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A MONTE CARLO SIMULATION APPROACH TO THIN FILM ELECTRON MICROPROBE ANALYSIS
BASED ON THE USE OF MOTT SCATTERING CROSS-SECTIONS
K. Murata, S. Cvikevich, J. Kuptsis
To cite this version:
K. Murata, S. Cvikevich, J. Kuptsis. A MONTE CARLO SIMULATION APPROACH TO THIN FILM ELECTRON MICROPROBE ANALYSIS BASED ON THE USE OF MOTT SCAT- TERING CROSS-SECTIONS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-13-C2-16.
�10.1051/jphyscol:1984203�. �jpa-00223758�
JOURNAL DE PHYSIQUE
Colloque C2, supplgment au n02, Tome 45, f6vrier 1984 page C2-13
A MONTE CARL0 SIMULATION APPROACH TO THIN FILM ELECTRON MICROPROBE ANALYSIS BASED ON THE USE OF MOTT SCATTERING CROSS-SECTIONS
K. Murata, S. ~vikevich* and J.D. ~uptsis*'
Uniu. of Osaka Prefecture, Sakai Osaka, 591 Japan
'IBM East F i s h k i l l , Hopewe22 Junction, +New York 12533, U.S.A .
** IBM Th.omas J. Watson Research Center , Y o r k t o m Heights, New York 10598, U.S.A.
~ 6 s u m e ' - ~ ' a n a l ~ s e de films minces par EPMA a Bt6 effectuee en utilisant une simulation Monte-Carlo bas6e sur les sections efficaces de Mott pour la diffusion glastique. Les sections efficaces pour divers elements sont deduites de celles d e quelques Bl6ments comme Al, Cu, Ag et Au par interpolation ou extrapolation. Un bon accord entre des rapports k experimentaux et calcul&s a kt15 obtenu pour des films de Pt sur Si, Pt sur Au, Mo sur Si et A1 sur Si.Ce nouveau msdi!le de simulation est applique 2 des films d'alliages ternaires de CuPdAu et discute en comparaison avec les resultats exp6rimentaux.
Abstract-EPMA thin film analysis has been performed using a Monte Carlo simulation which is based on the Mott cross sections for elastic scattering. The cross sections for various elements are derived from those for only a few elements such as Al, Cu, Ag and Au with interpolation or extrapolation. Good agreement between simulated and experimental k-ratios was obtained for films of Pt on Si, Pt on Au, Mo on Si and A1 on Si. The new simulation model is applied to ternary alloy films of CuPdAu and discussed in comparison with experimental results.
I. Introduction
Monte Carlo techniques have been utilized for quantitative electron microprobe analysis by many authors. Although the accuracy of the method is still being investigated and it requires a relatively long computational time with a large computer, it is especially useful for analyses of samples with unusual boundary conditions since it can easily handle such boundaries by modifying the program. Several analyses of thin films have been successfully performed using the old Monte Carlo calculation1 which is based on the Rutherford cross section for elastic scattering. However this cross section is not accurate at lower electron beam energies (typically 10 KeV or. less) or for heavy elements. Recently the old Monte Carlo simulation model for thin film analyses was improved by using Mott cross sections2, but its application was limited to such elements as aluminum, copper and gold where Mott cross sections are available. We can calculate Mott cross sections for any element, assuming a reasonable atomic potential. But it is not practical to calculate the cross sections each time a Monte Carlo simulation is done since this requires a computer program with long CPU running time to obtain the cross sections for various elements and energies.
The present paper proposes a new method to derive the Mott cross sections for other elements from these limited calculated Mott cross sections by using interpolation and extrapolation techniques. The method is applied t o analyses of pure elemental films and further to ternary alloy films of CuPdAu.
11. Calculation model
The following major changes are made in the old model.'
1. The screened Rutherford cross section is replaced by the Mott cross section for elastic scattering, which is given by
he authors performed most of the work at this location.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984203
JOURNAL DE PHYSIQUE
where f ( 0 ) and g ( 0 ) can be obtained from theoretical models of atomic potentials by calculation of the partial wave expansions of the relativistic wave equation of Dirac. The Mott differential cross sections are provided for aluminum, copper, silver and gold. By interpolation and extrapolation of the Mott cross sections for these four elements the cross sections can be derived for different elements and for various energies. Details will be presented elsewhere.
2 . There is a change in the energy loss equation to improve the accuracy at lower energies than E = 6.3385. This is given by the following3
We used the mean ionization potential of Duncumb and Reed (DR).4 Some studies with Berger-Seltzer (BS) values5 are discussed.
3. The following ionization cross section of Hutchins (H)6 is mainly used for x-ray production
Q( U ) = const. ln u/u'.~ (3)
But in some cases the Worthington-Tomlin expression (WT)' is investigated. The mass absorption coefficients are quoted from Heinrich's
111. Results and Discussion 1. k-ratios
k-ratios are calculated which are defined as the ratio of X-ray intensity emitted from an element in a thin film on a substrate to that generated by a pure element standard. In Fig.
1 the results are compared with the experimental ones by Reuter et.a19 for both Pt and A1 films on a Si substrate as a function of energy. Also the results are shown with the old Monte Carlo calculations. The failure of the Born approximation at low energies is suggested since the errors are increasing with a decrease in energy. A quite good agree- ment is obtained between the experimental results and the new Monte Carlo results except in the region of saturation at very low energies. There is a small contribution of the fluorescent effectlo from the substrate t o the X-ray intensity in the A1 film on the Si substrate.
We have also done the calculation with the WT expression for the ionization cross section. However, the calculated k-ratio is about 10% smaller than the above value except in the energy range lower than several keV. The reason for this discrepancy is described in detail in a previous paper." The evidence becomes clearer in the next section, that the WT cross section does not fit well into the present simulation model.
2 . X-ray intensity as a function of energy.
Further investigations were carried out for the X-ray intensities from the standard and from the film individually as a function of energy. One of the examples is shown in Fig. 2 for a Pt standard. Dots show experimental data. A solid line is a smoothed curve of the experimental data. The Monte Carlo results are shown by crosses and triangles with H and WT, for the ionization cross sections, respectively. Since the absolute values are not known, both calculated intensitites are matched with the experimental intensity at 10 KeV.
There is a clear difference between calculation and experiment even with the H cross section. The uncertainty of 10% in a mass absorption coefficient cannot account for this error. The calculations were performed with BS values for J, and it was found that the result does not change significantly. This discrepancy seems to be caused by an inaccurate choice for the ionization cross section. It means that the energy dependence of the ionization cross section is not correct in the present model. In Fig. 3 is shown the X-ray
intensity from the film as a function of energy. Discrepancies between theory and experi- ment are seen more clearly in this figure. The H-DR combination gives a relatively good agreement with experimental data, but seems t o still have some difference from experiment.
On the other hand the WT-DR shows a faster increase at low energies and too fast a decrease with an increase in energy.
3. Application of the present model to analysis of a ternary alloy film of CuPdAu Three ternary alloy films were prepared by a successive evaporation of Cu, Pd and Au with various layer thicknesses on a SiO, substrate, and followed by an annealing procedure.
Layer thicknesses of Cu, Pd and Au films before annealing have been determined with nuclear backscattering spectroscopy (NBS). The results of NBS are shown in Table I. The next column shows experimental k-ratios obtained by EPMA. Characteristic X-rays of CuKa, PdLa and AuMa are generated at an accelerating voltage of 20 keV with a take-off angle of 52.5'. Calibration curves for k-ratios are built up from calculations for various thicknesses and various concentrations. By using the calibration curves and experimental k-ratios, the concentration and the film thickness are found. One example is shown in Table I, in the column labelled Monte Carlo 1. The largest discrepancy from the NBS result amounts to about 9% for the Cu concentration. We examined the Monte Carlo results by setting the concentrations from the NBS as an input data. One example of the calculated calibration curves of k-ratios vs mass thickness is shown in Fig. 4, by using (H-DR). From this figure we can find the mass thickness which corresponds to the experimental k-ratio. If the concentration is accurate, then the mass thickness found in the above manner has to be identical. For both PdLa and AuMa, the results are close to the experimental value. However, for CuKa the mass thickness is not close to this value. We found similar results for the other two samples. The big difference between PdLa and AuMa and the CuKa characteristic lines is the overvoltage. It extends from 1 to about 6.3 and 8.9 for PdLa and AuMa, and from 1 to 2.2 for CuKa. The accuracy of Q (U) is very important for the CuKa. The WT cross section has been tried just for CuKa, which gives rise t o a larger increase in the intensity for the standard than that for the film, resulting in reduction of the k-ratios. The result is shown by WT in the figure. A significant improve- ment is seen. Similar results are obtained for the other two films with different compos- itions. Therefore, the WT cross section might be better for small values of U than the H cross section. A better expression can be found so that the mass thickness obtained for CuKa can come close to the ones for PdLa and AuMa However, there is still uncertainty in both experimental data and physical parameters such as'the mass absorption coefficient and the mean ionization potential. Further investigations have to be done in the future.
Analyses have been made by the Monte Carlo simulation by using the WT cross section for CuKa and the H cross section for both PdLa and AuMa. The results are shown in the last column (Monte Carlo 2) in Table I. Quite a good agreement is obtained between NBS and EPMA analyses.
Finally, the Monte Carlo simulation based on the Mott cross section has been applied to pure and ternary thin film analyses. Generally we obtained good agreement between theory and experiment. However, a detailed comparison has revealed inaccuracies in the ionization cross section Q (U). This kind of analysis can be a critical examination of the simulation model. Further study to develop a more accurate expression would also be useful for the ZAF correction procedure.
Acknowledgement
We would like to thank W. Reuter, R. Bowers, J. N. Ramsey and V. Brusic for their support and encouragement. Also F. Cardone for his excellent graphics work.
References
1. D. F. Kyser and K. Murata, IBM J. Res. Develop. 18, 352 (1974).
2. K. Murata, M. Kotera, and K. Nagami, J. Appl. Phys. 54, 1110 (1983).
3. T. S. Rao-Sahib and D. B. Wittry, J. Appl. Phys. 45 5060, (1974).
4. P. Duncumb and S. J. B. Reed, Ed., K. F. J. Heinrich Quantitative Electron Probe
C2-16 JOURNAL DE PHYSIQUE
Microanalysis, NBS Special Publication 298, p. 13 (1968).
5 . M. J. Berger and S. M. Seltzer, NAS/NRC 1133 p. 205 (Washington, D. C., 1964).
6. G. A. Hutchins, Eds., P. F. Kane and G. B. Larrabee, Characterization of Solid Surfaces (Plenum Press, New York, 1974), p. 441.
7. C. R. Worthington and S.G. Tomlin, Proc. Phys. Soc. A-69, 401 (1956).
8. K. F. J. Heinrich, Eds., T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, The Electron Microprobe (Wiley, New York, 1966), p. 296.
9. W. Reuter, J. D. Kuptsis, A. Lurio and D. F. Kyser, J. Phys.. D-11, 2633 (1978).
10. M. G. C. Cox, G. Love and V. D. Scott, J. Phys. D. Appl. Phys., 12, 1441 (1979).
11. K. Murata, S. Cvikevich and J. D. Kuptsis, Ed. R. Gooley, Microprobe Analysis San Francisco, 1983),p. 79.
-
\
\ +
: Expercn~cnt( Reuter et ul) : New Monte Carlo
+ : Old Monte Carlo
standard
x H -DR A 'A'-DR
Eo ( keV)
Energy (kev)" 10
Figure 1. Comparison of calculated k-ratios with
experimental ones as a function of energy. Figure 2. X-ray intensity from the standard as a function of energy.
pt (mg/cm2)
Figure 3. X-ray intensities from the film
Figure 4. k-ratios v.s. mass thickness.
as a function of energy.
The mass thicknesses are compared to experimental k-ratios.
Element Nuclear Backscatter k-ratio Monte Carlo 1 Monte Carlo 2 sample C(w/o) pt(mg/cm2) (EPMA) C ( w / o ) pt(mz/cm2) C(w/o) pt(mg/cm2
cu 0.319 0.191 0.292 0.302 Table I
A Pd 0.347 0.282 0.157 0.363 0.277 0.354 0.275
AU 0.334 0.157 0.345 0.344 Analysis of ternary alloy
Cu 0.607 0.301 0.590
B Pd 0.198 0.235 0.0766 0.209 0.230 films of CuPdAu on Si02
Au 0.195 0.0718 0.201
at 20 keV.
Cu 0.212 0.114 0.201
C Pd 0.576 0.229 0.243 0.583 0.251
Au 0.212 0.090 0.216
