
function e, of single-crystal Na+C222-Na' for E/IC and EIC at ~
-60 °C.

138

dielectric functions at low frequency are 3.5 for El/C and 3.0 for
ELLC. As a result, we suggest that the band gap for EIC is larger than
that for El/C [9]. In Figure 4-9, the absorption peak at 2.5 eV for
EIC and shoulder at 2.35 eV for E/IC would be related to the gap
energies.

The imaginary part of the dielectric function is the most
meaningful to compare with theory since this quantity is directly
related to the experimentally measured interband absorption
strength, at least in the region where the intraband contribution is
small. Theoretically, (0282(0)) is proportional to the absorption
strengths, and the peaks in 82 correspond directly to the positions of
interband transitions. The 82 spectra are shown in Figure 4-12.
Structures are apparent at 1.65 eV; 1.9 eV (main peak); and 2.35 eV
for E/IC and at 1.9 eV (main peak); and 2.5 eV for EIC. These
results confirm that the Na+C222-Na' has anisotropic optical
properties.

The function -Ime’l describes the energy loss of fast electrons
traversing the material and is called the energy loss function. In
figure 4-13, the maximum is at z 2.5 eV for EJ.C and = 2.6 eV for
E/IC. The latter has a broad-band shape rather than a sharp peak
with a maximum at z 2.6 eV. A sharp peak of this function is
frequently is associated with the existence of plasma oscillations, so
the determined plasma frequency at = 2.5 eV (see Figure 4-11) is
close to this value. However, the high-energy trend of the spectra
indicates that another peak may exist on the high energy side.

Figure 4-14 is the extinction coefficient spectrum calculated

from the reflectance spectrum measured with non-polarized light,

139

 

12

M”

10-

—E.LCaxis
------- E/ICaxis

 

Imaginary Dielectric Constant e,
O)
l

 

 

 

0 I I I I l
1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-12. Spectral dependence of the imaginary part of the
dielectric function 82 of single-crystal Na+C222-Na‘ for E/IC and

EIC at == -60 °C. The peaks with tick marks are not real, but are
due to the low signal-to—noise ratio.

140

 

1.5-

 

 

 

E

E

c

.9

‘6 1.0-

c

u:- — EICaxis

9, .............. E // C axis

0

..l

>

9’

g 0.5—

LLI

W
0 O I I I I I
1.0 1-5 2'0 2'5 3.0

Energy (eV)

Figure 4-13. Spectral dependence of the energy loss function,
-Im(e“), of single-crystal Na+C222-Na' for El/C and
EiC at== - 60 °C.

141

 

2.5-

2.0—

1.5—

1.0—

Extinction Coefficient k

0.5-

 

 

0.0

 

I I I I I
1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-14. Spectral dependence of extinction coefficient k of
single-crystal Na+C222-Na' at z - 60 °C. Non-polarized light was
used for this measurement. The small shoulder at 1.65 eV is
presumed to result from trapped electrons.

142

which is essentially a combination of the electronic transitions in all
possible orientations. The spectrum shows some differences from
the results of polarization, especially weaker features on the
shoulders. However, an average of combining the extinction
coefficients for El/C. and EIC yields the spectrum shown in Figure
4-15, which is very similar to Figure 4-14. This result provides
additional evidence for the anisotropic properties of Na+C222-Na’,
and these properties can only be observed by polarization methods.

This polarization method provides useful information about the
orientation-dependent properties. For the sake of comparison, these
results are listed in Table 4-3.

The absorption spectrum of Figure 4-7 can be converted into
the reflectance spectrum with Equation 4-13. The result is shown in
Figure 4-16, which is likely to have better resolution than the

measured reflectance spectra.

143

 

 

 

 

3.0

2.5- /\
.
E 2.0 "" l
.9 -'
.9 ;'
3: l
a , s
0 1-5‘ 5 ------- E.LC axis
E ,' -~------ E // C axis
.5 g — average
.5 .'
$2 1.0- i 't'
w ’. .\

0 . 5 - .’.l.’ .'§o‘.‘.~

1.0 1.5 2.0 2.5 3.0

Energy (eV)

Figure 4-15. The spectral dependence of the extinction coefficient
of single-crystal Na+C222-Na' at z - 60 °C. The solid line is the
average of the extinction coefficient for E/lC and EiC, and can be

used to compare with the extinction coefficient from non-polarized
light.

144

 

 

 

 

 

 

 

 

 

 

 

 

Table 4-3. Polarized and non-polarized studies of Na+C222-Na‘.*
Eyc EIC non-polarized

R peaks 1.6, 1.95, 2.05 2.05, 2.5, 3.1 1.6, 2.0, 2_,_6

position(eV) 3.1

R shoulders 2.4 misgu 2_,3_

(eV)

k peaks (eV) 1.91, 1.65 1.93. 2.3.. 2.5 1.6, 1.92, L55

k shoulders 2.35 none 2.35

(eV)

n ( at low 1.8 1.6 1.85

energy)

n (at 0 1.76 1.72 1.64

frequency)

8, (at low 3.5 3.0 3.6

frequency)

8, (at 0 3.1 3.0 2.6

frequency)

8, peaks (eV) 1.65, 1.9, 2.35 1.9, 2.5 1.6, 1.9, 2.3, 2.6

-Im(1/€) =2.6 =2.5 =2.5

peaks (eV)

 

 

 

 

* The data with under line are weak peaks.

 

145

 

40—

30—

20—

Reflectance °/o

10—

 

 

 

0 I I I I I
1.5 2.0 2.5 3.0 3.5

Energy (eV)

Figure 4-16. The reflectance spectrum obtained from Kramers-
Kronig conversion of the absorption spectrum in Figure 4-7.

146
IV.D. glonolttsions

From Kramers-Kronig conversions, the orientation-dependent
optical constants have been obtained. The transitional energies from
the ground state to the p-state are 1.91 eV for El/C and 1.93 eV for
EIC. The gap energy difference is even apparent, 2.35 eV for El/C
and 2.5 eV for E.LC. Comparison between Figure 4-7 and Figure 4-8,
shows that the absorption spectrum is closer to that for EIC. This
indicates that probably most of the polycrystals in the Na+C222-Na‘
film are with the c-axis face-up; that is, the planes in which the Na‘
ions are close together are parallel to the surface of the sapphire

substrate.

147
CHAPTERV

CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK

V.A. Conolusions

A photoemission system has been built that has the advantage
of loading a sample with minimum contact with gases or moisture.
The system has 3 vacuum chambers: loading, film-preparation and
photoemission measurement chambers. Such a design permits one to
perform sequential experimental procedures in different chambers
according to the functions of the chambers. The purpose is to keep
the main chamber clean and under good vacuum. The photoemission
measurements can be performed in the range from room
temperature to -130 °C, and the temperature is controlled with the
accuracy of i 2 °C. A data acquisition system has been built which
includes a home-built interface for the monochromator and an IEEE-
488 interface for the electrometer. The programs for data
acquisition were written in the GW—Basic language which are able to
control the output voltage of electrometer and the scanning speed of
monochromator, and to record data with respect to wavelength or
time. The combination of the photon source and the data acquisition
system could be widely used for optical studies, not just limited to
photoemission. What would have to be done is to modify the
programs.

The photoemission of alkalides, K+(15C5)2-K', Rb+(15C5)2-Rb‘,
Na+C222-Na', K+C222-K', Cs+C222-CS' and K+C222-Na' were measured.

1 4 8

The photoemission threshold energies were determined according to
the theory developed by 0. Kane [44]. The spectra can be divided
into three categories. A good crystalline sample with few defect
states in the band gap has a spectrum that shows only a high energy
emission peak of the valence electrons of M“ and very low emission
on the low energy side. If a polycrystalline sample contains a
number of defect states, and defect electrons the spectrum shows, in
addition to the high energy peak, an emission band and shoulder on
the low energy side. The spectra of partially decomposed samples
show only very weak emission on the high energy side.

Although the photoemission of electrides, K+(15C5)2-e',
K+C222°e' and Cs+(18C6)2-e" could be measured, the emissions seem
not to be from the true electrides. The samples are inferred to be
partially decomposed during the film—preparation.

Laser pulses had appreciable effects on Na+C222-Na' samples.
The polycrystalline samples contain both defect sites and defect
electrons. As a result, the laser pulses can both deplete and
replenish the trap sites. The surface of the sample may also be
modified due to the presence of lattice defects. The laser pulses
deplete trapped electrons within 532 nm below the vacuum level
and also populate trapping sites within 532 nm above the ground

state. As a result, there is an enhancement of the trapped electron

concentration (m) within 400 nm of the vacuum level but a decrease
of n,- within 600 nm of the vacuum level compared to the steady
state value. The recovery of the bleaching effect upon illumination
at 600 nm is shown to be a photon assisted process instead of a

thermal equilibrium process. The recovery rate constant decreases

1 4 9

with an increase in temperature, but the decay rate with 400 nm
xenon light seems not to be temperature-dependent. Two model are
suggested to describe the recovery effects. One is that photo-excited
electrons proceed via a cascading relaxation to refill the empty trap
sites; another model' suggests that refilling the empty trap sites by
photo-excited electrons is through the p-band. The second model is
preferred because the first one does not explain the temperature-
dependent recovery rates. To complete the analysis of the growth
rate, a slow growth rate obtained with a fresh film was included in
the second model.

The reflectance spectra have been successfully converted into
absorption spectra, and vice versa. The programs for the Kramers-
Kronig conversions have been tested with a set of CdS data taken
from a book [99]; the nearly identical results prove that the method
used for the numerical integration is correct. The programs can now
be routinely used for conversion of spectra. Several successful steps
made the reflectance studies possible. First, shiny single-crystals of
N a+C222-N a' were able to be grown with a special method. Second,
optical fibers and the Guided Wave spectrometer system were able
to transfer and process the signal, which makes the measurements
more reliable, accurate and efficient. Third, appropriately smoothing
the data with the Savitzky-Golay method made the conversion
possible even with somewhat noisy data.

The optical constants of Na+C222-Na‘ have been obtained,
which is a help in understanding the optical properties of the sodide.
For example, the peaks of the imaginary part of dielectric function

correspond to the interband transitions. The polarization-

1 5 0
dependence studies, and then the optical constants obtained, provide

important information about the anisotropic properties of

Na+C222-Na'.

V.B. inf Frhrer

The photoemission studies of electrides were always hampered
by partial decomposition. A possible way to solve this problem
would be to measure the PE without redissolving the samples to
make films. However, the contact of the sample with the sample
holder and the smoothness of the surface are still problems that need
to be overcome.

The PE energy distribution curve measurements were obscured
by the surface charge. To circumvent this problem, a higher energy
photon source is necessary, but it is costly. An alternate way to
make the measurements is to use a commercial UPS system such as
the one in Dr. Ledford’s laboratory. Unfortunately, two problems
remains. One is that the instrument is not working yet. Another
problem is that there is no cooling system in the instrument, so that
any measurement of temperature-sensitive compounds would be
very difficult.

The techniques for reflectance studies have been developed.
The same methods can be applied to study any alkalides or
electrides, but only if a shiny crystal can be grown and enough
reflectance data can be obtained in the range from 400 - 2400 nm.

The FTIR reflective microscope is an alternate choice for

measurement of reflectance due to the advantage of a broad range of

 

1 5 1

the light source (700 -5000 nm). However, two requirements have
to be fulfilled before the measurements can be made. First, the
platform has to have both X- and Y- directions adjustable as well as
the Z- direction. Second, an appropriate window for the transmission
of light at very low frequencies has to be employed.

Theoretical calculations of the band structure of these
compounds would provide very interesting results to compare to the
experimental data. This is especially true for Na+C222-Na', because

various measurements of the energy states have been made.

 

1 5 2
APPENDIX

MONOVOLT.BAS

10 REM PHOTOEMISSION DATA ACQUISITION SYSTEM.
15 REM 9/29/92, WRITTEN BY C. T. KUO

20 DIM DDAT(2000,3)

30 PRINT

************************************************************************

INPUT FILE NAME AND STOPPING WAVELENGTH

************************************************************************

40 INPUT "INPUT FILE NAME FOR DATA";FILE$

50 '

60 INPUT "STOP WAVELENGTH?";FINWAV

70 '

80 INPUT "DO YOU WANT AUTOMATIC CORRECTION WAVELENGTH
(Y/N)";ANS$

90 CORR=0

100 '

110 IF ANS$="Y" THEN CORR=10

120 '

************************************************************************

OPEN THE SERIAL PORT RS-232 TO LISTEN AND TALLK, AND

RESERVE A FILE FOR DATA STORAGE.

************************************************************************

130 OPEN "COMl:9600,N,8,1,DS,CS,CD,RS" AS #1

140 OPEN FILE$ FOR APPEND AS #2

150 IF LOF(2)=0 THEN CLOSE #2

160 ELSE PRINT"FILE ALREADY EXISTS ":CLOSE #2

170 OPEN FILE$ FOR OUTPUT AS #2

180 PRINT

******************************************$*****************************

INITIALIZE THE IEEE-488 INTERFACE BOARD, SET BIAS VOLTAGE

AND TIME INTERVAL BETWEEN DATA POINTS.

************************************************************************

1 5 3
MONOVOLT.BAS (continued)

190 INPUT "TIME INTERVAL FOR DATA IN SECONDS";RUNTIME
200 INPUT "VOLTAGE IN VOLTS";PVO

500 'INTTIALIZE THE BOARD

510 DEF SEG=&HC000

520 CMD$="SYSCON MAD=3,CIC=1,NOB=1,BAO=&H300"

530 VAR%=0:FLG%=0:BRD%=0:IE488=0

540 CALL IE488(CMD$,VAR%,FLG%,BRD%)

550 IN = ASC(INPUT$(1,#]))

560 PRINT IN

570 IF IN<>2 THEN GOTO 540
******************************************************************#****$
SET PARAMETRS FOR THE INTERFACE OF MON OCHROMATOR
CONTROLLER
********************************************t***************************
1000 C$=CHR$(3):M$=CHR$(4):GO$=CHR$( 18)

1010 STA$=CHR$(80):STB$=CHR$(96):STC$=CHR$(121)

1020 NHUN$=CHR$(160):NDEC$=CHR$(144):NUNI$=CHR$(128)
1030 FIELD #1,] AS A03

1040 LSET AO$=GO$

1050 PUT #1,]

1060 FIELD 1, 1 AS 13$

1070 LSET E$=STA$

1080 PUT #1,]

1090 FIELD #1,] AS ASTB$

1100 LSET ASTB$=STB$

1110 PUT #1,]

1120 FIELD 1,] AS ASTC$

1130 LSET ASTC$=STC$

1140 PUT #1,]

***************************************III********************************

COMMUNICATE WITH THE IEEE-488 INTERFACE BOARD
*********************************t*****************************#*****#**
1150 CMD$="REMOTE 27"

1160 CALL IE488(CMD$,VAR%,FLG%,BRD%)

 

15.
155
156
157(
158(
l59(
1600
1610
I620

1 5 4
MONOVOLT.BAS (continued)

1170 CMD$= "OUTPUT 2715131"

1180 A$="F1X"

1190 CALL IE488(CMD$,A$,FLG%,BRD%)
1200 X$="X"

1210 CMD$="OUTPUT 27[$E]"

1220 VON$= "01x"

1230 CALL IE488(CMD$,VON$,FLG%,BRD%)
1240 COUNT%=0

1250 V$="V"

1260 VO$=V$+STR$(PVO)+X$

1270 CMD$="OUTPUT 27[$E]"

1230 TIMER1=TIMER

1290 CALL IE488(CMD$,VO$,FLG%,BRD%)
***********************************************II!************************
COMMUNICATE WITH THE INTERFACE OF MONOCHROMATOR
CONTROLLER
************************************************************************
1300 FIELD 1,1 AS DS

1310 LSET D$=C$

1320 PUT #1,1

1330 PERIOD=0

1500 FOR 1:] TO 1000

1510 FIELD #1,1 AS NUN$

1520 LSET NUN$=NUNI$

1530 PUT 411.1

1540 NU=ASC(INPUT$(1,#1))

1550 PRINT NU

1560 FIELD 1,1 AS NDE$

1570 LSET NDE$=NDEC$

1580 PUT #1,1

1590 ND=ASC(INPUT$(1,#1))

1600 PRINT ND

1610 FIELD 1,1 AS NHU$

1620 LSET NHU$=NHUN$

 

1 5 5
MON OVOLT.BAS (continued)

1630 PUT #1,1

1640 NH=ASC(INPUT$(1,#1))
1650 PRINT NH

1660 NAMP$=SPACE$(20)
1670 COUNT%=COUNT%+1
1680 CMD$="ENTER 27[$]"

*********************##3##****iltaltII!altalt3|!1|!allall**3k*III********************III********

SET TIME INTERVAL BETWEEN DATA POINTS
************************************$***********************************
1690 TIM=TIMER-TIMER1

1700 CALL IE488(CIVID$,PVOL$,FLG%,BRD%)

1710 PRINT NAMP$

1720 E1 =VAL(MID$(PVOL$,5,20))

1730 DDAT(COUNT%,1)=E1

1740 DDAT(COUNT%,2)=TIM

1750 IF INKEY$="P" THEN GOTO 2000

1760 ST=TIMER

1770 WHILE PERIOD < RUNTINIE

1780 PERIOD =TIMER-ST

1790 WEND
*****************************************t***********tt*******#*********
CHECK AND CORRECT THE WAVELENGTHS SHIPPED BY RECORDING-
TINIE LAGS
*********************************************************************$**
1800 DDAT(J,3)=]00*NH+10*ND+NU

1810 IF DDAT(J,3)=FINWAV THEN GOTO 2000

1820 IF DDAT(J ,3)-DDAT(.I -1,3)>=10 THEN DDAT(J,3)=DDAT(J,3)-CORR
1830 IF DDAT(J,3)-DDAT(.I-1,3)<=-10 THEN DDAT(J,3)=DDAT(.I,3)+CORR

184(IITED(T'J
************************************************************************
(:L£)SI3TTTEEUVTTERIWACJES
**************************t**************************#**$J2232:2331:****

 

2000 FIELD #1, 1 As F$
2010 LSET F$=M$

I . I ( d l I 1 1 .

1 5 6
MONOVOLT.BAS (continued)

2020 PUT #1,1

2030 CMD$="OUTPUT 27[$E]"

2040 VO$="OOX"

2050 CALL IE488(CMD$,VO$,FLG%,BRD%)
2060 CMD$="LOCAL 27"

2070 CALL IE488(CMD$,VAR%,FLG%,BRD%)
2080 CLOSE #1

************************************************************************

RECORD DATA INTO HARD DISK
***************************************t***************************#****
2110 FOR K=1 TO COUNT%

2120 WRITE #2,DDAT(K,1),DDAT(K,2),DDAT(K,3)

2130 NEXT K

2140 CLOSE #2

2150 END

VOLT‘SCANBAS

10 'VOLTSCAN.BAS, 2/23/92

20 'PROGRAM TO RECORD PHOTOEMISSION DATA AT A SPECIFIC
30 'WAVELENGTH AS A FUNCTION OF BIAS VOLTAGE

4O 'USES THE KEITHLEY MODEL 617 PROGRAMMABLE ELECTROMETER
50 'AS VOLTAGE SOURCE AND VOLTMETER

6O 'WRITTEN BY C. T. KUO

70 '

80 .DIM DDAT(1200,4)

90 '

100 'CHOOSE A DATA FILE

110 '

120 PRINT

130 PRINT

************************************************************************

INPUT FILE NAME AND SET TIME INTERVAL BETWEEN DATA POINTS

************************************************************************

157

VOLTSCANBAS (continued)
140 INPUT "INPUT FILE NAME FOR DATA";FILE$
150 CLOSE #1
160 OPEN FILES FOR APPEND AS # 1
170 IF LOF(1)=0 THEN CLOSE #1
180 ELSE PRINT "FILE ALREADY EXISTS" :CLOSE #1
190 INPUT "TIME INTERVAL FOR DATA IN SECONDS";RUNTIME
200 INPUT "DATA NUMBER";N1
210 '

***********************************t************************************

IN ITIALIZE THE IEEE-488 INTERFACE BOARD
************************************************************************
220 'INITIALIZE THE BOARD

230 OPEN FILE$ FOR OUTPUT AS #1

240 DEF SEG=&HC000

250 CNID$="SYSCON MAD=3, CIC=1, NOB=1, BAO=&H300"

260 VAR%=0 : FLG%=0 : BRD%=0 : IE488=0

270 CALL IE488(CMD$, VAR%, FLG%, BRD%)

280 PRINT

************************************************************************

INPUT STARTING AND INCREMENT VOLTAGES
************************************************************************
290 INPUT "INPUT STARTING VOLTAGE IN VOLTS"; PVO
291 INPUT "VOLTAGE INCREMENT FOR EACH CY CLE",PIN
300 '

310 CMD$="REMOTE 27"

320 CALL IE488(CMD$, VAR%, FLG%, BRD%)

330 CMD$= "OUTPUT 27[$E]"

340 A$="FOX"

350 CALL IE488(CMD$,A$,FLG%,BRD%)

360 X$="X"

370 CMD$="OUTPUT 27[$E]"

380 VON$= "01X"

390 CALL IE488(CMD$, VON$, FLG%, BRD%)

400 COUNT%=0

621
63(
646
650
660

1 5 8
VOLTSCAN.BAS (continued)

401 TIMER1=TIMER

410 V$="V"

411 FOR N=1 TO N1

420 VO$=V$+STR$(PVO)+X$

430 CMD$="OUTPUT 27[$E]"

450 CALL IE488(CMD$, VO$, FLG%, BRD%)
470 PERIOD=0

480 PVOL$=SPACE$(20)

490 COUNT%=COUNT%+1

500 CMD$="ENTER 27[$]"

510 TIM=TIMER-TIMER1

520 CALL IE488(CMD$,PVOL$,FLG%,BRD%)
530 PRINT PVOL$

540 E1=VAL(MID$(PVOL$,5,20))

550 DDAT(COUNT%,1)=E1

560 DDAT(COUNT%,2)=TIM

561 DDAT(COUNT%,3)=PVO

562 PVO=PVO+PIN

*********************link*Il!*III*II‘II:***Illlltlink*4!*********************************

HIT “P” TO CLOSE THE PROGRAM AT WHATEVER BIAS VOLTAGE
************************************************************************
563 IF INKEY$=“P” THEN GOTO 620

570 ST=TIMER

580 WHILE PERIOD<RUNTII\IIE

590 PERIOD=TII\'IER-ST

600 WEND

60] PRINT "PERIOD TIME";PERIOD

610 NEXT N

620 CMD$="OUTPUT 27 [$E]"

630 VO$="OOX"

640 CALL IE488(CMD$, VO$, FLG%, BRD%)

650 CMD$="LOCAL 27"

660 CALL IE488(CMD$,VAR%,FLG%,BRD%)

1 5 9
VOLTSCAN.BAS (continued)

*************Ildnlt*****************************II:*III***************#********

WRITE DATA INTO THE OPEN FILE
**********************************************t*************************
670 FOR 1:] TO COUNT%

680 WRITE #1, DDAT(I,1), DDAT(I,2), DDAT(I,3)

690 NEXT I

695 CLOSE #1

700 END

PHOLASERBAS

10 'PROGRAM PHOLASERBAS ADAPTED FROM VOLTSCAN, 2/23/92
20 'PROGRAM TO TAKE PHOTOENIISSION DATA AT A SPECIFIC BIAS
30 'VOLTAGE AND WAVELENGTH AS A FUNCTION OF TIME

40 'USES THE KEITHLEY MODEL 617 PROGRAIVIMABLE ELECTROMETER
50 'AS VOLTAGE SOURCE AND VOLTMETER

60 'WRITIEN BY C.T.KUO

70 '

80 DIM DDAT(2400,4)

90 '

100 'CHOOSE A DATA FILE

110 '

120 PRINT

130 PRINT
************************************************************************
INPUT FILE NAME, TINIE INTERVAL BETWEEN DATA POINTS AND
NUMBER OF DATA EXPECTED TO COLLECT
******************************$*****************************************
140 INPUT "INPUT FILE NAB/IE FOR DATA";FILE$

150 CLOSE #1

160 OPEN FILE$ FOR APPEND AS # 1

170 IF LOF(1)=0 THEN CLOSE #1

180 ELSE PRINT "FILE ALREADY EXISTS" :CLOSE #1

1 6 0
PHOLASER.BAS (continued)

190 INPUT "TIME INTERVAL FOR DATA IN SECONDS";RUNTIME
200 INPUT "DATA NUMBER";NI

210 PRINT '

220 PRINT '

230 ‘

************************************************************************

INPUT THE SPECIFIC WAVELENGTH OF LIGHT SOURCE
************************************************************************
240 INPUT " THE SPECIFIC WAVELENGTH";SWAVE

250 ‘

260 '

************************************************************************

INITIALIZE THE IEEE-488 INTERFACE BOARD
************************************************************************
270 'INITIALIZE THE BOARD

280 OPEN FILES FOR OUTPUT AS #1

290 DEF SEG=&HC000

300 CMD$="SYSCON MAD=3, CIC=1, NOB=1, BAO=&H300"
310 VAR%=0 : FLG%=0 : BRD%=0 : IE488=0
320 CALL IE488(CMD$, VAR%, FLG%, BRD%)
330 PRINT

340 INPUT "INPUT VOLTAGE IN VOLTS"; PVO
350 '

360 CMD$="REMOTE 27"

370 CALL IE488(CMD$, VAR%, FLG%, BRD%)
380 CMD$= "OUTPUT 27[$E]"

390 A$="FOX"

400 CALL IE488(CMD$,A$,FLG%,BRD%)

410 X$="X"

420 CMD$="OUTPUT 27[$E]"

430 VON$= "01X"

440 CALL IE488(CMD$, VON$, FLG%, BRD%)
450 COUNT%=0

460 V$="V"

16 l
PHOLASER.BAS (continued)

470 VO$=V$+STR$(PVO)+X$

480 CMD$="OUTPUT 27[$E]"

490 TIMER1=TIMER

500 CALL IE488(CMD$, VO$, FLG%, BRD%)
510 FOR N=1 T0 N1

520 PERIOD=O

530 PVOL$=SPACE$(20)

540 COUNT%=COUNT%+1

550 CMD$="ENTER 27[$]"

560 TIM=TIMER-TIMER1

************************************************************************

READ SIGNAL VOLTAGE
************************************************************************
570 CALL IE488(CMD$,PVOL$,FLG%,BRD%)

580 PRINT PVOL$

590 E1=VAL(MID$(PVOL$,5,20))

600 DDAT(COUNT%,1)=E1

610 DDAT(COUNT%,2)=TIM

************************************************************************

HIT “P" TO CLOSE PROGRAM AT ANY TIME
*****************************************************t***********$*t*t*$
611 IF INKEY$="P" THEN GOTO 680

620 ST=TIMER

630 WHILE PERIOD<RUNTIME

640 PERIOD=TIIVIER-ST

650 WEND

660 PRINT "PERIOD TIME";PERIOD

670 NEXT N

680 CMD$="OUTPUT 27[$E]"

690 VO$="OOX"

700 CALL IE488(CMD$, VO$, FLG%, BRD%)
710 CIVID$="LOCAL 27"

720 CALL IE488(CMD$,VAR%,FLG%,BRD%)

l 6 2
PHOLASER.BAS (continued)

************************************************************************

WRITE DATA TO THE OPEN FILE
************************************************************************
730 FOR I=l TO COUNT%

740 DDAT(I,3)=SWAVE

750 WRITE #1, DDAT(I,1), DDAT(I,2), DDAT(I,3)

760 NEXT 1

765 CLOSE #1

770 END

163

This is Kramers-Kronig calculations-program KKFAB02.FOR
integer dn
real kk (2200,2), tern (2200,3), ref (2200,3)
open(l,file='b:fa15en7.prn',status='old')
open(2,file='c:test#2.dat',status='unknown')
m=1
100 read(1,*,err=5000) ref(m,1),ref(m,2),ref(m,3)
m=m+1
go to 100
5000 confinue
dn=m~1
do 200 n =1, dn,l
do400i=1,dn,1
if (n.eq.i) goto 400
tem(i,l) = log(ref(i,3)+ref(n,3))-log(abs(ref(i,3)-ref(n,3)))
400 confinue
do 500 k =1, dn,1
tem(k,3) = ref(k,2)*tem(k,1)
500 continue
do 600j=1, dn,1
kk(n,1) = kk(n,1)+tem(j,3)
600 continue
kk(n,2) = -0.15915494*kk(n,1)
200 continue
do 7001 = 1, dn,l
write(2,'(lx,3e15.5)') ref(l,1), kk(l,2),ref(l,3)
700 continue
close(l)
close(2)
end

164

This is Kramers-Kronig calculations- Program FORKRONFOR
integer dn
real kk (2200,2), tem (2200,3), ref (2200,4)
open(1,fi1e='b:kkdat325.prn',status='old')
open(2,file='C:test#1.dat',status='unknown')
m=1
100 read(1,*,err=5000) ref(m,1),ref(m,2),ref(m,3),ref(m,4)
m=m+1
go to 100
5000 confinue
dn=m-1
do 200 n =1, dn,1
do 400 i = 1, dn,1
if (n.eq.i) goto 400
tem(i,1) = log(abs(ref(n,3)-ref(i,3)))*(ref(n,3)-ref(i,3))
tem(i,2) = log(ref(n,3)+ref(i,3))*(ref(n,3)+ref(i,3))
400 confinue
do 500 k =1, dn,1
tem(k,3) = ref(k,4)*(tem(k,1)+tem(k,2))
500 confinue
do 600j=1, dn,1
kk(n,l)=kk(n,l)+tem(j,3)
600 confinue
kk(n,2)=(1./6.2831853)*kk(n,1)
200 confinue
do7001=1,dn,1 -
write(2,'(lx,3e15.5)') ref(l,1), kk(l,2),ref(l,3)
700 confinue
close(l)
close(2)
end

165

This is Kramers-Kronig calculations-program KKRFAB02.FOR
integer dn
real kk (2200,2), tem (2200,3), ref (2200,3)
open(l,file='b:rfa1521.prn',status='old')
open(2,fi1e='b:rfa1521.dat',status='unknown')
n1=1
100 read(1,*,err=5000) ref(m,1),ref(m,2),ref(m,3)
m=m+1 I
go to 100
5000 confinue
dn=m-1
do 200 n =1, dn,1
do 400 i = 1, dn,l
if (n.eq.i) goto 400
tem(i,1) = log(ref(i,3)+ref(n,3))+log(abs(ref(i,3)-ref(n,3)))
400 confinue
do 500 k =1, dn,l
tem(k,3) = ref(k,2)*tem(k,1)
500 confinue
do 600j = 1, dn,1
kk(n,1) = kk(n,1)+tem(j,3)
600 continue
kk(n,2) = -0.3664678*2*kk(n,1)
200 confinue
do 7001 = 1, dn,1
write(2,'(lx,3e15.5)') ref(l,1), kk(l,2),ref(l,3)
700 confinue
close(l)
close(2)
end

 

166
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