Monte Carlo Methods for Electron Transport: Scalability Study

The Monte Carlo methods (MCMs) are very convenient for parallel implementation because in many cases they can use powerful High performance computing (HPC) resources for achieving accurate results without losing their parallel efficiency. This advantage of MCMs is used by the scientists for solving large-scale mathematical problems derived from the life science, finances, computational physics, computational chemistry, and many other fields. In this work we consider a Monte Carlo method for solving quantum-kinetic integral equations describing electron transport in semiconductors. The presented algorithm is a part of set of algorithms involved in SET (Simulation of Electron Transport) application which is developed by our team. The SET application can be successfully used to support simulation of semiconductor devices at the nano-scale as well as other problems in computational electronics. Here we study scalability of the presented a Monte Carlo algorithm using Bulgarian HPC resources. Numerical results for parallel efficiency and computational cost are also presented. In addition we discuss the coordinated use of heterogeneous HPC resources from one and the same application in order to achieve a good performance.

[1]  Paula A. Whitlock,et al.  An efficient backward Monte Carlo estimator for solving of a quantum-kinetic equation with memory kernel , 2002, Math. Comput. Simul..

[2]  Dirk P. Kroese,et al.  Handbook of Monte Carlo Methods , 2011 .

[3]  Emanouil I. Atanassov,et al.  Ultra-fast Semiconductor Carrier Transport Simulation on the Grid , 2009, LSSC.

[4]  I. B. Levinson.  Translational Invariance in Uniform Fields and the Equation for the Density Matrix in the Wigner Representation , 1969 .

[5]  M. Kalos,et al.  Monte Carlo methods , 1986 .

[6]  Siegfried Selberherr,et al.  A Wigner equation for the nanometer and femtosecond transport regime , 2001, Proceedings of the 2001 1st IEEE Conference on Nanotechnology. IEEE-NANO 2001 (Cat. No.01EX516).

[7]  Tilmann Kuhn,et al.  Electron-phonon quantum kinetics for spatially inhomogeneous excitations , 2003 .

[8]  Siegfried Selberherr,et al.  Femtosecond relaxation of hot electrons by phonon emission in presence of electric field , 2002 .

[9]  I. Dimov,et al.  A new iterative Monte Carlo approach for inverse matrix problem , 1998 .

[10]  Dragica Vasileska,et al.  Femtosecond Evolution of Spatially Inhomogeneous Carrier Excitations Part I: Kinetic Approach , 2005, LSSC.

[11]  S. Selberherr,et al.  Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices , 2004 .

[12]  Ivan Tomov Dimov,et al.  Femtosecond Evolution of Spatially Inhomogeneous Carrier Excitations Part II: Stochastic Approach and Grid Implementation , 2005, LSSC.

[13]  S. Selberherr,et al.  SEMICLASSICAL APPROXIMATION OF ELECTRON-PHONON SCATTERING , 2004 .

[14]  Yaohang Li,et al.  Grid-based Quasi-Monte Carlo Applications , 2005, Monte Carlo Methods Appl..

[15]  Ivan Dimov,et al.  Monte Carlo algorithms: performance analysis for some computer architectures , 1993 .

[16]  G. A. Mikhaĭlov.  New Monte Carlo Methods With Estimating Derivatives , 1995 .