Parallel implementation of stochastic cellular automata model of electron-hole recombination in 2d and 3d heterogeneous semiconductors

Karl K. Sabelfeld, Anastasia E. Kireeva

Abstract


Parallel programs implementing stochastic cellular automata (CA) model of electron-hole recombination in an inhomogeneous semiconductor for two- and three-dimensional cases are developed. The spatio-temporal distributions of particles are investigated by the CA simulation. Spatial separation of electrons and holes with clusters formation is found and analyzed. Parallel implementation of the CA model allows us to calculate integral characteristics of the recombination process (particle densities and radiative intensity) in acceptable time. Recombination kinetics in the vicinity of the recombination centers and diffusion in two- and three-dimensional space is investigated using the parallel program.


Keywords


electron-hole recombination, semiconductor, parallel implementation, stochastic cellular automaton, radiative intensity

References


Туркин А. Нитрид галлия как один из перспективных материалов в современной оптоэлектронике // Компоненты и технологии. 2011. No 5. С. 6--10.

Gorgis A., Flissikowski T., Brandt O., Cheze C., Geelhaar L., Riechert H., and Grahn H.T. Time-resolved photoluminescence spectroscopy of individual GaN nanowires // Physical review B. 2012. No. 86. 041302(R).

Sabelfeld K.K., Brandt O., Kaganer V.M. Stochastic model for the fluctuation-limited reaction-diffusion kinetics in inhomogeneous media based on the nonlinear Smoluchowski equations // J. Math. Chem. 2015. Vol. 53, Issue 2. P. 651--669.

Kolodko A.A. and Sabelfeld K.K. Stochastic Lagrangian model for spatially inhomogeneous Smoluchowski equation governing coagulating and diffusing particles // Monte Carlo Methods and Applications. 2001. Vol. 7, No. 3-4. P. 223--228.

Kolodko A., Sabelfeld K. and Wagner W. A stochastic method for solving Smoluchowski's coagulation equation // Mathematics and Computers in Simulation. 1999. Vol. 49, No 1-2. P. 57--79.

Sabelfeld K.K., Levykin A.I., Kireeva A.E // Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations, Monte Carlo Methods and Applications. 2015. Vol. 21, No 1. P. 33--48. (DOI:10.1515/mcma-2014-0012)

Toffoli T., Margolus N. Cellular Automata Machines: A New Environment for Modeling // USA: MIT Press, 1987. 259 p.

Бандман О.Л. Клеточно-автоматные модели пространственной динамики // Системная информатика. Методы и модели современного программирования. 2006. No 10, С. 59--113.

Bandman O.L. Mapping physical phenomena onto CA-models // AUTOMATA-2008. In: Adamatzky A., Alonso-Sanz R., Lawniczak A., Martinez G.J., Morita K., Worsch T. (eds.) Theory and Applications of Cellular Automata. Luniver Press, UK, 2008. P. 381--397.

Ермаков С.М., Михайлов Г.А. Статистическое моделирование. М.: ФИЗМАТЛИТ, 2-е изд., дополн., 1982. 296 с.




DOI: http://dx.doi.org/10.14529/cmse170106