Transport Equations for Semiconductors

Basic Semiconductor Physics.- Microscopic Semi-Classical Models.- Derivation of Macroscopic Equations.- Collisionless Models.- Scattering Models.- Macroscopic Semi-Classical Models.- Drift-Diffusion Equations.- Energy-Transport Equations.- Spherical Harmonics Expansion Equations.- Diffusive Higher-Order Moment Equations.- Hydrodynamic Equations.- Microscopic Quantum Models.- The Schr#x00F6 dinger Equation.- The Wigner Equation.- Macroscopic Quantum Models.- Quantum Drift-Diffusion Equations.- Quantum Diffusive Higher-Order Moment Equations.- Quantum Hydrodynamic Equations.

[1]  David Enskog,et al.  Kinetische theorie der Vorgänge in Mässig verdünnten Gasen , 1917 .

[2]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

[3]  J. Yvon,et al.  La théorie statistique des fluides et l'équation d'état , 1935 .

[4]  J. Kirkwood.  Errata: Statistical Mechanics of Transport Processes I. General Theory , 1946 .

[5]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[6]  W. V. Roosbroeck.  Theory of the flow of electrons and holes in germanium and other semiconductors , 1950 .

[7]  A. E. D. Barr.  Introduction to Solid State Physics , 1957 .

[8]  N. N. Bogolyubov,et al.  Problems of a Dynamical Theory in Statistical Physics , 1959 .

[9]  R. A. SMITH,et al.  Physics of Semiconductors , 1960, Nature.

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

[11]  Richard L. Longini,et al.  Introduction to Semiconductor Physics , 1965 .

[12]  A. Shepherd,et al.  Semiconductors , 1967, Nature.

[13]  O. H. Hughes,et al.  Semiconductor Physics , 1967, Nature.

[14]  H. Fédérer.  Geometric Measure Theory , 1969 .

[15]  L. Boltzmann.  Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen , 1970 .

[16]  K. Blotekjaer.  Transport equations for electrons in two-valley semiconductors , 1970 .

[17]  S. Chapman,et al.  2 – The Kinetic Theory of Simple and Composite Monatomic Gases: Viscosity, Thermal Conduction, and Diffusion* , 1972 .

[18]  A. Leggett,et al.  Path integral approach to quantum Brownian motion , 1983 .

[19]  B. Ridley.  Quantum Processes in Semiconductors , 1982 .

[20]  P. Carruthers,et al.  Quantum collision theory with phase-space distributions , 1983 .

[21]  G. Baccarani,et al.  An investigation of steady-state velocity overshoot in silicon , 1985 .

[22]  C. Hamaguchi.  Hot electron transport in very short semiconductors , 1985 .

[23]  L. Reggiani,et al.  Hot-Electron Transport in Semiconductors , 1985 .

[24]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[25]  F. Poupaud.  Etude mathematique et simulations numeriques de quelques equations de boltzmann , 1988 .

[26]  Christian Ringhofer,et al.  An Analysis of the Quantum Liouville Equation , 1989 .

[27]  H. Neunzert,et al.  On the equivalence of the Schrödinger and the quantum Liouville equations , 1989 .

[28]  P. Lions,et al.  On the Cauchy problem for Boltzmann equations: global existence and weak stability , 1989 .

[29]  F. Poupaud,et al.  On a system of nonlinear Boltzmann equations of semiconductor physics , 1990 .

[30]  C. Schmeiser,et al.  Semiconductor equations , 1990 .

[31]  Craig S. Lent,et al.  The quantum transmitting boundary method , 1990 .

[32]  M. Lundstrom.  Fundamentals of carrier transport , 1990 .

[33]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[34]  F. Poupaud,et al.  Diffusion approximation of the linear semiconductor Boltzmann equation : analysis of boundary layers , 1991 .

[35]  R. J. DiPerna,et al.  Global solutions of Boltzmann's equation and the entropy inequality , 1991 .

[36]  F. Golse,et al.  Fluid dynamic limits of kinetic equations. I. Formal derivations , 1991 .

[37]  N. Goldsman,et al.  A physics-based analytical/numerical solution to the Boltzmann transport equation for use in device simulation , 1991 .

[38]  D. Neamen.  Semiconductor physics and devices , 1992 .

[39]  P. Dmitruk,et al.  High electric field approximation to charge transport in semiconductor devices , 1992 .

[40]  A. Gnudi,et al.  Two-dimensional NOSFET Simulation by means of Multidimensional Spherical Harmonics Expansion of the Boltzmann Transport Equation , 1992, ESSDERC '92: 22nd European Solid State Device Research conference.

[41]  U. Ravaioli,et al.  An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects , 1992, IEEE Electron Device Letters.

[42]  François Golse,et al.  Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation , 1993 .

[43]  S. Varadhan,et al.  Nonequilibrium Problems in Many-Particle Systems , 1993 .

[44]  B. Perthame.  Advances in Kinetic Theory and Computing: Selected Papers , 1994, Series on Advances in Mathematics for Applied Sciences.

[45]  H. Grubin,et al.  Modeling of Quantum Transport in Semiconductor Devices , 1994 .

[46]  Quantum hydrodynamic models in semiconductor crystals , 1995 .

[47]  P. Degond,et al.  An energy-transport model for semiconductors derived from the Boltzmann equation , 1996 .

[48]  F. Poupaud.  Mathematical Theory of Kinetic Equations for Transport Modelling in Semiconductors , 1996 .

[49]  Pierre Degond,et al.  On a hierarchy of macroscopic models for semiconductors , 1996 .

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

[51]  Christian Ringhofer.  Computational methods for semiclassical and quantum transport in semiconductor devices , 1997, Acta Numerica.

[52]  C. David Levermore,et al.  Entropy-based moment closures for kinetic equations , 1997 .

[53]  Christian Schmeiser,et al.  ELASTIC AND DRIFT–DIFFUSION LIMITS OF ELECTRON–PHONON INTERACTION IN SEMICONDUCTORS , 1998 .

[54]  H. Babovsky,et al.  Die Boltzmann-Gleichung: Modellbildung — Numerik — Anwendungen , 1998 .

[55]  W. T. Wenckebach.  Essentials of Semiconductor Physics , 1999 .

[56]  Z. Xin,et al.  Some Current Topics on Nonlinear Conservation Laws , 2000 .

[57]  L. Erdős,et al.  Fokker–Planck Equations as Scaling Limits of Reversible Quantum Systems , 2000 .

[58]  Ansgar Jüngel,et al.  Numerical Discretization of Energy-Transport Models for Semiconductors with Nonparabolic Band Structure , 2000, SIAM J. Sci. Comput..

[59]  David Swanson,et al.  The co-area formula for Sobolev mappings , 2001 .

[60]  C. Villani.  Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory , 2002 .

[61]  M. Czubak,et al.  PSEUDODIFFERENTIAL OPERATORS , 2020, Introduction to Partial Differential Equations.

[62]  François Golse,et al.  Chapter 3 - The Boltzmann Equation and Its Hydrodynamic Limits , 2005 .

[63]  Pierre Degond,et al.  Quantum Energy-Transport and Drift-Diffusion Models , 2005 .

[64]  P. Degond,et al.  Mathematical Modelling of Microelectronics Semiconductor Devices Acknowledgments: This Work Originates from Lecture Notes of Courses , 2022 .

[65]  F. V..  Carrier Scattering in Metals and Semiconductors , 2022 .