This paper discusses the algorithm and error estimates for solving space inhomogeneous semiconductor Boltzmann equations with multi-valley, which describe the transport properties of carriers in semiconductor materials and devices. The high-dimensional feature and the singularity of the collision terms make the numerical approximation of these equations difficult. The new contributions presented in this study are the presentation of an efficient direct simulation Monte Carlo (DSMC) method and the convergence results for solving space inhomogeneous semiconductor Boltzmann equations with multi-valley. Numerical tests and typical applications are carried out to demonstrate that the proposed method has a competitive advantage for solving this kind of problem.  

　　Publication:  

　　Multiscale Modeling & Simulation, Volume 21, Issue 3 (2023)  

　　http://dx.doi.org/10.1137/22M1469511  

　　Author:  

　　Jiachuan Cao  

　　Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.  

　　Li-qun Cao  

　　 LSEC, NCMIS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China  

　　University of Chinese Academy of Sciences, Beijing 100049, China.  

　　Email: clq@lsec.cc.ac.cn