The stationary semiconductor device equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wien u.a.
Springer
1986
|
| Series: | Computational microelectronics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 193 S. graph. Darst. |
| ISBN: | 3211818928 0387818928 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Introduction 1
A Review of Semiconductor Device Modeling 1
About This Book 2
Semiconductors 3
References 5
2. Mathematical Modeling of Semiconductor Devices 7
2.1 Derivation of the Basic Semiconductor Device Equations 7
Maxwell s Equations 7
Poisson s Equation 8
Continuity Equations 10
Current Relations 11
Summary 13
2.2 Parameter Models 14
The Doping Profile 14
The Recombination Generation Rate 16
Carrier Mobility Models 18
2.3 Boundary Conditions and Device Geometry The Static Problem 19
Boundary Conditions 19
The Static Problem 24
Geometric Properties of Devices 24
2.4 Dependent Variables and Scaling Transformation of State Variables 25
The Singular Perturbation Scaling 26
References 29
3. Analysis of the Basic Stationary Semiconductor Device
Equations 31
3.1 Preliminaries 31
3.2 Existence of Solutions 33
3.3 Global Regularity 41
3.4 Uniqueness for Small Voltages 43
VIII Contents
3.5 Global Continuous Branches of Solutions 48
The Zero Recombination Generation Case 49
Voltage Current Characteristics 52
Non vanishing Recombination Generation Terms Impact Ionisation 54
3.6 Approximate Solutions 56
Approximation Analysis by Decoupling 57
Iteration Schemes 60
References 66
4. Singular Perturbation Analysis of the Stationary Semiconductor
Device Problem 68
4.1 The Device Equations As Singular Perturbation Problem 68
4.2 A Singularly Perturbed Second Order Model Problem 72
Structure of Solutions 73
Slow and Fast Scales 76
4.3 Asymptotic Expansions 80
Local Coordinate Transformations 81
The Outer Expansion 83
The Junction Layer Expansion 83
Boundary Layer Expansions 87
A. Ohmic Contacts 88
B. Neumann Segments 89
C. Schottky Contacts 89
D. Semiconductor Oxide Interfaces 90
4.4 The Zero Space Charge Approximation 93
4.5 The Layer Problems 95
4.6 Representation and Structure of Solutions 100
4.7 Extensions 109
Graded Junctions 110
Strongly One sided Junctions 112
Field dependent Mobilities Velocity Saturation 115
4.8 Scaling Revisited and Conditioning 120
Rescaling Poisson s Equation 120
Conditioning of the Continuity Equations 124
References 129
5. Discretisation of the Stationary Device Problem 131
5.1 Construction of Discretisations 132
Discretisation of Poisson s Equation 133
A. The Ritz Galerkin Approximation 133
B. Piecewise Linear Finite Element Approximation 133
C. Finite Difference Schemes 137
Contents jX
Discretisation of the Current Relations and Continuity Equations 139
A. Weak Formulations 140
B. The Failure of the Standard Discretisation 141
C. Finite Element Scharfetter Gummel Discretisations 143
D. The Finite Difference Scharfetter Gummel Schemes 148
5.2 Solutions of Static Discretisations 149
The Coefficient Matrices 150
5.3 Convergence of Discretisations 151
Decoupled Convergence Analysis 152
Classical Convergence Theory 154
Convergence Analysis of the SG Schemes 158
Convergence Analysis for Poisson s Equation 162
Current Density and Outflow Current Approximations 167
5.4 Extensions and Conclusions 169
Semiconductor Oxide Interfaces 169
Schottky Contacts 170
Adaptive Mesh Construction 171
References 176
6. Numerical Simulation A Case Study 178
References 183
Appendix 184
Notation of Physical Quantities 184
Mathematical Notation 185
A. Device Geometry 185
B. Scalars, Vectors and Matrices 186
C. Functions 186
D. Landau Symbols 187
E. Linear Spaces of Functions and Norms 187
F. Functionalanalytic Notations 189
Subject Index 191
|
| any_adam_object | 1 |
| author | Markowich, Peter A. 1956- |
| author_GND | (DE-588)136248330 |
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| dewey-ones | 621 - Applied physics |
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| dewey-search | 621.3815/2 |
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| discipline | Physik Elektrotechnik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| indexdate | 2024-07-09T15:17:13Z |
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| isbn | 3211818928 0387818928 |
| language | English |
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| physical | IX, 193 S. graph. Darst. |
| publishDate | 1986 |
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| publishDateSort | 1986 |
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| series2 | Computational microelectronics |
| spelling | Markowich, Peter A. 1956- Verfasser (DE-588)136248330 aut The stationary semiconductor device equations Peter A. Markowich Wien u.a. Springer 1986 IX, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational microelectronics Semiconducteurs - Modèles mathématiques Mathematisches Modell Semiconductors Mathematical models Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Halbleiterbauelement (DE-588)4113826-0 gnd rswk-swf Halbleiterschaltung (DE-588)4158811-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Halbleiter (DE-588)4022993-2 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Halbleiterschaltung (DE-588)4158811-3 s Simulation (DE-588)4055072-2 s DE-604 Mathematisches Modell (DE-588)4114528-8 s Halbleiterbauelement (DE-588)4113826-0 s Halbleiter (DE-588)4022993-2 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000406066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markowich, Peter A. 1956- The stationary semiconductor device equations Semiconducteurs - Modèles mathématiques Mathematisches Modell Semiconductors Mathematical models Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Halbleiterbauelement (DE-588)4113826-0 gnd Halbleiterschaltung (DE-588)4158811-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Halbleiter (DE-588)4022993-2 gnd Simulation (DE-588)4055072-2 gnd |
| subject_GND | (DE-588)4128900-6 (DE-588)4113826-0 (DE-588)4158811-3 (DE-588)4114528-8 (DE-588)4022993-2 (DE-588)4055072-2 |
| title | The stationary semiconductor device equations |
| title_auth | The stationary semiconductor device equations |
| title_exact_search | The stationary semiconductor device equations |
| title_full | The stationary semiconductor device equations Peter A. Markowich |
| title_fullStr | The stationary semiconductor device equations Peter A. Markowich |
| title_full_unstemmed | The stationary semiconductor device equations Peter A. Markowich |
| title_short | The stationary semiconductor device equations |
| title_sort | the stationary semiconductor device equations |
| topic | Semiconducteurs - Modèles mathématiques Mathematisches Modell Semiconductors Mathematical models Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Halbleiterbauelement (DE-588)4113826-0 gnd Halbleiterschaltung (DE-588)4158811-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Halbleiter (DE-588)4022993-2 gnd Simulation (DE-588)4055072-2 gnd |
| topic_facet | Semiconducteurs - Modèles mathématiques Mathematisches Modell Semiconductors Mathematical models Nichtlineare partielle Differentialgleichung Halbleiterbauelement Halbleiterschaltung Halbleiter Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000406066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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