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Field name	Details
Dewey Class	515
Title	Semiconductor Equations ([EBook] /) / by Peter A. Markowich, Christian A. Ringhofer, Christian Schmeiser.
Author	Markowich, Peter A.
Added Personal Name	Ringhofer, Christian A. author.
Added Personal Name	Schmeiser, Christian author.
Other name(s)	SpringerLink (Online service)
Publication	Vienna : : Springer Vienna, , 1990.
Physical Details	X, 248 p. : online resource.
ISBN	9783709169612
Summary Note	In recent years the mathematical modeling of charge transport in semi conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simula tion of the electrical behavior of semiconductor devices, are by now mathe matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffu sion model is of a highly specialized nature. It concentrates on the explora tion of possibly more efficient discretization methods (e.g. mixed finite elements, streamline diffusion), on the improvement of the performance of nonlinear iteration and linear equation solvers, and on three dimensional applications. The ongoing miniaturization of semiconductor devices has prompted a shift of the focus of the modeling research lately, since the drift diffusion model does not account well for charge transport in ultra integrated devices. Extensions of the drift diffusion model (so called hydrodynamic models) are under investigation for the modeling of hot electron effects in submicron MOS-transistors, and supercomputer technology has made it possible to employ kinetic models (semiclassical Boltzmann-Poisson and Wigner Poisson equations) for the simulation of certain highly integrated devices.:
Contents note	1 Kinetic Transport Models for Semiconductors -- 1.1 Introduction -- 1.2 The (Semi-)Classical Liouville Equation -- 1.3 The Boltzmann Equation -- 1.4 The Quantum Liouville Equation -- 1.5 The Quantum Boltzmann Equation -- 1.6 Applications and Extensions -- Problems -- References -- 2 From Kinetic to Fluid Dynamical Models -- 2.1 Introduction -- 2.2 Small Mean Free Path—The Hilbert Expansion -- 2.3 Moment Methods—The Hydrodynamic Model -- 2.4 Heavy Doping Effects—Fermi-Dirac Distributions -- 2.5 High Field Effects—Mobility Models -- 2.6 Recombination-Generation Models -- Problems -- References -- 3 The Drift Diffusion Equations -- 3.1 Introduction -- 3.2 The Stationary Drift Diffusion Equations -- 3.3 Existence and Uniqueness for the Stationary Drift Diffusion Equations -- 3.4 Forward Biased P-N Junctions -- 3.5 Reverse Biased P-N Junctions -- 3.6 Stability and Conditioning for the Stationary Problem -- 3.7 The Transient Problem -- 3.8 The Linearization of the Transient Problem -- 3.9 Existence for the Nonlinear Problem -- 3.10 Asymptotic Expansions on the Diffusion Time Scale -- 3.11 Fast Time Scale Expansions -- Problems -- References -- 4 Devices -- 4.1 Introduction -- 4.2 P-N Diode -- 4.3 Bipolar Transistor -- 4.4 PIN-Diode -- 4.5 Thyristor -- 4.6 MIS Diode -- 4.7 MOSFET -- 4.8 Gunn Diode -- Problems -- References -- Physical Constants -- Properties of Si at Room Temperature.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-7091-6961-2
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Chemometrics . Computational Intelligence . Electrodynamics . Electronics . Electronics and Microelectronics, Instrumentation . Math. Applications in Chemistry . Mathematical analysis . Mathematics . Microelectronics . Optics . Optics and Electrodynamics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Markowich, Peter A. . Ringhofer, Christian A. . Schmeiser, Christian . Corporate Authors: SpringerLink (Online service) . Classification: 515 .

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Semiconductor Equations

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