Advanced Search
Article Contents
Article Contents

Some properties of the kinetic equation for electron transport in semiconductors

Abstract Related Papers Cited by
  • The paper studies the kinetic equation for electron transport in semiconductors. New formulas for the heat generation rate are derived by analyzing the basic scattering mechanisms. In addition, properties of the steady state distribution are discussed and possible extensions of the deviational particle Monte Carlo method to the area of electron transport are proposed.
    Mathematics Subject Classification: 82D37, 65C05.


    \begin{equation} \\ \end{equation}
  • [1]

    L. L. Baker and N. G. Hadjiconstantinou, Variance reduction for Monte Carlo solutions of the Boltzmann equation, Phys. Fluids, 17 (2005), 051703.doi: 10.1063/1.1899210.


    M. H. A. Davis, Markov Models and Optimization, Monographs on Statistics and Applied Probability, 49. Chapman & Hall, London, 1993.


    A. Eibeck and W. Wagner, Stochastic interacting particle systems and nonlinear kinetic equations, Ann. Appl. Probab., 13 (2003), 845-889.doi: 10.1214/aoap/1060202829.


    M. V. Fischetti, S. E. Laux, P. M. Solomon and A. Kumar, Thirty years of Monte Carlo simulations of electronic transport in semiconductors: Their relevance to science and mainstream VLSI technology, Journal of Computational Electronics, 3 (2004), 287-293.


    T. M. M. Homolle and N. G. Hadjiconstantinou, Low-variance deviational simulation Monte Carlo, Phys. Fluids, 19 (2007), 041701(1-4).


    C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation, Springer, New York, 1989.doi: 10.1007/978-3-7091-6963-6.


    C. Jacoboni and L. Reggiani, The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials, Rev. Modern Phys., 55 (1983), 645-705.doi: 10.1103/RevModPhys.55.645.


    A. Jüngel, Transport Equations for Semiconductors, vol. 773 of Lecture Notes in Physics, Springer-Verlag, Berlin, 2009.doi: 10.1007/978-3-540-89526-8.


    A. Majorana, Trend to equilibrium of electron gas in a semiconductor according to the Boltzmann equation, Transport Theory Statist. Phys., 27 (1998), 547-571.doi: 10.1080/00411459808205642.


    P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.doi: 10.1007/978-3-7091-6961-2.


    O. Muscato and V. Di Stefano, An energy transport model describing heat generation and conduction in silicon semiconductors, J. Stat. Phys., 144 (2011), 171-197.doi: 10.1007/s10955-011-0247-2.


    O. Muscato and V. Di Stefano, Heat generation and transport in nanoscale semiconductor devices via Monte Carlo and hydrodynamic simulations, COMPEL, 30 (2011), 519-537.doi: 10.1108/03321641111101050.


    O. Muscato, V. Di Stefano and W. Wagner, A variance-reduced electrothermal Monte Carlo method for semiconductor device simulation, Comput. Math. Appl., 65 (2013), 520-527.doi: 10.1016/j.camwa.2012.03.100.


    O. Muscato, W. Wagner and V. Di Stefano, Numerical study of the systematic error in Monte Carlo schemes for semiconductors, M2AN Math. Model. Numer. Anal., 44 (2010), 1049-1068.doi: 10.1051/m2an/2010051.


    O. Muscato, W. Wagner and V. Di Stefano, Properties of the steady state distribution of electrons in semiconductors, Kinetic and Related Models, 4 (2011), 808-829.doi: 10.3934/krm.2011.4.809.


    C. Ni, Z. Aksamija, J. Y. Murthy and U. Ravaioli, Coupled electro-thermal simulation of MOSFETs, Journal of Computational Electronics, 11 (2012), 93-105.


    J.-P. M. Péraud and N. G. Hadjiconstantinou, Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations, Phys. Rev. B, 84 (2011), 205331(1-15).


    J.-P. M. Péraud and N. G. Hadjiconstantinou, An alternative approach to efficient simulation of micro/nanoscale phonon transport, Applied Physics Letters, 101 (2012), 153114(1-4).


    N. J. Pilgrim, W. Batty and R. W. Kelsall, Electrothermal Monte Carlo simulations of InGaAs/AlGaAs HEMTs, Journal of Computational Electronics, 2 (2003), 207-211.doi: 10.1023/B:JCEL.0000011426.11111.64.


    E. Pop, S. Sinha and K. E. Goodson, Heat generation and transport in nanometer-scale transistors, Proceedings of the IEEE, 94 (2006), 1587-1601.doi: 10.1109/JPROC.2006.879794.


    G. A. Radtke, N. G. Hadjiconstantinou and W. Wagner, Low-noise Monte Carlo simulation of the variable hard sphere gas, Phys. Fluids, 23 (2011), 030606.doi: 10.1063/1.3558887.


    K. Raleva, D. Vasileska, S. M. Goodnick and M. Nedjalkov, Modeling thermal effects in nanodevices, IEEE Transactions on Electron Devices, 55 (2008), 1306-1316.doi: 10.1109/TED.2008.921263.


    S. Rjasanow and W. Wagner, Stochastic Numerics for the Boltzmann Equation, Springer Series in Computational Mathematics, 37. Springer-Verlag, Berlin, 2005.


    W. Wagner, Deviational particle Monte Carlo for the Boltzmann equation, Monte Carlo Methods Appl., 14 (2008), 191-268.doi: 10.1515/MCMA.2008.010.

  • 加载中

Article Metrics

HTML views() PDF downloads(58) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint