Fresenius' Journal of Fresenius J Anal Chem (•99•) 341:116-120

© Springer-Verlag 1991

Deconvolution of XPS spectra D. Sprenger 1 and O. Anderson 2

1 Institut ffir Anorganisehe und Analytische Chemic, Universitfit Mainz, W-6500 Mainz, Federal Republic of Germany 2 SCHOTT Glaswerke, Postfach 2480, W-6500 Mainz, Federal Republic of Germany

Received February 25, 1991

Summary. The resolution of XPS spectra is limited mainly by instrumental parameters like the spectral line width of the exciting X-ray source and the finite energy resolution of the electron analyzer. If the line broadening functions resulting from the instrumental setup can be estimated and expressed by a spectrometer function, a mathematical re- calculation of the intrinsic signal is possible by deconvolu- tion. With the method presented in this paper, a resolution enhancement by a factor of 3 can be obtained. Measured spectra of physically correlated spin orbit doublets have been deconvoluted, and it is shown, that the intensity ratios and the positions are comparable with results obtained by highly resolved measurements using monochromatized X-rays and long acquisition times. Informations on phase compositions by an interpretation of chemical shifts of less then 0.6 eV are possible, too.

Introduction

XPS is an useful analytical tool for the investigation of solid surface layers to yield qualitative and quantitative informa- tion about the composition of the sample [1, 2]. By recording highly resolved spectra small differences in the binding energy of elements due to different chemical en- vironments (chemical shifts), may be detected and therefore a determination of the phase composition may be possible [31.

Whereas the intensity of an observed signal is pre- dominantly determined by the sample, the linewidth is strongly influenced by apparative parameters. In particular, in the case of composite spectra resulting from small chemical shifts, the energy resolution can be insufficient. An improvement of the energy resolution can be obtained by the use of an X-ray monochromator, which results in a reduction of the X-ray line width from 0.85 eV to less than 0.4 eV for A1 K~ excitation [4]. Unfortunately, the acquisition time strongly increases in this case. Another possibility is given by a mathematical treatment of the measured spectra. The lineshape g(x) of an observed XPS signal can be de-

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scribed by a convolution of the intrinsic signal f(x) of the photoemission process with a spectrometer function h(x),

+ o o t ~

g(x) = } f(x - t) h(t) dt -= f(x) ® h(x), (1)

- o o

with

h(x) = EQ(x) ® EX(x) ® EA(x),

which includes all line broadening contributions of the in- strumental setup. These line broadening functions are the analyser resolution function EA(x), the Gaussian distribu- tion EQ(x) caused by the charging effects on insulators, and the line shape of the exciting photons of the X-ray source EX(x). If the spectrometer function h(x) is known accurately, it should be possible to recalculate the intrinsic signal f(x) by inversion of Eq. (1). This procedure is called 'deconvolu- tion'. In practice, the solution of the inversion of the integral Eq. (1) is not unique because any function F(x) which satisfies Eq. (2), may be added to a solution f(x) and results in another solution:

+ o o

f F ( x - t ) h(t) = (2) dt 0.

- c o

This is given, for example, for a noise function consisting of rapid fluctuations around their zero intensity. Before a successful deconvolution can be applied, the noise has to be reduced by smoothing or low-pass filtering, and the spectrometer function has to be determined with sufficient accuracy.

Smoothing

Smoothing is a process that attempts to increase the correla- tion between the measured points while supressing the uncorrelated noise. This operation has to be carried out in a most effective and least distorting way. For performing a deconvolution, the usually performed smoothing by spline and polynomial algorithms is insufficient. Good results were obtained by a least squares approach [5] and by optimal filtering based on Fourier transform methods [6]. To avoid noise and spurious oscillations to be transferred into the

0 C)

100000

80000

60000

40000

20000

0

Au 4 f

, M g K a t

92 8;2 72 Binding energy [eV]

Fig. 1. Fitted XPS spectrum of the Au 4f signal of an evaporated gold sample excited with Mg K~, after background subtraction

deconvoluted spectrum, as it is often seen in the literature, the initial data should have a good signal-to-noise ratio. A correct digital filtering is an indispensable requirement to obtain good deconvolution results.

Determination of the spectrometer function

The spectrometer function h(x) includes the line broadening functions of the electron analyser and the contributions caused by the exciting X-ray source, and results in a convolu- tion with each other.

a) The analyser function

The resolution and intensity behaviour of the electron ana- lyser is determined by geometric parameters like the width of the entrance and exit slits and by the selected pass energy. If the analyser is used in the constant pass energy mode, the transmission energy (pass energy) and the absolute energy resolution remain constant in the whole energy area. A theo- retical calculation of the analyser function [7] does not produce satisfying results for a successful deconvolution. Therefore an experimental determination is necessary. If an UV-source is used, an accurate determination of the analyser function in dependence on the pass energy is possible [8].

These analyser function consists of a Gaussian line shape at lower pass energy, which becomes more triangular with increasing pass energy. These results are in agreement with theoretical calculations [7].

b) Energy distribution of the exciting X-rays

The X-ray lines mainly used in XPS investigations are A1 K~ and Mg K~ with characteristic energies of 1486.6 and 1253.6 eV and a theoretical FWHM of 0.85 and 0.70 eV, respectively. The Lorentzian shape of the X-ray emission lines and their intensity ratios are well known [9], and the energy distribution of the X-rays can be calculated. In practice, the exact distribution depends on the oxidation state of the anode, which results mainly in changed energy and intensity ratios of the satellites [9, 10]. An exact determi- nation of the energy distribution of the X-ray source required

117

1.0

0.6-

o.4-

O.2-

a o.o- i :1 / 0.0 _ b

0.4-

o.2-

0.0

10 a Binding energy [eV]

==

2 ro

4J~ -0 .4

-0 .8

4~ -1 .2 H

-1 .6

-2 .0

0,8-

Fig. 2. Simulated spectrum b consisting of 3 Gaussian lines with a FWHM of 0.2 eV, its convolution with a Gaussian response func- tion with a width of 1.0 eV a, the 2-nd derivative spectrum c of the convoluted spectrum a, and the deconvoluted spectrum after 50 iterations d

for deconvolution applications is always affected by the energy distribution of the analyser function. Therefore, the Au 4f lines of a clean gold sample (Au sputtered onto Ta) was measured over an energy region of 20 eV and, after background subtraction [11], fitted with a symmetric Voigt profile (Fig. 1). Small asymmetries resulting from valence band interaction, could be neglected [12]. The summation of the Au 4f 7/2 subspectra and the corresponding satellites (Fig. 1) results after deconvolution with the intrinsic lineshape of the Au 4f state (FWHM = 0.25 eV [13]) in the spectrometer function, which is valid for all spectra mea- sured under the same apparative conditions. This response function can be used for deconvolution and should be verified after some time to take changes of the anode surface into account.

Deconvolution

Several deconvolution procedures to solve Eq. (2) (for a review see [14]) have been used in the literature. All these methods are based on the convolution theorem, which states that the convolution of two functions could be expressed by the product of the Fourier transform of these functions. Most of them are strongly influenced by the overall presence of noise or produce artifacts in the deconvoluted spectrum like nonphysical satellites which are related to the Gibbs phenomenon. Useful results can be obtained by an applica-

118

c

r - J

1 .4 15.6

X Ar 3p

5'.8 ' ' I 16.0 16.2

Binding energy [eV] Fig. 3. UPS spectrum of the Ar 3p signal excited with HeI after background subtraction a, after smoothing b, after several steps of deconvolution c, d, and a measured spectrum with a comparable energy resolution

f-- f8

4 J

43

H

'1.0

0 . 8

0.6

0.4

0 .2 .

0.0

0.2

0.0

°i] 0

S 2p

k

160.0 t 6 2 . 0 t 6 4 . 0 166.0 168.0

Bind&ng Energy (eV)

Fig. 4. XPS spectrum of the S 2p signal of a sulphur sample excited with Mg K, after background subtraction a, after smoothing b, and after deconvolution c

tion of the iterative "point simultaneous over-relaxated Jansson algorithm" [15, 16]:

f,(x) = f , - l(X) + a,(y) [g(x) - f,_ t(x) (9 h(x)]. (3)

The essence of this method lies in a successive refinement of an approximate solution fn(x) of the intrinsic signal fix). The so-called relaxation function an(y) influences the conver- gence of the algorithm, but also affects the relative intensities and the peak shapes in the deconvoluted spectrum. For XPS spectra with intrinsic Lorentzian shapes, the function

an(y) = amax(Y 2 4- y)/2 with y(x) = If, - l(x)l (4)

produces good results. Too high values for area x makes the method divergent, so the most suitable values of amax depend on the data. In practice, we start with a value for the parame- ter amax of 1.0 increasing by 0.1 in each iteration, to make the convergence as rapid as possible. The number of iterations depends on the number and distances of the overlapping lines and on the accuracy of the response function, but does not exceed 50 iterations. If the initial data have a good signal- to-noise ratio, a resolution enhancement of more than a factor of 3 can be obtained. With our program written in MS-QuickBasic and Assembler the deconvolution of one spectrum needs less than 5 min on an IBM-AT [17].

Results from deconvolution studies

For an initial demonstration of the method several syn- thetically and measured spectra of physically correlated spin orbit doublets were deconvoluted.

A synthetical spectrum consisting of 3 Gaussian peaks with a FWHM of 0.2 eV (Fig. 2b) was convoluted with a Gaussian response function of 1.0 eV FWHM. The positions of the minimum negative intensities in the second derivative (Fig. 2c) of the convoluted spectrum (Fig. I a) represent the

peak positions in the primary spectrum (Fig. 2 b). After 50 iterations, the peak positions and the relative intensities of the final results (Fig. 2d) are identical to the initial spectrum, only the linewidths show some remaining broadening.

The spin-orbit doublet of the Ar 3 p level excited with He I was measured with a pass energy of 20 eV corresponding to an energy resolution of 230 mV (Fig. 3a). After de- convolution with the analyser function, the spectrum results in a line of 75 meV FWHM (Fig. 3 d). This result is compar- able to a measured spectrum with a pass energy of 5 eV and a corresponding linewidth of 70 meV FWHM (Fig. 3 e) [8].

Further tests are concerned with the deconvolution of signals collected from solids excited with Mg K~ radiation and measured with a pass energy of 20 eV and a slit width of 3 x 10 mm. For this, elemental sulfur and KBr were pre- pared in small discs. The measured S 2p signal of the sulfur sample after background subtraction is shown in Fig. 4a. After smoothing and deconvolution the spectrum results in a line for the S 2pa/2 signal with a FWHM of 0.52 eV (Fig. 4c) and a spin-orbit separation of 1.25 eV. Only small differences between the fitted theory and the deconvoluted spectrum occur from a surface contamination and the statis- tics of the measured spectrum.

The measured Br 3d signal of the KBr sample (Fig. 5 a) shows a strong asymmetric line resulting from the spin-orbit splitting. After smoothing and 20 iterations the spectrum results in two well separated lines with a FWHM of 0.71 eV for the Br 3d5/2 signal, and a spin-orbit separation ofl.01 eV (Fig. 5c).

The Si 2p spectrum recorded from a mechanically cleaned silicon wafer after background subtraction, is shown in Fig. 6 a. A small signal appearing at higher energy, repre- sents an oxidic coverage. No spin-orbit doublet is visible in the measured spectrum, only a weak asymmetry can be observed. The deconvolution [18] results in two well separated signals (Fig. 6d) with a distance of 0.62 eV and an

119

2 ==

4~ C

~.0

0.B

0.B

0 ,4

0 .2

0 .0

0 .2

0 .0

0 .2

0.0

/ -,~, Br 5d

/

_ _ b

C

Table 1. Parameters and binding energies (BE) from a silicon wafer, a sulfur- and a KBr disc after deconvolution

Sample Signal BE FWHM Relative (eV) (eV) intensity (%)

Sulfur S 2p3/2 163.81 0.52 66.30 S 2px/z 165,06 0.64 33.70

KBr Br 3d5/2 68.43 0.71 60.04 Br 3d3/2 69.44 0.81 39.96

Silicon wafer Si 2p3/2 99,54 0,52 65.82 Si 2p~/2 100.16 0.56 34.18

~°1 0.8 t

Au 4f

65.0 67.0 69.0 7 t . 0 73.0

B ind ing Ener'gy (eV)

Fig. 5. XPS spectrum of the Br 3d signal of a KBr sample excited with Mg K, after background subtraction a, after smoothing b, and after deconvolution e

1.0-

0.8-

0.6~

0.4

0.2-

0.0~,

0.2

H 0.0

0"2 I

0.0

0"2 I

0.0

97.0 99.0 t0:t .0 ~03.0 J,05.0

B ind ing Ener'gy (eV)

Fig. 6. XPS spectrum of the Si 2p signal of a silicon wafer excited with Mg K, after background subtraction a, after smoothing b, intermediate result c and final result d of the deconvolution

area ratio of 2: ~l, which agree welt with results recorded on a Si(111) crystal face with a high resolution ESCA instru- ment [19].

The experimental values of the measured sulfur and KBr " samples and the silicon wafer are summarized in Table 1.

In addition to the limited resolution by use o f a non-

c

x~ [_

m c m 4J c H

b

°- i!Dj :

ok. : : . ]

20 zx B ind ing Energy (eV)

Fig. 7. XPS spectrum of the Au 4f signal of an evaporated gold sample excited with Mg K, with the calculated background a, after smoothing b, after deconvolution of the contributions of the X-ray source c and after an additional deconvolution o£ the anatyser function d

monochromat ized X-ray source, the measured spectra are distorted also by the appearence of X-ray satellites, which can be removed by a deconvolution with a response function including the characteristic distribution of the X-ray source. Fig. 7 a shows the recorded Au 4f signal. After background subtraction and smoothing (Fig. 7b), first the distribution of the X-ray source is deconvoluted (Fig. 7 c), and finally the distribution of the analyser (Fig. 7d). This deconvolution results in two lines with a F W H M of 0.3 eV, which is close to the assumed intrinsic line width o f 0.25 eV [13]. In practice, it is much better to deconvolute the spectrum in a single step with a response function including the analyser function as well as the distribution of the X-ray source.

A typical application of the deconvolution is given in the interpretation of signals from insulators. Because o f the

120

1 . 0

• ~ 0 . 8

0 . 6

0.4

0 . 2 ,

H

0 . 0

0 . 2

0 . 0

0 . 2

0 . 0

/ / ' / "~" - - A1203_Si02 / \ ceramics

/

/"

5 2 8 , 0 5 3 0 . 0 5 3 2 , 0 5 3 4 . 0 5 3 6 , 0 5 3 8 . 0

B i n d i n g Ene rgy (eV)

Fig. 8. XPS Ols spectrum of an A1203 • SiOz ceramics after back- ground subtraction a, after smoothing b and the fitted result after deconvolution c

Table2. Parameters and binding energies (BE) from the Al/O3 • SiO2 sample after deconvolution

Oxygen bond BE FWHM Relative (eV) (eV) intensity (%)

= A 1 - O - A I = 531.6 1.17 24.13 - S i - O - S i - = 532.3 1.00 35.06 - S i - O - H 532.9 1.01 30.08 = A 1 - O - H 533.4 1.14 10.72

shifts, quantitative determinations of relative compositions without use of sensitivity factors are possible. The re- quirements are a well known spectrometer function, a good statistics of the initial data, and a correct application of digital smoothing filters. With the procedure described, it is possible to use the deconvolution as a standard procedure in the evaluation of XPS-spectra.

Acknowledgements. The authors are grateful to H. Bach (Schott Glaswerke) and W. Meisel (University of Mainz, FRG) for enlightening discussions. One of the authors (D.S.) gratefully acknowledges the financial support granted by the "Schott Glaswerke Fonds zur F6rderung des wissenschaftlichen Nach- wuchses."

surface charging, the signals are broadened and an interpre- tation in terms of elemental signals corresponding to dif- ferent chemical states is not possible. In Fig. 8a, the O Is signal of a sintered A1203 • SiO2 ceramics is shown [19]. After background subtraction and smoothing, a slight fine structure can be observed (Fig. 8b). The deconvolution taking into account that the response function is broadened by a Gaussian charging distribution [19], results in four well separated peaks (Fig. 8 c). The molar composition A1: Si 44:56 as calculated from the intensity ratios obtained by a least squares fit, is close to the theoretical composition of 41 : 59. The absolute binding energies calibrated by use of a gold dot, are in good agreement with the published data of 531.6 eV and 533.3 eV for oxygen in A1203 and AI(OH)3, respectively [20]. The fitting results are summarized in Table 2.

Conclusion

It is demonstrated that by correct application the Jansson algorithm can be used for routine investigations without producing artifacts and additional noise. In dependence on the signal-to-noise ratio of the initial data, a resolution en- hancement of at least a factor of 2 - 3 is possible. The algorithm can also be used for the elimination of the satellites occurring from a non-monochromatized X-ray source. In connection with an accurate determination of chemical

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