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Monte Carlo Modeling of Electron Scattering in Nonconductive Specimens

Published online by Cambridge University Press:  01 December 2004

H.-J. Fitting ,
E. Schreiber  and
I.A. Glavatskikh
H.-J. Fitting
Affiliation:
Physics Department, University of Rostock, Universitätsplatz 3, D-18051 Rostock, Germany
E. Schreiber
Affiliation:
Physics Department, University of Rostock, Universitätsplatz 3, D-18051 Rostock, Germany
I.A. Glavatskikh
Affiliation:
Institute of Technical Physics, Urals State Technical University, Mira street 19, RUS-620002 Ekaterinburg, Russia
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Abstract

Very low energy electrons in a solid should behave like Bloch electrons and will interact with perturbations of the atomic lattice, that is, with phonons. So we use the acoustic phonon scattering for replacing the elastic binary encounter approximation of the Mott scattering for electrons with low energies E < 100 eV. For ballistic electrons (1 eV < E < Eg) and higher energies up to 1 keV we determined the acoustic phonon scattering and the impact ionization rate by means of the “backscattering-versus-range” proof and respective η(E0) − R(E0) diagrams. Electron trajectories demonstrate the relatively short range of primary electrons (PE) with energies E > 50 eV due to strong impact ionization losses (cascading) and the much greater range of secondary electrons (SE) with E < 50 eV, finally as a consequence of less effective phonon losses. The field-dependent transport parameters allow us to model the self-consistent charge transport and charging-up of insulating SiO2 layers during electron bombardment maintained by the current components of primary electrons jPE, secondary electrons jSE, and associated ballistic holes jBH, as well as by Fowler–Nordheim field injection jFN from the substrate. The resulting distributions of currents j(x,t), charges ρ(x,t), electric fields F(x,t), and the potential V(x,t) across the dielectric layer explain the phenomena of field-enhanced and field-blocked secondary electron emission with rates δ [gel ] 1.

Keywords

secondary electron emissioninsulating targetselectron beam charging
Type
Research Article
Information
Microscopy and Microanalysis , Volume 10 , Issue 6 , December 2004 , pp. 764 - 770
Copyright
© 2004 Microscopy Society of America

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References

REFERENCES

Cazaux, J. (1999). Some conclusions on the secondary electron emission, delta, from e(−) irradiated insulators. J Appl Phys 85, 1137–1147.Google Scholar
Fischetti, M.V. (1984). Monte Carlo solution to the problem of high-field electron heating in SiO2. Phys Rev Lett 53, 1755–1758.Google Scholar
Fitting, H.-J. (1974). Transmission, energy distribution, and SE excitation of fast electrons in thin solid films. Physica Status Solidi (a) 26, 525–535.Google Scholar
Fitting, H.-J. (1978). Elektronenstrahlinduzierte Ladungsträger in Festkörpertargets. Habilitation thesis, Rostock University.
Fitting, H.-J. & Boyde, J. (1983). Monte Carlo calculation of electron attenuation in SiO2. Phys Stat Sol (a) 75, 137–142.Google Scholar
Fitting, H.-J. & Friemann, J.-U. (1982). Monte Carlo studies of the electron mobility in SiO2. Phys Stat Sol (a) 69, 349–358.Google Scholar
Fitting, H.-J., Glaefeke, H., & Wild, W. (1977). Electron penetration and energy transfer in solid targets. Phys Stat Sol (a) 43, 185–190.Google Scholar
Fitting, H.-J., Glaefeke, H., Wild, W., Franke, M., & Müller, W. (1979). Elektronenstrahlinduzierter Ladungstransport in SiO–2-Schichten. Experimentelle Technik der Physik 27, 13–24.Google Scholar
Fitting, H.-J., Hingst, Th., Franz, R., & Schreiber, E. (1994). Electronic trap microscopy—A new mode for SEM scanning microscopy. Scanning Microsc 8, 165–174.Google Scholar
Fitting, H.-J., Schreiber, E., Kuhr, J.-Ch., & von Czarnowski, A. (2001). Attenuation and escape depths of low energy electron emission. J Electr Spectrosc Rel Phenom 119, 35–47.Google Scholar
Fröhlich, H. (1973). Theory of electrical breakdown in ionic crystals. Proc Royal Soc (London) 160, 230–241.Google Scholar
Ganachaud, J.P., Attard, C., & Renoud, R. (1997a). Study of the space charge induced by an electron beam in an insulating target. 1. Monte Carlo simulation model. Phys Stat Sol (b) 199, 175–184.Google Scholar
Ganachaud, J.P., Attard, C., & Renoud, R. (1997b). Study of the space charge induced by an electron beam in an insulating target. 2. Presentation of the results. Phys Stat Sol (b) 199, 455–465.Google Scholar
Glavatskikh, I.A., Kortov, V.S., & Fitting, H.-J. (2001). Self-consistent electrical charging of insulating layers and metal-insulator–semiconductor structures. J Appl Phys 89, 440–448.Google Scholar
Joy, D.C. (1995). A data-base of electron–solid interaction. Scanning 17, 279–275.Google Scholar
Kortov, V., Isakov, V., Gaprindoshvily, A., Fitting, H.-J., Glaefeke, H., & Wild, W. (1979). Untersuchungen des Austritts von Exoelektronen aus geladenen Isolatorschichten mit Hilfe des Monte-Carlo-Verfahrens. Phys Stat Sol (a) 54, 633–638.Google Scholar
Kuhr, J.-Ch. & Fitting, H.-J. (1999a). Monte Carlo simulation of electron emission from solids. J Electr Spectrosc Rel Phenom 105, 257–273.Google Scholar
Kuhr, J.-Ch. & Fitting, H.-J. (1999b). Monte Carlo simulation of low energy electron scattering in solids. Phys Stat Sol (a) 172, 433–449.Google Scholar
Llacer, J. & Garwin, E.L. (1969). Electron–phonon interaction in alkali halides. 1. Transport of secondary electrons with energies between 0.25-ev and 7.5-ev. J Appl Phys 40, 2766.Google Scholar
Ning, T.H. (1976). High-field capture of electrons by Coulomb-attractive centers in silicon dioxide. J Appl Phys 47, 3203–3208.Google Scholar
Schreiber, E. & Fitting, H.-J. (2002). Monte Carlo simulation of secondary electron emission from the insulator SiO2. J Electr Spectrosc Rel Phenom 124, 25–37.Google Scholar
Stevens Kalceff, M.A., Thorogood, G.J., & Short, K.T. (1999). Charge trapping and defect segregation in quartz. J Appl Phys 86, 205–208.Google Scholar
Stobbe, M., Könis, A., Redmer, R., Henk, J., & Schattke, W. (1991). Interband transition rate in GaAs. Phys Rev B 44, 11105–11110.Google Scholar
Vicario, E., Rosenberg, N., & Renoud, R. (1994). Simulation of insulator charging by a narrow electron-beam. Surf Interface Anal 22, 115–119.Google Scholar
Ziman, J.M. (1962). Electrons and phonons. Scanning 17, 279.Google Scholar