Abstract
Algorithms for using the Galerkin projection method and the projection least squares method to analyze the three-dimensional model of the diffusion of minority charge carriers generated by an electron probe in a semiconductor material are presented. The results obtained using these methods are compared with the analytical solution. An estimate of the error is given, and the condition for the computation stability of the projection least squares method in the form of the limiting relation is obtained.
Similar content being viewed by others
References
W. Van Roosbroeck, J. Appl. Phys. 26 (1), 380 (1955).
E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 3 (3), 468 (2009).
E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 6 (2), 330 (2012).
M. A. Stepovich, A. G. Khokhlov, and M. G. Snopova, Proc. SPIE 5398, 159 (2004).
I. V. Burylova, V. I. Petrov, M. G. Snopova, and M. A. Stepovich, Semiconductors 41 (4), 444 (2007).
E. V. Seregina, M. A. Stepovich, and A. M. Makarenkov, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 7 (6), 1077 (2013).
E. V. Seregina, M. A. Stepovich, and A. M. Makarenkov, Usp. Prikl. Fiz. 1 (3), 354 (2013).
N. N. Mikheev, V. I. Petrov, and M. A. Stepovich, Izv. Akad. Nauk SSSR, Ser. Fiz. 55 (8), 1474 (1991).
A. A. Belov, V. I. Petrov, and M. A. Stepovich, Izv. Ross. Akad. Nauk, Ser. Fiz. 66 (9), 1317 (2002).
P. K. Suetin, Classical Orthogonal Polynomials (Fizmatlit, Moscow, 2007) [in Russian].
S. V. Lapin and N. D. Egupov, Theory of Matrix Operators and its Application to Problems on Automatic Control (Bauman Moscow State Technical Univ., Moscow, 1997) [in Russian].
V. A. Abilov, M. V. Abilov, and M. K. Kerimov, Comput. Math. Math. Phys. 55 (7), 1094 (2015).
S. M. Nikol’skii, Approach for Multivariable Functions and Embedding Theorems (Nauka, Moscow, 1969) [in Russian].
V. K. Lashchenov, Izv. Vyssh. Uchebn. Zaved., Mat., No. 1 (224), 44 (1981).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.V. Seregina, M.A. Stepovich, A.M. Makarenkov, 2018, published in Poverkhnost’, 2018, No. 1, pp. 93–100.
Rights and permissions
About this article
Cite this article
Seregina, E.V., Stepovich, M.A. & Makarenkov, A.M. Analysis of the Three-Dimensional Model of Diffusion of Minority Charge Carriers Generated by an Electron Probe in a Heterogeneous Semiconductor Material by Means of Projection Methods. J. Surf. Investig. 12, 80–86 (2018). https://doi.org/10.1134/S1027451018010160
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1027451018010160