-
Previous Article
Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension
- KRM Home
- This Issue
-
Next Article
Convex analysis and thermodynamics
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. |
| [1] |
Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano. Properties of the steady state distribution of electrons in semiconductors. Kinetic and Related Models, 2011, 4 (3) : 809-829. doi: 10.3934/krm.2011.4.809 |
| [2] |
Giacomo Dimarco. The moment guided Monte Carlo method for the Boltzmann equation. Kinetic and Related Models, 2013, 6 (2) : 291-315. doi: 10.3934/krm.2013.6.291 |
| [3] |
Zhiyan Ding, Qin Li. Constrained Ensemble Langevin Monte Carlo. Foundations of Data Science, 2022, 4 (1) : 37-70. doi: 10.3934/fods.2021034 |
| [4] |
Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems and Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81 |
| [5] |
Ajay Jasra, Kody J. H. Law, Yaxian Xu. Markov chain simulation for multilevel Monte Carlo. Foundations of Data Science, 2021, 3 (1) : 27-47. doi: 10.3934/fods.2021004 |
| [6] |
Theodore Papamarkou, Alexey Lindo, Eric B. Ford. Geometric adaptive Monte Carlo in random environment. Foundations of Data Science, 2021, 3 (2) : 201-224. doi: 10.3934/fods.2021014 |
| [7] |
Youcef Mammeri, Damien Sellier. A surface model of nonlinear, non-steady-state phloem transport. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1055-1069. doi: 10.3934/mbe.2017055 |
| [8] |
Michael B. Giles, Kristian Debrabant, Andreas Rössler. Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3881-3903. doi: 10.3934/dcdsb.2018335 |
| [9] |
Jiakou Wang, Margaret J. Slattery, Meghan Henty Hoskins, Shile Liang, Cheng Dong, Qiang Du. Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow. Mathematical Biosciences & Engineering, 2006, 3 (4) : 683-696. doi: 10.3934/mbe.2006.3.683 |
| [10] |
Johannes Giannoulis. Transport and generation of macroscopically modulated waves in diatomic chains. Conference Publications, 2011, 2011 (Special) : 485-494. doi: 10.3934/proc.2011.2011.485 |
| [11] |
Chjan C. Lim, Joseph Nebus, Syed M. Assad. Monte-Carlo and polyhedron-based simulations I: extremal states of the logarithmic N-body problem on a sphere. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 313-342. doi: 10.3934/dcdsb.2003.3.313 |
| [12] |
Joseph Nebus. The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 125-136. doi: 10.3934/dcdsb.2005.5.125 |
| [13] |
Olli-Pekka Tossavainen, Daniel B. Work. Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data. Networks and Heterogeneous Media, 2013, 8 (3) : 803-824. doi: 10.3934/nhm.2013.8.803 |
| [14] |
Mazyar Zahedi-Seresht, Gholam-Reza Jahanshahloo, Josef Jablonsky, Sedighe Asghariniya. A new Monte Carlo based procedure for complete ranking efficient units in DEA models. Numerical Algebra, Control and Optimization, 2017, 7 (4) : 403-416. doi: 10.3934/naco.2017025 |
| [15] |
Yuxiang Li. Stabilization towards the steady state for a viscous Hamilton-Jacobi equation. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1917-1924. doi: 10.3934/cpaa.2009.8.1917 |
| [16] |
Piotr Zgliczyński. Steady state bifurcations for the Kuramoto-Sivashinsky equation: A computer assisted proof. Journal of Computational Dynamics, 2015, 2 (1) : 95-142. doi: 10.3934/jcd.2015.2.95 |
| [17] |
Daniel Ginsberg, Gideon Simpson. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1305-1321. doi: 10.3934/dcdsb.2013.18.1305 |
| [18] |
Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 57-71. doi: 10.3934/dcdsb.2011.16.57 |
| [19] |
Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation. Evolution Equations and Control Theory, 2015, 4 (1) : 39-59. doi: 10.3934/eect.2015.4.39 |
| [20] |
Li Chen, Xiu-Qing Chen, Ansgar Jüngel. Semiclassical limit in a simplified quantum energy-transport model for semiconductors. Kinetic and Related Models, 2011, 4 (4) : 1049-1062. doi: 10.3934/krm.2011.4.1049 |
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]