Recent developments in appearance potential spectroscopy

Surface Science 48 (1975) 80-98 0 North-Holland Publishing Company

RECENT DEVELOPMENTS

IN APPEARANCE

POTENTIAL

SPECTROSCOPY* Robert L. PARK** Sundia Lab~ra~~~~s~ A~b~querq~~, New Mexico 87115,

USA

Appearance potential spectroscopy measures the probability for the creation of a hole in an inner atomic shell as a function of electron bombardment energy. The spectrum of excitation thresholds provides a simple means of examining the elemental composition in the surface region of a solid. Near threshold the excitation transitions indirectly probe the unoccupied conduction band states. The localized core state, however, overlaps only part of the conduction band, and the line shapes are thus related to a very local density of states. The interpretation is complicated by broadening introduced by the finite lifetime of the core hole, variations in the magnitude of the atomic matrix elements which suppress some thresholds, and the screening response of the conduction electrons to the suddenly altered core potential. These problems are illustrated by spectra of Th, Nb, Re, SczOa, Ni, and Si surfaces. Distinct spectral characte~stics related to crysta~ograp~c orientation are reported for nickel single crystals.

1. Introduction Techniques for the study of material properties are less frequently discovered than rediscovered. The revival of an old technique may result from technological innovations which alleviate experimental constraints, or from theoretical advances which extend the usefulness of the information obtained. Both elements are present in the development of soft X-ray appearance potential spectroscopy (SXAPS). The “critical potentials” for the excitation of characteristic X-rays by electron bombardment were widely used in the late 1920’s to construct X-ray energy-level diagrams of the elements. The method consisted of detecting abrupt, albeit small, changes in the slope of the total X-ray yield of an anode as a function of the applied potential. The emission from a metal photocathode exposed to the X-rays was used as a measure of the total yield. The method was not particularly sensitive, because of the large bremsstrahlung background which tends to obscure the subtle changes in the total yield that result from the excitation of characteristic radiation. * Supported by the US Atomic Energy Commission. ** Present address: Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

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81

With the development in the 1930’s of dispersive X-ray analyzers which could filter out continuum radiation, the critical potential measurements were abandoned. The study of critical or “appearance” potentials was revived briefly in the 1950’s by Shinoda, Suzuki, and Kato [l] who demonstrated that it is possible to suppress the bremsstrahlung without a dispersive analyzer by electronically differentiating the yield. More significantly, they recognized that the shapes of the edges provide a means of studying the chemical environment of atoms in a solid. The latest resurrection of this method by Park, Houston and Schreiner [2] involves the use of potential modulation differentiation and synchronous detection to extract the excitation edges. In this form, soft X-ray appearance potential spectroscopy (SXAPS) represents an important technique for the study of the electronic structure and composition of solid surfaces. It is also a remarkably simple technique; but in the sense of being uncomplicated rather than easy. Failure to appreciate this distinction has led to some disenchantment among dilettantes. As in any measurement involving small signal levels, careful attention to experimental detail is a necessity. SXAPS has been recently and thoroughly reviewed by Park and Houston [3], by Bradshaw [4], and by Kato [5]. The reader is referred to these reviews for additional detail and more complete bibliographies. In the present paper the technique will be briefly described and illustrated with recent measurements on polycrystalline and single-crystal surfaces. The emphasis will be on unresolved puzzles in the acquisition and interpretation of spectra.

2. Production

of X-rays

If a potential, I/‘, is applied between a thermionic emitter and an anode, electrons will arrive at the anode surface with an energy eV + ep, + kT relative to the Fermi energy of the anode, where eq, is the emitter work function and kT is the average energy of the thermionically emitted electrons just outside the cathode surface (fig. la). If an electron is captured by a state el above the Fermi energy, energy may be conserved by the direct emission of a bremsstrahlung photon of energy hv, =eVteq,tkT-el.

(I)

The number of photons of energy hv, is thus a measure of the density of states available at el. This elegant method of directly probing the density of unoccupied states in the surface region of a solid is accomplished experimentally by fixing the pass band of an X-ray spectrometer at an arbitrary wavelength removed from any characteristic line, and varying the incident electron energy to move the short wavelength limit of the bremsstrahlung spectrum across the pass band [6]. As with all direct methods of probing the density of states, the “bremsstrahlung isochromat” spectrum measures some sort of average state density over all atomic species at the surface. Thus the interpretation of the spectra is relatively straightforward for pure

82

R.L. Park/Appearance

potential spectroscopy

(a)

cb)

+kT

+kT

ev

II

SAMPLE

SAMPLE

Fig. 1. Production of continuum and characteristic X-rays by electron bombardment. (a) The incident electron may be radiatively captured in a state er above the Fermi level. The emitted bremsstrahlung photon will have an energy hv = e V + eqc + kT - el The bremsstrahlung spectrum near the cutoff at er = 0 directly probes the density of conduction band states. (b) The incident electron may scatter from a core electron exciting it into a state ~2 = eV + elpc + kT - ~1 - EB, The core hole may subsequently decay by the emission of a characteristic X-ray photon. The excitation probability, measured by the number of characteristic X-rays, is a two-electron probe of the conduction band.

elemental solids [7], but for materials such as alloys [8] the interpretation may be quite ambiguous. In the capture of an incident electron, energy may also be conserved by the excitation of a core electron into a state e2 as shown in fig. lb. e2 is given by e2 =eV+eq,+kT-El

-EB,

(2)

where EB is the binding energy of the core electron relative to the Fermi energy. The recombination of the core hole may take place radiatively by the emission of a characteristic X-ray photon, but unlike the production of bremsstrahlung, the characteristic process has a distinct threshold at e Vcrit = EB - ep, - kT. Above this threshold, the core level excitation

(3) probability

is determined

by the den-

R.L. Park/Appearance

potential spectroscopy

83

sity of unoccupied states, but the view of the conduction states is very different from that provided by the bremsstrahlung spectrum. In the first place, the excitation probability is a two-electron probe of the conduction band. The excited core electron, as well as the incident electron, must be fitted into available states above the Fermi level. The density of final states for the two electrons is determined by all the combinations of eI and e2 allowed by the conservation of energy as expressed by eq. (2). The two-electron density of states N2&!?) is thus given by the self-convolution of the density of conduction band states for one electron N,(E), i.e., E &(E)

=s

N,(E’)N,(E

- E’) dE’.

0

Assuming constant oscillator strengths, the excitation probability is proportional to the integral product of the final-state distribution given by NZJE) and the initialstate distribution Ni(E) corresponding to the filled core level. The width of the core level is a consequence of the finite lifetime r of the hole that must be created to verify its existence. The core level is thus represented by a Lorentzian of width h/r [9], and the transition density function [lo] is given by E T(E)

= J 0

Nzc(E’)Ni(E

+ Eg - E’) dE’.

According to this simple picture, the edge should have the shape of the self-convolution of the density of conduction states broadened by the core level, in contrast to the direct sampling of the conduction band in bremsstrahlung isochromat spectroscopy. There is a second and more important difference in the picture of the conduction states that these two processes provide. The excitation edges are specific to a single element. This makes it possible to separately examine the states accessible to core electrons of different elements on the same surface. This very local view of the density of states can provide information on such questions as the extent to which atoms retain their own electronic states or share them with other elements in a common band [ 111. It is a necessary consequence of the uncertainty principle that this local view will be smeared out relative to that measured by bremsstrahlung isochromat spectroscopy. This smearing takes the form of the lifetime broadening of the core hole. Thus the density of states viewed by transitions involving a 2s core hole shows less detail than the view involving a 2p hole because of the strong 2p + 2s Coster-Kronig transition [ 121.

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second derivative

200

POTENTIAL

400

600 (volts)

800

Fig. 2. The extraction of core-level excitation edges of 304 stainless steel from the bremsstrahiung background by differentiation. The total yield was measured photoelectrically. Only the Fe L2,s and Cr Lzp edges can be detected in the total yieId. The second derivative of the photoelectron current was obtained by the potential modulation method using 1.25 V rms oscillation. Vanadium has been found as an impurity on every stainless steel sample examined. It has not been reported in AES studies because of the diffieualty of separating it from Cr and 0.

3. Sensitivity and background To observe the core-level excitation spectrum, it must first be distinguished from the background of bremsstrahlung radiation. This distinction is based on the fact that the bremsstrahlung yield rises smoothly with electron energy, whereas the characteristic radiation produced by the decay of a core hole should exhibit abrupt onsets at the critical potentials defined by eq. (3). This is apparent in fig. 2 which shows the total X-ray yield of an electron-bombarded stainless steel specimen measured photoelectrically. The slope of the total yield curve is visibly greater above the Cr and Fe 2p thresholds (L~J). In addition, some slight structure can be distinguished at the Fe L, and L, thresholds. To examine these thresholds more sensitively, it is necessary to somehow suppress the rapidly increasing bremsstrahlung background. It might be supposed that the relatively simple functional dependence of the bremsstrahlung background would allow it to be subtracted. This may simplify analysis of the spectrum but it will not increase the sensitivity. To underst~d why, we must consider the sources of noise which tend to obscure the edges. These can be divided into statistical or “white” noise sources, such as shot effect [ 131 or thermal agitation in the measurement circuit [ 141, and low-frequency “flicker” noise, which is usually represented

R.L. ParkfAppearance

potential spectroscopy

85

by a l/fspectrum. It is this latter form of noise that limits sensitivity, since the contribution of white noise can be made arbitrarily small by integrating for a sufficiently long period. The I/fnoise on the other hand increases in direct proportion to the time required for the measurement. A great deal has been written on the sources of flicker noise [ 15 1, but in general it can be regarded as a measure of the instability of the entire measurement system. Thus if a scientist exercises too much patience in making a measurement, something will go wrong before he finishes. The effect of a background is to amplify the flicker noise. Changes in the background level, due to small variations in any parameter of the measurement system, may completely overwhelm a weak signal. Increasing sensitivity is thus equivalent to suppressing the low-frequency Fourier components of the spectrum. In the appearance potential technique, this suppression is achieved by differentiating the spectrum which has the effect of weighting the Fourier components of the spectrum by their frequency. To more fully suppress the background, it may be desirable to go to the second dirivative, in which case the Fourier components of the spectrum are weighted by the square of their frequency, etc. The extent to which differentiation assists in extracting excitation edges from the smoothly increasing bremsstrahlung background is evident from a comparison of the total yield curve in fig. 2 with the second-derivative spectrum. Giving weight to the higher frequency Fourier components of the spectrum also emphasizes the high-frequency components of the noise. This discriminates against the l/f flicker noise, but not the white noise. A catastrophic increase in high-frequency noise is averted only by the inability of the instrument to respond to sudden changes. Thus, associated with differentiation there must be an instrument response function which smooths the spectrum.

4. Resolution and instrument response The derivative spectrum is conveniently obtained by the potential modulation technique [ 161. If the sample potential is modulated about some value V such that V(t) = V + Vu cos ot, the output current will also be modulated. If the yield curve Z(V) is linear over the region of oscillation, the output current will exhibit a sinusoidal modulation whose amplitude is proportional to the slope of Z(V). If Z( V) is nonlinear, however, the output waveform will be distorted. The spectrum of harmonic frequencies in the output can be obtained from the Fourier cosine transform of the functional I [V(t)] : 7{I[V(t)]~=;~Z[V(t)]cosnwrdot.

(7)

0

The spectral components

derived from eq. (7) represent the broadened

derivatives

86

R.L. Park/Appearance potential spectroscopy

of I(V) [ 171. The response to a hypothetical is given by

T,(V)=;j%(V+ P’ucoswt)cosnwtdwt,

spectrum in the form of a unit impulse

(8)

0 which can be directly integrated

T,(V) =

to give

-$+$, 0

where case = - v/v,.

(10)

A knowledge of the impulse response r,(V) allows us to calculate the nth harmonic of the output current waveform, which corresponds to the nth derivative, from the convolution integral:

dnW) _ dVLxis

s”

-v

I( v’) TJ V-

V’) dV’.

(11)

0

r,(V) is of course only a partial instrument response function. The energy spread of the incident electrons must also be considered. The over-all instrument response function is just the convolution product of the derivative response T,(V) and the energy distribution of incident electrons. The oscillation amplitude can of course be made arbitrarily small at the cost of increased high-frequency noise, which must be compensated for by increasing the measurement time. The energy spread of the incident electrons is due in part to a potential drop along the emitting portion of the filament. This can be made negligible by using a heavy filament operated at high currents and low voltages, or eliminated entirely with an indirectly heated cathode. The average thermal energy of the emitted electrons is kT, which even for a tungsten filament is only about 0.25 eV. All spectroscopic measurements rely on the limited response of the instrument to filter out high-frequency noise. The usual problem is that the instrument performs its smoothing responsibilities too well. Because of the nondispersive nature of SXAPS, however, the resolution can generally be kept below 0.5 eV, which makes it perhaps the highest resolution core-level spectroscopy in use.

5. Experimental The arrangement used to obtain the differential yield is shown in fig. 3. The sample is bombarded by electrons from a bare tungsten filament. Although the relatively high temperature of the tungsten emitter is a disadvantage from the standpoint of

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potential spectroscopy

FILAMENT MULTIPLIER

SUPPLY 1”

IOA

“0’

1

L!k ”

RAMP

-

SUPPLY

+

0 - 2000”

’

+“”

OSCILLATOR v. cos *

Fig. 3. Schematic diagram of the soft X-ray appearance potential spectrometer. The sample is bombarded with electrons from a bare tungsten filament. Photons produced by electron impact pass through a grid, biased to reject electrons from the filament, and are absorbed by a gold photocathode. The resulting photoelectrons are collected on a positively biased coaxial wire. To obtain the nth derivative of the collector current, a small oscillation is superimposed on the sample potential. The nth harmonic of the oscillator frequency is selected by a resonant high-Q circuit and synchronously detected with a phase-lock amplifier.

resolution (kT = 0.25 eV), its work function is accurately known (4.52 eV) [ 181 and very stable in ultrahigh vacuum. The sample potential is supplied by a programmable high-voltage power supply, programmed with a linear ramp from a simple integrating circuit. Photons produced by electron impact pass through a ground potential grid and are absorbed by a cylindrical gold photocathode. The filament is biased a few volts above the grid to prevent electrons from entering the photocathode can. Electrons from the photocathode are collected on a positively biased coaxial collector wire. The work function of the gold photocathode is sufficiently high as to discriminate against low-energy bremsstrahlung and most of the filament incandescence. The high-energy tail of the filament radiation does contribute some shot noise, however, and a cooler filament would be an advantage from this standpoint. Additional shot noise results from ions which can Auger neutralize at the photocathode surface [ 191, but in the case of clean surfaces in ultrahigh vacuum this is not a problem. At high energies, these sources of shot noise can be completely eliminated by using a nondispersive filter such as beryllium or aluminum to screen out ions and low-energy photons [20]. The collector current is a measure of the total X-ray yield. To obtain the first-derivative spectrum, a small sinusoidal oscillation is superimposed on the potential of the sample. That portion of the collector current that varies at the frequency of the oscillation is selected by a high-Q resonant L-C circuit and further filtered and detected by a phase-lock amplifier. The use of a tuned input makes it possible to measure the alternating component of the collector current with a high impedance ( > IO7 fin) without the necessity of a preamplifier. To measure the nth harmonic of the modulation frequency (nth derivative), the

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potential spectroscopy

oscillator frequency is reduced by l/n, and a frequency multiplier is used to provide a reference at the resonant frequency of the L-C tank circuit. The oscillation amplitude determines the resolution that can be achieved. For elemental identification the resolution is not critical and it is advantageous to use a larger oscillation. In the first derivative, however, the signal-to-background ratio may be degraded if the oscillation amplitude exceeds a few volts. To go to larger amplitudes therefore, it is necessary to go to the second derivative to further suppress the background and in some cases, even the third derivative may be called for.

6. Elemental analysis of surfaces Faced with a problem involving the elemental analysis of a surface, the scientist has a choice between some dozen possible analytical techniques [2 11. Each technique provides somewhat different information, and each is hampered by its own uncertainties. Much of the uncertainty in SXAPS results from secondary features of the spectra which are related to the chemical environment of the atoms. These effects must be viewed with some ambivalence, since they frequently interfere with quantitative determinations of elemental abundance and are generally imperfectly understood. Thus the problem of elemental analysis cannot be divorced from the study of electronic structure. The principal advantage of SXAPS for elemental analysis, as compared to Auger electron spectroscopy (AES), is the relative simplicity of the spectrum. The L Auger spectrum alone consists of hundreds of lines for a heavy element, the energies of which are not susceptible to first-principles calculation. Except for very light elements therefore, elemental identification in AES is generally based on matching spectra against “standard” plots taken from samples of known composition. For elements above about 2 = 20 it is frequently possible to identify spectral groups, but not individual features within these groups. Since the appearance potential spectrum involves just the core-level binding energies and not their term differences, edges can generally be identified unambiguously from standard X-ray tables [22] even for the actinide elements [23,24]. This is seen in the second-derivative thorium spectrum shown in fig. 4 in which all of the thorium levels below 800V are observed. As an example, we have been able to identify vanadium, which occurs primarily as an impurity in chromium, on the surface of every 304 stainless steel sample we have examined in amounts ranging from a trace [25] to the fairly substantial quantity (- 5%) indicated in fig. 2. Vanadium cannot be unambiguously separated from chromium and oxygen by AES, and has not been reported in any of the numerous AES studies of stainless steel. The principal difficulty in the use of SXAPS for elemental identification is the enormous variation in sensitivity to different elements.Thus, although the technique has been used to study elements from lithium [4] to uranium [23], the detection limits range from much less than 1% of a monolayer for lanthanide lements [3,21,24],

R.L. Park/Appearance

potential spectroscopy

89

THORIUM

04

POTENTIAL

(volts)

Fig. 4. Second-derivative appearance potential spectrum of a Th surface after sputter cleaning. All of the thorium levels in this energy range can be identified. The positions of the levels are in good agreement with measurements by other techniques. Thoria is the most refractory metal oxide and is usually present in high-purity thorium at concentrations of several percent. The prominent NT, Ne spectrum demonstrates that the edges of high engular momentum core states are not necessarily suppressed.

to palladium [26] and gold [3] which have not been shown to produce detectable spectra. There appear to be at least three effects which can result in a low sensitivity to particular elements: (1) A small density of states above the Fermi energy. (2) A low fluorescent yield for the recombination of holes in those core levels accessible to study (i.e., binding energies below about 2 keV). (3) A weak oscillator strength for electron-induced inner-shell ionization near the thresholds of these accessible levels. In fact, only the first of these effects would seem to apply to all edges of a given element. As pointed out above, the detection of an edge by differentiation depends on an abrupt change in X-ray yield. The effect of the density of states above the Fermi energy on this change is illustrated schematically in fig. 5. The type of spectrum expected from a transition metal, in which the Fermi level lies in a narrow band, is compared with a noble metal in which the band is just filled. Transition metal spectra are characterized in the first derivative by a sharp peak at the threshold [ 12], whereas for a metal such as copper, in which the d band is completely tilled, the edges appear as weak steps [27]. Thus nickel is much easier to detect than its neighbor in the periodic table. It may also be concluded that the sensitivity to an

90

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(b)

1

Fig. 5. A highly schematic representation of the density-of-states effect in appearance potential spectroscopy. (a) For a transition metal the Fermi energy EF lies in a narrow partially tilled band. The one-electron density of states is given by N(E). The two-electron density of conduction states IV&E) is given by the self-convolution of N(E) above EF. The derivative of this function is given by the dashed curve and is characterized by a sharp peak at EF followed by a negative dip. (b) For a noble metal the d band is just filled, with the result that the derivative of Mac (E) is a step-like function clearly resembling the one-electron density of states. The first-derivative appearance potential spectrum should look like the dashed curves broadened by the corelevel lifetime width and the instrument response.

element can be strongly in~uenced by its chemical environment. It is interesting to note, however, that although the derivative spectrum is much weaker in the case of the noble metal, the excitation probability a few volts from edge rises at about the same rate in both spectra. The dynamic background subtraction technique of Houston [28] exploits this fact to provide a more quantitative measure of elemental abundance [29]. The density-of-states effect, however, can be partially overcome by simply operating at lower resolution. It should in fact be clear that a similar problem exists in Auger spectroscopy for elements at the other end of the transition series. It is less apparent simply because Auger spectra are commonly taken with low resolution. In contrast to the density-of-states effect, fluorescent yields can be expected to vary widely for different levels of the same element. Thus, for example, although

R.L. ParkfAppearance

potential spectroscopy

Rhenium

91

M4 MS I

I 1860

1900 POTENTIAL

1940 (v&s)

1980

Fig. 6. The first-derivative 3d (M43) spectrum of a rhenium surface. The shapes of edges are in qualitative agreement with the simple model shown in fig. 5a. The binding energies, obtained by multiplying the threshold potential by the electronic charge and adding the filament work function, are 1888 and 1954 eV, respectively, which is somewhat higher than the values of 1883 and 1949 tabulated by Bearden and Burr.

the N levels of the Sd transition elements are relatively difficult to detect, the M levels of tungsten (2 = 74) and platinum (Z = 78) have been shown to be quite easily studied [30]. The first-derivative M, ,M4 spectrum of Re (Z = 75) is shown in fig. 6. As expected from the simple model in fig. 5, the edges have the same characteristic shape observed previously for the 3d transition metals [ 121, with the inclusion of an appropriate core-level broadening. The binding energies obtained from fig. 5, after correcting for the work function, are 1888 and 1954 eV, respectively, for the M, and M, levels as compared to 1883 and 1949 tabulated by Bearden and Burr [22]. Thus it is generally possible to find levels which give reasonable sensitivity, but there seems to be cases where this is not so. Gold is one of the elements for which no detectable edges have been found below 2 kV. In this case the problem seems not to be just the result of a low density of unoccupied states, since copper is quite easily detected [27]. Smith, Gallon, and Matthew [3l]have shown that the electron-induced ionization cross section of the 4f levels (N6,7) of gold is suppressed for 60-70 eV above the expected threshold. Smith et al. [31] suggest that the anomalous thresholds, which they also observe for bismuth and lead, result from a mechanism related to that which has been invoked to explain the “delayed transitions” in X-ray absorption studies of Au 4f levels [32]. According to this picture, the magnitude of the matrix elements connecting the 4f core states to states above the Fermi energy is small near threshold because of the centrifugal barrier term in the effective potential experienced by the ejected core

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potential spectroscopy

NIOBIUM (oxidized)

Nb M4.5

Nb M2.3

‘2.3 s

100

200

300

400

5w

6W

I

700

a

POTENTIAL (voltsI

Fig. 7. Second-derivative spectrum of an oxidized niobium surface with small amounts of sulfur and carbon impurities. The spectrum was taken in response to assertions by Tracy [ 261 that SXAPS could not be used to study insulators, 4d transition metals, electronegative impurities, and low-Z elements. All of the niobium levels can be identified. The structure just above the Nb M4,s spectrum in the MO M4,s (another 4d element). We need only a semiconductor on the surface to complete Tracy’s list. Si is evident as an impurity in fig. 2 and in bulk form in fig. 11.

electron. This has been treated by Fano and Cooper [33] for photoabsorption. Although the situation is more complicated for electron impact ionization, one might expect to see anomalies in the excitation thresholds of high angular momentum core states. However, in contrast to the case of Au N6 7, the N6 and N, excitation thresholds are quite strong in the actinides, as seen in hg. 4 for thorium, and they occur at energies which are in good agreement with X-ray photoelectron measurements [23]. Thus it appears that, in addition to a theoretical treatment of electron-induced core-level excitations in solids, we need systematic experimental studies of excitation probabilities for a wider range of elements and levels. Unfortunately, generalizations regarding the sensitivity of SXAPS have in some cases been based on incomplete or erroneous experiments. It has been reported, for example, that SXAPS is insensitive to 4d transition elements, low-2 elements, electronegative impurities, and insulators [26]. The accuracy of these generalizations can be judged from fig. 7 which shows the spectrum of a 4d transition metal oxide, contaminated with low-Z electronegative impurities.

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Fig. 8. A comparison of the 2p (Lzg) spectrum of scandium for a clean surface and for an f&O3 surface. The shape of the oxide spectrum has not been interpreted in terms of density of states, but it shows the extent to which the shape provides a fingerprint of the chemical environment of the scandium atoms. Sc2O3 is an insulator.

7. Electronic structure of surfaces The binding energy of a core state can be measurably affected by changes in the distribution of valence electrons. This chemical shift is generally quite small compared to the binding energy and does not seriously interfere with elemental identification. It does, however, provide a clue to the chemical configuration of the elements. The interpretation of chemical shifts in terms of charge transfer requires a knowledge of bond lengths and angles, which is unfortunately beyond our best efforts for the surface region in spite of recent progress in low-energy electron diffraction. A much more sensitive indicator of the chemical state of the surface is provided by the shapes of the excitation edges, which as we have discussed, are determined by the states accessible to the ejected core electron. As an example, fig. 8 compares the first-derivative 2p spectrum (L29) of a clean evaporated film of scandium with the same film after oxidation to Sc2O3. The threshold for the oxide spectrum is poorly defined in this case, and it is not possible to accurately determine a chemical shift by the appearance potential technique. The principal limitation on the use of SXAPS to measure chemical shifts is in fact the uncertainty introduced by changes in spectral shape. In the case of nickel oxidation, Ertl and Wandelt [34] have interpreted the change in the nickel 2p spectrum in terms of a separation of the 3d and 4s bands. Quite apart from an interpretation of the shapes, however, the spectrum provides a sensitive fingerprint associated with the chemical state of the

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Nickel

V

I

I

840

860 POTENTIAL

I 880

(volts)

Fig. 9. Comparison of the 2p (Lz,~) appearance potential spectrum of a clean polycrystalline nickel surface with the (110) and (111) faces of nickel single crystals. The spectra were taken with a resolution of - 0.5 eV. The lifetime broadening of the L3 level [ 341 is expected to be much greater than the width of the unfilled portion of the nickel 3d band [37]. Thus the shape of the spectrum provides little information on the unfilled density of d band states. It is, however, possible to distinguish different crystallographic orientations by the differences in the energy loss region. In particular, the small peak 6.5 eV above the threshold maximum in polycrystalline nickel is absent in the single-crystal spectra.

surface. In many cases, it is possible to demonstrate a close connection between the spectral features and the density of conduction band states [ 12,35,36]. There are, however, a number of effects which tend to alter or obscure the density-of-states information. To fully exploit appearance potential spectroscopy it will be necessary to take these effects into account. One such effect is the broadening introduced by the finite lifetime of the core hole. For example, the width of the unfilled portion of the Ni 3d band is expected to be only about 0.1 eV [37]. Based on atomic calculations, however, the width of the 2p3,2 (L3) core level is expected to exceed 0.6 eV. Thus, regardless of instrumental resolution, the L3 appearance potential spectrum of nickel provides essentially no information on the width of the unfilled 3d band. The conduction band

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95

Fig. 10. The first-derivative Sd (0s ,04) spectrum of clean Th showing the large resonance above the 04 edge. The spectrum is nearly identical to that obtained by Murthy and Redhead [24]. A similar but less pronounced resonance may account for the shape of the 0s edge. There is also an indication of some precursor structure similar to that reported for the X-ray absorption spectrum of Pr [32].

viewed through other levels will exhibit even greater broadening. The general shape of the 2pu2 spectrum [ 121 does nevertheless conform to the simple model described by eq. (5). It is in fact possible to distinguish between different faces of nickel single crystals and polycrystalline Ni on the basis of subtle differences in the L2,3 spectrum, as shown in fig. 9, despite the smearing effect of the core level window. The smearing is, as we have pointed out, an unavoidable consequence of the localized view of the density of states centered on a particular site. The excitation edges of the 3d, 4d, and 5d transition metals exhibit the same general shape as the Re M45 (fig. 6) and the Ni ba (fig. 9), as suggested by the model in fig. 5a. For the rare earths, however, the situation is sometimes much more complicated. Many-body resonances are found associated with the M, and N, levels of Sm [38], La [24], and Gd [24], and with the 0, ,04 levels of Th [24]. The very large resonance above the 0, edge of Th, which was reported first by Murthy and Redhead [24], is shown in fig. 10. This spectrum strongly resembles the praseodimiurn Nh5 X-ray absorption edge [32], including the suggestion of a precursor structure below the 0, edge. Similar resonances have been reported in the spectrum of Ba [39]. Anomalous structure is also reported for the low-energy region in the spectrum of Ba as an impurity on Fe [40]. Recent studies [41] indicate that the resonances may persist when the rare-earth is present as only a few atomic percent in a

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!il

‘colculoted

-.__/-4J 1820

1840 POTENTIAL

I

I 1860 (voltd

I

I 1880

Fig. 11. Comparison of the measured and calculated K excitation edge of a clean Si surface. The density of conduction band states calculated by Van Dyke [42] was convoluted with itself and differentiated using an interval determined by the lifetime broadening of the core-level calculated by McGuire [ 341 and the instrument response. There is no a priori reason to expect the excitation edge to show quantitative agreement with density-of-states calculations since the final state may find electrons in states localized on the excited atom rather than in bands uniformly distributed throughout the crystal.

Ni-Cr alloy, thus indicating the local character of the interaction. Althou~ appearance potential studies have thus far concentrated mainly on metals and their oxides, there is no reason why the technique cannot be used to examine elemental semiconductors f42], although at one time it was reported that SXAPS could not detect semiconductors in general and Si in particular [26]. The measured K edge of Si is compared in fig. 11 to the calculated edge. The calculated edge makes use of the Si density of states calculated by Van Dyke in connection with a study of interband optical transitions in Si [43], The self-convolution of Van Dyke’s density of states was broadened to account for the lifetime of the core hole calculated by McGuire [44] (- 0.5 eV) and the instrumental response due mostly to the oscillation amplitude, which in this case produced a broadening of about 1.2 eV. As Van Dyke [45] has pointed out, however, there is no a priori reason to expect X-ray absorption edges to agree quantitatively with the calculated density of states, and the same is true of the excitation edges in appearance potential spectroscopy. As a result of localization of the core hole, the final state of the system may find the ejected core electron in a state localized about the atom on which the core hole is located, rather than in a band state uniformly distributed throughout the crystal. The interpretation of spectral shapes is, moreover, complicated by the dynamic screening of the suddenly created core hole by the conduction electrons. This problem is of course common to all core-level spectroscopies, although the coupling to the suddenly altered core potential can be quite different for dissimilar spectroscopies [461.

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8. Summary The unique view which core-level spectroscopies provide of the local electronic environment of atoms in the surface region of a solid is complicated by variations in the magnitude of the atomic matrix elements, the lifetime broadening of the corelevel, and the screening response of the conduction electrons to a sudden change in core potential. Although the consequences of these effects have been identified, they are still imperfectly understood. All core-level spectroscopies suffer to a greater or lesser extent from the same problems. What is needed is a theoretical treatment of the excitation process which considers the localization of the final state to the vicinity of the excited atom. The importance of the local atomic environment to surface science justifies the effort required to gain understanding.

Acknowledgement I am indebted to J.P. Van Dyke for providing density-of-states calculations of Si, and to S. Kato, A.M. Bradshaw, and P.O. Nilsson for providing prepublication copies of their recent papers. I also wish to thank D.G. Schreiner, who obtained and processed many of the spectra shown in this paper. I am particularly grateful to J.E. Houston, who has contributed more than any other single person to the development and understanding of appearance potential spectroscopy.

References [l] [2] [3] [4] [5] [6] (71 [8] [9] [lo] [ll] [12] [13] [14] [15] [16] [17] [18] [19]

G. Shinoda, T. Suzuki and S. Kato, Phys. Rev. 95 (1954) 840. R.L. Park, J.E. Houston and D.G. Schreiner, Rev. Sci. Instr. 41 (1970) 1810. R.L. Park and J.E. Houston, J. Vacuum Sci. Technol. ll(1974) 1. A.M. Bradshaw, in: Surface and Defect Properties of Solids, Vol. 4 (Chemical Society, London, 1974). S. Kato, Oyo Buturi 43 (1974) 360 (52). H. Merz and K. Ulmer, Z. Physik 210 (1968) 92. R.R. Turtle and R.J. Liefeld, Phys. Rev. B 7 (1973) 3411. H. Rempp, Z. Physik 267 (1974) 187. L.C. Parratt, Rev. Mod. Phys. 31 (1959) 616. B. Dev and H. Brinkman, Ned. Tijdschr. Vacuumtechn. 8 (1970) 176. G. Ertl and K. Wandelt, Phys. Rev. Letters 29 (1972) 218. R.L. Park and J.E. Houston, Phys. Rev. B 6 (1972) 1073. W. Schottky, Ann. Physik 57 (1918) 541. J.B. Johnson, Phys. Rev. 32 (1928) 97. A. van der Ziel, Noise (Prentice-Hall, New York, 1954). L.B. Leder and J.A. Simpson, Rev. Sci. Instr. 29 (1958) 571. J.E. Houston and R.L. Park, Rev. Sci. Instr. 43 (1972) 1437. W.B. Nottingham, Phys. Rev. 47 (1935) 806 (A). H.D. Hagstrum, Phys. Rev. 96 (1954) 336.

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