9780136143307

Semiconductor Devices

by ;
  • ISBN13:

    9780136143307

  • ISBN10:

    013614330X

  • Edition: CD
  • Format: Hardcover
  • Copyright: 1997-12-01
  • Publisher: Prentice Hall
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List Price: $105.00

Summary

A book/disk for general to complex semiconductor simulations. Professionals and students can use the software and approach described to set up and examine models of semiconductor devices, including power semiconductors.

Table of Contents

1 Introduction
1(18)
1.1 Why Simulation?
2(3)
1.2 Purpose of the Book
5(3)
1.3 Physical Processes in Semiconductors and Their Numerical Description
8(2)
1.4 Simulation of Semiconductor Devices
10(1)
1.5 An Example Simulation: The Game of Life
11(4)
1.6 Organization of the Text
15(4)
I Basics 19(146)
2 Fundamentals of Electromagnetism and its Numerical Analysis
21(101)
2.1 Introduction to Numerical Differentiation
22(6)
2.2 Vector Calculus
28(3)
2.2.1 Plotting Vectors
29(1)
2.2.2 Plotting Field Lines
29(2)
2.3 Gradient of Scalar Functions
31(1)
2.4 Divergence of Vectors
32(13)
2.4.1 Calculation of the Divergence
34(11)
2.5 Curl of Vectors
45(10)
2.5.1 Derivation of Curl
49(5)
2.5.2 The Importance of Div and Curl
54(1)
2.6 Vector Operators in Curvilinear Coordinates
55(1)
2.7 Electrostatics
56(3)
2.7.1 The Electric Dipole
56(2)
2.7.2 Solution of Laplace's Equation
58(1)
2.8 Solution of PDEs on Irregular Meshes
59(17)
2.8.1 The Functions elen and ilen
63(9)
2.8.2 3D Meshes
72(4)
2.9 Electromagnetism
76(4)
2.9.1 Maxwell's Equations
77(1)
2.9.2 Integral Form of Maxwell's Equations
77(2)
2.9.3 Properties of Maxwell's Equations
79(1)
2.10 Boundary Conditions on the Electromagnetic Fields
80(3)
2.10.1 Divergence Equations
80(1)
2.10.2 Curl Equations
81(2)
2.11 Boundary Conditions on a Mesh
83(10)
2.11.1 The Potential Mesh
83(1)
2.11.2 The Field Mesh
84(1)
2.11.3 Electromagnetic Waves and Boundary Conditions
84(9)
2.12 Propagators in Electromagnetism
93(3)
2.13 Solution of Problems in Electrostatics
96(18)
2.13.1 Equations for Static Electric Fields
97(1)
2.13.2 Boundary Conditions on a Perfect Conductor
98(1)
2.13.3 Displacement Current
99(1)
2.13.4 Solution of Laplace's Equation - Numerical Examples
100(3)
2.13.5 Conductors in an Applied Electric Field
103(2)
2.13.6 A Dielectric in an Electric Field
105(3)
2.13.7 Use of Complex Geometries: a MEMS Example
108(6)
2.14 Summary
114(8)
3 Transport Phenomena and their Numerical Analysis
122(43)
3.1 Conservation Equations
123(2)
3.1.1 Boundary Conditions for Conservation Equations
124(1)
3.2 Finite-Difference Solution of Transport Equations
125(18)
3.2.1 Accuracy of Finite-Difference Schemes
128(1)
3.2.2 Conservative Schemes
128(1)
3.2.3 Diffusion of Dopants
129(9)
3.2.4 Diffusion of Charged Particles in an Electric Field
138(1)
3.2.5 Steady-State Diffusion
138(1)
3.2.6 Steady-State Convection
139(4)
3.3 Propagators in Transport Theory
143(16)
3.3.1 Numerical Implementation of the Transport Propagator
145(8)
3.3.2 Numerical Diffusion and Instability: a Comparison of the Propagator and an Explicit Scheme
153(6)
3.4 Summary
159(6)
II Semiconductor Simulation 165(130)
4 The Semiconductor Equations
167(43)
4.1 Introduction
167(1)
4.2 Equilibrium Carrier Behavior in Semiconductors
167(6)
4.3 Transport Equations for Semiconductors
173(7)
4.3.1 Particle-Conservation Equations for Semiconductors
173(2)
4.3.2 Heat-Conservation Equation
175(2)
4.3.3 Boundary Conditions
177(2)
4.3.4 Alternate Sets of Independent Variables
179(1)
4.4 The Semiconductor Parameters
180(16)
4.4.1 Permittivity
180(1)
4.4.2 Carrier Mobilities
180(4)
4.4.3 Carrier Velocity Saturation
184(1)
4.4.4 Surface Scattering
185(1)
4.4.5 Carrier Diffusion Coefficients
185(1)
4.4.6 Recombination and Generation
185(6)
4.4.7 Minority-Carrier Lifetimes
191(2)
4.4.8 Degeneracy and Band-Gap Narrowing
193(2)
4.4.9 Specific Mass Density and Specific Heat
195(1)
4.4.10 Thermal Conductivity
195(1)
4.4.11 Thermal Generation
195(1)
4.4.12 Parameter Models for High-Field Transport
196(1)
4.5 The Momentum Conservation Equation
196(1)
4.6 Summary
197(1)
4.7 Appendix
197(13)
4.7.1 Solution of the Momentum Equation
197(8)
4.7.2 Models for Ion Stopping
205(5)
5 Numerical Solution of PDEs
210(36)
5.1 Introduction
210(1)
5.2 Numerical Techniques for Solving PDEs
211(11)
5.2.1 Finite-Difference Methods
211(1)
5.2.2 Substitution of Difference Operators for Differential Operators
212(2)
5.2.3 Box Integration Method
214(7)
5.2.4 Finite-Element Methods
221(1)
5.2.5 Other Numerical Methods
221(1)
5.3 Discretizing the Semiconductor Equations
222(7)
5.3.1 Scaling the Semiconductor Equations
222(2)
5.3.2 Discretization of Semiconductor Equations
224(3)
5.3.3 The Scharfetter-Gummel Discretization
227(2)
5.4 The Solution of Nonlinear Systems of Algebraic Equations
229(2)
5.4.1 Fixed-Point Iterative Methods
230(1)
5.4.2 Relaxation Methods
231(1)
5.5 The Solution of Sparse Linear Systems of Algebraic Equations
231(4)
5.5.1 Direct Methods
232(2)
5.5.2 Indirect Methods
234(1)
5.6 Review of Software for the Solution of PDEs
235(1)
5.7 Validation of the Results of Simulations
236(3)
5.8 Summary
239(7)
6 The SGFramework
246(49)
6.1 Introduction
246(2)
6.2 An Overview of the SGFramework
248(2)
6.3 The SGFramework Translator
250(13)
6.3.1 The Scanner
252(1)
6.3.2 The Parser
253(2)
6.3.3 The SGFramework Grammar
255(1)
6.3.4 The Parser's Finite-State Table
255(1)
6.3.5 The Error Handler
256(1)
6.3.6 The Symbol Table
256(1)
6.3.7 The Math Expression Module
256(4)
6.3.8 The Indices Module
260(1)
6.3.9 The Statements Module
260(1)
6.3.10 The Code Generator
261(2)
6.4 The SGFramework Minimum-Degree Ordering Program
263(1)
6.5 The SGFramework Mesh Generation Program
263(10)
6.5.1 Mesh Specification File
264(1)
6.5.2 Mesh Skeleton
264(2)
6.5.3 Generating the Initial Mesh
266(1)
6.5.4 Data Structures for Mesh Generation
266(3)
6.5.5 Polygon Division into Rectangular Elements
269(1)
6.5.6 Polygon Division into Triangular Elements
270(2)
6.5.7 Summary
272(1)
6.6 The SGFramework Mesh Refinement Program
273(8)
6.6.1 Mesh Refinement
273(2)
6.6.2 Refinement of Triangular and Rectangular Elements
275(2)
6.6.3 Data Structures for Mesh Refinement
277(4)
6.6.4 Summary
281(1)
6.7 Interfacing the Mesh and Equation Specifications
281(9)
6.7.1 Mesh Connectivity
281(2)
6.7.2 Box-Integration Method
283(2)
6.7.3 Finite-Difference Schemes and User-Defined Functions
285(2)
6.7.4 Naming Scheme and Specification of PDEs
287(3)
6.8 Specification of Boundary Conditions on Irregular 2D Meshes
290(3)
6.9 SGFramework Build Script
293(1)
6.10 SGFramework Visualization Tools
293(1)
6.11 Summary
293(2)
III Semiconductor Devices 295(242)
7 PN Junction Diodes
297(94)
7.1 Electrostatic Description of a Simple Junction
298(15)
7.1.1 One-Dimensional Semiconductor Device Electrostatics
299(1)
7.1.2 PN Junctions -- Analytic Treatment
300(1)
7.1.3 Step Junction
300(2)
7.1.4 The Built-In Potential
302(1)
7.1.5 Linearly Graded Junction
303(1)
7.1.6 Numerical Modeling of the PN Junction
304(9)
7.2 (i,v) Characteristics
313(44)
7.2.1 (i,v) Characteristics for Low Currents and Voltages
313(8)
7.2.2 Numerical Evaluation of PN Junction (i,v) Characteristics
321(6)
7.2.3 Reverse-Bias Breakdown and Avalanching
327(15)
7.2.4 High-Current and High-Level Injection
342(15)
7.3 Two-Dimensional Modeling of a Device
357(15)
7.3.1 2D Input File
358(7)
7.3.2 Review of Mesh Construction
365(5)
7.3.3 Graphical Output
370(2)
7.4 Small-Signal Analysis
372(8)
7.4.1 Reverse-Bias Characteristics
372(1)
7.4.2 Forward-Bias Characteristics
372(2)
7.4.3 Numerical Modeling of Small-Signal Behavior
374(6)
7.5 Transients in PN Junctions
380(3)
7.5.1 Transient Behavior During Turn-Off
380(2)
7.5.2 Transient Behavior During Turn-On
382(1)
7.6 Photodiodes Based on PN and PIN Junctions
383(3)
7.6.1 Light Absorption in a Semiconductor
383(1)
7.6.2 Semiconductor Light Detectors
384(1)
7.6.3 A Model of a PIN Diode Light Detector
384(2)
7.7 Summary
386(5)
8 Bipolar Junction Transistors
391(37)
8.1 Static Characteristics
391(3)
8.2 The Ebers-Moll Equations
394(2)
8.3 BJT Time-Dependent Behavior
396(3)
8.3.1 Small-Signal Analysis
396(2)
8.3.2 Turn-On Transients in the BJT
398(1)
8.3.3 Turn-Off Transients in the BJT
398(1)
8.4 BJT Circuits
399(5)
8.5 Numerical Model of the BJT
404(18)
8.6 Summary
422(6)
9 Junction Field-Effect Transistors
428(13)
9.1 Static Characteristics
428(3)
9.2 Small-Signal Analysis
431(1)
9.3 Numerical Model of a JFET
431(9)
9.4 Summary
440(1)
10 Metal-Oxide-Semiconductor Structures
441(42)
10.1 Electrostatics of the One-Dimensional MOS Structure
441(7)
10.1.1 CV Characteristics of a MOS Capacitor
443(5)
10.2 Metal-Oxide-Semiconductor Field Effect Transistors
448(4)
10.2.1 (i,v) Characteristics of MOSFETs
448(4)
10.2.2 Small-Signal Analysis of MOSFETs
452(1)
10.3 Submicron Devices and VLSI
452(5)
10.3.1 Scaling MOS Structures
452(5)
10.4 MOSFET Mesh Specification File
457(1)
10.5 MOSFET Equation Specification File
458(6)
10.6 Results of the MOSFET Simulations
464(6)
10.7 MOSFET Circuits
470(11)
10.8 Summary
481(2)
11 Power Semiconductor Devices
483(54)
11.1 Introduction
483(1)
11.2 Simulation of Breakdown in Semiconductors
484(6)
11.2.1 Basic Semiconductor Equations with Impact-Ionization Model
485(1)
11.2.2 Nonlinear Poisson Model
485(1)
11.2.3 Derivation of the Nonlinear Poisson Model
485(1)
11.2.4 Calculation of the Breakdown Voltage
486(1)
11.2.5 Linear Poisson Model with Depletion-Region Logic
487(1)
11.2.6 Justification of Linear Poisson Model with Depletion-Region Logic
487(1)
11.2.7 Comparison of Breakdown Models
488(2)
11.3 Power Diodes
490(9)
11.3.1 Theory and Operation of PIN Diodes
491(1)
11.3.2 Basic Structure and (i,v) Characteristics
491(3)
11.3.3 Switching Characteristics
494(1)
11.3.4 Breakdown Voltage
495(2)
11.3.5 Conductivity Modulation
497(2)
11.4 Optimization of a Semiconductor Device
499(15)
11.4.1 Optimization of PIN Diodes with Field-Limiting Rings
499(3)
11.4.2 Method of Optimization
502(12)
11.5 Power MOSFETs
514(13)
11.5.1 (i,v) Characteristics
518(1)
11.5.2 Switching Characteristics
518(9)
11.6 Thyristors
527(4)
11.6.1 (i,v) Characteristics
530(1)
11.6.2 Switching Characteristics
531(1)
11.7 IGBTs
531(3)
11.7.1 (i,v) Characteristics
533(1)
11.8 Electrothermal Simulation of Power Devices
534(1)
11.9 Summary
534(3)
IV Advanced Topics 537
12 Mixed-Mode Simulations
539(39)
12.1 Time-Dependent Circuits
539(10)
12.2 Circuit Boundary Conditions for Device Models
549(20)
12.2.1 A Diode Bridge Circuit
549(9)
12.2.2 BJT with Inductive Load and Shunt Diode
558(11)
12.3 Summary
569(9)
13 Kinetic Transport Models
578(27)
13.1 Kinetic Simulations
579(2)
13.2 Monte Carlo Particle Simulation
581(1)
13.3 Motion of Charged Particles in a Semiconductor
582(1)
13.4 Integral Equation Methods in Kinetic Theory
583(1)
13.5 Distribution Function Found from the Convected Scheme
584(7)
13.5.1 The Ballistic Move
584(4)
13.5.2 The Collision Operator
588(1)
13.5.3 An Alternative Approach to Kinetic Calculations
588(1)
13.5.4 Self-Consistent Calculations
589(1)
13.5.5 Charged Particles in a Constant Electric Field
589(2)
13.6 Kinetic Simulations Based on the Scattering Rates
591(10)
13.6.1 Ion Motion Inside a Crystal
594(2)
13.6.2 Ballistic Motion
596(4)
13.6.3 Angular Distribution
600(1)
13.6.4 Collisions of Injected Ions
601(1)
13.6.5 Implementation of the Transition Matrix
601(1)
13.7 Summary
601(4)
14 Related Work
605(3)
14.1 Dry Etching of Semiconductors
606(2)
15 The SGFramework User's Manual
608
15.1 The Syntax and Grammar of the Equation Specification File
609(31)
15.1.1 Comments
610(1)
15.1.2 Numbers
610(1)
15.1.3 Strings
611(1)
15.1.4 Identifiers
612(2)
15.1.5 Operators
614(1)
15.1.6 Constants
615(2)
15.1.7 Variables and Arrays
617(3)
15.1.8 Functions
620(5)
15.1.9 Constraint Equations
625(3)
15.1.10 Procedures
628(9)
15.1.11 Numerical Algorithm Parameters
637(3)
15.2 The Syntax and Grammar of the Mesh Specification File
640(7)
15.2.1 An Overview of the Mesh Specification File
640(2)
15.2.2 Comments, Numbers, Identifiers and Constants
642(1)
15.2.3 Coordinates
643(1)
15.2.4 Points
643(1)
15.2.5 Edges
644(1)
15.2.6 Regions
644(1)
15.2.7 Labels
645(1)
15.2.8 Refinement Statements
645(1)
15.2.9 Mesh Parameters
646(1)
15.2.10 Element Refinement Criteria
647(1)
15.3 Interfacing the Equation and the Mesh Specification Files
647(10)
15.3.1 Importing an Irregular Mesh
648(1)
15.3.2 Using Labels in Equation Specification Files
649(1)
15.3.3 Mesh Connectivity Functions
650(1)
15.3.4 Mesh Geometry Functions
651(2)
15.3.5 Mesh Summation Functions
653(1)
15.3.6 Precomputed Functions
654(3)
15.4 SGFramework Executables
657
15.4.1 Build Script
657(2)
15.4.2 Mesh Parser
659(2)
15.4.3 Mesh Generator
661(1)
15.4.4 Mesh Refiner
662(1)
15.4.5 SGFramework Translator
663(4)
15.4.6 Ordering Module
667(1)
15.4.7 SGFramework Simulations
667(1)
15.4.8 Extract Program
668(1)
15.4.9 Group Program
669(1)
15.4.10 Graphical Output
670

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