Semiconductor Equations
This book contains the first unified account of the currently used mathematical models for charge transport in semiconductor devices. It is focussed on a presentation of a hierarchy of models ranging from kinetic quantum transport equations to the classical drift diffusion equations. Particular emphasis is given to the derivation of the models, an analysis of the solution structure, and an explanation of the most important devices. The relations between the different models and the physical assumptions needed for their respective validity are clarified. The book addresses applied mathematicians, electrical engineers and solid-state physicists. It is accessible to graduate students in each of the three fields, since mathematical details are replaced by references to the literature to a large extent. It provides a reference text for researchers in the field as well as a text for graduate courses and seminars
1 online resource (x, 248 pages 33 illustrations)
9783709169612, 3709169615
840302816
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
English
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