Abstract
Some possibilities of implementing a procedure for estimating statistical characteristics (expectation and autocorrelation function) of the distribution of minority charge carriers (MCCs) generated in a homogeneous semiconductor material are studied. The developed procedure is based on the projection method and the matrix operator technique. It is assumed that the electrophysical parameters of the material (lifetime, diffusion coefficient, and surface recombination rate of MCCs) are random quantities (variables) and obey the Gaussian distribution law. The effect of the variance of these quantities on the depth distribution of MCCs is considered. Some possibilities of this method are illustrated for the case of MCC excitation by a broad beam of electrons with moderate energies.
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References
A. A. Belov, V. I. Petrov, and M. A. Stepovich, Izv. Akad. Nauk, Ser. Fiz. 66, 1317 (2002).
N. N. Mikheev and Yu. G. Dorogova, Elektron. Tekhn. Mater., No. 4, 44 (1988).
D. F. Kyser and D. B. Wittry, Proc. IEEE 55, 733 (1967).
M. G. Snopova, I. V. Burylova, V. I. Petrov, et al., Poverkhnost’, No. 7, 1 (2007) [J. Surf. Invest. 1, 406 (2007)].
M. A. Stepovich, M. G. Snopova, and A. G. Khokhlov, Prikl. Fiz., No. 3, 61 (2004).
I. V. Vurulova, V. I. Retrov, M. G. Snorova, et al., Fiz. Tekh. Poluprovodn. 41, 458 (2007) [Semiconductors 41, 444 (2007)].
N. N. Mikheev and M. A. Stepovich, Zavod. Lab. 62(4), 20 (1996).
S. V. Lapin and N. D. Egupov, Theory of Matrix Operators and Its Application to Problems of Automatic Control (Mosc. Gos. Tekh. Univ., Moscow, 1997) [in Russian].
E. S. Ventzel, Theory of Probabilities (Akademiya, Moscow, 2005) [in Russian].
V. I. Petrov, A. A. Samokhvalov, M. A. Stepovich, et al., Izv. Akad. Nauk, Ser. Fiz. 66, 1310 (2002).
P. K. Suetin, Classical Orthogonal Polynomes (Fizmatlit, Moscow, 2007) [in Russian].
E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, Poverkhnost’, No. 6, 80 (2009).
K. A. Pupkov, N. D. Egupov, A. M. Makarenkov, et al., Theory and Computer Methods of Stochastic Systems Investigation (Fizmatlit, Moscow, 2003) [in Russian].
V. V. Solodovnikov and V. V. Semenov, Spectral Theory of Nonstationary Systems of Control (Nauka, Moscow, 1974) [in Russian].
G. M. Fikhtengoltz, Course of Differential and Integral Calculus (Nauka, Moscow, 1969) [in Russian].
M. A. Lavrent’ev and B. V. Shabat, Methods of Complex Analysis (Nauka, Moscow, 1973) [in Russian].
M. A. Evgrafov, Asymptotic Estimates and Entire Functions (Fizmatgiz, Moscow, 1962; Gordon and Breach, New York, 1961).
A. N. Dmitriev, N. D. Egupov, A. M. Shestopalov, and Yu. G. Moiseev, Machine Methods of Calculation and Design of Systems of Electroconnection and Control, The Schoolbook (Radio i Svyaz’, Moscow, 1990) [in Russian].
D. K. Fadeev and V. N. Fadeeva, Calculation Methods of Linear Algebra (Fizmatlit, Moscow, 1960) [in Russian].
V. I. Smirnov, Course of Higher Mathematics (Nauka, Moscow, 1967), Vol. 3, part 1, p. 323 [in Russian].
V. L. Girko, Spectral Theory of Random Matrixes (Nauka, Moscow, 1988) [in Russian].
R. Edwards, Functional Analysis. Theory and Applications, Dover Books on Mathematics (Holt, Rinehart and Winston, New York, 1965; Mir, Moscow, 1071).
N. S. Bakhvalov, Numerical Methods: Analysis, Algebra, Ordinary Differential Equations (Nauka, Moscow, 1975). [in Russian].
V. L. Goncharov, Interpolation Theory and Function Approximations (Gostekhizdat, Moscow, 1954) [in Russian].
A. A. Samarskii, Theory of Differential Schemes (Nauka, Moscow, 1977) [in Russian].
V. I. Lebedeva and S. A. Finogenova, Zh. Vych. Mat. Mat. Fiz., No. 2, 11 (1971).
K. Kanaya and S. Okayama, J. Phys. D: Appl. Phys. 5(1), 43 (1972).
N. N. Mikheev, V. I. Petrov, and M. A. Stepovich, Izv. Akad. Nauk SSSR, Ser. Fiz. 55, 1474 (1991).
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Original Russian Text © E.V. Seregina, A.M. Makarenkov, M.A. Stepovich, 2009, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya, No. 10, pp. 75–86.
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Seregina, E.V., Makarenkov, A.M. & Stepovich, M.A. On the possibilities of implementing a stochastic model for the distribution of nonequilibrium minority charge carriers in a semiconductor material. J. Surf. Investig. 3, 809–819 (2009). https://doi.org/10.1134/S1027451009050255
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DOI: https://doi.org/10.1134/S1027451009050255