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Applied Surface Science 81 (1994) 351-356

Modified relative sensitivity factors for Auger spectra Ferenc Pavlyak Department of Atomic Physics, Technical University of Budapest, XI. Budafoki ut 8, H-l111 Budapest, Hungary Received 5 April 1994; accepted for publication 21 June 1994

Abstract The quantitative evaluation method of Auger electron energy spectra using the relative sensitivity factors of pure materials is widely used for complex multicomponent samples. Nevertheless, the traditional "relative sensitivity factors" method leaves matrix effects out of consideration. In the present work new, modified values of the relative sensitivity factors can be calculated for the most common elements in different matrices. In this new method the most important matrix effects are taken into consideration, namely the electron inelastic mean free path and the backscattering factor.

1. Introduction

supposed to be constant.) This formula does not take the matrix effects into consideration.

A quantitative analysis of Auger electron energy spectra using the relative sensitivity factors of pure materials is widely used for alloys and other multicomponent samples [1,2]. This method can be called relative sensitivity factor method (RSFM). However, in this method the different matrix effects are not taken into account. In the RSFM generally the relative sensitivity factors and formula are used which were determined by Palmberg and Davis [3]. According to this formula the atomic concentration of element x:

C~

Ix/Sx ~,,I,/s,'

(l)

n

where I s is the peak-to peak amplitude of element x, s x is the relative sensitivity factor of element x, and n is the number of components. (During the measurement the lock-in amplifier sensitivity, the modulation energy and the primary beam current are

2. Theory and discussion On the basis of many experimental quantitative investigations of alloys it was clear that the abovementioned RSFM must be modified for a more precise quantitative evaluation of Auger electron energy spectra. The matrix dependence of the two most important parameters, namely, electron inelastic mean free path (IMFP) and backscattering factor, influencing the Auger yield of the alloys has been taken into account. In this paper the backscattering factors are calculated by the Ichimura equations [4] and the IMFP values are described by the modified Tokutaka equations [5]. In the course of working out the new evaluation method some permissible simplifying assumptions must be taken if we want to use it for a routine investigation of alloy samples, and we have to be

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352

F. Pay(yak~Applied Surface Science 81 (1994) 351-356

satisfied with the accuracy which is expected in practice. These assumptions are as follows: (a) The determination of the average composition of a few top monolayers is sufficient. (b) The surface of the samples is regarded as a flat surface. This can be done to a reasonable accuracy by rotating the sample under sputtering or by polishing or through an investigation of flat grain-boundaries. (c) The measurements are carried out with the same CMA energy analyzer and same geometry as with which the relative sensitivity factors were determined. So the effect of the angular distribution of Auger electrons can be neglected. (d) It is common knowledge that mainly the energies of the most external (valence) electron shells of elements are influenced by the matrix effects. These external valence bands contribute to produce the low-energy Auger electron energy peaks. So if the high-energy and deep-level Auger electron energy peaks are considered in the course of evaluation, then the matrix effects on the ionization cross-section ( o ' ) and the probability of the Auger process ( p ) are low-rate in the case of alloys. (The values of o- and p depend on the ionization energies of electron shells and the primary electron energy.) As it is well known from numerous previous papers, the Auger electron yield of component i coming from the electron transitions W, X and Y can be written

I i ..~Ip R ( E p ) Pi(WXY) o-/(Ep, E . ) N A ( E p ) Ci, (2)

where s, is the relative sensitivity factor of element x if the measurement parameters are the same as for the element Ag [3]. In the case of diluted binary alloys if the element x is present to some percent (max.) in the majority material y, generally (apart from assumption (d)) the following expression can be written for the modified relative sensitivity factor S~y of the element x: p.,y o~,yRxy A~ N~y sx, =

t,

RxyAxvNv sty -

--

lAg

=

=~,

PAg O'AgRAg)tAgNAg

R, A,N,

.~,,

(5)

where s,,. is the modified sensitivity factor of element x in the majority material y if the above-mentioned assumptions are considered. The data of atomic densities are known. The values of R and A must be stated partly in the own material, partly in the foreign material. For the calculation of R the Ichimura equation was chosen [4], supposing that the primary electron beam is at right angles to the surface of the samples. The values of A were described by Tokutaka equations [5] but these equations were modified in order to get smaller electron mean free path values to be in keeping with results of some other authors, e.g. Powell, Penn, Tanuma and Jablonski [6-8]. The new, modified equations for calculating the A values (in angstr6m, according to the original paper of Tokutaka et al. [5]) are as follows. If 350 < E < 1200 eV and Z < 24, or E > 350 eV and Z > 74, or E > 1200 eV and 14 < Z < 24, then: ln[ B( Z) /3.32] In A =

1n(7.74/3.32)

(1.6551 - 0 . 2 8 9 1 In E)

+ ( - 3.6[)4 + 0.9395 In E ) . If E > 1200 eV and Z < 14, then: ln[ B ( Z ) / 3 . 3 2 ] In A =

pxo-xR~axU~

(4)

Considering the above-mentioned assumption (d) and the fact that in the case of real diluted binary alloys N~v ~ Iv,., Eq. (4) can be written:

where Ip iS the primary ion current, R is the backscattering factor, N is the atomic density, A is the electron mean free path, C~ is the atomic concentration of element i, and Ep is the primary electron energy. So the normalized Auger intensity of a pure element x (to that of silver):

sx.

!n(7.74/3.32)

( 1 . 6 5 5 1 - 0 . 2 8 9 1 In E)

(3)

+ ( - 4 . 1 2 + 0.9395 In E ) .

F. Pavlyak/Applied SurfaceScience81 (1994)351-356 Table 1 Values of the electron mean free path (Axv), the backscattering factor (Rxy), the ratio of atomic densities (Ny/N~) and the modified relative sensitivity factor (S~y) of iron in the case of different majority materials Majority material (y)

A,~. (nm)

Rxv

Ny/ Nx

Sx~.

AI Ag As Au Cd Ca Cr Co Cu Fe Ga Mn Mo Mg Ni Pt Pb Sn Sb Si Ti V W Zn

1.67 1.17 1.37 1.00 1.25 1.62 1.27 1.20 1.20 1.24 1.36 1.27 1.18 1.88 1.20 0.97 1.17 1.41 1.35 1.73 1.47 1.36 1.00 1.28

1.37 1.81 1.69 2.01 1.81 1.51 1.55 1.61 1.64 1.61 1.66 1.59 1.76 1.34 1.64 2.01 2.01 1.84 1.84 1.39 1.54 1.55 1.99 1.66

0.71 0.69 0.55 0.69 0.55 0.27 0.98 1.06 0.99 1 0.60 0.96 0.76 0.51 1.08 0.78 0.39 0.34 0.39 0.59 0.67 0.85 0.74 0.77

0.18 0.16 0.14 0.15 0.14 0.07 0.21 0.23 0.22 0.22 0.15 0.21 0.17 0.14 0.23 0.17 0.10 0.10 0.11 0.16 0.17 0.20 0.16 0.18

Table 2 Values of the electron mean free path (Axy), the backscattering factor (Rxv), the ratio of atomic densities (N~./N~) and the modified relative sensitivity factor (sx~.) of copper in the case of different majority materials

ln[B(Z)/3.32] ln(4.5/3.32)

( 0 . 6 8 4 7 - 0 . 1 1 6 9 In E )

+ ( - 3 . 6 0 4 + 0 . 9 3 9 5 In E ) . If E > 3 5 0 e V a n d 4 2 < Z < 74, t h e n :

In[ B( Z) /4.5] In A =

ln(7.74/4.5)

( 0 . 9 7 0 4 - 0 . 1 7 2 1 In E )

+ ( - 2 . 9 2 + 0 . 8 2 2 6 In E ) . If E < 3 5 0 e V a n d for a n y v a l u e o f Z:

ln[ B( Z) /4.5] In A =

ln(7.74/4.5)

( 0 . 0 1 0 7 - 0 . 0 0 8 3 In E )

+ ( 0 . 3 8 + 0 . 2 5 9 5 In E ) .

(6)

In t h e s e m o d i f i e d T o k u t a k a e q u a t i o n s the r e l a t i o n holds, w h e r e E d e n o t e s the A u g e r

B(Z) = Z p / M

e l e c t r o n e n e r g y a n d Z, p a n d M are the a v e r a g e v a l u e o f the a t o m i c n u m b e r , d e n s i t y a n d a t o m i c w e i g h t in the matrix, r e s p e c t i v e l y . In the o r i g i n a l p a p e r s o f T o k u t a k a et al. [5] p is in g / c m 3 a n d M is in g / m o l . F o r the sake o f u s i n g the a b o v e calculation, Tables 1 a n d 2 s h o w the v a l u e s o f hxy, Rxy, Ny/Nx a n d Sxy in case o f iron a n d c o p p e r in different m a j o r i t y materials. T h e c a l c u l a t i o n s w e r e p e r f o r m e d for 5 k e V p r i m a r y e l e c t r o n energy. In the case o f n o n - d i l u t e d b i n a r y alloys a n d m u l t i c o m p o n e n t alloys a n iteration p r o c e d u r e w a s c r e a t e d as follows: (a) Firstly the n o n - e x a c t c o m p o s i t i o n o f the s a m p l e h a s to b e c a l c u l a t e d b y Eq. (1). So the v a l u e o f C i c a n b e stated. ( b ) B y m e a n s o f C i the w e i g h t e d a v e r a g e v a l u e s o f Z, M, N a n d p h a v e to b e calculated. T h e p c a n b e m e a s u r e d b y u s i n g a p y c n o m e t e r , too.

If E > 3 5 0 e V a n d 24_< Z < 42, then: In A =

353

Majority material (y)

Axy (nm)

Rxy

Nv/N x

sxy

A1 Ag As Au Cd Ca Cr Co Cu Fe Ga Mn Mo Mg Ni Pt Pb Sn Sb Si Ti V W Zn

2.35 1.46 1.81 1.20 1.58 2.39 1.64 1.52 1.52 1.58 1.79 1.62 1.47 2.74 1.50 1.15 1.46 1.85 1.75 2.45 1.97 1.78 1.20 1.65

1.33 1.74 1.63 1.92 1.74 1.47 ! .51 1.56 1.58 1.56 1.60 1.53 1.69 1.31 1.58 1.92 1.92 1.76 1.76 1.36 1.50 1.51 1.90 1.60

0.71 0.69 0.55 0.70 0.55 0.27 0.99 1.06 1 1.01 0.60 0.97 0.76 0.51 1.08 0.78 0.39 0.34 0.39 0.59 0.67 0.85 0.75 0.78

0.21 0.17 0.16 0.15 0.15 0.09 0.23 0.24 0.23 0.24 0.17 0.23 0.18 0.18 0.24 0.16 0.11 0.11 0.12 0.19 0.19 0.22 0.16 0.20

354

F. Paclyak / A p p l i e d Surface Science 81 (1994) 3 5 1 - 3 5 6

(c) The values of Ai must be determined by means of Eq. (6) and using the average values of Z, M, and p. (d) The values of R/ must be determined by means of the Ichimura equation by using the average value of Z. (e) The values of Nav/NX have to be calculated where N,,, is the average density of the sample (determined, for example, by pycnometer) and N~ is the atomic density of the component in question. (f) The product of AxR x relating to the relevant pure material must be determined. (g) The new, modified relative sensitivity factor (sire) of the component i has to be calculated by the equation: Sire :

AiRiNdv AxR xNx

- - S i ;

(7)

i refers to all components of the sample. (h) By means of Eq. (1) using the new S~m the improved Cim values have to be calculated for every component. After this, the whole cycle has to be done from beginning to end by the improved values of Cim. This procedure must be continued until the change in concentration of elements is negligible.

3. Experimental details The efficiency of the above-described evaluation method was checked by means of some multicomponent standard samples. The measurements of two standard samples are shown. These were stainless steel samples which contained nickel, chromium, silicon and (in case of the second sample) molybdenum in a concentration > 0.5 wt%. The exact (nominal) compositions of the standard samples are shown in the last column (c o ) of Tables 3 and 4. The standard samples were prepared by up-to-date patented processes and their chemical compositions were certified by the Hungarian National Office of Metrology on the basis of results of interlaboratory tests carried out in numerous national and several foreign laboratories according to standardized methods. The standard samples were purchased from

Table 3 Relative sensitivity factor and concentration data of the first standard sample Element

si

si,~

C i (wt%)

Ci, n (wt%)

C,

Fe Ni Cr Si

(1.22 0.27 (I.31 (I.(]38

0.21 0.25 (I.31 l).037

77.0 12.5 7.4 3.1

77.2 12.9 7.1 2.8

77.8 12.8 7.0 2.4

commercial suppliers and with regard to the abovementioned patented processes, knowledge of the preparation procedure was not at the author's disposal. The scatter in the nominal chemical composition was 0.1 wt%. The measurements were carried out on SAM equipment PHI 5 4 5 / A . The experimental parameters were: primary electron energy 5 keV, primary electron current 10 7 A, diameter of primary electron beam ~ 7 g m , ultimate pressure in the vacuum chamber 10 s Pa. At the beginning of the measurements argon ion sputtering was used in order to eliminate contaminations from the uppermost surface layers to reach the bulk region as the nominal composition data were given in this region. The sputtering argon ion current was 10 6 A, the ion energy was 1 keV and the diameter of the ion beam was about 1 ram. The sputtering was carried on just until the Auger intensities of the surface contaminants (firstly C and O) became zero. In addition to this, fortunately the preferential sputtering does not have to be taken into account as it is well known that in the case of metallic elements (e.g. Fe, Ni, Cr), which are next to each other in the Periodic System, the effect of the preferential sputtering is negligible (as the sputtering rates are practically the same). So the bulk concentrations (and not the surface

Table 4 Relative sensitivity factor and concentration data of the second standard sample Elemcnt

si

Sim

C i (wt%)

Cim (wt%)

C, (wt%)

Fc Ni Cr Si Mo

0.22 0.27 0.31 (I.038 0.28

0,22 0.26 (t.32 0,037 0.34

67.9 21.6 4.2 1.4 4.9

68.0 22.5 4.1 1.3 4.1

68.3 22.3 4.11 1.3 4.1

[i Pavlyak /Applied Surface Science 81 (1994) 351-356

NI

Fe I

Fe Fe

goo

r~o

ELECTRON ENERGY, eV BOO

J.duu

• z'..-J

z~o

iBoo

Fig. 1. Auger electron energy spectrum of first standard sample. The nominal bulk chemical composition of this sample is shown in the last column (Co) of Table 3.

355

mately show the average values of the measuring results. The data of the quantitative evaluation are summarized in the Tables 3 and 4. In these tables s i and Ci mean the unmodified values of the relative sensitivity factors and concentrations (in weight percent), respectively. The S~m and Cim mean the modified values of the relative sensitivity factors and concentrations determined after the first iteration cycle. The scatter in the CZm values was 0.2 wt%. The C o values show the original data of the concentrations. It can be seen (especially in the case of sample 2) that practically the original concentration values are obtained after the first iteration cycle.

4. Conclusion concentrations) were only determined similarly to the nominal data of the standard samples. Because the surface layers were sputtered away, the known composition changes (for example, Ni and Cr enrichment) in the surface layers of the stainless steel samples were not studied in this work, but this was not the aim of the present paper. In the course of the measurements a lot of Auger electron energy spectra were taken from many areas of the sample surfaces and the Auger peak intensities were determined from the average values of the peak-to-peak heights. By way of illustration, two Auger electron energy spectra are shown in Figs. 1 and 2 taken from the first and second samples. These spectra approxi-

The original relative sensitivity factor method is not suitable to evaluate quantitatively the Auger electron energy spectra in case of multicomponent alloy samples. In the new, modified relative sensitivity factor method of Auger electron energy spectra the IMFP values are described by the modified Tokutaka equations and the high-energy as well as deep-level Auger energy peaks must be considered. In the case of diluted binary alloys the " P a l m b e r g " calculation can be suitable to get the right concentration data but the new, modified sensitivity factors must be used. In the case of non-diluted binary alloys and multicomponent alloys a new iteration procedure was worked out. In this procedure the concentration data of the components are determined by the gradually improved relative sensitivity factors having regard to the influence of the matrix effects on the IMFP values and the backscattering factors. In this way the real quantitative composition of the metal and alloy samples can be approximated successively. The efficiency of this evaluation method was controlled by means of some multicomponent standard alloy samples.

Fe ~1'ItON

2o0

4o0

6oo

obo

ldoo

l~co

1Xoo

ENE~Y~

eV

Acknowledgements

1~oo

Fig. 2. Auger electron energy spectrum of second standard sample. The nominal bulk chemical composition of this sample is shown in the last column (Co) of Table 4.

The author would like to thank Prof. Dr. P6ter Richter and Prof. Dr. J~nos Giber for aiding this research work.

356

F. Pavlyak /Applied Surface Science 81 (1994) 351-356

References [1] T. Tanabe, M. Tanaka and S. Imoto, Surf. Sci. 187 (1987) 449. [2] D.E. Peebles and L.E. Pope, Appl. Surf. Sci. 28 (1987) 395. [3] L.E. Davis, N.C. MacDonald, P.W. Palmberg, G.E. Riach and R.E. Weber, Handbook of Auger Electron Spectroscopy (Physical Electronics Industries, Perkin-Elmer, Eden Prairie, MN, 1976).

[4] S. Ichimura, R. Shimizu and J. Langeron, Surf. Sci. 124 (1983) L49. [5] H. Tokutaka, K. Nishimori and H. Hayashi, Surf. Sci. 149 (1987) 349. [6] S. Tanuma, C.J. Powell and D.R. Penn, Surf. lntcrf. Anal. 11 (1988) 577. [7] P. Mrozek, A. Jablonski and A. Sulyok, Surf. Interf. Anal. l 1 (1988) 499. [8] A. Jablonski and H. Ebel, Surf. Interf. Anal. 11 (1988) 627.