{"title":"半导体异质结构中激子传输的随机模拟","authors":"Karl Sabelfeld, I. Aksyuk","doi":"10.1515/rnam-2024-0014","DOIUrl":null,"url":null,"abstract":"\n Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic simulation of exciton transport in semiconductor heterostructures\",\"authors\":\"Karl Sabelfeld, I. Aksyuk\",\"doi\":\"10.1515/rnam-2024-0014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.\",\"PeriodicalId\":49585,\"journal\":{\"name\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/rnam-2024-0014\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Numerical Analysis and Mathematical Modelling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/rnam-2024-0014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Stochastic simulation of exciton transport in semiconductor heterostructures
Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.
期刊介绍:
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.
Topics:
-numerical analysis-
numerical linear algebra-
finite element methods for PDEs-
iterative methods-
Monte-Carlo methods-
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.