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

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Title:
Quantitative x-ray photoelectron spectroscopic methods and their application to lead ion-selective electrode surface studies
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vi, 225 leaves : ill. ; 28 cm.
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English
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McCaslin, Paul C., 1960-
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Subjects / Keywords:
Surface roughness -- Measurement -- Data processing   ( lcsh )
X-ray spectroscopy   ( lcsh )
Photoelectron spectroscopy   ( lcsh )
Electrodes, Ion selective   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

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

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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Full Text
















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















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 my 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.















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS..... ............. .............. .... .. ....... .... i

ABSTRACT............................................................ v

CHAPTERS

1 INTRODUCTION..... .........................................

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........................... ................. 121
Theoretical Basis...................................121










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 HCO................................. 170
Effects of Fe ..................................175

7 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK............ 184

Summary and Conclusions................................. 184
Future Work...................... ...................... 186

APPENDICES

A SURFACE ROUGHNESS PROGRAM SOURCE CODE...................189

B NILT PROGRAM SOURCE CODE. ................................203

REFERENCES.. ..................................................... 220

BIOGRAPHICAL SKETCH ............................................. 225















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









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.


i














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 Ek relative to the measuring spectrometer is given in

the absence of surface electric double layers by the expression


Ek = hv Eb f


where Eb is the binding energy of the electron in the atomic or

molecular system measured relative to the Fermi level and of is the

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


jl









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.


-li









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









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., 10-9

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-rays--which may travel 100-1000 nm before being appreciably

attenuated--but 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
















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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, macrobeam ion gun, electron energy analyzer,

detector system, and a chamber pumping system. The X-ray gun

furnishes either Al Ka (1486.6 eV) or Mg Ka (1253.6 eV) radiation,

allowing differentiation between kinetic energy-invariant 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 Al 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







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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 1800 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









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

-6 -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-" 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 1011 Torr; typical operating pressures are in the low 10 to
-10
high 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 -1500C to +6000C. 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.









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, such 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









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/As2S3 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 HC104

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

effects of Cu2+ and Zn2+ 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


) I









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 sample's 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 are 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 A). 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









intensity I (E ,y) of photoelectrons from level y of species c in

sample s is given as (29)


I (E ,y) Io(hv) doY/dg(hv,*) F(E ,EA) T(E ,EA,Q )

SD(E ,E) G(Q ,e) f( N (z) exp(-z/A (E )*sin 9) dz.
c A o o0 s a

Here, I (hv) corresponds to the incident X-ray flux of energy hv;

doa/dQ(hv,0) is the differential photoionization cross-section of sub-

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)


do /do (ac/4w)C1 Bn(Ec)/4 (3 cos2 1)],


where ao is the total cross-section of sub-shell y of species c,
C
typically measured at 1487 eV in units of the C is cross-section of

13600 barns, and 1(Ec ) is the angular asymmetry factor, a function

of the electron energy Ec. The values of aY have been theoretically
c
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 800;

thus, this factor becomes a constant for a given peak. Theoretical

values for n1(Ec) have been reliably calculated for all core levels

and tabulated as a function of atomic number (35), and the effects of









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


Resolving power AE/E = (W/2R) + Ka2


where W is the slit width, R is the mean analyzer radius, a is the

semi-angle in the dispersive plane, and K is a constant. For a slit

width of 8 mm 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 ,EAo ) is dependent on electron

kinetic energy, the analyzer energy, and the solid angle of









acceptance o for the analyzer; D(E ,EA) is the detector efficiency;

and G( o,9) 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 e when operating in the FRR

mode. N (z) refers to the atom concentration (atoms/cm3) of species c

at depth z; As(E ) is the electron IMFP, dependent on the sample and

electron energy; and 8 is the photoelectron escape angle. The

product A (Eo )sin 9 denotes the effective IMFP, the effective depth

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


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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









discussed in this work. Secondly, surface roughness may have a

significant effect on e and on G(Qo,e). Quantitative VAXPS will be

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 (9) Kc(9) fo N (z) exp E-z/A (E0 )sin 9] dz.


The angular dependence of K (9), if present, can typically be

determined empirically. Results from VAXPS experiments may be used to

characterize the nature of the intensity I (9) as a function of the
c
photoelectron take-off angle e. The use of such VAXPS data in this

equation provides an opportunity for obtaining information about the

depth profile Nc(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


I









analyzed, no systematic experimental investigation of surface

roughness effects was undertaken. The change in emission angle was

focused upon. Baird et 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 BrUmmer (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 Bernardez et 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


d









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









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(E ,y) of photoelectrons from level y of species c in

sample s has been shown to follow the form


Ic(Ey) Io(hv) daY/dQ(hv,) F(Ec EA) T(Ec,EA' o)
SD(E ,E ) G(R ,9) J N (z) exp(-z/A (E )*sin 8) dz.


Of interest in this chapter are the geometric factor G(Q ,9) 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









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 setting--which is based on the

assumption of an atomically flat surface--by 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 N (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.










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


hi + nb < hi+n n = 1,2,...


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, hi represents the height of point i, b Tx tane,

where Tx 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 hi 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


I











L = 2 + (h h )2
x i+1

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 Es 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 e to the average actual value

<9'>, the value of 8i' 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 rx separating them.

In this manner,


91' 9 + i'

where


i Arctan(hi hi+ /Tx)


A weighted average over all points previously found to be unshaded is

carried out for 9i' and sin 8'l, to yield <8'>, , the

distribution of over the range [0,1], and the value of the

ratio /sin 8. It should be noted that sin <9'> is not in
















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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 8 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 8 890 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









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, this

function would provide information about any periodicities in the

data. Also, the autocorrelation length--the average distance over

which the structure is correlated--can 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









to calculate Axx(j) is

-1 n
A x(J) (n) E (hi ) (h + ) j=1,...,K.
i1I

The variance s2 of the vector is calculated by

2 -1 n 2
s (n) Z (h ) .
i-i

The autocorrelation vector is then given by A xx(j)/s2.

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





42



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 Bernardez

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


.I








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 surface--has 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's

output.

Sinusoidal Function Results

For the sinusoidal function S(x) given by


S(x) A sin (2wx/A),


where A is the amplitude and A is the wavelength, the shading fraction








Fs is given by


fx2 "1 + [(2wA/A) cos (2rx/A)]2 dx
F -
s 2 J1 + [(2wA/A) cos (2wx/A)]2 dx


where


x1 = (A/2w) cos-1 [(A/2wA) tan e]


and


A cot 9 sin (2wx2/A) x2 = A cot 9 sin (2rx /A) x A.


The instrumental setting for the photoelectron take-off angle is given

by 9. It can be deduced from the above equations that no

photoelectron shading occurs if (A/2wA)-tan 0 > 1.0. Once x1 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 does not possess an analytic

solution, it can be numerically integrated to any desired precision to

give values for Fs algebraically. Calculation of the parameters

related to the photoelectron escape angle 9 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









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 100 9 < 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 Fs,

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 9 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 F.

increases as 9 is increased. At some cutoff angle 9c, 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















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sinusoidal function, the cutoff angle 89 increases as the wavelength

decreases; for a rougher surface, the shading effect is apparent over

a greater range of 9 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 9 as a function of escape angle e. Here,

represents the average value for the sine of the true

photoelectron take-off angle, which differs from the instrumental

setting sin 9 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 9c 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 9 is increased, with the curve leveling out beyond 9G. Note that

at low values of 9, the ratio is in general greater than unity, while

the reverse is true at high values of 9. This observation has









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 discontinuities--points of

indeterminate slope--in 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

angle p, then the surface is fully illuminated and Fs 1. Otherwise,

one must use a geometric approach to the determination of Fs.

Recognizing that the function has a peak-to-trough amplitude of 2.0,

the initial cutoff point x1 is given by


x 2.0/tan p.








By drawing a series of right triangles and using elementary analytic

geometry, the second cutoff point x2 is determined as

x + A + 2 cot e (tan Y/tan p)
x2 1 + cot 9 tan Y

The equation for Fs turns out to be


F (1/L) (x x )2 + (h 2.0) ,


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


hx 2.0 + 2.0 (tan Y/tan p) x2 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 Fs (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.















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0)

ct s

















+
4.
t





4.




I


o"


V.

+








k i






N
c
J!




m e

I,
oD


r tt ci


4.

+

4.

+


II


1b N 1i


('a S~C


I I I I I i









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 9, 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 9c, 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, or--to be more

precise--to 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 q C/2 p


C 4F (R F) m R/2 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


n-1
p = x E F .
i-=1





























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


.,rlnrll,,,,,,,.,,lll,,.lllliilllili.il
















co

-4
0
bO












CO
0
4)








4)
(D








C
0


0











0
4-
























0o
0
0

































I-
0
1)






CU
0-I
0


0






-4
0}
0


0
0







-4
L

c0


b-














ao

0r
60a











eeIp~ -Ioo4


LL


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r








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(NO3)2 (MCB Chemicals, Reagent grade) and AgNO3 (MCB Chemicals,

Reagent grade) in deionized water in amounts such that 2np nAg. A

0.1 M Na2S solution is then prepared. In the first procedure, the

Na2S solution is added in excess to the mixture of Pb2+ and Ag+ salts,

while stirring at room temperature. The second procedure is similar;

the mixture of Pb2+ and Ag+ salts is added to an excess of Na2S

solution. The resultant precipitates are isolated and washed several

times with 0.1 M HNO3 to remove any excess sulfide. The powders are

finally washed with deionized water, filter dried overnight, dried in

a 1100 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 um.






(A)


(B)




























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 969S


111
: ..II


8 12 15


ll. ll


EI..


- I ~- ~`-~-- ~ ~I.- ~---


18 21 24 27 38 33 42 45 48 4 1
PARTICLE DIAMETER )


SEN PHOTO 0065


18


.1


PARTICLE I


Il


EI m m


M3DETER 338 CRO X 2F86
DIRIETER MICHROH X 209)


8 12 15


atrurrcIL








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 um, while the particles in photo 0009 (procedure 1)

possess a mean diameter of 0.15 um. 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 0 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 8 (deg), derived from the
SEM photomicrographs shown in Figure 4-7: a) F versus
9 plot for the powder depicted in Figure 4-7 (a3; b) F
versus 9 plot for the powder depicted in Figure 4-7 (bT.





71











S )

75. ** -
..



.5 .' PHOTO e889


.25



30 THETA 6"' 90









I. (B)

F.



5 .*' PHOTO 8885


.25-


fl_1 "_


3B THETA 68


90






























Figure 4-10.


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


I






















(A)
PHOTO 8889




'..


38 THETA 6


98


B>)
PHOTO 8885


DJ T T 68 9|


2.5

R 2



1.5


1


.5.


2.5

R
2





1*


.5-


+
*
*.


Y- -r-


\


36 THETA 6


98









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 periodic 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 e. 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 4f7/2 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









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 (LO magnification mode) was used. The peak area of

the Au 4f7/2 and 4f5/2 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

AT (count) Energy step size (eV/ch)
AN (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
















-4

V-





04
0





00)
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0












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4 0

0














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Cu,


































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io
















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60





















cW






Cu

















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8-

r
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w
5,









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 angle settings ranging from 900

to 50. 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

Al Ka radiation. The decrease in peak area at 9 900 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 9 900, 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 900 were to be used in the surface roughness studies, the Al

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



















0.
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* *

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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 curves--plots of total doublet peak area as a

function of photoelectron escape angle 9--for 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 9, then actually increases as 9 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 e, 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 9. Obviously, this observation has important ramifications

when one is varying the angle setting in order to maximize the XPS

signal. In addition, the tacit assumption that surface roughness

















C C









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+


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+ X a


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a x +
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OC> M I0 CD G
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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 pm in diameter; for the -20 +60 mesh powder, particle

diameters range from 250-841 pm. 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








(-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 [50,90]0. The C 181/2 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.




















+


RUFFLE FUNCTION

+


A 1.8
A 2e. 0


5 38 THETA 6 9S


I.









25


1-













.75
1-




.5o


.25


4 +


6+++


THET ,, 98_=


SFO L SAMPLE


JO THETA 6-S


9Q




























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.



















i. RUFFLE FUNCTION


A
A *


1 .
10.0


a38 THETA 6 8 98


.+ FLAKE SAMPLE


4- 4


t" _- I- I


.75.




.5.


.75


.5.


.2S


14.4.4.


4. -I


3S THETA 68


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.



















.RUFFLE FUNCTION

+


A


38 THETA 68


1' POWDER SAMPLE


39 THETAr 68


4. 4.


i.e
0.2


25+


- I-


98


.75%


.25+


Sn -


90








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 F 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 8 89. As 8 is decreased, portions of the surface

are shaded, but the unshaded portions emit a greater number of

photoelectrons. At higher instrumental take-off angles, 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 e. The vertical scale
is in arbitrary units.




















SURFACE SLOPE EFFECT ON X


SURFACE SLOPE EFFECT ON A


SURFRCE SLOPE EFFECT ON X