Abstract
Stationary temperature fields due to the interaction of an electron probe with a GaN sample are examined. In order to calculate the density of generated heat, the process of electron energy loss is modeled by the Monte Carlo method. The heat generation region is assumed to have the shape of a half-ellipsoid. In the case of uniform heat generation in the ellipsoid, an analytical solution to the heat conduction problem is found and expressed in terms of elementary functions. It is shown that the maximum heating temperature and the temperature field distribution depend only slightly on the shape of the heat generation region. An approximation of the density of heat sources by a uniform distribution over a hemisphere of radius equal to the ultimate range of electrons leads to a considerably underestimated maximum heating temperature. An expression is derived for determining the characteristic size of the heat generation region in GaN; this expression allows one to calculate the maximum heat temperature with an accuracy of 3% in a wide range of electron beam energies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Castaing, Adv. Electron. Electron Phys. 13, 317 (1960).
G. S. Almasi, J. Blair, R. E. Ogilvie, and R. J. Schwartz, J. Appl. Phys. 36(6), 1848 (1965).
C. F. Friskney and C. W. Haworth, J. Appl. Phys. 38(9), 3796 (1967).
H. Amano, M. Kito, K. Hiromatsu, and I. Akasaki, Jpn. J. Appl. Phys. 28(12), L2112 (1989).
S. K. Obyden, G. A. Perlovskii, G. V. Saparin, and S. I. Popov, Izv. Akad. Nauk SSSR, Ser. Fiz. 48(12), 2374 (1984).
I. G. Stoyanova and E. M. Belavtseva, Izv. Akad. Nauk SSSR, Ser. Fiz. 23(6), 754 (1959).
I. G. Stoyanova and I. V. Anaskin, Physical Foundations of Transmission Electron Microscopy Methods (Nauka, Moscow, 1972).
V. N. Korolyuk and Yu. G. Lavrent’ev, in X-ray Microanalysis with Electron Probe in Mineralogy (Nauka, Leningrad, 1980), p. 7.
M. N. Filippov, Izv. Akad. Nauk, Ser. Fiz. 57(8), 165 (1993).
T. E. Everhart and P. H. Hoff, J. Appl. Phys. 42(13), 5837 (1971).
Electron Database, http://www.ioffe.rssi.ru/ES.
T. Rao-Sahib and D. B. Wittry, J. Appl. Phys. 45(11), 5060 (1974).
H.-J. Fitting, H. Glaefeke, and W. Wild, Phys. Status Solidi A 43(1), 185 (1977).
S. G. Konnikov, V. A. Solov’ev, V. E. Umanskii, and V. M. Chistyakov, Fiz. Tekh. Poluprovodn. (Leningrad) 21(11), 2028 (1987) [Sov. Phys. Semicond. 21, 1229 (1987)].
N. N. Lebedev, I. P. Skal’skaya, and Ya. S. Uflyand, Collection of Problems of Mathematical Physics (Moscow, 1955).
K. Kanaya and S. Okayama, J. Phys. D 5(1), 43 (1972).
J. I. Goldstein et al., Scanning Electron Microscopy and X-ray Microanalysis (Plenum, New York, 1981; Mir, Moscow, 1984).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizika Tverdogo Tela, Vol. 43, No. 5, 2001, pp. 779–785.
Original Russian Text Copyright © 2001 by Bakale\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\)nikov, Galaktionov, Tret’yakov, Tropp.
Rights and permissions
About this article
Cite this article
Bakaleinikov, L.A., Galaktionov, E.V., Tret’yakov, V.V. et al. Calculation of the thermal effect of an electron probe on a sample of GaN. Phys. Solid State 43, 811–817 (2001). https://doi.org/10.1134/1.1371357
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/1.1371357