Electron Transmission Coefficient for Oblique Angle of Incidence
Starting from a scattering model the transmission coefficient of electrons for oblique angle of incidence is derived. The decrease of the transmitted fraction is described by the backscattering of electrons and the energy loss caused by the decreasing mea
- PDF / 560,090 Bytes
- 8 Pages / 595.278 x 793.684 pts Page_size
- 66 Downloads / 174 Views
© Springer-Verlag 1996
Electron Transmission Coefficient for Oblique Angle of Incidence Michael Andrae*, Peter Klein, Kurt Rohrbacher, and Johann Wernisch Institute for Applied and Technical Physics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
Abstract. Starting from a scattering model the transmission coefficient of electrons for oblique angle of incidence is derived. The decrease of the transmitted fraction is described by the back scattering of electrons and the energy loss caused by the decreasing mean free path. The angular- and energy-distribution of electrons is replaced by the most probable angle and mean energy. A comparison with other models and measurements valid for normal incidence is performed. The altered transmission characteristics by tilting the sample are verified by comparison with results from Monte Carlo simulations and results from Neubert and Rogaschewski, which are based on measurements. An analytical expression for the transmission law is obtained.
Key words: transmission coefficient, tilted specimen. The exact knowledge of the transmission characteristics is important to understand how electrons penetrate into the sample and therefore necessary for EPMA. Unfortunately, hardly any experimental material regarding the transmission coefficient for tilted specimens has been published. Moreover transmission coefficients were only published for AI, Cu, Ag and Au. For normal incidence Cosslett and Thomas [IJ made detailed measurements for Cu and Au with various acceleration energies. Young [2J published measurements for A1 2 0 3 , whereas measurements for Al and Au were performed by Seidel [3]. Transmission coefficients for tilted specimens with EPMA-relevant-energies are available from Oppel [4J and from Neubert and Rogaschewski [5]. These investigations, however, only refer to Al and Au. This is why we used the Monte Carlo program "mcsing" published by Henoc and Maurice [6J to investigate the variation of the transmission for various atomic numbers and tilt angles. It is impossible to extend existing models conceived for normal incidence to the application to tilted specimens. In spite of itssimple mathematical form, the model of Kanaya and Okayama [7J shows good agreement with the experimental findings for AI, Cu and Au (see Figs. 5-7). Neubert and Rogaschewski [5J adopted the equation
*
To whom correspondence should be addressed
D. Benoit et al. (eds.), Microbeam and Nanobeam Analysis © Springer-Verlag Wien 1996
M, Andrae et al.
218 Henoc & Maurice y=55", 10keV Henoc & Maurice y=O", 10keV - - new expression (eq. 1) .., Cosslet! & Thomas, 1OkeV (exp.)
1.0
o o
60 50
AI
(Jl
c
e t5 08
- - new expression o Henoc & Maurice, 10keV Neubert & Rogaschewski
Q)
Q)
-g
40
::::
35.
0.6
'E
30
(Jl
-
AI
20
c
0.4
o C o
0.2
jg
o.o+--~---,--~-,---~-~g~~""",,_~
jg
10
t5 0.1
0.0
0.2
0.3
reduced mass depth
0.4
0.2
0.0
0.4
0.6
0.8
reduced mass depth
1 1.0
1.0
Cu
0.8
Au o
-
0.6
Henoc & Maurice, 10keV new expression
o Henoc &
Data Loading...
