Exact Maximum Entropy Closure of the Hydrodynamical Model for Si Semiconductors: The 8-Moment Case

An exact closure is obtained of the 8-moment model for semiconductors based on the maximum entropy principle in the case of silicon semiconductors. The validity of the model is assessed, and comparisons with an approximate closure are presented and discussed.

[1]  A. M. Anile,et al.  Recent Developments in Hydrodynamical Modeling of Semiconductors , 2003 .

[2]  Michael Junk,et al.  MAXIMUM ENTROPY FOR REDUCED MOMENT PROBLEMS , 2000 .

[3]  Stanley Osher,et al.  Solution of the hydrodynamic device model using high-order nonoscillatory shock capturing algorithms , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  C. Milazzo,et al.  Charge transport in 1D silicon devices via Monte Carlo simulation and Boltzmann‐Poisson solver , 2004 .

[5]  V. Romano Non‐parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices , 2001 .

[6]  K. Tomizawa,et al.  Numerical simulation of submicron semiconductor devices , 1993 .

[7]  Nailong Wu The Maximum Entropy Method , 1997 .

[8]  Michael Junk,et al.  Domain of Definition of Levermore's Five-Moment System , 1998 .

[9]  I. Müller,et al.  Rational Extended Thermodynamics , 1993 .

[10]  Vittorio Romano,et al.  Simulation of Gunn oscillations with a non‐parabolic hydrodynamical model based on the maximum entropy principle , 2005 .

[11]  Donald J. Rose,et al.  Numerical methods for the hydrodynamic device model: subsonic flow , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[12]  Armando Majorana Equilibrium solutions of the non-linear Boltzmann equation for an electron gas in a semiconductor , 1993 .

[13]  E. Tadmor,et al.  New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations , 2000 .

[14]  E. Tadmor,et al.  Non-oscillatory central differencing for hyperbolic conservation laws , 1990 .

[15]  G. Russo,et al.  NUMERICAL SOLUTION FOR HYDRODYNAMICAL MODELS OF SEMICONDUCTORS , 2000 .

[16]  Vittorio Romano,et al.  Extended Hydrodynamical Model of Carrier Transport in Semiconductors , 2000, SIAM J. Appl. Math..

[17]  Vittorio Romano,et al.  Central Schemes for Balance Laws of Relaxation Type , 2000, SIAM J. Numer. Anal..

[18]  Vittorio Romano 2D numerical simulation of the MEP energy-transport model with a finite difference scheme , 2007, J. Comput. Phys..

[19]  Vittorio Romano,et al.  Non parabolic band transport in semiconductors: closure of the moment equations , 1999 .

[20]  C. Jacoboni,et al.  Electron drift velocity in silicon , 1975 .

[21]  Anile,et al.  Improved hydrodynamical model for carrier transport in semiconductors. , 1995, Physical review. B, Condensed matter.

[22]  Alexander Kurganov,et al.  Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations , 2001, SIAM J. Sci. Comput..

[23]  A. M. Anile,et al.  Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors , 2000 .

[24]  V. Romano,et al.  Hydrodynamical model of charge transport in GaAs based on the maximum entropy principle , 2002 .

[25]  Carl L. Gardner,et al.  Numerical simulation of a steady-state electron shock wave in a submicrometer semiconductor device , 1991 .

[26]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[27]  S. Osher,et al.  Uniformly High-Order Accurate Nonoscillatory Schemes. I , 1987 .

[28]  C. D. Levermore,et al.  Moment closure hierarchies for kinetic theories , 1996 .

[29]  M. Junk,et al.  Maximum entropy moment system of the semiconductor Boltzmann equation using Kane’s dispersion relation , 2005 .

[30]  G. Lebon,et al.  Extended irreversible thermodynamics , 1993 .

[31]  R. LeVeque Numerical methods for conservation laws , 1990 .

[32]  G. V. Chester,et al.  Solid State Physics , 2000 .

[33]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[34]  V. Romano Non parabolic band transport in semiconductors: closure of the production terms in the moment equations , 2000 .

[35]  Irene M. Gamba,et al.  A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods , 2003 .