Skip to main content
Log in

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

  • Published:
Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. Van Roosbroeck, J. Appl. Phys. 26 (1), 380 (1955).

    Article  Google Scholar 

  2. E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 3 (3), 468 (2009).

    Article  Google Scholar 

  3. E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 6 (2), 330 (2012).

    Article  Google Scholar 

  4. M. A. Stepovich, A. G. Khokhlov, and M. G. Snopova, Proc. SPIE 5398, 159 (2004).

    Article  Google Scholar 

  5. I. V. Burylova, V. I. Petrov, M. G. Snopova, and M. A. Stepovich, Semiconductors 41 (4), 444 (2007).

    Article  Google Scholar 

  6. E. V. Seregina, M. A. Stepovich, and A. M. Makarenkov, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 7 (6), 1077 (2013).

    Article  Google Scholar 

  7. E. V. Seregina, M. A. Stepovich, and A. M. Makarenkov, Usp. Prikl. Fiz. 1 (3), 354 (2013).

    Google Scholar 

  8. N. N. Mikheev, V. I. Petrov, and M. A. Stepovich, Izv. Akad. Nauk SSSR, Ser. Fiz. 55 (8), 1474 (1991).

    Google Scholar 

  9. A. A. Belov, V. I. Petrov, and M. A. Stepovich, Izv. Ross. Akad. Nauk, Ser. Fiz. 66 (9), 1317 (2002).

    Google Scholar 

  10. P. K. Suetin, Classical Orthogonal Polynomials (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  11. 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].

    Google Scholar 

  12. V. A. Abilov, M. V. Abilov, and M. K. Kerimov, Comput. Math. Math. Phys. 55 (7), 1094 (2015).

    Article  Google Scholar 

  13. S. M. Nikol’skii, Approach for Multivariable Functions and Embedding Theorems (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  14. V. K. Lashchenov, Izv. Vyssh. Uchebn. Zaved., Mat., No. 1 (224), 44 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. V. Seregina.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1027451018010160

Keywords

Navigation