Abstract
In this work we solve the Barker-Ferry equation which accounts for the quantum character of the electron-phonon interaction in semiconductors in the framework of the Monte Carlo (MC) method. The first part of the work considers the zero electric field formulation of the equation in spherical coordinates. Different MC algorithms for solving the equation are suggested and investigated. In the second part of the work we consider the case of an applied electric field. It is shown that the second algorithm from the first part can be successfully modified to account for the cylindrical symmetry of the task.
Supported by ONR Grant N00014-96-1-1-1057
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J. Barker and D. Ferry. Self-scattering path-variable formulation of high field time dependent quantum kinetic equations for semiconductor transport in the finite collision-duration regime, Physical Review Letters, 42(26), 1779–1781, 1979.
T. V. Gurov and P. A. Whitlock. An efficient backward Monte Carlo estimator for solving of a quantum kinetic equation with memory kernel, Mathematics and Computers in Simulation, 2001, (submitted).
M. Mascagni. SPRNG: Ascalable library for pseudorandom number generation, in O. Iliev et al. (eds.), Recent Advances in Numerical Methods and Applications II, World Scientific, Singapore, 284–295, 1999.
G. A. Mikhailov. New Monte Carlo Methods with Estimating Derivatives, Utrecht, The Netherlands, 1995.
M. Nedjalkov, T. Gurov, and I. Dimov. Statistical modeling of pulse excited electron quantum kinetics in a one-band semiconductor, Math. and Comp. in Simulation, 47(2–5), 391–402, 1998.
J. Schilp, T. Kuhn, and G. Mahler. Physical Review B, 47(8), 5435–5447, 1994.
I. M. Sobol. Monte Carlo numerical methods, Nauka, Moscow, 1973, (in Russian).
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© 2001 Springer-Verlag Berlin Heidelberg
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Gurov, T.V., Whitlock, P.A. (2001). Statistical Algorithms for Simulation of Electron Quantum Kinetics in Semiconductors - Part I. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2001. Lecture Notes in Computer Science, vol 2179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45346-6_14
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DOI: https://doi.org/10.1007/3-540-45346-6_14
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