Inelastic electron background function for ultraviolet photoelectron spectra

Journal of Electron Spectroscopy and Related Phenomena, 63 (1993) 253-265 036%2048/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

Inelastic electron background photoelectron spectra Xiaomei

Li, Zhaoming

Zhang,

Victor

function

253

for ultraviolet

E. Henrich”

Surface Science Laboratory, Department of Applied Physics, Yale University, New Haven, CT 06517, USA (First received

21 November

1992; in final form 19 March

1993)

Abstract We present a simple approach to the determination of inelastic backgrounds in low-energy electron spectra such as UPS that fits the spectra much better than does the iterative integral background which is generally used in higher-energy spectroscopies such as XPS. Including the secondary-electron cascade process explicitly yields a non-iterative function that gives a good description of the inelastic background in UPS spectra from transition-metal oxides for low photon energies. For photon energies above about 40 eV but below the XPS region, the background function is not always able to adequately model the spectra; the discrepancy cannot be removed by a more sophisticated treatment of the electron scattering function.

I. Introduction One of the major concerns in all types of spectroscopy is how to separate the signal, which contains the information that you want (usually resulting from a single physical process), from the background, which is the intensity contributed by all of the other processes that you do not want to study; this must be done in order to determine the true shape and amplitude of the signal peak. The separation of signal from background can be a particularly difficult problem in photoelectron spectroscopy utilizing low photon energies (i.e. ultraviolet photoelectron spectroscopy (UPS)), where the cross-sections for contributions to the background are often comparable to that for the signal. A case in point is illustrated in Fig. 1, where the solid curve is an angle-integrated UPS spectrum from a Cr,O,(lOi2) surface for hv = 40 eV [l]. The signal, which occurs between 0 and 13 eV binding energy, consists of emission from the 02p and Cr3d orbitals of the valence *Corresponding

author.

X. Li et aE./J. Electron

254

Spectrosc.

Relat. Phenom.

63 (1993) 253-265

Crz03 (1012) - - - Integral background -

-

Total background

0 1

I

I

15

10

5

I

EF = 0

Binding Energy (eV) Fig. 1. Angle-integrated UPS spectrum from Crz03 (lOi2) for hv = 40 eV (solid curve) [l]; total background (long dashed line); and integral background (short dashed line).

band. All of the emission below 13 eV binding energy is background and arises from inelastic scattering of electrons that originated at higher kinetic energies. While a great deal of attention has been paid to the analytical form of backgrounds under higher-energy X-ray photoelectron (XPS) and Auger signals, little effort has been devoted to backgrounds in UPS. Methods as simple (and incorrect) as drawing a straight line under the signal or sketching what one thinks the background might look like have been used in the literature, In some cases the integral background function (which will be discussed below) that is generally applied to XPS and Auger spectra has been used, but it gives a very poor fit for low photon energies; the short dashed line in Fig. 1 is such an integral background. In this paper we will examine the properties of background functions that are more appropriate for use in the UPS regime. While the backgrounds in experimental UPS spectra cannot, in general, be fit as well as those in the higher-energy spectroscopies, they can be fit well enough for many applications_

X. Li et aL./J. Electron

Spectrosc.

Relat.

Phenom.

63 (1993) 253-265

255

n (El

E,(eV)

Fig. 2. Secondary-electron

II. Background

spectrum

functions

from stainless

steel excited by 140 eV incident

used in XPS and Auger

electrons.

spectroscopy

Methods of modelling the inelastically scattered background in electronemission spectra have been discussed in the literature for nearly forty years. The background arises from initially excited (i.e. primary) electrons that have suffered inelastic losses as they travel through the material, and from secondary electrons that are created in the process. The secondary electrons in turn excite additional secondaries by a cascade process_ On the average, electrons lose a large fraction (of the order of one-half) of their energy in each inelastic collision [2], which results in an increase in the inelastic background at lower kinetic energies. At very low kinetic energies the measured secondary-electron spectrum is cut off by the inability of electrons to surmount the vacuum barrier, resulting in a peak in the secondary-electron background in the region below 10 eV for all materials. A typical secondary-electron spectrum, excited by a 140eV incidentelectron beam on polycrystalline stainless steel, is shown in Fig. 2. (The use of the term “primary” electron here is somewhat different than that conventionally used in electron-excited spectra. There the primary electrons are the ones that are incident on the sample, while here the term refers to the emitted electrons, whether electron or photon excited, that have not been inelastically scattered in travelling through and out of the sample, i.e. the signal electrons.) In spectra in which the electron kinetic energies are greater than a few

256

X. Li et al./J. Electron

Spectrosc.

Relat. Phenom.

63 (1993) 253-265

hundred electron volts, it is found empirically that the dominant change in the inelastic background on either side of a signal peak consists of an increase in the level of the background for energies below the peak, but that the background is relatively flat (i.e. independent of electron kinetic energy) within several electron volts on either side of the peak [3]. At energies farther away from signal peaks the background has been modwhere E is the electron kinetic elled by functions as simple as A/E”, energy [4,5] and by extremely complex convolutions based upon detailed electron-electron scattering calculations [6-91. Very complicated procedures have been developed to model the background in the vicinity of a signal: some deconvolute the data by utilizing experimentally measured electron-backscatter spectra (which include the effects of intrinsic and extrinsic losses) [6,10-141; others use theoretically calculated differential inelastic-electron-scattering cross-sections [2,7-g]. However, the most widely used background for this purpose, which is appropriate in the XPS, Auger and soft X-ray regions where the electron kinetic energy of spectral features is larger than 100 eV or so, is a simple integral background that was first introduced by Shirley [3]. It assumes that each primary electron has some energy-independent probability of being inelastically scattered as it travels through the crystal, and thus of contributing to the background, either directly or through the creation of one or more secondary electrons. (It is well known that the inelastic scattering probability does depend on electron energy [2,9], but over a small energy range the energy dependence can often be ignored.) If the electron kinetic energy is larger than 100eV or so, there is a small probability that a primary electron will produce a secondary electron whose energy is close to the signal peak. In deriving an integral background, it is therefore assumed that each primary electron in a peak has a constant, energy-independent, probability of producing a secondary electron at any kinetic energy lower than its own. In order to produce a change in the level of the background across a signal peak and yet have a flat background on both sides of the peak, it is necessary to assume that secondaries are produced only by the primary electrons; i.e. that secondaries do not in turn create other secondaries. (This assumption is clearly not valid for low electron kinetic energies; if it were, the true secondary peak in Fig. 2 would not exist.) The amplitude of the background under a signal is then proportional to the integral of the number of primary electrons (i.e. the signal) from the kinetic energy in question to the largest kinetic energy of the peak. That is E InzN Ibb(E)

m

I, s

E

(23’)

dE’

(1)

X. Li et aL/J. Electron

Spectrosc.

Relat. Phenom.

63 (1993) 253-265

257

where I,(E) is the intensity of the actual signal above background, and E ma*is the highest kinetic energy of the signal. Since the measured spectrum 1,,,(E) is a sum of the background and the signal

&cat(E)= Is,(E) +

(4

IbcE)

and I*,(E) is not known a priori, Ib(E) must be found by an iterative procedure [3,15,16]. This procedure rapidly converges, and this approach is a convenient and widely used method of modelling inelastic backgrounds. III. Backgrounds

for lower-energy

electron

emission

spectra

The above approximation breaks down, however, when the electron kinetic energy of the signal in question is only a few tens of electron volts, as is the case for most UPS spectra. In that case the background is not flat in the region below and close to the peak, as shown in Fig. 1. In many UPS studies the amplitude of signal peaks, above background, is not of critical importance. However, in some applications, such as the resonant UPS study of the nature of the bandgap in Cr203 from which the spectrum in Fig. 1 is taken [l], it is important to accurately determine the amplitude of the signal above background, and an integral background, which is necessarily flat below the peak, is clearly insufficient. Two modifications of the assumptions that are made in deriving the integral background function must be considered in modelling low-energy electron-emission spectra: (1) the cross-section for the creation of secondary electrons by primary electrons depends upon energy, and (2) secondary electrons can in turn create their own secondaries whose energies still lie in the vicinity of the signal. We will return later to the first of those issues, and we will find that using more sophisticated models for the cross-section does not improve the agreement of the background function with experimental data. The second effect, however, is the one that makes the largest difference in the background function at low energies, and we will consider the simplest model for inclusion of all the true secondary electrons. In the integral background model, each electron in the signal (i.e. primary electron) is assumed to have a constant probability, independent of kinetic energy, of creating a secondary electron which contributes to the background, but the further inelastic scattering of those secondary electrons is not considered [3]. However, those secondary electrons that fall in the region of a signal peak have the same kinetic energies as do primary electrons, and, since the sample has no way of knowing where an electron came from, one should consider the secondary electrons generated by inelastic scattering of all of the electrons as they move through the crystal. This is particularly important at low kinetic energies where the electrons lose a smaller amount of energy per collision. The simplest way of

X. Li et al/J.

258

Electrcm Spectrosc.

Relat. Phenom.

63 (1993) 253-265

incorporating an inelastic scattering of all of the electrons is to assume that the background at any kinetic energy is proportional to the integral of the total spectrum I,,,(E) at all higher kinetic energies and not just to the integral of the signal above background. We will refer to the background function generated in this way as a total background. The first step in generating a total background function is definition of the energy range over which the signal occurs. This requires the determination of two energies: one is the energy Em,, above which there is no signal (usually slightly above the Fermi energy EF for UPS spectra, or just to the high-kinetic-energy side of an Auger or XPS peak), and the other is the energy below which the measured electron spectrum consists only of the background. While the choice of E,,, is usually trivial, the determination of Emin requires some educated guesswork in the case of UPS spectra where the background is not constant below the signal. For the UPS data in Fig. 1, the actual photoemission spectral features are believed to occur in the region above about 13eV binding energy, so below 13 eV the data presumably consist only of the inelastically scattered background. (Those energy limits are the only “adjustable” parameters in the fit, and there is, in fact, little leeway in their choice.) For computational purposes it is convenient to define

The background function Ib(E) is then E max

&(E) = ~tot(~max)+ A

J

&(E')

dE’

(4)

E

where Jzmax I&(E’) dE’ 1s . directly integrable without iteration. The constant A is determined from

since the spectrum there consists entirely of the inelastically background. Thus A

=

[lt,tot(Emin)

-

ltot(Emax)l

Emax P

J

1:&E’)

Emin

dE’

scattered

(6)

X. Li et al.lJ. Electron

Spectrosc.

Relat. Phenom.

63 (1993) 253-265

259

Therefore the total background function can be written simply as

J&&E’) Ib(E)

=

h.(&nax)

+

[&ot(Exnin)

-

ltot(Etnax)l

x

dE’

(7)

off:,. I

.II&??)

dE’

Equation (7) is exactly the same as the first iteration in the procedure employed for generating an integral background [3]. However, viewing it from that perspective obscures the physics involved: that the creation of secondaries by all electrons is explicitly included. Total backgrounds have sometimes been used in the analysis of high-energy XPS and Auger spectra [13,14,17]. However, since the background on the high-binding-energy side of such emission peaks is generally quite flat, iterative integral backgrounds have been more widely applied. No reports of the application of total backgrounds to lower-energy UPS spectra have appeared in the literature to date. The total baekground function computed for the UPS spectrum of Crz03(10i2) in Fig. 1 is shown by the long dashed curve. It gives a much better fit to the actual background in the region several electron volts below the 02p band than does either an integral background (short dashed curve) or a straight line. In our work on transition-metal oxides, we have found that a total background gives a fairly good fit to the background in UPS spectra for low photon energies. Examples are given in Fig. 3 for three different compounds: (a) the (110) surface of rutile TiOs, (b) the (lOi2) cleavage face of corundum VsOs, and (c) the (001) face of the layered , . * monoclinic oxide VsO,s. IV. Discrepancies between low-energy spectra

calculated

and

actual

backgrounds

in

Although the total background always gives a better fit to experimental data below emission peaks in UPS spectra than does an integral background, it does not describe all spectra well, particularly for intermediate photon energies. (The situation for higher-energy XPS spectra, where the change in background level from one side of the emission peak to the other is small, will be discussed in Section V below.) An example of the problem encountered is shown in Fig. 4, which plots angle-integrated UPS spectra from stoichiometric Ti02(110) for three photon energies along with their total background functions. While the total background does a fairly good job of fitting the 30 eV spectrum, the deviation between the actual spectrum

260

X. Li et aE./J. Electron Spectrosc. Relat. Phenom. 63 (1993) 253-265

hu = 30 eV

TiC12(110) ----

Total background

N(E)

-\

‘\ ‘\ ‘.

‘\ ‘. ‘. ‘\

JI

15

.

.

10

I

-_ yy----_______

.

El==0

5

Bin&ng

Energy

(eV)

hu = 42 eV

v203

(ioiz)

Total background

I

I

15

_._,I_,,,,,,~.

,

10

5

EF - 0

Binding Energy (eV) Fig. 3. UPS spectrum (solid curve) and total background functions (dashed lines) from, (a) TiOAllOI for hv = 30eV [18]; (b) V,O,(lOi2) for hv = 42eV [19]; and (c) V,O,,(OOl) for hv = 21.2eV 1201.

X. Li et d/J.

Electron Spectrosc. Relat. Phenom. 63 (1993) 253-265

261

(4 \

hu = 21.2 eV ----

Total background

0 I

10

5

Binding Energy (eV)

Ep=O

Fig. 3. Continued.

and the calculated background below the emission peaks increases with photon energy. While the example shown here for TiOz is one of the most severe discrepancies that we have observed, the trend is the same in most other oxide spectra. (Similar, although smaller, discrepancies can be seen in Figs. 3(a) and (c).) The function defined by Eq. (7) yields a background that increases exponentially with decreasing electron kinetic energy in regions that do not contain any signal; it is this exponential that produces the true secondary peak in Fig. 2. The steepness of the exponential rise with decreasing electron kinetic energy below the emission peak is directly proportional to the difference in background level above and below the peak; there are no adjustable parameters. There is therefore no way in which that total background function can model the steeper background encountered in spectra such as those in Fig. 4. Both the total and integral backgrounds use the simplest possible model for the spectrum of secondaries created by an electron as it travels through the crystal: they assume that each electron (only primaries in the integral model) generates an energy-independent distribution of secondary electrons at all lower kinetic energies. As shown empirically (see Fig. 2) and theoretically [4-91, that is not the case; the distribution of secondaries is more heavily weighted at low kinetic energies. Replacing the simple

X. Li et al.lJ. Electron

262

Spectrosc.

Relat. Phenom.

63 (1993) 253-265

f

hu (eV)

N(E)

I

15

*

.,

.I,

,

~

10

Binding

,

,

Energy

,

,

I

EF = 0

5

(eV)

Fig. 4. Angle-integrated UPS spectra for Ti&(llO) (solid curves) (dashed curves) for photon energies of 30,34 and 38 eV [Ml.

and total

backgrounds

assumption of an energy-independent cross-section with a more realistic one would therefore make the discrepancy with experiment worse for higher photon energies. Quantitatively, however, changing the model of the electron scattering cross-section would make only a small change in the background function; the slope of the secondary-electron distribution below an emission peak in the total background is determined predominantly by the magnitude of the difference in background level above and below the peak rather than by the functional dependence of the background produced by each electron.

X. Li et al./J. Electron

hu

Spectrosc.

= 1482.6

eV

Relat. Phenom.

263

63 (1993) 253-265

Ti 2~3/2

TiOz(110) r

- - _ Integral background -

-

Total background

NW

c I

470

I

I

I

460

465

Binding Energy

455

(eV>

Fig. 5. Al KCYXPS spectrum of the Ti2p core levels in single-crystal TiOz (solid curve) [21]; total background (long dashed curve); and integral background (short dashed curve).

The observed discrepancy between signal and background must therefore arise from other sources. It may well depend on the nature of the data collection and may, for example, be different for angle-resolved than for angle-integrated UPS spectra. Detector sensitivity, the bandpass characteristics of the electron spectrometer, sources of stray electrons, the spectral distribution in the photon source, etc., may also play a role. More experiments on different classes of materials utilizing different spectrometer systems would be necessary in order to better determine the origin of the discrepancies. V. Comparison

of total and integral

backgrounds

for XPS spectra

As discussed above, both integral and total backgrounds have been used to fit XPS spectra. It is therefore interesting to compare the two approaches in this higher-kinetic-energy regime, where the difference in background level across a peak is relatively small. Figure 5 shows a TiZp XPS spectrum for TiOz taken with Al Ka X-rays, and the background functions obtained using each approach. The total background will always lie slightly below

X. L.i et al./J. Electron Spectrosc.

264

Relat. Phenom.

63 (1993) 253-265

the integral one in the region under a peak since both backgrounds are normalized at the same point on the high-binding-energy side of the peak. The differences, while small, are not insignificant. In cases where accurate amplitudes and lineshapes of core-level peaks are required, both backgrounds are probably too simple, and more rigorous deconvolution procedures should be used. VI. Conclusion In order to adequately describe the inelastic background function in low-energy electron spectra such as UPS, it is necessary to include the secondary-electron cascade process explicitly. A simple, non-iterative background function that takes into account the inelastic scattering of all the excited electrons is found to fit UPS data on metal oxides fairly well. This total background function is appropriate for UPS spectra where the inelastic background rises with decreasing electron kinetic energy. However, the total background does not always do an adequate job of fitting UPS spectra in the intermediate energy regime; the reasons for this are not clearly understood. Refinement of the models by including an energy-dependent scattering cross-section would not improve the agreement with experiment. Acknowledgments The authors thank Lizhong Liu for assistance in acquisition of some of the synchrotron data and Keith Goodman for valuable discussions. This work was partially supported by NSF Solid State Chemistry Grant DMR 9015448 and DOE Office of Basic Energy Sciences Grant DE-FGW87ER13773,

References 1

2 3 4 5 6 7 6 9 10 11 12

X. Li, L. Liu and V.E. Henrich, Solid State Commun., 84 (1992) 1103. P.A. Wolff, Phys. Rev., 95 (1954) 56. D.A. Shirley, Phys. Rev. B, 5 (1972) 4709. E.N. Sickafus, Phys. Rev. B, 16 (1977) 1436. E.N. Sickafus, Surf. Sci., 100 (1980) 529. M.C. Burrell and N.R. Armstrong, Appl. Surf. Sci., 17 (1983) 53. A. Tofterup, Phys. Rev. B, 32 (1985) 2808. A. Tofterup, Surf. Sci., 167 (1986) 70. See S. Tougaard, Surf. Interface Anal., 11 (1988) 453, and references cited therein. W.M. Mulaire and W.T. Peria,Surf.Sci., 26 (1971) 125. J.E. Houston, J. Vat. Sci. Technol., 12 (1975) 255. H.H. Madden and J.E. Houston, J. Appl. Phys., 47 (1976) 3071.

X. Li et al.lJ. Electron

13 14 15 16 17 18 19 20 21

Spectrosc.

Relat.

Phenom.

63 (1993) 253-265

P. Steiner, H. HSchst and S. Hiifner, Z. Phys. B, 30 (1978) 129. M.F. Koenig and J.T. Grant, J. Electron Spectrosc. Relat. Phenom., 33 (1984) 9. A. Proctor and P.M.A. Sherwood, Anal. Chem., 54 (1982) 13. A. Proctor and D.M. Hercules, Appl. Spectrosc., 38 (1984) 505. A. Barrie and F.J. Street, J. Electron Spectrosc. Relat. Phenom., 7 (1975) 1. Z. Zhang, S.-P. Jeng and V.E. Henrich, Phys. Rev. B, 43 (1991) 12004. K.E. Smith and V.E. Henrich, J. Vat. Sci. Technol. A, 6 (1988) 831. L. Liu, unpublished results. R.L. Kurtz, Ph.D. Thesis, Yale University, unpublished.

265