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E-raamat: Physics of Semiconductor Devices

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  • Ilmumisaeg: 11-Dec-2014
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493911516
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Physics of Semiconductor DevicesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Dec-2014
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781493911516
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This book describes the basic physics of semiconductors, including the hierarchy of transport models, and connects the theory with the functioning of actual semiconductor devices. Details are worked out carefully and derived from the basic physics, while keeping the internal coherence of the concepts and explaining various levels of approximation. Examples are based on silicon due to its industrial importance. Several chapters are included that provide the reader with the quantum-mechanical concepts necessary for understanding the transport properties of crystals. The behavior of crystals incorporating a position-dependent impurity distribution is described, and the different hierarchical transport models for semiconductor devices are derived (from the Boltzmann transport equation to the hydrodynamic and drift-diffusion models). The transport models are then applied to a detailed description of the main semiconductor-device architectures (bipolar, MOS). The final chapters are devoted to the description of some basic fabrication steps, and to measuring methods for the semiconductor-device parameters.

Part I A Review of Analytical Mechanics and Electromagnetism
1 Analytical Mechanics
3(22)
1.1 Introduction
3(1)
1.2 Variational Calculus
4(2)
1.3 Lagrangian Function
6(4)
1.3.1 Force Deriving from a Potential Energy
7(1)
1.3.2 Electromagnetic Force
7(2)
1.3.3 Work
9(1)
1.3.4 Hamilton Principle-Synchronous Trajectories
10(1)
1.4 Generalized Coordinates
10(2)
1.5 Hamiltonian Function
12(1)
1.6 Hamilton Equations
13(2)
1.7 Time-Energy Conjugacy-Hamilton-Jacobi Equation
15(2)
1.8 Poisson Brackets
17(1)
1.9 Phase Space and State Space
18(1)
1.10 Complements
19(4)
1.10.1 Higher-Order Variational Calculus
19(1)
1.10.2 Lagrangian Invariance and Gauge Invariance
20(1)
1.10.3 Variational Calculus with Constraints
20(1)
1.10.4 An Interesting Example of Extremum Equation
21(2)
1.10.5 Constant-Energy Surfaces
23(1)
Problems
23(2)
2 Coordinate Transformations and Invariance Properties
25(18)
2.1 Introduction
25(1)
2.2 Canonical Transformations
26(3)
2.3 An Application of the Canonical Transformation
29(1)
2.4 Separation-Hamilton's Characteristic Function
30(1)
2.5 Phase Velocity
31(1)
2.6 Invariance Properties
32(3)
2.6.1 Time Reversal
32(1)
2.6.2 Translation of Time
33(1)
2.6.3 Translation of the Coordinates
33(1)
2.6.4 Rotation of the Coordinates
34(1)
2.7 Maupertuis Principle
35(1)
2.8 Spherical Coordinates-Angular Momentum
36(2)
2.9 Linear Motion
38(1)
2.10 Action-Angle Variables
39(2)
2.11 Complements
41(1)
2.11.1 Infinitesimal Canonical Transformations
41(1)
2.11.2 Constants of Motion
41(1)
Problems
42(1)
3 Applications of the Concepts of Analytical Mechanics
43(28)
3.1 Introduction
43(1)
3.2 Particle in a Square Well
43(1)
3.3 Linear Harmonic Oscillator
44(1)
3.4 Central Motion
45(2)
3.5 Two-Particle Collision
47(2)
3.6 Energy Exchange in the Two-Particle Collision
49(2)
3.7 Central Motion in the Two-Particle Interaction
51(1)
3.8 Coulomb Field
52(1)
3.9 System of Particles near an Equilibrium Point
53(2)
3.10 Diagonalization of the Hamiltonian Function
55(2)
3.11 Periodic Potential Energy
57(3)
3.12 Energy-Momentum Relation in a Periodic Potential Energy
60(1)
3.13 Complements
61(9)
3.13.1 Comments on the Linear Harmonic Oscillator
61(1)
3.13.2 Degrees of Freedom and Coordinate Separation
61(1)
3.13.3 Comments on the Normal Coordinates
62(1)
3.13.4 Areal Velocity in the Central-Motion Problem
63(1)
3.13.5 Initial Conditions in the Central-Motion Problem
64(1)
3.13.6 The Coulomb Field in the Attractive Case
65(2)
3.13.7 Dynamic Relations of Special Relativity
67(1)
3.13.8 Collision of Relativistic Particles
68(2)
3.13.9 Energy Conservation in Charged-Particles' Interaction
70(1)
Problems
70(1)
4 Electromagnetism
71(16)
4.1 Introduction
71(1)
4.2 Extension of the Lagrangian Formalism
71(3)
4.3 Lagrangian Function for the Wave Equation
74(1)
4.4 Maxwell Equations
75(2)
4.5 Potentials and Gauge Transformations
77(2)
4.6 Lagrangian Density for the Maxwell Equations
79(1)
4.7 Helmholtz Equation
80(1)
4.8 Helmholtz Equation in a Finite Domain
81(1)
4.9 Solution of the Helmholtz Equation in an Infinite Domain
82(1)
4.10 Solution of the Wave Equation in an Infinite Domain
83(1)
4.11 Lorentz Force
84(1)
4.12 Complements
85(1)
4.12.1 Invariance of the Euler Equations
85(1)
4.12.2 Wave Equations for the E and B Fields
85(1)
4.12.3 Comments on the Boundary-Value Problem
86(1)
Problems
86(1)
5 Applications of the Concepts of Electromagnetism
87(24)
5.1 Introduction
87(1)
5.2 Potentials Generated by a Point-Like Charge
87(2)
5.3 Energy Continuity-Poynting Vector
89(1)
5.4 Momentum Continuity
90(1)
5.5 Modes of the Electromagnetic Field
91(2)
5.6 Energy of the Electromagnetic Field in Terms of Modes
93(2)
5.7 Momentum of the Electromagnetic Field in Terms of Modes
95(1)
5.8 Modes of the Electromagnetic Field in an Infinite Domain
96(1)
5.9 Eikonal Equation
97(2)
5.10 Fermat Principle
99(1)
5.11 Complements
99(8)
5.11.1 Fields Generated by a Point-Like Charge
99(2)
5.11.2 Power Radiated by a Point-Like Charge
101(1)
5.11.3 Decay of Atoms According to the Classical Model
102(2)
5.11.4 Comments about the Field's Expansion into Modes
104(1)
5.11.5 Finiteness of the Total Energy
105(1)
5.11.6 Analogies between Mechanics and Geometrical Optics
106(1)
Problems
107(4)
Part II Introductory Concepts to Statistical and Quantum Mechanics
6 Classical Distribution Function and Transport Equation
111(18)
6.1 Introduction
111(1)
6.2 Distribution Function
111(2)
6.3 Statistical Equilibrium
113(3)
6.4 Maxwell-Boltzmann Distribution
116(3)
6.5 Boltzmann Transport Equation
119(1)
6.6 Complements
120(7)
6.6.1 Momentum and Angular Momentum at Equilibrium
120(1)
6.6.2 Averages Based on the Maxwell-Boltzmann Distribution
121(2)
6.6.3 Boltzmann's H-Theorem
123(1)
6.6.4 Paradoxes - Kac-Ring Model
124(1)
6.6.5 Equilibrium Limit of the Boltzmann Transport Equation
125(2)
Problems
127(2)
7 From Classical Mechanics to Quantum Mechanics
129(26)
7.1 Introduction
129(1)
7.2 Planetary Model of the Atom
130(4)
7.3 Experiments Contradicting the Classical Laws
134(6)
7.4 Quantum Hypotheses
140(7)
7.4.1 Planck's Solution of the Black-Body Problem
141(1)
7.4.2 Einstein's Solution of the Photoelectric Effect
142(1)
7.4.3 Explanation of the Compton Effect
142(1)
7.4.4 Bohr's Hypothesis
143(2)
7.4.5 De Broglie's Hypothesis
145(2)
7.5 Heuristic Derivation of the Schrodinger Equation
147(2)
7.6 Measurement
149(4)
7.6.1 Probabilities
150(2)
7.6.2 Massive Bodies
152(1)
7.6.3 Need of a Description of Probabilities
153(1)
7.7 Born's Interpretation of the Wave Function
153(1)
7.8 Complements
154(1)
7.8.1 Core Electrons
154(1)
8 Time-Independent Schrodinger Equation
155(20)
8.1 Introduction
155(1)
8.2 Properties of the Time-Independent Schrodinger Equation
155(5)
8.2.1 Schrodinger Equation for a Free Particle
157(1)
8.2.2 Schrodinger Equation for a Particle in a Box
158(1)
8.2.3 Lower Energy Bound in the Schrodinger Equation
159(1)
8.3 Norm of a Function-Scalar Product
160(2)
8.3.1 Adjoint Operators and Hermitean Operators
162(1)
8.4 Eigenvalues and Eigenfunctions of an Operator
162(6)
8.4.1 Eigenvalues of Hermitean Operators
163(1)
8.4.2 Gram-Schmidt Orthogonalization
164(1)
8.4.3 Completeness
165(2)
8.4.4 Parseval Theorem
167(1)
8.5 Hamiltonian Operator and Momentum Operator
168(1)
8.6 Complements
169(5)
8.6.1 Examples of Hermitean Operators
169(1)
8.6.2 A Collection of Operators' Definitions and Properties
170(3)
8.6.3 Examples of Commuting Operators
173(1)
8.6.4 Momentum and Energy of a Free Particle
173(1)
Problems
174(1)
9 Time-Dependent Schrodinger Equation
175(12)
9.1 Introduction
175(1)
9.2 Superposition Principle
175(3)
9.3 Time-Dependent Schrodinger Equation
178(1)
9.4 Continuity Equation and Norm Conservation
179(1)
9.5 Hamiltonian Operator of a Charged Particle
180(1)
9.6 Approximate Form of the Wave Packet for a Free Particle
181(2)
9.7 Complements
183(3)
9.7.1 About the Units of the Wave Function
183(1)
9.7.2 An Application of the Semiclassical Approximation
183(1)
9.7.3 Polar Form of the Schrodinger Equation
184(1)
9.7.4 Effect of a Gauge Transformation on the Wave Function
185(1)
Problems
186(1)
10 General Methods of Quantum Mechanics
187(14)
10.1 Introduction
187(1)
10.2 General Methods
187(2)
10.3 Separable Operators
189(1)
10.4 Eigenfunctions of Commuting Operators
190(2)
10.5 Expectation Value and Uncertainty
192(1)
10.6 Heisenberg Uncertainty Relation
193(1)
10.7 Time Derivative of the Expectation Value
194(1)
10.8 Ehrenfest Theorem
195(1)
10.9 Complements
196(1)
10.9.1 Minimum-Uncertainty Wave Function
196(1)
Problems
197(4)
Part III Applications of the Schrodinger Equation
11 Elementary Cases
201(16)
11.1 Introduction
201(1)
11.2 Step-Like Potential Energy
201(5)
11.2.1 Case A: 0 < E < Vo
202(1)
11.2.2 Case B: E > V0
203(3)
11.3 Energy Barrier
206(4)
11.3.1 Case A: 0 < E < V0
206(2)
11.3.2 Case B: 0 < V0 < E
208(2)
11.4 Energy Barrier of a General Form
210(3)
11.5 Energy Well
213(2)
Problems
215(2)
12 Cases Related to the Linear Harmonic Oscillator
217(10)
12.1 Introduction
217(1)
12.2 Linear Harmonic Oscillator
217(4)
12.3 Quantization of the Electromagnetic Field's Energy
221(2)
12.4 Quantization of the Electromagnetic Field's Momentum
223(1)
12.5 Quantization of a Diagonalized Hamiltonian Function
224(1)
12.6 Complements
225(2)
12.6.1 Comments About the Linear Harmonic Oscillator
225(2)
13 Other Examples of the Schrodinger Equation
227(26)
13.1 Introduction
227(1)
13.2 Properties of the One-Dimensional Schrodinger Equation
227(2)
13.3 Localized States-Operator's Factorization
229(5)
13.3.1 Factorization Method
229(2)
13.3.2 First-Order Operators
231(1)
13.3.3 The Eigenfunctions Corresponding to 1 < n
232(1)
13.3.4 Normalization
233(1)
13.4 Schrodinger Equation with a Periodic Coefficient
234(2)
13.5 Schrodinger Equation for a Central Force
236(4)
13.5.1 Angular Part of the Equation
237(2)
13.5.2 Radial Part of the Equation in the Coulomb Case
239(1)
13.6 Complements
240(11)
13.6.1 Operators Associated to Angular Momentum
240(2)
13.6.2 Eigenvalues of the Angular Equation
242(1)
13.6.3 Eigenfunctions of the Angular Equation
243(3)
13.6.4 Eigenvalues of the Radial Equation-Coulomb Case
246(1)
13.6.5 Eigenfunctions of the Radial Equation-Coulomb Case
247(1)
13.6.6 Transmission Matrix
248(3)
Problems
251(2)
14 Time-Dependent Perturbation Theory
253(16)
14.1 Introduction
253(1)
14.2 Discrete Eigenvalues
254(1)
14.3 First-Order Perturbation
255(1)
14.4 Comments
256(1)
14.5 Degenerate Energy Levels
257(1)
14.6 Continuous Energy Levels
258(3)
14.7 Screened Coulomb Perturbation
261(1)
14.8 Complements
262(3)
14.8.1 Perturbation Constant in Time
262(1)
14.8.2 Harmonic Perturbation
263(2)
14.8.3 Fermi's Golden Rule
265(1)
14.8.4 Transitions from Discrete to Continuous Levels
265(1)
Problems
265(4)
Part IV Systems of Interacting Particles-Quantum Statistics
15 Many-Particle Systems
269(24)
15.1 Introduction
269(1)
15.2 Wave Function of a Many-Particle System
269(2)
15.3 Symmetry of Functions and Operators
271(1)
15.4 Conservation of Symmetry in Time
272(1)
15.5 Identical Particles
273(4)
15.5.1 Spin
275(2)
15.6 Pauli Exclusion Principle
277(1)
15.7 Conservative Systems of Particles
278(2)
15.8 Equilibrium Statistics in the Quantum Case
280(6)
15.8.1 Fermi-Dirac Statistics
283(2)
15.8.2 Bose-Einstein Statistics
285(1)
15.9 Complements
286(6)
15.9.1 Connection with Thermodynamic Functions
286(1)
15.9.2 Density of States for a Particle in a Three-Dimensional Box
287(2)
15.9.3 Density of States for a Two- or One-Dimensional Box
289(1)
15.9.4 Density of States for Photons
290(1)
15.9.5 Derivation of Planck's Law
291(1)
Problems
292(1)
16 Separation of Many-Particle Systems
293(12)
16.1 Introduction
293(1)
16.2 System of Interacting Electrons and Nuclei
294(1)
16.3 Adiabatic Approximation
295(2)
16.4 Hartree Equations
297(2)
16.5 Hartree-Fock Equations
299(1)
16.6 Schrodinger Equation for the Nuclei
300(1)
16.7 Complements
301(4)
16.7.1 Ritz Method
301(4)
Part V Applications to Semiconducting Crystals
17 Periodic Structures
305(64)
17.1 Introduction
305(1)
17.2 Bravais Lattice
306(3)
17.3 Reciprocal Lattice
309(2)
17.4 Wigner-Seitz Cell-Brillouin Zone
311(1)
17.5 Translation Operators
312(6)
17.5.1 Bloch Theorem
314(1)
17.5.2 Periodic Operators
315(1)
17.5.3 Periodic Boundary Conditions
316(2)
17.6 Schrodinger Equation in a Periodic Lattice
318(26)
17.6.1 Wave Packet in a Periodic Potential
321(1)
17.6.2 Parabolic-Band Approximation
322(4)
17.6.3 Density of States in the Parabolic-Band Approximation
326(1)
17.6.4 Crystals of Si, Ge, and GaAs
327(1)
17.6.5 Band Structure of Si, Ge, and GaAs
328(7)
17.6.6 Further Comments About the Band Structure
335(2)
17.6.7 Subbands
337(2)
17.6.8 Subbands in a Periodic Lattice
339(5)
17.7 Calculation of Vibrational Spectra
344(7)
17.7.1 Labeling the Degrees of Freedom- Dynamic Matrix
346(1)
17.7.2 Application of the Bloch Theorem
347(2)
17.7.3 Properties of the Eigenvalues and Eigenvectors
349(2)
17.8 Complements
351(18)
17.8.1 Crystal Planes and Directions in Cubic Crystals
351(2)
17.8.2 Examples of Translation Operators
353(1)
17.8.3 Symmetries of the Hamiltonian Operator
354(2)
17.8.4 Kronig-Penney Model
356(4)
17.8.5 Linear, Monatomic Chain
360(3)
17.8.6 Linear, Diatomic Chain
363(4)
17.8.7 Analogies
367(2)
18 Electrons and Holes in Semiconductors at Equilibrium
369(34)
18.1 Introduction
369(1)
18.2 Equilibrium Concentration of Electrons and Holes
370(4)
18.3 Intrinsic Concentration
374(3)
18.4 Uniform Distribution of Impurities
377(14)
18.4.1 Donor-Type Impurities
379(6)
18.4.2 Acceptor-Type Impurities
385(5)
18.4.3 Compensation Effect
390(1)
18.5 Non-Uniform Distribution of Dopants
391(2)
18.6 Band-Gap Narrowing
393(3)
18.7 Complements
396(7)
18.7.1 Si, Ge, GaAs in the Manufacturing of Integrated Circuits
396(1)
18.7.2 Qualitative Analysis of the Impurity Levels
397(1)
18.7.3 Position of the Impurity Levels
398(5)
Part VI Transport Phenomena in Semiconductors
19 Mathematical Model of Semiconductor Devices
403(48)
19.1 Introduction
403(1)
19.2 Equivalent Hamiltonian Operator
404(7)
19.2.1 Electron Dynamics
405(2)
19.2.2 Expectation Values-Crystal Momentum
407(2)
19.2.3 Dynamics in the Parabolic-Band Approximation
409(2)
19.3 Dynamics in the Phase Space
411(8)
19.3.1 Collision Term
413(3)
19.3.2 Point-Like Collisions
416(2)
19.3.3 Perturbative Form of the BTE
418(1)
19.4 Moments Expansion of the BTE
419(10)
19.4.1 Moment Equations
422(3)
19.4.2 Hierarchical Models
425(4)
19.5 Hydrodynamic and Drift-Diffusion Models
429(15)
19.5.1 HD Model
430(1)
19.5.2 DD Model
431(3)
19.5.3 DD Model for the Valence Band
434(2)
19.5.4 Coupling with Maxwell's Equations
436(2)
19.5.5 Semiconductor-Device Model
438(1)
19.5.6 Boundary Conditions
439(3)
19.5.7 Quasi-Fermi Potentials
442(1)
19.5.8 Poisson Equation in a Semiconductor
443(1)
19.6 Complements
444(5)
19.6.1 Comments on the Equivalent Hamiltonian Operator
444(1)
19.6.2 Special Cases of Anisotropy
445(1)
19.6.3 α-Moment at Equilibrium
445(1)
19.6.4 Closure Conditions
445(2)
19.6.5 Matthiessen's Rule
447(1)
19.6.6 Order of Magnitude of Mobility and Conductivity
448(1)
19.6.7 A Resume of the Transport Model's Derivation
449(1)
Problems
449(2)
20 Generation-Recombination and Mobility
451(34)
20.1 Introduction
451(1)
20.2 Net Thermal Recombinations
451(11)
20.2.1 Direct Thermal Recombinations
452(3)
20.2.2 Trap-Assisted Thermal Recombinations
455(2)
20.2.3 Shockley-Read-Hall Theory
457(5)
20.3 Auger Recombination and Impact Ionization
462(3)
20.3.1 Strong Impact Ionization
465(1)
20.4 Optical Transitions
465(3)
20.5 Macroscopic Mobility Models
468(7)
20.5.1 Example of Phonon Collision
469(2)
20.5.2 Example of Ionized-Impurity Collision
471(1)
20.5.3 Bulk and Surface Mobilities
472(1)
20.5.4 Beyond Analytical Modeling of Mobility
473(2)
20.6 Complements
475(10)
20.6.1 Transition Rates in the SRH Recombination Function
475(3)
20.6.2 Coefficients of the Auger and Impact-Ionization Events
478(1)
20.6.3 Total Recombination-Generation Rate
479(1)
20.6.4 Screened Coulomb Potential
480(5)
Part VII Basic Semiconductor Devices
21 Bipolar Devices
485(24)
21.1 Introduction
485(1)
21.2 P-N Junction in Equilibrium
485(7)
21.2.1 Built-In Potential
486(3)
21.2.2 Space-Charge and Quasi-Neutral Regions
489(3)
21.3 Shockley Theory of the P-N Junction
492(6)
21.3.1 Derivation of the 1(V) Characteristic
496(2)
21.4 Depletion Capacitance of the Abrupt P-N Junction
498(3)
21.5 Avalanche Due to Impact Ionization
501(3)
21.6 Complements
504(4)
21.6.1 Weak-Injection Limit of the Drift-Diffusion Equations
504(1)
21.6.2 Shockley's Boundary Conditions
505(1)
21.6.3 Depletion Capacitance-Arbitrary Doping Profile
506(2)
21.6.4 Order of Magnitude of Junction's Parameters
508(1)
Problems
508(1)
22 MOS Devices
509(32)
22.1 Introduction
509(1)
22.2 Metal-Insulator-Semiconductor Capacitor
510(10)
22.2.1 Surface Potential
512(3)
22.2.2 Relation Between Surface Potential and Gate Voltage
515(5)
22.3 Capacitance of the MOS Structure
520(2)
22.4 Simplified Expression of the Inversion Charge
522(4)
22.4.1 Quantitative Relations in the MOS Capacitor
524(2)
22.5 Insulated-Gate Field-Effect Transistor-MOSFET
526(1)
22.6 N-Channel MOSFET-Current-Voltage Characteristics
527(7)
22.6.1 Gradual-Channel Approximation
529(1)
22.6.2 Differential Conductances and Drain Current
530(4)
22.7 Complements
534(7)
22.7.1 Poisson's Equation in the MOSFET Channel
534(3)
22.7.2 Inversion-Layer Charge and Mobility Degradation
537(4)
Problems 538
Part VIII Miscellany
23 Thermal Diffusion
541(16)
23.1 Introduction
541(1)
23.2 Continuity Equation
542(3)
23.3 Diffusive Transport
545(1)
23.4 Diffusion Equation-Model Problem
546(1)
23.5 Predeposition and Drive-in Diffusion
547(6)
23.5.1 Predeposition
548(3)
23.5.2 Drive-in Diffusion
551(2)
23.6 Generalization of the Model Problem
553(1)
23.7 Complements
553(3)
23.7.1 Generation and Destruction of Particles
553(1)
23.7.2 Balance Relations
554(1)
23.7.3 Lateral Diffusion
554(1)
23.7.4 Alternative Expression of the Dose
555(1)
23.7.5 The Initial Condition of the Predeposition Step
555(1)
Problems
556(1)
24 Thermal Oxidation-Layer Deposition
557(18)
24.1 Introduction
557(1)
24.2 Silicon Oxidation
558(2)
24.3 Oxide-Growth Kinetics
560(2)
24.4 Linear-Parabolic Model of the Oxide Growth
562(1)
24.5 Layer Deposition and Selective Oxide Growth
563(3)
24.6 Epitaxy
566(1)
24.7 Kinetics of Epitaxy
567(1)
24.8 Complements
568(4)
24.8.1 An Apparent Contradiction
568(1)
24.8.2 Elementary Contributions to the Layer's Volume
569(1)
24.8.3 Features of the Oxide Growth and Epitaxial Growth
570(1)
24.8.4 Reaction Velocity
570(1)
24.8.5 Molecular Beam Epitaxy
571(1)
24.8.6 Secondary Reaction in the Epitaxial Growth
571(1)
Problems
572(3)
25 Measuring the Semiconductor Parameters
575(10)
25.1 Introduction
575(1)
25.2 Lifetime Measurement
575(3)
25.3 Mobility Measurement-Haynes-Shockley Experiment
578(3)
25.4 Hall-Voltage Measurement
581(2)
25.5 Measurement of Doping Profiles
583(2)
Appendix A Vector and Matrix Analysis 585(10)
Appendix B Coordinates 595(8)
Appendix C Special Integrals 603(22)
Appendix D Tables 625(2)
Solutions 627(18)
Bibliography 645
M. Rudan (b. 1949) graduated in Electrical Engineering (1973) and in Physics (1976), both at the University of Bologna, Italy. Lecturer (1978), Associate Professor (1985), and Full Professor of Electronics (1990) at the Faculty of Engineering of the same University. Early investigations (1975-1980) in the field of the analytical modeling of semiconductor devices. Since 1980 M. R. has been working in a group involved in investigations on physics of carrier transport and numerical analysis of semiconductor devices. Visiting scientist, on a one-year assignment (1986), at the IBM T. J. Watson Research Center, studying solution methods for the Boltzmann Transport Equation. Reviewer and Guest Editor of the IEEE Transactions on Computer-Aided Design and IEEE Transactions on Electron Devices; Editor of COMPEL and of the International Journal of Numerical Modeling; Reviewer of the IEEE Electron Device Letters, Solid-State Electronics, Electronics Letters, Physical Review B, Journal of Applied Physics; Program Chairman, Chairman, or Committee Member, of the IEDM, SISDEP (SISPAD), ESSDERC, and IWCE International Conferences. With H. Baltes and W. Göpel, M. R. is a recipient of the 1998 Körber Foundation Award for the Project Elektronische `Mikronase für flüchtige organische Verbindungen (Electronic `Micronose for Volatile Organic Compounds). In 2001 M. R. was one of the founders of the Advanced Research Center for Electronic Systems (ARCES) of the University of Bologna. Distinguished Lecturer of the Electron Device Society of the IEEE (2004) and IEEE Fellow (2008).
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