- Email: [email protected]
AES depth profile studies of interdiffusion in thin polycrystalline Au-Ag multilayer films
Applied Surface Science 45 (1990) 57-64 North-Holland
57
AES depth profile studies of interdiffusion in thin polycrystalline Au-Ag multilayer films Antoni Bukaluk Instytut Matematyki i Fizyki, Akademia Techniczno-Rolnicza, ul. Kaliskiego 7, 85-790 Bydgoszcz, Poland
and Wac/aw Bala lnstytut Fizyki, Uniwersytet Mikotaja Kopernika, ul. Grudziqdzka 5, 87-100 Torun, Poland
Received 3 January 1990; accepted for publication 6 April 1990 Interdiffusion in thin polycrystallineAu-Ag multilayer films was studied in the temperature range of 175-250 o C. Auger electron spectroscopy (AES) with simultaneous argon ion sputtering was employed for determination of the concentration distribution of diffusing species. It was observed that after annealing the initial concentration distribution, which was almost rectangular in the unheated samples, changed into a sinusoidal one in the annealed films. Interdiffusion coefficients were calculated from the amplitudes of the sinusoidal distribution. The activation energy was determined from the Arrhenius plot. 1. Introduction The extensive use of thin polycrystalline layers in many areas of microelectronics and photovoltaics has focused considerable attention on the phenomena of diffusion processes occurring in thin films. Although our understanding of kinetics of lattice, grain boundary and defect-enhanced diffusion mechanisms in thin layers has been greatly advanced by the development of surface analytical techniques such as Auger electron spectroscopy (AES), secondary ion mass spectroscopy (SIMS) Rutherford backscattering spectroscopy (RBS), and many others, the phenomenon remains incompletely understood due to the difficulty in analysing interfaces at atomic levels. Interdiffusion phenomena, occurring in thin polycrystalline A u - A g films, are both of an academic and technological interest. They were the subject of m a n y papers [1-12] dealing with the problems of interdiffusion [1-3,6,7,9,11], grain boundary diffusion [5-10,12] and defect-enhanced diffusion [3,4]. All of these investigations were performed for the bilayer A u - A g systems.
For the purpose of determining the interdiffusion parameters Auger electron depth profile analysis was the chosen technique, which allows diffusion parameters to be obtained with a very good accuracy. The following methods, based on the variation of composition in the proximity of the interface are mainly employed; the so-called "centre-gradient" method [3,6,7,13] and the Boltzm a n n - M a t a n o method [11,14,15]. A serious shortcoming of both above-mentioned double-layer methods is the need for a deconvolution of the measured sputter profile in cases when the depth resolution is insufficient for the observed diffusion effect. Sometimes these methods can not be applied at all since the slope of the depth profile at the interface does not differ from that of the unheated sample. In this case another method, employing the change of concentration distribution in the multilayer films can be applied with better result [15-17]. The aim of this paper is to report results of interdiffusion studies in the multilayer A u - A g thin film structures in the temperature range of 175-250 o C. Since this temperature range is lower
0169-4332/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
58
than that used for studies in the previous works [7-10] by using the same AES spectrometer, the present studies can be treated as supplementary to the studies performed previously by using the "centre-gradient" and the "plateau-rise" methods [7,18] applied to double-layer A u - A g films.
argon pressure of 6.8 x 10 -5 hPa, ion current density of 1.8 × 10 .2 A m -2 and ion energy of 1 keV were kept during profiling. A static electron b e a m with energy of 3 keV and current of 10 #A, and with a diameter of 0.3 m m was used.
3. Interdiffusion in the muitilayer structure 2. Experimental The diffusion samples were deposited onto copper substrates of 99.9 wt% purity. The substrates (4 × 4 m m 2 squares of 2 m m thickness) were mechanically polished, and then rinsed in methanol and distilled water. The roughness amplitude of the substrates prepared in such a way, determined by using a Talysurf method, and given by centre-line average R a, was equal to 18 _+ 2 nm. The cleaved substrate was then covered by a Ag layer of about 100 nm thickness in order to minimize interdiffusion between the substrate and multilayer film. Immediately after deposition of the Ag layer a multilayer A u - A g structure was formed. Evaporation rates of both Au and Ag were 0.8 n m s -1. The structure consisted of three Ag layers and two Au layers of H/2 = 40 _+ 5 nm thickness each, and of two boundary Au layers of H/4 = 20 _+ 5 nm thickness, where H is the film periodicity. A schematic drawing of the multilayer A u - A g thinfilm structure is presented in 'fig. 1. The thickness of the first and the last layers of the multiple film was one half that of the " b u l k " layers in order to preserve translational symmetry. The total thickness of the structure, as measured by optical interferometry, was 243 _4- 10 nm. AES depth profiles were obtained by simultaneous Ar ion sputtering and Auger analysis. The
The initial concentration profile of a periodic multilayer A B A B A B . . . structure of a rectangular initial distribution can be expressed as a Fourier series [15-17]: 1
sin
C(z'O)=2 q-m= 1
(1)
H ]'
where H is the periodicity depth interval of the profile, z is the depth and m = 1, 3, 5 . . . . After diffusion, in the present case concerning one-dimensional diffusion system of miscible components, solutions of Fick's second law are used as an approximation of actual diffusion profiles. Taking into account that atomic fluxes are equal to zero on the surface and on the interface between the boundary Au layer and Ag underlayer, these solutions can be expressed as a Fourier series with time-dependent coefficient [15-17]:
c(z,
1
t)=~+
m=l
m Xp[
(k 27rm ~2
]
--g--) Dt]
• [2rrmz~
× s,n[ - - - H - - ) '
(2)
where D is the diffusion coefficient (assumed to be independent of concentration) and t is the time of annealing. For annealing times and diffusion coefficients usually met in practical diffusion studies in thin films one can assume that t > ( 0 . 3 / D ) ( H / 2 7 r ) 2. In such conditions the higher Fourier components decay very rapidly with time t, and the amplitude of the sinusoidal distribution in (2) can be written as follows: 1 ~max- ?min _ 1 (2~max _ 1) 2 Cmax"q-Cmin 2
HI4
N =80nm
H/2
H/2
H/2 H/4
d:100 nm
Fig. 1. Schematic drawing of the multilayer A u - A g structure.
[ 2~r X2 ] = 2eXPqr - t - i f ) D,],
(3)
ttun film
where ?max is the m a x i m u m concentration of the
59
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayerfilms
element B inside the layer B, and ?mi, is the concentration of the element A at the same depth: Cmin = 1 - Cm~x (and inversely inside the layer A). From (3) it follows that the diffusion coefficient D can be obtained from a semilogarithmic plot of the concentration amplitude ½(2Cmax --1) versus annealing time t.
altered layer radiation-induced damage permits rapid mixing of the components in such a way that within the altered layer the concentration is uniform. Moreover, it is assumed that sputter probabilities of the elements do not depend on the concentration and no diffusion of material between the altered layer and the bulk alloy takes place. Based on these assumptions and taking into account the mass balance of Au and Ag at the surface, one can derive the following relation for the sputter rate VA~_A~ of the A u - A g system [21]:
4. Results
The main problem of quantitative Auger depth profiling is to convert the temporal variation of the measured Auger intensities to spatial variation of the composition. In the present study a simple linear relation between Auger intensity and concentration was assumed, and the Auger signals were quantified by applying Auger sensitivity factors of Au(66, 69 eV) and Ag(351, 357 eV) Auger lines, measured by means of pure elements [19]. The transformation of time of sputtering into depth was achieved by using a simple kinetic sputter model, developed by Ho et al. [20]. Basically, in the model it is assumed that sputter-induced composition changes affect a surface layer of finite thickness, the so-called altered layer. Within the
v.°( v,,g OA~)CAg
VAu_A~(CAg)=VAu+VA,CAs + (1 -- cag) rAg , -
(4)
where Vnu, vAg and Va~_hg are the sputter rates of pure gold, silver and gold-silver alloy, respectively, and CAg is the atomic concentration of silver in the alloy. The sputter rates of gold and silver, determined by sputter removal of definite thicknesses of pure Au and Ag films, were found to be VAu= 0.12 nm min -1 and vAg = 0.14 nm min - l for argon ions with energy of 1 keV, current density of 1.8 x 10 -2 A m -2 and angle of incidence of 75 °. These values were used for transformation of sputtering time into depth, based on eq. (4).
90 80 ~•*
•
: -'•"o"°"'o'..o•
o~ 70
".
4A
.,•
.o*,*.. ,°
•:
60
":
**~'~%
...':'~t
@
cO
:.
"..
*,,r" %
,~
K
-..
~6 50 L..
.j,
•%
C-
..
x •
C"
x
X
0 0
3O
x • °°
° °.
"...(
~ "
•
•
o" ".
.Z"
".( Z
•. •"""•
x
•
°
20
1%
4'o
I
12o
I
16o
I
depth [nm] Fig. 2. Auger electron depth profile of the multilayer Au-Ag film annealed for 10 h at 200 o C: (X) Au concentration, (@) Ag concentration.
A. Bukaluk, IV. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
60
}
'!!! I2
it) ('.4
0.01 0
1
I
I
2
3
4
5
[
I
6
7
8
9 10 time [104 s]
Fig. 3. Amplitude of the concentration distribution in the multilayer Au-Ag thin films as a function of annealing time: (×) 175 o C, (e) 200 o C, (o) 225 °C and (A) 250 o C.
Fig. 2 presents a typical depth profile of a multilayer A u - A g film annealed for 10 h at 200 o C. From fig. 2 it follows that during annealing the concentration distribution, which is almost rectangular in the as-deposited film, changes into a slightly distorted sinusoidal distribution by interdiffusion. The distortions of the sinusoidal distribution of depth profiles are presumably due to a sputtering effect. The concentrations amplitude l(26"ma x 1) decreases from the initial value of 0.5 in the non-annealed sample to about 0.25 in the annealed one. The other feature to be mentioned is the decrease of the concentration amplitude of the annealed sample with sputtered depth. This indicates a degradation of depth resolution during sputtering. Therefore the amplitude ½(2Cmax - - 1 ) was taken from the first silver layer, where the effect of sputtering artefacts was the least. In fig. 3 the amplitudes ½(2~ma× - 1) of the Auger signal, measured for multilayer A u - A g films after a heat treatment of 175,200, 225 and 250 o C, are plotted logarithmically against the time of annealing t. One can see that the measured amplitudes fit the exponential relation in (3) very well. The slope of the straight lines shown in this figure increases with annealing temperature. This proves -
that at higher temperature higher diffusivities are observed. On the basis of the results presented in fig. 3 the values of the interdiffusion coefficients were calculated to be D = (4.4 + 0.6) × 10 -]8 cm 2 s 1 [°C]
temperature 10-14
325
300
275
250
225
200
175
I
I
I
F
I
f
]
, \
I 2.0
-
10.
\,,
lo-~
\ 10-~8 1.6
,
i 1.8
~ 1000 T
i 2.2
[ K-l]
Fig. 4. Arrhenius plots of interdiffusion coefficients: ( x ) present work, ( o ) the values obtained by using the "centre-gradient" method [7], (O) the values obtained by using the "plateau-rise" method [7,9].
A. Bukaluk, W.. Bata / lnterdiffusion in thin polycrystalline Au-Ag multilayer films
at 175°C, D = (2.5 + 0.3) x 10 -17 cm 2 s -1 at 200° C, D = (1.4 + 0.4) x 10 -16 cm 2 s - I at 2 2 5 ° C and D = (7.0 + 0.5) × 10 -16 cm 2 s -1 and 250°C. These values have been marked by crosses and plotted in the form of an Arrhenius plot in fig. 4. One can see that the data obey an Arrhenius law: D = D O e x p ( - E a / k T ), where D O is the pre-exponential diffusivity term, Ea is the activation energy, k is the Boltzmann constant and T is the temperature. The values of D O= 1.1 × 10 -2 cm 2 s-1 and E a = 1.4 eV have been obtained from the data presented in fig. 4.
5. Discussion The measurements of interdiffusion coefficients in the multilayer A u - A g thin film system were carried out in the temperature range 175-250 ° C. At higher temperatures interdiffusion was so fast that the concentration of diffusing species changed very rapidly even after a very short annealing time. For longer annealing times an almost homogeneous concentration distribution was obtained. Therefore, it was impossible to obtain some experimental points of the ln[l(2gmax- 1)] versus t dependence with satisfactory accuracy and afterwards to calculate the interdiffusion coefficient D. On the other hand, aging at lower temperature did not cause noticeable changes in the concentration distribution inside the A u - A g multilayer structure. In both cases, the effect to be measured was comparable with the experimental error.
61
In the present work the values of interdiffusion coefficients were extracted from the amplitude of the concentration distribution, taken from the uppermost silver layer. The data obtained in such a way obey an Arrhenius equation. Attempts made for determination of D from the amplitudes taken from further layers failed, since the experimental points plotted in the form of ln[½(2gma x --1)] versus t did not form a straight fine. The reason for this fact was the detrimental effect of sputtering, observed particularly for a larger depth. An accurate calibration of the concentration in quantitative AES needs the knowledge of m a n y parameters, the most important of which are the Auger electron escape depth ~, and the backscattering factor r B. If one neglects the influence of both ?~ and r s on the concentration, one obtains underestimated values of the true composition [22]. As a consequence, the values of the concentration amplitude, presented in fig. 3, are also underestimated. The above-mentioned effect influences less the points corresponding to larger concentration amplitude and more the points with smaller values of ½ ( 2 ? m a x -- 1) in the plot of ln[½(2Emax - 1 ) ] versus t dependence~ Therefore, the slope of the ln[½(2Emax - 1)] versus t plot is overestimated. This is turn results in an overestimation of the values of the interdiffusion coefficients. The depth profile shown in fig. 2 exhibits the apparent excess of silver at the surface. The same feature was observed for all profiles. The presence of Ag atoms at the Au surface is probably caused
Table 1 Values of the pre-exponential diffusivity term D O and the activation energy E a in thin film A u - A g couples Ref.
Specimen type
Temperature range
DO (cm 2 s - l )
Ea (eV)
1.2 7.7 1.0 1.9 5.6 3.9 1.1
1.7 ± 0 . 4 1.8 ±0.1 1.55±0.15 1.95±0.05 1.5 ±0.1 1.8 ±0.1 1.4 ±0.1
(°C) [1] [3] [6] [11] [7] a) [7,9] b) Present work
Polycrystalline Single crystal (111) Polycrystalline Single crystal (111) Polycrystalline Polycrystalline Polycrystalfine
a) The "centre-gradient" method. b) The "plateau-rise" method,
199-242 250-350 282-394 200-400 250-325 250-300 175-250
× × × x x
10 2 10-a 10-1 10-1 10-3
x 10 - z
62
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayerfilms
by spreading out of Ag atoms, moving along grain boundaries from the bottom layer, by surface diffusion. Hence the silver spreading across the surface served as a secondary source for diffusion back into the bulk of the film. One can expect that this effect could disturb the depth profile of the uppermost Au layer only. In table 1 the experimental results of the present work in comparison with the results reported elsewhere for the bilayer A u - A g films are listed. In this table the values of the activation energy E a and the pre-exponential diffusivity term D O in the Arrhenius equation are specified. As it can be seen the activation energy is a little smaller than those obtained for single-crystal films [3,11]. Most likely the reason for the lower value of E a is a larger defect density in the multilayer structure. The values of D O and Ea obtained for polycrystalhne layers in refs. [1,7,9] show better conformity with the results presented in this work. The values of the activation energy extracted from the bilayer depth profile data by using the "centre-gradient" method [6,7] are almost equal to the value of E a in the multilayer structure. The value of D O in the present study is comparable with those reported by other authors [1,3,6,7]. Fig. 4 presents the results of the present work in comparison with the results acquired previously by using the same AES spectrometer and the samples prepared in the similar conditions in the same vacuum chamber. One can see that the values of the interdiffusion coefficients obtained for multilayer thin films are about an order of magnitude larger than those extracted previously for bilayer films by using the "centre gradient" [7] and the "plateau-rise" [7,9] methods. The difference between the values obtained for multilayer and bilayer films can be mainly ascribed to differences in the structure of the analysed films, although this difference may be also due to the above-mentioned overestimation of the values of D, caused by the neglect of ~ and r B in calculation of the concentration. The films investigated in the present work had an average grain size of about 100 nm, comparable with those reported in refs. [7,9]. However, the thickness of particular layers of the multilayer structure was 2.5 times smaller than that in refs. [7,9]. Therefore, the films
studied in the present paper contained much more grain boundaries and other defects than the double-layer ones. This influenced the interdiffusion data to a larger extent. The fact that interdiffusion in multilayer films is considerably influenced by the grain boundary diffusion can be noticed in fig. 3. One can see that the straight lines in this figure do not extrapolate to the initial concentration amplitude at t = 0. A possible reason is the presence of a very rapid diffusion process occurring at relatively short annealing times during heating the samples from room temperature to the final temperature. In thin polycrystalline films the grain boundary diffusion is such a fast diffusion mechanism. Therefore, the interdiffusion data obtained in this paper must be treated as averaged values which include both volume and grain boundary effects. Recently R011 has proposed a formalism allowing the extraction of both lattice and grain boundary diffusion parameters from the data obtained in a multilayer thin film structure [17]. In this model it is assumed that the grains are cylindrical cells of radius r0, perpendicular to the film surface, surrounded by prismatic grain boundaries. The material transport in grains and grain boundaries is described by diffusivities D and D', respectively. To extract D and D ' from measured depth profiles of annealed multilayer films, the concentration amplitudes ½(2~max - 1) of the profiles are plotted versus normalized time ~-= D t / r 2. Next it is needed to fit curves obtained for particular values of A = D ' / D - 1 to experimental data. Recently two papers have been published, in which the results of investigations of both grain boundary and volume diffusion in thin C u - N i films, acquired by the method based on a periodical solution of the diffusion equation, have been reported [23,24]. In both studies thin films with very reproducible, small (20 nm) grain sizes, examined by careful and precision transmission electron microscopy (TEM) measurements, have been analysed. For such films Auger depth profile data were evaluated by a numerical analysis and the grain boundary diffusion coefficients were separated from the lattice diffusion coefficients. Attempts made to distinguish the contribution
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
from the lattice and grain boundary interdiffusion failed in the case of the present studies. The data did not fit the curves obtained for the specified values of A with good enough accuracy. In particular parts of the ln[½(2?max - 1)] versus ~- dependence experimental points fitted different curves, corresponding to the values of A differing from one another by an order of magnitude, at least. This caused a large uncertainty in the determination of A, and as a consequence, a large uncertainty in the determination of interdiffusion coefficients. The reason that RtSll's model could not be applied in the present case was most probably large scattering of the values of the grain size of the films (from 50 nm up to 200 nm, as measured by TEM). On the other hand, it is also possible that the grains with small sizes (like in refs. [23,24]) better conformed to the assumption of the model that the grains had a circular cross section. For larger grain sizes (100 nm in the present work) such as assumption may be invalid. The main aim of the present paper was to obtain the values of interdiffusion coefficients in the temperature range lower than the range applied previously for the bilayer samples obtained in similar conditions and analyzed by the same AES spectrometer [7,9]. In this field our investigations succeeded, giving the values of D obeying the Arrhenius law in the temperature range of 175-250°C. However, in order to separate the volume and the grain boundary diffusion coefficients further investigations performed on films with smaller and repeatable grain sizes are needed. It is the purpose of future studies to perform such investigations. 6. Conclusions
The present work has shown that the method based on the analysis of changes of the concentration amplitude of diffusant in the multilayer film with time and temperature of heating, can be used as a very sensitive technique for the measurement of interdiffusion at relatively low temperatures. The method is greatly aided by the availability of Auger electron spectroscopy as a sensitive and quantitative technique for measuring the concentration distribution of the diffusing species.
63
The accuracy of the measurement of the interdiffusion coefficient D is influenced by the experimental method. In the present case the values of D were calculated from the concentration amplitude, taken from the top silver layer, and the influence of the Auger electron escape depth and the backscattering factor on the concentration has been ignored. Therefore, as it was pointed above, the values of D obtained in a multilayer structure are overestimated. On the other hand, multilayer films contained much more structural defects, mainly grain boundaries, in comparison with bilayer films. Both the above-mentioned effects are presumably responsible for the observed larger values of D compared with the values obtained previously for the bilayer films by using the "centre-gradient" and the "plateau-rise" methods [7,9]. The comparison of the values of the activation energy E a and the pre-exponential factor D O obtained in the present study with those acquired elsewhere for the bilayer A u - A g couples indicates that the values presented here are lower than those obtained for single-crystal films [3,11j. The same concerns the values of E a and D O obtained in the interior of the polycrystalline A u - A g couple by using the "plateau-rise" method [7,9]. In both cases defect-enhanced diffusion disturbed the lattice diffusion less than in the multilayer film, because of the lower concentration of defects in the analysed region of the films studied in refs. [3,7,9,11]. In polycrystalline films the values of D O obtained in refs. [1,7] appear generally consistent with the value acquired in the present work. Next the values of E a obtained in refs. [6,7] are almost equal to the value extracted from the Arrhenius plot in this work. Other discrepancies observed in the data obtained in different studies can be mainly ascribed to structural differences between the studied films. One must also add that the method of data acquisition, the state of purity of the materials used and even the composition of the residual atmosphere in the UHV chamber may also cause discrepancies in the results of diffusion measurements in thin films performed in different laboratories. The results reported in this paper are of particular interest, since the measurements were car-
64
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag rnultilayer films
ried out at unusually low temperatures. Moreover, the reported results have been obtained for the first time in the multilayer structure. Therefore, the studies reported here can be treated as valid supplement to the studies performed previously in the bilayer A u - A g couples.
Acknowledgement The work was sponsored by CPBP 01.08 research project.
References [1] H.E. Cook and J.E. Hilliard, J. Appl. Phys. 40 (1969) 2191. [2] R.G. Kirsch, J.M. Poate and M. Eibschutz, Appl. Phys. Lett. 29 (1976) 772. [3] F. Sofia and J.L. Saced6n, Thin Solid Films 60 (1979) 113. [4] K. Meinel, M. Klaua and H. Bethge, Thin Solid Films 34 (1976) 157. [5] J.C.M. Hwang, J.D. Pan and R.W. Balluffi, J. Appl. Phys. 50 (1979) 1349. [6] S.K. Sen, P.M. Kluge-Weiss and C.L. Bauer, Thin Solid Films 82 (1981) 299. [7] A. Bukaluk, Surf. Interf. Anal, 5 (1983) 20. [8] A. Bukaluk, M. Rozwadowski and R. Siuda, Appl. Phys. A 34 (1984) 193.
[9] A. Bukaluk, R. Siuda and M. Rozwadowski, Acta Univ. Wratisl. 782 (1984) 37. [10] A. Bukaluk, in: Physics of Solid Surfaces, Vol. 23 of Studies in Surface Science and Catalysis, Ed. J. Koukal (Elsevier, Amsterdam, 1985) p. 170. [11] K. Meinel, M. Klaua, Ch. Ammer and H. Bethge, Phys. Status Solidi (a) 106 (1988) 493. [12] A. Bukaluk, Appl. Surf. Sci. 35 (1988-89) 317. [13] P.M. Hall and J.M. Morabito, Surf. Sci. 54 (1976) 79. [14] J.E.E. Baglin, Metal-metal interdiffusion, in: thin Films Interdiffusion and Reactions, Eds. J.M. Poate, K.N. Tu and J.W. Mayer (Wiley, New York, 1978) p. 305. [15] W. Pamler, Appl. Phys. A 42 (1987) 219. [16] K. R~511and W. Reill, Thin Solid Films 89 (1982) 221. [17] K. Ri311, Habilitation Thesis, Universit~it Regensburg (1981). [18] P.M. Hall, J.M. Morabito and J.M. Poate, Thin Solid Films 33 (1976) 107. [19] P.W. Palmberg, Anal. Chem. 45 (1973) 549. [20] P.S. Ho, J.E. Lewis and J.K. Howard, J. Vac. Sci. Technol. 14 (1977) 322. [21] K. Meinel, M. Klaua and H. Bethge, Phys. Status Solidi (a) 106 (1988) 133. [22] S. Hofmann and J.M. Sanz, in: Thin Film and Depth Profile Analysis, Ed. H. Oechsner (Springer, Berlin, 1984) p. 143. [23] R. Venos and K. R011, Beitr. Elektronenmikroskop. Direktabb. Oberfl. 21 (1988) 347. [24] R. Venos, W. Pamler and H. Hoffmann, Thin Solid Films 162 (1988) 155.
57
AES depth profile studies of interdiffusion in thin polycrystalline Au-Ag multilayer films Antoni Bukaluk Instytut Matematyki i Fizyki, Akademia Techniczno-Rolnicza, ul. Kaliskiego 7, 85-790 Bydgoszcz, Poland
and Wac/aw Bala lnstytut Fizyki, Uniwersytet Mikotaja Kopernika, ul. Grudziqdzka 5, 87-100 Torun, Poland
Received 3 January 1990; accepted for publication 6 April 1990 Interdiffusion in thin polycrystallineAu-Ag multilayer films was studied in the temperature range of 175-250 o C. Auger electron spectroscopy (AES) with simultaneous argon ion sputtering was employed for determination of the concentration distribution of diffusing species. It was observed that after annealing the initial concentration distribution, which was almost rectangular in the unheated samples, changed into a sinusoidal one in the annealed films. Interdiffusion coefficients were calculated from the amplitudes of the sinusoidal distribution. The activation energy was determined from the Arrhenius plot. 1. Introduction The extensive use of thin polycrystalline layers in many areas of microelectronics and photovoltaics has focused considerable attention on the phenomena of diffusion processes occurring in thin films. Although our understanding of kinetics of lattice, grain boundary and defect-enhanced diffusion mechanisms in thin layers has been greatly advanced by the development of surface analytical techniques such as Auger electron spectroscopy (AES), secondary ion mass spectroscopy (SIMS) Rutherford backscattering spectroscopy (RBS), and many others, the phenomenon remains incompletely understood due to the difficulty in analysing interfaces at atomic levels. Interdiffusion phenomena, occurring in thin polycrystalline A u - A g films, are both of an academic and technological interest. They were the subject of m a n y papers [1-12] dealing with the problems of interdiffusion [1-3,6,7,9,11], grain boundary diffusion [5-10,12] and defect-enhanced diffusion [3,4]. All of these investigations were performed for the bilayer A u - A g systems.
For the purpose of determining the interdiffusion parameters Auger electron depth profile analysis was the chosen technique, which allows diffusion parameters to be obtained with a very good accuracy. The following methods, based on the variation of composition in the proximity of the interface are mainly employed; the so-called "centre-gradient" method [3,6,7,13] and the Boltzm a n n - M a t a n o method [11,14,15]. A serious shortcoming of both above-mentioned double-layer methods is the need for a deconvolution of the measured sputter profile in cases when the depth resolution is insufficient for the observed diffusion effect. Sometimes these methods can not be applied at all since the slope of the depth profile at the interface does not differ from that of the unheated sample. In this case another method, employing the change of concentration distribution in the multilayer films can be applied with better result [15-17]. The aim of this paper is to report results of interdiffusion studies in the multilayer A u - A g thin film structures in the temperature range of 175-250 o C. Since this temperature range is lower
0169-4332/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
58
than that used for studies in the previous works [7-10] by using the same AES spectrometer, the present studies can be treated as supplementary to the studies performed previously by using the "centre-gradient" and the "plateau-rise" methods [7,18] applied to double-layer A u - A g films.
argon pressure of 6.8 x 10 -5 hPa, ion current density of 1.8 × 10 .2 A m -2 and ion energy of 1 keV were kept during profiling. A static electron b e a m with energy of 3 keV and current of 10 #A, and with a diameter of 0.3 m m was used.
3. Interdiffusion in the muitilayer structure 2. Experimental The diffusion samples were deposited onto copper substrates of 99.9 wt% purity. The substrates (4 × 4 m m 2 squares of 2 m m thickness) were mechanically polished, and then rinsed in methanol and distilled water. The roughness amplitude of the substrates prepared in such a way, determined by using a Talysurf method, and given by centre-line average R a, was equal to 18 _+ 2 nm. The cleaved substrate was then covered by a Ag layer of about 100 nm thickness in order to minimize interdiffusion between the substrate and multilayer film. Immediately after deposition of the Ag layer a multilayer A u - A g structure was formed. Evaporation rates of both Au and Ag were 0.8 n m s -1. The structure consisted of three Ag layers and two Au layers of H/2 = 40 _+ 5 nm thickness each, and of two boundary Au layers of H/4 = 20 _+ 5 nm thickness, where H is the film periodicity. A schematic drawing of the multilayer A u - A g thinfilm structure is presented in 'fig. 1. The thickness of the first and the last layers of the multiple film was one half that of the " b u l k " layers in order to preserve translational symmetry. The total thickness of the structure, as measured by optical interferometry, was 243 _4- 10 nm. AES depth profiles were obtained by simultaneous Ar ion sputtering and Auger analysis. The
The initial concentration profile of a periodic multilayer A B A B A B . . . structure of a rectangular initial distribution can be expressed as a Fourier series [15-17]: 1
sin
C(z'O)=2 q-m= 1
(1)
H ]'
where H is the periodicity depth interval of the profile, z is the depth and m = 1, 3, 5 . . . . After diffusion, in the present case concerning one-dimensional diffusion system of miscible components, solutions of Fick's second law are used as an approximation of actual diffusion profiles. Taking into account that atomic fluxes are equal to zero on the surface and on the interface between the boundary Au layer and Ag underlayer, these solutions can be expressed as a Fourier series with time-dependent coefficient [15-17]:
c(z,
1
t)=~+
m=l
m Xp[
(k 27rm ~2
]
--g--) Dt]
• [2rrmz~
× s,n[ - - - H - - ) '
(2)
where D is the diffusion coefficient (assumed to be independent of concentration) and t is the time of annealing. For annealing times and diffusion coefficients usually met in practical diffusion studies in thin films one can assume that t > ( 0 . 3 / D ) ( H / 2 7 r ) 2. In such conditions the higher Fourier components decay very rapidly with time t, and the amplitude of the sinusoidal distribution in (2) can be written as follows: 1 ~max- ?min _ 1 (2~max _ 1) 2 Cmax"q-Cmin 2
HI4
N =80nm
H/2
H/2
H/2 H/4
d:100 nm
Fig. 1. Schematic drawing of the multilayer A u - A g structure.
[ 2~r X2 ] = 2eXPqr - t - i f ) D,],
(3)
ttun film
where ?max is the m a x i m u m concentration of the
59
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayerfilms
element B inside the layer B, and ?mi, is the concentration of the element A at the same depth: Cmin = 1 - Cm~x (and inversely inside the layer A). From (3) it follows that the diffusion coefficient D can be obtained from a semilogarithmic plot of the concentration amplitude ½(2Cmax --1) versus annealing time t.
altered layer radiation-induced damage permits rapid mixing of the components in such a way that within the altered layer the concentration is uniform. Moreover, it is assumed that sputter probabilities of the elements do not depend on the concentration and no diffusion of material between the altered layer and the bulk alloy takes place. Based on these assumptions and taking into account the mass balance of Au and Ag at the surface, one can derive the following relation for the sputter rate VA~_A~ of the A u - A g system [21]:
4. Results
The main problem of quantitative Auger depth profiling is to convert the temporal variation of the measured Auger intensities to spatial variation of the composition. In the present study a simple linear relation between Auger intensity and concentration was assumed, and the Auger signals were quantified by applying Auger sensitivity factors of Au(66, 69 eV) and Ag(351, 357 eV) Auger lines, measured by means of pure elements [19]. The transformation of time of sputtering into depth was achieved by using a simple kinetic sputter model, developed by Ho et al. [20]. Basically, in the model it is assumed that sputter-induced composition changes affect a surface layer of finite thickness, the so-called altered layer. Within the
v.°( v,,g OA~)CAg
VAu_A~(CAg)=VAu+VA,CAs + (1 -- cag) rAg , -
(4)
where Vnu, vAg and Va~_hg are the sputter rates of pure gold, silver and gold-silver alloy, respectively, and CAg is the atomic concentration of silver in the alloy. The sputter rates of gold and silver, determined by sputter removal of definite thicknesses of pure Au and Ag films, were found to be VAu= 0.12 nm min -1 and vAg = 0.14 nm min - l for argon ions with energy of 1 keV, current density of 1.8 x 10 -2 A m -2 and angle of incidence of 75 °. These values were used for transformation of sputtering time into depth, based on eq. (4).
90 80 ~•*
•
: -'•"o"°"'o'..o•
o~ 70
".
4A
.,•
.o*,*.. ,°
•:
60
":
**~'~%
...':'~t
@
cO
:.
"..
*,,r" %
,~
K
-..
~6 50 L..
.j,
•%
C-
..
x •
C"
x
X
0 0
3O
x • °°
° °.
"...(
~ "
•
•
o" ".
.Z"
".( Z
•. •"""•
x
•
°
20
1%
4'o
I
12o
I
16o
I
depth [nm] Fig. 2. Auger electron depth profile of the multilayer Au-Ag film annealed for 10 h at 200 o C: (X) Au concentration, (@) Ag concentration.
A. Bukaluk, IV. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
60
}
'!!! I2
it) ('.4
0.01 0
1
I
I
2
3
4
5
[
I
6
7
8
9 10 time [104 s]
Fig. 3. Amplitude of the concentration distribution in the multilayer Au-Ag thin films as a function of annealing time: (×) 175 o C, (e) 200 o C, (o) 225 °C and (A) 250 o C.
Fig. 2 presents a typical depth profile of a multilayer A u - A g film annealed for 10 h at 200 o C. From fig. 2 it follows that during annealing the concentration distribution, which is almost rectangular in the as-deposited film, changes into a slightly distorted sinusoidal distribution by interdiffusion. The distortions of the sinusoidal distribution of depth profiles are presumably due to a sputtering effect. The concentrations amplitude l(26"ma x 1) decreases from the initial value of 0.5 in the non-annealed sample to about 0.25 in the annealed one. The other feature to be mentioned is the decrease of the concentration amplitude of the annealed sample with sputtered depth. This indicates a degradation of depth resolution during sputtering. Therefore the amplitude ½(2Cmax - - 1 ) was taken from the first silver layer, where the effect of sputtering artefacts was the least. In fig. 3 the amplitudes ½(2~ma× - 1) of the Auger signal, measured for multilayer A u - A g films after a heat treatment of 175,200, 225 and 250 o C, are plotted logarithmically against the time of annealing t. One can see that the measured amplitudes fit the exponential relation in (3) very well. The slope of the straight lines shown in this figure increases with annealing temperature. This proves -
that at higher temperature higher diffusivities are observed. On the basis of the results presented in fig. 3 the values of the interdiffusion coefficients were calculated to be D = (4.4 + 0.6) × 10 -]8 cm 2 s 1 [°C]
temperature 10-14
325
300
275
250
225
200
175
I
I
I
F
I
f
]
, \
I 2.0
-
10.
\,,
lo-~
\ 10-~8 1.6
,
i 1.8
~ 1000 T
i 2.2
[ K-l]
Fig. 4. Arrhenius plots of interdiffusion coefficients: ( x ) present work, ( o ) the values obtained by using the "centre-gradient" method [7], (O) the values obtained by using the "plateau-rise" method [7,9].
A. Bukaluk, W.. Bata / lnterdiffusion in thin polycrystalline Au-Ag multilayer films
at 175°C, D = (2.5 + 0.3) x 10 -17 cm 2 s -1 at 200° C, D = (1.4 + 0.4) x 10 -16 cm 2 s - I at 2 2 5 ° C and D = (7.0 + 0.5) × 10 -16 cm 2 s -1 and 250°C. These values have been marked by crosses and plotted in the form of an Arrhenius plot in fig. 4. One can see that the data obey an Arrhenius law: D = D O e x p ( - E a / k T ), where D O is the pre-exponential diffusivity term, Ea is the activation energy, k is the Boltzmann constant and T is the temperature. The values of D O= 1.1 × 10 -2 cm 2 s-1 and E a = 1.4 eV have been obtained from the data presented in fig. 4.
5. Discussion The measurements of interdiffusion coefficients in the multilayer A u - A g thin film system were carried out in the temperature range 175-250 ° C. At higher temperatures interdiffusion was so fast that the concentration of diffusing species changed very rapidly even after a very short annealing time. For longer annealing times an almost homogeneous concentration distribution was obtained. Therefore, it was impossible to obtain some experimental points of the ln[l(2gmax- 1)] versus t dependence with satisfactory accuracy and afterwards to calculate the interdiffusion coefficient D. On the other hand, aging at lower temperature did not cause noticeable changes in the concentration distribution inside the A u - A g multilayer structure. In both cases, the effect to be measured was comparable with the experimental error.
61
In the present work the values of interdiffusion coefficients were extracted from the amplitude of the concentration distribution, taken from the uppermost silver layer. The data obtained in such a way obey an Arrhenius equation. Attempts made for determination of D from the amplitudes taken from further layers failed, since the experimental points plotted in the form of ln[½(2gma x --1)] versus t did not form a straight fine. The reason for this fact was the detrimental effect of sputtering, observed particularly for a larger depth. An accurate calibration of the concentration in quantitative AES needs the knowledge of m a n y parameters, the most important of which are the Auger electron escape depth ~, and the backscattering factor r B. If one neglects the influence of both ?~ and r s on the concentration, one obtains underestimated values of the true composition [22]. As a consequence, the values of the concentration amplitude, presented in fig. 3, are also underestimated. The above-mentioned effect influences less the points corresponding to larger concentration amplitude and more the points with smaller values of ½ ( 2 ? m a x -- 1) in the plot of ln[½(2Emax - 1 ) ] versus t dependence~ Therefore, the slope of the ln[½(2Emax - 1)] versus t plot is overestimated. This is turn results in an overestimation of the values of the interdiffusion coefficients. The depth profile shown in fig. 2 exhibits the apparent excess of silver at the surface. The same feature was observed for all profiles. The presence of Ag atoms at the Au surface is probably caused
Table 1 Values of the pre-exponential diffusivity term D O and the activation energy E a in thin film A u - A g couples Ref.
Specimen type
Temperature range
DO (cm 2 s - l )
Ea (eV)
1.2 7.7 1.0 1.9 5.6 3.9 1.1
1.7 ± 0 . 4 1.8 ±0.1 1.55±0.15 1.95±0.05 1.5 ±0.1 1.8 ±0.1 1.4 ±0.1
(°C) [1] [3] [6] [11] [7] a) [7,9] b) Present work
Polycrystalline Single crystal (111) Polycrystalline Single crystal (111) Polycrystalline Polycrystalline Polycrystalfine
a) The "centre-gradient" method. b) The "plateau-rise" method,
199-242 250-350 282-394 200-400 250-325 250-300 175-250
× × × x x
10 2 10-a 10-1 10-1 10-3
x 10 - z
62
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayerfilms
by spreading out of Ag atoms, moving along grain boundaries from the bottom layer, by surface diffusion. Hence the silver spreading across the surface served as a secondary source for diffusion back into the bulk of the film. One can expect that this effect could disturb the depth profile of the uppermost Au layer only. In table 1 the experimental results of the present work in comparison with the results reported elsewhere for the bilayer A u - A g films are listed. In this table the values of the activation energy E a and the pre-exponential diffusivity term D O in the Arrhenius equation are specified. As it can be seen the activation energy is a little smaller than those obtained for single-crystal films [3,11]. Most likely the reason for the lower value of E a is a larger defect density in the multilayer structure. The values of D O and Ea obtained for polycrystalhne layers in refs. [1,7,9] show better conformity with the results presented in this work. The values of the activation energy extracted from the bilayer depth profile data by using the "centre-gradient" method [6,7] are almost equal to the value of E a in the multilayer structure. The value of D O in the present study is comparable with those reported by other authors [1,3,6,7]. Fig. 4 presents the results of the present work in comparison with the results acquired previously by using the same AES spectrometer and the samples prepared in the similar conditions in the same vacuum chamber. One can see that the values of the interdiffusion coefficients obtained for multilayer thin films are about an order of magnitude larger than those extracted previously for bilayer films by using the "centre gradient" [7] and the "plateau-rise" [7,9] methods. The difference between the values obtained for multilayer and bilayer films can be mainly ascribed to differences in the structure of the analysed films, although this difference may be also due to the above-mentioned overestimation of the values of D, caused by the neglect of ~ and r B in calculation of the concentration. The films investigated in the present work had an average grain size of about 100 nm, comparable with those reported in refs. [7,9]. However, the thickness of particular layers of the multilayer structure was 2.5 times smaller than that in refs. [7,9]. Therefore, the films
studied in the present paper contained much more grain boundaries and other defects than the double-layer ones. This influenced the interdiffusion data to a larger extent. The fact that interdiffusion in multilayer films is considerably influenced by the grain boundary diffusion can be noticed in fig. 3. One can see that the straight lines in this figure do not extrapolate to the initial concentration amplitude at t = 0. A possible reason is the presence of a very rapid diffusion process occurring at relatively short annealing times during heating the samples from room temperature to the final temperature. In thin polycrystalline films the grain boundary diffusion is such a fast diffusion mechanism. Therefore, the interdiffusion data obtained in this paper must be treated as averaged values which include both volume and grain boundary effects. Recently R011 has proposed a formalism allowing the extraction of both lattice and grain boundary diffusion parameters from the data obtained in a multilayer thin film structure [17]. In this model it is assumed that the grains are cylindrical cells of radius r0, perpendicular to the film surface, surrounded by prismatic grain boundaries. The material transport in grains and grain boundaries is described by diffusivities D and D', respectively. To extract D and D ' from measured depth profiles of annealed multilayer films, the concentration amplitudes ½(2~max - 1) of the profiles are plotted versus normalized time ~-= D t / r 2. Next it is needed to fit curves obtained for particular values of A = D ' / D - 1 to experimental data. Recently two papers have been published, in which the results of investigations of both grain boundary and volume diffusion in thin C u - N i films, acquired by the method based on a periodical solution of the diffusion equation, have been reported [23,24]. In both studies thin films with very reproducible, small (20 nm) grain sizes, examined by careful and precision transmission electron microscopy (TEM) measurements, have been analysed. For such films Auger depth profile data were evaluated by a numerical analysis and the grain boundary diffusion coefficients were separated from the lattice diffusion coefficients. Attempts made to distinguish the contribution
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag multilayer films
from the lattice and grain boundary interdiffusion failed in the case of the present studies. The data did not fit the curves obtained for the specified values of A with good enough accuracy. In particular parts of the ln[½(2?max - 1)] versus ~- dependence experimental points fitted different curves, corresponding to the values of A differing from one another by an order of magnitude, at least. This caused a large uncertainty in the determination of A, and as a consequence, a large uncertainty in the determination of interdiffusion coefficients. The reason that RtSll's model could not be applied in the present case was most probably large scattering of the values of the grain size of the films (from 50 nm up to 200 nm, as measured by TEM). On the other hand, it is also possible that the grains with small sizes (like in refs. [23,24]) better conformed to the assumption of the model that the grains had a circular cross section. For larger grain sizes (100 nm in the present work) such as assumption may be invalid. The main aim of the present paper was to obtain the values of interdiffusion coefficients in the temperature range lower than the range applied previously for the bilayer samples obtained in similar conditions and analyzed by the same AES spectrometer [7,9]. In this field our investigations succeeded, giving the values of D obeying the Arrhenius law in the temperature range of 175-250°C. However, in order to separate the volume and the grain boundary diffusion coefficients further investigations performed on films with smaller and repeatable grain sizes are needed. It is the purpose of future studies to perform such investigations. 6. Conclusions
The present work has shown that the method based on the analysis of changes of the concentration amplitude of diffusant in the multilayer film with time and temperature of heating, can be used as a very sensitive technique for the measurement of interdiffusion at relatively low temperatures. The method is greatly aided by the availability of Auger electron spectroscopy as a sensitive and quantitative technique for measuring the concentration distribution of the diffusing species.
63
The accuracy of the measurement of the interdiffusion coefficient D is influenced by the experimental method. In the present case the values of D were calculated from the concentration amplitude, taken from the top silver layer, and the influence of the Auger electron escape depth and the backscattering factor on the concentration has been ignored. Therefore, as it was pointed above, the values of D obtained in a multilayer structure are overestimated. On the other hand, multilayer films contained much more structural defects, mainly grain boundaries, in comparison with bilayer films. Both the above-mentioned effects are presumably responsible for the observed larger values of D compared with the values obtained previously for the bilayer films by using the "centre-gradient" and the "plateau-rise" methods [7,9]. The comparison of the values of the activation energy E a and the pre-exponential factor D O obtained in the present study with those acquired elsewhere for the bilayer A u - A g couples indicates that the values presented here are lower than those obtained for single-crystal films [3,11j. The same concerns the values of E a and D O obtained in the interior of the polycrystalline A u - A g couple by using the "plateau-rise" method [7,9]. In both cases defect-enhanced diffusion disturbed the lattice diffusion less than in the multilayer film, because of the lower concentration of defects in the analysed region of the films studied in refs. [3,7,9,11]. In polycrystalline films the values of D O obtained in refs. [1,7] appear generally consistent with the value acquired in the present work. Next the values of E a obtained in refs. [6,7] are almost equal to the value extracted from the Arrhenius plot in this work. Other discrepancies observed in the data obtained in different studies can be mainly ascribed to structural differences between the studied films. One must also add that the method of data acquisition, the state of purity of the materials used and even the composition of the residual atmosphere in the UHV chamber may also cause discrepancies in the results of diffusion measurements in thin films performed in different laboratories. The results reported in this paper are of particular interest, since the measurements were car-
64
A. Bukaluk, W. Bata / Interdiffusion in thin polycrystalline Au-Ag rnultilayer films
ried out at unusually low temperatures. Moreover, the reported results have been obtained for the first time in the multilayer structure. Therefore, the studies reported here can be treated as valid supplement to the studies performed previously in the bilayer A u - A g couples.
Acknowledgement The work was sponsored by CPBP 01.08 research project.
References [1] H.E. Cook and J.E. Hilliard, J. Appl. Phys. 40 (1969) 2191. [2] R.G. Kirsch, J.M. Poate and M. Eibschutz, Appl. Phys. Lett. 29 (1976) 772. [3] F. Sofia and J.L. Saced6n, Thin Solid Films 60 (1979) 113. [4] K. Meinel, M. Klaua and H. Bethge, Thin Solid Films 34 (1976) 157. [5] J.C.M. Hwang, J.D. Pan and R.W. Balluffi, J. Appl. Phys. 50 (1979) 1349. [6] S.K. Sen, P.M. Kluge-Weiss and C.L. Bauer, Thin Solid Films 82 (1981) 299. [7] A. Bukaluk, Surf. Interf. Anal, 5 (1983) 20. [8] A. Bukaluk, M. Rozwadowski and R. Siuda, Appl. Phys. A 34 (1984) 193.
[9] A. Bukaluk, R. Siuda and M. Rozwadowski, Acta Univ. Wratisl. 782 (1984) 37. [10] A. Bukaluk, in: Physics of Solid Surfaces, Vol. 23 of Studies in Surface Science and Catalysis, Ed. J. Koukal (Elsevier, Amsterdam, 1985) p. 170. [11] K. Meinel, M. Klaua, Ch. Ammer and H. Bethge, Phys. Status Solidi (a) 106 (1988) 493. [12] A. Bukaluk, Appl. Surf. Sci. 35 (1988-89) 317. [13] P.M. Hall and J.M. Morabito, Surf. Sci. 54 (1976) 79. [14] J.E.E. Baglin, Metal-metal interdiffusion, in: thin Films Interdiffusion and Reactions, Eds. J.M. Poate, K.N. Tu and J.W. Mayer (Wiley, New York, 1978) p. 305. [15] W. Pamler, Appl. Phys. A 42 (1987) 219. [16] K. R~511and W. Reill, Thin Solid Films 89 (1982) 221. [17] K. Ri311, Habilitation Thesis, Universit~it Regensburg (1981). [18] P.M. Hall, J.M. Morabito and J.M. Poate, Thin Solid Films 33 (1976) 107. [19] P.W. Palmberg, Anal. Chem. 45 (1973) 549. [20] P.S. Ho, J.E. Lewis and J.K. Howard, J. Vac. Sci. Technol. 14 (1977) 322. [21] K. Meinel, M. Klaua and H. Bethge, Phys. Status Solidi (a) 106 (1988) 133. [22] S. Hofmann and J.M. Sanz, in: Thin Film and Depth Profile Analysis, Ed. H. Oechsner (Springer, Berlin, 1984) p. 143. [23] R. Venos and K. R011, Beitr. Elektronenmikroskop. Direktabb. Oberfl. 21 (1988) 347. [24] R. Venos, W. Pamler and H. Hoffmann, Thin Solid Films 162 (1988) 155.