Introduction to modeling HBTs

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Title:

Personal Author:

Rudolph, Mathias

Series:

Artech House microwave library

Publication Information:

Boston, MA : Artech House, 2006

ISBN:

9781580531443

Subject Term:

Bipolar transistors -- Mathematical models

Electronic circuit design

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010106360	TK7871.96.B55 R82 2006	Open Access Book	Book	Searching... Unknown

Heterojunction bipolar transistors (HBTs) are a quite young technology and this book aims not only to give a reference of relevant HBT models, but also to discuss their background from a circuit-designer's point of view.

Author Notes

Matthias Rudolph is a senior scientist at the Ferdinand-Braun-Institut fur Hochstfrequenztechnik (FBH) in Berlin, Germany, where he is responsible for the characterization and modeling of FETs and HBTs for circuit design, and for the design of MMICs

Preface	p. xiii
Chapter 1 Introduction	p. 1
1.1 Heterojunction Bipolar Transistors	p. 1
1.2 Three Types of Models for Circuit Simulation	p. 6
1.2.1 Physics-Based Models	p. 6
1.2.2 Empirical Models	p. 6
1.2.3 Table-Based Models	p. 7
1.2.4 Comparison of the Modeling Approaches	p. 8
1.3 Preconditions for Model Development and Use	p. 10
1.4 The Model as a Nonlinear Circuit	p. 11
1.5 Two Model Restrictions in Circuit Simulators	p. 14
References	p. 19
Chapter 2 Compact Modeling Concepts	p. 21
2.1 Consistency of Large- and Small-Signal Models	p. 21
2.1.1 Nonlinear Resistances	p. 22
2.1.2 Nonlinear Capacitances	p. 24
2.2 Numerical Considerations	p. 32
2.2.1 Definition Range, Derivatives, and Overflow	p. 33
2.2.2 Asymptotic Correctness	p. 41
2.2.3 Unique Solution	p. 41
2.2.4 Model Parameters	p. 43
2.2.5 Circuit Topology	p. 44
2.3 Dispersion	p. 45
2.4 Calculating Self-Heating with a Circuit Simulator	p. 48
2.4.1 The Nonlinearity of the Thermal Resistance	p. 50
2.5 Statistical Modeling	p. 52
2.5.1 Types of Fluctuations	p. 52
2.5.2 Properties of Random Variables	p. 54
2.5.3 Objectives of a Statistical Model	p. 57
2.5.4 Principal Component Analysis	p. 58
2.5.5 Physics-Based Statistical Modeling	p. 60
2.5.6 Limitations of the Linear Approximation	p. 62
References	p. 62
Chapter 3 HBT Physics and Technology	p. 65
3.1 Emitter-Base Junction	p. 65
3.1.1 DC Current at Low-Current Densities	p. 65
3.1.2 Temperature Dependence of the Diode Current	p. 69
3.1.3 Recombination in the Space-Charge Region	p. 70
3.1.4 High-Current Densities	p. 71
3.1.5 Injection Efficiency	p. 72
3.1.6 Heterojunction	p. 73
3.1.7 Stored Charges - Junction Capacitances	p. 75
3.2 Base Transport	p. 79
3.2.1 Early Effect	p. 82
3.2.2 Current Crowding	p. 83
3.3 Base-Collector Junction	p. 84
3.3.1 Collector Transit Time and Depletion Capacitance	p. 84
3.3.2 High-Current Injection	p. 86
3.3.3 Avalanche Breakdown	p. 95
3.3.4 Heterojunction	p. 98
3.4 HBT Technology	p. 99
References	p. 107
Chapter 4 Modeling of HBTs	p. 109
4.1 The Equivalent Circuit	p. 109
4.1.1 Ideal T- and Hybrid-[pi]-Topologies at DC	p. 109
4.1.2 Nonideal Currents, Parasitic Elements, and Capacitances	p. 112
4.2 Basic Electrothermal Properties of HBTs	p. 118
4.2.1 DC Properties of HBTs	p. 118
4.2.2 The Gummel Plot	p. 119
4.2.3 Output I/V Curves	p. 120
4.2.4 Transit Frequency and Maximum Frequency of Oscillation	p. 124
4.2.5 The Typical Shape of HBT S-Parameters	p. 128
4.3 The Gummel-Poon Charge-Control Relation	p. 133
4.3.1 The Charge Function Q[subscript b]	p. 136
4.4 Constant Time Delay	p. 140
4.4.1 Base-Emitter Time Constant	p. 141
4.4.2 Base-Collector Transcapacitance	p. 143
4.4.3 Excess-Phase Network	p. 145
4.4.4 Transit-Time Approximations - [pi]-Topology	p. 147
4.4.5 Excess-Phase Network - [pi]-Topology	p. 148
4.4.6 Time Delay - [pi]-Topology	p. 150
4.5 Bias-Dependent Time Delay	p. 151
4.6 Thermal Instabilities	p. 156
4.6.1 Thermal Runaway	p. 157
4.6.2 Numerical Instability Due to Self-Heating	p. 160
4.6.3 Distributed Thermal Effects and Hot Spots	p. 165
References	p. 173
Chapter 5 Noise Model	p. 175
5.1 Physical Noise Sources	p. 175
5.1.1 The Link from Fluctuations in Time Domain to Noise Spectra	p. 176
5.1.2 Thermal Noise	p. 178
5.1.3 Shot Noise	p. 180
5.1.4 Diffusion Noise	p. 180
5.1.5 Low-Frequency Noise	p. 182
5.2 Noise Sources at Large-Signal Excitation	p. 184
5.3 Noise Calculation with Correlation Matrices	p. 186
5.4 HBT Noise Model	p. 190
5.4.1 Shot Noise	p. 190
5.4.2 Thermal Noise	p. 196
5.4.3 Complete White Noise Model	p. 196
5.4.4 1/f Noise	p. 201
References	p. 205
Chapter 6 HBT Models	p. 207
6.1 The SPICE Gummel-Poon Model	p. 208
6.1.1 DC Model	p. 208
6.1.2 Capacitances and Transit Times	p. 211
6.1.3 Substrate Capacitance	p. 212
6.1.4 Temperature Scaling	p. 212
6.1.5 Area Scaling	p. 214
6.1.6 Noise Model	p. 214
6.2 The VBIC Model	p. 216
6.2.1 Basic Transistor Isothermal DC Operation and Breakdown	p. 217
6.2.2 Capacitances and Transit Times	p. 220
6.2.3 Quasi-Saturation Model	p. 222
6.2.4 Substrate Transistor	p. 223
6.2.5 Self-Heating	p. 225
6.2.6 Noise Model	p. 228
6.3 The UCSD HBT Model	p. 232
6.3.1 DC Model	p. 233
6.3.2 The Depletion Capacitances	p. 235
6.3.3 The Forward Diffusion Charge	p. 236
6.3.4 The Substrate Branch	p. 244
6.3.5 Thermal Model	p. 245
6.3.6 Noise Model	p. 247
6.4 The Agilent HBT Model	p. 250
6.4.1 DC Model	p. 252
6.4.2 The Depletion Capacitances	p. 253
6.4.3 The Diffusion Capacitances and Transit-Time Model	p. 254
6.4.4 Resistances and Extrinsic Parameters	p. 257
6.4.5 Thermal Model	p. 257
6.4.6 Noise Model	p. 260
6.5 The FBH HBT Model	p. 263
6.5.1 DC Model	p. 264
6.5.2 The Depletion Capacitances	p. 267
6.5.3 Base-Collector Capacitance and Transit Times	p. 268
6.5.4 Resistances and Extrinsic Parameters	p. 271
6.5.5 Thermal Model	p. 272
6.5.6 Model Scaling	p. 273
6.5.7 Noise Model	p. 273
References	p. 276
Chapter 7 Measurement and Parameter Extraction	p. 279
7.1 General Considerations	p. 280
7.1.1 Systematic Sources of Extraction Uncertainty	p. 280
7.1.2 Influence of Measurement Equipment	p. 284
7.1.3 Choosing the Right Device	p. 284
7.2 Deembedding Techniques - Extrinsic Parameters	p. 285
7.2.1 Deembedding from Test-Structure Measurements and EM Simulation	p. 286
7.2.2 Determining R[subscript e] and R[subscript c] from DC Measurements	p. 289
7.2.3 Determining Extrinsic Elements from S-Parameter Measurements	p. 290
7.3 Intrinsic Small-Signal Parameters	p. 294
7.3.1 Extraction of R[subscript b2] and C[subscript ex]	p. 295
7.3.2 Extracting the Other Parameters	p. 297
7.4 Thermal Resistance and Time Constants	p. 298
7.4.1 Thermal Resistance	p. 298
7.4.2 Thermal Time Constants	p. 306
7.5 Large-Signal Model Parameters	p. 308
7.5.1 DC Parameters	p. 308
7.5.2 Charge Functions	p. 311
7.6 Model Verification	p. 313
References	p. 314
About the Author	p. 317
Index	p. 319

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