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Quantitative x-ray photoelectron spectroscopic methods and their application to lead ion-selective electrode surface studies

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Quantitative x-ray photoelectron spectroscopic methods and their application to lead ion-selective electrode surface studies
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McCaslin, Paul C., 1960-
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English
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vi, 225 leaves : ill. ; 28 cm.

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Analyzers ( jstor )
Carbon ( jstor )
Electrons ( jstor )
Geometric angles ( jstor )
Modeling ( jstor )
Photoelectrons ( jstor )
Signals ( jstor )
Surface areas ( jstor )
Surface roughness ( jstor )
Topography ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Electrodes, Ion selective ( lcsh )
Photoelectron spectroscopy ( lcsh )
Surface roughness -- Measurement -- Data processing ( lcsh )
X-ray spectroscopy ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
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Typescript.
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Vita.
Statement of Responsibility:
by Paul C. McCaslin.

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QUANTITATIVE X-RAY PHOTOELECTRON SPECTROSCOPIC METHODS
AND THEIR APPLICATION TO
LEAD ION-SELECTIVE ELECTRODE SURFACE STUDIES






BY






PAUL C. MCCASLIN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1988




QUANTITATIVE X-RAY PHOTOELECTRON SPECTROSCOPIC METHODS
AND THEIR APPLICATION TO
LEAD ION-SELECTIVE ELECTRODE SURFACE STUDIES
BY
PAUL C. MCCASLIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1 988


ACKNOWLEDGMENTS
I would first like to thank Dr. V. Y. Young for her guidance,
patience, and fruitful suggestions, all of which led to the present
work. Her support has been invaluable during ray graduate years.
In addition, I wish to acknowledge the aid of my other committee
members, J. D. Winefordner, A. Brajter-Toth, G. M. Schmid, and G. B.
Hoflund. Their assistance along the way is greatly appreciated.
Special thanks are due Gar Hoflund, who was kind enough to read an
early version of this dissertation.
Ken Matuszak, Rustom Kanga, Jack Davis, Linda Volk, and Mike Clay
have helped me out along the way with their discussions, opinions, and
friendship. I appreciate the many hours we have shared.
Finally, I want to thank my wife, Ann, who has been uniformly
loving, supportive, and tolerant. Without her, graduate school would
have been much more trying and much less enjoyable.
ii


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
X-Ray Photoelectron Spectroscopy (XPS) 1
Quantification in XPS 3
Measurement in XPS 4
Instrumentation 7
Lead Ion-Selective Electrodes 12
2 THEORETICAL BACKGROUND 16
3 MODELING OF SURFACE TOPOGRAPHY EFFECTS IN XPS 24
Introduction . 24
Theory of Modeling 27
Methodology 29
4 TESTING AND APPLICATIONS OF THE SURFACE ROUGHNESS MODEL...43
Testing of Roughness Program 43
Sinusoidal Function Results 44
Grating Function Results 52
Particulate Surface Model Results and Applications 58
Experimental Surface Roughness Studies 74
Results of Gold Studies 75
Results of Carbon Studies: Model Comparison 84
The Effect of Pressure on the VAXPS Curve 95
Peak Structure Studies on Abraded Surfaces 99
5 THEORY AND TESTING OF A METHOD FOR NONDESTRUCTIVE
DEPTH PROFILING 119
Introduction 119
Numerical Inverse Laplace Transform (NILT) Method
Development 1 21
Theoretical 3asis 121
iii


Mathematical Model 123
Testing with Theoretical Functions 133
Experimental Testing of the NILT Method 143
6 QUANTITATIVE XPS OF LEAD ION-SELECTIVE ELECTRODE
MEMBRANES 151
Introduction 151
Experimental Analysis of Pb ISE Membranes 152
Operating Conditions and Preliminary Data
Treatment 152
Composition and Preparation Effects 156
Effects of HClOij 170
Effects of Fe3 + 175
7 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 184
Summary and Conclusions 184
Future Work 186
APPENDICES
A SURFACE ROUGHNESS PROGRAM SOURCE CODE 1 89
B NILT PROGRAM SOURCE CODE 203
REFERENCES 220
BIOGRAPHICAL SKETCH 225
iv


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
QUANTITATIVE X-RAY PHOTOELECTRON SPECTROSCOPIC METHODS
AND THEIR APPLICATION TO
LEAD ION-SELECTIVE ELECTRODE SURFACE STUDIES
BY
PAUL C. MCCASLIN
April, 1988
Chairperson: Vaneica Y. Young
Major Department: Chemistry
The development of methods applicable to the X-ray photoelectron
spectroscopic (XPS) analysis of solid surfaces, in general, and solid
state lead ion-selective electrode (ISE) membranes, in particular, is
the focus of the present dissertation. These methods fall into two
categories. The potential effects of surface roughness on XPS
analysis have been investigated. In addition, a method has been
developed which allows the composition of the near-surface region to
be investigated in a nondestructive fashion.
The study of surface roughness effects has been carried out from
both a theoretical and an experimental perspective. A program has
been developed to determine the nature and magnitude of effects
attributable to surface topography. Its predictions have been
compared to experimental data; the agreement obtained is quite good.
The effects of the pressure used in sample preparation, which is
related to the sample topography, on the XPS signal have been
v


investigated. Finally, the effect of increasing surface abrasion (and
thus increasing surface roughness) on the relative makeup of the
signal from the various species present in the near-surface region has
been studied.
In order to obtain depth profile information nondestructively
from a solid sample, a technique known as variable angle XPS (VAXPS)
can be utilized. In this technique, the photoelectrons are collected
at a series of take-off angles with respect to the mean plane of the
surface. These VAXPS results contain the desired depth profile
data. However, the data must be mathematically treated in order to
obtain the depth profile. A method of performing this data
transformation has been developed. Its description is presented,
along with testing of the theory behind it.
Finally, these methods, although developed for general usage,
have been applied to the study of the surface composition of lead ISEs
consisting of a mixture of lead sulfide and silver sulfide. Several
studies have been carried out, investigating the effects of membrane
composition, preparation, cleaning, and poisoning of the response on
the surface composition. The results are presented, along with
several conclusions related to the optimization of lead ISE behavior.
vi


CHAPTER 1
INTRODUCTION
X-Ray Photoelectron Spectroscopy
The roots of X-ray photoelectron spectroscopy (XPS) may be traced
far back. One of the four fundamentally important papers published by
Einstein in 1905 concerned an explanation for the photoelectric effect
(1). This effect had long been known to occur; however, Einstein was
the first person to correctly describe the nature of the photoelectric
effect. The phenomenon, which is the physical basis for XPS, can be
described simply as an excitation process, whereby a photon of energy
hv impinges on a solid, interacts with an atom's electron density
cloud, and causes the emission of a so-called photoelectron, whose
kinetic energy E^ relative to the measuring spectrometer is given in
the absence of surface electric double layers by the expression
where E^ is the binding energy of the electron in the atomic or
molecular system measured relative to the Fermi level and instrumental work function, all typically measured in eV (2). Thus,
the electron's kinetic energy is independent of the incident photon
intensity. Early attempts to construct a high-resolution electron
spectrometer made use of magnetic focusing and thus were susceptible
to stray magnetic fields. The theory behind such instrumentation can
1


2
be traced back to 1956, when the first double-focusing magnetic
spectrometer was described in the literature by Siegbahn and co
workers (3). However, the potential usages of such an instrument were
vastly increased with the report by the same group that not only did
the instrument yield elemental information about the surface, but
chemical state information as well. It was discovered that Cu 2p
electrons from copper and copper oxide samples had different kinetic
energies and thus different binding energies. Combined with its
sensitivity to species at the surface and in the near-surface region
(typically, down to approximately 10 nm), this factor has been
responsible for the development of XPS as an analytical technique.
The next major step in the evolution of XPS was the elimination
of the problems caused by external stray magnetic fields. Carlson and
Krause were the first researchers to design an instrument using
electrostatic focusing. This development was the crucial step needed
to induce several instrument manufacturers to construct and market
photoelectron spectrometers. The field experienced a dramatic
increase in popularity in the early 1970s, as the first generation of
commercial instruments were introduced. Since then, such instrumental
advances as X-ray monochromators (to reduce the X-ray linewidth and
thus enhance resolution), multi-channel detectors (to increase the
collection efficiency and thus reduce run times), elaborate lens
systems (to further improve resolution), various in situ sample
treatment methods, and small-spot XPS instruments (to enhance the
spatial resolution) have been introduced.


3
Quantification in XPS
The achievement of quantitative XPS results may be approached
from two directions. One may make use of a number of standards to
construct a series of empirical sensitivity factors based on a
comparative analysis of peak areas. This method was applied early on
to collect a limited number of sensitivity factors (4). However, the
difficulty in preparing suitable standards has limited the
applicability of this technique primarily to the study of homologous
series of compounds. The other approach involves a theoretical
analysis of the chain of events leading from the excitation of the
photoelectron to its energy determination and subsequent detection. A
fundamental work by Fadley et al. (5) laid the foundation for
quantification in XPS. This paper outlined for the first time the
basic principles of angular distribution experiments in XPS, the
methodology for analysis of thin surface films and their effect on
quantitative analysis of the bulk sample, and the possible effects of
surface topography on the XPS signal. Since then, much progress has
been made in characterizing the various contributing factors in the
XPS peak intensity equation. Reports of methods for quantitative
analysis without standards began appearing around 1977 (6,7). A more
comprehensive approach taking a larger number of possible factors into
account was introduced in 1982 (8) and has been revised since then
(9). The early models typically made the implicit assumptions that
the sample composition was homogeneous throughout the volume of sample
analyzed, and the surface topography had a negligible effect on the
XPS signal. Later modifications have made an attempt to address these


4
two factors in a simplistic fashion. They allow for the possibility
of an impurity overlayer's interfering with the signal. The problem
of surface roughness in quantification has not been addressed in
detail; however, some experimental results have been reported (10)
indicating its effect on the determination of overlayer thicknesses.
Measurement in XPS
The basic measurement process in XPS is outlined in Figure 1-1.
The technique makes use of a photon source of constant energy,
typically the Ka X-ray lines of aluminum or magnesium, aimed at a
surface from which photoelectrons are emitted. The commonly used
electron energy analyzer for XPS, the hemispherical analyzer (HSA),
consists essentially of two closely spaced hemispherical plates,
across which a potential can be applied, so that only electrons of a
specified energy may pass through to the detector. The entire
measurement process must take place under higher vacuum, e.g., 10"^
Torr, in order to slow the buildup of ubiquitous hydrocarbon
contamination layers, keeping the surface as clean as possible and
allowing for greater sensitivity toward the true surface species. The
surface sensitivity arises not from the depth of penetration of the
incident X-rayswhich may travel 100-1000 nm before being appreciably
attenuatedbut from inelastic scattering of the photoelectrons. This
process accounts for the exponential decay of the photoelectron
population as a function of depth, with the characteristic inelastic
mean free path (IMFP) defined as the straight-line distance an
electron population travels before its number drops to 1/e (37%) of


Figure 1-1. Schematic illustration of the measurement process in XPS. Shown are the excitation source
(X-ray gun), the emission source (sample), the energy analyzer (electron lens and
hemispherical analyzer), and the detector.


X-ray
Source
Hemispherical
Analyzer
Electron
Lens


7
its original value due to inelastic collisions. For photoelectrons
with typical kinetic energies of 500-1500 eV, the IMFP ranges from
0.1-10 nm.
Instrumentation
The instrument used to collect the majority of the XPS data is a
Kratos XSAM 800 X-ray photoelectron spectrometer. A block diagram of
the spectrometer is shown in Figure 1-2. This unit consists of an
ultra-high vacuum (UHV) spectrometer console, a sample introduction
system, an electronics console, and a computer for instrument control
and data manipulation. The spectrometer console comprises a spherical
sample analysis chamber, with a water cooled dual anode X-ray gun,
electron flood gun, macrobeara ion gun, electron energy analyzer,
detector system, and a chamber pumping system. The X-ray gun
furnishes either A1 Ka (1486.6 eV) or Mg Ka (1253.6 eV) radiation,
allowing differentiation between kinetic energy-invari ant processes,
such as Auger electron spectroscopy (AES), and binding energy-
invariant processes, such as XPS. For reasons mentioned below, the
bulk of the experimental work was carried out using the A1 anode. The
X-ray gun may be isolated from the analysis chamber and separately
pumped with a small dedicated ion pump, to reduce main chamber vacuum
degradation. The electron flood gun is used to neutralize the charge
buildup on the surface of insulating samples due to electron
emission. The ion gun is differentially pumped using a Leybold-
Heraeus TMP 150 turbomolecular pump, which has a nominal pumping speed
of 150 L/s. The ion gun is typically used to sputter clean surfaces


Figure 1-2. Block diagram of the Kratos XSAM 800 X-ray photoelectron spectrometer, illustrating the
pumping and electronics systems.


pop-1r
COMPUTER
OI 8K
STORAGE


10
for analysis using Ar+ ions, thus reducing the intensity of the
ubiquitous hydrocarbon signal to a manageable level; it may also be
used as an excitation source in performing ion scattering spectroscopy
(ISS), or as an etching source when carrying out destructive depth
profiling of a sample surface. The XSAM 800 uses a 180 deflection
double focusing hemispherical electrostatic analyzer with a mean
radius of 127 mm and an aberration compensated input lens (ACIL)
system. A choice of two analyzer modes is given. In the fixed
retarding ratio (FRR) mode, the kinetic energy of each electron
entering the ACIL is reduced by a fixed fraction of its initial
kinetic energy as it moves through the HSA. In the fixed analyzer
transmission mode (FAT), the electron's kinetic energy is reduced to a
constant value for all electrons passed to the detector. The relative
kinetic energy information necessary to distinguish the electrons
energetically is thus contained in the ACIL focusing program to reduce
electron energy. The FRR mode gives higher count rates for peaks with
low binding energies (high kinetic energies); this region being
predominantly the region of study, the FRR mode was used in nearly all
experiments. The detector system consists of a fast single channel
multiplier and a fast response head amplifier. It can be operated in
either a pulse counting mode, which gives a true electron count rate,
or a current mode, which acts as a pulse count integrator. The former
mode is more sensitive; however, it leaves the electron multiplier
susceptible to saturation. For this reason, the current mode was used
universally in these studies. The chamber pumping system comprises a
rotary vane roughing pump, the dedicated X-ray ion pump, the


11
turbomolecular pump (which can also be valved to pump on the main
chamber), a titanium sublimation pump, a 200 L/s ion pump, associated
pumping manifolds and valves, and several vacuum measuring devices.
Pressure in the roughing vacuum lines is monitored by two thermocouple
gauges. An ionization gauge is attached to the sample chamber; it
-4 -6
serves to monitor pressure predominantly in the 10 10 Torr
range. For UHV pressure measurements, a cold cathode Penning trigger
C *"11
gauge is provided, with an operating range of 10 10 Torr. In
order to prevent inadvertent instrument operation, an interlock system
has been provided. If the ionization gauge cannot be energized, i.e.,
the pressure is >10-it Torr, the analysis and detection electronics
cannot be turned on. Also, if the X-ray gun ion pump is not on, or if
the anode cooling water flow is not sufficient, the X-ray source
cannot be operated. The system has a base operating pressure of
-11 -9
5 x 10 Torr; typical operating pressures are in the low 10 to
high 10 10 Torr range.
The sample introduction system allows a sample to be entered into
the UHV chamber from atmospheric pressure in a matter of minutes. It
comprises a direct insertion lock with an isolation ball valve and a
fast insertion sample probe. The insertion lock is pumped by the
rotary vane roughing pump. The sample probe can accommodate a variety
of probe tips for analyzing different types of samples. It can also
be heated or cooled over a temperature range of -150C to +600C. The
probe can be rotated on its axis, thus altering the orientation of the
sample surface relative to the X-ray gun and ACIL entrance slit.


12
The electronics console contains the control units for pressure
monitoring and sample temperature setting, X-ray power supply, X-ray
filament emission current stabilizer, ion gun control and raster
units, electron flood gun control unit, and control units for both ion
pumps and the titanium sublimation pump. It also contains the scan
control unit and a display control unit, both of whose functions have
been largely usurped by the computer control and display system.
The instrument is controlled by a Digital Equipment Corporation
Micro PDP-11 computer. A Tektronix 4105A color computer display
terminal serves as a user interface, and a Tektronix 4695 seven-color
graphics copier provides hardcopy output. The computer has 256 Kbytes
of random access memory, a dual 5 1/4" floppy diskette drive system,
and a Winchester hard disk system with a formatted capacity of 11.059
Mbytes. The DS800 data system included with the system resides on the
hard disk. Backup files can be stored on floppy diskettes, each
having a capacity of 400 kbytes. The data system allows computer
control of data acquisition, including spectrometer control and
extensive data display and manipulation features, 3uch as peak area
determination, background subtraction, peak deconvolution, and curve
fitting.
Lead Ion-Selective Electrodes
Electrodes selective to lead ions date from 1969 (11). The first
such electrodes utilized a homogeneous membrane consisting of a co
precipitate of lead sulfide (PbS) and silver sulfide (Ag2S) pressed
into a pellet, the potential across which can be related to the lead
concentration. Other lead ion-selective electrodes (ISEs) were soon


13
introduced, including a liquid membrane ISE (12); a homogeneous
membrane using lead selenide (PbSe) or lead telluride (PbTe) in place
of PbS (13); another homogeneous system consisting of PbS, Ag2S, and
Cu2S (14); and several homogeneous membranes with PbS or PbS/Ag2S
present at the electrode surface (15,16). Since then, other lead ISEs
have been proposed, utilizing PbS/Ag2S on a PTFE/graphite support
(Selectrode), PbS deposited on an ionic conducting support material
(17), Pb02 on a Selectrode body (18), coated wire type Pb ISEs (19),
and PbS/Ag2S/As2S^ glass membranes (20).
However, by far the most popular designs have been the
homogeneous PbS/Ag2S membrane electrode and, to a lesser extent, the
Selectrode body with PbS/Ag2S impregnated on the surface. For this
reason, we have concentrated our investigations on this powder mixture
pressed into a homogeneous pellet. The number of studies carried out
on such membranes is too great to fully document. Several detailed
electrochemical studies have been carried out (21-23). The electrodes
typically show a linear response in a potential versus log apb plot,
with a response sensitivity of 27-30 mV/decade, close to the Nernstian
value for Pb2+ of 29.5 mV/decade. Several common ions interfere with
the response of the ISE, including Ag+, Cu2+, and Hg2+, all of which
2-
cause surface species deposition. The ions MnO^ and Cr20^ act as
oxidizing agents, thus interfering irreversibly with the electrode
response. The response tends to degrade over a period of several
weeks' usage; however, the electrode can be rejuvenated by polishing
its surface, or exposing it to either ammoniacal EDTA or HClOjj
solution.


Relatively few studies have been carried out to investigate the
surface behavior of Pb ISEs. Chaudhari et al. (24) were the first
investigators to use surface sensitive techniques to analyze this
system. They investigated the effects of various cleaning agents on
the surface composition. Fixed angle XPS was also used to examine the
2+ 2+
effects of Cu and Zn on these membranes (25). Scanning electron
microscopy (SEM) with an energy-dispersive X-ray spectrometer has also
been applied to the investigation of these ISEs (26). A more
sophisticated XPS study involving a rudimentary approach to resolving
the species concentrations as a function of depth below the surface
has been carried out (27).
Thus, precedent exists for using surface techniques for
investigating Pb ISE membranes. The choice of XPS as the analytical
tool of choice can be justified by the nature of such electrode
membranes. Their response is governed chiefly by the interaction of
the solution being monitored with the electrode surface. An
understanding of the surface chemistry is critical to elucidating the
mechanism of Pb ISE behavior, particularly with regard to the
destruction of this behavior by various agents present in solution.
As opposed to other surface techniques, XPS stands out as the method
of choice because of its ability to resolve chemical state information
of surface species. The PbS/Ag2S system is a complex one, with
several different molecular species present at the surface. A mere
knowledge of the relative amounts of Pb, Ag, and S is not sufficient
to provide a description of the method of membrane operation; one must
know the nature of the species which interact with the electrolyte


15
solution. However, the concentration gradients of the important
species in the near-surface region have not been investigated in
detail. In addition, the possibility that the samples surface
topography may affect the XPS results must be considered in order for
the results to be treated with confidence. These factors have led to
the present study. A model for determining the possible effects of
surface topography on the nature and magnitude of the XPS signal has
been developed and applied to the study of Pb ISEs. In addition,
several more general ramifications of the surface roughness effect
have been elucidated by a combination of theoretical and experimental
investigation. These results are reported in the following chapters.


CHAPTER 2
THEORETICAL BACKGROUND
In order to present an equation for the XPS intensity, certain
assumptions must be made. We initially assume a surface in which
elastic scattering and electron transport anisotropies are
neglected. Elastic scattering refers to the process where an
electron's directional vector is altered with a conservation of
energy. Thus, the electron, if detected, will appear in the species
peak of interest. More will be said about this factor below. The
condition of negligible electron transport anisotropies implies that
no preferences sire observable for electron motion along a particular
direction. This condition is generally met in practice when dealing
with polycrystalline or amorphous solids; however, single crystals
show evidence of anisotropies which can be used to obtain information
about surface bond orientation (28). Also, X-ray reflection and
refraction are assumed to be negligible. This condition is met for
all geometries except grazing photoelectron exit, which is not of
interest in the present study. Finally, the X-rays and electrons are
assumed to be attenuated exponentially, the decay being characterized
by a mean free path (MFP). For the electrons, the characteristic
decay length is the inelastic mean free path (IMFP or \). The X-ray
MFP is typically much larger than the electron IMFP for the electron
kinetic energies of interest in XPS. Given these assumptions, the
16


17
intensity I (E ,y) of photoelectrons from level y of species c in
O G
sample s is given as (29)
I (E .y) = I (hv) d//d2(hv,4>) F(E .E.) T(E ,E.,fl )
CC O C CA CAO
D(E E.) G(fl ,0) ( N (z) exp(-z/X (E )*sin 9) dz.
CA 0J0C sc
Here, IQ(hv) corresponds to the incident X-ray flux of energy hv;
y
da /dfl(hv,) is the differential photoionization cross-section of sub-
c
shell y of species c, also dependent on X-ray energy and the angle
between the incident X-rays and the emergent photoelectrons which can
reach the analyzer. It is given by (30)
da^/dn = (a^/4ir)[1 Bn1(EQ)/4 (3 cos2* 1)],
where ay is the total cross-section of sub-shell y of species c,
G
typically measured at 1487 eV in units of the C 1s cross-section of
13600 barns, and 3 (E ) is the angular asymmetry factor, a function
nl c
V
of the electron energy E. The values of a have been theoretically
determined and reported as a function of atomic number and core level
(31), and they agree well with experimental results (32-34). Although
the photoelectron energy does not depend on the angle between the
incident X-ray excitation beam and the detected photoelectron stream,
the intensity does. The angular asymmetry term takes this variation
into account. On the Kratos XSAM 800, this angle is fixed at 80;
thus, this factor becomes a constant for a given peak. Theoretical
values for 3 ,(E ) have been reliably calculated for all core levels
m c
and tabulated as a function of atomic number (35), and the effects of


18
elastic scattering on the angular distribution of photoelectrons have
been studied as well (36,37). The electron-optical factor F(EC,EA)
allows for the effects of deceleration of the photoelectrons from
energy Ec to analyzer energy EA. In order to explain why the
electrons must be decelerated before being energy analyzed, it is
necessary to examine the resolving power of the photoelectron energy
analyzer. For a point source imaged into a point image, the resolving
power is given by
2
Resolving power = AE/E = (W/2R) + Ka ,
where W is the slit width, R is the mean analyzer radius, a is the
serai-angle in the dispersive plane, and K is a constant. For a slit
width of 8 ram and a mean analyzer radius of 127 mm, the resolving
power is >0.012. Thus, for an electron with 1000 eV kinetic energy,
resolution is about 12 eV, far too poor to distinguish between
chemical states from a particular core level. By removing energy from
the electron before it is energy analyzed, one can improve the
resolving power, at the expense of a loss in sensitivity. Two methods
of energy removal can be applied. In fixed analyzer transmission
(FAT) mode, the transmission energy of the analyzer is held constant,
and the electrons are retarded by a varying proportion. In fixed
retarding ratio (FRR) mode, electrons entering the analyzer have their
energy retarded by a fixed ratio of their initial kinetic energy. The
analyzer transmission function T(E ,E.,£J ) is dependent on electron
C A O
kinetic energy, the analyzer energy, and the solid angle of


19
acceptance 0 for the analyzer; D(E ,E ) is the detector efficiency;
O G A
and G(,) is a geometric factor allowing for the change in effective
area of sample analyzed. For the Kratos XSAM 800 instrument, the
geometric factor is not a function of 0 when operating in the FRR
mode. N (z) refers to the atom concentration (atoras/cm^) of species c
c
at depth z; A (E ) is the electron IMFP, dependent on the sample and
3 G
electron energy; and 0 is the photoelectron escape angle. The
product X (E )*sin 0 denotes the effective IMFP, the effective depth
s c
from which photoelectrons emerge (Figure 2-1). For a series of peaks
collected at various values of 0, the average distance an electron
travels before being inelastically scattered remains constant, even
though the effective depth below the surface from which the electron
emerged varies. The lower the angle of photoelectron exit from the
surface with respect to the tangent, or slope, at the point of exit,
the smaller will be the depth from which the electron emerged. As
will be seen in later chapters, this effect has a profound impact on
the nature of XPS depth profiling experiments and the determination of
quantitative information from them.
The actual determination of the IMFP is difficult to achieve from
either an experimental or a theoretical approach. Experimentally,
several researchers have published universal mean-free path curves as
a function of electron kinetic energy (38-41). A power law dependence
with an exponent in the range of 0.5-0.75 is typically reported,
although more sophisticated methods of determination exist (41). From
a theoretical viewpoint, several workers (42-44) have modeled the mean
free path of a free-electron-like material and shown agreement between


Figure 2-1. Illustration of the relationship between the inelastic mean free path A, the photoelectron
take-off angle 0, and the effective mean free path Xe, which defines the sampling depth.


x-rays
e
Vacuum
Substrate


22
their results and experimental measurements. Neither approach yields
results of sufficient accuracy to preclude further research in this
area, which is ongoing. The uncertainty in the IMFP determination is
a chief complicating factor in performing absolute quantitative XPS
completely-from basic principles. At least part of the uncertainty
arises from the unaccounted-for contribution of the elastic mean free
path to the overall mean free path, as well as its effect on the XPS
signal intensity; the latter effect is related to the variation in the
angular asymmetry term discussed above. The general consensus among
researchers is that there is a significant elastic scattering effect,
but it does not in general affect the exponential decrease of the
signal. Rather, it acts to effectively increase the electron mean
free path (45,46). The elastic scattering contribution can be reduced
by using small solid angles of acceptance at the energy analyzer; it
is also more pronounced at smaller values of the photoelectron escape
angle (47).
The equation shown above indicates that the intensity depends on
many parameters and points out what are likely to be some major
limitations of quantitative XPS. First of all, a reliable method of
estimating the asymmetry parameter, photoemission cross-section, and
IMFP must be found, in order to account for these factors effects on
the XPS intensity. As discussed above, extensive work has been
directed toward this end. The first two factors are generally
recognized to be well characterized; however, research is still
ongoing into the nature of the IMFP. Provision has been made for the
uncertainty in this parameter in the development of the methods to be


23
discussed in this work. Secondly, surface roughness may have a
significant effect on 0 and on G(Q ,0). Quantitative VAXPS will be
o
generally useful only when the effect of surface roughness may be
adequately taken into consideration. One of the purposes of this work
is to clarify the surface topography effect, both from a theoretical
and an experimental standpoint. The various instrument-dependent
functions remain constant in a VAXPS experiment, where only the escape
angle is changed. Thus, keeping in mind the possible surface
topography effects, as well as the uncertainty in the IMFP, these
factors can be collected for a VAXPS experiment into an equation of
the form
I (0) = K (0) f N (z) exp [-z/X (E )*sin 0] dz.
C C J 0 c sc
The angular dependence of K (0), if present, can typically be
G
determined empirically. Results from VAXPS experiments may be used to
characterize the nature of the intensity I (0) as a function of the
c
photoelectron take-off angle 0. The use of such VAXPS data in this
equation provides an opportunity for obtaining information about the
depth profile NQ(z) of the species under investigation. The
methodology necessary for extracting depth profiles from VAXPS data is
presented in a later chapter, as are several applications.


CHAPTER 3
MODELING OF SURFACE TOPOGRAPHY EFFECTS IN XPS
Introduction
In order to achieve the desirable goal of quantitative analysis
of surface species by electron microscopy, one important prerequisite
is the characterization of the surface topography of the sample under
study. Surface roughness may, depending on its magnitude, affect the
relationship between the instrumental setting of the angle of
photoelectron escape and the nature and magnitude of the resultant XPS
signal.
Previous studies of the effects of surface topography on the
magnitude and nature of photoelectron signal almost unanimously
involved attempts to model the surface roughness as a periodic
function. Ebel et. al_. (48) made use of a model based on close-packed
cubes to approximate the effects of surface roughness on the
photoelectron signal magnitude of gold films on abraded surfaces.
Their rudimentary model took account of photoelectron shading
(discussed below), but did not examine the changes in sampling depth
occasioned by the topography of a sample surface. A more
comprehensive study by Fadley et al. (5) made use of a one-dimensional
sinusoidal model to predict changes in the average emission angle,
photoelectron intensity reduction effects, and the alteration of the
average photoelectron escape depth. Although several samples were
24


25
analyzed, no systematic experimental investigation of surface
roughness effects was undertaken. The change in emission angle was
focused upon. Baird £t al. (49,50) experimentally verified the
presence of surface roughness effects in the XPS analysis of
triangularly periodic aluminum diffraction gratings and
unidirectionally polished aluminum foil samples. On the basis of
their findings, they stated that the effects of surface topography
would be nonnegligible if the roughness was at least of the same
magnitude as the inelastic mean free path A.
More recently, Wagner and Brmmer (51) investigated four one-
dimensional models of surface roughness, the two models discussed
above as well as a close-packed semi-circular model and a rectangular
roughness model. No experimental comparison was made. Wu et al. (52)
carried out a purely experimental analysis of surface roughness
effects on gold films, concentrating on the reduction in photoelectron
intensity with increasing surface area, as measured by the Brunauer,
Emmett, and Teller (BET) technique. They made no attempt to
investigate the variation of the XPS signal as a function of escape
angle. De Bernrdez £t al. (53) constructed curves showing the
effects of surface roughness on the number of photoelectrons as the
escape angle was varied. These curves were constructed using a two-
dimensional conical surface roughness model, whose photoelectron
emission was computed using a Monte Carlo electron trajectory
simulation. They compared their theoretical results to the
experimental work of Wu et al. (52). The effect of electron shading


26
on the determination of thin overlayer thicknesses has also received
some attention (10,54).
Surface roughness effects are important in Auger electron
spectroscopy (AES) as well. The importance of induced surface
roughness due to the use of Ar+ ion sputtering was recognized early on
(55,56) and has generated extensive interest. Surface roughness
affects Ar+ ion sputtering by decreasing depth resolution (57),
reducing ion sputtering yield (58), and changing the evolution of
topography during sputtering (59). Holloway (60) investigated the
surface roughness effect on the AES signal, concluding that its
presence tends to reduce signal magnitudes and affect quantification,
regardless of whether absolute or relative intensities are used.
In a recent paper (27), a sinusoidal model of surface roughness
using data derived from profilometer tracings showed a negligible
roughness effect for the particular samples studied at the
experimental resolution. However, the results suggested that a more
detailed analysis of the effects of surface topography on the XPS
signal was necessary. It has been shown that the depth resolution is
lowered by the presence of surface roughness (50). In addition,-other
effects related to the change in the angle of photoelectron escape are
present, and they affect the makeup of the XPS signal. Also, the
presence of photoelectron shading acts to reduce the overall area
sampled by XPS; one must account for its effects. In this chapter,
the theory and methodology of a technique developed for the analysis
of surface roughness is presented. Applications of the technique for
the analysis of variable angle X-ray photoelectron spectral data, as


27
well as a comparison to such experimental data and a discussion of the
results, are presented in the next chapter.
Theory of Modeling
In order to present an equation for the XPS intensity, certain
assumptions must be made. We initially assume a surface in which
elastic scattering and electron transport anisotropies are
neglected. Also, X-ray reflection and refraction are assumed to be
negligible. Finally, the X-rays and electrons are assumed to be
attenuated exponentially, the decay being characterized by a mean free
path (MFP). For the electrons, the characteristic decay length is the
inelastic mean free path (IMFP or X) described above. The X-ray MFP
is typically to be much larger than the electron IMFP. In this case,
the intensity Ic(Ec>y) of photoelectrons from level y of species c in
sample s has been shown to follow the form
I (E .y) = I (hv) doJVdfldiv,*) F(E ,E.) T(E .E.,Q )
CC O C CA CAO
D(E ,E) G(fl ,0) f N (z) exp(-z/X (E )*sin 0) dz.
cA oJoc sc
Of interest in this chapter are the geometric factor G(,0) and
the integral term. A surface with appreciable topography possesses a
surface area greater than the apparent area defined by the projection
of the aperture onto the surface, due to the presence of peaks and
valleys rather than a planar surface. However, only a fraction of
this rough surface is typically capable of emitting photoelectrons
which may reach the analyzer aperture, due to electron shading of
portions of the surface (i.e., valleys) by other areas of the surface
(i.e., peaks). This electron shading is an important factor to


28
consider in quantitative analysis, since its magnitude is related to
the actual amount of surface area "visible" to the analyzer. The
method of determination of the shading fraction assumes that the
electrons act as particles traveling in straight lines after exiting
the surface. A geometrical approach to the shading phenomenon is
utilized, wherein electrons free of the surface and travelling toward
the analyzer entrance slits are inelastically scattered if their path
causes them to re-enter the surface. Within the integral term, the
angle of photoelectron escape is affected by surface roughness as well
(Figure 3-1). Note that the photoelectron escape angle is defined for
a point on a surface relative to a tangent drawn at that point. Thus,
at any point on a rough surface, the actual photoelectron escape angle
differs from the instrumental settingwhich is based on the
assumption of an atomically flat surfaceby a factor related to the
tangent, or slope, of the surface at that point. As mentioned above,
the actual value for the sine of the angle of photoelectron escape is
directly related to the effective sampling depth. If the species c
has a nonconstant depth profile NQ(z), then the surface roughness will
affect the XPS signal by changing the depth from which the
characteristic photoelectrons are emerging. Since the concentration
of atoms may vary with depth, this change can affect the total number
of photoelectrons generated. To summarize, among the effects which
surface roughness may exert on the XPS signal intensity, the change in
surface area, the presence of electron shading, and the change in the
actual range of photoelectron escape depths are prominent.


29
Methodology
A program to estimate the magnitude of these factors has been
developed. A flow chart is shown in Figure 3-2. As input, it relies
on a digitized vector or, in the more general case, a matrix of values
representing the height above or below some defined surface level as a
function of displacement along the surface. From these data, a
shading fraction Fs, which represents the amount of surface free from
shading, is calculated by comparing the height of a point on the
surface with the heights of the other successive points along the
direction of photoelectron emission, as shown in Figure 3*3.
Specifically, if
h, + nb < h. n = 1,2,...,
i i+n
then that particular point i will be shaded from emitting photo
electrons capable of reaching the analyzer aperture. Thus, the
program works under the assumption that adjacent, shading areas of the
surface do so completely, with no probability of electron trans
mission. Here, h represents the height of point i, b = tx tanG,
where xx is the distance between successive height values and 9 is the
instrumental setting for the photoelectron escape angle with respect
to the plane of the surface, and hi+n refers to the heights of points
along the analyzer axis. A "length of surface along the direction of
analysis is computed as the vector distance between points h^ and
hi+n; this surface length value is used to properly weight the
parameters associated with point i. The vector distance L is
calculated using the equation


30
L =>
This normalization process rests on the assumption that a larger
surface area pixel (greater value of L) emits a proportionately larger
number of electrons. All the points in the vector or matrix are
scanned in this manner, and F.a is found by carrying out a weighted sum
over all unblocked points and dividing by the sum of surface length
values, representing the total surface length along that particular
vector.
In order to account for the change in the angle of photoelectron
escape from the instrumental setting 9 to the average actual value
<0'>, the value of 0i' at each point is approximated (Figure 3-4).
The slope at a point on the surface is estimated to be the difference
in two successive points divided by the distance tx separating them.
In this manner,
0i' 0 + i,
where
i i i+1 x
A weighted average over all points previously found to be unshaded is
carried out for 0^ and sin 0^, to yield <0>, , the
distribution of over the range [0,1], and the value of the
ratio /sin 9. It should be noted that sin <0> is not in


Figure 3~1. Comparison of the take-off angles 0 and 0' at a point on a smooth and rough surface,
respectively. For the rough surface, the darkened area represents the unshaded region of
the surface.


Electrons to Analyzer


Figure 3-2. Flow chart outlining the various routines in the surface roughness program.




Figure 3-3. Comparison of the shading effect at two different take-off angles, 01 and 02, with 01 >
02. As the angle decreases, the shading fraction increases.


10,
36


Figure 3-4
Illustration of the relationship between 0, 4^, and 0[
for the three possible cases.


38


39
general equal to . The assumption is made that a general idea
of the average depth analyzed, which has been shown to be directly
related to sin 9 for an ideally flat surface, may be obtained by
looking at , which represents the average taken over the
entire rough surface. The program does output the distribution of
sin 9[ values as well, in order that a more complete analysis may be
carried out if called for.
In order to determine how the population of electrons which can
reach the analyzer entrance slits varies as a function of take-off
angle and surface roughness, it is necessary to take two factors into
account. First, the area of each pixel which is unshaded must be
determined. Second, the depth below the surface from which the
photoelectrons may emerge without being inelastically scattered must
be found for each pixel. These two values may then be multiplied
together for each pixel to yield its effective sampling volume.
Finally, the volume values over all the unshaded pixels are summed.
The surface roughness modeling program then reports these values
normalized so that near normal exit at 9 = 89 yields an electron
population of unity. The routine for determining the normalized
electron population of a surface while taking surface topography into
account has little precedent. It provides a valuable means of
comparing the normalized peak areas obtained in XPS as a function of
escape angle with expected results determined from the surface
roughness model. A literature review indicates that little progress
has been reported along these lines of investigation. However, in
order to adequately account for the effects of surface topography, and


40
thus come one step closer to a truly quantitative XPS methodology,
such investigations are called for to provide critical information
about electron populations and the factors which go into their makeup.
A means of presenting an alternative method of characterizing the
nature of the surface roughness is provided as well. The program has
the capability of calculating the autocorrelation vector for each
height vector taken along the axis of analysis. These vectors are
then summed over the entire matrix to give an effective
autocorrelation vector for the height matrix in the direction which
the photoelectrons must travel to reach the analyzer slits. This
approach has been applied to modeling the surface roughness effect on
the AES signal (60), where it affects both the excitation and
detection processes. Other researchers (61,62) have also made use of
autocorrelation functions to characterize the surface roughness
profile. If one were to input an experimental roughness vector, thi3
function would provide information about any periodicities in the
data. Also, the autocorrelation lengththe average distance over
which the structure is correlatedcan be used as a measure of the
effective magnitude of the topography; rough surfaces are in general
less correlated over large distances than smooth surfaces.
An IMSL subroutine is used in the program to perform the actual
autocorrelation calculation. For a given height vector in the
x-direction (i.e., along the analyzer axis), the average height is
first calculated. Then the autocovariance vector Axx(j) is calculated
for a specified number of point offsets K, which is typically about
10$ of the number of points in the height vector. The equation used


41
to calculate Axx(j) is
-1 n
Axx(j) (n) E (h. ) (hi+j ) J-1 K.
The variance s2 of the vector is calculated by
n .
s2 = (n)"1 E (h ) .
i-1
2
The autocorrelation vector is then given by A (j)/s .
xx
Finally, the program attempts to estimate the total surface area
for a matrix of digitized height values. The approach is to divide
the surface into a series of triangles joining three near-spaced
points, calculating the area of these triangles, and summing. Better
surface area measurement techniques are readily available in cases for
which the quality of the data justifies a more quantitative measure.
It is simply designed to give another, qualitative measure of the
magnitude of surface roughness.
The program thus allows an evaluation of the two major factors
related to a sample's surface topography which are responsible for
varying the XPS signal. The signal can be decreased in magnitude by a
certain region of the sample blocking electrons emanating from another
region in the direction of the analyzer entrance slits. In addition,
electrons from unshaded regions may leave the surface at an angle
quite different from the instrumental photoelectron escape angle.
This phenomenon leads to a change in the effective sampling depth of
the photoelectrons, which is related to . The interplay of
these two factors to create the overall electron population as
affected by the surface topography is determined by the electron


H2
population modeling subroutine. The auto-correlation behavior of the
surface matrix along the axis of analysis is also available as a means
of characterizing the surface topography. Finally, provision is made
for approximating the total unshaded surface area represented by the
input matrix of height values.


CHAPTER 4
TESTING AND APPLICATIONS OF THE SURFACE ROUGHNESS MODEL
In this chapter, the various analytical roughness patterns used
to evaluate the performance of the surface roughness model are
discussed and the results obtained are compared to the expected
values. In addition, several applications of the program output to
experimental data are presented. Lastly, the experimental
investigations into the magnitude and nature of surface topography
effects are presented and discussed in light of the theoretical
results.
Testing of Roughness Program
Two functions which have been applied several times previously to
the analysis of possible surface topography effects are the sinusoidal
function and a generalized grating function. Both functions are one
dimensional in their surface height variation; in fact, all known
previous studies have treated the surface roughness problem as
effectively a unidirectional one, with one exception. De Bernrdez
et_ al_. (53) were interested in modeling the effects of damage from a
static electron or ion beam, and so they used an axially symmetric
cone-shaped surface. The rationale behind one-dimensional modeling
arises from the geometric relationship between the sample surface and
the electron energy analyzer entrance slits. The technique of
variable angle XPS (VAXPS) does not, and in fact cannot, make use of
43


an attractive potential between the sample and the analyzer entrance
slits. If such a potential were to exist, then photoelectrons from a
large range of escape angles, and thus a large range of depths, would
be energy-analyzed and detected in the species peak. In effect, depth
and kinetic energy resolution would be severely degraded. Thus, since
the axis of sample rotation in VAXPS is perpendicular to the direction
which the emergent photoelectrons must possess to enter the energy
analyzer, essentially only one dimension of the surface roughness
that dimension perpendicular to the axis of rotation and in the plane
of the sample surfacehas any effect on the resultant XPS signal in
the limit of an infinitesimally narrow analyzer entrance slit.
For both the sinusoidal and grating functions, the shading
fraction, vector length, and values related to the photoelectron
escape angle can be predicted algebraically as a function of the ratio
of amplitude to wavelength for the periodic function. A definition of
these parameters, as well as their method of calculation, was
presented in the previous chapter. The ability to compare program
results with the analytic solutions made these functions excellent
candidates for testing the accuracy of the surface roughness model'3
output.
Sinusoidal Function Results
For the sinusoidal function S(x) given by
S(x) = A sin (2irx/A),
where A is the amplitude and A is the wavelength, the shading fraction


45
Fs is given by
I 2 7l + [(2ttA/A) cos (2irx/A)]2 dx
F_- ^
(2ir J1 + C(2irA/A) cos (2irx/A)]2 dx
J o
where
x1 = (A/2it) cos 1 [(A/2irA) tan 0]
and
A cot 9 3in (2irx2/A) x^ = A cot 0 sin (2-itx^A) x^ A.
The instrumental setting for the photoelectron take-off angle is given
by 0. It can be deduced from the above equations that no
photoelectron shading occurs if (A/2irA)*tan 0 > 1.0. Once X-, is
obtained from the first expression, it can be substituted into the
second expression to obtain x2. These values can in turn be
substituted into the integral equation to yield the shading
fraction. Although this integral form doe3 not possess an analytic
solution, it can be numerically integrated to any desired precision to
give values for Fg algebraically. Calculation of the parameters
related to the photoelectron escape angle 0 from first principles is
more complex. Essentially, the procedure involves the determination
of the surface tangent for a vector element dx, multiplying it by the
length of dx, summing over all the unshaded vector elements, and
dividing by the overall unshaded length. Again, numerical integration


46
techniques are required to obtain an algebraic solution to the
problem.
Comparison between the analytic results and the program output
for the one-dimensional sinusoidal function can be seen in Figures 4-1
and 4-2 for several different wavelengths (holding the amplitude
constant) over the range of escape angles such that 10 £ 0 £ 89.
The curves in Figure 4-1 represent the true, algebraically arrived-at
values for F, while the points represent the roughness program
results for a sinusoidal vector consisting of 50 wavelengths digitized
to 5000 points. As A is increased relative to the amplitude, the
surface topography becomes less pronounced. Thus, A = 0.1 represents
an analogy to a very rough surface, while A = 20.0 corresponds to a
smooth, essentially flat surface. In general, the agreement is quite
satisfactory; relative errors are greatest at very low values of F3,
where the program must make use of a small number of points in its
calculation. This error can in principle be reduced by increasing the
digitized resolution. However, constraints on the memory available
for array storage during execution of the program make such error
reduction difficult to achieve. The general trend followed by Fs as a
function of escape angle can be seen. As 0 is increased, more of the
surface has the direct line-of-sight to the analyzer entrance slits
necessary for emitted photoelectrons to be collected. Thus Fg
increases as 0 is increased. At some cutoff angle 0C, the surface is
fully visible to the analyzer, with no shaded areas. At this and all
higher escape angles, the shading fraction is unity. For the


Figure 4-1. Plots of the shading fraction Fg as a function of photoelectron take-off angle 0 (deg) for
several wavelength values of a one-dimensional sinusoidal function. The curves represent
expected results, and program output (+) is shown in comparison.


30
6*0
90
THE T ft
Jr
00


Figure 4-2. Plots of the ratio R = /sin 0 as a function of take-off angle 0 (deg) for a
sinusoidal function, as in Figure 4-1.


A = 1.0
A 0.1
2
1
3^ THETA
R
5'
4
3
+
A 1.0
A 5.0
2
1
3*0
60
THETA
A = 1.0
A 1.0
3J THETA 90
A = 1.0
A 20.0
+ +- +
3*0
6*0
THETA
90
m
o


51
sinusoidal function, the cutoff angle 0C increases as the wavelength
decreases; for a rougher surface, the shading effect is apparent over
a greater range of 0 values. Finally, the curves demonstrate that not
only is there shading over a greater escape angle range for a rougher
surface, but the shading is greater, apparently allowing less of the
actual emitted photoelectrons to make their way to the analyzer
entrance slits.
In Figure 4-2 are several curves showing the variation in the
ratio R =* /sin 0 as a function of escape angle 0. Here,
represents the average value for the sine of the true
photoelectron take-off angle, which differs from the instrumental
setting sin 0 for rough surfaces. Results for the same four
sinusoidal vectors as those shown in Figure 4-1 are illustrated here;
again, the curves represent an analytic determination of R, while the
points correspond to program output. Agreement is in general better
between output and true values. This value is not quite as sensitive
to the use of small numbers of points in its calculation as the
shading fraction. For a perfectly smooth surface, R is equal to
unity.- Over much of the range of escape angles, R is close to unity
for the analogous smooth vector where A = 20.0. Only below the cutoff
angle 0C does it begin to show an increase. For the lower values of A
corresponding to rougher surfaces, a general decrease in R is observed
as 0 is increased, with the curve leveling out beyond 0C. Note that
at low values of 0, the ratio is in general greater than unity, while
the reverse is true at high values of 0. This observation has


52
ramifications for the determination of the overall sampling volume to
be discussed below.
Grating Function Results
The second analytic test function, a grating function, was chosen
for several reasons. It has been previously studied by several
researchers. Also, its use addresses the ability of the surface
roughness program to deal with discontinuitiespoints of
indeterminate slopein the topography of a surface. Finally, this
function is not in general isotropic in its roughness along the
direction of measurable photoelectron exit. It has a different
surface area facing toward the analyzer from the side facing away from
the analyzer, a category into which certain real world surfaces may
fall. For the one-dimensional grating function, analytic solution can
be accomplished as well. The variable parameters are the primary and
secondary blaze angles p and Y, respectively; the baseline-to-peak
distance is fixed at 2.0. The wavelength A is then given by
A = 2.0 (sin p + sin Y).
If the photoelectron escape angle is greater than the primary blaze
cingle p, then the surface is fully illuminated and Fs = 1. Otherwise,
one must use a geometric approach to the determination of Fa.
Recognizing that the function has a peak-to-trough amplitude of 2.0,
the initial cutoff point x1 is given by
2.0/tan p.


53
By drawing a series of right triangles and using elementary analytic
geometry, the second cutoff point x2 is determined as
x^ + A + 2 cot 0 (tan Y/tan p)
X2 1 + cot 9 tan Y
The equation for Fg turns out to be
Fg (1/L) (x2 x^2 + (hx 2.0)2 ,
where the surface length L across one wavelength is given by
L = 2.0 (1/sin p + 1/sin Y)
and the height hx at point x2 equals
h^ = 2.0 + 2.0 (tan Y/tan p) tan Y.
The same basic procedure used for calculating the parameters related
to the angle of photoelectron escape in the case of the sinusoidal
function is again used for the grating function.
Comparison between analytic results (curve) and program output
(points) is shown for the grating function in Figures 4-3 and 4-4.
For the program's input height vector, 20 wavelengths were digitized
to give 1000 points. As the blaze angles increase, the effects
associated with increased surface roughness increase as well. The
same general trends observed for Fg (Figure 4-3) and R (Figure 4-4) as
a function of photoelectron escape angle in the sinusoidal functional
case are reproduced here as well, lending an air of generality to such
behavior. In this case, the cutoff angle is easily seen to equal the
primary blaze angle; only below this angle can shading occur.


Figure 4-3. Plots of the shading fraction Fg as a function of photoelectron take-off angle 0 (deg) for
a triangular grating function. Shown are results for several combinations of primary and
secondary grating angles p and Y, denoted by (p,Y). The curves represent expected
results, while program output (+) is shown in comparison.


1
. 75
FS
It
. 75
FS
.5
25
+ + ~ +
BLAZE-(45,60)
It
.75
FS
.5
. 25
0
30
0
^0
0
THETA
BLAZE-(60,30)
+
3*0
6*0
THETA
90
+ + -*~
BLAZE-(30,30) *
+
3*0
THETA 60
90
VJ1


Figure 4-4. Plots of the ratio R = /sin 0 as a function of take-off angle 0 (deg) for a
grating function, as in Figure 4-3.


BI_AZE = <75,75)
4
2
3*0
THETft
60
6
4'
+
BLAZE"<45,60)
3*0
6*0
THETA
90
BLAZE"(60,30)
310 THETA £5
BLAZE"(30,30)
6^3
3&
THETA


58
Agreement between the program output and the analytic values is better
for the grating function than the sinusoidal function, primarily
because the pixel slope, upon which several key calculations are
based, does not vary continuously in this case, but can take at most
only one of two discrete values. Note also that the slope of the
curves near 0Q is sharper in this function. This factor arises from
the periodic point discontinuities in the roughness vector. The
greater the blaze angles p or Y, the more the surface vector behavior
deviates from that for a smooth surface; increasing p causes an
increase in 0C, while increasing Y reduces Fs and increases R.
Particulate Surface Model Results and Applications
The surface roughness program was first used to test for any
difference in the effects of surface topography on two different
surfaces. As experimental data, powder size distributions derived
from scanning electron micrographs were compiled. In order to
transfer these data to a form suitable for input into the program, the
particulate surface model (PSM) was developed. The PSM is a simple
approximation to the actual surface topography vector. At present, it
is strictly one-dimensional in its approach. The inherent assumptions
are as follows:
1) Surface roughness effects on the determination of the shading
fraction and the effective escape angle parameters are
predominant primarily along the analyzer axis.
2) Given a particle size distribution, it is assumed that the
particles are close-packed along the analyzer axis.


59
3) The maximum height of each particle above a surface baseline
is modeled by taking a random fraction of its radius.
4) The particles are assumed to be spherical, orto be more
preciseto give a circular cross-section along the "slice"
of surface which is analyzed by the program.
The resulting model surface resembles that shown in Figure 4-5 (a).
This surface is then digitized to give a vector of height values in
Figure 4-5 (b). Given a vector representing the randomized fraction
of each particle's radius, the height h as a function of surface
displacement p for a particle with diameter R is given by
h = 0.5 /4d (R d) m,
where
d R/2 F
C = /4F (R F)
F = (R/2) RND (0,1),
as seen in Figure 4-6. The function RND (0,1) represents a random
number generator with output s such that 0 < s < 1. The displacement
Pn from the edge of particle n is related to the total displacement x
by
q = C/2 p
m = R/2 F
n-1
- Z
i-1
x


Figure 4-5.
Illustration of a portion of surface height vector
obtained from the PSM: a) construction of the vector
from a close packing of particles; b) result of
digitization, yielding a suitable input vector.


Particulate Surface Model
Digitized Height Values
niiii.iiillii.l


Figure M-6. Illustration of the geometrical relationships required by the PSM to generate the height
vector.




64
The sample powders whose surface topography effects are to be
compared are homogeneous Pb ISEs manufactured from a co-precipitation
of PbS and Ag2S. Two slightly different powder preparation techniques
have been used. The general experimental procedure is to dissolve
Pb(N0^)2 (MCB Chemicals, Reagent grade) and AgNO^ (MCB Chemicals,
Reagent grade) in deionized water in amounts such that 2nl_ = n. A
Pb Ag
0.1 M Na2S solution is then prepared. In the first procedure, the
P+ +
Na2S solution is added in excess to the mixture of Pb and Ag salts,
while stirring at room temperature. The second procedure is similar;
?+ +
the mixture of Pb and Ag salts is added to an excess of Na2S
solution. The resultant precipitates are isolated and washed several
times with 0.1 M HNO^ to remove any excess sulfide. The powders are
finally washed with deionized water, filter dried overnight, dried in
a 110 oven for 24 hours, and stored in a dessicator.
The scanning electron microscopy (SEM) photographs shown in
Figure 4-7 were taken on a JEOL JSM-35CF microscope operating at 25 kV
accelerating potential and 20.000X magnification. These micrographs,
which are representative of those for each powder, correspond to
powders prepared using procedure 1 (Figure 4-7 (a)) and procedure 2
(Figure 4-7 (b)) described above.
Certain general differences between the two powders may be
noted. The particles from the first procedure appear to be larger as
a rule and more widely scattered in size. These indications are borne
out by an analysis of the particle size distributions, shown in
Figure 4-8. The skewedness of the distribution in Figure 4-8 (b) may
be due in part to the lower resolution of the SEM photo in


Figure 4-7. Scanning electron photomicrographs of two PbS/Ag2S
powders: a) preparation by procedure 1, and (b)
preparation by procedure 2; both of which are described
in the text. The bar at the bottom of each photograph
corresponds to 1 pm.




Figure 4-8. Particle size histograms, showing the number of
particles as a function of particle diameter, derived
from the SEM photomicrographs shown in Figure 4-7: a)
histogram of particle sizes from the SEM photo in Figure
4-7 (a); b) histogram of particle sizes from the SEM
photo in Figure 4-7 (b).


SEM PHOTO 0089
B)


69
Figure 4-7 (b). The presence of any smaller particles would only
strengthen the argument that the average particle size differs in the
two photomicrographs. In the particle size distributions determined
from the two micrographs, photo 0005 (procedure 2) shows a mean
diameter of 0.13 uni, while the particles in photo 0009 (procedure 1)
possess a mean diameter of 0.15 pm. If we make the assumption that
each particle population follows a Gaussian distribution in particle
diameter, then the hypothesis that the second mean diameter is not
greater than the first mean diameter can be rejected at a 99.5%
confidence level. The histogram shown for photo 0005 probably
underestimates the sample standard deviation and overestimates the
sample mean. However, this hypothesis rejection holds even if we use
the larger of the two sample standard deviations as a measure of the
population standard deviation, as opposed to pooling, or if we lower
our estimate of the first sample mean.
These powder distributions were then used as the input vector for
the PSM and an analysis of the comparative surface roughness effects
was carried out. The comparison results are shown for the shading
fraction Fs in Figure 4-9, and for the ratio R = /sin 9 in
Figure 4-10. It is immediately apparent that the difference in
particle diameters is not sufficient to cause a noticeable difference
in their XPS signals attributable to the differing surface
topography. A statistical comparison between the results for both
powders supports this statement. However, both powders are expected
to show appreciable surface roughness effects in their respective
VAXPS signals, especially at low values for the photoelectron escape


Figure 4-9.
Plots of the shading fraction F as a function of
photoelectron take-off angle 0 (deg), derived from the
SEM photomicrographs shown in Figure 4-7: a) F versus
9 plot for the powder depicted in Figure 4-7 (a); b) F
versus 0 plot for the powder depicted in Figure 4-7 (b)


71
PHOTO 0009
30 THETA 60
9^0
1-
.75
.5-
.25-
1*


y
PHOTO 0005
30 THETA 60
90


Figure 4-10. Plots of the ratio R = /sin 9 as a function of
take-off angle 0 (deg), derived from the SEM
photomicrographs shown in Figure 4-7: a) plot of R
versus 0 for the powder depicted in Figure 4-7 (a); b)
plot of R versus 0 for the powder depicted in Figure 4-7
(b).


2.5-
R
2-
1.5-
1
.5-
+

PHOTO 0005
00 THETA s'0


74
angle. Also, note that no sharp transitions can be observed in the
curves. As has been previously seen, such transitions arise from
periodicities in the surface roughness vector; since the PSM produces
an essentially aperiodic roughness vector, as most randomly rough
surfaces would be expected to produce, this observation is expected.
Thus, the PSM results provide several useful pieces of
information. They more closely approximate the expected behavior of
Fs and R of randomly rough surfaces as a function of 9. In the
present case, the results allow the conclusion that the two methods of
Pb ISE preparation do not produce different surface topographical
effects. This factor is of importance to the discussion of Pb ISEs in
a later chapter. Finally, and of more general interest, the PSM
provides a means of estimating the surface roughness effect of a
powder sample using particle size distributions readily available from
SEM photomicrographs.
Experimental Surface Roughness Studies
An analysis of the effects of varying surface roughness has been
carried out on two surface chemical systems of relative simplicity.
The first system consists of sputter-cleaned gold surfaces. These
surfaces are essentially free of significant levels of contamina
tion. Therefore, their normalized peak areas as a function of
photoelectron escape angle can be used to characterize the instru
mental response of the XPS instrument. The Au 4f^2 peak at 83.80 eV
is also commonly used to standardize the instrumental binding energy
response. The second system is a carbon sample with measurable
surface oxidation. Such samples are more readily available than gold


75
samples, and they provide easily observable evidence of the contribu
tion of oxidized species to the overall carbon concentration. Gold is
relatively inert, and the Au 4f7/2 Peak does not show the presence of
oxides. The value of being able to resolve oxidized and unoxidized
carbon arises from the information about the electron sampling depth
available from such measurements. If the sampling depth is relatively
small, then the carbon peak envelope shows a significant contribution
from oxidized carbon species. For greater sampling depths, the bulk
graphitic carbon contribution is predominant.
Results of Gold Studies
Initial studies using gold samples focused on the determination
of the response function of the XPS instrument. In order to minimize
surface topography and vertical inhomogeneity effects, a gold foil
sample (Alfa Chemicals, 99.9+$ purity, 0.25 mm thick) was sputter
cleaned until the residual carbon contamination peak was minimized in
intensity. Source power was 300 W (15 kV, 20 mA), and a small solid
angle of detection (L0 magnification mode) was used. The peak area of
the Au ^f'y/2 and ^5/2 Peak doublet was determined after subtraction
of the background signal (Figure 4-11) using an iterative technique
developed by Shirley. Peak area is calculated using the equation
A (count) Energy step size (eV/ch)
A a
N (count*eV/sec) Dwell time (sec/ch)
where AT represents the sum of counts in all the channels in the peaks
after background subtraction, the energy step size is an instrumental
setting defining the ultimate energy resolution of the


Figure 4-11. Illustration of the nature of the background signal in the neighborhood of a
photoelectron peak. Here, the Au 4f signal from a gold foil is depicted. The satellite
peaks are visible as well.


Intensity (counts)
Gold foil sample. Au 4f peak window.
Runs AU17 Regs 1 (AU4F ) Scans 1 Bases 849 Max Cts/ss £3431


78
spectrum, and the dwell time is given by
Dwell time Scan time (sec) // of sweeps Step size (eV/ch)
(sec/ch) ~ Energy scan range (eV)
Since the X-rays used are not strictly monochromatic, satellite lines
are visible in this spectrum. The satellites do not interfere with
the peak area determination in this instance. The area was determined
for a series of photoelectron escape single settings ranging from 90
to 5. This area was then normalized by dividing by the largest peak
area value for the range of escape angle settings. The results of
these variable angle plots are shown in Figure 4-12 for both Mg Ka and
A1 Ka radiation. The decrease in peak area at 9 = 90 when using the
Mg anode results from the arrangement of the anode faces. The anode
tip is wedge-shaped, with the upper side aluminum-coated and the lower
side magnesium-coated. For 9 = 90, the sample surface is
approximately even with the tip of the wedge and, thus, does not
receive the total X-ray flux when using the Mg anode. Since data
taken at 90 were to be used in the surface roughness studies, the A1
anode was used throughout the investigation.
In order to ascertain the basic effects of increasing surface
topography on the results of VAXPS experiments, two other gold samples
were prepared and analyzed. As a model for the behavior of a very
rough surface, a gold powder (Alfa Chemicals, 99.995$ purity, -20 mesh
powder size) was sprinkled onto the surface of conducting copper tape,
which was then affixed to the sample holder using colloidal silver
adhesive. In this manner, a rough gold surface could be examined
without any of the sample charging effects due to the use of


Figure 4-12. Comparison of VAXPS response curves for the Au 4f peaks from a gold foil using the A1
anode (+) and the Mg anode (x) on the Kratos XSAM 800. In this and all subsequent VAXPS
response curves, 0 is shown in units of degrees.


NORM. PEAK AREA
1-
75- + AL ANODE
5-
O.
x MG ANODE
K
m
m

* *
V
V .+
V
K
0
30 THETA
6i0 *


81
common adhesive tape. In addition, this powder was pressed at 7 psi
into a pellet to be analyzed as well. This pellet was analyzed to
determine the general surface roughness behavior of a sample prepared
using a common, simple hand press which is often used in sample
preparation for routine XPS. Operating conditions were the same as
above, and the VAXPS curvesplots of total doublet peak area as a
function of photoelectron escape angle 0for the foil, pellet, and
powder samples are compared in Figure 4-13. In this graph, all the
peak areas were normalized only to account for any differences in the
peak collection times. Thus, the overall peak areas as a function of
escape angle are compared for the three samples. Several noteworthy
changes are apparent as the surface roughness increases in the order
foil < pellet < powder. First, the doublet peak area drops off
significantly at high values of 0, then actually increases as 0 is
decreased. As the surface roughness increases, the escape angle where
the maximum peak area is obtained decreases. In addition, in the
range of low 0, the peak area is greater for rougher surfaces. These
two factors combine to lower the range of peak area values over the
range of escape angle settings. Whereas the peak area for the foil
increases by 2.5 orders of magnitude over the range of angles, only an
order of magnitude increase is seen for the pellet sample, followed by
a decrease at higher take-off angle settings. For the powder sample,
the peak area increases only by a factor of 3 before decreasing at
higher 0. Obviously, this observation has important ramifications
when one is varying the angle setting in order to maximize the XPS
3ignal. In addition, the tacit assumption that surface roughness


Figure 4-13. Comparison of VAXPS response curves for a gold foil (+), pressed gold pellet (x), and
gold powder (), illustrating the effects of surface topography. The area axis has
units of count eV/sec.


25000-
+
N
X
20000-

15000-
10000-

5000-
.
X
0:
- FOIL
- PELLET
- POWDER
Â¥
x
a a 5? ^
+
30 THE T ft
X +
+
+
+
x X
X
6 910
Co
UJ


84
effects are negligible with pressed pellet samples is shown to be
false, due to the difference in VAXPS signal between gold foil and
compressed powder pellet. This point forms the basis of a study of
the effect of pressure on the XPS signal, presented below. Finally,
the effects of surface roughness may be quite dramatic, as shown in
the VAXPS response curve for the gold powder sample.
Results of Carbon Studies: Model Comparison
The first series of experiments investigating a graphitic carbon
surface were designed to test the predictions of the electron
population model which was developed as a routine in the surface
roughness program. As discussed above, this model outputs an
approximation to the normalized VAXPS curve as a function of the
topography of the input surface height vector or matrix. The
predictions of the model about the changes in the VAXPS curve are
compared here with some experimental studies of carbon surfaces of
various roughness.
Experimentally, the samples studied included a carbon foil
(Goodfellow Metals, 99.8+$ purity, 0.125 mm thickness) which, although
smooth, is not as smooth as the gold foil sample. Also, studied were
two carbon powder samples (Alfa Products, 99.5$ total purity, -325
mesh and -20 +60 mesh). For the -325 mesh powder, all particles are
smaller than 44 ym in diameter; for the -20 +60 mesh powder, particle
diameters range from 250-841 ym. However, for the latter powder, the
particles flake together, forming smooth sections of surface. Both
powders were sprinkled onto conductive copper tape, then affixed to
the sample holder using colloidal silver. The carbon powder


85
(-325 mesh) sample forms a surface with appreciable topography; it
serves to act as a very rough surface. The carbon flake (-20 +60
mesh) sample consists of disjointed sections of smooth surface; its
surface roughness is intermediate between the powder and the carbon
foil. The instrumental operating conditions for data collection were
the same as in the case of the gold samples. For all three samples, a
series of VAXPS experiments was carried out by varying the
instrumental setting of the photoelectron take-off angle 0 in the
range [5,90]. The C l31/2 Peak areas were normalized in each case
so that at the angle where the peak area was maximum, the area had a
value of unity. The electron population model results over the same
range of 0 were compared for a series of wavelengths using the one-
dimensional sinusoidal function and matching the best approximations
to the experimental results. The curves are compared for the three
samples in Figure 4-14 (carbon foil), Figure 4-15 (carbon flakes), and
Figure 4-16 (carbon powder). The average percent difference between
model and experimental points is 2.34$ for the carbon foil, 4.57$ for
the carbon flakes, and 1.81$ for the carbon powder. The carbon foil
shows a response very close to an ideally flat surface. In fact, the
percent difference between the carbon foil and a model flat surface is
2.42$. Thus, the carbon foil serves to act as an experimental flat
surface standard. Note the good agreement between model and
experimental results. As is expected, the wavelength of the
sinusoidal function which best matches the experimental curve
increases as the roughness of the sample decreases. That is, a
smoother model surface vector is required to fit a smoother


Figure 4-14. Comparison of theoretical electron population and
experimental VAXPS response curves for a ruffle function
(A = 20.0) and a carbon foil, respectively.


NORM. PEAK AREA NORM. E POPULATION
.75+
RUFFLE FUNCTION
+ +
A =* 1.0
A 20.0


Figure 4-15. Comparison of theoretical electron population and
experimental VAXPS response curves for a ruffle function
(A = 10.0) and a flaky carbon sample, respectively.


NORM. PEAK AREA NORM. E POPULATION
1 RUFFLE FUNCTION
75
25
+ +
A
A
1.0
10.0
30 THETA 60
90


Figure 4-16. Comparison of theoretical electron population and
experimental VAXPS response curves for a ruffle function
(A = 0.2) and a carbon powder sample, respectively.


NORM. PEAK AREA NORM. E~ POPULATION
RUFFLE FUNCTION
1*
. 73
A 1.0
A 0.2
3G
THETA
60


92
experimental surface. The uneven nature of the theoretical curve in
Figure 4-16 is attributable to the small shading fractions for this
very "rough surface. The results are obtained by averaging over a
relatively small number of points and are, thus, more subject to
random error.
Even though the surface roughness varied dramatically among these
samples, they all show somewhat similar VAXPS curves. This phenomenon
is due to the offsetting nature of the two effects of the surface
topography on the magnitude of the XPS signal. The first effect is
the shading fraction Fg variation. For a rough surface, the shading
fraction is low, and a smaller signal is expected. However, for this
same rough surface, the electron population model predicts that the
regions of the sample which are capable of emitting analyzable
photoelectrons emit proportionately more photoelectrons. An
examination of Figure 4-17 helps to explain this result. Here, the
relative population of analyzable photoelectrons emitted by each
surface pixel is plotted in bar chart form directly below that pixel
for several escape angle settings. For this portion of a hypothetical
surface roughness vector, the electron population is relatively evenly,
distributed for 0 = 89. As 0 is decreased, portions of the surface
are shaded, but the unshaded portions emit a greater number of
photoelectrons. At higher instrumental take-off cingles, the decrease
in the signal due to a lower shading fraction is more important, and
an overall lowering of the signal is observed. At lower escape angle
settings, the increase in the sampling depth is more important than


Figure 4-17
. Plots of the relative populations of emitted
photoelectrons from each pixel of a small portion of a
surface height vector for several different values of
the instrumental take-off angle 9. The vertical scale
is in arbitrary units.


Full Text
UNIVERSITY OF FLORIDA
3 1262 08554 2883



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