Mathematical Model of Qualitative Properties of Exciton Diffusion Generated by Electron Probe in a Homogeneous Semiconductor Material
- 6 Downloads
The qualitative properties of the two-dimensional mathematical model of excitons diffusion excited by an electron beamin a semiconductormaterial are investigated. For the studied model proved continuous dependence of the solution from the input data. It is shown that the model can be applied to estimate the diffusion coefficient and the mobility of excitons on the results of experimental measurements. In the simulation are used parameters that are typical for gallium nitride.
Keywords and phrasesCauchy problem mathematical model diffusion uniqueness continuous dependence on data
Unable to display preview. Download preview PDF.
- 1.D. V. Turtin, “Uniqueness theorems for Cauchy problem solutions for evolution equations and systems with growing coefficients,” Cand. Sci. Dissertation (Vladimir, 2012).Google Scholar
- 2.V. S. Vladimirov and V. V. Zharinov, Equations of Mathematical Physics: Tutorial for Higher Schools, 2nd ed. (Fizmatlit, Moscow, 2004) [in Russian].Google Scholar
- 3.A. N. Polyakov, M. Noltemeyer, T. Hempel, J. Christen, and M. A. Stepovich, “Two-dimensional diffusion and cathodoluminescence of excitons generated by an electron beam in a semiconductor material: results of mathematical modeling,” J. Surf. Invest.: X-ray, Synchrotr. Neutron Tech. 6, 901–906 (2012).CrossRefGoogle Scholar
- 4.I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic, New York, 1980).Google Scholar
- 5.N. N. Lebedev, Special Functions and Their Decomposition, 2nd ed. (Uchpedgiz, Moscow, 1963) [in Russian].Google Scholar
- 7.A. N. Polyakov, M. Noltemeyer, T. Hempel, J. Christen, and M. A. Stepovich, “About the practical implementation of same time-of-flight measurements scheme in cathodoluminescence microscopy,” Prikl. Fiz., No. 4, 11–15 (2015).Google Scholar