1
Electron Spectroscopy of Rutile-type Metal Oxides r
Sigrun Eriksen B.Sc. A.R.C.S.
A thesis submitted for the degree of Doctor of
Philosophy of the University of London and for
the Diploma of Membership of Imperial College.
Department of Chemistry
Imperial College
London SW7 2AZ
August 1987 2
Abstract
This thesis presents a study of defective and defect-free rutile
TiO (110) surfaces, using ultraviolet photoelectron spectroscopy (UPS),
X-ray photoelectron spectroscopy (XPS) and high resolution electron energy loss spectroscopy (HREELS). The use of argon ion and electron bombardment for creation of surface defects is investigated. An oxygen -20 -2 desorption cross section of 1.5 x 10 cm is found for electron irradiation, and a desorption mechanism suggested. An electronic excitation due to the oxygen vacancies is identified; this modifies the effective surface dielectric constant. The oscillator strength for this excitation is found to be 0.1, indicating an allowed transition.
The adsorption of water on the TiO2(110) surface is also studied.
From HREELS and He(II) UPS, it is found that water will not adsorb on a defect-free TiO^MIO) surface at 300K, but will adsorb on a
surface in which oxygen vacancy defects have been created. It is shown that this adsorption involves dissociation of the water molecule, leaving 0-H species bonded to the surface.
Finally, the effects of oxygen vacancies on the rutile SnO^MIO)
surface are investigated. It is confirmed that argon ion bombardment gives rise to selective oxygen loss, and the Sn species on the 2 + 4 + resulting defective surface are Sn and Sn ; total oxygen loss is never greater than 502. This process also creates deep band-gap states which do not give rise to conductivity. Electron irradiation of the surface is found to be capable of desorbing at least 702 of surface 2 + 4 + oxygen, and as well as Sn and Sn , clusters of metallic tin are formed on the surface. EELS shows that this situation leads to a broad spread of bandgap states, whose distribution is not readily controllable. Acknowledgements
I would like to express my thanks to all those people who have helped and assisted during the course of this work. In particular, I am very grateful to the following people:
Russell Egdell, for supervision, advice and encouragement throughout the last three years.
Wendy Flavell, for support, advice and valuable discussions, as well as considerable help with the SnO^ work.
David Bassett for introducing me to surface science in the first place, for encouragement over the years and for the loan of a very useful power supply.
Chris Jones, Bill Young, Mark Appleton, Humphrey Drummond and Steve
Bleazard for a great deal of assistance with the computing; specifically Humphrey for help with Padread, Bill for the FFT algorithm, Mark for the Epson Emulator and Chris for introducing me to
Pascal and the Z80.
Chris Jones, again, for unfailing support, endless patience, and the loan of the Rotring drawing equipment.
John Albery and his group, past and present, for providing a lively social life, and invaluable relief from the frustrations of research.
Gail Craigie, for typing the figure captions and Zoeta Brown for numbering the pages. 4
Contents page
Abstract 2
Acknowledgements 3
Table of Contents 4
List of Figures 8
List of Tables 11
List of Symbols and Abbreviations 12
Chapter 1 Introduction 15
1.1 The Structure of the Rutile Oxides 15
1.2 Applications of Ti02 21
1.3 Previous Studies of Ti02 - a Summary 22
1.3.1 Defects on Ti02 Surfaces 22
1.3.2 Adsorbates on Ti02 Surfaces 25
1.3.3 A Brief Look at Some Other Titanium Oxides 29
1.4 Applications of Sn02 30
1.5 Previous Studies of Sn02 - a Summary 31
1.6 An Outline of this Thesis 34
Chapter 2 Theory 36
2.1 Principles of Photoelectron Spectroscopy 36
2.1.1 Surface Sensitivity 38
2.1.2 Ultraviolet Photoelectron Spectroscopy 40
2.1.3 X-ray Photoelectron Spectroscopy 41
2.1.4 Fine Structure in PES 47
2.2 Auger Electron Spectroscopy 49
2.3 Low Energy Electron Diffraction 51
2.3.1 LEED for Lattice Characterisation 52
2.4 Electron Energy Loss Spectroscopy 53
2.4.1 The Nature of Dipole Scattering 54
2.4.2 Excitations in Dipole Scattering 57 2.4.3 EELS of Ionic Solids - a Brief Historical Survey 60
2.4.4 Introducing the Theory of Dipole Scattering 61
2.4.5 The Energy Loss Probability 62
2.4.6 The Explicit Form of the Dielectric Constant 71
Chapter 3 Apparatus and Experimental Methods 75
3.1 The Need for Ultrahigh Vacuum 75
3.2 The Ultrahigh Vacuum System 75
3.3 The HREEL Spectrometer 80
3.3.1 The Spectrometer Construction 80
3.3.2 The Effect of the Analyser Acceptance Angle 82
3.3.3 Calibration of the Spectrometer 86
3.3.4 Operation of the Spectrometer 86
3.3.5 Overcoming Difficulties 90
3.4 The General Surface Analysis Facilities 92
3.4.1 The Radiation Sources 93
3.4.2 The Energy Analyser 94
3.5 The LEED Optics 97
3.6 Data Collection and Processing 101
3.6.1 Data Collection 101
3.6.2 Data Processing 102
3.7 Sample Preparation and Mounting 105
3.7.1 Initial Sample Treatment 105
3.7.2 Sample Mounting 105
3.7.3 Cleaning the Samples In Vacuo 111
Chapter 4 The (110) Surface of Rutile TiO^ 112
4.1 Sample Preparation 112
4.1.1 Preparation of a Defect Free TiO2(110) Surface 112
4.1.2 Criteria for Stoichiometry 113
4.1.3 Criteria for Surface Order 116
4.1.4 Criteria for Cleanliness 121 6
4.2 HREELS of the Stoichiometric TiO^dlO) Surface 124
4.2.1 Symmetry and Phonons in the HREELS of TiO^ 124
4.2.2 The Effect of Anisotropy 131
4.2.3 The HREEL Spectrum of TiOgdIO) 131
4.3 The Creation of Oxygen Deficiency in TiO^MIO) 135
4.3.1 The Knotek Fiebelman Mechanism 138
4.3.2 The Practice of Electron Bombardment 138
4.3.3 The Oxygen Desorption Cross Section 140
4.3.4 The Depth of the Oxygen Vacancy Defects 145
4.4 The Effect of Oxygen Deficiency on UPS, ELS and HREELS 147
4.4.1 The UPS of Defective TiOgdIO) 147
4.4.2 The ELS of Defective Ti02(110) 151
4.4.3 The HREELS of Defective TiO (110) 155
4.5 Towards an Explanation 163
4.5.1 The Oscillator Strength of the Excitation 163
4.5.2 The Nature of the Defect Sites 164
4.5.3 The Final Model 165
4.5.4 Notes on Previous Work 166
Chapter 5 The Adsorption of Water on TiO^f110) 168
5.1 A Detailed Look at Some Previous Work 168
5.1.1 Water on TiO^ 168
5.1.2 Water on SrTi03 174
5.1.3 Water on Other Oxides 180
5.2 Some Experimental Aspects 181
5.2.1 Water Dosage 182
5.2.2 Sample Mounting and Attempts to Cool the Surface 182
5.3 UPS of Water on TiOgdIO) 184
5.3.1 The Spectra Obtained 184
5.3.2 A Discussion of the Results 187 5.A HREELS of Water on TiO (110) 190
Chapter B The (110) Surface of Rutile SnO^ 194
6.1 Sample Preparation 194
6.2 Oxygen Loss and the Desorption Cross Section 196
6.2.1 Oxygen Loss by Argon Ion Bombardment 196
6.2.2 Oxygen Loss by Electron Bombardment 198
6.2.3 ELS of the Defective Surface 205
Appendix A Classical Theory of Dipole Electron Scattering 208
Appendix B Program Collect 216
Appendix C Program Padread 221
Appendix D Program Stripper 229
Appendix E Program Fitter 235
Appendix F Program Eelsim 240
References 250 8
List of Figures page
Figure 1: (a) structure of the rutile unit cell and (b) orientation of orbitals in the rutile unit cell 16
Figure 2: DOS diagram for TiO^ 18
Figure 3: DOS digram for SnO^ 19
Figure 4: Atomic arrangement of the (110) face of rutile 20
Figure 5: Illustration of the photoelectric effect 37
Figure 6: Variation of inelastic mean free path with photoelectron energy 39
Figure 7: UPS He(I) of defect free TiO (110) 42
Figure 8: UPS He(II) of defect free TiO (110) 43
Figure 9: Wide scan XPS of defect free TiO (110) 45
Figure 10:: Narrow scan XPS of defect free TiO^t110) 46
Figure 1 1 :: The Auger process 50
Figure 12:: Polar plot of the dipole scattering lobe in HREELS 55
Figure 13:: Illustration of the dipole selection rule 56
Figure 14 :: Phonon dispersion curve 59
Figure 15:: EELS dipole scattering mechanisms 63
Figure 16:: Plot of variation of {Q/[Q^+1]^> with Q 65
Figure 17:: Geometry of the EELS two-layer model 69
Figure 18:: Plot of variation of e(u>) with u) 73
Figure 19:: Photograph of the Leybold Heraeus vacuum system 77
Figure 20:: Schematic diagram of the vacuum system 79
Figure 21 :: Diagram of the construction of the HREELS optics 81
Figure 22:: The geometry of scattering in EELS 84
Figure 23:: Photograph of the HREELS instrumentation panel 88
Figure 24:: Montage of XPS MgKa Ag spectra at different Eq 98
Figure 25:: Plot of variation in FWHM with E in the spectra of figure 24 99 9
page
Figure 26: Plot of variation in peak height with Eq in the spectra of figure 24 100
Figure 27: XPS of TiOgtHO) before and after stripping by the computer program "Stripper" 103
Figure 28: XPS of TiO^ with "fitted" curves as created by the computer program "Fitter" 104
Figure 29: Photograph of two of the samples used 106
Figure 30: Drawing of the room-temperature sample mount 109
Figure 31 : Drawing of the "low temperature" sample mount 110
Figure 32: XPS of TiO (110), defective and defect-free, showing Ti4+ and Ti3+ core peaks 115
Figure 33: ELS of TiO^lHO), defective and defect-free 117
Figure 34: UPS He(I) of TiO (110), defective and defect-free 118
Figure 35: UPS He(II) of TiOgtllO), defective and defect-free 119
Figure 36: LEED photograph of the ordered TiO^MIO) surface 120
Figure 37: Plot of the variation in HREELS TiO (110) elastic peak intensities with deviation of the collection angle from the specular 122
Figure 38: As figure 37, but for a well-ordered GaAs surface 123
Figure 39: XPS TiO_(110) showing the carbon peak for clean and contaminated surfaces 125
Figure 40: Diagram of the translations in the rutile unit cell involved in phonon excitations 129
Figure 41 : HREELS of defect-free TiO^tHO) 132
Figure 42: Calculated HREELS of defect-free TiO^MIO) 134
Figure 43: XPS of a typical argon-etched TiOgMIO) surface 137
Figure 44 : Diagram of the Knotek Feibelman Mechanism 139
Figure 45: Diagram of the electron bombardment assembly 141
Figure 46: XPS of TiO_(110) showing changes as electron bombardment progresses 142
Figure 47: Log plot of variation in surface oxygen concentration with electron bombardment for the TiOgUIO) surface 144
Figure 48: UPS He(I) of defect free and argon ion bombarded TiO (110) 148 Figure 49: UPS He(I); detail of fig. 48 showing defect feature 149
Figure 50: UPS He(I) of electron bombarded TiO2(110) 150
Figure 51 : ELS of progressively argon ion bombarded TiO^tllO) 152
Figure 52: ELS of progressively electron bombarded TiO2(110) 153
Figure 53: HREELS of progressively electron bombarded TiO^C110) 156
Figure 54: HREELS of progressively argon ion bombarded Ti02(110) 157
Figure 55: Simulated HREELS of defective surfaces, mimicking those of figure 53 160
Figure 56: Plot of the variation of loss function and loss energies with the surface dielectric function 161
Figure 57: UPS He(I) of gaseous water 169
Figure 58: UPS He(I) of Henrich22 170 22 Figure 59: UPS He(I) difference spectra of Henrich 170
Figure 60a , b, c: UPS He(I) of Lo30 172
Figure 61 : UPS He(II) of ice on SrTi03(100) 176
Figure 62: UPS He(II) of H O at room temperature on SrTi03 (100) 1 179
Figure 63: UPS He(II) of H^O on electron bombarded TiO^UIO) 185
Figure 64: UPS H e (I) of H^O on electron bombarded TiO^UIO) 186
Figure 65: UPS He(II) of H^O on argon ion bombarded TiO^MIO) 188
Figure 66: HREELS of H^O on electron bombarded TiO^MIO) 192
Figure 67: XPS of SnO (110) defect free, and after argon ion bombardment 197
Figure 68: XPS of SnOgHIO) after heavy electron bombardment 199
Figure 69: Log plot of decay of surface oxygen with time of electron bombardment 201
Figure 70: XPS of SnO (110) with progressive electron bombardment, and corresponding surface concentrations of Sn(IV), Sn(II) and Sn(0) 203
Figure 71 : ELS of SnO (110) with progressive electron bombardment, and after argon ion bombardment 206 11
List of Tables page
Table I: Lines in the XPS source 48
Table II: Typical settings for a satisfactory EELS spectrum 91
Table III: Values for core peak binding energies used for calibration of the hemispherical analyser 96
Table IV: Point symmetry operations for the rutile cell 126
Table V: Group theory character table for the rutile cell 127
Table VI: Parameters used for calculating HREEL spectra 130 12
Symbols and Abbreviations
o -10 A AngstrOm unit = 1 0 m
AES Auger electron spectroscopy
ADC analog to digital converter
BE binding energy
* CAE constant analyser energy
cs crystallographic shear
DAC digital to analog converter
DOS density of states
binding energy eb Fermi energy ef energy of incident beam (in EELS) EI kinetic energy ek analyser pass energy Eo optical excitation energy Eo energy of scattered beam (in EELS) Es valence band maximum Ev EELS electron energy loss spectroscopy
ELS energy loss spectroscopy; used in this thesis to describe high energy, low resolution EELS
ESD electron stimulated desorption
FFT fast Fourier transform
FT Fourier transform
FWHM full width at half maximum
He (I) radiation from the He(I) line of excited helium
He(II) radiation from the He(II) line of excited helium
HREELS high resolution electron energy loss spectroscopy
I detectable intensity
I total intensity 0 IMFP inelastic mean free path 13
IRS infra-red reflection spectroscopy
Ka x-radiation from the Ka transition in the relevant metal atom
KE kinetic energy -6 L Langmuir; 1 second at 10 torr
LEED low energy electron diffraction
* LH Leybold Heraeus, K51n, Germany
LO longitudinal optical (phonon)
MBE molecular beam epitaxy
N(E) intensity measured directly as a function of energy
P (UJ) loss probability in EELS
Q the wavevector of an excitation in EELS
the component of Q in the plane of the sample surface
Q_l the component of Q perpendicular to the sample surface
SO surface optical (phonon)
TO transverse optical (phonon)
UHV ultra high vacuum
UPS ultraviolet photoelectron spectroscopy
VG Vacuum Generators, East Grinstead, Surrey
a the Bohr radius; 5.291 x 10 ^ m 0 a -a anodes of the HREELS optics 1 3 8 -1 c the speed of light; 2.998 x 10 ms
channeltron channel electron multiplier -19 e the charge on an electron; -1.602 x 10 C
electrodes of the HREELS optics V e4 oscillator strength fd -3 A h Planck s constant; 6.626 x 10 Js
h / 2tt
k the wavevector 2ir/X of radiation
k1 the wavevector of the incident electron beam in EELS 14
KS the wavevector of the scattered electron beam in EELS
the component of k in the plane of the sample surface k !l
K j. the component of k perpendicular to the sample surface * m effective mass -31 m the mass of an electron; 9.109 x 10 kg e the main analyser of the HREELS optics •> m a
mm the main monochromator of the HREELS optics
pm the pre-monochromator of the HREELS optics
r the position vector of an electron relative to the sample surface
sa the secondary analyser of the HREELS optics -2 torr unit of pressure; 1/760 atmospheres, or 132.22 Nm
V velocity of electron approaching/leaving sample surface
component of v in the plane of the sample surface V ll
vj_ component of v perpendicular to the sample surface
damping constant
6E energy difference
£ (surface) dielectric constant -12 -1 £ permittivity of free space; 8.85 x 10 Fm 0 high frequency or background dielectric constant £00
8 maximum angle over which the scattered beam in EELS is c collected by the analyser
hui / 2Ej 8 e
A the inelastic mean free path
A wavelength of radiation
E effective (surface or combined) dielectric constant
Q dipole strength
0 cross section for oxygen desorption
Ul angular frequency of an oscillation; *tTu) is the energy of the oscillation, and thus its loss energy in EELS 15
Chapter 1 - Introduction
This thesis covers a study of the (110) surfaces of the rutile oxides liOg anc* Sn02, us^n9 a variety of ultrahigh vacuum (UHV) spectroscopic techniques. Both materials have a wide range of important applications in modern technology, the majority of which depend upon the surface properties of the oxides; thus it is valuable to gain as much knowledge as possible of the physics and chemistry of these properties. In the present work, Ti02 *s studied in the
particularly important contexts of surface oxygen deficiency and the
adsorption of water. The rather smaller scale investigation of SnO^ deals only with oxygen deficiency.
Completely stoichiometric rutile Ti02 is a transparent insulator, whose resistivity is approximately 101^Qm1. As oxygen vacancies are -3 introduced, the resistivity can be reduced to below 10 Qn, and the material becomes dark blue. Its intrinsic electrical conductivity,
photoconductivity and absorption spectroscopy have been reported on in 2-4 . . . some detail by D.C. Cronemeyer . Stoichiometric SnO^ is also a 5 transparent insulator, however Robertson comments that its conduction
band has a low effective mass (0.27 m^), giving easy ionisation of
donor levels and thus making the material a useful semiconductor. In . . 6 fact it is found that both bulk oxygen deficiency and n-type donor
impurities^, such as Sb and F, promote conductivity.
1.1 The Structure of the Rutile Oxides
The structure of the rutile unit cell is depicted in figure 1(a)8. 14 . . . The cell belongs to the point group Df. , some important implications 4h of which will be discussed in a later section. In both TiO^ and Sn02
it contains two formula units; two metal and four oxygen atoms, giving
a 2:4 coordination. Figure 1(b) illustrates the orientations of the 16
8 Figure 1(a) The structure of the rutile unit cell.
Figure 1(b) : The (110) plane of the unit cell showing the orientation of the anion orbitals. Large and small open circles - correspond to cation and anion respectively. 17
atomic orbitals within the lattice, as presented by Robertson .
The relatively low symmetry of the rutile system leads to a rather complicated bandstructure; in this work we shall restrict ourselves to the somewhat simplified "density of states" (DOS) approach.
Theoretical studies by K. Vos9 and by S. Munnix and M. Schmeits10'11 of the electronic structure of Ti02 describe the bonding as resulting from interaction of the oxygen 2p and titanium 3d states. The bond is of fairly high ionicity, and produces a semiconductor with a 3 eV bandgap. As can be seen from figure 2, the valence band is of 0 2p character, whilst the conduction band is Ti 3d-like.
The bonding in SnO^ has also been modelled by Munnix and 101213 5 Schmeits ' * and by Robertson , and it has been found, as might be expected, that the Sn-0 bonds result from overlap of oxygen 2p with tin
5s and 5p orbitals. The bandgap, at 3.6 eV, is somewhat larger than in
Ti02- The DOS bandstructure is illustrated in figure 3, and shows that the conduction band in this case has predominantly tin 5s character.
The upper valence band is composed mainly of states resulting from interactions between lattice oxygen lone pairs. The results of these studies were in good agreement with the experimental ultraviolet 14 photoelectron spectroscopy (UPS) work of P.L. Gobby and G.J. Lapeyre , where synchrotron radiation was used to examine the structure of the valence band at the Sn02 surface. Figure 4 shows the atomic arrangement of the (110) face of the rutile crystal. It is appropriate to comment that most single crystal studies of Ti02 consider the (110) face; this is due to its particular thermodynamic stability. Several
4 C 4 C workers, including L.E. Firment and R.H. Tait and R.V. Kakowski have used low energy electron diffraction (LEED) to study the (100) and
(001) faces, and report the onset of faceting at temperatures of 600°C.
No such reconstruction is reported for the (110) surface, which is Energy/eV
0
-N(E)
Figure 2 : The density of states diagram for TiC^', Shading denotes a filled band. *UNDOPED’ Sn02
N(E)
Figure 3: The density of states diagram for Sn02» Shading denotes a filled band. 20
= 0
= M
Figure 4: The atomic arrangement of the (110) face of the rutile structure. 21 found to be stable through the full temperature range studied.
1.2 Applications of Ti02
The best-known application of Ti02 is in the photoelectrocatalytic splitting of water^. In an aqueous cell with a Ti02 and a Pt electrode, irradiation with ultraviolet light (351, 364 nm) causes evolution of at the rutile electrode and H_ at the Pt electrode, 2 2 with an 0 :H ratio of 1:2. The overall reaction may be represented 2 2 as;
hv H20 ------> H2 + 1/2 02 photoassistance agent
It has been found that this reaction is not entirely self-driven, and in a homogeneous cell, an applied potential of at least 0.25 eV is required for conversion to proceed. However the energy realised from the conversion is significantly greater than that drawn from the driving power supply and it is concluded that the reaction is catalytic with respect to Ti02- The conversion efficiency is strongly affected by the wavelength of the incident light; the onset of response for the Ti02 electrode is generally about 400nm, which is very close to the bandgap of Ti02> It has been found that n-type doping can shift the response onset by up to 0.5eV further into the ultraviolet; unfortunately no means has yet been found of shifting the response into the more useful region closer to the visible.
Rutile is also useful as a selective absorber for conversion of solar energy, since it absorbs light in the ultra violet and visible 1 8 regions, but is transparent in the infrared . When doped with suitable donor species, it can serve as an effective heterogeneous catalyst; TiO. containing about 3 Vo0_ and 2-10Z W0„ catalyses the 2 l 2 5 3 19 20 reduction, in the presence of ammonia, of NO in waste gases The 22
oxidation of CO to CO^ is catalysed by V or Ga-doped rutile, whilst xylene can be oxidised to phthalic anhydride with the aid of V-doped
TiO^ containing promoters such as Al, W, P or rare earth metals.
1.3 Previous studies of Ti02 - a summary
It is known that the catalytic properties of Ti02 depend strongly upon the physical condition of the surface, in particular upon its oxygen content. For example, the catalysis of water photolysis does not take place unless the rutile electrode is first reduced in H2>
However, the true nature of this dependency, and the reasons for it, are not fully understood. A number of studies have been carried out in an attempt to improve the understanding of both surface defects and adsorption on Ti02> using both single crystals and polycrystalline samples.
1.3.1 Defects on Ti02 surfaces
21-25 A number of studies have shown that there are no electronic states in the bandgap of defect-free, unreconstructed rutile Ti02 surfaces. Such states can, however, be created by introducing oxygen- vacancy defects into the surface; this may be done by ion 24 26-29 28 29 bombardment ’ or heat treatment ' . The precise nature of the defects, particularly those arising from ion bombardment, is not generally agreed upon. However it seems certain that in altering the electronic structure of the surface, they play an important part in its interaction with external species, thus influencing its catalytic properties.
2 6 V.E. Henrich and coworkers have used ultraviolet photoelectron spectroscopy (UPS), electron energy loss spectroscopy (EELS), Auger spectroscopy (AES) and LEED to study the argon ion bombarded Ti02 23
(110) surface. Here it was suggested that three different surface- defect phases exist, depending upon the defect density. It was proposed that at low density, extrinsic surface states about 0.7 eV . 3 + below the conduction band edge are due to disorder-induced Ti
oxygen-vacancy complexes. As the level of defects increases, a 3+ 3 + pairing of Ti ions occurs, and finally the Ti pairs order into a
Ti203-like surface structure. 30 A slightly later work by W.J. Lo et. al. used techniques similar
to those of Henrich. On argon sputtered surfaces, EELS showed a loss
feature at 1.6 eV, and emission was seen in UPS 0.6 eV below the Fermi
edge. It was concluded that both phenomena arose from the presence of .3+ . . Ti on the surface, and it was reported that a maximum occurred m
the emission intensity of the UPS feature at a surface composition
equivalent to Ti203. However no explicit mechanism was suggested for
either excitation; nor was any structure proposed for the defect
sites. 31 32 In recent papers, Munnix and Schmeits ' presented a theoretical
model of defects in rutile, using the so-called scattering theoretic method. It was suggested that band gap states are produced by
vacancies local to the oxygen plane immediately below the surface;
bulk vacancies were claimed to induce no gap states at all. The model
requires that electrons associated with oxygen vacancies in other
lattice positions must occupy the t2g conduction band of TiOg,
producing a quasimetallic state.
Over the last few years, the relatively new technique of high-
resolution electron energy loss spectroscopy (HREELS) has become
available in a number of research laboratories. This has mainly been
applied to the study of the vibrational spectrum of adsorbates on metal surfaces. However, as will be explained in greater detail in
chapter 2, HREELS can also be used to study phonons and similar 24
excitations on insulator and semiconductor surfaces, including TiO^.
In fact the loss intensity due to these excitations is so great in comparison to the vibrational features of adsorbates that the latter are often very difficult to observe. Surface phonons, first described 33 by R. Fuchs and K.L. Kliewer in 1965 , are generally sensitive to the electronic structure of their environment, and thus to anything that might alter it. Thus, HREELS, in providing a method for their detailed study, is a potentially useful tool for the investigation of surface defects in Ti02.
The first HREELS study of a Ti02 surface was carried out by L.L. 34 Kesmodel and colleagues in 1980. The surface in this work was defect-free, and it was confirmed that surface phonons could indeed be observed on rutile; the observed frequencies were in good agreement 35 with dielectric response theory , and could be related to those of 3 6 bulk phonons observed in infra-red spectroscopy . However it was not found possible to resolve all three of the expected phonon loss peaks; only two features, at 54 and 95 meV, were observed. It was pointed out that the spectrum has a very strong background due to multiphonon excitations, and that difficulties in detecting adsorbate spectra on
Ti02 should be expected.
In 1984, W. Gopel and his research team applied HREELS to the 29 37 study of defects on the TiO„ (110) surface * . Three distinct 2 Fuchs-Kliewer phonons were resolved, at loss energies of 46, 54 and 95 meV, on the defect-free surface. Defects were introduced into the surface by argon ion bombardment or by heating the sample to 1310 K.
Thermally produced defects had previously been characterised by this 28 same reseach group , and it had been concluded that they were point defects"; oxygen vacancies each associated with two paramagnetic Ti^+ surface ions acting as paramagnetic donors. It was proposed that argon 25 bombardment leads to a spread of different defect types, and a generally higher defect concentration.
In HREELS it was noted that the phonon excitations on defective surfaces had much reduced intensities, and were all shifted downwards in energy by 2 meV. Lower resolution EELS showed broad loss features between 0.5 and 1.5 eV for the argon bombarded surface, and a fairly sharp feature at 0.8 eV for the thermally defected sample. Intrinsic electronic interband transitions at higher energies were unaffected by the thermally induced defects, but argon ion bombardment caused marked broadening in this region.
The new features in EELS were interpreted as being due to excitations from gap states, as would be expected from previous observations (see above). The broader damage of the argon bombarded surface resulted in a range of state types, and hence many overlapping loss features, as well as disrupting intrinsic interband excitations of the crystal. The origin of the changes in the HREELS spectrum was admitted to be poorly understood. It was suggested, however, that a qualitative understanding may be gained by considering the collective vibrational modes of the surface to be damped in the presence of defect-induced conduction electrons. It was then proposed that a plasmon due to free carriers in the sample could couple with the
Fuchs-Kliewer phonons, giving results corresponding, within experimental error, to those observed in the study.
In conclusion, the general understanding of the nature of surface defects on TiOg surfaces is still rather vague, and conflicting theories abound. It is important that this aspect of Ti02 chemistry should be the subject of further, thorough, investigation.
1.3.2 Adsorbates on TiO„ 2
The nature of the adsorption of various species on the rutile 26
surface is also a matter of some debate. Until now, the major techniques for adsorbate studies on TiO^ have been UPS He(I) difference spectroscopy and various types of infra-red spectroscopy, complemented to some extent by low resolution EELS, LEED and desorption techniques. Only one set of results has been reported for 37 a HREELS study of adsorption on Ti02
The importance of Ti02 the photolysis of water has generated great interest in the HgO / rutile adsorption system. In 1973, R.W. 38 Rice and 6.L. Haller used infrared internal reflection spectroscopy
(IRS) to investigate the adsorption of water on a number of oxide surfaces, including TiO^ (0001). After water dosage, IRS spectra showed strong absorbance in the 3400 cm ^ region, indicating a high concentration of surface hydroxyl. However, the absence of sharp bands at higher frequency was interpreted to mean that these hydroxyl species could not be considered to be "properly isolated", but must be involved in some interactions such as hydrogen bonding, which would prevent the expected vibrations at 3600-3800 cm ^. In addition, it was observed that water adsorbed on the surface in two separate phases. The first was easily removable by pumping at moderate temperatures, and was associated with a peak maximum just above 3400 -1 .o cm , whilst the second could only be desorbed by heating to 400 C, and had a less well-defined absorbance maximum in the 3250-3350 cm 1 region. It was concluded that the less strongly adsorbed phase consisted of undissociated water, whereas the more persistent phase was assumed to have reacted to produce separate OH and H species bonded to the surface. It was suggested that such dissociation would be more prevalent on less perfect surfaces. 22 Hennch and co-workers used UPS He (I) difference spectra to find that water adsorbs on both argon bombarded and defect-free Ti02. For 27
both surface types at water exposures of less than 30 L, adsorption was deduced to be dissociative, but as exposure was increased towards Q 10 L, the adsorption became progressively more associative. On the
defect-free surface, heavy exposure appeared to result in exclusively
associative adsorption, whilst on the defective surface it seemed that
considerable dissociation remains. 30 W.J. Lo and colleagues have used similar techniques to produce
results in rough agreement with those of Henrich. In this case
adsorption on the TiO^ (100) face was considered. Thermal control of
the reconstruction of this face was used to create varying .3+ . concentrations of Ti ions on the surface. It was found that, in
general, adsorption was associative on defect-free surfaces. On
surfaces rich in Ti3+ species, the adsorption became dissociative, and .3 + it was concluded that there was a direct relationship between Ti
concentration and degree of dissociation.
In consideration of these results, it was clearly of relevance to
carry out similar investigations into the behaviour of oxygen and
hydrogen separately. In a study of hydrogen impurities on TiO^ using 39 electron-stimulated desorption, Knotek reported that hydrogen bonds
to surface Ti by a hydride-type interaction. It was also found bonded
to sub-surface or bridge-bonded 0 to form a hydroxyl-like species. 30 The above work by Lo also considered the adsorption of 0 and On
a defect-free surface, oxygen adsorption was found to produce three
new peaks in the UPS spectrum, and to increase the surface work
function by 0.2 eV. Adsorption on argon bombarded surfaces gave rise to the same three features, and the work function rose by 0.3 eV. In
addition, the intensity of the characteristic defect-induced emission
at -0.6eV was significantly reduced. Exposure of the defect-free
surface to also caused changes in the UPS, with a work function
drop of 0.4 eV, and three new emission features. On the argon 28
bombarded surface, however, the work function rose by 0.1 eV, and the three new features were shifted slightly towards the Fermi edge. Thus the presence of Ti^+ species on the surface was deduced to have an effect on the adsorption of 0^ and H^. 23 Contemporary work by Henrich once again involved UPS difference spectra to look at 0 adsorption on the argon bombarded (110) rutile face. Here two adsorption phases were observed, each giving rise to only two new emission features. The first phase occurred for dosages of less than 30 L, and had a high sticking coefficient (0.2-1), whilst the second appeared at larger dosages, with a sticking coefficient of -3 at most 10 . The first phase was considered to consist of adsorbed
2 - 0 ions, but the second phase remained unidentified. No change in work function was reported in either case. 27 A more recent study by Henrich cast serious doubt upon whether hydrogen adsorbs on rutile surfaces at all. Exposure of the defective
TiO^ (110) surface to 20 L H^ produced no changes in the He(I) UPS spectrum, nor did light bombardment with hydrogen ions. Heavy H^+ bombardment appeared to create further surface defects, but there was still no evidence for adsorption of hydrogen. It was suggested that dosage with atomic hydrogen might give rise to adsorption.
The most recent studies of adsorbates on rutile appear to be those
2 8 of W. Gopel and coworkers. In 1983 , their research team used a range of techniques, including XPS, thermal desorption and surface conductivity measurements, to investigate the adsorption of 02< CO and COg. The results implied that COg adsorbs on the TiOg (110) surface independent of surface defect concentration, and without evidence of dissociation. On the other hand, CO and H^ adsorption increased with defect concentration; it was suggested that CO might react at the defect sites to form C02> but desorption of hydrogen resulted only in 29
H2. Oxygen adsorption was also found to have a defect dependency, and it was expected that the adsorbed 0^ interacted with the defects to restore stoichiometry.
Finally, this group have extended their work on hydrogen adsorption 37 by means of a recent HREELS study . Here they have exposed both defective and defect-free surfaces to atomic H. Characteristic 0-H stretch vibrations at 455 meV were observed on both surfaces; evidence that adsorption was taking place. Although an expected excitation at
260 meV, due to a Ti-H species occurring specifically at vacancies, was not observed, it was suggested that this feature was masked by
surface phonon peaks.
To summarise, it is apparent that there is little unanimity regarding the behaviour of adsorbates on TiO^, although the more recent work indicates a strong dependence on defect concentration for most species. Particularly, it has not been firmly established whether water adsorbs associatively or dissociatively on the surface.
1.3.3 A Brief Look at Some Other Titanium Oxides
Since the defects under consideration generally arise from oxygen deficiency in the TiO^ crystal surface, it is of relevance also to 40-42 consider lower oxides of titanium. Hennch and coworkers have investigated Ti^O^ itself, which has a corundum crystal structure.
This is seen to bear some resemblance to defective rutile TiO^,
particularly in the presence of states just below the Fermi edge in
UPS, but in some respects is quite different. For example, it has a
strong temperature dependent semiconductor-metal transition, and it is not itself a useful catalyst. The range of sub-oxides often referred
to as the Magneli phases Ti 0.. .. have been studied by a number of n (Zn-1) research groups, particularly with reference to bulk crystallographic
structure. The work was begun in the 1950's by S. Andersson and 30
4344 45 coworkers ' and followed up by and by J. Anderson and B.G. Hyde 46 47 More recently, R.J.D. Tilley and colleagues ' have carried out
experimental work on such systems by means of electron microscopy and 48 electron diffraction, and Catlow and James have undertaken
theoretical studies. The general conclusion is that the bulk rutile
TiO^ crystal does not tolerate point defects for oxygen deficiency -3 greater than 10 atoms per formula unit. It is found that
crystallographic shear (CS) planes form, causing elimination of the
defects; these are thought to consist of face-sharing TiO octahedra 6 resembling those present in Ti^O^. There have, however, been no
attempts so far to link this phenomenon with surface behaviour.
Strontium titanate, SrTiO^, is often considered as an analogue of
TiO^, not least because it has Ti present in the octahedrally
coordinated 4+ oxidation state. Both the electronic structure and the 22 23 40 49 adsorption behaviour have been studied by Henrich et. al. * * ’ , 50 51 Egdell and colleagues ' , and most recently by Thornton and his 52-54 research group . This work will be considered in greater detail at
a later stage (section 5.1.2), in conjunction with the discussion of
the present studies.
1.4 Applications of SnO^
There are many similarities between the uses of SnO^ and those of
TiO^. but also considerable differences. The tin oxide is almost
exclusively used in doped form, usually containing antimony as an n-
type donor. In solar energy conversion, antimony-doped Sn02 is used
as a heat mirror reflector, rather than a dark mirror absorber as
rutile is, because it reflects in the infra-red instead of absorbing,
and is transparent to higher energy radiation . 55 A review by F.J. Berry discussed the use of antimony-doped tin 31 dioxide as an oxidation catalyst. Important reactions include the selective oxidation of propylene to acrolein, and analogous oxidations of other olefins. By varying the surface and bulk composition of the doped oxide, its selectivity for various reactions can be controlled, but despite numerous investigations, the mechanisms involved in the catalysis are not fully understood. It is suggested that isolated antimony(111) cations surrounded entirely by tin(IV) cations may form active sites for the catalysis, and that oxygen for the reactions is supplied by the SnO^ lattice.
A related application of SnO^ is in gas sensors, where the presence of gases such as H_, CO and C_Hn decreases the resistance of the doped Z o o 56,57 oxide. It is suggested that this is caused by the reaction of the sensor surface with adsorbed oxygen, or the removal of adsorbed hydroxyl, by the gases in question. Thus the effectiveness of the
sensors is affected by the oxidising ability of the oxide surface, and hence by the dopants present on it. The most effective SnO^-based sensors at present appear to be those containing Pd, which promotes higher-temperature oxidation, and ThO^, which removes adsorbed hydroxyl.
1.5 Previous studies of SnO^ - a summary
From the previous section it is clear that rutile tin dioxide is an important material for modern technology. Unfortunately, the mechanisms behind its usefulness are generally poorly understood.
Studies of SnO^ have not been as widespread as that of Ti02; this is at least in part due to the great difficulty of obtaining good single crystals of the material. A number of research groups have, however, persevered with ceramics and powders, and a certain amount of theoretical work has also been carried out.
In the 1970's, a number of research groups carried out XPS studies 32
on tin oxides , with rather poor agreement on the results for the tin 3d chemical shift. In 1978, however, a paper by Lau and
6 2 Wertheim attempted to define the XPS spectra of SnO and SnO^ by preparing the oxides in vacuo, and it was found that the chemical shifts of the Sn 3d core peaks for the two oxides are not distinguishable. Thus, when using core-peak XPS, it is necessary to measure relative surface oxygen concentration in order to distinguish between them; alternatively valence band XPS can be used with some degree of success. Similarly, UPS can prove very useful for such studies.
Electron energy loss spectroscopy may also be used to distinguish 6 3 between the two oxides of tin, as has been shown by R.A. Powell , who made use of the sensitivity of the lower resolution ELS to the structure of the valence band density of states. Egdell and 64 colleagues have used HREELS to study the surface phonons of SnO^; clearly these are quite distinct from those of SnO, due to the difference in crystal structure and bonding between the two materials.
More recently, D.F. Cox and collaborators have used a combination of 65 ELS and valence band XPS to study the electronic structure of Sn02, and its interactions with w a t e r ^ ’^, as well as its properties as a 60 gas sensor . The results of their electronic structure study are generally in good agreement with previous experiments and calculations.
As mentioned above (page 1), it has been shown that shallow donor states can be introduced into Sn02 both by bulk oxygen 6 7 deficiency and by n-type impurity dopants . By using a number of G 9 - 7 1 surface spectroscopic techniques, Egdell and coworkers have observed conduction electrons in Sn02 as a result of antimony doping, and it has been reported that the material becomes metallic for 19 -3 carrier concentrations above 10 cm . However, de Fresart and 33
72 73 colleagues ' have shown that in contrast to results for TiO^, oxygen defects produced by argon bombardment of SnO (110) do not act as donor states in the first instance. If the bombarded crystal is o o subsequently annealed at temperatures from 350 to 500 C, reconstructions are observed, and the surface becomes highly conducting. A number of possible rearrangements of the surface atoms are suggested, along with an analysis on the basis of the surface space charge theory. It is interesting to compare these results with 74 75 those of Pyke, Reid and Tilley ' , who have have investigated the crystal structure of bulk of Sn02 both undoped and doped with antimony, using electron microscopy and diffraction techniques. It was found that in contrast to the situation with Ti02, pure Sn02 did not tend to form CS planes when oxygen was removed, and a higher level of local defects was thought to be maintained. On the other hand, the doped oxide tended to form twinned crystals, and at low temperatures was quite disordered; it was suggested that this structural environment might promote catalytic activity. 76 In a UPS study, Flavell at Oxford University has shown that bandgap states are introduced by argon-ion bombardment of SnO (110), but that they lie well towards the bottom of the bulk bandgap, and are thus unable to act as donors. This contrasts somewhat with the results of a theoretical study by Munnix and Schmeits^; using the scattering theoretic calculation method, they proposed that unrelaxed oxygen vacancies in the SnO^(110) surface do not produce bandgap states at
all.
To summarise, the studies already carried out on Sn02 indicate that whilst bulk oxygen vacancies can produce conducting bandgap states,
surface defects created by argon ion bombardment do not. The lack of
observable shear-plane formation in Sn02 indicates that oxygen
vacancies in this material are likely to be quite different in nature 34
from their counterparts in rutile. However it is possible that using a different means of creating surface oxygen vacancies may lead to a type which will introduce shallow bandgap states, in a similar way to those in the bulk. This might provide a useful alternative to doping
by other elements, a procedure which is often difficult to control
precisely.
1.6 An outline of this thesis
The basis of the present work is a comparative study of the
defective and defect-free conditions of the TiO^ (110) surface, using
XPS, UPS, LEED and HREELS. In particular an attempt has been made to
gain more knowledge of the nature of oxygen vacancies in the surface,
and the accompanying electronic excitations. The techniques of argon
ion bombardment and electron beam irradiation for the creation of
surface defects have been investigated; this has led to a suggestion
for a mechanism for oxygen removal under electron bombardment, and
a cross-section for oxygen desorption has been obtained. The effect of
oxygen vacancies on the HREELS spectrum of TiO^ have been analysed in
terms of an accompanying electronic excitation and its influence on the
surface dielectric constant of the solid. In the light of this
analysis., a value has been deduced for the oscillator strength of the
excitation, leading to the proposal of a model for the structure of the
surface defects.
The adsorption of water on TiO^ (110) has also been examined, by
combining the surface sensitive techniques of He(II) UPS and HREELS,
which have been little used in this type of study. It is believed that
this has resulted in a better understanding of the behaviour of the
water-TiO^ system, an analysis of which is proposed.
In addition to this, a brief study of the effect of oxygen removal 35
on the surface of the structurally analogous oxide Sn02 has been carried out. It was hoped that it would be possible to create point defects in the Sn02 surface by means of electron irradiation, giving rise to n-type conductivity without the need for introducing other elements. In the event, experiments have led to results which are rather more complex and less immediately useful than had been expected. They are nonetheless interesting. 36
Chapter 2 - Theory
Before the experimental part of this thesis may be fully appreciated, it is necessary to consider the theoretical background to the work. Particularly important are the principles behind electron spectroscopy itself, especially for HREELS, which is perhaps less well covered in the literature than the more established techniques.
2.1 Principles of Photoelectron Spectroscopy
The basis of photoelectron spectroscopy is the photoelectric effect. When atoms or molecules are irradiated by photons of suitable energy, electrons will be ejected from their orbitals according to the
Einstein equation^8;
hv = E. + E, (1 ) b k where hv is the energy of the incident irradiation, E. is the binding b or ionisation energy of the electron relative to the vacuum and E^ is the kinetic energy with which the electron leaves its orbital. In solids, we are dealing with bandstates rather than discrete orbitals, and the equation must be modified to the form
hv = Eb + Ek +
Figure 5 ; The photoelectric effect in a generalised solid. 38 resulting electrons, we should gain considerable information about the binding energy of the electron states. In practice it is found that energies derived from this theorem are often between 2 and 10 eV too high, because the approximation does not allow for relaxation effects.
However when this failing is borne in mind, the results of PES can be extremely useful.
2.1.1 Surface Sensitivity
When dealing with macroscopic samples, as in the present work, it is important to be aware of the sampling depth of the technique employed.
In PES, it is found that this is limited not by the penetration of the electromagnetic radiation into the solid, but by the distance which the 7 9 excited photoelectrons can travel . This is governed by the inelastic mean free path (IMFP), A, which is determined by interactions with
8 0 atoms and electrons within the lattice. Leckey and coworkers have derived a theoretical expression for A for the range 200eV Prutton and colleagues55*5 at York University have reported that A = k exp(1-m), where k is the wave vector for the photoelectron and m varies 1 / 2 between 0.5 and 1.5 dependent on the sample (i.e. A*E ). This expression has been found to hold down to low values of Ek« The relationship between A and the detectable photoelectron intensity I 8 2 from a layer a distance d below the surface is given by I = IQ exp[-d/(Acosa)] (3) where a is the angle between the surface normal and the path to the 39 Photoelectron energy/eV 81 Figure 6 : The variation of X with photoelectron energies for a range of heavy metals. Shading denotes the range of experimental data. 40 analyser. From this it can be seen that the sampling, or escape depth is of the same order as A, and is restricted to the uppermost 2-50 atomic layers, and hence that the technique is inherently surface sensitive. Equation (3) also illustrates the angle dependence of the sampling depth. It is usual for the electron analyser to be placed normal to the surface, for maximum spectral intensity. However, surface sensitivity can clearly be enhanced by reducing a, and continuous variation of a can give insight into surface layer thicknesses. Reference 81 includes a detailed discussion of the use of PES for surface depth profiling. There are two main photoelectron-spectroscopic techniques, both of which have been mentioned in the introduction. They are ultraviolet photoelectron spectroscopy (UPS) and X-ray photoelectron spectroscopy (XPS), and are based respectively on the use of low-energy and high- energy radiation to give rise to photoemission. The difference between the two is sufficient to warrant a separate treatment of each. 2.1.2 Ultraviolet Photoelectron Spectroscopy 83 The UPS technique was first developed by Turner and colleagues , who found that a helium discharge gave virtually monochromatic radiation of a useful energy. Initially, only the He(I) line was used; this has an energy of 21.21 eV, and the linewidth obtained is typically 1meV or less. It was later found that the use of lower pressures of helium in the discharge lamp, along with increased power dissipation, produced an intense He(11) line at 40.8eV due to excited + He . The energies of these lines are too low for ejection of core electrons, but are quite suitable for the study of valence levels. The 41 first such studies were carried out on gas-phase molecules, and gave information on the nature of the bonding in a number of systems such as water and 02*. bonding, antibonding and nonbonding orbitals could be 83 resolved, along with a certain amount of vibrational structure When UPS is applied to polycrystalline solids, the orbital picture derived from spectra of discrete molecules is replaced by a useful representation of the electron structure in terms of the solid state DOS profile. Also, since the photoelectrons emitted under UPS must have low kinetic energy, the technique is extremely surface sensitive, probing only the top few Xngstrfims of a sample. It has thus found wide application in the study of surface electronic structure, and is often used as a criterion against which model calculations are assessed. Figure 7 shows a typical He(I) UPS spectrum of a Ti02 (110) surface, with indications of the important features. It should be noted that the low energy end of the spectrum is dominated by a strong background signal due to secondary electrons; this structure is extremely sensitive to surface conditions. In figure 8, the corresponding He(II) spectrum is shown; this also has a certain amount of secondary electron background intensity. However, this is considerably smaller relative to the main spectral features than its He(I) counterpart, and is much more reproducible. Thus, real spectroscopic changes in this region can be observed more clearly in He(II) UPS than in He(I) spectra. 2.1.3 X-ray Photoelectron Spectroscopy X-ray photoelectron spectroscopy was first used in Uppsala in 1957 84 85 by K. Siegbahn and colleagues ' , who developed a spectrometer producing MoKa^a2 radiation at an energy of 17479eV; more than adequate for the study of deep core levels. However it is found that the linewidth of Ka lines increases with the atomic weight of the E54.XY UPS He(I) Ti02C110) defect free Figure 7: A UPS He(I) spectrum of nominally defect free TiC^CllO). E55.XY UPS HeCII) Ti02C110) defect free -4.0 0.0 4.0 8.0 12.0 16.0 Binding Energy /eV Figure 8: A UPS He(II) spectrum of nominally defect free TiO^CllO). 44 source metal, and most modern spectrometers use magnesium or aluminium sources, which are sufficiently energetic for ionisation of outer core levels. The MgKa line has an energy of 1253.6eV and a linewidth of 0.85eV; AlKa is more energetic at 1 486.6eV, but its linewidth (1.0eV) 82 is larger . It is possible to reduce the linewidth further by monochromatisation, but this greatly reduces emission intensity, and 82 improved detectors are necessary The most common application of XPS is in the study of core-level 8 6 spectra. In 1964 Siegbahn and coworkers reported that the binding energies (E. ) at which core-peaks appear in XPS are characteristic of b the constituent atoms. The study includes a classification of the binding energies of 232 different levels in 76 elements. Different chemical conditions such as oxidation state and neighbouring environment result in small binding energy alterations known as 79 chemical shifts; these are also useful diagnostic tools . In addition, the intensity of the core peaks is found to be in direct proportion to the number of atoms of the parent atom within the sampling region. Figure 9 shows an MgKa XPS spectrum of TiO (110) between binding energies 0 and 1000eV, indicating the major features; figure 10 is a narrower section of the same spectrum. Attention is drawn particularly to the doublet Ti 2p peaks; this derives from spin-orbit coupling. Thus for an orbital where the quantum number 1>0, the peaks arise from final states characterised by the quantum number J; J = L ± S S = 1/2. (4) giving J = 3/2, 1/2. Also apparent are satellite and shake-up peaks, whose origin will be briefly discussed in the next section. Valence band ionisation does occur at low energy, but is of low intensity, and are not apparent on this figure. In the very high binding energy 0.0 200.0 400.0 600.0 800.0 1000.0 Binding energy /eV Figure 9 : A wide-range XPS scan of nominally defect-free TiC^CllO). The weak Ta core peaks arise from the Ta sample-mount. D54.XY XPS Ti02C110) defect free Binding Energy /eV Figure 10: A narrow range XPS scan of nominally defect-free Ti02(110), showing core peaks and satellite and shake-up features. 47 region, Auger excitations can be observed, followed by a steeply rising background due to inelastic secondary photoelectrons. 2.1.4 Fine Structure in PES Unmonochromated exciting radiation will generally give rise to fine structure in the photoelectron spectrum. This is usually most prominent in the form of "satellite" peaks, caused by minor lines in the source, whose energies differ slightly from that of the dominant 2 radiation. He(I) radiation arises from a 1s2p -> 1s transition in the excited He atom; however the discharge may give rise to further excited states, causing a series of 1snp -> 1s 2 lines. A similar situation arises for He(II), where the excited He+ ion gives rise both to the dominant 2p -> 1s transition and to higher energy emissions. The majority of these lines are weak; the one most commonly observed is the He(I)(3 ( 23.09eV) line, which makes up nearly 21 of the He (I) intensity, and the He(II)0 line, which accounts for about 10Z of the 8 8 He(II) radiation . In UPS, such satellites are often hidden beneath other features, and thus only hinder interpretation when accurate intensity determination is required. The strongest lines in the exciting radiation used for XPS are Ka^ 2 1 . . . and Ka^, due to P ^ ^ j (3/2) S transitions in source-metal 10ns. Also present, however, are Ka^ and Ka^ lines, as summarised in table 89 I . Resulting satellites can be clearly seen beside the Ti 2p core peak in figure 10; these are strong, and must be removed prior to quantitative analysis. Very low intensity may also occur from further Ka lines, as well as a little from KB radiation, but this is usually n disregarded in practice. Due to relaxation effects, photoemission involves simultaneous excitation of more than one electron, giving a final state differing by two or more electrons from the initial configuration. This phenomenon 48 Table J.; The intensities of the main XPS lines and their satellites A1 Line E /eV I . E /eV rel rel rel *rel 0 1 0 1 K“l .2 8.4 0.085 9.6 0.072 K°3 Ka. 10.1 0.046 11.6 0.036 4 49 is known as shake-up, if the additional electron(s) remains within the atom, or shake-off if it is ejected completely. Features due to shake- up, and to a lesser extent shake-off, can often be seen in XPS spectra, to higher binding energy, or lower kinetic energy of the core peaks. In general, all spectra based on elastic interaction of photons or electrons with the sample will suffer from background intensity due to inelastic events. As observed above, this is particularly marked in the high binding-energy regions of UPS and XPS, however it tends to make additional small contributions to the rest of the spectrum. Like satellite intensity, this can be troublesome in quantitative analyses. Fortunately it is often possible to remove such features in a reliable manner, as will be seen in later sections. 2.2 Auger Electron Spectroscopy Auger electron spectroscopy (AES) has been used to a small extent in the present study, and a short description of its principles is justified. Further detailed information can be found in reference 82. The Auger process is essentially due to the relaxation of an atom after the ejection, by incident radiation or electrons, of a core electron. In general the initial ionisation will cause an electron from an outer level (B) to move down and fill the resultant core (A) hole. The energy of this transition (E - E ) may simply be dispersed A D by the emission of X-ray photons, or it may give rise to the ejection of a third outer electron, synchronous with the core-hole decay. This electron is now known as an Auger electron, and has an energy characteristic of its transition, and thus dependent upon its parent atom; a number of tables correlating Auger peaks with source elements 90 have been prepared . The Auger process is illustrated in Figure 11. Epes= hv - (Ey -Ea } E4ugel.= A E -(E v -EB) Figure 11: A schematic diagram of the Auger process, 51 The dependence of the Auger cross-section upon the energy of the 91 incident radiation is such that optimal Auger emission is reached when hv is approximately 5xEb> Thus although Auger excitations can be observed in XPS, AES generally employs an electron beam of 5 - 10keV, rather than electromagnetic radiation. Of course, since the kinetic energies of the Auger electrons depend only on inter-atomic transitions in the parent atoms, they are unaffected by the energy of the incident radiation, and it is unnecessary to have a monochromatic source. 2.3 Low Energy Electron Diffraction Low energy electron diffraction (LEED) is another technique which was only occasionally used in the present work. Like AES, its background will be briefly considered here; a more detailed discussion can be found in reference 92, as well as a range of other texts and journals. LEED is based on the ability of a regular crystalline solid lattice to diffract elastically scattered electrons of a suitable wavelength. Under the correct conditions, such electrons constructively interfere to yield a diffraction pattern which represents, to a first approximation, the two-dimensional reciprocal lattice of the solid surface. In most LEED experiments, the electron beam is directed so as to impinge normally upon the solid surface; a fluorescent spherical- section screen is placed with the electron beam as its axis, and collects the scattered electrons from the sample. A series of grids remove any inelastically scattered electrons, such that only the coherent diffraction pattern appears on the screen, as a series of bright spots. The de Broglie wavelength A of an electron is given by; A = h / p (5) 52 or X = {1.5/V )^1 ^ nm (6) where V is the potential in volts through which the electron is accelerated. For a coherent diffraction pattern to be formed, we require the two-dimensional Bragg condition; nA = d sin 0 (7) where n is the order of diffraction and d is the lattice parameter of the sample unit cell; 0 is the angle between the scattered beam and the surface normal, and must be < 90° to be observed. We can see from equation (7) that X must be of the order of the atomic spacing, and thus V is usually between 10 and 400eV, with the most useful range being about 20 - 100eV. From the discussion in section 2.1.1, this clearly leads to great surface sensitivity. LEED can be used to study the surface of any flat, ordered material. The obvious application is to the ideal surface of a solid single crystal, but studies can also be made of regular surface adlayers or ordered surface reconstructions, sometimes involving quite complicated atomic arrangements. However the LEED electron beam is usually thermally broadened to a FWHM of approximately 500meV. This limits the coherence length of the electrons at the surface to about 5nm, so that longer range ordering cannot produce a discernible diffraction pattern. 2.3.1 LEED for Lattice Characterisation The reciprocal lattice of the surface as observed in LEED is defined by; ' b.. = 6 (i,j = 1,2) (8) where a, and a„ are basis vectors of the surface lattice and b and b 1 2 1 2 are basis vectors of the reciprocal lattice; 6 is a scalar quantity 53 The spacing within the lattice can be calculated from the spacing of the diffraction spots using the above equations . 92 (6) and (7), and the relationship 0. = (a./ 2r) x (a/2) (9) l l where r is the radius of the screen, and a is the angle that it subtends at the sample. 93 Pendry , amongst many others, has described how the use of LEEO can be extended to the study of the relative intensities of the spots in the diffraction pattern. This supplies information about the positions of atoms within the surface unit cell, and of adlayer atoms on the surface relative to those of the substrate. It can similarly be used to study surface crystallography. These aspects of the technique have not, however, been employed in the present work. 2.4 Electron Energy Loss Spectroscopy As we have seen above, an electron beam impinging upon a solid surface may give rise to Auger events, if of high energy, or diffraction patterns if elastically scattered. Another interaction which can be employed spectroscopically is the excitation by low energy electrons of vibrational or electronic modes on the surface. If the ingoing beam has energy E^, analysis of the energy E^ of the inelastically scattered electron beam reveals the frequencies ui of surface modes through the following relationship; E$ = Ej - 'Kui (10) Although it is possible to use this technique to study excitations with energies of up to several electron volts, as has indeed been done to some extent in the present work, the emphasis in this thesis has been placed on EELS in the low energy, high resolution regime. In high resolution EELS (HREELS), Ej is normally between 3 and 50 eV, and 54 the beam is highly monochromatic. Modern analysers are capable of resolving down to 4 meV or better, given ideal conditions. Although this is considerably lower resolution than that offered by most optical spectroscopies, it is adequate for many applications. HREELS also has the advantage of extreme surface sensitivity, making it extremely useful for the study of the topmost atomic layers of a sample. The energy loss events in which the ingoing electron may be involved can be divided into three distinct groups; dipole scattering, impact scattering and scattering via intermediate dipole resonance. In the present work we shall only be concerned with dipole scattering, the nature and theory of which is described below. 2.4.1 The Nature of Dipole Scattering Certain vibrations at the surface of a solid give rise to fluctuations in the surface dipole moment. An incoming electron subjected to such fluctuations undergoes intense small-angle inelastic 95 94 ' scatterings ; figure 12 shows the resulting dipole scattering lobe", which is strongly peaked close to the specular direction. It is found that such energy loss events are only observed at a metal surface if the change in dipole moment is perpendicular to the surface. This is known as the surface dipole selection rule, and can 95 be easily understood by reference to figure 13 . A dipole extending into the vacuum will give rise to an image dipole an equal distance below the surface. Figure 13(a) shows the situation for a dipole perpendicular to the surface; if this were to oscillate as indicated, its dipolar nature would clearly be maintained. However in figure 13(b), where the parallel dipole is illustrated, it can be seen that oscillation would tend to cause the image dipole to cancel out its surface counterpart. Froitzheim has shown that if e is the 55 Figure 12 A polar plot of the variation in intensity of the scattered dipole lobe in EELS with angle o © Real Dipole S 7 ////////// y // / / / / / O Image Dipole © (a) (b) 95 Figure 13 An illustration of the dipole selection rule. Ln O n 5 surface dielectric constant, parallel dipole changes are less likely _2 by a factor of |e| than perpendicular changes to scatter electrons. 2.4.2 Excitations in Dipole Scattering Dipole scattering commonly arises from the vibrations of atoms or molecules adsorbed on the surface of the sample, in a manner analogous to molecular infra-red spectroscopy. This can give a wealth of information about the nature both of the bonding within the adsorbed species, and its interaction with the surface. However, anv elementary excitation of the sample which gives rise to a suitable charge fluctuation will also be involved in loss events. This includes phonon and plasmon excitations and single electron interband and intraband transitions. When considering metal samples, dipole fluctuations from such excitations may be screened out by electrons in the conduction band. However, in insulating samples, they are often both intense and long-ranging, particularly those due to phonons, the vibrations of the crystal lattice. The loss spectra from these excitations can be most informative about the structure of the solid sample itself. In the bulk of a crystalline solid, two types of lattice phonons can be distinguished; acoustic and optical. Acoustic modes are due to in-phase vibration within the unit cell, and thus to the motion of the entire cell relative to its neighbours. Optical modes are due to vibration of individual atoms within the unit cell, and derive their name from their generation, in ionic crystals, of oscillating dipoles which can interact with electromagnetic radiation. Of the 3N normal modes available to the lattice for each value of the wave vector k, where N is the number of atoms in the unit cell, three will clearly be acoustic, whilst the remainder will be optical. Those modes 58 propagating perpendicular to the atomic displacements are known as transverse, whilst those propagating in the same direction as the displacements are called longitudinal. The acoustic modes are always 97 present as one longitudinal and two transverse modes. Figure K shows typical dispersion curves for the phonons in a lattice where N=2. The reason for the flat appearance of the optical dispersion curves relative to their acoustic counterparts, is that the vibrations involved in optical modes are virtually independent of k, depending rather on electrostatic interactions within the unit cell. 33 Fuchs and Kliewer were the first to report that at the surface of a crystal, the phonons are present in a different form. These are known as surface optical (SO) or Fuchs Kliewer phonons, and propagate in the two dimensions of the surface plane. The SO phonons have frequencies intermediate between those of LO and TO bulk modes, but cannot be described as either transverse or longitudinal in their properties. They are often regarded as being due to the changes in the electrostatic properties of the lattice caused by the presence of the surface. They have long wavelengths, and their vibration may be described by expCik^-r^), where represents the two dimensions of the surface plane. Their intensity falls off as exp(-kjjZ) , where z is the axis normal to the surface, implying a penetration below the surface of the order of kjj ^, which often reaches several hundred Xngstrftms. These relationships are considered in greater detail in the following sections of this chapter and in Appendix A. SO phonons have rather low energies, and occur close to the elastic peak in EELS; usually within 200meV. Thus it is particularly important to use low energy high resolution EELS to study them in any detail. Plasmon excitations can be regarded as vibrations of electrons in the conduction band of a solid. They behave in the same way as 59 u{k) 94 Figure 14 Typical dispersion curves for optical and acoustic phonons along a general direction in k-space, for a lattice with a two-ion basis. 60 longitudinal phonons, with the electrons playing the part of the negative ions. An electron beam, for example in EELS, can excite a plasmon by interaction of the incident electron coulomb field with the electrostatic field of the conduction "plasma”, and may be scattered by the resulting surface dipole fluctuation. 2.4.3 EELS of Ionic Solids - a Brief Historical Survey Although there has also been a wealth of EELS work on metal surfaces, it seems relevant to concentrate here on its application to ionic solids. The first such work was the pioneering studies of SO 98,99 phonons m HREELS, carried out in the early seventies by Ibach , who investigated the (1100) surface of ZnO. Since then, the technique has been used in a similar way by a range of workers to study a variety of insulators and semiconductors. A continuation of the ZnO 100,101 studies has been carried out by Gersten and colleagues , who have also studied the adsorption of hydrogen and oxygen on the surface. Egdell, P.A. Cox and colleagues have used HREELS on the surfaces of several different metal oxide systems, to study adsorbates and in some cases plasmons, as well as phonon excitations. Surface phonons and water adsorption on SrTiO^ have been thoroughly studied by this 102,50,51 group , as have the same phenomena for tungsten 103,104 bronzes . They have also done HREELS experiments on doped 64,71 and undoped SnO^ , on metallic and non-metallic lanthanum . . . ..105 . ^ 106,107 strontium vanadate and on various faces of NiO Surface phonons on NiO have also been studied by Bertolini et. 108,109 al. Thiry and coworkers have used HREELS to study SO phonons on the a-Al£03 (0 0 0 1 ) surface, introducing new techniques to limit sample charging^ \ and 61 on MgO 112 , where they find good correlation with infra-red results. In addition to this, of course, there has been the EELS work on Ti02 mentioned in the introduction, which is followed up by the experiments described in this thesis. 2.4.4 Introducing the Theory of Dipole Scattering The theory of dipole scattering has been presented in considerable depth by a number of workers, including Mills and colleagues 95,113,114 M . 115 kl 94 116 „ _ .. . . 96 _ ... , Mahan , Newns , Cox and Froitzheim . In this section an attempt will be made to draw together the most important aspects of this work in a clear and concise manner. For the sake of brevity, the derivation of the classical dielectric theory of electron scattering is presented in Appendix A; its results will be discussed, and extended to meet specific situations in this chapter. If an electron with wave vector k* approaches a sample surface and interacts with a dipole excitation, it will leave, or be scattered, S with a wave vector k , where Q„A = ,k„ I - .k„ S where Q is the wave vector of the surface excitation in the plane of the surface. Thus, components of wave vector parallel to the surface are conserved. However, it is not necessary for perpendicular components of the wave vector to be conserved. Recalling equation (10), we can see that if we know Q and the frequency uj of the excitation, the direction of the scattered electron can be found. An important result from Appendix A is that the potential cp(Q^ ,z,ui) exerted by the dipole oscillation at the surface depends on exp(-QjjZ). Thus for Laplace's equation to be obeyed, the charge fluctuation must extend into the vacuum for a distance 1 roughly equal to Q , and 62 must also reach the same distance into the solid, below the surface. 95 It is found that if 1 < ignored; this is valid for a typical scattering event, where Q^ is of 6 " 1 8 — 1 the order of to cm ; oj/Qu is then of the order of 10 cm s , over two orders of magnitude smaller than c = 3x10^cm s \ 113 Mills has shown that if the probability amplitude is calculated for the scattering of an incoming electron with wave vector I S k such that its wave vector becomes k , four different scattering processes are involved. These are illustrated in figure 15. It is observed that the processes 15(a) and 15(d) give rise to large-angle scattering; large and large momentum change parallel to the surface. Conversely, 15(b) and 15(c) result in small-angle scattering, small Q^ and small momentum change. Hence in the small- angle scattering regime, which is the one with which we are concerned, 113 15(b) and 15(c) are the dominant scattering mechanisms. Mills finds that it is adequate to consider only those two contributions as significant. 2.4.5 The Energy Loss Probability The calculations in Appendix A culminate in an expression for the loss probability, given by: 2e2 Q, e(u>,Q|| )-1 P(Q Im ( 12) 2* 2,„2 _ ui_ 2.2 e (u), Q ||) +1 tt nv (Q + [-] ) where all parameters are in atomic units. P(Q^,ui) is also known as the loss function, and gives the probability of an incident electron losing energy “tiiD to an excitation with wave vector Qn. It should be noted that this expression ignores motion of the electron parallel to / 113 Figure 15 The four dipole scattering processes involved in EELS. ON LO 64 the surface. As can be seen in figure 16, this function peaks at « (uj/v ). A lobe of maximum P (uj, Q^ ) occurs close to the specular direction, as mentioned above and depicted in figure (1 2 ). When motion of the electron parallel to the surface is ignored, we 95 are considering the case where v = vx only. However, Ibach and Mills have derived an expression for the loss function without this approximation, so that both vx and v„ are considered: 0 2 2n 2e v , Q, etui.Qjj )-1 P (Q „ , uj ) Im (13) 2v m 2 2 r A ,2,2 e ( uj , Q ) + 1 tt n (Q..V.+ [ U) - V...Q.,] ) in this case, the function again peaks at « (uj/v ), but v now covers all v, rather than purely vx . We shall now consider three distinct situations in which e(ui,Q^) can be more specifically defined to suit our purposes. The first, which involves the greatest simplification and leads to the most tractable expressions is where we neglect the dependence of e on Q^, and say that e{ui,Q|j) = c (uj,0 ) = e ( uj ) . The second is where we retain the dependence of e on Q^ in considering a two-layer substrate, and the third is where dependence of e on Q^ is necessary due to anisotropy of the surface. In what follows, we shall treat each of these situations separately. i) The case where e (uj,Q..) = e(u>) Since we are dealing with scattering where Q^ is very small, and since t is independent of , as an approximation we can use P in the long-wavelength limit, and consider P (ui, 0) , or simply P(ui). For the present, we shall also retain independence of electron motion parallel to the surface. P(uj) is defined as: 2 2 Figure 16: The variation of CQ/(Q + 1) 1 with Q which in turn shows the variation of P(co) with (oj) . 66 P (ui) = 2ttQ(| P (Qn .ai) dQ (13a) Using the standard result IT dx (14) . 2 2.2 4a (x + a ) and equation (12), we have 2 £ (U)) - 1 - P(ui) = — Im [ (15) e(ui) + 1J ■fivu) Now, although this neglects motion of the incident electron parallel to the surface, it transpires that if this integration is carried out for all v, dependence on v^ vanishes in any case. Thus (15) is valid even when v^ is not neglected. If we let e(to) = e' + ie’ ’ then e (uj ) - 1 _ e ' + ie ' ‘ - 1 ( e ‘ + ie ' * - 1) (e' - ie ‘ ' + 1) e(u») + 1 e'+ ie ’ *+ 1 (e’+ ie''+ 1)(e‘- ie ‘‘+ 1) .2 . 2 e + e + 2e' + 2e' * 1 (16) . 2 (e' + 1 ) + e Hence, e(m)-1j Im[ 2e' ' e(ui) + 1 J 2 2 ( e' + 1) + e * ' which is a maximum when e'=-1. Thus P(uj) has a maximum where Re[e(uj)] = -1. 67 An advantage of the present approximation is that it is possible to calculate the total P(ui) by use of the integral P = J P(ui) tot o00 where "«>" is above all losses being considered, but may be below any higher losses. If we let this has singularities in the same region of the complex plane as e(ui). Because of this, both satisfy the same dispersion relations 118 (Kramers-Kronig relations) , which are of the form: 2 uj* Im [n (u>‘ ) dm* (17) Re[r| (w) ] IT . 2 2 UJ - Ul where P is the principal part of the Cauchy integral. If we let uj = 0, we have: 2 p r°° Im Cn(u>)] du> (18) ReCn (°°) ] - ReCn (0 ) ] IT J o UJ At o° and 0, Im (r|) should be zero, hence 2 e - 1 c - 1 P. . = — 7 - r] (19) 2t»v When considering this situation for phonon losses in a dielectric excited by a low-energy electron beam, we typically find e about 5, 00 e q very large, and P^ ^ of the order of 0.811^, which is also very large. This implies that an incident electron is likely to be involved in more than one loss event, giving rise, in the spectrum, to further loss peaks, whose energies are a multiple of the first loss. These peaks are often referred to as "overtones", though they are 68 clearly different in nature from the overtones observed in infra-red and similar optical spectroscopies. We can model this multi-excitation behaviour by means of Fourier Transform convolution of the different events with each other. If P (u>) is the single phonon loss function, the probability of a two- phonon loss peak at energy ftu) is given by: P2 (ui) = j P („’) P ^ ( uj - u>‘) du>’ (20) and in general, the probability of an n-phonon loss event can be expressed as: P (uj) = - J P.(ui') P (ui - u)’) dw’ (21) n n o 1 (n-1 ) If we let 6(0) represent the elastic peak, then the complete energy loss function can be represented by P(u>), where P (ui) = 6(0) + P1(u>) + P2(ui) + P3(u>) + ... (22) In fact, the form of (22) is also found for cases where e is dependent on Q||, assuming that we collect all scattered electrons. This will be discussed in more detail at a later stage. ii) The Two-layer Model The following model has been developed by Ibach, Mills and . 95,119 Froitzheim , to calculate the loss probability from a sample consisting of a semi-infinite substrate, with a complex but isotropic dielectric constant (ui), and a surface layer of thickness d with a dielectric constant (u>). This is illustrated in figure 17. The e s loss function may be expressed as: Figure 17: The geometry for the two-layer model in EELS. O' VO 70 , 2 2 U e v Q -1______P (Q „, io) = Im (23) 2y rn2 2 , A .2.2 [ E (Q „, ui) + 1] tt n [ Q „ Vx+ (10 - V.. Q..) ] where 1 + A(to)exp(-2Q||d) E (Q „ , to) = e (to) 24) ll s 1 - A(to)exp(-2Q..d ) where A(to) = [e(io)-e (to)]/[e (ui)+e. (to)] (25) b s s b 95 The authors of this theory show that in the limit Q^d<<1, (24) can be broken down into two terms: P(Q„ ,to) = P (Q..,to) + P (Qn ,to) (26) II s II b II P (Qn,to) is proportional to d, and describes scattering due to dipole s II fluctuations in the surface layer, whilst Pb(Q||,to) survives as d -> 0, and describes scattering due to bulk effects. These expressions for the loss function do not, as equation (15) does, have a form suitable for analytical integration. Thus in order to calculate a full EELS spectrum under this model, it is necessary to integrate numerically over the acceptance "area" of the energy analyser which would be used experimentally. iii) The Anisotropic Surface In what follows, we shall restrict ourselves to consideration of the (110) surface of a tetragonal crystal; this is directly applicable to the rutile samples studied in this thesis. The theory of EELS for 120 anisotropic materials of this type is due to Lucas and Vigneron Once again we can use the expression 71 -1 Im- (23) [ ^ (Q „. uj) + 1] for the loss function. However, here the effective dielectric constant is defined as: 1/2 (27) where Q and Q are the components of the total momentum transfer Q„ x y II parallel and perpendicular to the crystallographic c axis respectively. In off-specular scattering within the plane of electron incidence, two limiting loss functions may be observed. The first is determined by Cj_(uj), and requires the electron beam to be in the [110] azimuth; this ensures dominant momentum transfer perpendicular to the 1/2 c axis. The other is determined by [Ej_(w)e^ (ui) ] , and requires the electron beam to be in the [001] azimuth; this ensures dominant momentum transfer parallel to the c axis. 2.4.6 The Explicit Form of the Dielectric Constant We now have a number of expressions for the loss function as a function of the dielectric function e, and for e as a function of Q^. We need now to consider the explicit form of e as a function of the oscillator frequency u). This may be determined experimentally from reflectivity data by means of the following equation: R (ui) = { [n(ui) - 1]2 + k (w) 2}/{ [n (ui) + 1]2+ k(ui) > (28) where R is the reflectivity of radiation at normal incidence, n is the refractive index and k is the extinction coefficient. We can then 72 obtain e(uj) by consideration of 2 2 e' (ui) = n - k (29) and e' ' (u)) = 2nk (30) where e‘ and e’’ are the real and imaginary parts of e respectively. In the complex oscillator analysis, dielectric functions may be written in the form: 2 N 4ttq .uj . e(u>) = e(oo) + E — ----jLJ----- (31) j = 1 tu . - uj + iuj-y . 3 3 where e(«>) is the high frequency dielectric constant due to (for our purposes infinitely) high energy excitations, g.., ok and are the dipole strength, transverse frequency and damping constant respectively, and m is the frequency for which fuu is the energy transfer in the loss event. The forms of o ., uj . and y. vary with the 3 3 3 nature of the excitation, and in particular one can distinguish between the four cases of surface adsorbate vibration, plasmon, interband transition and phonon. Each case is thoroughly discussed in reference 95; here we shall concentrate on c(ui) for phonon excitations. In this case (31) becomes N r, *2i 4Trne e(w) = e(«>) + E (32) M 3=1 J L r J where n is the number of unit cells per unit volume, e is the transverse effective charge and M is the reduced mass of the unit r cell, ujj is the frequency of the active mode; the number N of such modes is deduced through group theory. In figure 18, the real and imaginary parts of e(u>) are plotted Figure 18: The variation in the real (e1) and imaginary (e”) parts of e(to) with to. 74 against ui for a dielectric solid with a single optical phonon mode, cq and are the static and high frequency dielectric constants respectively. Although there are two points at which e'=-1, we bear in mind that when e'=-1, the loss probability depends on e’* \ and thus the SO phonon is observed where e’=-1 and c’' is a minimum. The frequencies corresponding to TO and LO phonons are also indicated; it 33 can be seen that uj^ c u k ^ uj, In fact Fuchs and Kliewer predict TO SO LO that “so = “T0C,V ,l/,e-*,1],/2 1331 provided t.. is sufficiently small. 75 Chapter 3 - Apparatus and Experimental Methods 3.1 The Need for Ultrahigh Vacuum The atoms at the surface of any crystalline solid differ from their bulk counterparts in that they are not completely surrounded by nearest neighbours; they are coordinatively unsaturated, and are thus unusually reactive. Typically, a metal surface exposed to an ambient pressure of -6 10 torr would be expected to have a monolayer coating of “atmospheric" molecules within one second (the quantity 1 second at 10 ^ torr is known as 1 Langmuir). Thus, in order to study uncontaminated surface atoms, it is necessary to use ambient pressures well below this. In addition, since many surface spectroscopies rely on the use of monochromatic soft x-ray or UV photons which interact strongly with atmospheric molecules, it is desirable to prevent spurious energy changes through collisions between the radiation source and the surface. The study of most surfaces requires pressure not higher than -9 10 torr; this is termed ultrahigh vacuum (UHV). Techniques involving long scanning times, or very reactive surfaces need even lower pressures. Most modern UHV systems can attain 10 ^ torr or better. 3.2 The Ultrahigh Vacuum System The experiments described in this thesis were all carried out in a purpose-built stainless steel UHV chamber which was constructed by Leybold Heraeus, Koln, West Germany, and was delivered to Imperial College in December 1984. Although the chamber arrived equipped with a number of facilities, some of these, notably the HREEL spectrometer, had complex high precision instrumentation. As will be discussed in section 3.3, the HREELS spectrometer requires extensive manual adjustments for optimum performance, and some practice was necessary 76 before serious use was possible. It was also necessary to add several items in order that the chamber should provide a comprehensive surface analysis system. Thus the commissioning of the apparatus took a considerable time, and some equipment did not become available for almost a year after experimentation started. Figure 19 shows a recent photograph of the system. The chamber is entirely of bakeable stainless steel, with a p-metal lining throughout, to protect the electron optics from stray electro-magnetic fields. All the ports and joints are sealed by double knife-edge flanges with metal gaskets; most of the gaskets are copper, but the very large flanges use gold 0-rings. The vacuum in the system is created and maintained by a Leybold Heraeus turbo-molecular pump and ion pump, backed by ordinary two-stage rotary pumps, with foreline traps. This pumping arrangement is capable of reaching and maintaining -10 a pressure of about 10 mbar, which can be further improved by means of a titanium sublimation pump situated immediately above the ion pump. For an even better vacuum, the sublimation pump has a jacket which can be filled with liquid nitrogen; this has not been used for the present studies. As is standard practice, the chamber is baked as part of the evacuation process, to remove tenacious adsorbates from the chamber walls. The bakeout heaters can be seen in figure 19, fixed to the metal sheet covering the chamber stand. During bakeout, the chamber is shielded by an aluminised cloth shroud, which in the photograph can be seen folded above the assembly. This shroud is relatively light, and easier to manipulate than traditional box-type bakeout shields, particularly for such a large UHV system. The recommended bakeout o conditions are 10-15 hours at 200 C. After bakeout, but before the chamber is cold, all filaments, gauge-heads etc. are heated to operating temeratures to desorb any remaining impurities. Figure 19: the Leybold UHV system 78 Below the left-hand end of the chamber is the gas-handling assembly, in which vacuum is maintained by a separate rotary pump. This system connects to the main chamber through bakeable leak valves, and is itself partly bakeable. Whilst any gas- or liquid-containers must remain outside the bakeout shroud, most of the piping remains within it. The pressure in the UHV chamber is monitored by two ion gauges. One is an extractor gauge, and is situated above the sublimation pump, always measuring the pressure of the main chamber. The other is a conventional Bayert-Alpert ion gauge, and is situated on the outlet to the turbomolecular pump; when the pump is sealed off from the main chamber, this gauge is sealed off with it, and measures the pump pressure rather than that within the chamber. The pressure in the rotary pump lines, including the gas-handling assembly, is monitored by Pirani gauges. As illustrated in figure 20, the chamber has 4 main instrumental sections. From right to left, the first section contains a Leybold- Heraeus ELS 22 HREELS spectrometer, below which are the sublimation, ion and turbomolecular pumps. The second contains a set of Vacuum Generators LEED optics, and is also the section in which sample heating takes place. The third contains a Vacuum Generators Penning ion gun and a Vacuum Generators Masstorr quadropole mass spectrometer, as well as any filaments or evaporators which may be in use. Finally, the fourth section contains a range of general purpose surface analysis equipment, centred around a Leybold Heraeus EA 10 100mm hemispherical analyser. For XPS, there is a twin-anode (Mg/Al) x-ray source built by Vacuum Science Workshops; for UPS a Leybold UV lamp is available. A Leybold Heraeus electron source is present for lower resolution EELS and N(E) AES. The sample is mounted on a horizontal, motor-driven Figure 20: Schematic diagram of the Leybold Heraeus UHV system. 80 manipulator, which can traverse the full length of the chamber, allowing change of techniques with minimal effort. 3.3 The HREEL Spectrometer A detailed account of the theory and practice of HREELS instrumentation may be found in reference 95. It is the intention in this thesis to give a brief description of the particular spectrometer in use, with some comments on its operation and capabilities. The LH ELS 22 is a relatively recent model, being designed by Professor H. Froitzheim for Leybold Heraeus in the early 1980’s. It is supplied 121 with an adequate instruction manual , which will no doubt be improved as experience is gained. 3.3.1 The Spectrometer Construction o The ELS 22 spectrometer is based on a double-tandem 127 cylindrical sector capacitor construction, as shown in figure 21. o There are a total of four such 127 capacitor units, acting as pre monochromator (pm), monochromator (mm), analyser (ma) and secondary s. analyser (sa). The electron beam is generated by pasing current A through the filament shown at the top of the diagram; its energy may be varied continuously between 0 and 50eV, although the usual operating value is in the range 5-10eV. The beam is directed into the pre-monochromator by means of a repeller (R) and and a three-anode (a .a^a^l optics arrangement. Once through the monochromators, the beam is focussed onto the sample by two electrodes, e^ and e^l a further two electrodes, e_ and e., guide the reflected beam into the J b analyser. Finally, the electrons reach the detector, a channel electron multiplier (channeltron). The channeltron used in this spectrometer is a Galileo Continuous Dynode Electron Multiplier, manufactured by Galileo Electro-Optics 81 121 Figure 21 The construction of the Leybold ELS 22 HREELS spectrometer. 82 Corp. (Massachusetts, USA); its properties and characteristics are 122 described by Henkel and Gray . The signal from the channeltron is further processed by Ortec amplification electronics; Fast Preamplifier (9301S), Single Channel Analyser (550) and Spectroscopy Amplifier (572), finally being output on an Ortec 449 log/lin ratemeter. The analog output may simultaneuosly be sent to an XY chart recorder. The spectrometer is constructed of copper plates, which are coated with graphite dag to eliminate as far as possible erratic surface potentials. Conducting leads between the external power supply and the target components are insulated with glass-fibre sleeving ("reprosil"); this creates a certain amount of fibre dust, but no adverse effects have yet been noticed. The assembly is suspended, beam source uppermost, in a doubly p-metal lined chamber. A mechanical pulley o system allows the analyser to be rotated through a 60 arc, enabling off-specular sampling. As mentioned previously, the sample can also be rotated, so that a wide range of incidence angles may also be explored. 3.3.2 The Effect of the Analyser Acceptance Angle The acceptance aperture through the electrodes to the analyser is a rectangular slit, 1mm x 4mm. This means that the sampling of the o scattered beam is restricted to a 1 solid angle. The EELS theory discussed in chapter 2 is based on fully angle integrated acceptance, in which it is assumed that the entire range of scattered electrons reach the analyser. By further consideration of the theory o and the scattering geometry, we can gain insight into how the 1 sampling angle is likely to affect the spectra collected on the ELS 22 . We have seen in chapter 2 that the EELS loss function can be 83 expressed by the equation (13 in chapter 2); -1 Im (1 ) e(Q(I,uj) + 1 We now make reference to figure 22, which shows the scattering geometry in EELS. The angle between the wave vector kg of the scattered electron and that of the specular beam is 8, whilst «p measures the azimuthal orientation of kg looking down the specular beam; thus 6 and It is also useful to introduce the angle 8^ = tuu/2Ej, where iiu) is the energy of the loss under consideration. Now, in an actual experiment, the quantity measured is not simply the loss function, but the loss function integrated over the solid angle subtended by the entrance slit of the analyzer, Q (ks). This is assumed to be circular, centred on the specular direction, and collects all electrons scattered into the angular range 0 < 8 < 8c> If we now let 8' = 8/8^ be a reduced scattering angle, we have, with the polar axis of the spherical coordinate system aligned in the specular direction, dQ(k’ ) = 8d0dcp. Now we can write J P(8,tp,ui) = F (v , (jli ) Im 8' F(8’ ) ( 2 ) c e (uj ) + 1 where 2 F( v , oi) (3) which is independent of the angles which immediately concern us, and 84 z Figure 22: The scattering geometry in EELS, 85 can be regarded as constant for a given excitation, beam energy and angle of incidence. We are interested here specifically in the term dependent on the analyzer collection angle, and the angular spread of the scattered beam:795 2.2, 1/2 2tt 9' [ sin0 COS0 j cosip) + 0 sin Note that we have the limiting behaviour lim tt sin0„0' (5) 0 * c -> 0n F(0‘ c> I c and lim _.n, . 1 2 v F (0 ) = - n (6 ) c -> ~ c 2 Therefore, for a spectrometer which samples a sufficiently wide acceptance angle, equation (2) simplifies to give our original angle integrated loss function (equation (15) chapter 2): 2 e(ui) - 1 P(0 , Here, the integrated loss intensity falls off as v 1. However, when operating a spectrometer which, like the ELS 22, has a finite acceptance angle, F(0 * c) decreases as the beam energy decreases, and increases as the loss energy decreases; thus there is an optimum value for the scattering efficiency. From this we can see that the effect of the small acceptance cone of the ELS 22 spectrometer analyser will be to attenuate the signal intensity of higher energy losses relative to their theoretical values. This must be borne in mind when comparing experimental data 86 with calculated spectra originating purely from the theory described in chapter 2. In addition, the overall intensity of the spectrum will be decreased by operating at higher beam energies. 3.3.3 Calibration of the Spectrometer All HREEL spectra measured on this apparatus are referenced to the elastic peak, representing zero energy loss. This means that it is not necessary to calibrate the spectrometer for any absolute energy scale. It is, however, recommended to check the consistency of the power supply outputs against a reliable voltmeter, both at installation time and at regular intervals thereafter. Drifting of these potentials may give rise to problems in spectrometer operation. The operating manual lists the appropriate values for the various outputs. 3.3.4 Operation of the Spectrometer The process of optimising the electron optics to obtain a spectrum is at worst a very involved and time-consuming process; the first attempts with a new sample may take a week or much more. However, in theory, once a successful configuration of potentials has been obtained, the spectrometer should only require minor adjustments between samples (in practice this is not strictly true). When correctly adjusted, a spectrum should be obtainable whose elastic peak has a full width at half maximum (FWHM) of 4-5meV; this is occasionally achieved, but an FWHM of between 6 and 8meV is more usual from an oxide surface. The initial optimisation of the optics is carried out by tracing the electron beam through the system whilst altering the relevant potentiometers to maximise the beam current. The following parts of 87 the optics have potentiometers which generally require such adjustment; the repeller, the anodes, the pre-monochromator, the monochromator, the electrodes, the analyser and the secondary analyser. Most of these also have an MasymmetryM control, whose adjustment is often critical, the monochromator and analyser have "pass energy" controls, which affect both parts of the appropriate unit simultaneously. In addition, the filament current, the beam energy and the sample bias (if used) are likely to affect the signal. All of these controls are located on the HREELS instrumentation panel, which is illustrated in figure 23. The first step is carried out with the sample withdrawn from the scattering chamber and earthed. The filament is switched on, with a current of about 2A; a suitable beam energy should also be selected at this point. An electrometer is connected to the main monochromator, using the BNC socket on the front panel marked r . Now the mm potentiometers affecting all components preceding the monochromator are adjusted, as described in the manual, to obtain a current into the -8 monochromator of about 10 A. When this is achieved, the sample is moved into the scattering chamber such that the beam will hit the sample, and the picoammeter is connected to the sample, via the manipulator feedthroughs. Adjustment is now repeated to achieve a -10 current onto the sample of at least 2x10 A. It is important at this stage to have optimal sample position. For the next step, the sample is once more withdrawn and earthed, and the analyser is rotated so that the beam may pass in a straight line through the scattering chamber into the analyser; the "straight through" position. Now the channeltron is used as the detector, and the beam current is observed on the ratemeter. The channeltron potential should be kept close to 2kV; the use of higher potentials can seriously shorten its life. Since the beam is unscattered at this 88 Figure 23: the HREELS instrument panel 89 stage, and highly monochromatic, it is necessary to scan carefully through the analyser energy range to find its energy. This is done by using the "Ramp" potentiometer; the correct setting will depend on the spectrometer configuration at the time. Once a significant signal (>5cps) has been located, all potentiometers beyond the sample position 4 may be adjusted, as described in the manual. Once a signal of 10 cps is obtained, optimisation should be carried out in conjunction with a reduction in the filament current, keeping the signal to that level but slowly bringing the current down to 1.65A (a sustained high count level could damage the channeltron). At this stage, the next step can begin. The earthed sample is rotated so that it is vertical in the o chamber; this will give the usual incidence angle of 30 . It is then slowly introduced into the scattering chamber until the signal on the ratemeter cuts out completely; the sample is now in the path of the beam. Simultaneously, the filament current is returned to 2A. The o analyser is rotated up to form a 120 angle to the monochromator; this is the specular position. In theory, the scattered beam should now be detected by the channeltron. The following adjustments are, however, likely to be necessary. i) The energy of the elastic peak is likely to be slightly lower than that of the straight-through beam; the "Ramp" potentiometer should be adjusted by ±5meV. ii) The electrodes e -e, may need alteration. I * iii) The analyser position will probably require adjustment. iv) The sample position is absolutely critical. It is essential that it is correct, and should be adjusted in all possible directions. Some help can be obtained by measuring the current onto the sample as was carried out in the initial optimisation steps; it should be about 90 v) When a moderate signal has been obtained OlOOcps), careful adjustment of other potentiometers may help to improve the signal. If all is well, the ratemeter should now be displaying the elastic 3 peak intensity, which should be at least 10 cps. The stronger the signal, the better the signal to noise ratio should be. For a really good spectrum which can be expanded to show adsorbate peaks (typically 100 times smaller than the elastic peak), 10 cps or more is desireable. The FWHM of the elastic peak should be less than 8meV; the manual gives good advice on the improvement of this. Table II gives a typical set of potentiometer values for a satisfactory HREELS spectrum for TiO^. Now a HREEL spectrum can be measured. The scanning control in the "Ramp" section on the bottom right of the instrument panel provides a range of energy sweep rates. The energy sweep is fed to the X channel of an XY chart recorder, where the input to the Y channel comes directly from the ratemeter, and a spectrum is recorded in the form of cps versus energy. 3.3.5 Overcoming Difficulties At any stage in the preceding process, problems may occur. The most usual ones are failure to detect current on the sample, failure to detect a beam at the analyser in the straight-through position, and failure to obtain a good scattered signal from the sample. The following list of possible causes is not exhaustive, but all have been encountered by the author at some point. No current onto sample: a) The sample may be charging up; try moving a metallic part of the mount into the beam. b) There may be a loose connection somewhere, check everything, 91 Table 11: typical settings for a satisfactory HREELS spectrum 4 intensity = 2x10 cps FWHM = 8meV Potentiometer setting ]_ V I 2.04 R -1.204 -3.947 31 a2 20.59 -1.53 a3 Aa -0.032 A*; -1.77 3.18 *’3 Apm 0.229 Amm 0.300 monochromator pass energy -0.623 0.269 ei e 2 0.289 e 3 0.909 -0.494 *4 0.114 AeA®1 -0.150 0.103 Apa 0.307 Ama 0.298 analyser pass energy -0.632 Ep 7.362 incidence angle = 30° analyser position specular especially the connectors on the vacuum chamber. These tend to corrode during bakeout, and may need to be cleaned, c) The spectrometer surfaces may be dirty, suggesting bakeout is required. No signal in straight through position: any of the above, or a) The channeltron may not be functioning (no counts at all, plenty current on sample; this is rare). b) The ratemeter may not be working (check by trying XPS). Poor scattered signal If the previous steps have gone well, many of the above problems can be ruled out, but this step is more sensitive than the others to a "dirty" spectrometer and to sample charging (high count rate but low resolution, and no loss peaks; possibly abnormal elastic peak shapes) Another possibility is that the sample surface may be rough, very dirty or both (low count rate). 3.4 The General Surface Analysis Facilities As briefly discussed in section 3.2, in addition to the HREELS spectrometer the chamber also has a region devoted to general purpose surface spectroscopy; XPS, UPS, AES and EELS. For this purpose there are the previously mentioned three radiation sources (x-ray, UV and electron), and a hemispherical analyser. All the sources are used without monochromation; this is quite usual for XPS and UPS, but it means that the resolution of the EELS is rather poor, at about 0.5 eV In addition, there is no facility for differentiation of the Auger spectroscopy signal, so that this is used only in N(E) mode. 93 3.4.1 The Radiation Sources The x-ray source is of usual construction; two joined thoriated tungsten cathode filaments surround a water-cooled copper tube anode with a wedge-shaped end. This wedge is coated on one side with magnesium, and on the other with aluminium, each side facing one filament. In operation, 12-14kV is applied to the anode and heating current is passed through the filament on the side which is required as the source. This gives rise to an emission current of 12-14keV electrons passing between cathode and anode, sufficient to excite Ka radiation from the anode material. The filaments and anodes are separated from the main chamber by an aluminium foil window, which transmits the Ka radiation, but filters out any secondary electrons and bremsstrahlung which may arise during x-ray stimulation; the pressure on each side of the window is equalised by pumping (with the turbo pump) from behind the foil. It should be noted that when MgKa radiation is used, very low intensity peaks due to AlKa may also be noticed in the spectrum. Such features are known as ghost peaks; the radiation is chiefly due to the interaction of bremsstrahlung with the aluminium window. There may also be a tiny amount of emission from the aluminium side of the anode, but the rare observation of MgKa ghosts in AlKa spectra implies that this is less significant. The UV source is also of conventional design. Helium gas is leaked into a narrow quartz capillary where a discharge is passed between two tantalum electrodes. This causes excitation of the He atoms and emission of ultraviolet radiation, as discussed in chapter two. The radiation enters the chamber by continuing down the capillary, which extends well into the chamber. Two apertures near the lamp end of the capillary allow the lamp to be differentially pumped, preventing a large influx of helium to the chamber; nevertheless the 94 ambient He pressure in the chamber is about 10 ^ torr while the-lamp is in use. Fortunately, since helium is inert, this does not interfere significantly with the surface studies. However, both for this reason and because of the susceptibility of the discharge electrodes to corrosion, it is important that the helium gas should be as pure as possible. The Leybold Heraeus electron gun is a simple design within a rather ornate assembly. The beam source is a single filament which emits electrons on heating. The current is continuously variable up to 1mA and the beam energy may have any value between 0 and 5000eV. At the end of the gun are two deflectors, which enable the operator to direct the beam quite accurately; this is especially useful for small samples. Two problems were encountered with this electron gun; the first was that the construction is lacking in rigidity, and the weight of the deflectors causes severe drooping. This meant that if the sample was in a "natural" position, the beam tended to miss it. The second problem was severe beam instability at low filament currents, so that the operator was forced to use higher beam intensities than desireable. 3.4.2 The Energy Analyser All three sources are positioned such that emitted or scattered electrons may enter the EA 10 energy analyser. This is almost invariably used in constant analyser energy (CAE) mode, where electrons entering the analyser are retarded or (rarely) accelerated to a preselected energy (the "pass energy") Eq , before passing through the fixed aperture 2mm entrance slit. As the electrons pass through the analyser towards the detector, a retarding voltage R is applied, allowing their kinetic energies E^ to be measured according to 95 E, = R + E +ip (8) k o where 5E _ slit size _ 2 Eo 2 x mean radius 2 x 100 and hence 6E = E /100 (10) o Before use, the analyser was calibrated using a single crystal Ag sample. The calibration serves to ensure that the energy scale used by the spectrometer is correct and consistent over a wide energy range for all pass energies as well as for both anodes. In addition, an adjustment is made to compensate for the spectrometer work function, such that equation (1) becomes and true kinetic energies may be read directly from the spectra. 1 23 Table III shows the energies used for the calibration. The "work function" potentiometer was adjusted such that all three Ag peaks corresponded to the correct kinetic energies both for MgKa and AlKa radiation, thus ensuring consistency over at least a 530eV range. Next, the "calibration" potentiometer was adjusted to give correct peak position for each possible value of Eq . Finally, the positions of all three peaks were checked again to ensure that no errors had been introduced by the pass energy calibration. From equation (3), analyser resolution would be expected to improve as pass energy is reduced. At the same time, signal intensity should also decrease. In practice it is found that the resolution reaches a steady lower limit at the smallest pass energies, whilst the drop in 96 Table III: Ag peak energies used for XPS calibration core peak BE/eV KE(MgKa)/eV KE{AlKa)/eV 368 886 Ag 3d5/2 1118 573 A9 3p3/2 681 914 Auger 897 357 590 97 peak intensities continues, albeit at a reduced rate. In order to find the optimal pass energies, spectra were taken over the Ag 3d region using the full range of pass energies. Figure 24 shows a selection of the MgKa spectra; the least intense was recorded at a pass energy of 5eV, the more intense at 10, 20, 50 and 100eV respectively. Figure 25 shows the variation in resolution, represented in terms of FWHM of the Ag 3d_._ peak, with pass energy for both MgKa and AlKa b/2 radiation. Figure 26 shows the corresponding plot for the variation in the 3d_,_ peak height. By inspection of these spectra, it was decided 5/2 that MgKa radiation with an Eq value of 50eV gave satisfactory resolution (FWHM = 1.12eV) along with sufficient intensity to run an acceptable 20eV scan in 10 minutes. A smaller Eq would have greatly reduced the intensity without significantly improving the resolution. It is worth noting that, from equation (3), Eq = 50eV gives 6E = 0.5eV. The discrepancy between this and the observed value implies that resolution is limited not by the analyser, but by factors such as the linewidth of the exciting radiation, and core hole lifetime 88 broadening 3.5 The LEED Optics The LEED optics were supplied by Vacuum Generators, East Grinstead, West Sussex, and are of a conventional, three grid, front view design. The screen diameter is 14.1cm and the angle subtended at the sample is o 104 . In use, retard potential was applied to the front grid (G^); the second and third grids (G_ and G.) were earthed. Unfortunately, the J H LEED rarely worked particularly well, and never worked at beam energies below 60eV. The spots obtained were always diffuse, despite all attempts to remedy this. This indisposition was also found by other users studying metal samples, so it is concluded that it was the 98 Figure 24: XPS MgKot spectra of an Ag sample, using pass energies 5, 10, 20, 50 and 100 eV, showing that peak intensity and width increase with E . Pass Energy (Eo) / eV Figure 25: The variation in FWHM with pass energy, in XPS MgKa of the Ag sample. VO VO 0.0 25.0 50.0 75.0 Pass Energy (Eo) / eV Figure 26: The variation in peak intensity with pass energy in XPS MgKa of the Ag sample. 100 101 optics rather than the sample that was at fault. However as will be seen in chapter 4, it was possible to use the LEED to confirm the orientation of the sample. 3.6 Data Collection and Processing 3.6.1 Data Collection At the outset of this work, it was the intention that the system should be computerised, with an Apple lie microcomputer driving the spectrometers and collecting the data. Unfortunately this aspect of the work took some considerable time, since software development was entirely "in house". In addition, it was found that the performance of the ELS 22 spectrometer was severely impaired by the proximity of a computer. Attempts were made to shield all cables to and from the computer, to operate the computer at a distance and to use the computer in a Faraday cage, with no significant improvement. As a result, all data from the HREELS spectrometer has been (and is still being) collected on an XY chart recorder, directly onto chart paper. Progress was, however, made with computerising the other spectroscopies, and approximately 50Z of the XPS and UPS data in this thesis have been collected in this way, with the remainder also being collected by a chart recorder. The BASIC program "Collect" which was written for the data collection is listed and annotated in Appendix B, towards the end of this thesis. A small quantity of the analog data has been digitised by hand. The remainder has been digitised by use of a ‘Hi-Pad’ digitisation pad. The hardware aspects of interfacing this had already been carried out by the Imperial College Chemistry Department Microprocessor Unit (ICCMU). The computer to which it was linked was a combined Acorn BBC / Torch unit, and software to operate the data 102 collection process was required. This was written by the author in Propascal, and makes use of a number of standard ICCMU library routines. The program, MPadreadM, is listed and annotated in Appendix C, towards the end of this thesis. 3.6.2 Data Processing The data with the highest requirement for post-collection computer processing was that from XPS. As described in chapter 2, the spectra from this technique have significant intensity from other processes, which must be removed prior to quantitative analysis. For this purpose, the program "Stripper" was written; a listing along with documentation is presented in Appendix D. After processing by "Stripper", core peak intensities were found by integration using a trivial summation-type integration algorithm, and could thus be used as a measure of surface concentration of the relevant element. Figure 27 shows an XPS spectrum of the Ti 2p region before and after such stripping. In addition to the problem of secondary intensity, it is often found in XPS that core peaks overlap each other. In order to distinguish between such peaks it has become standard practice to fit model curves below the overlapping combination. The model curves are then used as representations of the experimental peaks, and their individual positions and intensities are used in the normal way. For the purposes of the present work, a simple program, "Fitter", was written. This allows the operator to place separate curves beneath an experimental spectrum, and to examine by eye the comparison between this and the sum of the model curves. Figure 28 shows a stripped 3 + experimental spectrum of the Ti 2p region, in which peaks due to Ti 4 + and Ti are both present, with curves produced by the "Fitter" program superimposed. The program is listed and documented in Binding Energy / «V Figure 27: XPS MgKa of nominally defect free TiC^CllO); (a) before and (b) after being stripped of satellite and background intensity by the program ’’stripper". 103 XPS SIMULATION Ti02 110 BOMBARDED 30 MINS ______Kinetic Energy / eU The r a t i o of T i 4+ to T i3+ i s 1.71 Figure 28: XPS MgKa of defective Ti09(110), superimposed upon a simulated spectrum created by the program "Fitter" from curves representing Ti3+ and Ti4+ core peaks. 104 105 Appendix E. 3.7 Sample Preparation and Mounting 3.7.1 Initial Sample Treatment The samples used for the experiments in this thesis are all single crystals of rutile structure, with (110) orientation. The TiO^ crystals were supplied by Hrand Djevahindjian (Monthey, Switzerland) in the form of 1cm x 1cm plates. The SnO^ crystals were obtained from Professor R. Helbig, one of which was roughly in plate form, with a 8mm x 8mm (110) face. The other was in the form of a needle, with 4 (110) surfaces each 2mm x 8mm. Figure 29 shows one of the TiO^ and one of the SnO^ crystals. In anticipation of problems due to sample charging, the larger SnO^ crystal had been very slightly antimony doped by prolonged annealing in contact with a lightly Sb-doped SnO^ powder. No Sb was ever detected in the XPS of this crystal, nor did UPS show Sb-induced states in the bandgap. The results obtained from both TiO^ crystals showed identical results, as did those from the two SnO^ samples. Before mounting, the larger crystals were all polished on a Kent lapping machine, using diamond paste down to 1pm and water-based lubricant. This resulted in a mirror-smooth finish. The small SnO^ crystal was used as-grown, since it appeared to have sufficiently smooth surfaces already. The crystals were then heated in air at 900- 1200°C for over 24 hours to ensure full stoichiometry, and to burn off any combustible residues. Finally, they were washed in several changes of isopropanol, followed by distilled deionised water. 3.7.2 Sample Mounting Sn02 1cm Figure 29: two of the samples used O O' 107 In the Leybold chamber, samples are mounted on the end of a central, coaxial manipulator rod. As mentioned previously, this can be motor-driven through the length of the chamber; it also has a certain amount of movement in "xM and "y“ directions, i.e. perpendicular to its longitudinal path, and can be fully rotated through 360°. The sample end of the manipulator is earthed, however six isolated feedthroughs also lead to the end of the rod. Of these, two are taken up by the thermocouple, and the remaining four are available for resistive heating or other applications. The core of the manipulator carries a copper tube through which coolants such as liquid nitrogen may be pumped; this gives a means of cooling the sample below room temperature. In designing a mount for the samples, there were a number of criteria to fulfill. Firstly, it was essential that the sample should initially be electrically isolated, and that it should be possible to either earth or bias it at will. XPS and UPS require that the sample be earthed, whereas for argon bombardment and for EELS it is useful to be able to measure a sample current. For electron bombardment, it must be possible to bias the sample. Secondly, it was necessary that o the sample could be heated to high temperatures, at least to 600 C, for cleaning and annealing. Finally, the sample had to be oriented with the face of interest parallel to the chamber axis. Thus it was clear that the sample itself must be mounted on an assembly made of a metal (or metals) which had reasonable thermal and electrical conductivity, good rigidity and tolerance to high temperatures; some degree of malleability was also desireable. It was decided that this task would be best fulfilled by tantalum. The crystals were mounted on trays of high purity tantalum, with the exception of the small SnO^ crystal, which was tied into a 108 "cradle" of high purity Ta wire. These were then suspended on twisted Ta wire between 1mm o.d. Ta rods. The rods were threaded at the far end, and screwed into appropriately tapped blocks of machineable 122 ceramic , which were in turn fastened with stainless steel studding to the manipulator block. Figure 30 shows the mount which was used for most of the TiO^ experiments. Heating was achieved by using two of the isolated manipulator cables to pass currents through the mount assembly, with connection being made onto the Ta rods just beyond the ceramic block. The temperature of the crystal was monitored by a chromel-alumel thermocouple clipped between the Ta support assembly and the crystal face. Currents in the range 10-20A provided useful heating; the twisted wire and foil tray reached red heat at about 15A, at which point the sample temperature was about 600°C. It should be noted that in atmospheric conditions, tantalum would rapidly oxidise -5 at such temperature. In vacuo, and even when heated in 10 L 0^, no extensive oxidation was observed, though after many cycles of such treatment, the wire became rather brittle. The mount design was modified in an attempt to cool the sample. Cooling was performed by pumping liquid nitrogen down the tube built into the manipulator for this purpose. It was necessary to thermally connect the sample to the manipulator end-block, but as discussed above, electrical insulation had to be maintained, and resistive heating had still to be possible. In addition, if HREELS was to be feasible, the presence of insulating material close to the sample had to be minimised, since this might divert the electron beam. The problem was approached by constructing the mount shown in figure 31. A copper block was attached to the end of the manipulator, and a 3mm diameter copper rod was tapped into it. The rod passsed through the ceramic block and between the sample-holding Ta rods as shown, ending about 3cm from the sample itself. A hollow copper holder was screwed 109 Figure 30: The sample mount for room temperature work, illustrated with a TiO^ sample. 110 ■ \ Figure 31: The sample mount for low temperature work, illustrated with a Ti0 2 sample. I l l onto the end of the rod, and a rod-shaped single crystal of sapphire was inserted. The protruding end of the sapphire was inserted into another copper holder on the end of a shorter copper rod, which was in turn fixed to the sample mounting plate. About 1mm of the sapphire was kept naked in order to ensure electrical insulation. The reason for choosing sapphire as the insulator was that although an excellent electrical insulator, the material becomes a relatively 1 25 good conductor of heat at low temperature . However it is still worse than most metals, and as much of the assembly as possible was made of copper to make thermal conductivity as high as possible. The naked sapphire connection was kept to a minimum both for this reason and to reduce the chances of it interacting with the HREELS beam. The use of this mounting assembly will be discussed further in chapter 5. 3.7.3 Cleaning the Samples in Vacuo It must be expected that despite all precautions, samples newly introduced into a vacuum chamber will be contaminated by atmospheric species, primarily CO and water. The first step in cleaning all of the samples in this work was moderately heavy argon bombardment (2kv/10pA, 10-15 minutes) to remove tenacious adsorbates. The o ™ 6 5 crystals were then heated to 650 C in oxygen (10 -10 torr) until stoichiometry was regained. The duration of this process varied, with the Sn02 requiring longer anneals than the Ti02. The means of characterising stoichiometry and cleanliness depended on the techniques available at the time, and upon the sample. This will be discussed in detail in the relevant chapters dealing with the specific cases. 112 Chapter 4 - The (110) Surface of Rutile TiO^ This chapter presents a study of the stoichiometric and non- stoichiometric rutile TiO^MIO) surface using HREELS, ELS, UPS and XPS. Particular attention is paid to the HREELS spectrum and its behaviour as the surface loses oxygen. For this purpose, the technique of electron bombardment is developed as a reproducible means of reducing the surface. An attempt is made to identify the nature of the defects caused by oxygen deficiency, and to explain the effect which they have on energy loss spectroscopy. 4.1 Sample Preparation Chapter 3 contains a description of the initial preparation of the samples, and of their mounting. What follows describes the final treatment of the 1cm x 1cm TiO^ single crystal which was used for all the experiments presented in this chapter. (About halfway through experimentation the crystal broke in half; work was continued on one of the 10mm x 5mm fragments.) All experimentation was carried out at room temperature; the mount used was thus of the type depicted in figure 30. The crystal was mounted with the (110) face exposed, and such that its c-axis was either parallel or perpendicular to the longitudinal axis of the spectrometer. The orientation of the crystal was determined by Laue x-ray diffraction, carried out by W.R. Flavell at Oxford University. This was supported by LEED patterns obtained by the VG optics in the Leybold chamber, as described below. 4.1.1 Preparation of a Defect Free TiO^ Surface The criteria by which the surfaces studied in this part of the work were determined to be stoichiometric, well-ordered and clean are 113 discussed in sections 4.1.2 - 4.1.4. After preliminary preparation as described in chapter 3, the following procedures consistently produced such surfaces. Once mounted in the evacuated chamber, the face of the crystal was bombarded with 2.5kV argon ions at a current of about 10pA for 10 minutes. The sample was then annealed in either of two ways. The first was employed when no gas supply was available; this involved resistively heating the sample in vacuo at about 750°C for at least fifteen hours. Apart from the long times involved, this was a satisfactory procedure and presented no problems. The second method was used after the gas manifold had been constructed; very high purity 0^ gas was leaked into the chamber to give an ambient pressure of 2 x 10 6mbar. The crystal was then resistively heated to about 700°C for one or two hours. The advantage of this method was its much greater speed, but if used frequently there was a tendency for the tantalum mounting wires to oxidise and become brittle. If for any reason the crystal surface was heavily contaminated, for example by fingerprints, it was usually necessary to repeat this process several times. It should be commented that this type of process is unlikely to significantly improve the flatness of an oxide surface which has not been properly polished. Although the heat treatment promotes diffusion of oxygen from the bulk to the surface, it would not be expected to cause sufficient rearrangements to counter deep scratches and other macroscopic imperfections. 4.1.2 Criteria for Stoichiometry In electron spectroscopy, particularly UPS and HREELS, completely oxidised Ti02 charges up and yields no meaningful spectrum. However a tiny amount of reduction, for example by heating at 600°C in vacuo for 30 minutes, will prevent such charging without showing any of the signs of reduction to be described. This is in fact the ideal 114 stoichiometry for the present work, and is that which one aims to achieve. It should thus be borne in mind that surfaces hereafter described as 'defect free’, are in fact very slightly oxygen deficient. The most simple and direct means of determining the stoichiometry of the Ti02 surface is by comparison of the Ti 2p and 0 1s core peaks in the XPS; however, investigation of the Ti 2p core peaks alone was found to give more consistent results. Titanium is present in stoichiometric 4 + TiO^ as Ti ion; as oxygen is lost, a proportionate amount is reduced, 3 + chiefly to Ti . The 2p core peaks of these two species have distinct chemical shifts; in the present work a separation of 1.9eV is found. This compares reasonably well with a value of 1.5eV obtained by Orchard 1 26 and colleagues in a study of Ti^O^ . Figure 32 shows XPS spectra obtained from a stoichiometric (a) and a moderately reduced (b) 4 + 3 + TiO C110) surface. Although the Ti and Ti core peaks overlap, the use of the programs "Stripper" and "Fitter" (as described in chapter 3 and appendix E) allows the separate intensities to be determined. Consideration of charge balance requires that each missing oxygen atom . 3+ + + generates two Ti ions, so that the ratio R between Ti and Ti is related to the composition parameter x in TiO^ x by the expression: x values obtained by this method were in general agreement with those derived from the 0 1s/Ti 2p intensity ratio, but showed considerably .3 + less scatter. Thus, not only can the absence of a Ti signal be used f + as an indication of full oxidation, but the Ti :Ti intensity ratio can serve as a measure of surface oxygen content. To confirm the stoichiometry of the surface, a number of other methods may be used. In ELS, stoichiometric TiO^ shows a completely XPS T i 02 C 1 ICO d«*-p«ao"t -Fr~«« and d«f aoti va «urf aoas 450.0 460.0 470.0 Binding Energy / «» V Figure 32: XPS MgKa of Ti02(H0) (a) nominally defect free and (b) slightly defective, showing the 115 appearance of Ti3+ core peaks. 116 flat and featureless bandgap region, whilst a reduced surface shows a distinct excitation; this can be seen in figure 33. In UPS, a reduced surface gives rise to states in the bandgap, immediately below the Fermi level; these are absent in the spectrum of the defect-free surface. Figure 34 illustrates this for He(I), and figure 35 for He(11) exciting radiation. In Auger spectroscopy, the Ti peak shows structure similar in appearance to that described above for XPS, with .3+ . an additional peak appearing to lower binding energy if Ti is present. However the Auger instrumentation available was rather limited, giving only an N(E) spectrum, and the acquisition of good spectra was particularly hampered by the electron gun's intensity drift, as described in chapter 3. Hence, this method was only used in the early stages of experimentation before XPS was available. As will be discussed below, the HREELS spectrum of TiO^MIO) is also affected by surface stoichiometry. 4.1.3 Criteria for Surface Order As discussed in chapter 2, a flat, well ordered single crystal surface would be expected to give a corresponding pattern of spots in LEED, whereas a rough surface would not. Although the LEED optics were not always operational, it was possible to obtain patterns at beam energies greater than 60eV. Figure 36 shows a photograph of such a pattern obtained from the crystal following the treatment described in 4.1.1, using the in vacuo annealing technique. From this pattern, which shows a (110) rutile lattice face with second order spots along the c axis and first order along the a axis, interatomic distances d c (in the c direction) and dg (in the a direction) were obtained (see equations in section 2.3). The values for the (110) direction were d c = 29.6nm and d = 65nm; these are within 1.7 and 2.3Z of literature a 9 values respectively. The LEED pattern also confirms the crystal 117 ELS T i 02 C 1 105 daf act ■fr—•• & daf acbi va I n t i ■fc y “5.0 0.0 5.0 10.0 15. Enorgy Loss / •V Figure 33: ELS of TiC^CllO), (a) nominally defect free and (b) defective, showing growth of defect loss peak in the band gap, 118 Binding Energy/eV Figure 34: UPS He(I) of TiC^CllO); (a) nominally defect free and (b) defective, showing appearance of defect states in the band gap. UPS H« C I I 5 T i 02 C 1 10 2 daf aot ■f'r'o« and dafootiva surf aoaa 4.0 0.0 4.0 G.O .12.0 1S.O Binding Enargy / •V Figure 35: UPS He(II) of 1102(110),; (a) nominally defect free and (b) defective, showing growth of defect states in the band gap. 119 j. 15 E F4 Figure 36: LEED of nominally defect free TiCLlTIO) ro o 121 orientation which had previously been determined by the Laue method, as mentioned above. In a HREELS experiment we can effectively measure the energy and angular distribution of electrons in the (0,0) LEED spot. The magnitude of the angular spread can be assessed by measuring the variation of the intensity of the elastic peak as the analyser is rotated about the specular position. One would expect a perfectly flat surface to show a sharp drop in intensity either side of the specular angle, almost vanishing within a few degrees. Figure 37 shows a plot of elastic peak intensity versus analyser angle for the surface which gave the LEED pattern in figure 36 (dots) and for the same surface after moderate electron bombardment (see section 4.3.2)(crosses). It can be clearly seen that the rougher surface not only produces a broader peak, but the proportion of the peak area within the large angle "wing" region is 1 27 much higher. This can be compared with figure 38 , which shows the same type of plot for a very well ordered GaAs surface grown by molecular beam epitaxy (MBE). Here the peak is very sharp, and the relative intensity of the large-angle "wings" is very low, even less than in the plot for the "flat" TiO^, illustrating the great difficulty of producing a perfect TiO^ surface. 4.1.4 Criteria for Cleanliness Once the TiO^ surface has been heated in vacuo, the majority of the contamination remaining is carbonaceous, originating either from fingerprints and similar greasy residues or from gaseous hydrocarbons present in the atmosphere. This can be removed by the cleaning process described in section 4.1.1, but tends to build up again after a few days. Initially, a small amount of potassium was also detected, but this disappeared completely after the first few cleaning cycles. HREELS Ti02(llQ) elastic intensity vs collection angle Collection Angle / deg. off specular Figure 37: Variation in elastic peak intensity with collection angle in HREELS of TiC^CllO); (•) smooth and (+) 122 rough surfaces. — ____1_____ ■ I-1 -10 0 10 9 /Degrees 127 . . . Figure 38 : Variation m elastic peak intensity with collection angle in HREELS of a flat sample of GaAs grown by MBE, 124 Carbon can be detected both by Auger spectroscopy and XPS, but it has a low cross section in both techniques and gives a rather weak signal. Because AES was only available in N(E) mode, carbon detection by this method was particularly difficult, so that when available, XPS was the preferred technique. When using AES, the criterion for cleanliness was simply the absence of an observable carbon peak, but the situation in XPS was easier to quantify. Reference 82 gives values for the relative sensitivities of XPS to Ti 2p and C 1s as 1.8 and 0.25 in terms of peak area respectively. Taking into account the fact that the Ti signal results from several layers (dependent upon the IMFP.A) into the surface, whilst the carbon signal can be assumed to result only from the top layer, a complete carbon monolayer would give a C 1s:Ti 2p area ratio of about 0.03. Thus, for a reasonably clean surface we require an area ratio of no more than 0.001. Figure 39 shows the XPS C 1s region for typical contaminated (a) and clean (b) TiO^UIO) surfaces; the ratio of the area of the C 1s peak of (b) to that of the corresponding Ti 2p core peaks is indeed 0.001. 4.2 HREELS of the Stoichiometric TiO^UlO) Surface 4.2.1 Symmetry and Phonons in the HREELS of Ti02 A clean, ordered TiO (110) surface would be expected to yield an HREELS spectrum showing only an elastic peak and losses due to the excitations of surface phonons. The nature of the latter depends largely upon the symmetry of the lattice. Rutile Ti02 contains two 14 formula units per unit cell, and belongs to the space group D,.,4 h as described in chapter 1. Table IV lists the 16 point symmetry operations for the group, and table V is the corresponding character 12 8 table . From these data, the 15 normal modes of non-vanishing XPS Ti02(110) showing oarbon region Binding Energy / eV Figure 39: XPS MgKa of TiC^CllO) showing the carbon region; (a) before and (b) after surface cleaning. 125 126 H Table IV: the 16 point symmetry operations for D.. 4 n Point operations Non-primitive Description translation E 0 identity + T tt/2 rotation about z axis C4 T -tt/2 rotation about z axis c;~ 0 tt rotation about z axis C2 T tt rotation about x axis Cv, T tt rotation about y axis Cv2 o 0 tt rotation about x + y axis Q. 0 tt rotation about x-y axis Cd2 I 0 inversion + + T inversion x C. S4 4 T inversion x C, V 0 reflection in xy plane °h T reflection in yz plane °V1 Q T reflection in xz plane < ro 0 reflection in (x-y)z plane °di 0 reflection in (x+y)z plane °d2 127 14 Table V; character table for D 4h _ 14 + E C °4h C4 C4_ 2 °v2 °di V °V1 °h 1 1 1 1 1 1 1 1 A1g'A2u 1 1 1 1 1 -1 -1 -1 -1 1 A,u’A2g 1 -1 -1 1 1 -1 -1 1 1 B1g'B2u 1 -1 -1 1 -1 1 1 -1 1 B2g,B1u E , E 2 0 0 -2 0 0 0 0 2 g u 18 0 0 “ 0 -4 12 0 6 ^disp 2 + I c V S4 V1 Cd2 Cd1 Cv2 A . , A _ 1 1 1 1 1 1 1 1g 2u A . i A _ 1 1 1 -1 -1 -1 -1 1u‘ 2g -1 -1 1 1 -1 -1 1 B1g *B2u -1 -1 1 -1 1 1 -1 B2g,B1u E , E 0 0 -2 0 0 0 0 9 u 0 0 -6 0 12 4 0 ^disp 128 frequency at k=0 can be shown to span irreducible representations r as follows: A + A. + B + B_ + 2 B + E + 3 E + Aiu vib 1g 2g 1g 2g 1u g u zw (3 ) This list does not include the acoustic normal modes; these transform as the translations x, y, z of the group, and hence have Ey and A2u symmetries. We recall from chapter 2 that for interaction in HREELS to be observed, the vibration must give rise to a normally oscillating dipole moment. In the rutile lattice, this condition is fulfilled only for the translational operations of A2u and Ey symmetry depicted 1 29 in figure 40 . Here it can be seen that the A2u mode corresponds to translation in the z direction, involving displacements parallel to the c axis, whilst the E^ modes correspond to x and y translations, with displacements perpendicular to the c axis. Table VI lists parameter values from a complex oscillator analysis 36,130 of the infrared reflection spectrum of Ti02 , along with corresponding calculated surface mode energies. "Parallel" and "perpendicular" dielectric functions can be written in the form: . 2 4 TTQ .U> . 3 3 (m) e(«) + E (4) t 2 2 3=1 UJ . - UJ + 1 W Y . 3 3 For the dielectric function parallel to the c axis, E||(id), the summation contains only the term for the A ^ mode, whereas it extends over the three E modes for the perpendicular dielectric function u Cj_(U») . 0 - 0 O =M Figure 40: The atomic translations involved in phonon excitations of the rutile unit cell. 130 Table VI Parameters used for calculating HREEL spectra Mode Energy hu Absorption strength Damping parameter (eV) UTTQj) (?/u) t (E . 1 u) 0.0227 81.5 0.1 0.0481 1.08 0.03 0.062 2.00 0.025 V Azu> 0.0207 165 0.025 Mode Energy hu Surface mode Energy hu (eV) (eV) 0.0462 si 0.0468 1ZIEJ 0.0568 sz 0.0573 V EJ 0.0999 S3 0.0945 0.1006 \ < Az J su 0.0903 El( oo) = 6-0 £,i Coo) = Q u 131 4.2.2 The Effect of Anisotropy It was shown in section 2.4.5 that for anisotropic materials such as rutile, it is necessary to take account of the tensor nature of the dielectric function. Contrary to simple expectations, scattering from (001) surfaces contains contributions from both Cj_(uj) and e^ (ui) ; not simply c|| (ui) alone. Likewise for (110) surfaces, both C||(id) and Ej_(u>) contribute to the EELS. This topic has been treated in some depth by 131 W.R. Flavell , and it has been found that the effects of crystal anisotropy on the HREELS of TiO (110) are rather small, the major effect being to introduce mixed E /A_ character into the highest u 2u a energy loss peak. This is due to an accidental near-degeneracy between the A„ surface loss feature and the highest energy E loss. 2u u 4.2.3 The HREEL Spectrum of TiO (110) Figure 41 shows a typical HREELS spectrum obtained from a flat, clean and stoichiometric TiO2(110) surface as obtained in the course of the present work. The energy of the exciting electron beam was o 7.35eV, and it was incident at 30 to the surface, directed along the [001] azimuth. The spectrum was recorded in specular mode. The elastic peak has a FWHM of 6meV, and three phonon loss peaks can be seen, at energies of 44meV, 52meV and 94meV. This compares very well 37 with a similar spectrum obtained by Rocker and colleagues (see chapter 1). Since the c-axis lies within the scattering plane, the 4 x 1mm slit of our spectrometer analyser then allows dominant momentum transfer perpendicular to the c axis; thus it is reasonable to neglect the dependence of the loss function on Q^ (see chapter 2), and to assume that E(ui) is dominated by Cj_(ui). Thus we obtain a simple expression for the angle integrated loss function P (ui) as follows: HREELS T i 02 C 1 10 3 daf aat. f naa« Ep"7 ■ 3aV . cang 1 aa30dagr~e«si -50.0 0.0 50.0 100.0 150.0 200.0 250.0 300.0 EnargyL.o*aa* / m«» V Figure 41: HREELS of nominally defect free Ti02(110), with a beam energy of 7.3 eV, and an incident angle of 30°. Collection is in the specular direction. 132 133 2 Cj_(uj) - 1 P (w) = — -— Im (5) Ej_(U)) + 1 Using this form of the loss function, it is relatively simple to develop a computer program to calculate and produce model HREELS 104 spectra. P.A. Cox and colleagues have proposed an algorithm for such a program, using a Fast Fourier Transform IFFT) technique to convolve into the initial loss function contributions for the thermal population of excited states, elastic peak broadening and for sequential scattering processes. This was then written in BASIC for a Research 8 8 Machines 380Z computer by P.A. Cox and W.R. Flavell and used in the anisotropy work described above. For the present work, the 380Z version was initially converted to run in BASIC on an Apple lie computer, however it was found to be extremely slow in operation. A twenty-fold improvement in running time was achieved by rewriting the program in Propascal with an improved FFT routine, and using a BBC/Torch (Z80/CPN) microcomputer. This version of the program is called "Eelsim", and is listed and documented in appendix F. Figure 42 compares the experimental HREELS of TiO2(110) with a model produced by "Eelsim”, using the parameters for the Ey modes as listed in table VI. The good agreement between the two spectra appears to justify the use of the modified equation for the loss function, equation (5). In particular, the measured energy of the strongest surface phonon loss (94meV) is very close to the predicted energy (94.5meV) of the highest Eu loss in the simulated spectrum. It 34 is encouraging that Kesmodel and coworkers found a very similar loss energy in the HREELS of TiO (100), giving further support to the view that anisotropy has little effect on experimental HREEL spectra 134 Figure 42: (a) as figure 41; (b) simulation of (a), as described in te x t. 135 of rutile. It should, however, be noted that the phonon loss peaks in the experimental spectrum are distinctly broader than expected from bulk damping parameters. Thus it was found necessary to modify slightly the values of -y in table VI for use in the calculations. This phenomenon has been noticed previously in HREELS studies of ionic . . . 111.112 solids It is also noticeable in figure 42 that features to higher loss energy are stronger in the calculated spectrum than in its experimental counterpart. This may be partly understood in the light of arguments put forward in section 3.3.2 regarding the sampling cone of the Leybold EELS analyser. One might indeed expect the experimental attenuation of high energy features relative to low energy ones to be even stronger than is in fact observed. For example, using the equations described along with data from reference 95, one would expect the intensity ratio of the highest energy phonon peak to the elastic peak in the experimental spectrum to be only 60Z of that seen in the model. The fact that it is actually larger than that may be accounted for by the observation in section 4.1.3 that the "flat" surface of the sample surface was still not perfect. This would result in angular smearing of the lower energy loss peaks and the elastic peak, and a decrease in their F(0* ) (see section 3.3.2), with c a commensurate reduction in their relative intensities. 4.3 The Creation of Oxygen Deficiency in TiO (110) In order to study the effects of oxgen deficiency on the surface of TiO^, it was important to establish a method for creating oxygen vacancies in a consistent and controllable manner. As we have seen from previous arguments, if we were to obtain good HREEL spectra, it was also desireable to find a method which maintains a reasonable degree of surface order. As mentioned in chapter 1, the techniques 136 28,29 used for this purpose in previous work were heat treatment and argon ion bombardment ' . In the present study, both of these methods were attempted. It was found that heat treatment maintained excellent surface flatness, but it was extremely slow, and in fact 132 detectable defect levels were rarely found. It is known that high 2- temperatures encourage diffusion of 0 ions through the TiO^ lat^lce towards the surface, and it is expected that thermally induced oxygen vacancies were largely eliminated in this way. The use of argon ion bombardment was also found to present problems; figure 43 shows the XPS of the Ti 2p region of the surface after bombardment with 2kV argon ions for 10 minutes. With the apparatus available for this work, it was found virtually impossible to regulate argon ion bombardment of the surface such as to produce small defect concentrations; the smallest achieved was approximately 0.15 per fomula unit, giving a stoichiometry of TiO, n_. It was also very difficult to predict the defect level that would be attained by the bombardment. This was compounded by the fact that argon ion bombardment produces a very broad and amorphous Ti 2p core peak in XPS, as illustrated in figure 43, making measurement of defect levels as described in 4.1.3 a difficult task. It is indeed debatable whether reduction by this .3 + method produces only Ti ; indeed Gopel and coworkers report 2+ o observation of Ti and Ti on a TiO^MIO) surface after similar 29 treatment . However the greatest problem was that the surfaces thus reduced were very rough, making HREEL spectroscopy very difficult. The intensity of the elastic signal was greatly reduced, giving very poor signal to noise; moreover the loss peaks were severely broadened, with a tendency to merge together. This will be illustrated in section 4.4.3. Finally, it was decided to attempt a method which had not XPS Ti02(110), argon ion bombarded .1 n t e n s i yt 440.0 460.0 *! 480.0 Binding Energy /eV Figure 43: XPS MgKa of a typical argon ion bombarded Ti02(110) surface. 138 previously been used in this context; electron bombardment. As will be seen, this method is controllable, reproducible and conserves much of the surface integrity. 4.3.1 The Knotek Fiebelman Mechanism Electron bombardment as a means of removing species from the 133,134 surfaces of solids has been known for some time . The traditional view of the mechanism involves excitement by the incident beam of a bonding electron to a non-bonding or an antibonding state, resulting in a repulsive potential between surface atom and solid, and ejection of the atom from the surface. However in 1978, Knotek and 135 Feibelman proposed a quite different mechanism for electron stimulated desorption (ESD) of oxygen from oxides in which the metal d electrons are fully ionised, as, for example, in TiO_, V_0_ and W0_. 2 2 b J 135 It is reported that for this type of oxide the yield from ESD is much higher than can be explained by the older mechanism; it is suggested that electron bombardment of such oxides gives rise to inter-atomic Auger events in which an incoming electron gives rise to a core hole in the metal atom. Since there are no d electrons available to "drop down" and fill this hole, an electron is instead 2 "donated by a nearest-neighbour 0 - ion, . with simultaneous emission of Auger electrons. The oxygen thus becomes relatively positively charged, and is repelled electrostatically from the lattice. Knotek and Feibelman present convincing arguments for the energetic feasability of this process, and describe the technique as an atom- specific, valence-sensitive surface probe. A diagram for the mechanism is presented in figure 44. 4.3.2 The Practice of Electron Bombardment The method employed for electron bombardment in the present work ejected core Figure 44: The Knotek Feibelman mechanism for electron stimulated desorption. 140 was developed through a sequence of trial experiments, finally culminating in a reliable and useful technique. The experimental assembly is illustrated in figure 45. The face of the crystal was positioned about 3mm from a sharply bent tungsten filament which formed the electron source. By means of a modified ion-gauge control unit, a potential of +160V was applied to the sample, whilst current was passed through the tungsten wire, causing electrons to be emitted. The control unit maintained a stabilised emission current, which was readily controllable in the range 1-10 mA. It should be noted here that tungsten was found to be a most suitable filament material at this modest potential, and no sputtering of tungsten onto the sample was detected. However, in earlier experiments using 2kV bombardment at higher (>20 mA) beam currents, it was found to be easy to coat the surface with tungsten, and an attempt to use a tantalum filament even at 160V resulted in heavy Ta contamination of the sample. When in doubt about the reliability of the filament, it was found to be quite possible to achieve ESD by ~ \r 4.3.3 The Oxygen Desorption Cross Section Oxygen loss from the surface under electron bombardment was quantified by XPS, as described in 4.1.2. Figure 46 shows the 3 + progressive rise of the peak due to Ti in the XPS as bombardment time increases; (a) is before bombardment, and (b), (c), (d) and (e) are 141 Ta backing — plate Figure 45: The experimental arrangement for electron bombardment. 142 Binding Energy/eV Figure 46: XPS MgKa of TiC^CllO) as electron bombardment progresses. 143 after 15, 30, 60 and 120 minutes respectively. The respective values of x in TiO^ x are ^' ®*12, 0-18, 0.21 and 0.25. The bombardment was carried out with a current of 5mA, and a potential of 160V. Figure 47 illustrates the smooth variation of the logarithm of the ratio (2 - x)/2 with bombardment time (x in TiO^ x^; ^ Particularly noticeable that the desorption rate falls off with time, reaching a limiting composition of Ti.0_. This is the same limiting composition as was * r found under argon ion bombardment. The data presented in figure 47 allow the derivation of a value for the cross section o for oxygen desorption to be derived through the relationship. 4.- u- 136 ln[{2-x)/2] = -oipt / e where (2 - x) / 2 gives the ratio between the oxygen stoichiometry at time t and its initial value, e is the electron charge and electron flux (current per unit area) onto the sample. Although the plot in figure 47 implies that the desorption cross section decreases with increasing oxygen deficiency, the initial slope can be used to give a value of 3 x 10 -212 cm for the cross section for desorption from stoichiometric TiO (110). The major source of uncertainty in the data lies in the assumption that the emission from the tungsten filament drains exclusively into the crystal, and not into the support assembly. As we have observed, it is actually possible to electron bombard, albeit with much less effect, from the rear of the crystal, implying that a certain proportion of the electrons do escape. However, the value obtained for o compares sensibly with cross -20 2 sections of around 10 cm for desorption of oxygen from the 0^ 1 37 adsorption phase on W (100), as reviewed by Bellard and Williams Qualitatively, the decrease of o with increasing concentrations of 144 0 60 120 t / min Figure 47: Che logarithmic decay of surface oxygen content fith duration of electron bombardment of Ci02 (110). 145 3+ . Ti is not unexpected if the desorption mechanism is indeed that 3 + proposed by Knotek and Feibelman. This is because Ti does have available d electrons, which may now allow for decay of shallow Ti core levels by an intra-atomic rather than an inter-atomic Auger 135 process. In fact Knotek and Feibelman themselves found that argon ion bombardment did reduce the yield of electron-beam desorbed oxygen ion from rutile surfaces. Whatever the detailed explanation of the decay curve, it is clear that this technique provides a convenient means of producing an oxygen deficient TiO^ surface in a controllable and reproducible way. Moreover, the Ti appears to be present on the surface exclusively as .3+ .4+ Ti and Ti , in contrast to argon-ion bombarded surfaces. 4.3.4 The Depth of the Oxygen Vacancy Defects It is of interest to know roughly to what depth the "vacancy layers" created by electron and argon ion bombardment extend. In HREELS such knowledge is useful in the context of the layer model for spectrum simulation, as described in chapter 2. From the point of view of the method being used here to assess stoichiometry, it is relevant to know what proportion of the photoelectrons are being emitted from a "defective" region of the sample. It should be noted that in practice it is assumed here that the entire signal arises from a uniformly defective sample. In order to justify the "uniform defects" approach, it is necessary to show that the oxygen deficient layer does extend considerably into the surface, in particular to a depth comparable in to the sampling depth of XPS. For this purpose, XPS spectra of the relevant surface types have been taken at a variety of emission angles, and the stoichiometries from the spectra have been measured. From equation (3) in chapter 2, it is clear that the smaller the emission angle, the 146 less deeply the sample is probed. Thus, if the depth of the defects is less than the probing depth at normal emission, a spectrum taken at grazing emission should show a higher concentration of defects than its normal emission counterpart. . 4+ . 3 + Spectra from the argon bombarded surface show identical Ti : Ti ratios at normal and grazing emission, confirming that the defects are found in uniform concentration to at least the limit of XPS probing. However, for the electron bombarded surface, the ratio at grazing emission is 20X lower than at normal emission. In order to quantify the depth to which the electron induced defects extend, the following simple model may be proposed. We postulate that the defects are 4+ 3 + present in a layer of constant Ti :Ti ratio of thickness D; below this, the composition is that of the bulk. We assume that the 3 + concentration fraction 0 of Ti found at grazing emission is that of 3+ 4 + the uniform defect layer, and we call the Ti :Ti ratio at normal emission x. Then we can say that J^8I exp[-l/A] dl o o . . x = — ------"------(6) J (1-0)1 exp[-l/A]dl + J_I exp[-l/A]dl o o D o where 1 is distance into the surface, and A is the inelastic mean free o 1 3 8 path discussed in chapter 2, which for Ti02 = 20.7a . From the measured spectra, an approximate value for D of 46$? was obtained. It is, however, most likely that the selvedge between the defect layer and the bulk is not sharp, but that the defect concentration tapers off gradually. This would give rise to a deeper defect layer, of rather less uniform stoichiometry. Thus, the value of 46$? is almost certainly a lower limit, but the layer is probably not as homogeneous as the model implies. In the light of this discussion, it certainly seems reasonable to 147 make the "uniform defects" assumption for the argon bombarded surface. In addition, the depth of the layer on the electron bombarded surface is large enough that the assumption should not introduce significant error, particularly to the simple empirical models employed in this thesis. 4.4 The Effect of Oxygen Deficiency on UPS, ELS and HREELS 4.4.1 The UPS of Defective TiO (110) As discussed in chapter 1, it is well known that oxygen deficiency caused by argon ion bombardment of TiO^ gives rise to donor states in the upper part of the bulk bandgap, which in the stoichiometric 26,30 material is empty . Figure 48 shows He(I) UPS spectra taken during the present work; the upper spectrum (a) shows the clean, stoichiometric surface, whilst the lower (b) shows the surface after argon ion bombardment. The spectra appear very similar to those 26 30 obtained by Hennch and Somorjai (see also discussion in chapter 1). The energy scale for the spectra was calibrated relative to the Fermi energy of the Ta support tray; nearly flat band behaviour was indicated by the fact that the energy separation between the Fermi energy and the valence band edge (which is admittedly difficult to locate accurately) corresponds reasonably well to the bulk bandgap of 139 3.1eV . It was assumed that the Fermi edge of the crystal was pinned by donor states lying close to the bottom of the bandgap. Figure 49 shows a detail of figure 48 (b), from which it can be seen that the feature in the bandgap due to the defects is at exactly 1.0eV. In figure 50, the He{I) UPS spectrum of the surface after electron bombardment is shown; it is clearly very similar to that for the argon ion bombarded surface. In particular, the UPS bandgap feature has the same position, but it does have distinctly lower 148 Figure 48: UPS He(I) of TiC^CllO); (a) nominally defect free and (b) after argon ion bombardment. 149 Figure 49: Detail of spectrum (b) in figure 48, showing exact position of defect states. ES6.XY UPS HeCI) Ti02(1105 electron b ombarded Binding Energy /eV Figure 50: UPS He (I) of electron bombarded TiC^dlO). 150 151 intensity. Since the electron bombarded surface has a lower defect concentration, this indicates a dependence of the number of gap states .3 + upon the number of oxygen vacancies, and thus upon the Ti species. It is interesting to note that surface defect states 1eV below the Fermi energy have been postulated to play an important part in the 140 photoelectrolysis of water in cells with TiO^ oxy9en electrodes 4.4.2 The ELS of Defective Ti02(110) ELS is the term used in this thesis to describe electron energy loss spectroscopy applied in the high beam-energy, low-resolution regime. In the work presented here, an incident beam energy of 500eV has been used, with the unmonochromated electron gun described in o chapter 3 as the beam source. The beam was incident at 45 to the surface. Energy analysis was carried out using the LH EA 10 hemispherical analyser. Although this type of EELS gives a resolution (elastic peak FWHM) of only 0.5eV, its wide range makes it possible to study excitations due to interband transitions, plasmons and states in the bandgap. Figure 51 shows the effect on the TiO (110) ELS of progressive argon ion bombardment. Spectrum (a) was taken from a defect free surface; (b) was taken after bombardment with 0.0015C 2kV argon ions, and (c) after bombardment with 0.006C 2kV argon ions. The crystal surface area was 1cm x 1cm. The growth of an electronic feature in the bandgap, 1.3eV from the elastic maximum, is clearly seen. In figure 52, a similar series of ELS spectra, this time for a 5mm x 10mm surface after electron bombardment by a 5mA/160V beam, is shown. Once more, spectrum (a) is from the surface before bombardment; (b) is after 7.5 minutes bombardment, (c) after 30 minutes and (d) after 60 minutes (note that these correspond to the XPS spectra in figure 46; 152 Energy Loss /eV Figure 51: ELS of TiC^CllO); (a) defect free, (b) and (c) after successive 153 Energy Loss/eV. Figure 52: ELS of TiC^CllO); (a) nominally defect free, (b), (c) and (d) after successive electron bombardments. 154 at the time of taking the ELS spectra in figure 51, the XPS facility was not available). In this case, also, a feature can be seen to grow in the bandgap with progressive oxygen removal, however this time its loss energy is only about 0.8eV. Nonetheless, the general similarity in the form of the spectra in the two figures indicates that there are unlikely to be major electronic differences between the argon bombarded and the electron bombarded surfaces. This is in agreement with the UPS results. In any case, the fact that the loss intensity increases with oxygen removal supports the idea that the excitation can be directly 3 + related to Ti ion concentration. It can also be seen that the intensity of the defect loss is comparable with that of the interband 3 + transition beginning at about 3.1eV, despite the fact that Ti ions are a minority species. This would suggest that the transition giving rise to the excitation is strongly allowed; this question will be given full discussion in section 4.5. It is interesting to compare the present results with those quoted in the literature (briefly mentioned in chapter 1). In studies of 2 6 argon ion bombarded TiO^ surfaces both Henrich and colleagues and . . 30 Somorgai measured loss spectra in the differential mode, and found defect-induced losses at 1.9eV and 1.6eV respectively. Both energies are certainly higher than in the present work, although the discrepancies may at least partly reflect difficulties in measuring loss energies from differential spectra. In studies of similar 29 37 surfaces, Gopel and coworkers * measured broad defect-induced features over the range 0.5-1.5eV. Spectra from surfaces with thermally induced defects showed sharper losses at O.0eV. For this work, they used a monochromatic 20eV electron beam and an HREELS o analyser with a 1 acceptance cone. Since this is comparable with the angular spread of the dipolar lobe for a 1eV excitation probed with a 155 20eV beam, it is possible that the loss structure is strongly influenced by the inability of the analyser to collect the full spread of the inelastically scattered electrons (see section 3.1.1). These considerations were borne in mind in the present work, where it was decided not to use the HREELS apparatus for these high loss-energy studies. 4.4.3 The HREELS of Defective TiO (110) Figure 53 shows HREEL spectra of TiO^MIO), (a) defect free, (b) after 15 minutes and (c) after 30 minutes of electron bombardment as for figure 52. The spectra show that it was not possible to avoid some degradation in the HREELS performance as a result of the electron beam treatment; there is a noticeable reduction in count rates, and some broadening of both the elastic peak and the phonon loss features in spectra (b) and (c). It can be seen that as electron bombardment progresses, the highest energy surface phonon loss peak shows a pronounced downward frequency shift, from 94meV in (a), through 91meV in (b) to 88meV in (c); the same loss peak also suffers an attenuation of intensity. The lower energy peaks are less affected in both of those respects. These effects can also be seen in figure 54, which shows the analogous series of spectra for the argon ion bombarded surface; these correspond to the ELS spectra in figure 51, having had the same amounts of bombardment. However figure 54 distinctly shows the severe degradation of the HREELS due to the extensive surface disruption caused by the argon ion beam; it is really quite difficult to assess accurately the phonon loss energies in these spectra. It is interesting that the present findings appear somewhat at 29 37 variance with the findings of Gopel and colleagues ' , which were 156 0 100 200 300 Energy Loss/meV • Figure 53: HREELS of TiC>2(110); (a) nominally defect free, (b) and (c) after successive electron bombardments. 157 Figure 54: HREELS of TiC>2(110); (a) nominally defect free, (b) and (c) after successive argon ion bombardments. 158 mentioned briefly in chapter 1. They found a concerted downward shift and attenuation of all three phonons as a result of oxygen deficiency, though the shift was only 2meV. It is not easy to explain these results in the light of the present findings. It is believed that the effects of oxygen deficiency on the HREELS of TiO (110) as reported in this thesis can be at least qualitatively explained in quite simple terms. It is already known that modification of surface dielectric properties can lead to pronounced changes in loss spectra; in the case of ZnO, formation of an accumulation layer on the surface leads to the appearance of coupled 141 2-D plasmon/phonon excitations with screening of the phonon modes In view of such observations it is proposed here that the low energy excitation introduced by oxygen vacancies modifies the dielectric behaviour of rutile TiO^ in the vibrational region. We consider the expression: e(ui) = e(«) + e .. (uj) + e.fai) (7) vib d where e . (ui) represents the vibrational oscillator summation in equation (4) and e .(u>) is the new contribution from the defect induced d electronic excitation: ( 8 ) At sufficiently low energies, c^tui) assumes an essentially constant value ^ Q d so that the new background dielectric constant in the vibrational region is increased to a new value e't00) where: e ■ (oo) = e (oo) + 4irgd (9) To confirm that the use of this model was justifiable for the case in hand, the model calculation program "Eelsim" was used to mimic the 159 HREELS spectra of the oxygen-deficient surfaces in figure 53. The program was used just as for modelling the defect-free HREELS, but the background dielectric constant was used as a variable parameter; the resulting spectra are shown in figure 55. From these spectra, model values of the perpendicular loss function (i.e. that determined by c_!_(ui) ) and the loss energies of the surface plasmon peaks were obtained; the results are summarised in figure 56. It is evident that the results of these calculations are in good agreement with the experimental results. In particular, with increasing e{°°) there is a downward shift and weakening of the highest energy loss, which is much less apparent for the lower energy phonon losses. However, as observed in the simulation of the defect free surface (section 4.2.3) the intensities of the loss peaks at higher energies are relatively larger than the experimental equivalent. This can be explained by the same reasoning as was used in section 4.2.3, with the additional observation that since the surface is now rougher, the effect should be even more pronounced. These observed changes in loss energy and intensity can be explained qualitatively as follows. Provided that phonon energies are well separated from each other, the ratio between surface and transverse bulk optical phonon frequencies is given by: e . (> ) + 4 tt d . + 1 3______3 u» . (to) e . ( > ) + 1 ( 10) 3 3 Here the symbol > is taken to indicate a frequency just above that of t h the j phonon mode. If the background dielectric constant is now modified as in equation (7), the new surface phonon frequency w ‘ .(so) is such that: 160 HREELS Ti02C1105 simulations - O . 1OO 0.000 0.100 0.200 O. 30 Ensrgy Loses: / «*V Figure 55: Simulated HREELS of TXO2 CIIO), intended to compare with the series of figure 53; see text for details. ILoss(Arbitrary Units). Eloss^V)- iue5: aito npsto n nest f theandinintensity Variationposition of 56:Figure --- » - mdl nrypoo (S -»!-energymiddlephonon ecie n the text.describedin ofcalculationsTi02(110), asfromtheobtained twolosses inhigher-energyphonon HREELS hgeteeg hnn (s^) energyhighest phonon 2 ) 161 162 l i / c Ul *. ( S 0 ) e .(>) Attq . + Attq . + 1 3____ 3______d ___ _J_ ( 11) U) . {to) G . ( > ) + 1 + WTIQj 3 3 Clearly there is a downward shift in the surface frequency as a result of the defect electronic excitation. The highest frequency mode experiences the biggest shift since it has the smallest initial value of £(>) (= e (“>)). In explaining the effects on intensities, we recall the discussions of section 2.A.5, where it was stated that making use of the function H(u>) = Cg (ui) - 1]/[g (uj) + 1] we find: , , 2 _ f°° Im[n(w)] , n 00 - n o = - - P J ------dui tt o U)- and the total loss intensity is given by: TTe^ g ( 0 ) -1 £ (°°) -1 tot ~ -> g (0)+1 g (»)+1 2fiv, Again with the assumption that the modes are well separated in energy, this total intensity can be broken down into contributions from individual modes: £ . ( > ) + ATTp .-1 £.(>)- 1 _3______3______3______P . ( 14) 3 G . ( > ) + Airg .+ 1 G . ( > ) + 1 3 3 3 Obviously, increasing ej(>) by introduction of defect excitations decreases P^., but again low energy modes are less affected than that of highest energy, since they experience a greater initial value for g . (>) due to screening from the high energy phonons. 163 4.5 Towards an Explanation In section 4.4.3 it has been argued that the effects of surface oxygen vacancies on the HREELS of TiC^ are due to an iteration in the effective background dielectric constant arising from the defect- induced excitation in the TiO^ bandgap. We now turn to a consideration of the specific nature of the excitation, and of the defects which cause it to occur. As will be recalled from chapter 1, this has been a matter of some debate. 4.5.1 The Oscillator Strength of the Excitation A useful indication of the nature of any electronic excitation is its oscillator strength f ., which is a dimensionless index of the d "allowedness" of a transition. For the present case, if we assume that the excitation intensity depends on the Ti3 + concentration, f^ is related to the dipole strength and the dielectric constant by the equations 4 TT Q E mm . , . . w c mu) d o d de (°°) V o d (15) dx 4 2 where N is the concentration of Ti 3d states per unit volume, and in the alternative expression V is the volume of the unit cell. The factor 4 allows for the fact that there are two formula units per unit cell, and that each oxygen vacancy gives rise to two Ti3 + states. Equation (14) has now been applied using the downward shift and attenuation of the highest phonon for seven different values of x (in TiO^ x) where 0 There is a fairly large uncertainty in these estimates, not least 164 due to the difficulty of measuring the phonon frequency shifts accurately; they are probably correct to within 2meV. The assumption that one probes a constant defect concentration over the full penetration range of the Fuchs Kliewer phonons is also questionable (section 4.3.4). For this reason, the above value for f . must d represent a lower limit. Nonetheless, the order of magnitude of this value for f. certainly indicates that the excitation arises from a d strongly allowed transition, confirming the suggestion in section 4.3.2 to this effect. It would thus be implausible to suggest that the defect band is related to a conventional Laporte forbidden d-d 142 transition . The high oscillator strength is instead more typical of intervalence charge-transfer transitions of the sort found in Prussian H 3 Blue 4.5.2 The Nature of the Defect Sites The surface disorder introduced by argon ion, and to a lesser extent by electron bombardment renders it unreasonable to discuss the defects in terms of highly specific atomic arrangements. However it is possible to develop a general picture of the defect structure by combining the present data with previously published information. It will be recalled from chapter 1 that work by a number of research 43-48 teams led to the conclusion that the rutile TiO^ crystal does not tolerate point defects for deviations from stoichiometry greater than -3 x«10 . Such defects are eliminated by the formation of shear planes comprising face-sharing TiOg octahedra; (121) shear planes found at large x eventually order to give the Magneli phases Tin0£n y Although one cannot expect formation of well-defined Magneli phases on the surfaces with which we are concerned, the bombardment processes are likely to provide sufficient energy to make local elimination of point defects kinetically allowed. One can thus envisage a final 165 atomic arrangement where titanium atoms below the selvedge retain six fold coordination by octahedral face-sharing. The energies of defect states are then largely determined by polaronic self-trapping of the "excess’* electrons provided by the vacancy. By means of a simple continuum model, it can be estimated that the Ti 3d defect states should lie E. below the edge of the Ti 3d(t. ) d 3 2g conduction band where e(«) e(0) 2 Here e{«») and e(0) are the high and low frequency dielectric constants, R is the effective radius of the small polaron state and W is the width of the Ti Sdft^) conduction band. Using this equation 139 144 with the values [1/e(<*») - 1/e(0)] = 1.7 , R = 7.4nm and W = 9 1.4eV , the value obtained for E. is 0.7eV. Now, Catlow and d 48 colleagues have calculated that trapping an electron at a shear plane rather than at a regular rutile titanium ion, as presumed in the simple calculation above, further lowers the defect energy by 0.3eV. . 4 + . The Ti ion originally at this site, has, in trapping the electron, .3+ . become a Ti ion, thus coulombically increasing the Ti-0 "bond length". Catlow’s contention is that the bonds at shear-plane sites are more easily polarisable than elsewhere in the lattice, increasing the energetic advantage of trapping at these locations. This gives a defect energy of 1.0eV, which is in perfect agreement with the observation made from the UPS spectra obtained in the present work. Further support for these ideas is obtained from conductivity 28 measurements carried out by Gopel and colleagues . It is a feature of polaronic excitations of the type proposed that activation energy 166 for conduction is not equal to the optical excitation energy. In fact with parabolic potential curves, the activation energy E is related 145 to the optical excitation energy Eq by the equation : (17) where E^ is the difference in trapping energy between shear plane and regular rutile sites. Thus with E = 1.0eV and E. = 0.3eV we have E o t a = 0.36eV, which compares very well with the activation energy for surface conduction of 0.325eV obtained by Gopel. 4.5.3 The Final Model We now have a model where an electron is trapped at a shear plane cation rather than at a regular cation. The electronic loss feature can be associated with an intervalence excitation from a self-trapped . 3 + . . 4 + Ti site to an adjacent Ti site; in energetic terms the excitation . 3 + takes place vertically from the Ti level to the potential energy curve, trapping the electron at the higher energy. This is thus a strongly allowed transition. In this we have correspondence with the estimated value for the oscillator strength, and further justification for the interpretation of the HREELS results as being due to a modification in the background dielectric constant. The relatively high intensity of the bandgap loss feature observed in ELS is also explained. In addition, the feature observed in UPS fits the model precisely, both in terms of energy and of the variation in intensity with defect concentration. 4.5.4 Notes on Previous Work It should be noted in conclusion of this chapter that the results and their interpretations presented here are at variance with 167 theoretical studies carried out by Munnix and Schmeits ' ; the major disagreements will now be discussed. The work of Munnix and 31 32 Schmeits * discussed in chapter 1 reports that band gap states are produced solely by oxygen vacancies in the immediately subsurface ionic plane. Oxygen vacancies elsewhere in the crystal are predicted to produce no gap states, so that the extra electrons necessarily associated with these vacancies would, in their model, be forced into the conduction band. It seems highly unlikely that the defects created in this work could possibly be so localised; in fact the results of section 4.3.4 demonstrate that they extend to at least a depth of 46A. In this situation it is hard to accept that the type of excitation which we propose, and which is well borne out by the results, would restrict itself to a small proportion of the defects. Indeed, if this were the case, one would expect to see saturation in the growth of the UPS band gap feature; this clearly does not occur. In addition, The HREELS data demonstrate that vacancies exert a strong influence on deeply-penetrating Fuchs-Kliewer phonons, which are certainly not localised to the top few lattice layers. The reason for this disagreement is likely to lie in the failure of the Munnix and Schmeits model to incorporate properly the ionic rearrangements accompanying the oxygen deficiency. This includes both elimination of point vacancies through octahedral face sharing and local lengthening of Ti-0 bonds at centres trapping an electron. 168 Chapter 5 - The Adsorption of Water on Ti02(110) 5.1 A Detailed Look at Some Previous Work 5.1.1 Water on Ti02 Previous studies of the adsorption of water on TiC^ were briefly discussed in chapter 1. It was seen that despite this work, conclusive evidence as to the precise nature of the adsorption was still not available. For comparison with the work to be presented 22 below, the results obtained by Henrich and colleagues and by Somorjai and coworkers'*0 merit closer examination here. Henrich and co-workers used UPS He{I) difference spectra to investigate the interaction of water with both argon bombarded and defect-free Ti02. Their spectra were compared with the He(I) UPS spectrum of gaseous water, taking account of possible shifts due to H 6 bonding interactions. Figure 57 shows a UPS spectrum of molecular water; figure 58 shows He(I) spectra from the work of Henrich showing the changes with water adsorption on an argon ion bombarded surface, and figure 59 shows the corresponding difference spectra. Peak positions were quoted relative to the valence band maximum (Ev), which was found to vary slightly with surface condition, but was generally about 3.5eV below the Fermi level (Ep). From defective surfaces at water exposures of less than 30 L, the spectra showed two features, at about 5 and 8eV below Ep (“two-peak” spectra), which were considered to resemble the tt and o bands of the hydroxyl species; it was concluded that adsorption had occurred, and was dissociative. As exposure was increased beyond 30L, the adsorption was thought to become progressively more associative, with a band appearing in the UPS spectrum at about 10.5eV below Ep. This was thought to correspond to the water b^ feature giving a "three-peak" spectrum which was Count Figure 57Figure 146 P fmlclr (gaseous)ofUPS molecular water. 169 An (E) 0 2 y0 2 -4 -2 Ey"0 2 4 6 - 8 10 4 2 0 1 12 14 NTA EEG (eV) ENERGY INITIAL I N I T I A L E N E R G Y ( e V ) 8 6 4 2 - 0 - , E 2 4 - Ti From theet al.; From ofHenrich work : 58Figure UPS He(I) of argon ionUPSHe(I)argon ofbombarded dosage. iue5 : 59Figure Difference spectra correspondingspectraDifference todata 58.raw figureof 2 0 ( 0 1 1 )progressive water with 22 22 170 171 attributed to molecular water. It was expected that the OH o band would overlap the H^O a^, and it was proposed that the "o" feature became a combination peak, also containing H^O a^ intensity. Exposure of the defect-free surface to water always resulted in the "three- peaked" spectrum, and it was inferred that the water had adsorbed on the surface without dissociation. Somorjai and Colleagues also used He(I) UPS difference spectra in their study of the adsorption of water on defect-free, argon-ion bombarded and thermally reconstructed TiO^UOO) surfaces. Spectra from 5 the defect-free surface after exposure to 10 L H^O showed 3 new peaks, at 6.1, 7.8 and 11.2eV below the Fermi edge, shown in figure 60{a). Similar exposure to water of the argon ion bombarded surface also yielded a spectrum with three new peaks, at 4.2, 7.5 and 10.1 eV below the Fermi edge, as in figure 60(c). Finally, the water-dosed thermally reconstructed surface gave rise to a UPS spectrum with four new peaks, at 4.8, 6.3, 7.9 and 10.8eV below Ep; this is illustrated in figure 60(b). In the interpretation of these results, it was proposed that for the spectrum from the defect-free surface the feature at -11.2eV could be aligned with the 1b^ orbital of molecular water, that at - 7.8eV with the 3a^ orbital and that -6.1eV with the 1b^, which was supposed to be slightly shifted by the surface bonding. Thus, water was thought to bond as an intact molecule to the defect-free Ti02(100) surface. There appeared in this work to be some confusion in the assignment of the peaks for water on the oxygen-deficient surfaces. It was finally proposed that on the thermally reconstructed surface, at least part of the water either decomposed or adsorbed to the surface in a manner different from that found on the defect-free surface, whilst it was suggested that the species on the argon ion bombarded 172 •12 -8 -4 Electron Binding Energy, eV (Ep«0) 30 Figure 60 From the work of Somorjai et al.; UPS He(X) difference spectra of water dosage on Ti02 (100). 173 surface was probably not undissociated water, but might be hydroxyl. 22 To summarise, Hennch and colleagues contend that difference spectra showing two peaks in the 0 2p valence band region and no other features signify dissociative adsorption of water, whereas adsorption without dissociation is diagnosed by two peaks in the valence band area plus one peak to higher binding energy. The former situation was seen only for low dosages of water on defective surfaces; the latter was observed for all dosages of water on defect-free surfaces, and for 30 high dosages on oxygen deficient surfaces. Somorjai and coworkers , on the other hand, reported one new feature to higher KE of the valence band on the spectra of all surface types after water exposure; they also found two peaks in the valence band region after dosage of defect- free and argon bombarded surfaces, and three after dosage of a thermally faceted surface. The diagnosis of dissociation of adsorbed water appeared to be based largely on a reduction in energy of the highest KE peak, and on the presence of a feature about 4.5eV below the Fermi level. This was observed for both types of oxygen-deficient surface at the high dosages of water which were used, but more so for the argon bombarded sample. Thus, Henrich and Somorjai have reached slightly different conclusions, in as much as Somorjai suggests that adsorption on defective surfaces is dissociative at high coverages, whilst Henrich feels that dissociation is largely confined to low coverages. Otherwise the proposals of the two groups are remarkably similar, given the differences in their spectroscopic results. In particular, the features reported in the UPS spectra vary both in number and in their relationship to surface condition and coverage. It appears that a fundamental problem has arisen from the way in which He(I) UPS spectroscopy has been used by Henrich and Somorjat- It will be recalled from the discussion in section 2.1.2 that the 174 uppermost 10eV or so of He(I) UPS spectra are dominated by a strong background due to secondary emission, which is very sensitive to sample charging, changes in surface work function and even sample position. Henrich and Lo have both based their work on difference spectra obtained by simply subtracting He(I) UPS spectra of clean surfaces from those of surfaces with adsorbates. Since surface work function usually changes with adsorbate type and coverage, it is clearly probable that the secondary electron intensity will vary in these two cases; thus the difference spectra will show features dependent on secondary intensity as well as those due to adsorbate orbitals. One might also question the methods used to ensure normalisation of the 0 2p peaks between spectra. Henrich appears to have normalised all spectra to the defect-induced feature in the bandgap. It is, however, doubtful whether this feature would remain constant as water adsorption increased. It might be envisaged that some oxidation of the surface could take place, either, by the reaction . 3 + . 4 + 2 — 2Ti + H.0 ----> 2Ti + 0 + H0 2 2 .3 + or by direct reaction of Ti with 0^ contaminant m the H^O, eliminating some defects and reducing the intensity caused by bandgap states. If normalisation did not take this into account, spurious features would arise in the difference spectra, corresponding simply to primary features in the valence band region. It is therefore desirable to interpret such spectra without resort to difference methods, in order to minimise such inconsistencies. 5.1.2 Water on SrTi03 As briefly mentioned in chapter 1, SrTi03 is similar in many respects to TiO^, also being a wide bandgap semiconductor with 175 4 + titanium present as Ti in an octahedral environment. It is useful, like TiO^, for photocatalysis of water decomposition; however in contrast to the situation for TiO^, no applied potential is required for the reaction to take place. Studies to investigate water adsorption on SrTiO^ have been more numerous than for TiO^, and the recent work has been quite equivocal. It is felt that particularly this later material can help to shed light on the problems experienced with TiOg’ w;*-H now ke discussed in some detail, though by no means exhaustively. , „ 50,51,147 Naylor, Egdell and Cox have investigated the adsorption of water on the (100) surface of SrTi03< both defect-free and oxygen deficient, at room temperature and at 150K using HREELS and He(II) UPS. Exposure of oxygen-annealed, stoichiometric SrTi03(100) to more 3 than 10 L H^O at room temperature led to no changes in HREEL or He(II) photoelectron spectra, leading to the conclusion that adsorption did not take place. Water dosage onto this surface was then attempted after cooling the crystal to approximately 150K. At this temperature adsorbate features were clearly seen in the He(II) photoelectron spectra, as shown in figure 61. Figure 61(c) shows the spectrum from an ice mutilayer built up on SrTiO^UOO) at 150K by exposure of the crystal to approximately 70L of water vapour. This spectrum is . . 148,149 similar to spectra of ice reported elsewhere , with three peaks in the spectrum at 8.1eV, 10.1eV and 14.2eV relative to the sample Fermi level, corresponding respectively to the b^, a^ and b^ levels of molecular H20. The separation between the b^ and b2 levels in UPS of free H^O is close to that for the ice multilayer, and in both spectra the separation A(b^ - a^ ) is snaUej- than A (a^ - b2). Figure 61(a) shows the He(11) UPS spectrum of the nominally undosed defect-free surface; on close inspection, two weak features can be seen below the 0 2p valence band. These were considered to arise from 176 Figure 6 1 ^ ^ : UPS He(II) of nominally defect free SrTiC^ClOO), showing adsorption of water at 150K. 177 background contamination, and to be equivalent to those seen at 11.0eV and 13.7eV in the spectrum in figure 61(b), which was taken after 2L exposure to H^O. Subtle changes in the shape of the valence band of figure 61(b) are consistent with a third peak at 7.5eV, equivalent to that seen for the ice-covered surface in 61(c). By comparison with the ice spectrum, this appearance of three adsorbate peaks, two of which lie below the valence band of the substrate oxide, was considered diagnostic of non-dissociative adsorption. In particular, the intensity ratio between a^ and peaks was similar to that for ice, and the separation A(b^ - b^) was close to that for molecular H^O. However, at low H20 exposures, it was found that Atb^ - a^) > A (a 1 - b^), indicating preferential stabilisation of the a^ level. This interpretation of the UPS results is supported by HREEL 51 spectra , where water adsorbed on cold defect-free SrTiO^ gives rise to loss peaks at 454meV, corresponding to the 0-H stretch mode, and at 209meV, due to the H-O-H scissor bend; these values are in reasonable agreement with those for free water. These data and their interpretation are both in general agreement with recent photoemission work on SrTiO^{100)/H20 excited by synchrotron 52-54 radiation, reported by Thornton and coworkers . The contention that non-dissociative adsorption of H20 is signalled by the appearance of two peaks below the 0 2p valence band also accords with experiments on 42 Ti20^(047)/H20 reported by Kurtz and Henrich . However, there is disagreement with the interpretation of the original experiments by 22 Henrich and colleagues on SrTi03(100) , where molecular adsorption (at room temperature) was diagnosed on the basis of a three-peaked He(I) difference spectrum with only one component below the 0 2p valence band. This latter work was carried out at the same time and in the same way as that discussed in section 5.1 178 For their studies of adsorption on oxygen deficient SrTiO^ 51,52,147 surfaces, Naylor and colleagues ' ‘ used argon bombarded surfaces with roughly one oxygen atom missing from every two unit cells. These surfaces were extremely reactive to water vapour at room temperature and saturated for exposures below 5L to give spectra such as that shown in figure 62. Similar spectra have been reported by Webb and 150 Lichtensteiger , who agreed with Naylor et. al. that such spectra with two adsorbate peaks below the oxide valence band were indicative of non-dissociative molecular adsorption. The corresponding HREEL 51 spectra taken by Naylor show an 0-H stretch peak at 450meV; this was thought still to be indicative of complete H^O molecules. The data was not good enough to confirm or deny presence of a scissor bend mode, but isotope exchange experiments with D^O implied that the adsorption was not dissociative. However, the intensity ratio between the two adsorbate features in figure 62 was different from that in figure 61(b), the first peak now having a much higher relative intensity. This led the authors to revise their analysis, and rationalise the data as follows. Hydroxyl groups formed by dissociation of H^O have two electronic levels of tt and o symmetry. The lower-lying o level gives an adsorbate peak at 10.8eV, overlapping the a^ level of molecular H^O. The higher-lying it level overlaps the 0 2p valence band and is thus not evident in raw He(II) spectra. Thus, the appearance of the second adsorbate peak at 13.3eV indicated that some molecular H^O was present on the surface, but its weakness relative to the first adsorbate feature implied the presence of OH species as well. In fact, it was found that the 0H:H 0 ratio was extremely sensitive to details of surface preparation, and upon gently heating the SrTiO^ surface to about 473K under 10 ^ torr of H^O vapour, the second adsorbate peak could be eliminated, indicating complete conversion to 179 Figure 6 2 ^ ^ : UPS He(XX) of argon ion bombarded SrTi0 3 (1 0 0 ) showing adsorption of water at room temperature. 180 dissociated hydroxyl groups (figure 62(c)). For comparison, in their experiments on stepped SrTiO^ (100) prepared by fracturing crystals on 53 UHV, Thornton and coworkers found only dissociative adsorption of H^O at room temperature, with photoemission spectra similar to that in figure 62(c). 5.1.3 Water on Some Other Oxides The adsorption of water on other metal oxides has also received some attention; of particular interest here are studies of related 1 51 oxides, and work using HREELS. Anderson and Davenport have studied water on NiO(111) by HREELS, and report that the interaction is dissociative. A loss feature due to the 0-H stretch mode of adsorbed hydroxyl species was observed at 460meV; this is rather higher than 51 the loss observed by Naylor et. al. for the molecular adsorption of 152 water on SrTiO^, as discussed above. Egdell and coworkers have used HREELS to study the interaction of water with the (100) surface of the tungsten bronze Na^ ^WO^. though only on ordered surfaces at low temperature (150K). It was found that adsorption would not take place at room temperature on the stoichiometric surface, and attempts to study defective surfaces were not reported. Due to the relatively small intensity of phonon losses on this material, the authors were able to observe all the expected water vibration modes; in addition to a stretching mode loss at 445meV, a bending mode at 215meV and a M-OH^ mode at 75meV were found. Thus it was possible to decisively conclude that the water did not dissociate on adsorption, and that the bonding to the surface was between the oxygen atom in the water molecule and a surface tungsten cation. 153 Almy and colleagues have investigated water on Al^O^ by UPS , but without clear-cut results, it being difficult to completely dehydrate 181 1 54 the alumina sample. Henrich and Kurtz have used UPS to look at 42 water chemisorption on the lower titanium oxide Ti^t^ , and the 154 structurally related . On defect-free cleaved water adsorption was rapid, but not dissociative. Adsorption on argon bombarded Ti^0^(047) was also quite rapid, but was found to be dissociative, at any rate for low coverages. As with the studies by this group on TiO^ (see section 5.1.1), UPS was analysed by means of difference spectra. However, peak positions were double-checked by use of He(11) spectra, which, as discussed in previous sections, are likely to prove more reliable than He(I). This led Henrich and Kurtz 50,51,147 to agree with Naylor and colleagues , Thornton and coworkers 52-54 150 and Liechtensteiger in saying that one peak below the 0 2p valence band is diagnostic of dissociative adsorption, whereas two peaks in this area implies the presence of molecular water (see section 5.1.2). On adsorption was found to be dissociative on both the cleaved and the defective surfaces; however the uptake of water appears to be at least as rapid as for Ti^^, with saturation being reached at exposures of less than 0.5L. Henrich has also 40 reported a UPS study of water on the corundum oxide a-Fe^O^(001), in which it was found that the surface was much less active for chemisorption than either Ti203(047 ) or V203 ( 047 ), with dosages of at 5 least 10 L H^O being required for observable features to arise in UPS. However the adsorption was deduced to be dissociative, with some molecular species observed at the very highest coverages. 5.2 Some Experimental Aspects The work in this chapter was carried out on two different TiO^ crystals; the first was that described in chapter 4, the second was an identical sample from the same suppliers. Facilities were not available to confirm absolutely the orientation of the second crystal, 182 but its appearance and spectroscopic behaviour were exactly as for the first. It was not considered that the experiments carried out in this section were critically dependent on precise crystal orientation. Both samples were given the same preparative treatments as described in chapters 3 and 4. Surface oxygen vacancies were created by either argon ion or electron bombardment, by the processes described in chapter 4; it will be made clear in the text which method was used for each spectrum. 5.2.1 Water Dosage Water dosage was carried out by admission of water vapour to the sample chamber to a measured partial pressure, for a measured length of time. The water was supplied to the gas-handling line from a small glass vial; it had previously been doubly distilled and deionised, then degassed by several freeze-pump-thaw cycles. Mass spectroscopy using the VG Masstorr revealed no significant contaminants. The water vapour was admitted to the chamber via a finely adjustable, bakeable leak valve. Exposure of the crystal to -6 the vapour was measured in Langmuirs, where 1L = 1 second at 10 4 torr. When the dosages were as high as 10 L or more, they were difficult to quantify to much better than an order of magnitude, since pumping was rather slow, leaving a relatively high residual background vapour pressure. However, at this stage the surface had generally reached saturation coverage, so that contamination was unlikely to be significant. 5.2.2 Sample Mounting and Attempts to Cool the Surface For room temperature experiments, the samples were mounted as the sample in chapter 4. By means of the second mounting assembly 183 described in section 3.7.2, attempts were made to cool the crystal, so that water could be adsorbed at temperatures below 200K. In fact, despite many attempts, the lowest temperature reached, as measured by the chromel/alumel thermocouple, was 200K. After exposure of the 5 sample to 10 L H^O at this temperature, a He(II) UPS spectrum of the Ta mounting plate showed a characteristic ice pattern, similar to that in figure 61(a). However no adsorbate peaks whatsoever were seen on corresponding spectra of the defect-free TiO^ sur^ace- Attempts to adsorb water on defective cold surfaces yielded spectra identical to those obtained for the same surfaces at room temperature (see section 5.3.1). It was concluded that the thermal conductivity of the sample was only just too poor to allow the surface to cool sufficiently for ice formation or even, in the case of the defect-free surface, for 53 adsorption. Indeed for comparison, Thornton and co-workers report that for adsorption on defect-free SrTi03, temperatures below 200K are necessary. A variety of modifications to the mount were tested, especially attempts to improve thermal conductivity at the sapphire/copper and copper/tantalum/TiO^ junctions, but no improvement was achieved. The idea of sandwiching a soft conductor, such as indium, between the sample and the tantalum plate was dismissed for fear of heavy sample or chamber contamination should the material evaporate during the cleaning process. Thus, attempts to study water adsorption on TiO^ at low temperatures were unsuccessful in the present study, and all the results presented below are from experiments carried out at room o temperature, 20 C. It would be of great interest to attempt more low temperature studies under different circumstances; in particular it is possible that a thinner TiO^ crystal, say less than 1mm, would make this feasible. Alternatively, an assembly with a shorter sample 184 manipulator and/or a smaller distance between the end of the manipulator and the sample itself might prove effective. 5.3 UPS of Water on TiOgMIO) 5.3.1 The Spectra Obtained Defect-free TiO^UIO) surfaces after exposure at room temperature 5 to up to 10 L of water vapour yielded UPS He(II) spectra which were not significantly different from those of surfaces known to be clean. In particular there were no features in the spectra below the 0 2p valence band which could be attributed to adsorbates; there was no evidence for the presence of either water or hydroxyl species on the surface. He(I) spectra differed only in the region dominated by secondary intensity; in particular any variation of this type was highly inconsistent from experiment to experiment, and was thus not considered to give useful information. Figure 63 shows He(II) UPS spectra of the TiO^MlO) surface after mild electron bombardment, producing a surface stoichiometry of roughly TiO^ gl (a) is from the clean surface, whereas (b) is from the 3 surface after dosage with 10 L water vapour. In spectrum (b), a small but distinct feature can be seen at 10.8eV below the Fermi level. The intensity of this feature was not increased by further dosage, so saturation of the surface was assumed. In figure 64, the corresponding He(I) UPS spectra are illustrated; (a) once more shows the clean surface, and (b) the surface after dosage with water. The chief difference between these spectra is the variation in the secondary electron region; this variation was also highly inconsistent between experiments, as found for the defect-free surface. As discussed previously, this could have a number of causes. It is thus not 15 Binding Energy/eV Figure 63: UPS He(II) of electron bombarded TiC^CllO) (a) before and (b) after 185 exposure to 10^L 1^0 at 293K. 186 Figure 64; UPS He Cl) of electron bombarded TiC^CllO); (a) before and (b) after exposure to 10^L H^O, at 293K, 187 possible to say whether there are any differences in the He{I) spectrum due to the presence of adsorbate band structure features. Figure 65 is analogous to figure 63, but in this case the sample has been argon ion bombarded, to give a stoichiometry of approximately TiO, Here, (a) is once more the spectrum from the clean surface; 1.75 4 spectrum (b) is from the surface following a 6 x 10 L exposure to water vapour. Greater exposures did not appear to alter the spectrum further, so this was taken to represent saturation coverage. Once more, the spectrum from the water-dosed sample shows a single new peak at 10.8eV below the Fermi level. The corresponding He(I) spectra were as uninformative as those presented in figure 64, and it was not considered worthwhile to include them here. 5.3.2 A Discussion of the Results The observation of a single adsorbate peak below the 0 2p valence band in the spectra 63(b) and 65(b) suggests strongly that adsorption of water on defective TiOg(110) is exclusively dissociative, both for electron and argon ion bombarded surfaces. The position of the observed peak corresponds exactly to the observation by Naylor et. 147 al. of a hydroxyl o band at 1O.0eV for the dissociative adsorption of water on SrTi03 (see section 5.1.3). Moreover, there is no sign of any feature in the vicinity of 13.5eV, which might have been due to the b^ band of molecular water. The present spectra are in fact in general agreement with those of both Hennch and colleagues 22 30 and of Somor^ai and coworkers , in that the previous authors also observed only one adsorbate peak below the 0 2p valence band. As we have seen, both were led to postulate non-dissociative adsorption on the basis of He(I) difference spectra containing two or more additional adsorbate features in the 0 2p valence band region. However, by consideration of the nature of He(I) difference spectra Figure 65: UPS He(II) of argon ion bombarded TiC>2(110); (a) before and (b) after exposure to 6 x lO^L H^O, at 293K. 188 189 (see section 5.1.1), and in the light of the results of the recent 50-54,147,150 SrTiO^ studies discussed m section 5.1.2, the present interpretation appears much more plausible. It is felt that the extra 22 30 features observed by Henrich and Somorjai in the valence band region were probably artefacts arising from unsuccesful normalisation of the 0 2p valence band. This opinion is reinforced by the fact that the two groups each report different features in this part of the spectrum, despite the fact that their raw data are similar. In addition, the method of alignment of adsorbate peaks in the UPS with corresponding band structure in the gas-phase water spectrum, as . .30 22 carried out by Somorgai and Henrich , seems somewhat arbitrary. 147 51-53 Naylor and colleagues and Thornton et. al. have used solid state ice spectra to determine the positions of the relevant water orbitals. An additional observation from the UPS spectra presented here is that although both the electron bombarded and the argon ion bombarded surfaces were dosed with water to saturation, the intensity of the adsorbate-derived peak in figure 64 is significantly greater than that in figure 63. Since the chief difference between the two surfaces is the defect concentration, it seems reasonable to suggest that the ability of the surface to adsorb water in this way is dependent on the number of oxygen vacancies present. Such a dependence is indeed much as would be expected, considering that only the defective surface appears capable of room-temperature adsorption at all. Because only two different defect concentrations have been used here, it is not possible to propose a specific defect/adsorbate relationship on the basis of this work alone; it would be interesting to carry out further research in this direction. The present UPS spectra thus lead to the contention that water does 190 not adsorb on defect-free TiO (110); it does, however, adsorb on the defective TiO (110) surface. The adsorption is dissociative, with the water molecules being split into 0-H and H species, and is dependent upon the concentration of surface vacancies. 5.4 HREELS of Water on TiO (110) As has been discussed in chapter 1, a major objective in the present study of TiO^ (11°) was to obtain HREEL spectra from water adsorbed on this surface. This proved less easy in practice than had been anticipated. The major difficulties experienced were largely due to the following factors. As discussed in foregoing chapters, HREELS of oxide surfaces is dominated by a strong background of intrinsic surface phonon excitation; these both obscure low energy adsorbate peaks and take a significant proportion of intensity out of the elastic peak. This makes the study of even high energy 0-H stretching vibrations intrinsically less easy than on a metal surface. In addition, defective TiO^ surfaces have a strong electronic loss structure extending up from the elastic peak to a maximum at about 1eV. This is the loss that was observed in the ELS spectra of defective TiO^ in section 4.4.2, and provides a strong background in the region of the 0-H stretch, where intensity due to phonon losses has almost disappeared. Finally, the defects created in the surface by the present methods, even by electron bombardment, smear out the spectrum over a wide angular range, resulting in rather poor signal to noise; this was also commented upon in section 4.4.3. Despite these difficulties, it was possible to carry out the required experiments. From the known frequency of the 0-H stretch in water and other hydroxyl species, it was expected that any loss 191 feature due to this mode would be observed between 445 and 465meV. The HREEL spectrum of the defect-free TiO (110) surface after room o 5 temperature (20 C) dosing with up to 10 L of water vapour showed no signal at all in this region. This implied that no water or water- derived species had adsorbed on the surface, in accord with the UPS results reported above. The surface was then subjected to mild electron bombardment, giving a surface stoichiometry of approximately 4 TiO^ , and dosed with 10 L of water vapour. Figure 66 shows the HREEL spectrum obtained, (a) before and (b) after dosage. In (b) we can see a small peak due to water adsorption at 458 ± 2meV. The signal to noise for the adsorbate peak is rather poor, as the peak height is only of the order of 1cps above the background count rate of 5cps, however the comparison with the undosed spectrum shows clearly that the feature is more than an artefact. Moreover, the spectrum was repeated on a number of occasions, with consistent appearance of the peak at the same position. 155 151 The adsorption of water on both Si(100) and NiO(111) (see section 5.1.3) is known to be dissociative. For these systems, loss energies of 459meV and 460meV respectively are observed, very close to our value for water on TiO^UIO). By contrast, in HREELS experiments on the H^O/ SrTiO^ system at 150K, the non-hydrogen-bonded 0-H stretch 51 due to molecular water was found at the lower energy of 454 ± 2meV , and HREELS of molecular water on tungsten bronze at 150K showed an 0-H 152 stretch loss at 445meV (see section 5.1.2). The first of these two energies is very close to the symmetric stretch energy of free HgO at 453meV. On the basis of comparison with these four systems, it would seem that the present data are best rationalised in terms of dissociative adsorption to give surface hydroxyl groups. It is realised that the accuracy in the determination of the position of the 0-H loss peak is not particularly good compared with the expected Energy Loss/meV 192 Figure 66: HREELS of electron bombarded TiC^CllO); (a) before and (b) after exposure to water. Spectroscopic conditions as for figure 41. 193 energy difference between the frequencies for molecular H^O and free hydroxyl. Thus, the HREELS evidence should perhaps not be regarded as decisive in itself. However it does support the results of the UPS study presented in section 5.3, and this leads the author to the conclusion that the present interpretation of the data as implying dissociative adsorption is correct. It would be interesting to continue this line of research by use of isotope exchange techniques, 51 as has been done by Naylor and colleagues for water on SrTiO^. 194 Chapter 6 - The (110) Surface of Rutile Sn02 As we have seen in chapter 1, SnO^ is a wide-bandgap 1 8 semiconductor with applications in high-efficiency solar cells , gas 56 57 55 monitoring ' and oxidation catalysis . In all these cases, surface properties are of prime importance, yet there have been few studies of Sn02 by contemporary surface science techniques. For the present work, two single crystals of SnO^ were available, courtesy of Professor R. Helbig; it has thus been possible to carry out a study of the influence of electron and ion bombardment on the surface stoichiometry and electronic structure of SnO (110). We have now seen from the results presented in chapter 4 that oxygen vacancies created by argon ion bombardment in TiO^ produce new states in the upper part of the bulk bandgap, whereas work by 7 6 Flavell has shown that similar vacancies in SnO^ result in states towards the bottom of the bandgap. Surface conductivity measurements ’ indicate that these surface defects on SnO^ do not act as donor states, in contrast both with bulk oxygen deficiency and with sputtered TiO^ surfaces. It has also been shown in the present work that bombardment with 160eV electrons provides a more controllable method for introduction of oxygen vacancies into the TiO^ surface. 69-71 It is already known that by appropriate n-type doping, for example with Sb, carriers may be introduced into the SnO^ conduction band, with metallic behaviour developing at carrier concentrations above 19 -3 10 cm . The work in this chapter investigates the possibility of using electron bombardment to induce "doping” of SnO^MIO) surfaces by controlled creation of oxygen vacancies. 6.1 Sample Preparation 195 The samples used in this study and their mounting and preliminary treatment were described in section 3.7.1. Sample cleanliness and stoichiometry were assesed by XPS; the former as for the TiO^ crystal (section 4.1.4), the latter using relative core-peak intensities to establish 0:Sn ratios, as will be described below. Cleanliness was attained by 2kV / 10pA argon ion bombardment for up to 15 minutes at a time, much as for the TiC^ sample. Stoichiometry was restored by _ 5 resistive heating at 700*C in a 1 x 10 mbar ambient atmosphere of 0^ for 2-3 hours; this was rather more than was required by the Ti02 crystal. 2 + 4 + As we have seen (chapter 1), the 3d core peaks for Sn and Sn 62 are virtually coincident . Thus in order to assess the stoichiometry of the surface it was not possible to rely upon the method used for TiO^ described in section 4.1.2. Instead it was necessary to determine accurately the intensity ratios of 0 1s and Sn 3d core peaks. Using the program "Stripper" (Appendix D), XPS spectra were stripped of inelastic background and satellite intensity ensuring that all measured intensity was due only to the relevant core-peak excitation. The computer was then used to integrate the 0 1s region and the Sn 3 d ^ 2 region of the stripped spectra, by means of a simple integration algorithm. For this purpose, the 3d3y2 Portion of the Sn 3d doublet was chosen because of its greater freedom from overlap with extraneous features. The surface was considered to have reached stoichiometry when repeated annealing in 0^ made no further difference to the 01s:Sn 3 d ^ 2 ratio. In addition, at this stage the EELS of the surface showed well defined loss structure with no features in the bandgap. It was found for both crystals that a stoichiometric SnO^ surface corresponded to a 0 1s:Sn 3d3/2 ratio of 0.30 (± 0.02). 196 6.2 Oxygen Loss and the Desorption Cross-section Creation of oxygen vacancies in the SnO^ samples was carried out by argon ion bombardment and by electron bombardment. Both these techniques were used in precisely the same way as for TiO^. and are described in detail in section 4.3. Oxygen loss was quantified by measuring the ratio 0 1s:Sn 3d3/2 ' the same waV as f°r assesment of surface stoichiometry described in section 6.1. 6.2.1 Oxygen Loss by Argon Ion Bombardment Bombardment of stoichiometric SnO (110) surfaces with 2kV argon ions for 5 minutes or more consistently resulted in an 0 1s:Sn 3 d ^ 2 ratio of about 0.15, corresponding to a surface composition of approximately SnO. It was difficult to produce argon ion bombarded surfaces of intermediate stoichiometry, indicating a high oxygen desorption cross-section under these conditions. It was, however, not found to be possible to remove more than half the surface oxygen by this method, even by prolonged bombardment. The chemical shifts of the Sn 3d core-peaks were unchanged by the ion bombardment, and no new XPS features were observed. Figure 67 shows the MgKa XPS of SnO (110), (a) from the stoichiometric surface and (b) after 5 minutes bombardment by 2kV argon-ions. The ion current was 10pA onto a 2 0.16cm face, and the stoichiometry reached was approximately SnO^ . We have seen that comparative XPS studies of the surfaces of SnO^ 62 and SnO have shown that the Sn 3d core-peaks in these materials have very similar chemical shifts. This is explained by consideration of differing coordination environments in the two oxides, and by 4 + comparison with previous work on PbO. The Sn ions in Sn02 occupy distorted octahedral 6-coordinate sites, whereas the tetragonal form of SnO is isostructural with PbO, having cations occupying sites with 197 Figure 67; XPS MgKa of Sn0 2 (1 1 0 ); (a) stoichiometric, (b) after argon ion bombardment. 198 only 4 nearest oxygen neighbours. This is apparently due to the 2 + 156 stereochemical influence of the Sn lone pair . The difference in site potential between the two oxides appears to exactly compensate for the chemical shift which would be expected for ions in differing oxidation states. Detailed calculations for the related materials PbO 1 57 and PbO^ demonstrate clearly that such compensation is possible It seems reasonable, therefore, to expect that a surface with both SnO-like Sn(II) and Sn(IV) present should produce overlapping Sn 3d XPS core-peaks. In the light of this, and by consideration of the + spectra in figure 67, it appears that Ar bombardment results in the reduction of tin species exclusively to Sn(II). 6.2.2 Oxygen Loss by Electron Bombardment Electron bombardment of the surface also caused loss of oxygen. However in this case, oxygen loss was accompanied by the growth of new XPS core-peaks 1.92eV lower in binding energy than the original Sn 3d features. Smaller, broader features appeared below the new core peaks, becoming correspondingly stronger as oxygen loss progressed; this is clearly seen in figure 68, where the 0.16cm 2 surface has been irradiated with a 160V/10mA electron beam for 1152 minutes. The energy separation between the new core feature and the higher energy satellite is 14.5 ± 0.5 eV. This corresponds well to the plasmon 158 energy of metallic tin , and it seems reasonable to interpret the new core peaks as being due to Sn(0) 3d photoelectrons, the smaller features being due to energy loss peaks associated with the excitation of tin metal plasmons. The observation of the plasmon loss peaks in XPS establishes that the tin metal resulting from the reduction of SnO^ must be present in well-defined droplets large enough to sustain the characteristic 199 200 plasmon modes of bulk tin; isolated tin interstitials would not support the plasmon mode. Moreover, the fact that the loss peak appears 14.5eV below the new core feature, but only about 12.5eV below the original SnO^ peak establishes that the dominant excitation of the plasmon mode must be synchronous with the creation of the core hole. If the plasmon mode arose from sequential inelastic scattering by the metallic tin, one would expect to see the satellite move in position as the dominant spectral weight in the Sn 3d peaks shifts from the Sn(IV) to the Sn(0) component. Experimentally, such a shift is not found. Oxygen loss was measured as for the argon bombarded surfaces, taking into account the complete Sn 3d^£ core structure. The desorption was more gradual and controllable than under ion irradiation, and it was possible to observe the variation in oxygen loss with irradiation time. The desorption rate was directly proportional to the electron beam current, and thus data from several runs at different beam currents could be normalised onto the same plot. 13 6 Using the relationship In ([2 - x] / 2) = - (o -20 2 value for o for SnO^ as well. This was found to be 2.8 x 10 cm , and remains constant until a surface stoichiometry of about SnO is reached. Therafter the cross-section falls off steeply in an apparently non-linear manner. However, in contrast to the situation found for ion-bombarded surfaces, oxygen desorption definitely continues at least to a stoichiometry of "Sn^O”. The situation is illustrated in figure 69, which is a plot of ln([2-x]/2) versus bombardment time. It will be recalled that the value of o obtained for TiO^ was 3 x 201 Electron Irradiation/mA-mins. Figure 69: The logarithmic decay of surface oxygen content in SnC^CllO) with duration of electron bombardments. 202 -21 2 137 10 cm , and that Ballard and Williams reported cross-sections of -20 2 around 10 cm for desorption of oxygen from the adsorption phase on W (110). Thus the value of o which we have found for Sn02 is in of the correct order. It seems reasonable to postulate that the dominant mechanism for oxygen desorption is the same as that suggested for Ti02, involving the interatomic Auger decay of the outermost metal core-hole states (see section 4.3.1). In this model the overall desorption cross section depends, as we have seen, both on the initial cross section for creation of a metal core-hole, and upon the probability that this core-hole decays by the inter-atomic Auger process. It is thus interesting to note that in general, the probability of inter-atomic Auger decay increases with covalency. In this light, the present findings are somewhat surprising, since it has been suggested that Sn02 is more ionic than Ti02 ' * It is also noticeable that whereas the desorption cross section in TiC^ fell off .3 + as Ti was formed and electrons became available for intra-atomic auger decay, this does not occur in the case of Sn02 until a surface Sn:0 ratio of approximately 1 is attained. These differences may reflect the fact that the reduction of TiO^ takes place within a single phase of variable stoichiometry Ti0,_ ., whereas SnO„ separates into two distinct phases, Sn02 and Sn, upon decomposition. In figure 70, the left-hand box shows XPS spectra of SnO^MIO), (a) from the stoichiometric surface and (b), (c) and (d) after 2 irradiation by a 10mA/160V electron beam onto a 0.16cm crystal face for 27, 192 and 1152 minutes. The stoichiometries of the surface in the last three spectra are approximately SnO. _, SnO_ _ and SnO_ . 1 . i U . b U . * respectively. However, from a consideration of the contribution of the Sn(0) peak to the overall Sn 3 d ^ 2 intensity along with the Sn 3d3/2 ^° 1s ratio, it is apparent that the growth of the Sn(0) peak is too 203 (a) f : (b) t : f : Y 7 L (A. o (c) f : f : j z z l v. (d) F JZZ]__ \Z\ 0 Sn‘* Sn2* Sn° Figure 70: LEFT: XPS MgKa of Sn0 2 (H 0 ); (a) stoichiometric; (b), (c), (d) after successive electron bombardments. RIGHT: Corresponding relative surface concentrations of the species Sn(XV), Sn(ll) and Sn(Q). 204 small to account for the total oxygen loss. It is therefore proposed that in addition to metallic Sn(0), electron bombardment generates a significant concentration of SnO-like Sn(II), whose core level peaks overlap those of the original SnO^. With this assumption, and by representing the Sn 3 d ^ 2 region as a sum of two overlapping gaussians, the Sn 3 d ^ 2 / 0 1s intensity ratio and the ratio of S n (0) / CSn(II) + Sn(IV)] peaks were used to calculate relative concentrations of Sn(IV), S n(II) and S n (0) at each stage of electron irradiation. This was carried out using the program "Fitter” and a modified version of "Stripper" (Appendices D and E) in much the same . 3 + . 4 + way as the separation of the Ti and Ti peaks described in section 4.1.2. The calculated surface concentrations are shown in the right-hand box of figure 70. alongside the corresponding XPS spectra. It will be seen that the concentration of SnIII) grows to a maximum after about 190 minutes irradiation, and thereafter declines. This behaviour is consistent with a mechanistic scheme of the sort: SnO ------> SnO ------> Sn 2 where the decomposition of Sn02 and SnO are characterised by different cross-sections. However the scatter in the data obtained was too large for the extraction of values for the individual cross-sections. In addition, the situation depicted above may be further complicated by the thermal disproportionation of SnO under heating by the electron beam: 2 SnO ------> Sn + Sn02 It is also likely that diffusion of oxygen from the bulk will occur, compensating in some measure for the oxygen desorption at the surface. 205 6.2.3 ELS of the Defective Surface High energy, low resolution electron energy loss spectra (ELS) of the surface were taken at most stages of the experimentation. A selection of these are presented in figure 71. The spectra were o measured in specular mode with a 500eV electron beam incident at 45 to the surface, and a pass energy of 5eV. 71(a) is from the stoichiometric surface, (b), (c) and (d) after irradiation by 2 10mA/160V electrons onto a 0.16cm crystal face for 10, 27 and 192 minutes (x in SnO^ = 0.6, 0.8 and 1.4) respectively, and (e) after 5 minutes bombardment by 2kV argon-ions (10pA onto a 0.16cm 2 crystal face, x = 0.8). As has already been mentioned, the defect-free surface gave rise to a well defined spectrum with a clear band-gap of 0 3.6eV, corresponding well to values quoted in the literature . After very slight electron bombardment, losses began to grow in the bandgap; these were approximately 1.4eV below the elastic peak, but were not particularly sharp. As electron bombardment time increased, the bandgap feature grew slightly, and became broader. Eventually, the electron irradiated surface yielded an EL spectrum fairly similar to that of the argon ion bombarded surface; generally broad and ill defined. Surprisingly, no distinct feature emerged in the 14eV region, where one might expect to see a loss peak due to the excitation of the Sn metal plasmon. This observation adds support to the idea that the dominant mechanism for plasmon excitation in XPS is intrinsic, i.e. the Sn(0) photoelectrons probe local excitations of the Sn in which they originate. By contrast, in ELS we measure the excitation spectrum of the Sn droplets plus the oxide matrix, and the well-defined Sn plasmon becomes lost in a background of oxide excitations. Energy Loss /eV Figure 71: ELS of Sn02 (110); (a) stoichiometric, (b), (c) and (d) after successive electron bombardments and (e) after argon ion bombardment. 207 The loss feature at 1.4eV may be tentatively assigned to a plasmon loss of SnO^ which becomes degenerately n-type due to oxygen deficiency. If we use the following expression for the dielectric function e (ui) ; 2 * 2 c(ui) = e(®») - ( ne / m e ui ) o * where n is the concentration of carriers, each of effective mass m and dynamic charge e, e(~) is the high frequency dielectric constant and is the permittivity of free space, we may calculate a carrier * concentration for the bombarded surface. Ass uming an effective mass m 1 59 = 0.30m for conduction electrons in Sn0o, and a background e 2 160 dielectric constant e(») of about 3.9 , we find that n ** 1.6 x 21 -3 . 10 cm is required to produce a plasmon at 1.4eV. This corresponds a surface composition of SnO^ , if each oxyge n vacancy is singly ionised. The highest carrier concentration in SnO^ achieved by 20 -3161 conventional chemical doping is n ^ 7 x 10 cm . However by use . _ 21 -3 . of the present electron bombardment n ^ 1.5 x 10 cm is not achieved without concommittant decomposition of the oxide to generate a distinct Sn metal phase. Thus electron beam irradiation of SnO^ does not provide us with a clean method of prepari ng degenerately doped n- type surface layers. 208 Appendix A - Classical Theory of Dipole Electron Scattering This appendix is largely pieced together from the work of 1 n1 o o inn 9798 Peplinskii , Flavell , Cox and Mills * , with the addition of further steps where the author has felt it necessary, particularly in the solution of the Poisson Equation. It is to be hoped that the derivation serves the purpose of increasing the reader's understanding of electrostatically induced electron energy loss events. It should be borne in mind that this derivation deals only with the situation where motion of the incident electron parallel to the surface is neglected, and further that probabilities and intensities for inelastic scattering are treated as relative to those for elastic scattering, rather than absolute. If an electron approaches the surface vertically, and we let t=0 be the time of impact with the surface, then if we neglect motion parallel to the surface, the position of the electron is given by: z = v|t| (1) where z describes the axis normal to the surface. If the vibration giving rise to the oscillation of the surface dipole has angular frequency uj and two-dimensional wavevector Qn in the plane of the surface, then the work done on the electron by the induced field is: W = - J°° 2irQ„ dQn J°° “Hui P(Ql|fui) duj (2) o II 11 o II where P(Q^,ui) is the probability of the electron losing energy tiui to an excitation with wavevector . If the velocity of the electron can be assumed to remain constant, we can regard its position and thus the interactive charge density as a 6 function: p = e 6(r„) 6(z - v|t|) (3) 209 where is a two-dimensional vector describing the plane of the surface. The potential tp(r^,z,t) must satisfy Poisson's equation both inside the surface (z<0) and outside (z>0) the surface. We have: V2ip(r(| ,z, t) = 4ire(rg,z,t) = 4ire 6 (r ^) 6(z - v|t|) (4) for z>0 and 72ip(r|Ifz,t) = 0 (5) for z<0 We also have the following boundary conditions: (i) ip -----> 0 as z -----> ± 00 (ii) {z> 0 ) = c (uj,Q|| )Ez(z<0) (iii) E „(z>0) = E „(z<0) r II r II Where E = - Vtp is the electric field, and e(tu,Q^) is the dielectric function of the material, and depends both on w and on . It would be preferable to solve the Poisson equation in terms of and u) rather than r^ and t, and it is convenient to use Fourier transforms to move between the two systems. The general Fourier equations are: (a) f(x) = Jg(a) e da oo -*n vi (b) g(a) = (1 /2tt) f(x) e dx Hence, with a potential of the form and collecting together, we obtain: -3 .00 .00 i (q .p -uit) ip(r..,z,t) = (2tt) J dQ J du) e II II tp(Q ,z,u>) ( 6 ) -00 -00 Due to the nature of the Fourier Transform of a delta function, . 00 i Q r* 5 (r II) = J e II II dQ. (7) It is a standard result that 6(ax) = (1/a) 5 1x) hence we can write 6(z - v|t|) = (1/v) 6[(z/v) - |t|] and along the same lines as equation (7), we have 1 tr/z , u n 1 r 00 -iwt. i(z/v)w -i(z/v)u). - 6[(-) - t ] = - J e [e + e ] dm ( 8 ) y y ' 1 V -00 which only has a value when (z/v)-t = 1 or -(z/v)-t = 1 Now, . i(z/v)m -ilz/viw. -nut z U) [e + e ] = e - cos -z v v Thus from equations (6), (7) and (8), we can write: / „ .-3r «> r °° z u) 1 (CL . r„-uit) g(rM,z,t) = (2tt) j dQ ..J dui - cos -z e II II II -«o lr-co v v (9) Now equation (4) becomes V(2tt)"3 J °°dQM J °° duj el(QirrirU,t)(p(Q z.iu) = —00 11 —00 11 14ire> { 2tt) 3J °°dQM J °°dui - cos -z e^ ^ °II ’r II -00 || -00 \/ ( 10) However if the Fourier transforms of two functions are equal, then the functions themselves must be equal, so we can write: 211 w 2 fA . i(Q. .r-uit) , z uj i(Q r-uit) V tp (Q „. z, ui) e I 4ire - cos-z e (11) v v Now 7 is only in dimensions of space, and we can ignore references to time or frequency in this respect. Thus: J l i(Q„ .r..-u)t) 9 r i i(Q„ .rn-ujt). Y tp (Q , z ) e II II — [ip(Q ,z)e II II ] + dr f " — ^Ccp(Q z)el(Qll *rll_U,t>] (12) 9z2 “ 9 \ i(Q„ . r,.-u)t) _ 2 . i (Q„. r..-u)t) — 2 tp (Q (|, z) e II II - 0 (| tp (Q||. z) e II II (13) d z Thus, equation (11) becomes; UJ 7 ~ 2ipl0 || .z.iu! On2 As can be verified by substitution, a general solution of this equation is: . -Q„z Q„z 8ire uj ip(Ql|(z,ui) = ae II + ce II ---~------— cos-z (15) ..2 v via,, * [j] ) Also, 2tp (Q||, z,ui) - Qjjip (Gy , z ,uj ) = 0 ( 16 ) for z<0 for which the general solution is: 212 ip(QM,z,u)) = be^ll2 + de % Z (17) We shall need two further results in order to solve these differential equations fully. The first is simply that: Ez (QII,z ,uj) = (18) - si «,tQr z 'u,) Next, we need to find E , and we start with UII Erll(rll-2 -t) = ‘ drlllptrll •z *t> Fourier transformation gives: 20 eqiitQii•z'u>) = O l0||-r » Vutr|-Z 't) d r |. ( ) Integrating by parts: = - [eiQll’rll tp (r „ , z, t) ] °°+ iQn J °° eiQH'rll ip(rn,z,t) II -o° II II and tp (r ^ , z , t) = 0 at both limits, hence: EQ|( (Q|( .z .uj) = iQ ip(Q ,z,iul ( 21) Now we recall the boundary conditions described above; from (i) and equation (15), we can see that c=0, giving: -Q..z 8ire U) Q„z 8ire . w E aQ„e sin-z (23) z 2 id 2 v v(Q„ + [-] ) II v 213 From the same boundary condition and equation (17), d=0, and therefore: q> (QII, z . ui) = be^ll2 (24) and E = bQ .e°IIZ (25) z II From the boundary conditions (ii) and (iii), and the solutions (22)- (25), we find: aQ„ = - bQ.. e (uj,Qm) (26) and 8Tre_____ a - = b = - (27) ,.2 .ui. 2. e (u>, Q „ ) V(°|, ♦ [ - ] 1 Thus: e (u), Q j|) 8ire a = (28) , J 2 r u). 2 . c (U), Q..) + 1 vton * i and: L - 8ire D = ------(29) v(Q|j + ) Ce(u>.Qn) + 1] So that for z>0, 8ire etui.QII )e ^llz .in, (p (QII, z, u)) cos(-)z ..2 r u). 2 . [ c (oi, Q ||) + 1] (30) v(Q|| ♦ [; ] ) and hence: 214 8ire e (u), Q li e II , id, , ui, E = V ■ --- 7T - (- ) sin (- ) z ( 31) z [ e (ui, Q „ + 1 ] v v v(Q* + C-]2) II v Now we can calculate the work done on the electron; the work done per unit time is given by: dW 5 t = Fv Substituting in for F gives: 5 1 = 1 O rn fodz vEz,rirz,t) 6 ,rii> #fz-v|t|) (32) where the + sign is for t<0, electron velocity negative, and the - sign for t>0, electron velocity positive. We now introduce a function s(t), where s(t)=+1 for t>0 and s(t)=-1 for t<0. Using this function, the total work done can be expressed by: W = - J“ °°dr J°° dz J ~dt s(t)vE (r .., z, t) 5 (rn) 6 (z-v 111 ) (33) -“H o z II II We now make use of the Fourier transform again: . 00 . 00 - 00 - 00 . 00 C ( t ) O \J W = -J dr..J dz J dt J dQ„J dui ---- r^E (Q„ ,z,u>) -“ Iro -“ -oo||J -oo 3 2 ||' ( 2tt ) i (Qn. r„-uit) 6 (r„)5(z-v111) e (34) Now due to the delta function, iQ„.r„ J dr.. 6 (r„) e‘ We next integrate with respect to t as in equation (8), incorporating v and s(t) in the delta function, with the result: W = -CZir)-3/ ~dO../“ du, ;“ d 2 eE(Q„,z.a,Ue-i(,“/vlz- eilul/v,z) 2i(2w) -oo_clQi|/ || -t1111-oo X„dz O eE (Q,.,z,ui) Z II sin(-)z V ( 35 ) 215 Equation (35) must now be compared with equation (2), where the difference in the limits in the integration with respect to uj should be noted: W = - J 2ttQ„ dQn J 'Ifiuj dm P(Qm ,uj) (2) o II II o II To find the probability of electron energy loss, we require only the real part of the work in equation (35). Now we can write: ip 00 fit P (Q „ , iu ) = ---- - Im J dz E (Qh ,z ,uj) sin(-)z (36) 11 1)iu (2ir)3 0 2 11 We now substitute in our expression for E ^ , equation (31), where the imaginary part comes from: - e (m , QII) 1 , 2 e (ui, QII) 1 r e (m, QII) -1 - Im 1] Im (37) e (uj , Qll) + 1J 2 Im e (uj , QII) +1 2 e (uj,QII) + 1J Then: 2e 8Tre e (m, QII) -1 -Q z . UJ P (Q „, m) Q Im[ ]J dz e sin-z , _2 _ui_ 2 . e (m, QII) +1 o v ifiui ( 2tt )3 v (Q „ + [ - ] II v 2e 2Q. Pe(u>,QII)-1, 1 «■—i-^TiTT— T-l I-) (38) E (U), QII ) + 1 ru-.2 V TT2flUJV ( C - 32 ) Q„+ [-] II V II V and finally: 2e2Q r e (m . QII) -1 P (Q it, u)) - Im (39) 2> 2,_2 rUJ,2,2 L e (u>, QII) +1J tt Tiv (Q „ + [ - ] II v The quantity P(Q^,uj) is often known as the loss function, and may be used for the calculation of EELS spectra, as described in section 2.4.4. 216 Appendix B - Program Collect The following program, Collect, is written in BASIC for the Apple lie 6502 microcomputer. Its broad purpose is to drive the Leybold Heraeus Sweep Generator module, and collect data from a conventional ratemeter as the sweep progresses, plotting the resulting spectrum on the computer screen. It is normally used for running UPS and XPS spectra with the Leybold EA 10 hemispherical analyser. The connections to the sweep generator and the ratemeter are made through digital to analog and analog to digital converters (DAC and ADC) respectively. When a spectrum is complete, it is saved to disc in binary file format. Because of the way in which the Leybold sweep generator works, it cannot be driven by simply computer-generating a complete ramp in the conventional way. Instead, it is necessary to insert a narrow-ranging fine ramp (0-1V) into the appropriate part of the wide-ranging coarse ramp (0-10V) which is already present. This restricts the range of the computer-driven sweep to a maximum of 190eV. Before each spectrum is run, the user has to calibrate the computer ramp manually. Nevertheless, a linear shift of about 2Z of the scan range is often noticed in the final spectrum. It is thus valuable to have a feature in the spectrum which can be used as a calibration check. As the spectrum is accumulated, successive scans are superimposed on the screen; it is possible to pause at the end of any scan to see a plot of the averaged spectrum. It is also possible to save the spectrum collected after any number of scans, and then return to scanning, adding new data to the old. In this case, spectra with added data will be stored with the filename originally chosen, but with an "XM appended for each new addition. The author would like to acknowledge the assistance of K.W. Senkiw 217 in writing this program. Collect - in BASIC, Apple lie Dialect 10 LOMEM: 17000: 20 TEXT 30 PRINT "GIVE DATE INPUT DK$ 40 PRINT “GIVE SAMPLE IDENTIFIER INPUT SA$ 45 REM...THE DATE AND SAMPLE IDENTIFIER WILL BE COMBINED TO GIVE THE SPECTRUM FILENAME. 50 DIM 11Z( 1025), 12( 1025) 60 HCOLOR = 3 70 Y$ = "Y" :STR = 0 : FIN = 0 : STZ = 1 80 D$ = " “ 90 FOR Z = 0 TO 256 100 12(Z) = 0 110 NEXT Z 120 MAXY = 0 130 A = 49152 + 256 * 5 140 FOR P = 0 TO 5 145 POKE (A + P),0 150 NEXT P 160B=A:C=B:D=A+4 170 POKE B.255 : POKE C,15 : POKE D,0 175 REM...LINES 130-170 ARE SETTING UP THE FINE CALIBRATION COMMUNICATION BETWEEN THE COMPUTER AND THE SWEEP GENERATOR. 180 PRINT "GIVE DVM (SWEEP GENERATOR) READING (FINE CAL)": INPUT AO 190 POKE B,0 :POKE C,0 :POKE D,0 200 B = A + 2 :C = B + 1 :D=A+4 210 POKE B.255 :POKE C.15 :POKE D,0 215 REM...LINES 190-210 SET UP THE COARSE CALIBRATION 220 PRINT "GIVE DVM READING (COARSE CAL)": INPUT AA 230 FOR P = 0 TO 5 235 POKE (A+P),0 240 NEXT P 250 PRINT "STATE A/D CHANNEL TO BE USED." 260 INPUT CHANNEL 270 PRINT "STATE GAIN REQUIRED; 0, 16, 32, 48" 280 INPUT GAIN 285 REM...IT IS USUAL TO USE A GAIN OF 0 290 PRINT "NOW SET SPECTRAL RANGES" 300 Y1Z = 1 310 PRINT " RANGE" : PRINT Y1Z 320 PRINT "STATE SCAN START":INPUT VB 330 PRINT "STATE SCAN WIDTH (NO MORE THAN 190)":INPUT VW 340 INPUT "THE DVM NOW SHOWS ITS ZERO READING; PLEASE ENTER IT ";ZC 350 VC = VB - ZC 360 PRINT "HOW MANY POINTS? ":INPUT PTS 370 PRINT "HOW MANY SCANS? ":INPUT SCANS 375 REM...LINES 380 - 400 GIVE THE OPTION OF MORE THAN ONE SPECTRAL REGION, AND ARE NOT NORMALLY USED. 380 PRINT "GIVE REGION IDENTITY":INPUT ID$ 390 PRINT "IS THERE ANOTHER REGION? ":INPUT ANS$ 400 IF ANS$ = Y$ THEN Y1Z = Y1Z + 1 : GOTO 310 405 REM...LINES 410 - 520 SET UP THE SWEEP RAMP 410 NS = 4095 * VC / AA 420 NSZ = NS 218 430 NCZ = (NS - NSZ) * 2 440 NSZ = NCZ + NSZ 450 B = A + 2 460 C = B + 1 470 D = A + 4 480 N1SZ = NSZ / 256 490 N2SZ = NSZ - N1SZ * 256 500 POKE B.N2SZ : POKE C.N1SZ : POKE D,0 510 MS = 4095 * VW / AO 520 INC = MS / PTS 530 REM...LINES 540 - *** RUN THE SPECTRUM 540 H6R 550 FOR J = 1 TO SCANS 560 B=A:C=B+1 : D = A + 4 570 S1SZ = 0 : S2SZ = 0 : SS = 0 580 POKE B.S2SZ 590 POKE C.S1SZ 600 POKE D.O 610 REM...LINES 620 Sr 630 SLOW DOWN COLLECTION 620 FOR K = 1 TO 2000 630 NEXT K 640 FOR I = 0 TO (PTS-1) 650 POKE B.S2SZ 660 POKE C.S1SZ 670 POKE D.O 600 PRINT (S1SZ * 256 + S2SZ) * (AA / 4095) 690 SS = SS + INC 700 SSZ = SS 710 HSZ = SSZ / 256 720 POKE 50240,(CHANNEL + GAIN) 730 A1 = PEEK(50240) 740 A2 = PEEK(50241) 750 11 = (A1 * 16) + (A2 / 16) 760 11 Z (I) = 11 770 12( 1 ) = 12( 1 ) + 1 1 Z (I) 780 11Z (I) = ( 1 59 / 4095) * I1Z(I) 790 IA = I * (256 / PTS) 800 IAZ = IA 810 IB = IA - IAZ 820 IF IB = 0 THEN GOTO 840 830 GOTO 850 840 HPLOT IAZ,(159 - 11 Z (I) ) 850 NEXT I 860 REM...THE FOLLOWING LOOKS AT THE KEYBOARD TO SEE IF ! HAS BEEN PRESSED 870 PRINT J : PRINT "PRESS ! TO STOP AT END OF SCAN" 880 QUITTER = PEEK(-16384) 890 TRASH = PEEK(-16368) 900 IF QUITTER = 161 THEN GOSUB 1480 910 NEXT J 920 GOSUB 1550 930 INPUT "DO YOU WANT A HARD COPY? "; REPLY$ 940 IF REPLY$ <> "Y" THEN GOTO 1030 950 PR£1 960 PRINT CHR$(9); "GD" 970 PRINT "THE ENERGY SPAN OF THE SPECTRUM IS ";VB;" TO ";VB + VW;" EV." 980 PRINT "THE NUMBER OF SCANS IS ";SCANS 990 PRINT "THE NUMBER OF POINTS IS ";PTS 219 1000PRINT "THE MAXIMUM Y VALUE IS ";MAXY 1010 PRINT "THE SPECTRUM IS FILED AS ";LABELS 1020 PR£0 1030 INPUT "WOULD YOU LIKE TO SEE YOUR SPECTRUM AGAIN? ";REPLY$ 1040 IF REPLY$ = "Y" THEN GOSUB 1100 1050 INPUT " HAVE YOU SEEN ENOUGH? ";REPLY$ 1060 IF REPLY$ = "Y" THEN TEXT 1070 INPUT "DO YOU WANT TO RUN AGAIN? ";REPLY$ 1080 IF REPLY$ = "Y" THEN GOTO 10 1090 END 1100 REM...... SUBROUTINE 1 110 INPUT "AT WHICH ENERGY WOULD YOU LIKE TO START? ";E1 1120 INPUT "AT WHICH ENERGY WOULD YOU LIKE TO FINISH? ”;E2 1130 SPTS = (El - VB) * PTS / VW 1140 FPTS = (E2 - VB) * PTS / VW 1150 XA = 0 : XB = 0 : YA = 0 : YB = 0 1160 FOR I = SPTS TO FPTS 1170 IF YA < 11Z(I) THEN YA = 112(1) 1180 IF I1Z(I) < YB THEN YB = 11Z (I) 1 190 NEXT I 1200 HGR 1210 HCOLOR = 3 1220 FOR I = SPTS TO FPTS - 1 1230 XB = XA * 279 / (FPTS - SPTS) 1240 XA = XA + 1 1250 HPLOT XB,( 159 - 155 * 11Z(I) / (YA - YB)) 1260 NEXT I 1270 HPLOT 0,0 TO 0,159 TO 279,159 TO 279,0 TO 0,0 1280 FOR K = 0 TO 279 STEP 28 1290 HPLOT K,159 TO K,156 1300 NEXT K 1310 GOSUB 1350 1320 INPUT "ANOTHER LOOK? ";REPLY$ 1330 IF REPLY$ = "Y" THEN GOTO 1100 1340 RETURN 1350 REM...... SUBROUTINE 1360 INPUT "DO YOU WANT A HARD COPY (Y/N)? ";REPLY$ 1370 IF REPLY$ <> "Y" THEN RETURN 1380 PR£1 1390 PRINT CHR$(9); "GD" 1400 PRINT "THE ENERGY SPAN OF THIS SPECTRUM IS ";E1;" TO ";E2;"EV" 1410 PRINT "THE NUMBER OF SCANS IS ";SCANS 1420 PRINT "THE NUMBER OF POINTS IS ";FPTS - SPTS 1430 PRINT "THE MAXIMUM Y VALUE IS ";YA 1440 PRINT "THE TICK INTERVAL IS ";(E2 - E1)/10;" EV" 1450 PRINT "THE SPECTRUM IS FILED AS ";LABELS 1460 PR£0 1470 RETURN 1480 REM...... SUBROUTINE 1490 GOSUB 1550 1500 INPUT "WOULD YOU LIKE TO SEE THE AVERAGED SPECTRUM? ";SPEC$ 1510 IF SPECS = "Y" THEN GOSUB 1100 : GOSUB 1350 1520 INPUT "DO YOU WANT TO CONTINUE SCANNING (Y/N)? ";BAK$ 1530 IF BAK$ = "N" THEN GOTO 930 1540 RETURN 1550 REM...... SUBROUTINE 1560 FOR I = 1 TO (PTS - 1) 1570 11Z(I) = 12(1) / SCANS 1580 IF 11Z(I) > MAXY THEN MAXY = 11 Z (I) 220 1590 NEXT I 1600 IF BAK$ = "Y" THEN DK$ = DK$ + "X" 1610 AS = PEEK(107) + PEEK (108) * 256 1620 STR = AS + 7 : FIN = 2 * PTS 1640 PRINT D$ "BSAVE " LABELS ".A M STR " ,L " FIN M ,D2 1650 PRINT "SPECTRUM SAVED AS "-.LABELS 1060 RETURN 221 Appendix C - Program "Padread" This program was written to provide an interface between a Torch microcomputer and a Houston HiPad. The HiPad is a sensitive device which is used by placing a graph on its surface and tracing it out with a special pen. The graph is converted into a sequence of binary digits, which can be sent to a computer and stored there. This program converts the raw HiPad data into numbers corresponding directly to the original figure; these can then be plotted and / or filed for subsequent analysis. The algorithm depends upon the first three values received being ‘’known" coordinates of the original graph; these must be supplied to the program from the keyboard. The values from the HiPad are placed in the matrix "himat", and the coordinates from the keyboard are placed in the matrix "keymat". These matrices are both 3x3, with the structure: x y z x y z x y z The procedure Gausj, which is a Gaus-Jordan matrix inversion 162 -1 algorithm , is used to invert the matrix himat, yielding himat The matrix multiplication procedure Matmult is then used to perform the manipulation; himat 1 x keymat = scalemat where scalemat can be multiplied, again using Matmult, with each matrix corresponding to a point from the HiPad, thus converting it to the equivalent point on the graph. Some Notes on the Programming Language The program listed here is written in ProPascal, a compiler 222 marketed by Prospero Software, which is widely used in academic institutions. Its conformity to Pascal standards is fairly close, and the majority of this program should be reasonably portable. However, a number of its features, principally I/O, depend upon the use of two libraries, CJLIB and CMULIBT, which were developed here at Imperial College and are largely machine specific, as well as the compiler’s own library PASLIB, which is not. All the procedures declared as EXTERNAL below originate from these libraries. However, features of this type are usually present in any modern, well implemented Pascal, and their operation within this program should present few problems. PROGRAM Padread; { ***************************************************************** * * * PADREAD, a program for use with the HiPad digitiser. It will * * convert an analog graph into digital form, file the digital * * data and plot the graph on the screen. The graph can be * * placed in any position on the Pad. * * * * Sigrun Eriksen Sr Humphrey Drummond 4 / 6 1986 * * * *****************************************************************} Const no_choice false; choose true; maxr 8 ; maxc 8 ; Type word = -32786..32767; datarray = ARRAY [1. .512] of REAL; styles = (dot,cross,line,markline) s6 = string[6] l s7 = string[7] 1 byte = 0..255; ary = ARRAYC1..maxr] of REAL; arys = ARRAYC1..maxr] of REAL; ary2s = ARRAYC1..maxr,1..maxc] of REAL; nmon xmin,xmax,ymin,ymax REAL; xgap.ygap REAL; gxmin,gxmax word; gymin.gymax word; 223 Var scalemat,keymat,himat ary2s; error BOOLEAN; count_pts,npts INTEGER; fromHiPad STRING; prefix CHAR; xVal.yVal.i.count INTEGER; xspec,yspec DATARRAY; fname.title,xlabel STRING; ylabel,trash STRING; xspace,xrange REAL; yrange.yspace REAL; xscale,yscale REAL; xone,xtwo,xthree REAL; yone,ytwo,ythree REAL; padmat.grapmat ary2s; {**************************************************} {The following procedures come from cjlib, cmulibt and paslib} Function Cstat : BOOLEAN; EXTERNAL; Procedure InitSerial; EXTERNAL; Procedure TimedRcvString(VAR i : STRING); EXTERNAL; Function StrIVaKVAR X : STRING; VAR count ; INTEGER) : INTEGER; EXTERNAL; Procedure Clear_text; EXTERNAL; Procedure Openworkstation(which : word); EXTERNAL; Procedure Closeworkstation; EXTERNAL; Procedure Osbyte (num.x.y : BYTE; Var rx.ry : BYTE); EXTERNAL; Procedure Oscli (cmnd : STRING); EXTERNAL; Procedure Cleargraph; EXTERNAL; Procedure Border; EXTERNAL; Procedure Set_size; EXTERNAL; Procedure Inputxy ( var x.y DATARRAY; var npts INTEGER; var title.xlabel STRING; var ylabel,other_info STRING); EXTERNAL; Procedure Set_axes (p datarray; npts INTEGER; var min.max.gap REAL; your_choice BOOLEAN); EXTERNAL; Procedure Plot_data (x.y datarray; npts INTEGER; style styles); EXTERNAL; Procedure filexy (fname string; xval,yval datarray; npts INTEGER; Title,xlabel,ylabel string; otherinfo string); EXTERNAL; Procedure Clear_three; EXTERNAL; Procedure Tick_xaxis; EXTERNAL; Procedure Tick_yaxis; EXTERNAL; Procedure Box; EXTERNAL; {***************************************************} 224 {Gausj is a matrix inversion routine, and is listed separately at the end of this appendix} {$1 gausj.pas} {****t**********************************************} {The following are procedures which are defined here} Procedure Printlnstructions; Begin writeln (’This program is called Padread; it reads data from the Hipad digitizer’); writeln; writeln (’Put your graph for digitisation onto the pad, and press the PAD reset button.'); writeln; writeln (’The first three points MUST be read with the pen in POINT mode, ’); writeln (’You must type the x,y coordinates of these points to the keyboard. ’); writeln ; writeln (’Then you may choose either POINT or SWITCH STREAM mode.’); writeln ; writeln (’If you require less than 500 points, press RETURN to finish. ’ ); writeln (’After 500 points counting stops automatically.’); end; Procedure GetPoint (n : INTEGER); var fromHiPad : STRING; Begin writeln ('Input a point from the Hipad now’); REPEAT TimedRcvString(fromHiPad); Until length(fromhipad) >0; count:=1; himat[n,1] := StrIVal(fromHiPad,count); himat[n,2] := StrIVal(fromHiPad,count); himat[n,3] := 1; write (’input x,y coordinates of the point on the keyboard (eg 2.3 0.0) ? ’); readln (keymatCn,1],keymatCn,2]); keymat[n,3] := 1 end; Procedure Matmult ( Var R, A, B : ary2s; n ,m, p : INTEGER); Var i,j,k : INTEGER; {returns matrix R(esult) as A*B: A is nxp, B is pxm} Begin 225 for i := 1 to n do for j := 1 to m do begin R[i,j] := 0 ; for k := 1 to p do R[i,j] := A[i,k] * B[k,j] + R[i,j] end end;{procedure matmult} {**********************************************************************} BEGIN {main program} InitSerial; Clear_graph; Clear_three; PrintInstructions; GetPoint(1 ) ; GetPoint(2); GetPoint{3); writeln; writeln ('When you are ready to start, press any key, then RETURN.'); readln; {Read points from the pad; use count_pts as counter} count_pts := 0 ; REPEAT TimedRcvString(fromHiPad); IF Length(fromHiPad) <> 0 THEN BEGIN prefix:=fromHiPad[1]; count:=1; xVal:=StrIVal(fromHiPad,count); yVal:=StrIVal(fromHiPad,count); Writelnprefix, ’ X= ',xVal:5,' Y= ’,yVal:5); count_pts := count_pts + 1 ; xspec[count_pts] := xVal; yspectcount_pts] := yVal; end UNTIL Cstat or (count_pts = 500); if Cstat then readln (trash); npts := count_pts; writeln ('Your data reading is now complete. '); writeln ('You have collected ’,npts,‘ data points.'); {use Gausj and matmult to convert pad values to graph values} Gausj(himat,3,error); matmult (scalemat,himat,keymat,3,3,3); for i := 1 to npts do begin padmat[1 ,1 ] := xspecCi]; padmat[1 ,2 ] := yspecti]; padmatt1,3] := 1 ; matmulttgrapmat.padmat,scalemat,1,3,3); xspecCi] := grapmat[1 ,1 ]; yspecti] := grapmat[1 ,2 ] end; {points now in graph form} 226 {file data in XYKBD format} writeln (’Enter a name for your data file.’); readln (fname); write (’enter a title for your file '); readln (title); write (’enter an x label ’); readln (xlabel); write (’enter a y label ’); readln (ylabel); filexy (fname,xspec,yspec,npts,title,xlabel,ylabel, ' ’); {plot data} set_axes(xspec,npts,xmin,xmax,xgap,no_choice); set_axes(yspec,npts,ymin,ymax,ygap,no_choice); Open_workstation(1 ); set_size; xgap := (xmax-xmin)/1 0 ; ygap := (ymax - ymin)/5; Border; Box; Tick_xaxis; Tick_yaxis; Plot_data(xspec,yspec,npts,dot); Clear_three; Close_workstation; write (’When you have seen enough, enter any key ’); readln; END. {******************************************************} Procedure Gausj {matrix inversion routine} (var b : ARY2S; ncol ; INTEGER; var error : BOOLEAN); Label 99; Var w : ARRAY [1..maxc,1..maxc] of REAL; index ; ARRAY [1..maxc,1..3] of INTEGER; i,j,k,l,irow,icol,n,l1 INTEGER; determ,pivot,hold,sum : REAL; t ,ab,big : REAL; Procedure swap (var a,b REAL); Var hold : REAL; Begin {swap} hold : = a; a : = b; b := hold end; {swap} Procedure gausj2; 227 Label 98; Var i.j.k.l.H : INTEGER; Procedure gausj3; Var 1 ; INTEGER; Begin {procedure gausj3} {interchange rows to put pivot on diagonal} if irow <> icol then begin determ := - determ; for 1 := 1 to n do swap (bCirow,1 ],b[icol,1 ]); end {if irow <> icol} end; {procedure gausj3} Begin {procedure gausj2} {actual start of gausj} error := false; n := ncol; for i ;= 1 to n do begin index[i,3] := 0 end; determ ;= 1 .0 ; for i := 1 to n do begin big := 0 .0 ; for j ;= 1 to n do Begin if index[j,3] <> 1 then begin for k := 1 to n do begin if index[k,3] > 1 then begin writeln (’ ERROR: matrix singular’); error := true; goto 98 { ABORT } end; if index[k,3] < 1 then if abs(b[j,k]) > big then begin irow := j; icol := k; big := abs(b[j,k]) end end {k loop} end end; {j loop} index[icol,3] := indexCicol,3] + 1 ; indexCi,1 ] := irow; index[i,2 ] := icol; Gausj3; {further division of gausj} {divide pivot row by pivot column} pivot := bCicol,icol]; 228 determ := determ * pivot; b[icol,icol] := 1 .0 ; for 1 := 1 to n do b[icol,l] := b[icol,l] / pivot; {reduce nonpivot rows} for 1 1 := 1 to n do begin if 1 1 <> icol then begin t := bC1 1 ,icol]; bC1 1 ,icol] := 0 .0 ; for 1 := 1 to n do bCH.l] := b[H , 1] - b[icol, 1] * t; end {if 1 1 <> icol} end end; {i loop} 98: end; {gausj} Begin {Gauss- Jordan main program} gausj2 ;{first half of gausj} if error then goto 99; {interchange columns} for i := 1 to n do begin 1 : = n - i + 1 ; if index[l,1 ] <> index[l,2 ] then begin irow := indextl,1 ]; icol := index[l,2 ]; for k := 1 to n do swap (btk.irow],b[k,icol]) end {if index} end; {i loop} for k := 1 to n do if index[k,3] <> 1 then begin writeln (’ERROR: matrix singular'); error := true; goto 99 {abort} end; 99: end; {procedure gausj} 229 Appendix D - Program Stripper As described in the text of chapter 2, this program strips the background due to inelastic intensity and satellite intensity from XPS spectra. It does this in two stages, first removing the inelastic background, then the satellites. The original program was devised and written in 380z BASIC by A.A. Williams, who gives a full account of 163 the principles behind it . This version has been adapted by the author to run in Pascal on a Torch computer; the notes on the programming language in Appendix C are equally applicable here. {*******t********************************************************} Program Stripper; {************************************************************** * * * This program will remove background and satellites from * * XPS spectra. The validity of the algorithm used is * * limited to data for which; * * * * a) there is no primary intensity to the high KE end. * * * * b) there is no primary intensity to the low KE end. * * * * This version will only support files in XYKBD form, and * * the new files it creates will also be in the XYKBD format.* * It is particularly important to note that energies, i.e. * * x values absolutely MUST be evenly spaced. If your data * * is not evenly spaced, the program interpol can be used to * * remedy the situation, creating a new spectrum with evenly * * spaced x. * * * ****************t*********************************************} Const choose = true; no_choice = false; Type datarray ARRAY [1..512] of REAL; word -32768..32767; s7 string[7]; s6 string[6 ]; str 15 string[15]; byte 0..255; styles (dot,cross.line,markline); smallarray ARRAY [1. . 10] of REAL; Common xmin,xmax,ymin,ymax,xgap,ygap : REAL; 230 gxmin,gxmax,gymin,gymax WORD; Var npts,pointlh(GR,i,j,k,n(CP,C3(CBlC4 INTEGER; xspec,yspec,stripspec.qspec DATARRAY; title,xtitle,ytitle,other_info,scrap STRING; specname,atext,btext STRING; trash,answer CHAR; style STYLES; low_energy,high_energy,IB,El,VC,cart REAL; b,c,t,KP,K3,K4,KB,IP,I3,I4 REAL; A , f SMALLARRAY; f name STRINGC15]; dfile TEXT; rx.ry BYTE; {******************************************************************} {The following are external procedures, obtained by linking up with cjlib, cmulibt and paslib. } Procedure Clear_text; EXTERNAL; Procedure Openworkstation(which : word); EXTERNAL; Procedure Closeworkstation; EXTERNAL; Procedure Gsxremove; EXTERNAL; Procedure Cleargraph; EXTERNAL; Procedure Osbyte (num.x.y : byte; VAR rx.ry : byte); EXTERNAL; Procedure Oscli (cmnd : string); EXTERNAL; Procedure Inputxytvar x,y DATARRAY; var npts INTEGER; var title,xlabel STRING; var ylabel,other_info STRING); EXTERNAL; Procedure Edit_data(var x,y DATARRAY; var npts INTEGER); EXTERNAL; Procedure Set_axes (p DATARRAY; npts INTEGER; var min,max,gap REAL; your_choice BOOLEAN); EXTERNAL; Procedure Border; EXTERNAL; Procedure Box; EXTERNAL; Function Mapx (x REAL) : INTEGER; EXTERNAL; Function Mapy (y REAL) : INTEGER; EXTERNAL; Procedure R_to_str(r REAL; var ans_string SB); EXTERNAL; Procedure Tick_xaxis; EXTERNAL; Procedure Tick_yaxis; EXTERNAL; Procedure Plot_data (x.y DATARRAY; npts INTEGER; style STYLES); EXTERNAL; Procedure Header_enter (var title : STRING; var xtitle,ytitle : STRING); EXTERNAL; Procedure Annotate (title : STRING; xtitle,ytitle : STRING); EXTERNAL; Function Get_key : CHAR ; EXTERNAL; Procedure Clear_three; EXTERNAL; Procedure set_size; EXTERNAL; Procedure in_xy_struc (fname : STR15; var xspec,yspec : DATARRAY; 231 var npts INTEGER; var title,xlabel,ylabel STRING; var otherinfo STRING); EXTERNAL; Procedure filexy(fname : STR15; xspec,yspec DATARRAY; npts INTEGER; title,xlabel,ylabel STRING; otherinfo STRING); EXTERNAL; Procedure aluminium(var KP,K3,K4,KB,IP,13,14,IB4 , IB : REAL); {these values are based on values supplied in the Oxford documentation accompanying the original stripping algorithm. They correspond to the following excitation lines from a V.G. X-ray gun; Ka‘, Ka3, Ka4, B1/2.> Begin KP := 5.8; K3 := 9.7; K4 := 11.7; KB := 72.7; IP := 0.007; 13 := 0.073; 14 := 0.031; IB := 0.024 end;{aluminium} Procedure magnesiumtvar KP,K3,K4,KB,IP,13,14,IB : REAL); {these values are based on values supplied in the Oxford documentation accompanying the original stripping algorithm. They correspond to the following excitation lines from a V.G. X-ray gun; Ka’, Ka3, Ka4, B1/2.> Begin KP := 4.6; K3 := 8.5; K4 := 10.1; KB := 49.9; IP := 0.01; 13 := 0.091; 14 := 0.051; IB := 0.017 end;{magnesium} {**********************************************************************} Begin {main program} Repeat writeln (’This program is called stripper; it will remove inelastic {+background and satellites from XPS spectra.’); write ('Enter the title of your spectrum file;’); readln (fname); write (’enter a title for your plotted spectrum;'); readln (title); in_xy_strue(fname,xspec,yspec,npts,scrap,scrap,scrap,scrap); write (’enter low energy,high energy'); readln (low_energy,high_energy); {This part of the program makes sure that the spectrum is the right way round for the stripping algorithm, i.e x[1 ] > x[n].} point:= 0 ; if (xspec[1 ] < xspecCnpts]) then begin point := 2 ; for i := 1 to pts do qspecti] := yspecCnpts + 1 - i] end else for i := 1 to npts do qspecCi] := yspecCi]; {Optimise A until f[a] = 0 and strip off background: stripspec stores new y values } A[ 1] := 0.001; k := 0 ; Repeat AC2] := AC 1 3 + 0.00001 ; A[3] := AC 1 3 - 0.00001 ; for i := 3 downto 1 do Begin t := 0 ; for n := 1 to npts do Begin stripspecCn] := qspecCn] - A[i] * t; t := t + stripspecCn] end;{n loop] fCi] := qspectnpts] - A[i] * t end;{i loop} writeln (* A = ’,AC 1]); writeln C F 1 , F2 , F3 are; ’ .fCl3.fC23.fC33); AC 1] := AC 13 - (fC1] * 0.00002 / (fC23 - fC33)); writeln (‘Next A = ',AC13.’ cycle ‘,k); k : = k ♦ 1; fC13 := fCU * 100; 6 R := trunctfCU) Until GR = 0; { Removes satellites and stores the new y values in stripspec } writeln (‘Enter excitation type...for Mg type m, for A1 type a answer := get_key; if (answer = ‘M’) or (answer = ‘m’) then magnesium(KP,K3,K4,KB,IP,I3,I4,IB); if (answer = *A‘) or (answer = ‘a’) then aluminium(KP.K3.K4,KB,IP,13,14,IB); VC := (high_energy - low_energy)/npts; CP := round(KP / VC); C3 := round(K3 / VC); C4 := round(K4 / VC); CB := round(KB / VC); for n := npts downto 1 do Begin if (n - CP) >= 1 then 233 stripspecCn - CP] := stripspecCn - CP] - stripspecCn] * IP if (n - C3) >= 1 then stripspecCn - C3] := stripspecCn - C3] - stripspecCn] * 13 if (n - C4) >= 1 then stripspecCn - C4] := stripspecCn - C4] - stripspecCn] * 14 if (n - CB) >= 1 then stripspecCn - CB] := stripspecCn - CB] - stripspecCn] * IB end; { of do loop } {If y values were rotated above, now rotate back for plotting} if (point <> 2 ) then for i := 1 to npts do yspecCi] := stripspecCi] else for i := 1 to npts do yspecCi] := stripspecCnpts - i + 1]; {now plot the new data. } set_size; Set_axes (yspec.npts,xmin,xmax,xgap,no_choice); ymax := 0 .0 ; for i := 1 to npts do Begin if yspecCi] > ymax then ymax := yspecCi] end; ymin := 0 .0 ; xmin := low_energy; xmax := high_energy; xgap := 1 0 ; ygap := 10; open_workstation(1); border; box; tick_yaxis; tick_xaxis; Annotate (titleKinetic energy / eV’.’NCe]’); Plot_data (xspec,yspec.npts.line); Clear_three; write (’Would you like a hard copy ? ’); answer := get_key; if (answer = ’y’) or (answer = 'Y') then Begin osbyte (5,1 ,1 ,rx,ry); oscli (* GDUHP 0 0 1 1 20’) end; { now file the stripped spectrum in XYKBD format.} write (’Would you like to file the stripped spectrum ? ’); answer := get_key; if (answer = ’y’) or (answer = ’Y’) then Begin write (’Enter a name for your file; ’); readln (specname); write (’Enter first line of text; ’); readln (atext); 234 write ('Enter second line of text; ’); readln (btext); filexytspecname.xspec.yspec.npts,title,atext,btext, * ‘ ); end; {if} {another go?} write ('another go ? ’); answer := get_key; Close_workstation ; until (answer = ’n’) or (answer = 'N') end. 235 Appendix E - Program Fitter The principle of this program is really very simple, and the code itself is essentially self-documenting. The reader's attention is, however, drawn to the notes on the programming language in Appendix C, which apply equally here. It should be noted that this version applies specifically to calculating the intensity ratio of the Ti 2p 3+ 4 + peaks due to Ti and Ti . It is, however, very easy to modify for other purposes. Program Fitter; {****************************************************** * * This program simulates stripped XPS spectra by calculating curves with a chosen proportion of Gaussian to Lorentzian character. It is designed for use with the Ti2p region of the spectrum. The sum of the curves will be plotted over the individual curves. An experimental spectrum will then be read in, as an ASCII text file, and plotted over the whole lot so that a visual comparison can be made. If the simulation is made up of 4 curves, the area ratio of the first to the third will be given as ratio Ti4 + to Ti3+, Created S. Eriksen and C.C. Jones February 1986 ******************************************************} Const choose = true; no_choice = false; gxmin = 3720; gxmax = 31600; gymin = 6150; gymax = 30930; type datarray ARRAYC1..500] of REAL; word -32768..32767; s7 string[7]; s6 string[6 ]; byte 0..255; styles (dot,cross,line,markline); Common xmin,xmax,ymin,ymax,xgap,ygap : REAL; 236 Var npts.i,j,n_curves INTEGER; sum,energy,xspec.yspec DATARRAY; ratio*to3,low_energy,en_step REAL; high_energy.gprop,a,b,c REAL; curve ARRAY!1..4,1..500] of REAL; title.xtitle.ytitle,other_info STRING; option,new_titles,trash,answer CHAR; junk,rx,ry BYTE; style STYLES; position.width,height ARRAY!1..4] of REAL; DFILE,printer TEXT; fname STRING!15]; {****************************************************************} {The following procedures are from cjlib, cmulibt and paslib} Procedure Clear_text ; EXTERNAL; Procedure Openworkstation(which : WORD) ; EXTERNAL; Procedure Closeworkstation; EXTERNAL; Procedure Gsxremove; EXTERNAL; Procedure Cleargraph; EXTERNAL; Procedure Osbyte(num,x,y : byte; VAR rx.ry : byte); EXTERNAL; Procedure Osclitcmnd : string); EXTERNAL; Procedure inputxy(var x,y : datarray; var npts ; INTEGER; var title,xlabel : string; var ylabel,other_info : string);EXTERNAL; Procedure edit_data(var x,y : datarray; var npts : INTEGER); EXTERNAL; Procedure integrate (y : datarray; npts : INTEGER; dx : real var ydx : datarray); EXTERNAL; Procedure Set_axes (p : datarray; npts ; INTEGER; var min,max,gap : REAL; your_choice : BOOLEAN); EXTERNAL; Procedure Border; EXTERNAL; Procedure Box; EXTERNAL; Function Mapx(x : REAL) : INTEGER; EXTERNAL; Function Mapyty : REAL) : INTEGER; EXTERNAL; Procedure R_to_str (r : REAL; var ans__string : s6 ); EXTERNAL; Procedure Tick_xaxis; EXTERNAL; Procedure Tick_yaxis; EXTERNAL; Procedure Plot_data(x,y :datarray; npts : INTEGER; style : styles); EXTERNAL; Procedure Header_enter(var title : string; var xtitle,ytitle : string); EXTERNAL; Procedure Annotate(title : string; xtitle,ytitle : string); EXTERNAL; Function Get__key : char ; EXTERNAL; Procedure Clear_three; EXTERNAL; Procedure overwritetext(message : string; 237 x,y : word); EXTERNAL; {*******************************************} {The next two functions are defined here} Function Gaussian(x,b,a : REAL) : REAL; Var x_min_b : REAL; Begin x_min_b := x - b; gaussian := exp(-0.693147*SQR(x_min_b/a)) end; Function Lorentzian(x,b,c : REAL) : REAL; Var x_min__b : REAL; Begin x_min__b := x - b; lorentzian := 1/(1+SQR(x_min_b/(c/2))) end; {*************************************} Begin{main program} Repeat write(*enter title '); readln(title); write(’name of file with experimental points '); readln(fname); assign(dfile,fname); reset(dfile); readln(dfile,other_info); readln(dfile,other_info) ; readlntdfile,other_info); readln(dfile,npts); for i := 1 to npts do readln(dfile,xspec[i],yspec[i]); write('enter low energy high energy / eV '); readln(low_energy,high_energy); writet'enter number of curves '); readln(n_curves); for i := 1 to n_curves do {enter the 4+ doublet, then the 3+ doublet, 3/2 peak first, for Ti} Begin writet’enter position / eV relative height '); readln(position[i],height[i]) end; for i :=1 to (n_curves div 2 ) do begin j := 2 * i -1 ; writet'enter width/eV '); readln(width!j]); width[j+1] := heightCj] * widthCj]/2 /height[j+1] end; writet'What proportion of gaussian to lorentzian would you like', 238 {+} ‘ - enter as decimal fraction ' ); readln(gprop); {set up x axis energy values} en_step := (high_energy - low_energy)/(npts-1 ); for i := 1 to npts do energy til := low_energy + i*en_step; for j := 1 to n_curves do BEGIN a := heighttjl; b := positiontj]; c := width!j]; for i := 1 to npts do curvetj.il := gprop * a * gaussian(energy[i],b,c) + (1 - gprop) * { + }a *lorentzian(energytil,b,c); end; for i := 1 to npts do sumCi] := curved, i ]; for j := 2 to n_curves do for i := 1 to npts do sumCi] := sumCi] + curve[j,i]; {plot the graph} Set_axes(sum,npts,ymin,ymax,ygap,no_choice); ymin := 0 .0 ; xmin := low_energy; xmax := high_energy; xgap := 10; open_workstation(1); border; box; tick_xaxis; Annotatettitle,'Energy / eV*,’ ’ ); Plot_data(energy,sum,npts.line); for j := 1 to n_curves do Begin for i := 1 to npts do sum[i] := curve[j,i]; Plot_data(energy,sum,npts,dot) end; plot_data(xspec.yspec,npts,line); Clear_three; If n_curves = 4 then begin for i ;= 1 to npts do sumCi] := curvet 1 ,i]; integrate(sum,npts,en_step,sum); ratio4to3 ;= sumtnptsl; for i := 1 to npts do sumti] := curveC3,i]; integrate(sum,npts,en_step,sum); ratio4to3 := ratio4to3/sumtnpts]; writeln('The ratio of Ti4 + to Ti3+ is *,ratio4to3:6 :2) end;{if} writet'do you want hard copy '); answer ;= get_key; if (answer = *Y’ ) or (answer = ’y’) then 239 Begin osbyte(5,1,1,rx,ry); osclit’GDUHP 0 0 1 1 20 * ) ; assign(printer,* LST:’); rewrite(printer); writeln(printer); writeln(printer); writeln(printer,'The first gaussian has position {+} *,positiont1 height height[1],‘ and width ’,width[1]); writeln(printerThe second gaussian has position *,position[2 ],’ , {+}height ', height[2],’ and width ’,width[2]); writeln(printer,’The third gaussian has position ’,position[3],' , {+}height ’,height[3],* and width ',width[3]); writeln(printerThe fourth gaussian has position ',position[4],', {+}height ’,height[4],* and width *,width[4]); end; write('Another go '); answer := get_key; Close_workstation; until (answer = ’n*) or (answer = ‘N’) end. 240 Appendix F - Program "Eelsim" This program calculates EELS spectra according to the theory presented in chapter 2, as discussed in chapter 4, using a Fourier transform technique. The application of this method to EELS simulation 104 was developed by Cox, Flavell and Williams , who discuss its basis fully in their work. What follows is a brief summary of the steps involved. The first part of the program calculates the loss function P^(ui) using equation (12) from chapter 2, then plots it out. Next, thermal excitation is introduced by use of Bose-Einstein statistics. The loss function is then transformed into Fourier space, where it is self- convoluted in accordance with the Poisson distribution to yield the multiple-excitation overtones. The complete loss function (chapter 2, equation 2 2 ) is then convoluted with a function representing instrumental broadening. This is carried out as follows; in pre- transform frequency space, the total loss function including broadening, elastic peak and all overtones, P^^tu)), can be represented as: P. . (ui) = i (ui) * (6(0) + P.(u>) + J P. (uj)*P . (uj) + ...} (1) tot 1 2 ! 1 1 where * denotes convolution, 6 (0 ) is a delta function representing the 104 elastic peak and i(ui) is the broadening function . Once in Fourier space, however, convolution becomes multiplication; also the Fourier transform of a delta function is 1. Thus, in Fourier space, (1) becomes S. .(t ) = i(f) {1 + S (t ) + 5 ,S.(t ? +...} = i(i)exp[S (t )], (2) where S(i) is the Fourier transform of P(ui). Now back transforming the result of (2), returns a fully simulated EEL spectrum, which may be 241 plotted and / or filed to disk. It should be noted that the calculations in this program use atomic units throughout. The notes on the programming language in appendix C apply equally to this program. ********************************************** Program EELSIM; {***************************************************** * * * This program will calculate HREELS spectra * * from a number of parameters entered by the user. * * First it calculates the fundamental loss function,* * then it convolves in an elastic feature, thermal * * broadening and overtones due to multiple * * scattering events. The convolution is carried * * by means of a Fast Fourier transformroutine. * * The simulated spectrum may then be filed as a * * data file in XYKBD format. * * * * * * Program by Sigrun Eriksen * * 24 / 2 / 86 * * * * * *****************************************************} Const choose = true; no_choice = false; small = 0 .1 ; Type complex = record x,y REAL; end; comarray = ARRAY E0. .5121 of complex; datarray = ARRAY [0. .512] of real; word = -32768..32767; s7 string[7]; s6 string[6 ]; byte = 0. .255; styles = (dot,cross,line,markline); smallarray = ARRAY C1..10] of REAL; bbit_num = 0. .7; flag_type = (normal,inverse); str15 = STRING E15]; Common xmin,xmax,ymin,ymax ; REAL xgap.ygap ; REAL gxmax.gxrnin.gymax.gymin : WORD Var 242 flag FLAG_TYPE; npts,halfpts,qrpts,nophon INTEGER; spec,trans COMARRAY; yspec,xspec DATARRAY; title,xtitle,ytitle STRING; other_info,scrap STRING; specname,atext,btext STRING; trash,answer CHAR; style STYLES; low_energy, high_energy REAL; fwhm.elvel,e1 ,e2 ,q,air,bir REAL; i,j,k,l,m,n,ai,bi,power_2 INTEGER; viper,W1 ,x1 ,x2 ,y1 ,y2 REAL; en_gap,spacer,widebit,temp REAL; shuttlel,shuttie2,shuttle3 REAL; elastic,nchan.mixer,ehf REAL; imcos,imsin,qcos,qsin,cart REAL; enphon.widphon,inphon SMALLARRAY; exy,adder,tempterm,enspan REAL; dfile,epson TEXT; rx, ry BYTE; {******************************************************************} {The following are external procedures, obtained by linking up with cjlib, cmulibt and paslib. } Procedure Clear_text; EXTERNAL; Procedure Openworkstation(which : word EXTERNAL; Procedure Closeworkstation; EXTERNAL; Procedure Gsxremove; EXTERNAL; Procedure Cleargraph; EXTERNAL; Procedure Osbyte (num,x,y byte; VAR rx.ry byte); EXTERNAL; Procedure Oscli (cmnd : string) EXTERNAL; Procedure Inputxy(var x,y DATARRAY; var npts INTEGER; var title,xlabel STRING; var ylabel,other_info STRING); EXTERNAL; Procedure Edit_data(var x.y DATARRAY var npts INTEGER) EXTERNAL; Procedure Set axes (p DATARRAY npts INTEGER; var min,max,gap REAL; your_choice BOOLEAN) EXTERNAL; Procedure Border; EXTERNAL; Procedure Box; EXTERNAL; Function Hapx (x REAL) : INTEGER; EXTERNAL; Function Mapy (y REAL) : INTEGER; EXTERNAL; Procedure R_to_str(r REAL; var ans_string S6 ); EXTERNAL; Procedure Tick_xaxis; EXTERNAL; Procedure Tick_yaxis; EXTERNAL; Procedure Plot_data (x,y DATARRAY; npts INTEGER; style STYLES); EXTERNAL; Procedure Header_enter (var title : STRING; var xtitle,ytitle : STRING); EXTERNAL; Procedure Annotate (title STRING; xtitle,ytitle STRING); EXTERNAL; Function Get_key CHAR ; EXTERNAL; Procedure Clear_three ; EXTERNAL; Procedure set_size ; EXTERNAL; Procedure filexytfname str15; xspec,yspec DATARRAY; npts INTEGER; title,xlabel,ylabel STRING; otherinfo STRING); EXTERNAL; {The following procedures are defined here} Procedure init_work_array(var trans : COMARRAY); var i : INTEGER; air : REAL; Begin air := 8 * arctan(1) / npts; for i := 0 to (npts -1 ) do begin with transti] do begin x := cos (air * i ); if (flag = inverse) then y := -sin(air * i) else y := sin(air * i) end end end; {of procedure initialise work array} Procedure scramble(var spec COHARRAY); var i.j.k.l INTEGER; twix COMPLEX; begin for i := 1 to (npts-1 ) do begin 1 := i; k := 0 ; for j := 0 to (power_2 - 1 ) do begin k := 2 * k + 1 mod 2 ; 1 := 1 div 2 end; if i < k then begin twix := specCi]; specCi] := specCk]; specCk] := twix end end end; {end of procedure scramble} Procedure sum(z,w : COMPLEX; var s : COMPLEX); begin with s do begin x := z.x + w.x; y ;= z.y + w.y end end; {of procedure sum} Procedure dif(z,w : COMPLEX; var s : COMPLEX); begin with s do begin x : = z.x - w.x; y := z.y - w.y end end; {of procedure dif} Procedure prod(z,w ; COMPLEX; var s : COMPLEX); begin with s do begin x := z.x * w.x - z.y * w.y; y := z.x * w.y + z.y * w.x end end; {of procedure product} Procedure neg(u : COMPLEX; var w : COMPLEX); begin w.x := -u.x; w.y := -u.y end; {of procedure negate} Procedure trftvar spec : COMARRAY) var lvl.tla.tlb.expon.p.i,j.k : INTEGER; s i z : COMPLEX; begin tla := 2 ; tlb ;= 1 ; for lvl ;= 1 to power_2 do begin p ;= npts div tla; expon ;= 0 ; for j := 0 to (tlb - 1 ) do begin i : = j; s := trans[expon]; while i < npts do 245 begin k := i + tlb; if j = 0 then z := spectk] else prod(spec[k],s,z); dif(spec[i], z.spectk]); sum(specti],z,specti]); i := i + tla end; expon := expon + p end; tla := 2 * tla; tlb := 2 * tlb end end; {of procedure transform} {*******************t**************************************************} Begin {main program} writeln ('This program is called eelsim. It will simulate HREELS spectra *); writeln ('from various parameters which you must supply. It convolves'); writeln ('thermal broadening, overtones and an elastic peak into the’); writeln ('spectrum by means of a Fast Fourier transform routine.'); writeln (' '); writeln ('Your spectrum will be calculated using a power of 2 points;'); writeln (' ’ ) ; writeln ('What power of 2 ? - CAUTION, THIS MUST NOT BE MORE THAN 9' ); readln (power_2 ); writeln (’Enter a title for your spectrum.'); readln (title); write ('Enter low energy high energy / eV. ’); readln (low_energy,high_energy); enspan := high_energy - low_energy; write ('Enter the electron velocity perpendicular to the surface /eV *); readln (elvel); write (’Enter epsilon HF, the dielectric constant of the surface:'); readln (ehf); write ('How many phonon modes?’); readln (nophon); for i := 1 to nophon do Begin write (’Enter energy, width and intensity / eV.’); readln (enphonCi],widphon[i],inphon[i]) end; {of do loop} { This bit defines some values used later on } npts := round(exp(power_2*ln(2 ))); halfpts := npts div 2 ; qrpts := npts div 4; {calculates loss function} spacer := enspan / (npts - 1 ); W1 := 0; adder := 0 ; for n := 1 to (npts - 1 ) do Begin W 1 :=W1 + spacer; viper:= 2 * spacer / W1 / elvel; e 1 := ehf; e2 := 0 ; for i := 1 to nophon do Begin shuttlel := enphonCi] * enphonCi] - W 1 * W 1 ; shuttle2 := W 1 * widphon[i]; shuttle3 := shuttlel * shuttlel + shuttle2 * shuttle2; e1 := e1 + (inphonCi] * shuttlel / shuttle3); e2 := e2 - (inphonCi] * shuttle2 / shuttle3) end; yspecCn] := -e2 / ( sqr(e1 + 1) + sqr(e2 )) * viper; adder : = adder + yspecCi] end; {of do loop} writeln ('Total loss intensity is adder); {Reads in data for elastic and thermal features} write ('Enter elastic peak width: '); readln (fwhm); widebit := fwhm * (npts-1) / enspan; nchan := low__energy * (npts-1 ) / enspan; write ('Enter temperature /eV ’); readln (temp); tempterm := temp * (npts-1 ) / enspan; {plotting out the calculated loss function} ymax:= 0 ; for i := 0 to npts do if ymax < yspecCi] then ymax := yspecCi]; xmin := low_energy; xmax := high_energy; xgap := 0 .1 ; for i := 0 to (npts-1 ) do begin xspecCi] := xmin + i * spacer; end; ymin := 0 ; set_size; open_workstation (1 ); box; border; tick_xaxis; Annotate (titleKinetic energy / eV'.’N/e’); Plot_data (xspec,yspec,npts,line); Clear_three; write ('Would you like a hard copy ?'); answer := get__key; 247 if (answer = 'y'J or (answer = *Y') then Begin osbyte (5,1 ,1 ,rx,ry); oscli (’GDUMP 0 0 1 1 20* ) end; {Creating complex array} for i := 0 to (npts-1 ) do begin specCil.x := yspec[i]; spec[i].y := 0 end; {Thermal excitation with Bose-Einstein statistics} for i := 1 to (halfpts - 1 ) do begin j := npts - i; shuttlel := i / tempterm; if shuttlel < 20 then begin cart := spec[i].x / (exp(tempterm) - 1 ); spec[i].x := spec[i].x + cart; specCjl.x ;= spec[j].x + cart end {if} end; {of do loop} {Forward FT} flag := inverse; {flag must be INVERSE for forward transform} init_work_array(trans); scramble(spec); trf(spec); {Exponential of the FT - this bit self-convolutes the function to give elastic peak and overtones} for i := 0 to (npts-1 ) do begin exy := exp(specCil.x); spec[i].x := exy * cos(specti].y); spec[i].y ;= exy * sin(spec[i].y) end; {Gaussian broadening} shuttlel := (2 * widebit / (npts - 1 )) / ln(2 ); for i := 1 to (npts-1 ) do begin shuttle2 := exp(-i * shuttlel); specCil.x ;= shuttle2 * specCil.x; specCil.y := shuttle2 * specCil.y end; {shifting the FT by nchan channels} q := 8 * nchan * arctanU) / (npts - 1 ); for i ;= 0 to (npts-1 ) do begin 248 qcos := cos(i*q); qsin := sin(i*q); mixer := (qcos * spec[i].x) - (qsin * spec[i].y); spec[i].y := (qcos * spec[i].y) + (qsin * spec[i].x); spec[i].x := mixer end; {of do loop} { Back FT} flag := normal; {flag must be NORMAL for the back transform} init_work_array(trans); scramble(spec); trf(spec); {Replacing old data in yspec with new data} for i 0 to (npts - 1 ) do yspecti] := spec[i].x; { The program now allows the user to plot the new data. } ymax:= 0 ; for i := 0 to (npts-1 ) do if ymax < yspecti] then ymax := yspecCi]; xgap ;= 0 .1; xmin := low_energy ; xmax := high_energy; xspecCO] := xmin; for i := 1 to (npts-1 ) do xspecCi] := xspec[i-1] + spacer; set_size; Set_axes(yspec,npts,ymin,ymax,ygap,no_choice); ymin := 0 ; open_workstation(1 ); box; border; Tick_xaxis; Annotate (titleKinetic energy / eV’,’N/e'); Plot_data (xspec,yspec,npts,line); Clear_three; write ('Would you like a hard copy ?'); answer := get_key; if (answer = ’y*) or (answer = 'Y') then Begin osbyte (5,1,1,rx,ry); oscli ('GDUMP 0 0 1 1 20‘); assign(epson,'LST:'); rewrite(epson); writeln(epson); writeln(epson,' Phonon | energy/eV | width/eV | intensity'); writeln(epson,' ------'); writeln(epson,' 1 | ’,enphont1]:6 :4,' : ’.widphonC1];6 :4,’ | ',inphonC1]:6 :4); writeln(epson,' 2 | ',enphon[2 ]:6 ;4,' : ',widphon[2]:6 :4,’ | ',inphonC2 ]:6 :4); writeln(epson,' 3 | ',enphon[3]:6 ;4,' : ',widphon[3]:6 :4,’ | ',inphon[3]:6 :4); writeln(epson); 249 writelntepson,* The width of the elastic peak is: ',fwhm,' eV‘); writeln(epson,'Temperature is '.temp,' eV'); writeln(epson,'The perpendicular electron velocity is ’.elvel,’ eV’ ); writeln(ep s o n T h e surface dielectric constant is ',ehf); end; { The program now allows the user to file the simulated spectrum. } writet'Would you like to file the simulated spectrum? '); answer := get_key; if (answer = 'y') or (answer = ’Y‘) then Begin write ('Enter a name for your file; '); readln (specname); write ('Enter first line of text; ’); readln (atext); write (’Enter second line of text; '); readln (btext); filexy (specname,xspec,yspec,npts,* atext,btext,' '); end; {if} close_workstation; end. 250 References 1. N. Izumi, Japanese Journal of Applied Physics 16, 273 (1977). 2. D.C. Cronemeyer and M.A. Gilleo, Phys. Rev. 82, 975 (1951). 3. D.C. Cronemeyer, Phys. Rev. 87, 876 (1952). 4. D.C. Cronemeyer, Phys. Rev. 113, 1222 (1959). 5. J. Robertson, Phys. Rev. C 12, 4767 (1979). 6 . J. Robertson, Phys. Rev. B 30, 3520 (1984). 7. V.K. Miloslavskii, Optika i Spektroskopiia VII, 154 (1959). 8 . P.A. Cox, R.G. Egdell, W.R. Flavell and R.Helbig, Vacuum 33, 835 ( 1983) . 9. K. Vos, J. Phys. C 10, 3919 (1977). 10. S. Munnix and M. Schmeits, Surf. Sci. 126, 20 (1983). 11. S. Munnix and M. Schmeits, Pys. Rev. B 30, 2202 (1984). 12. S. Munnix and M. Schmeits, Solid State Communications 43, 867 ( 1982). 13. S. Munnix and M. Schmeits, Phys. Rev. B 27, 7624 (1983). th 14. P.L. Gobby and G.J. Lapeyre, 13 Conf. on Physics of Semiconductors, edited by F.G. Fumi, North-Holland, Amsterdam (1976). 15. L.E. Firment, Surface Science 116, 205 (1982). 16. R.H. Tait and R.V. Kakowski, Phys. Rev. B. 20, 5178 (1979). 17. M.S. Wrighton, D.S. Ginley, P.T. Wolczanski, A.B. Ellis, D.L. Morse and A. Linz, Proc. Nat. Acad. Sci. 72, 1518 (1975). 18. "Solar energy conversion: Solid State Physics Aspects", in Topics in Applied Physics 31, edited by B.0. Seraphim, Springer Verlag, Berlin (1981). 19. A. Inone, T. Ono and T. Ohhara, Japan Kokai Patent (1977), (C1.B01J27/16). 20. K. Nishimoto, S. Yokoyama and T. Sera, Japan Koka Tokkyo Koko Patent (1980), (Cl.B01J23/30). 21. V.E. Henrich, G. Dresselhaus and H.*J.. Zeiger in "Physics of Semiconductors" p.726, edited by F.G. Fi/mi, North-Holland, Amsterdam ( 1 976). 22. V.E. Henrich, G. Dresselhaus and H.cj!. Zeiger, Solid State Commun. 24, 623 (1977). 251 23. V.E. Henrich, G. Dresselhaus and H.J. Zeiger, J. Vac. Sci. Technol. 15, 534 (1978). 24. V.E. Henrich, G. Dresselhaus and H.J. Zeiger, Phys. Rev. B 17, 4908 (1978). 25. W.J. Lo and G.A. Somorjai, Phys. Rev. B 17, 4942 (1978). 26. V.E. Henrich, G. Dresselhaus and H.J. Zeiger, Phys. Rev. Letters 36, 1335 (1976). 27. V.E. Henrich and R.L. Kurtz, Phys. Rev. B 23. 6280 (1981). 28. W. Gopel, G. Rocker and R. Feierabend, Phys. Rev. B 28, 3427 ( 1983). 29. W. Gopel, J.A. Andersen, D. Fraenkel, M. Jaehnig, K. Phillips, J .A. Schaefer and G. Rocker, Surf. Sci. 139, 333 (1984). 30. W.J. Lo, Y.W. Chung and G.A. Somorjai, Surf. Sci. 71, 199 (1978). 31 . S. Munnix and M. Schmeits, Solid State Commun 50. 1087 ( 1984 ) . 32. S. Munnix h M. Schmeits, Phys. Rev. B 31, 3369 ( 1986) . 33. R. Fuchs and K.L. Kliewer, Phys. Rev. 140, A2076 (1965) • 34. L. Kesmodel, J.A. Gates and Y.W. Chung, Phys. Rev. B 23 , 489 (1981). 35. G.D. Mahan, unpublished; reported in 46. 36. D.M. Eagles, J. Phys. Chem. Solids 25. 1243 (1964). 37. G. Rocker, J.A. Schaefer and W. Gopel, Phys. Rev. B 30, 3704 ( 1984 ). th 38. R.W. Rice and G.L. Haller, Proc. 5 Intern. Congr. Catal. (1973), edited by J.W. Hightower, North-Holland, Amsterdam. 39. M.L. Knotek, Surf. Sci. 101, 334 (1980). 40. V.E. Henrich, Progress in Surf. Sci. 14, 175 (1983). 41. R.L. Kurtz and V.E. Henrich, Phys. Rev. B 25, 3563 (1982). 42. R.L. Kurtz and V.E. Henrich, Phys. Rev. B 26, 6682 (1982). 43. S. Andersson, B. Collin, U. Koyhnsherna and A. Magneli, Acta Chem. Scand. 11, 1641 (1957). 44. S. Andersson and A.D. Wadsley, Nature 11, 581 (1966). 45. J.S. Anderson and B.G. Hyde, J. Phys. Chem. Solids 28, 1393 (1967). 46. R.J.D. Tilley, RSC Specialist Periodical Report on Chemical Physics of Solids and Surface, p. 121 vol. 8 , edited by M.W. Roberts 252 and J.M. Thomas, The Chemical Society, London (1980). 47. J.S. Anderson and R.J.D. Tilley, J. Solid State Chem.2, 472 ( 1970) . 48. C.R.A. Catlow and R. James, RSC Specialist Periodical Report on Chemical Physics of Solids and Surface, p.108 vol. 8 , edited by M.W. Roberts and J.M. Thomas, The Chemical Society, London (1980). 49. V.E. Henrich, Progress in Surf. Sci. 9, 143 (1979). 50. R.G. Egdell and P.D. Naylor. Chem. Phys. Lett. 91, 200 (1982). 51. P.A. Cox, R.G. Egdell and P.D. Naylor, J. Electron Spectroscopy and Relat. Phenom. 29, 247 (1983). 52. N.B. Brookes, D.S.-L. Law, T.S. Padmore, D.R. Warburton and G. Thornton, Solid State Commun. 57, 473 (1986). 53. I.W. Owen, N.B. Brookes, C.H. Richardson, D.R. Warburton, F.M. Quinn, D. Norman and G. Thornton, Surf. Sci., in press. 54. N.B. Brookes, F.M. Quinn and G. Thornton, Physica Scripta, in press. 55. F.J. Berry, Advances in Catalysis 30, 97 (1981). 56. M. Nitta, S. Kanefusa and M. Haradome, J. Electrochem. Soc. 125, 1676 (1978). 57. M. Nitta, S. Ohtani and M. Haradome, J. Electronic Mater. 9, 727 ( 1980). 58. R.J. Bird, Metal Sci. 7, 109 (1973). 59. T. Farrell, Metal Sci. 10, 87 (1976). 60. W.E. Morgan and J.R. Van Wazer, J. Phys. Chem. 77, 964 (1973). 61. P.A. Grutsch, M.V. Zeller and T.P. Fehlner, Inorg. Chem. 12, 1431 (1973). 62. C.L. Lau and G.K. Wertheim, J. Vac. Sci. Technol. 15, 622 ( 1978). 63. R.A. Powell, Appl. Surf. Sci. 2,397 (1979). 64. P.A. Cox, R.G. Egdell, W.R. Flavell and R. Helbig, Vacuum 33, 835 (1983). 65. D.F. Cox and G.B. Hoflund, Surf. Sci. 151, 202 (1985). 6 6 . D.F. Cox, G.B. Hoflund and H.A. Laitinen, Appl. Surf. Sci. 20, 30 (1984). 67. D.F. Cox, S. Semancik and P.D. Szuromi, J. Vac. Sci. Technol. (Summ. Abs.) 4, 627 (1986). 6 8 . S. Semancik and D.F. Cox, J. Vac. Sci. Technol. (Summ. Abs.) 4 253 626 (1986). 69. P.A. Cox, R.G. Egdell, C. Harding, A.F. Orchard, W.R. Patterson and P.J. Tavener, Solid State Commun. 44, 873 (1982). 70. P.A. Cox, R.G. Egdell, C. Harding, W.R. Patterson and P.J. Tavener, Surf. Sci. 123, 179 (1982). 71. R.G. Egdell, W.R. Flavell and P.J. Tavener, J. Solid State Chem. 51. 345 (1984). 72. E. de Fresart, J. Darville and J.M. Gilles, Solid State Commun. 37, 13 (1980). 73. E. de Fresart, J. Darville and J.M. Gilles, Appl. Surf. Sci. 11/12, 637 (1982). 74. D.R. Pyke, R. Reid and R.J.D. Tilley, J. C. S. Faraday I 76, 1174 (1980). 75. D.R. Pyke, R. Reid and R.J.D. Tilley, J. Solid State Chem. 25, 231 (1978). 76. W.R. Flavell, Part II Thesis, Oxford 1984: published as part of R.G. Egdell, S. Eriksen and W.R. Flavell, Solid State Commun. 60, 835 (1986). 77. S. Munnix and M. Schmeits, Phys. Rev. B 33, 4136 (1986). 78. A. Einstein, Ann. Physik 17, 132 (1905). 79. B.P. Straughan and S. Walker (editors); "Spectroscopy", Vol. 3, Chapman & Hall Ltd., London (1976). 80. J. Szajman and R.C.G. Leckey, J. Electron Spectroscopy and Relat. Phenom. 23, 83 (1981). 81. D. A. Shirley in "Photoemission in Solids I. General Principles", Topics in Applied Physics 26, edited by M. Cardona and L. Ley, Springer Verlag, Berlin (1978). 82. D. Briggs and M.P. Seah (editors), "Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy", John Wiley & Sons, Chichester (1983). 83. D.W. Turner and M.I. Al-Joboury, J. Chem. Phys. 37, 3007 (1962). 84. C. Nordling, E. Sokolowski and K. Siegbahn, Phys. Rev. 105, 1676 ( 1957). 85. E. Sokolowski, C. Nordling and K. Siegbahn, Arkiv Physik 12, 301 (1957). 8 6 . S. Hagstrom, C. Nordling and K. Siegbahn, Phys. Lett. 9, 235 ( 1964 ). 87. K. Siegbahn, C. Nordling, G. Hohansson, J. Hedman, P.F. Heden, K. Hamrin, U. Gelius, T. Bergmark, L.O Werne, R. Manne and Y. Baer, "ESCA Applied to Free Molecules", North Holland, Amsterdam (1969). 254 8 8 . W.R. Flavell, D. Phil. Thesis, Oxford (1906). 89. H .0. Krause and J.G. Ferreira, J. Phys. B8 , 2007 (1975). 90. See e.g. F.P. Larkins, Atromic Data and Nuclear Tables 20, 311 (1977). 91. H.E. Bishop and J.C. Riviere, J. Appl. Phys. 40, 1740 ( 1969) . 92. M.W. Roberts and C.S. McKee, "Chemistry of the Metal-Gas Interface", Oxford University Press, Oxford (1978). 93. J.B. Pendry, "Low Energy Electron Diffraction", Academic Press, New York (1974). 94. D.M. Newns in "Vibrational Spectroscopy of Adsorbates", Springer Series in Chemical Physics 15, edited by R.F. Willis, Springer Verlag, Berlin (1980). 95. H. Ibach and D.L. Mills, "Electron Energy Loss Spectroscopy and Surface Vibrations", Academic Press, New York (1982). 96. H. Froitzheim, in "Electron Spectroscopy for Surface Analysis", Springer Series in Chemical Physics, edited by R.F. Willis, Springer- Verlag, Berlin (1977). 97. R.F. Wallis, Prog. Surf. Sci. 4, 233 (1974). 98. H. Ibach, Phys. Rev. Lett. 24, 1416 (1970). 99. H. Ibach, J. Vac. Sci. Technol. 9, 713 (1972). 100. Y. Goldstein, A. Many, I. Wagner and J. Gersten, Surface Science 98, 599 (1980). 101. A. Many, I. Wagner, A. Rosenthal, J.I. Gersten and Y. Goldstein, Phys. Rev. Lett. 46, 1648 (1981). 102. A.D. Baden, P.A. Cox, R.G. Egdell, A.F. Orchard and R.J.D. Wilmer, J. Phys. C 14. L1081 (1981). 103. D.G. Aitken, P.A. Cox, R.G. Egdell, M.D. Hill and I. Sach, Vacuum 33, 753 (1983). 104. P.A. Cox, M.D. Hill, F. Peplinskii and R.G. Egdell, Surf. Sci. 141, 13 (1984). 105. R.G. Egdell, M.R. Harrison, M.D. Hill, L. Porte and G. Wall, J. Phys. C 17. 2889 ( 1983 ) . 106. P.A. Cox, W.R. Flavell, A.A. Williams and R.G. Egdell, Surf. Sci. 152/153, 784 (1985). 107. P.A. Cox and A.A. Williams, Surf. Sci. 152/153, 791 (1985). 108. G. Dalmai-Imelik, J.C. Bertolini and J. Rousseau, Surf. Sci. 63, 67 (1977). 255 109. J.C. Bertolini, G Dalmai-Imelik and J. Rousseau, J. Microsc. Spectrosc. Electron. 2, 575 (1977). 110. M. Prutton, private communication. 111. M. Liehr, P.A. Thiry, J.J. Pireaux and R. Caudano, J. Vac. Sci Technol. A2, 1079 (1984). 1 1 2 . P.A. Thiry, M. Liehr, J.J. Pireaux and R. Caudano, Phys. Rev. B 29, 4824 ( 1984 ) . 113. E. Evans and D.L. Mills, Phys. Rev. B 5, 4126 (1972). 114. D.L. Mills, Surface Science 48, 59 (1975). 115. G.D. Mahan, in "Elementary Excitations in Solids, Molecules and Atoms: Part B", edited by J.T. Devrese, A.B. Kurz and T.C. Collins, Plenum, New York (1974). 116. P.A. Cox, Solid State Commun. 45, 91 (1983). 117. F.J. Peplinskii, Part II Thesis, Oxford (1983). th 118. C. Kittel, "Introduction to Solid State Physics", 5 edition, John Wiley and Sons, New, York, (1976). 119. H. Froitzheim, H. Ibach and D.L. Mills, Phys. Rev. B 11, 4980 ( 1975). 120. A.A. Lucas and J.P. Vigneron, Solid State Commun. 49, 327 ( 1 984 ). 121. Leybold Heraeus ELS 22 Instruction Manual (1983). 122. P. Henkel and J. Gray, "The Mass Spectroscopy Handbook of Service". 123. C.D. Wagner, W.M. Riggs, L.E. Davis, J.F. Moulder and G.E. Muilenberg, "Handbook of X-ray Photoelectron Spectroscopy", Perkin Elmer Corporation, Eden Prairie (1979). 124. William McGeoch & Co., Witton, Birmingham. 125. G. Samsonov, editor of "The Oxide Handbook", IFI / Plenum, New York (1982). 126. N. Beatham, A.F. Orchard and G. Thornton, J. Phys. Chem. Solids 42, 1051 (1981). 127. Z.J. Gray-Grychowski, R.G. Egdell, B.A. Joyce, R.A. Stradling and K. Woodbridge, Surface Science, in press. 128. J.G. Gay, W.A. Albers and F.J. Arlinghaus, J. Phys. Chem Solids 29, 1448 (1968). 129. R.S. Katiyar, J. Phys. C 3, 1087 (1970). 130. W.G. Spitzer, R.C. Miller, D.A. Kleinman and L.E. Howorth, Phys. 256 Rev. 126. 1710 (1962). 131. W.R. Flavell, D. Phil. Thesis, Oxford (1986): published as part of P.A. Cox, R.G. Egdell, S. Eriksen and W.R. Flavell, J. Electron Spectroscopy and Relat. Phenom. 39, 117 (1986). 132. J. McKay and V.E. Henrich, Surface Science 137, 463 (1984). 133. D. Menzel and R.Gomer, J. Chem. Phys. 41, 3311 (1964). 134. P.A. Redhead, Can. J. Phys. 42, 886 (1964). 135. M.L. Knotek and P.J. Feibelman, Phys. Rev. Lett. 40, 964 (1978). 136. M.A. Langell and S.L. Bernasek, J. Vac. Sci. Technol. 17, 1287 (1980). s 137. S.W. Bellard and E.M. Williams, Surface Science 80, 450 (1979). 138. M.P. Seah and W.A. Dench, Surface Interface Analysis 1, 1 (1979). 139. A. Hamnett in Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, edited by K.F. Hellwege and O. Madelung, Vol III/17g, Springer Verlag, Berlin (1984). 140. J.G. Mavroides, D.I. Tchernev, J.A. Kafalas and D.F. Kolesar, Mater. Res. Bulletin 10, 1023 (1975). 141. J.I. Gersten, I. Wagner, A. Rosenthal, Y. Goldstein, A. Many and R.E. Kirby, Phys. Rev. B 29, 2458 (1984). 142. A.B.P. Lever, "Inorganic Electronic Spectroscopy", Elsevier, Amsterdam (1968). 143. P. Day, p.3 of "Mixed Valence Compounds", edited by D.R. Brown, Reidel, Dordrecht (1980). 144. D.M. Adams, "Inorganic Solids", John Wiley, London (1974). 145. R.D. Canon, "Electron Transfer Reactions", Butterworths, London ( 1980) . 146. D.W. Turner, C. Baker, A.D. baker and C.R. Brundle, "Molecular Photoelectron Spectroscopy", John Wiley, London (1970). 147. P.D. Naylor and R.G. Egdell, published as part of S. Eriksen, P. D. Naylor and R.G. Egdell, Spectrochimica Acta, in press. 148. M.J. Campbell, L. Liesegang, J.D. Riley, R.C.G. Leckey, J.G. Jenkin and R.T. Poole, J. Electron Spectroscopy 15, 83 (1979). 149. D. Scmeisser, F.J. Himpsel, G. Hollinger, B. Reihl and K. Jacobi, Phys. Rev. B 27. 3279 (1983). 150. C. Webb and M. Lichtensteiger, Surface Science 107, L305 (1981). 151. S. Anderson and J.W. Davenport, Solid State Commun. 28, 677 ( 1978). 257 152. D.G. Aitken, P.A. Cox, R.G. Egdell, M.D. Hill and I. Sach, Vacuum 33. 753 (1983). 153. D.B. Almy, D.C. Foyt and J.M. White, J. Electron Spectroscopy 11, 129 (1977). 154. R.L. Kurtz and V.E. Henrich, Phys. Rev. B 28, 6699 (1983). 155. H. Ibach, H. Wagner and D, Bruchman, Solid State Commun. 42, 457 ( 1902) . th 156. A.F. Wells, "Structural Inorganic Chemistry", 4 edition, Oxford University Press, London (1975). 157. J.M. Thomas and M.J. Tricker, J. Chem. Soc. Faraday Trans II 71, 329 (1975). 158. P. Bayat-Mokhtari, S.M. Barlow and T.E. Gallon, Surface Science 83, 131 (1979). 159. Z. M. Jarzebski and J.P. Marton, J. Electrochem. Soc.123, 299C ( 1976). 160. R. Summitt, J. Appl. Phys. 39, 3762 (1968). 161. H. Kostlin, Festkorperprobleme XXII, 229 (1982). 162. A.R. Miller, "Pascal Programs for Scientists and Engineers", Sybex, Berkeley (1981). 163. A.A. Williams, Part II Thesis, Oxford (1982).