Automated recognition of Auger electron spectra

Vacuum~volume36/numbers 7-9/pages 437 to 440/1986

0042-207X/8653.00 + .00 Pergamon Journals Ltd

Printed in Great Britain

Automated recognition of Auger electron spectra Lud~,k F r a n k , Institute of Scientific Instruments, Czechoslovak Academy of Sciences, Kr~lovopolsk~ 147. 612 64 Brno, Czechoslovakia

The paper describes the physical basis and the structure of the algorithms included in the software package for automatic spectrum processing developed recently as an option to the Tesla BP 350.1 Automatic Auger electron spectrometer.

1. Introduction

The AES measurements in an analytical scanning electron microscope (SEM) typically provide spectra of a low signal-tonoise ratio. To extract basic chemical information from them in a routine way is very time consuming and reliable results are not always obtained. The aim of the work was to automate the recognition of the spectrum peaks under the given conditions. The processing steps include curve smoothing, background correction, peak detection, and classification with respect to their mean statistical authenticity, peak area measurement, and output of the results. The complete software package was implemented in the Tesla BP 350.1 spectrometer t'2 and tested. In this paper the main problems are discussed, some details will be published separately 3-5. 2. Auger spectrum as the data set

In the BP 350.1 spectrometer signal detection is by counting electrons and signal sampling is clocked by counting either oscillator pulses or phenomenon-dependent events, e.g. pulses with frequency proportional to integral secondary electron emission. This eliminates some spurious effects such as primary current fluctuations and topographic contrast in the mapping mode 2'6. The measurement start signal and both pulse signals are mutually asynchronous, so that the resulting quantising error lies between - 2 and + 1 counts 5. Except for this, the signal samples exactly represent discrete values of the spectral curve convoluted with the instrument response function (IRF). The spectral signal itself consists of peaks, of background, and of random statistical noise. The natural shape of a single Auger peak is Lorentzian 7. After convolution with the IRF we obtain a general shape which can best be examined experimentally at the elastic peak. Its energy width is negligible for the cold field emission cathode used in the BS 350 uhv SEM. Figure 1 shows that the measured peak shape can be considered as a Gaussian. The exact energy dependence of the background signal is not important for the processing purposes. It is sufficient to regard it as expressible by a low order curve with dominant absolute and linear terms.

=°

Figure 1. The measured shape of the elastic peak compared with best fitted Gaussian.

A detailed study of the noise showed 5 that it has the character of white Gaussian noise with a variance approximately equal to the square root of the mean value No, i.e. the character of an ideal gas in equilibrium conditions. The 'chi-square' compatibility test proved that the central part of the data distribution (withi n + 3tr/2) was very well represented by a normal distribution while the sides exhibit larger departures as high as _ 10%. The variance has been found to be larger than ~ 0 by 5.2%. 3. Curve smoothing

In low signal conditions smoothing is necessary for the improvement of the curves and for the facilitation of the peak detection. From among all possible alternatives (low-pass filtering, spline functions, etc.) we have chosen the polynomial curve fitting by the Savitzky-Golay convolution algorithm 8. This method fits the nth order polynomial to (2m+ 1) consecutive equidistantly sampled data points (2m + 1 < n) using the best mean square fit. The least squares criterion leads to a set of equations giving for the central point of the interval the smoothed signal value and smoothed 437

Lud~kFrank:Automated

recognition of Auger electron spectra

values of the first n derivatives in the form of linear combinations of the measured data points. In other words, we obtain (n + 1) finite symmetric or anti-symmetric discrete (2m + 1) point filters. First of all, the error arising in the non-random signal component due to filtering was examined 3. Expanding the measured dependence into a Taylor series we can obtain the upper estimate of the relative error in the function value as

6y(Xo) < IK=_! (kx)~ m a x y'V(x), Y(Xo) - 24 ly(x0)l x_~_
ay(Xo)<0.

(1)

~[Axy'(Xo)] I~C,~I (Ax) 4 < max lY V(x)l, 6y'(Xo) < O. Axy'(Xo) 120 [y'(Xo) I x m--
(2) For n = 3 we then have 8 2 -- $ 2 5 6

5 2 _ 8458

(3)

Evaluating the errors for the Gaussian peak shape we find that the departures from the peak height and width remain well within the order of a few per cent (below 2%) when choosing the filter width (2m+ 1) approximately equal to the peak FWHM expressed in sampling steps. Since the filter weights are normalized to unity, the peak area is not affected. The changes in the peak height and width are then mutually inverse and can be rectified for Gaussian peaks by using a multiplication factor

Fs = 1 + 81n22 IK,,I \ A L E j ,

(4)

where 6E is the energy step and ALE is the peak FWHM. The background vs energy curve has relatively low higher derivatives and its change due to filtering can be neglected. The random signal component obtains some finite correlation length due to smoothing and its variance decreases. After a single pass through the smoothing filter, the variance becomes

(7~ -- (72/m.

FBG-- 1 + R . ELSB(EL) + 24

E{ Sn(EL) SB(EL) '

(7)

where PL is the area of the peak at energy E L and Se(E) is the background signal. The same factor also corrects in this approximation the peak area.

5. Peak detection

Similarly, we can derive for the change in the first derivative

K,. - SoS4_ S~ ' 1C,.- $ 2 8 6 - S ~ ' Sj= i=~-= i j.

shape. The peak height can be rectified by multiplying it by a factor

The main problem inherent to any peak detection method is the separation of true spectrum details from noise-induced artefacts, i.e. from the maxima of the random signal component. When processing an unknown spectrum, no a priori information about peak positions and heights is available for this separation. The only possibility is to utilize the available knowledge about the noise properties. Suppose we know the distribution of relative heights of local noise maxima. This gives us the mean rate of occurrence of such maxima and, consequently, the probability ( l - a ) that any detected maximum is due to noise. First of all we compile a complete list of local extremes on the curve simply by comparing the data values. For each maximum we then compute the relative height N,. Comparing the corresponding mean statistical authenticity a of the maximum with a pre-selected limit we can either accept the maximum as the spectral peak or delete it from the list. The following algorithm for the deletion has been developed: at both sides of a non-acceptable maximum the nearest not yet deleted minima are found and, from them, the higher one is cancelled. Starting from this list item in both directions the nearest still valid maxima are again found and the lower one is deleted. The procedure then continues and the list is repeatedly passed as long as all maxima are accepted within the whole pass. The algorithm is capable of processing an arbitrary combination of true and noise peaks as documented by Figure 2. No more than two passes are necessary to process a triple peak. 1.

2.

(5)

4. Background correction As already mentioned, by clocking the measurement with some phenomenon-dependent events we can suppress effects influencing both the clock and the spectrum signals6. When using for this purpose an output from a broader concentric reference spectral window we can even flatten the background. It is possible in principle to do this on-line9. Here we shall simulate the effect by normalizing the data to the constant moving average, i.e. by transforming the data points N~ as

Figure 2. The scheme of handling of local extremes on the experimental curve (open circles denote still valid extremes while the solid circles indicate the items being just deleted).

By adjusting the interval of averaging (i.e. the reference window width) we should obtain some balance between good transfer of the peaks and sufficient background suppression. A suitable value of the reference window resolution R e is around 25%. This procedure will again produce some changes in the peak 438

6. Authenticity analysis of spectral peaks As mentioned above, for the peak classification we have to know the distribution of the relative heights of noise maxima. Considering the noise signal samples as a random variable N~

Lud~k Frank." Automated recognition of Auger electron spectra

SPEC -N rl-

with the known three-dimensional distribution w(N;, N2, N3) and the mean value No, we can write for the absolute heights of maxima

$/N $ENS VEXP

0040 O O O 0 TO t O O O (BOpSD) STEP= 1 -gee 11 20010 CTS =2re-tO RUN ,, e 2 196

eV e¥ FS

~ NM-No f NM-No w M(N M - No) = J _

OD

J - oo

w(Nx, ArM- U 0, N 3) d N 1 d N 3 .

(8)

If the height N, is measured with respect to the line connecting the neighbouring minima, the task to find the appropriate distribution is practically unsolvable due to too high dimension of the problem. Nevertheless, when assuming the formation of local noise maxima and minima as statistically independent phenomena, we can derive`)

(9)

The upper estimate of the error of this approximation amounts to several per cent. Transforming ~M(N,) into N,/a units, we obtain a general authenticity function applicable to fast classification of each maximum found on the curve containing the given number of experimental points. The distribution (9) can be easily computed for white Gaussian noise. The same authenticity function was also used for smoothed noise via the transformation ~ ' t ( N , ) = A,,,~vM(Bm,N,) ,

(1 O)

where factors A and B depend on the filter width (2m+ 1) and on the number of passes through the filter n. Both factors remain in the order of unity `). 7. Peak intensity measurement

The problem of the peak area measurement is usually complicated by possible peak overlaps and non-uniform background level. Nevertheless, the peak area integration is preferred as the most reliable noise resistant method. In our case, the background is already corrected to give a constant. Only the difficulties with overlaps remain. It has been found that artificial side-minima appearing as a byproduct of the background correction (see Figure 4) facilitate the

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2t4~ 1 1 ::'.~t-le / 32

TD STEP= 2e~24

lOOe 1 CTS RUN 196

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integration because they suitably define the integration limits. The integration of a single peak area then gives an exact result. The largest error arises in the case of a just-resolved non-symmetric doublet where an intermediate minimum appears. Then the error in the area is as high as + 10% for the higher peak and - 20% for the lower one. This error rapidly decreases as the peak separation increases. In principle, it is possible to correct the peak area with respect to positions and areas of the neighbouring peaks. 8. Implementation in the BP 350.1 spectrometer

The procedures described above are programmed in Assembler language for the Z-80A-based system. Together with the operation program for the control, input of parameters and output of results, they occupy 8 kbytes of the program memory. All algorithms were optimized with respect to computer time, any action is finished within few seconds even for 103 spectral points and the complete processing sequence takes 6.4 s. The operation of the program is realized by using numeral keys and a single function key only. They enable a program code and parameters to be inserted--the display of results is governed with standard function keys of the instrument. As an example of spectrum processing the original and processed spectra (Figures 3-5) of a metal glass sample composed of Fe(40%), Ni(40%) and B(20%). The recognized peaks belong to the main constituents of the sample and to the usual surface PERKS

X

488

6eO

eSOeeV

Figure 3. The original Auger spectrum of the metal glass.

DETECTED

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4 5 6

t46.8 162.8 261.8

78 18e 188

7 8 9

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lee tee 188

642.e

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697.e 769.e

le8 tee

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and peak detection procedures.

5ou" WM(N, -- X -- Y)WM(N, -- X + y) [So~ WM(U -- X) du] 2 d y dx.

ND •

mOO

Figure 4. The spectrum processed by smoothing, background correction

WM(Nr)=4;~_WM(X)

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11 12 13 14 15 16

9te.e 925.e

99 65

5e 7t 137 15~5

224 69 284 793

156 47

Figure 5. Thefinallistoftherecognizedtruepeaks.

439

Lud~.k Frank: Automated recognition of Auger electron spectra

impurities (C, N, O, S). Collecting the necessary factors of relative sensitivity from the literature ~°:1 (which are, of course, not mutually compatible) we obtain from our peak intensity measurement the composition F e ( 3 1 - 4 7 % ) + N i ( 4 5 6 0 % ) + B ( 6 - 1 3 % ) . The differences in the composition can be due to incompatibility of the sensitivity factors used, but they can also correspond to the difference between the bulk and surface compositions in particular due to sample preparation. 9. Conclusions The developed algorithms and the implemented software package are an easy-to-handle and powerful tool for fast extraction of analytical information from Auger spectra taken even under poor signal conditions in an analytical SEM. The system is intended for routine spectra processing to provide basic qualitative or approximate quantitative chemical information. Detailed AES studies will require that more attention be paid to background

440

behaviour under and in the neighbourhood of the peaks, to changes of the peak shape and to peak positions.

References i L Frank and P Vagina, lnst Phys (GB) ConfSer, No 52, Chapter 8, p 371 (1980). 2 L Frank and P Vagina, Comp Phys Communs, 26, 113 (1982). 3 L Frank, To the Savitzky~Golay least-squares smoothing and differentiating algorithm, to be published. 4 L Frank, Authenticity analysis of spectrum-like experimental curves, to be published. 5 L Frank, Statistical properties of energy and angle selected secondary electron emission, to be published. 6 L Frank and P Vagina, Czech patent pending No 1817 (1984). 7 E H S Burhop and W N Asaad, Adv Atom Mol Phys, 8, 163 (1972). s A Savitzky and M J E Golay, Analyt Chem, 36, 1627 (1964). 9 L Frank and P Vagina, Czech patent No 204900 (1980). 10 p M Hall, J M Morabito and D K Conley, Surface Sci, 62, 1 (1977). 11 F Pons, J Lett6ricy and J P Langeron, Surface Sci, 69, 547, 565 (1977).