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Grazing incidence Mössbauer spectroscopy: a new method for surface layer analysis Part III. Interpretation of experimental data
2225 __
Nuclear Instruments and Methods in Physics Research B 103 (I 995) 35 I-358 NOHI
__
B
Beam Interactions with Materials&Atoms
@ ELSEVIER
Grazing incidence Mijssbauer spectroscopy: a new method for surface layer analysis Part III. Interpretation of experimental data
*,
Sobir M. Irkaev a, Marina A. Andreeva b, Valentin G. Semenov Genadii N. Belozerskii ‘, Oleg V. Grishin ’
‘,
a InstituteforAnalyiicai instrumentation. Russian Academy ofSciences, 198103. St.Petersburg, Russian Federation b Department of Physics, Moscow State Uniuersity, 117234, Moscow, Russian Federation ’ Department of Geography, St. Petersburg State University, 199164, St. Petersburg, Russian Federation
Received 21 December 1993; revised form received 28 April 1995 Abstract Quantitative
analysis of two sets of experimental GIMS data is presented. A computation procedure, which allows us to determine the distribution versus depth separately for each kind of hyperfine interaction in “Fe film for different states of oxidation is described. The result of our analysis shows that grazing incidence Mossbauer spectroscopy is really a new technique for surface investigation.
1. Introduction
Grazing Incidence MSssbauer Spectroscopy (GIMS) is a new method for investigation of chemical and magnetic states of Mossbauer atoms in ultrathin layers near the surface. The depth selectivity of this technique is based on the abrupt decrease of the penetration depth of MSssbauer radiation into a solid sample at angles where total external reflection (TER) takes place. In part 1 [I] we have discussed aspects concerning the Mlissbauer TER effect and presented a description of our experimental set-up for simultaneous observation of four types of Miissbauer spectra at TER conditions: y-radiation specularly reflected by the sample (RGM spectra); secondary electrons (conversion, Auger and photo-electrons), created during absorption of Mtissbauer radiation (CEM spectra); characteristic X-rays (CXM spectra) and resonantly scattered y-radiation (SGM spectra). Qualitative illustration of the interference nature of the TER effect and surface sensitivity of the GIMS method has been done using GIM spectra of a slightly oxidized “Fe film. In part II [z] we gave the general theory of the Miissbauer TER effect and secondary particle creation at TER conditions for the case of anisotropic multilayered resonant films. We have shown that the well known standard computation technique for the fitting of Miissbauer ’ Corresponding author. Tel +7 812 2519055, fax +7 812 2517038, e-mail irkaev@ lanin.spb.su.
spectra is not applicable in our case. A substantial complication of the interpretation of GIM spectra arises from the different interference effects which distort the shapes of separate lines and leads to nonadditivity of different contributions to the whole spectrum. Therefore the interpretation of GIMS spectra may be done only by means of numerical simulation. Now in part III we present an example of quantitative analysis of experimental spectra which were obtained for nonoxidized and slightly oxidized 57Fe films on beryllium substrates. We describe the computation procedure for determination of the depth profiles of the different spectral components from such spectra. The GIMS technique is based on two physical effects: resonant absorption (or scattering) and specular reflection of Miissbauer radiation. So GIM spectra depend on a lot of new parameters which are not significant in conventional Mijssbauer spectroscopy. Besides the values of resonant energies, relative intensities and widths of separate resonant lines we must take into account some additional parameters of the resonant medium such as the electronic and nuclear susceptibilities of the medium and their variations versus depth, and the distribution with depth of nuclei corresponding to different spectral components, the relative contribution of nonresonant photoelectrons to the CEM spectrum and escape functions of secondary electrons. But for just these reasons GIMS experiments can yield information which could not be obtained by conventional Miissbauer spectroscopy. The increase of the num-
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00645-1
SM.
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Irkaev et al. / Nucl. Instr. and Meth. in Phys. Res. 3 103 119951351-358
1.0
ber of parameters which should be determined is compensated to some extent by the possibility to measure a whole series of RGM, CEM, CXM and SCM spectra for one and the same sample by means of variation of glancing angle in the TER region. -1 L Ill
2. Experiment
The sample was a thin Fe layer (- 50 nm). enriched in “Fe by up to 90%. which was sputtered onto a beryllium substrate. A beryllium substrate was chosen to decrease the yield of photoelectrons from the substrate. The substrate has the form of a disk with diameter 50 mm and thickness 10 mm. In our experiments the surface of the sample should be of good quality, therefore the surface of the substrate had been grinded and then thoroughly polished. We investigated this sample at the different stages of oxidation. These stages of oxidation were produced by means of treatment at different temperatures: initial sample; heating in air at 150°C during 4 hours; heating at 270°C during 4 hours and heating at 450°C during 10 min. Such modification of the investigated sample leads to formation of a number of oxide phases at different depths. Below we present in detail only the results of analysis for two samples: initial sample (sample I) and after heating at 150°C (sample II). The full results of investigation of the various stages of oxidation will be done elsewhere. For checking of the surface quality and for determination of the critical angle of the substrate and the film we measured the reflection curve using MO K, radiation. For sample 1 this curve is shown in Fig. 1. A reflection curve gives additional information concerning the electronic susceptibilities in the film and the variation versus depth. We INITIAL
GLANCING
multilayered
MO Kd
ANGLE (mrad)
film with lower density near the surface (see Fig. 3).
take into account this information during interpretation of our GIM spectra. For each sample we measured the conventional CEM spectrum at 0 = 90”. These spectra may be fitted in the usual way and give us the hyperfine field parameters which characterize our resonant films. Although sample II was obtained from sample I by only very moderate treatment its surface layer acquired a considerable change. We see it from CEM spectra at grazing angle 8= 2.2 mrad (Fig. 2, bottom). Comparison of the top and bottom spectra of Fig. 2 clearly shows that the GIMS technique is more sensitive to the changes of chemical and magnetic states of ultrathin surface layers than the conventional CEMS. OXIDE SAMPLE .
4.4 +
H l-l UY z 2.4 w H z H 1.0 1.4 w P w H 1.2 4 &I w G 1.0
\
Fig. I. MO K, radiation specular reflection curves from sample I (points - experiment, lines - theory). The dotted line is calculated for the model of a homogeneous 57Fe film whith thickness - 50 nm, the solid line is the result of fitting which uses the model of a
SAMPLE
+I 3.8
\
I
a
2.7--
8
I
1,1111,1111,)111111”1” -10.0
-5.0
RELATIVE Fig. 2. Experimental
0
VELOCITY
= 2.2 mrad
8
1
+5.0
+lO.O (m&s)
IIII(IIII,II
II,IIII(bfiII
-10.0 RELATIVE
= 2.2 mrad
-5.0
0
60
VELOCITY
+lO.O (mm/s)
CEM spectra for sample I and sample II for normal incidence f3= 90” and grazing angle 0 = 2.2 mrad.
S.M. Irkmv e! al. / Nucl. Instr. and Merh. in Phys. Res. B 103 (I 995) 351-358
For detailed analysis of the film structure we have measured a set of RGM and CEM spectra at various glancing angles. This set for sample II was presented in part I of this work (Fig. 6). The results for sample 1 we will discuss below. When we vary the glancing angle the most pronounced change in the RGM and CEM spectra consists in an alteration of the weights of the different contributions to the whole spectrum. That gives the best illustration of depth selectivity of GIMS method and has only one reasonable explanation: the films are not homogeneous over depth. Detailed information about the depth profile of the different hyperfine interactions we may get only after quantitative analysis of the GIM spectra.
3. Discussion
of the computation
procedures
and results
As we have shown before, a direct fitting of GIM spectra is impossible and for their interpretation we should use computer simulations. Such a procedure is very cumbersome and complex because the number of variable parameters is very large. So it would be of significant value to find some of these parameters before the computations. The first very useful step is the determination of the multiplet parameters of the different phases by fitting of the 90” CEM spectrum. But for the determination of some of these parameters it turns out to be essential to include additional information gained from the GIM spectra. Resonant parameters of all multiplets taken into consideration for both samples are presented in Table 1. These data require some discussion. The existence of a-Fe in our film is not questionable. The parameters of this sextet from the 90” CEM spectra correspond well to published data [3]. The doublet and the asymmetric broad lined sextets (sextet II), which we clearly seen on both spectra measured at 2.2 mrad (Fig. 2) are caused by ferric (i.e. oxidized) iron
Table I Miissbauer
parameters
of the samples
Phases
Sample I
sextet I (a-Fe)
sextet II sextet III doublet Sample II
sextet I (a-Fe)
sextet II sextet 111 doublet
% +0.8
AEd gl,Sl(mm/s) * 0.04
*0.06
[kOeI *5
76 15 7 2
0.00 0.41 -0.12 0.39
-0.2 0.1 1.2
330 364 318 -
-0.14 0.0 1.03
331 364 320 -
70 16 10 4
0.01 0.54 0.00 0.3 1
’ IS values are given relative to a-Fe at room temperature.
Hen
353
in a paramagnetic and magnetically ordered state, respectively. The area of the doublet in 90” CEM spectrum for sample I is very small (ca. 2%) and for sample II 4%. But the necessity of taking this contribution into account became more clear when we considered GIM spectra where this contribution is much more prominent and clearly seen. From Table 1 we also see that the parameters of the doublet in sample 1 and sample II differ slightly. This difference is probably caused by a change of relative weights of paramagnetic components. The hyperfine parameters of doublet and sextet II correspond to the literature data of the P-FeOOH and c+FeOOH [4-71, but the present data does not allow an unambiguous identification. Further specification of different multiplet parameters was done by comparison of a set of computed and experimental spectra at different grazing angles. By this way it became clear that in order to improve the agreement between theory and experiment we should take into account the existence of some distribution of the hyperfine magnetic field in the a-Fe component. For simplicity we simulated this distribution by adding a broadened sextet (sextet III) with a slightly smaller magnetic splitting than in a-Fe. Its contribution to the 90” CEM spectra is small (_ 7% for sample I and u 10% for sample II). Some disagreement of the parameters for this sextet in &he two investigated samples we can explain by difficulties in their exact determination due to very large linewidths (u l-2 mm/s). We think that parameters determined for sample II are better because the share of this component in the whole spectrum is greater. This component is more clearly seen in spectra at grazing angles. The difference of relative intensities of the lines in the cw-Fe sextet for the 90” CEM spectrum and the GIM spectra suggests the existence of magnetic texture in the surface plane of the film. So when we calculate the polarization dependence of the scattering processes at grazing angles we have a possibility to restrict our consideration to two independent polarization states of incident radiation and use the theory of TER in scalar form. It is clear also that the relative intensities of the sextet lines in the GIM spectra for T-polarization are the same as for the 90” CEM spectra so we should find only relative intensities of sextet lines for u-polarization of radiation by means of numerical simulation of the GIM spectra. The ratio of intensities of sextet lines for r-polarization we determined as I, : I, : I, = 2.45 : 3.37: 1.OO from the 90” CEM spectrum and for interpretation of the GIMS spectra we had use for o-polarization the ratio of intensities 2.45 : 0.34: 1.00. Some magnetic texture we find also for the other two sextets. Another group of independently determined parameters concerns the TER effect itself. They are the electronic susceptibilities of our films. Theoretical values of electronic susceptibilities and critical angles 0, = (Rex,,)“’ of
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S.M. Irkaev et al. / Nucl. Insrr. and Merh. in Phys. Rex B 103 (1995) 351-358
pure (-Y-Feand beryllium substrate for 14.4 keV radiation
are as follows: xc? = (- 14.633 + 0.691 i) X 10m6,
0, = 3.83 X 10e3;
,$‘! = (-3.261
0, = 1.81 x 10-j.
+ 0.001 i) X 10m6,
(1) For nonresonant MO K, radiation, which we used for measuring of the reflection curves, these values can be approximately re-calculated by means of the relation x,/x2 _ (A,/&>* which gives: x;E: = (-9.97
+ 0.47 i) X 10W6,
0, = 3.16 X 10-3;
x;;‘, = (-2.22
+ 0.001 i) X 10e6,
0, = 1.49 X 10e3, (2)
where A, and A, are the wavelength of Miissbauer and MO K, radiations. Comparison of theoretical reflection curves calculated for the susceptibilities of a homogeneous film and substrate with experimental ones reveal a very poor agreement (see Fig. 1, dotted line). The difference could be explained if we take into account that real films have a lower density near the surface due to the partial oxidation, adsorption of C, N and other atoms and existence of some roughness of the surface. Much better agreement can be achieved when we use the model of multilayer films with a different density of each layer. Such a model approximates the real continuous variations of density versus depth. Parameters of electronic susceptibilities of the layers obtained by fitting of the reflection curves are given in Fig. 3. It should be noted that a complete analysis with respect to the parameters of electronic susceptibilities involves simultaneous analysis of RGM spectra near the critical angle at 0 = 3.5 mrad and 0 = 4.2 mrad taking in mind the recalculation coefficients for the two wavelengths. RGM spectra are very sensitive to the electronic and nuclear densities of
1.0
density of electrons
1 I
nonresonant absorption ..._._..._..m..... “.-.__.I.-.--. 20
30
40
O!&
-10
-5
RELATIVE
0
5
VELOCITY
10
5
(mm/s)
Fig. 4. Experimental RGM spectrum of sample I for glancing angle 0 = 3.5 mrad (points) and theoretical RGM spectra calculated for two simple models: the homogeneous a-Fe film (curve I) and the multilayered film in which each layer is characterized by only one hyperfine interaction in the following sequences (from the surface): doublet, sextet II, sextet III and sextet I (a-Fe). Parameters of different multiplets are given in Table 1. Thicknesses of layers are chosen proportional to the areas of corresponding multiplets in the 0 = 90” CEM spectrum.
the sample near the surface and may be used for determination of the electronic density as well as a reflection curve. At the beginning of numerical simulation of GIM spectra we considered two simple models: a homogeneous Fe film with the same set of spectral components at each depth (Fig. 4, curve 1) and a multilayer model, in which only one kind of hyperfine interaction exists in each layer and the thicknesses of the layers are proportional to the relative areas of the different multiplets in the 90” CEM spectrum (Fig. 4, curve 2). We see that both these simple models do not agree with experiment. As a potentially better model we allow any possible mixture of different kinds of hyperfine interactions in each layer, which with a sufficient number of layers is almost equivalent to a continuous distribution of hyperfine fields versus depth. For this purpose we introduce a matrix of hypertine field distribution V,,,, which describes the relative densities of nuclei embodied a k-kind of hyperfine interaction in layer n. So we characterize the susceptibilities of the separate layers in the film by means of the expression: A;., ck/2
50
DEPlH (nm)
Fig. 3. Depth profile of the electronic parameters of layers: Re xel (the density of electrons) and Im xe, (absorption by electrons) giving the best agreement between theory and experiment for X-ray reflection curve (solid line in Fig. 1) and shapes of experimental GIM spectra (Fig. 5). Dependences are normalized with respect to Re xe, in a-Fe.
X,=xel.,+FCLC k
i E-Eik+i&/2’
(3)
where xe,,” describes the interaction of the radiation with electrons, i numerates the lines in multiplet k; Al,, rjl, and Eik are the amplitudes, the widths and the energies of the separate resonant lines. The values A:,, 6; differ from Aik, 4, that were obtained by fitting the 90” CEM spectrum due to convolution with source line having width
355
S.M. irkaev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (199s) Ml-358 where P,
is the total density of resonant nuclei in the layer n in units of that in a-Fe, then we get the following value of the factor F from which the absolute values of the nuclear part of susceptibility in Eq. (3) depends
r,. Using the approximation of a thin absorber we have the following relations for these values: rile A;, = ----Ai,. rik - r,
r,; = r;, - 4;
(4)
F = 8.35 X lO-6 mm/s.
If we normalize the values A:, for each multiplet in the following way c A;k r;,/2
= 1
For the calculation sion:
(7)
of Eq. (7) we use the general expres-
(9
(8)
F=
and use the following normalization of the matrix V: y,, + V”, + . . •c V”, = P”.
where fr,,, is the probability of the Miissbauer effect, Q is
(6)
YIELD OF ELECTRONS
REFLECTION 1.41
t t; Z w l-
‘PuoloEtEcTRctis 0.8 1.41
0.6~ 1.23Smtnd
1.0.
Z -
0.6.
w
0.6.
> ;
I 0.4J
'a ;
’
0.81
PHurclELEolRoNs
2.5 mw
1.0.
CC 0.8.
0.6.
o-4l6 4
_10
-5
0
5
RELATIVE
10
15 I
--115
VELOCITY
-10
-5
0
5
10
15
(mm/s)
Fig. 5. Series of experimental (points) and theoretical (solid lines) GIM spectra for sample I: RGM spectrum on the left and CEM spectra on the right. Theoretical spectra represent the result of fitting using the model of multilayered film with mixed hypertine interaction in each layer. The calculated contribution of photoelectrons to MSssbauer electron spectra is represented by dotted lines.
SM. I&rev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (I 995) 351-358
356 1.0
INITIAL SAMPLE
OXIDE SAMPLE
-
IIEP’I’H(nm)
I)EP’l’H (nm)
Fig. 6. Depth profiles of the density of nuclei embodied definite kind of hyperfme interaction (marked in insert) in units of that for a-Fe5’ for the sample I (left) and II (right). Note that according to Eq. (9) the area under each step function is proportional to the percentages of the phase content in Table I and determines its contribution to the 90” CEM spectrum.
the enrichment of the film by resonant isotope, r,,, is the natural linewidth, (Y is the internal conversion coefficient, I,_, are the spins of exited and ground states of the Mossbauer nucleus. For our iron film we put fM = 0.7, Q = 0.9, N = 8.47 nme3, A = 0.086 nm. During numerical simulation of the theoretical spectrum by variations of the elements of matrix V,, we should keep constant the ratio of total number of nuclei having a given resonant interaction. In the opposite case we would change the shape of the theoretical 90” CEM spectra. This condition takes the following form: zV,,,d,: n
zV,,d,: n
x&d,: n
...
=S,:S,:S,:
.... (9
where S, is the relative area of the partial spectrum corresponding to k-kind of hyperfine splitting in the 90“ CEM spectrum. Such a model allows to include in the fitting procedure the variation of the electronic density and the density of nuclei having different hyperfme interactions versus depth By this fitting we have achieved a much better agreement between the theory and the experiment (Fig. 5). Obtained step-functions X+ and V,,, are shown in Figs. 3 and 6. A great number of parameters which should be matched by optimization procedure for the series of spectra raises some mathematical problems such as the uniqueness and physical credibility of the results. These problems certainly need further development. In our work we only demonstrate that such a treatment is possible and variations of the shape of GIM spectra versus angle can be. reasonably good described. Some remarks should be made about the numerical simulation. First we examined RGM spectra depending mainly on electronic and nuclear densities. We began from
RGM spectra for the lowest angles which depend only upon parameters of top layers, then move gradually into the bulk, including into consideration spectra, obtained at larger angles, and parameters of deeper layers. The most complex thing in this simulation is the necessity to obtain a good agreement for all spectra in the sets simultaneously. After we get a reasonably good fitting for the RGM series we include into the analysis also the series of CEM spectra. Simultaneously we began to simulate some additional parameters, which influence only CEM spectra at grazing angles. Such parameters are those which determine the escape functions for conversion and photoelectrons and relative photoelectron yield. The photoelectron yield abruptly changes the shape of the spectra as we.see from Fig. 5 (right) where the photoelectron contribution to the theoretical CEM spectra is shown. We see also that this contribution is drastically different for different grazing angles and this leads to a change of background asymmetry for the angles lower and larger than the critical one [8]. We have explained the reasons for such energy dependence of the yield of photoelectrons in part II 121. We use for the escape function T(z) an analytical expression from Ref. [9] where we can vary the mean electron path r,.,, the part of photoelectron yield P, and relative conversion electrons yield (for a single photoelectron or nuclear resonant absorption event ‘). We get reasonably good agreement between theoretical CEM spectra and experimental ones when we put rB = 700 nm, and Pa = 0.7. We think also that the general expression for the escape
’ In Ref. [lo] we use a more general model for the analysis of yield funtions itself.
S.M. Irkaev
et al. / Nucl. Instr.and Meth. in Phys. Rex B IO3 (I 995) 351-358
function T(z), which was calculated in Ref. [9] for the ideal case of a homogeneous medium, should be re-examined for our inhomogeneously layered structure with mixed phases and such re-examination is possible empirically on the basis of our experiment. At least we do not know any other experimental methods which allow to compare the photoelectrons and conversion electron yield in real systems. The detailed discussion of these problems was presented in Ref. [lo]. During our simulation of the sets of GIM spectra we adjust the hyperfine field parameters, such as IS, A E. and H,, especially for those subspectra that are more pronounced seen at grazing angles. The criteria of the quality of fitting of GIM spectra does not exist yet but the experience in theoretical treating of GIM spectra reveals that our estimations are rather sensitive (- 5%) to the relative and absolute amount of resonant nuclei at the very top layer (up to 5 nm) because top layers give a large contribution to spectra for all glancing angles of incidence but especially for the smallest ones. Such evaluation of accuracy follows from many independent attempts to fit such spectra beginning from different initial conditions. Accuracy of results drops down very strong with increasing depth and for depths above 20 nm we cannot guarantee an accuracy more than 20-30%. We have however very serious problems with determinations of the exact value of hyperfine parameters which are not known for interface regions. This circumstance inserts an additional ambiguity to our consideration. Our analysis has resulted in step distribution functions for all hypertine interactions as a function of depth in both sample I and II. These are shown in Fig. 6. We see from Fig. 6 that most of the oxide iron atoms are concentrated at the surface layer of the films. The modification of the surface which increases from sample I to sample II due to the heat treatment leads to the appearance of oxidized iron in paramagnetic states as in the case of ultrafine particles. But the a-Fe phase is present at the top layer also. This could indicate the existence of island structures on the surface. We should underline that this result is not connected with restrictions of surface sensitivity of the method. It is easily to recalculate the theoretical spectra removing this a-Fe contribution from the most top layer (2 nml: the shapes of spectra will alter drastically. The sensitivity of spectra to transfening of the nuclei in the nonmagnetic state (giving doublet contribution into resonant spectrum) over depth is not so strong because the total amount of such kind of nuclei is rather small. But we noticed something unexpected. We cannot put (without sufficient distortion between the theoretical spectra and experimental ones) all amount of this kind of nuclei to the top layer (in sample I its density in the most top layer is 0.002 and is hardly seen on Fig. 6). So we can assume that either the rest amount of this phase dilutes over the whole film with very small density or it is concentrated at the
357
other side of film in interface region with substrate. The latter conclusion was confirmed also in paper [ 111 but our film is rather thick and we cannot “see” the interface region by our method. We also see that the different phases are not localized in any definite layer. It indicates that oxides appear as patches that penetrate down to the bottom boundary of the film. The destruction of the film due to the oxidation process concerns not only the most top layer but partially refers to the deeper layers: the “bulk” layer where a-Fe predominantly exist contains some amount (it is more noticeable for sample II) of nuclei having other hyperfine parameters than that in a-Fe. If we assume that sextet 111 describing hyperfine magnetic splitting in defected o-Fe can appear in interface regions between pure a-Fe grains and oxidized phases then transformation of its depth distribution due to the oxidation process is rather clear. For sample I their distribution has a relative sharp maximum before the a-Fe layer, in sample II this distribution function is broadened, moves deeper and overlaps partially with the a-Fe distribution function. The sum of nuclear densities presented in Fig. 6 is not equal to 1 even in the “bulk” of the film and for sample II it is smaller than that for sample I. But it is an averaged density over the given layer where not only a-Fe grains exist but also the oxidized phases (as we see in Fig. 6 at any depth) where Fe-atoms are diluted by oxygen atoms. Besides that it is clear that the total mean nuclear density should decrease due to distortion of the crystalline structure, vacancies in grain boundaries and other defects. Notice that obtained electronic density (Fig. 3) is not also equal to the electronic density of pure a-Fe at any depth. Note also that although the total amount of a-Fe atoms in the different phases differs slightly for samples I and II (see Table 1 and Fig. 2), their distribution versus depth in both samples changes drastically. From distributions of the hyperfine fields versus depth in two samples which were obtained from fitting of GIM spectra we can explicitly see how different oxide phases develop further into the sample during oxidation processes.
4. Conclusion The article is the third and final part of three papers that are devoted to the development of a new method for ultrathin surface layer analysis: Grazing Incidence Miissbauer Spectroscopy (GIMS). We presented consecutively our setup for realization of a GIMS experiments [l], the general theory of coherent processes arising at TER conditions, which give the basis for interpretation of experimental data [2] and in this last part we have realized for the first time the quantitative analysis of a series of RGM and CEM spectra. We have shown that fitting of GIM spectra with respect to the depth distribution functions of electronic and hyper-
358
S.M. Irkaev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (1995) 351-358
fine parameters is possible, but for such analysis it is necessary to deal simultaneously with the whole series of RGM and CEM spectra at different grazing angles and the X-ray reflection curve. Maybe it will be worthwhile for removal of some ambiguity of our results to use also an ellipsometry method and diffraction of slow electrons. As a result of the present investigation, however, we have obtained very detailed information about the investigated films with respect to distribution versus depth for each kind of hyperfine interaction existing in the 57Fe film before oxidation (as prepared) and after some oxidation processes. In this way we observe the advancement of different oxide phases into the bulk of the film during this process. Our analysis demonstrates the possibility of depth selective investigations (on the scale 2-50 nm) of ultrathin films by means of the GIMS technique. Treatment of GIM spectra is not a simple procedure and a reliable analysis will need further improvements and development on the basis of modem computer power and recent achievements of mathematics. But now it is clear that “the game is worth the candle”, because it gives unique information that could not have been obtained by conventional Mijssbauer spectroscopy.
Acknowledgements The authors would like to thank D. Liljequist helpful discussions of some aspects of this trilogy.
for
We are also pleased to acknowledge the Joint-Stock Company “DEKA” and JV “VA Instruments” for financial supports of this work (Grant No. 94/52-05CM).
References [I] SM. Irkaev, M.A. Andreeva. V.G. Semenov, G.N. Belozerskii and O.V. Gtishin, Nucl. Instr. and Meth. B 74 (1993) 545. [2] SM. Irkaev, M.A. Andreeva, V.G. Semenov, G.N. Belozerskii and O.V. Grishin, Nucl. Instr. and Meth. B 74 (1993) 554. [3] W.R. Dunham, C.T. Wu, R.M. Polichar, R.N. Sands and L.J. Harding, Nucl. Instr. and Meth. 145 (1977) 537. [4] P. Ayyub. M. Multani, M. Barrna, V.R. PaIkar and R. Vijayaraghavan, J. Phys. 21 (1988) 2229. [5] W. Meisel, Kern. Kozlem 48 (1977) 41. [6] L.H. Bowen, MSssbauer Effect Reference and Data J. 2 (1979) 76. [7] M. Stratmann and K. Hoffmann, Corrosion Sci. 29 (1989) 1329. [8] M.A. Andreeva, G.N. Belozerskii, O.V. Grishin, S.M. Irkaev. V.I. Nikolaev and V.G. Semenov, Sov. Phys. JETP Lett. 55 (1992) 62. [9] D. Liljequist, T. Ekdahl and U. Baverstam, Nucl. Instr. and Meth. 155 (1978) 529. [lo] M.A. Andreeva, S.M. Irkaev and V.G. Semenov, Zh. Eksp. Teor. Fiz. 105 (1994) 1767. [I I] S.A. Isaenko, AI. Chumakov and S.I. Shinkarev, Phys. Lett. A 186 (1994) 274.
Nuclear Instruments and Methods in Physics Research B 103 (I 995) 35 I-358 NOHI
__
B
Beam Interactions with Materials&Atoms
@ ELSEVIER
Grazing incidence Mijssbauer spectroscopy: a new method for surface layer analysis Part III. Interpretation of experimental data
*,
Sobir M. Irkaev a, Marina A. Andreeva b, Valentin G. Semenov Genadii N. Belozerskii ‘, Oleg V. Grishin ’
‘,
a InstituteforAnalyiicai instrumentation. Russian Academy ofSciences, 198103. St.Petersburg, Russian Federation b Department of Physics, Moscow State Uniuersity, 117234, Moscow, Russian Federation ’ Department of Geography, St. Petersburg State University, 199164, St. Petersburg, Russian Federation
Received 21 December 1993; revised form received 28 April 1995 Abstract Quantitative
analysis of two sets of experimental GIMS data is presented. A computation procedure, which allows us to determine the distribution versus depth separately for each kind of hyperfine interaction in “Fe film for different states of oxidation is described. The result of our analysis shows that grazing incidence Mossbauer spectroscopy is really a new technique for surface investigation.
1. Introduction
Grazing Incidence MSssbauer Spectroscopy (GIMS) is a new method for investigation of chemical and magnetic states of Mossbauer atoms in ultrathin layers near the surface. The depth selectivity of this technique is based on the abrupt decrease of the penetration depth of MSssbauer radiation into a solid sample at angles where total external reflection (TER) takes place. In part 1 [I] we have discussed aspects concerning the Mlissbauer TER effect and presented a description of our experimental set-up for simultaneous observation of four types of Miissbauer spectra at TER conditions: y-radiation specularly reflected by the sample (RGM spectra); secondary electrons (conversion, Auger and photo-electrons), created during absorption of Mtissbauer radiation (CEM spectra); characteristic X-rays (CXM spectra) and resonantly scattered y-radiation (SGM spectra). Qualitative illustration of the interference nature of the TER effect and surface sensitivity of the GIMS method has been done using GIM spectra of a slightly oxidized “Fe film. In part II [z] we gave the general theory of the Miissbauer TER effect and secondary particle creation at TER conditions for the case of anisotropic multilayered resonant films. We have shown that the well known standard computation technique for the fitting of Miissbauer ’ Corresponding author. Tel +7 812 2519055, fax +7 812 2517038, e-mail irkaev@ lanin.spb.su.
spectra is not applicable in our case. A substantial complication of the interpretation of GIM spectra arises from the different interference effects which distort the shapes of separate lines and leads to nonadditivity of different contributions to the whole spectrum. Therefore the interpretation of GIMS spectra may be done only by means of numerical simulation. Now in part III we present an example of quantitative analysis of experimental spectra which were obtained for nonoxidized and slightly oxidized 57Fe films on beryllium substrates. We describe the computation procedure for determination of the depth profiles of the different spectral components from such spectra. The GIMS technique is based on two physical effects: resonant absorption (or scattering) and specular reflection of Miissbauer radiation. So GIM spectra depend on a lot of new parameters which are not significant in conventional Mijssbauer spectroscopy. Besides the values of resonant energies, relative intensities and widths of separate resonant lines we must take into account some additional parameters of the resonant medium such as the electronic and nuclear susceptibilities of the medium and their variations versus depth, and the distribution with depth of nuclei corresponding to different spectral components, the relative contribution of nonresonant photoelectrons to the CEM spectrum and escape functions of secondary electrons. But for just these reasons GIMS experiments can yield information which could not be obtained by conventional Miissbauer spectroscopy. The increase of the num-
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00645-1
SM.
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Irkaev et al. / Nucl. Instr. and Meth. in Phys. Res. 3 103 119951351-358
1.0
ber of parameters which should be determined is compensated to some extent by the possibility to measure a whole series of RGM, CEM, CXM and SCM spectra for one and the same sample by means of variation of glancing angle in the TER region. -1 L Ill
2. Experiment
The sample was a thin Fe layer (- 50 nm). enriched in “Fe by up to 90%. which was sputtered onto a beryllium substrate. A beryllium substrate was chosen to decrease the yield of photoelectrons from the substrate. The substrate has the form of a disk with diameter 50 mm and thickness 10 mm. In our experiments the surface of the sample should be of good quality, therefore the surface of the substrate had been grinded and then thoroughly polished. We investigated this sample at the different stages of oxidation. These stages of oxidation were produced by means of treatment at different temperatures: initial sample; heating in air at 150°C during 4 hours; heating at 270°C during 4 hours and heating at 450°C during 10 min. Such modification of the investigated sample leads to formation of a number of oxide phases at different depths. Below we present in detail only the results of analysis for two samples: initial sample (sample I) and after heating at 150°C (sample II). The full results of investigation of the various stages of oxidation will be done elsewhere. For checking of the surface quality and for determination of the critical angle of the substrate and the film we measured the reflection curve using MO K, radiation. For sample 1 this curve is shown in Fig. 1. A reflection curve gives additional information concerning the electronic susceptibilities in the film and the variation versus depth. We INITIAL
GLANCING
multilayered
MO Kd
ANGLE (mrad)
film with lower density near the surface (see Fig. 3).
take into account this information during interpretation of our GIM spectra. For each sample we measured the conventional CEM spectrum at 0 = 90”. These spectra may be fitted in the usual way and give us the hyperfine field parameters which characterize our resonant films. Although sample II was obtained from sample I by only very moderate treatment its surface layer acquired a considerable change. We see it from CEM spectra at grazing angle 8= 2.2 mrad (Fig. 2, bottom). Comparison of the top and bottom spectra of Fig. 2 clearly shows that the GIMS technique is more sensitive to the changes of chemical and magnetic states of ultrathin surface layers than the conventional CEMS. OXIDE SAMPLE .
4.4 +
H l-l UY z 2.4 w H z H 1.0 1.4 w P w H 1.2 4 &I w G 1.0
\
Fig. I. MO K, radiation specular reflection curves from sample I (points - experiment, lines - theory). The dotted line is calculated for the model of a homogeneous 57Fe film whith thickness - 50 nm, the solid line is the result of fitting which uses the model of a
SAMPLE
+I 3.8
\
I
a
2.7--
8
I
1,1111,1111,)111111”1” -10.0
-5.0
RELATIVE Fig. 2. Experimental
0
VELOCITY
= 2.2 mrad
8
1
+5.0
+lO.O (m&s)
IIII(IIII,II
II,IIII(bfiII
-10.0 RELATIVE
= 2.2 mrad
-5.0
0
60
VELOCITY
+lO.O (mm/s)
CEM spectra for sample I and sample II for normal incidence f3= 90” and grazing angle 0 = 2.2 mrad.
S.M. Irkmv e! al. / Nucl. Instr. and Merh. in Phys. Res. B 103 (I 995) 351-358
For detailed analysis of the film structure we have measured a set of RGM and CEM spectra at various glancing angles. This set for sample II was presented in part I of this work (Fig. 6). The results for sample 1 we will discuss below. When we vary the glancing angle the most pronounced change in the RGM and CEM spectra consists in an alteration of the weights of the different contributions to the whole spectrum. That gives the best illustration of depth selectivity of GIMS method and has only one reasonable explanation: the films are not homogeneous over depth. Detailed information about the depth profile of the different hyperfine interactions we may get only after quantitative analysis of the GIM spectra.
3. Discussion
of the computation
procedures
and results
As we have shown before, a direct fitting of GIM spectra is impossible and for their interpretation we should use computer simulations. Such a procedure is very cumbersome and complex because the number of variable parameters is very large. So it would be of significant value to find some of these parameters before the computations. The first very useful step is the determination of the multiplet parameters of the different phases by fitting of the 90” CEM spectrum. But for the determination of some of these parameters it turns out to be essential to include additional information gained from the GIM spectra. Resonant parameters of all multiplets taken into consideration for both samples are presented in Table 1. These data require some discussion. The existence of a-Fe in our film is not questionable. The parameters of this sextet from the 90” CEM spectra correspond well to published data [3]. The doublet and the asymmetric broad lined sextets (sextet II), which we clearly seen on both spectra measured at 2.2 mrad (Fig. 2) are caused by ferric (i.e. oxidized) iron
Table I Miissbauer
parameters
of the samples
Phases
Sample I
sextet I (a-Fe)
sextet II sextet III doublet Sample II
sextet I (a-Fe)
sextet II sextet 111 doublet
% +0.8
AEd gl,Sl(mm/s) * 0.04
*0.06
[kOeI *5
76 15 7 2
0.00 0.41 -0.12 0.39
-0.2 0.1 1.2
330 364 318 -
-0.14 0.0 1.03
331 364 320 -
70 16 10 4
0.01 0.54 0.00 0.3 1
’ IS values are given relative to a-Fe at room temperature.
Hen
353
in a paramagnetic and magnetically ordered state, respectively. The area of the doublet in 90” CEM spectrum for sample I is very small (ca. 2%) and for sample II 4%. But the necessity of taking this contribution into account became more clear when we considered GIM spectra where this contribution is much more prominent and clearly seen. From Table 1 we also see that the parameters of the doublet in sample 1 and sample II differ slightly. This difference is probably caused by a change of relative weights of paramagnetic components. The hyperfine parameters of doublet and sextet II correspond to the literature data of the P-FeOOH and c+FeOOH [4-71, but the present data does not allow an unambiguous identification. Further specification of different multiplet parameters was done by comparison of a set of computed and experimental spectra at different grazing angles. By this way it became clear that in order to improve the agreement between theory and experiment we should take into account the existence of some distribution of the hyperfine magnetic field in the a-Fe component. For simplicity we simulated this distribution by adding a broadened sextet (sextet III) with a slightly smaller magnetic splitting than in a-Fe. Its contribution to the 90” CEM spectra is small (_ 7% for sample I and u 10% for sample II). Some disagreement of the parameters for this sextet in &he two investigated samples we can explain by difficulties in their exact determination due to very large linewidths (u l-2 mm/s). We think that parameters determined for sample II are better because the share of this component in the whole spectrum is greater. This component is more clearly seen in spectra at grazing angles. The difference of relative intensities of the lines in the cw-Fe sextet for the 90” CEM spectrum and the GIM spectra suggests the existence of magnetic texture in the surface plane of the film. So when we calculate the polarization dependence of the scattering processes at grazing angles we have a possibility to restrict our consideration to two independent polarization states of incident radiation and use the theory of TER in scalar form. It is clear also that the relative intensities of the sextet lines in the GIM spectra for T-polarization are the same as for the 90” CEM spectra so we should find only relative intensities of sextet lines for u-polarization of radiation by means of numerical simulation of the GIM spectra. The ratio of intensities of sextet lines for r-polarization we determined as I, : I, : I, = 2.45 : 3.37: 1.OO from the 90” CEM spectrum and for interpretation of the GIMS spectra we had use for o-polarization the ratio of intensities 2.45 : 0.34: 1.00. Some magnetic texture we find also for the other two sextets. Another group of independently determined parameters concerns the TER effect itself. They are the electronic susceptibilities of our films. Theoretical values of electronic susceptibilities and critical angles 0, = (Rex,,)“’ of
354
S.M. Irkaev et al. / Nucl. Insrr. and Merh. in Phys. Rex B 103 (1995) 351-358
pure (-Y-Feand beryllium substrate for 14.4 keV radiation
are as follows: xc? = (- 14.633 + 0.691 i) X 10m6,
0, = 3.83 X 10e3;
,$‘! = (-3.261
0, = 1.81 x 10-j.
+ 0.001 i) X 10m6,
(1) For nonresonant MO K, radiation, which we used for measuring of the reflection curves, these values can be approximately re-calculated by means of the relation x,/x2 _ (A,/&>* which gives: x;E: = (-9.97
+ 0.47 i) X 10W6,
0, = 3.16 X 10-3;
x;;‘, = (-2.22
+ 0.001 i) X 10e6,
0, = 1.49 X 10e3, (2)
where A, and A, are the wavelength of Miissbauer and MO K, radiations. Comparison of theoretical reflection curves calculated for the susceptibilities of a homogeneous film and substrate with experimental ones reveal a very poor agreement (see Fig. 1, dotted line). The difference could be explained if we take into account that real films have a lower density near the surface due to the partial oxidation, adsorption of C, N and other atoms and existence of some roughness of the surface. Much better agreement can be achieved when we use the model of multilayer films with a different density of each layer. Such a model approximates the real continuous variations of density versus depth. Parameters of electronic susceptibilities of the layers obtained by fitting of the reflection curves are given in Fig. 3. It should be noted that a complete analysis with respect to the parameters of electronic susceptibilities involves simultaneous analysis of RGM spectra near the critical angle at 0 = 3.5 mrad and 0 = 4.2 mrad taking in mind the recalculation coefficients for the two wavelengths. RGM spectra are very sensitive to the electronic and nuclear densities of
1.0
density of electrons
1 I
nonresonant absorption ..._._..._..m..... “.-.__.I.-.--. 20
30
40
O!&
-10
-5
RELATIVE
0
5
VELOCITY
10
5
(mm/s)
Fig. 4. Experimental RGM spectrum of sample I for glancing angle 0 = 3.5 mrad (points) and theoretical RGM spectra calculated for two simple models: the homogeneous a-Fe film (curve I) and the multilayered film in which each layer is characterized by only one hyperfine interaction in the following sequences (from the surface): doublet, sextet II, sextet III and sextet I (a-Fe). Parameters of different multiplets are given in Table 1. Thicknesses of layers are chosen proportional to the areas of corresponding multiplets in the 0 = 90” CEM spectrum.
the sample near the surface and may be used for determination of the electronic density as well as a reflection curve. At the beginning of numerical simulation of GIM spectra we considered two simple models: a homogeneous Fe film with the same set of spectral components at each depth (Fig. 4, curve 1) and a multilayer model, in which only one kind of hyperfine interaction exists in each layer and the thicknesses of the layers are proportional to the relative areas of the different multiplets in the 90” CEM spectrum (Fig. 4, curve 2). We see that both these simple models do not agree with experiment. As a potentially better model we allow any possible mixture of different kinds of hyperfine interactions in each layer, which with a sufficient number of layers is almost equivalent to a continuous distribution of hyperfine fields versus depth. For this purpose we introduce a matrix of hypertine field distribution V,,,, which describes the relative densities of nuclei embodied a k-kind of hyperfine interaction in layer n. So we characterize the susceptibilities of the separate layers in the film by means of the expression: A;., ck/2
50
DEPlH (nm)
Fig. 3. Depth profile of the electronic parameters of layers: Re xel (the density of electrons) and Im xe, (absorption by electrons) giving the best agreement between theory and experiment for X-ray reflection curve (solid line in Fig. 1) and shapes of experimental GIM spectra (Fig. 5). Dependences are normalized with respect to Re xe, in a-Fe.
X,=xel.,+FCLC k
i E-Eik+i&/2’
(3)
where xe,,” describes the interaction of the radiation with electrons, i numerates the lines in multiplet k; Al,, rjl, and Eik are the amplitudes, the widths and the energies of the separate resonant lines. The values A:,, 6; differ from Aik, 4, that were obtained by fitting the 90” CEM spectrum due to convolution with source line having width
355
S.M. irkaev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (199s) Ml-358 where P,
is the total density of resonant nuclei in the layer n in units of that in a-Fe, then we get the following value of the factor F from which the absolute values of the nuclear part of susceptibility in Eq. (3) depends
r,. Using the approximation of a thin absorber we have the following relations for these values: rile A;, = ----Ai,. rik - r,
r,; = r;, - 4;
(4)
F = 8.35 X lO-6 mm/s.
If we normalize the values A:, for each multiplet in the following way c A;k r;,/2
= 1
For the calculation sion:
(7)
of Eq. (7) we use the general expres-
(9
(8)
F=
and use the following normalization of the matrix V: y,, + V”, + . . •c V”, = P”.
where fr,,, is the probability of the Miissbauer effect, Q is
(6)
YIELD OF ELECTRONS
REFLECTION 1.41
t t; Z w l-
‘PuoloEtEcTRctis 0.8 1.41
0.6~ 1.23Smtnd
1.0.
Z -
0.6.
w
0.6.
> ;
I 0.4J
'a ;
’
0.81
PHurclELEolRoNs
2.5 mw
1.0.
CC 0.8.
0.6.
o-4l6 4
_10
-5
0
5
RELATIVE
10
15 I
--115
VELOCITY
-10
-5
0
5
10
15
(mm/s)
Fig. 5. Series of experimental (points) and theoretical (solid lines) GIM spectra for sample I: RGM spectrum on the left and CEM spectra on the right. Theoretical spectra represent the result of fitting using the model of multilayered film with mixed hypertine interaction in each layer. The calculated contribution of photoelectrons to MSssbauer electron spectra is represented by dotted lines.
SM. I&rev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (I 995) 351-358
356 1.0
INITIAL SAMPLE
OXIDE SAMPLE
-
IIEP’I’H(nm)
I)EP’l’H (nm)
Fig. 6. Depth profiles of the density of nuclei embodied definite kind of hyperfme interaction (marked in insert) in units of that for a-Fe5’ for the sample I (left) and II (right). Note that according to Eq. (9) the area under each step function is proportional to the percentages of the phase content in Table I and determines its contribution to the 90” CEM spectrum.
the enrichment of the film by resonant isotope, r,,, is the natural linewidth, (Y is the internal conversion coefficient, I,_, are the spins of exited and ground states of the Mossbauer nucleus. For our iron film we put fM = 0.7, Q = 0.9, N = 8.47 nme3, A = 0.086 nm. During numerical simulation of the theoretical spectrum by variations of the elements of matrix V,, we should keep constant the ratio of total number of nuclei having a given resonant interaction. In the opposite case we would change the shape of the theoretical 90” CEM spectra. This condition takes the following form: zV,,,d,: n
zV,,d,: n
x&d,: n
...
=S,:S,:S,:
.... (9
where S, is the relative area of the partial spectrum corresponding to k-kind of hyperfine splitting in the 90“ CEM spectrum. Such a model allows to include in the fitting procedure the variation of the electronic density and the density of nuclei having different hyperfme interactions versus depth By this fitting we have achieved a much better agreement between the theory and the experiment (Fig. 5). Obtained step-functions X+ and V,,, are shown in Figs. 3 and 6. A great number of parameters which should be matched by optimization procedure for the series of spectra raises some mathematical problems such as the uniqueness and physical credibility of the results. These problems certainly need further development. In our work we only demonstrate that such a treatment is possible and variations of the shape of GIM spectra versus angle can be. reasonably good described. Some remarks should be made about the numerical simulation. First we examined RGM spectra depending mainly on electronic and nuclear densities. We began from
RGM spectra for the lowest angles which depend only upon parameters of top layers, then move gradually into the bulk, including into consideration spectra, obtained at larger angles, and parameters of deeper layers. The most complex thing in this simulation is the necessity to obtain a good agreement for all spectra in the sets simultaneously. After we get a reasonably good fitting for the RGM series we include into the analysis also the series of CEM spectra. Simultaneously we began to simulate some additional parameters, which influence only CEM spectra at grazing angles. Such parameters are those which determine the escape functions for conversion and photoelectrons and relative photoelectron yield. The photoelectron yield abruptly changes the shape of the spectra as we.see from Fig. 5 (right) where the photoelectron contribution to the theoretical CEM spectra is shown. We see also that this contribution is drastically different for different grazing angles and this leads to a change of background asymmetry for the angles lower and larger than the critical one [8]. We have explained the reasons for such energy dependence of the yield of photoelectrons in part II 121. We use for the escape function T(z) an analytical expression from Ref. [9] where we can vary the mean electron path r,.,, the part of photoelectron yield P, and relative conversion electrons yield (for a single photoelectron or nuclear resonant absorption event ‘). We get reasonably good agreement between theoretical CEM spectra and experimental ones when we put rB = 700 nm, and Pa = 0.7. We think also that the general expression for the escape
’ In Ref. [lo] we use a more general model for the analysis of yield funtions itself.
S.M. Irkaev
et al. / Nucl. Instr.and Meth. in Phys. Rex B IO3 (I 995) 351-358
function T(z), which was calculated in Ref. [9] for the ideal case of a homogeneous medium, should be re-examined for our inhomogeneously layered structure with mixed phases and such re-examination is possible empirically on the basis of our experiment. At least we do not know any other experimental methods which allow to compare the photoelectrons and conversion electron yield in real systems. The detailed discussion of these problems was presented in Ref. [lo]. During our simulation of the sets of GIM spectra we adjust the hyperfine field parameters, such as IS, A E. and H,, especially for those subspectra that are more pronounced seen at grazing angles. The criteria of the quality of fitting of GIM spectra does not exist yet but the experience in theoretical treating of GIM spectra reveals that our estimations are rather sensitive (- 5%) to the relative and absolute amount of resonant nuclei at the very top layer (up to 5 nm) because top layers give a large contribution to spectra for all glancing angles of incidence but especially for the smallest ones. Such evaluation of accuracy follows from many independent attempts to fit such spectra beginning from different initial conditions. Accuracy of results drops down very strong with increasing depth and for depths above 20 nm we cannot guarantee an accuracy more than 20-30%. We have however very serious problems with determinations of the exact value of hyperfine parameters which are not known for interface regions. This circumstance inserts an additional ambiguity to our consideration. Our analysis has resulted in step distribution functions for all hypertine interactions as a function of depth in both sample I and II. These are shown in Fig. 6. We see from Fig. 6 that most of the oxide iron atoms are concentrated at the surface layer of the films. The modification of the surface which increases from sample I to sample II due to the heat treatment leads to the appearance of oxidized iron in paramagnetic states as in the case of ultrafine particles. But the a-Fe phase is present at the top layer also. This could indicate the existence of island structures on the surface. We should underline that this result is not connected with restrictions of surface sensitivity of the method. It is easily to recalculate the theoretical spectra removing this a-Fe contribution from the most top layer (2 nml: the shapes of spectra will alter drastically. The sensitivity of spectra to transfening of the nuclei in the nonmagnetic state (giving doublet contribution into resonant spectrum) over depth is not so strong because the total amount of such kind of nuclei is rather small. But we noticed something unexpected. We cannot put (without sufficient distortion between the theoretical spectra and experimental ones) all amount of this kind of nuclei to the top layer (in sample I its density in the most top layer is 0.002 and is hardly seen on Fig. 6). So we can assume that either the rest amount of this phase dilutes over the whole film with very small density or it is concentrated at the
357
other side of film in interface region with substrate. The latter conclusion was confirmed also in paper [ 111 but our film is rather thick and we cannot “see” the interface region by our method. We also see that the different phases are not localized in any definite layer. It indicates that oxides appear as patches that penetrate down to the bottom boundary of the film. The destruction of the film due to the oxidation process concerns not only the most top layer but partially refers to the deeper layers: the “bulk” layer where a-Fe predominantly exist contains some amount (it is more noticeable for sample II) of nuclei having other hyperfine parameters than that in a-Fe. If we assume that sextet 111 describing hyperfine magnetic splitting in defected o-Fe can appear in interface regions between pure a-Fe grains and oxidized phases then transformation of its depth distribution due to the oxidation process is rather clear. For sample I their distribution has a relative sharp maximum before the a-Fe layer, in sample II this distribution function is broadened, moves deeper and overlaps partially with the a-Fe distribution function. The sum of nuclear densities presented in Fig. 6 is not equal to 1 even in the “bulk” of the film and for sample II it is smaller than that for sample I. But it is an averaged density over the given layer where not only a-Fe grains exist but also the oxidized phases (as we see in Fig. 6 at any depth) where Fe-atoms are diluted by oxygen atoms. Besides that it is clear that the total mean nuclear density should decrease due to distortion of the crystalline structure, vacancies in grain boundaries and other defects. Notice that obtained electronic density (Fig. 3) is not also equal to the electronic density of pure a-Fe at any depth. Note also that although the total amount of a-Fe atoms in the different phases differs slightly for samples I and II (see Table 1 and Fig. 2), their distribution versus depth in both samples changes drastically. From distributions of the hyperfine fields versus depth in two samples which were obtained from fitting of GIM spectra we can explicitly see how different oxide phases develop further into the sample during oxidation processes.
4. Conclusion The article is the third and final part of three papers that are devoted to the development of a new method for ultrathin surface layer analysis: Grazing Incidence Miissbauer Spectroscopy (GIMS). We presented consecutively our setup for realization of a GIMS experiments [l], the general theory of coherent processes arising at TER conditions, which give the basis for interpretation of experimental data [2] and in this last part we have realized for the first time the quantitative analysis of a series of RGM and CEM spectra. We have shown that fitting of GIM spectra with respect to the depth distribution functions of electronic and hyper-
358
S.M. Irkaev et al. / Nucl. Instr. and Meth. in Phys. Rex B 103 (1995) 351-358
fine parameters is possible, but for such analysis it is necessary to deal simultaneously with the whole series of RGM and CEM spectra at different grazing angles and the X-ray reflection curve. Maybe it will be worthwhile for removal of some ambiguity of our results to use also an ellipsometry method and diffraction of slow electrons. As a result of the present investigation, however, we have obtained very detailed information about the investigated films with respect to distribution versus depth for each kind of hyperfine interaction existing in the 57Fe film before oxidation (as prepared) and after some oxidation processes. In this way we observe the advancement of different oxide phases into the bulk of the film during this process. Our analysis demonstrates the possibility of depth selective investigations (on the scale 2-50 nm) of ultrathin films by means of the GIMS technique. Treatment of GIM spectra is not a simple procedure and a reliable analysis will need further improvements and development on the basis of modem computer power and recent achievements of mathematics. But now it is clear that “the game is worth the candle”, because it gives unique information that could not have been obtained by conventional Mijssbauer spectroscopy.
Acknowledgements The authors would like to thank D. Liljequist helpful discussions of some aspects of this trilogy.
for
We are also pleased to acknowledge the Joint-Stock Company “DEKA” and JV “VA Instruments” for financial supports of this work (Grant No. 94/52-05CM).
References [I] SM. Irkaev, M.A. Andreeva. V.G. Semenov, G.N. Belozerskii and O.V. Gtishin, Nucl. Instr. and Meth. B 74 (1993) 545. [2] SM. Irkaev, M.A. Andreeva, V.G. Semenov, G.N. Belozerskii and O.V. Grishin, Nucl. Instr. and Meth. B 74 (1993) 554. [3] W.R. Dunham, C.T. Wu, R.M. Polichar, R.N. Sands and L.J. Harding, Nucl. Instr. and Meth. 145 (1977) 537. [4] P. Ayyub. M. Multani, M. Barrna, V.R. PaIkar and R. Vijayaraghavan, J. Phys. 21 (1988) 2229. [5] W. Meisel, Kern. Kozlem 48 (1977) 41. [6] L.H. Bowen, MSssbauer Effect Reference and Data J. 2 (1979) 76. [7] M. Stratmann and K. Hoffmann, Corrosion Sci. 29 (1989) 1329. [8] M.A. Andreeva, G.N. Belozerskii, O.V. Grishin, S.M. Irkaev. V.I. Nikolaev and V.G. Semenov, Sov. Phys. JETP Lett. 55 (1992) 62. [9] D. Liljequist, T. Ekdahl and U. Baverstam, Nucl. Instr. and Meth. 155 (1978) 529. [lo] M.A. Andreeva, S.M. Irkaev and V.G. Semenov, Zh. Eksp. Teor. Fiz. 105 (1994) 1767. [I I] S.A. Isaenko, AI. Chumakov and S.I. Shinkarev, Phys. Lett. A 186 (1994) 274.