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Some properties of the kinetic equation for electron transport in semiconductors
1. | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39 - 10117 Berlin |
References:
[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. |
[2] |
M. H. A. Davis, Markov Models and Optimization, Monographs on Statistics and Applied Probability, 49. Chapman & Hall, London, 1993. |
[3] |
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. |
[4] |
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. |
[5] |
T. M. M. Homolle and N. G. Hadjiconstantinou, Low-variance deviational simulation Monte Carlo, Phys. Fluids, 19 (2007), 041701(1-4). |
[6] |
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. |
[7] |
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. |
[8] |
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. |
[9] |
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. |
[10] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[11] |
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. |
[12] |
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. |
[13] |
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. |
[14] |
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. |
[15] |
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. |
[16] |
C. Ni, Z. Aksamija, J. Y. Murthy and U. Ravaioli, Coupled electro-thermal simulation of MOSFETs, Journal of Computational Electronics, 11 (2012), 93-105. |
[17] |
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). |
[18] |
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). |
[19] |
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. |
[20] |
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. |
[21] |
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. |
[22] |
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. |
[23] |
S. Rjasanow and W. Wagner, Stochastic Numerics for the Boltzmann Equation, Springer Series in Computational Mathematics, 37. Springer-Verlag, Berlin, 2005. |
[24] |
W. Wagner, Deviational particle Monte Carlo for the Boltzmann equation, Monte Carlo Methods Appl., 14 (2008), 191-268.
doi: 10.1515/MCMA.2008.010. |
show all references
References:
[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. |
[2] |
M. H. A. Davis, Markov Models and Optimization, Monographs on Statistics and Applied Probability, 49. Chapman & Hall, London, 1993. |
[3] |
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. |
[4] |
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. |
[5] |
T. M. M. Homolle and N. G. Hadjiconstantinou, Low-variance deviational simulation Monte Carlo, Phys. Fluids, 19 (2007), 041701(1-4). |
[6] |
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. |
[7] |
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. |
[8] |
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. |
[9] |
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. |
[10] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[11] |
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. |
[12] |
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. |
[13] |
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. |
[14] |
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. |
[15] |
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. |
[16] |
C. Ni, Z. Aksamija, J. Y. Murthy and U. Ravaioli, Coupled electro-thermal simulation of MOSFETs, Journal of Computational Electronics, 11 (2012), 93-105. |
[17] |
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). |
[18] |
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). |
[19] |
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. |
[20] |
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. |
[21] |
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. |
[22] |
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. |
[23] |
S. Rjasanow and W. Wagner, Stochastic Numerics for the Boltzmann Equation, Springer Series in Computational Mathematics, 37. Springer-Verlag, Berlin, 2005. |
[24] |
W. Wagner, Deviational particle Monte Carlo for the Boltzmann equation, Monte Carlo Methods Appl., 14 (2008), 191-268.
doi: 10.1515/MCMA.2008.010. |
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