High-Frequency Bipolar Transistors Physics, Modelling, Applications

This book provides a rather comprehensive presentation of the physics and modeling of high-frequency bipolar transistors with particular emphasis given to silicon-based devices. I hope it will be found useful by those who do as well as by those who intend to work in the field, as it compiles and extends material presented in numerous publications in a coherent fashion. I've worked on this project for years and did my best to avoid errors. De­ spite all efforts it is possible that "something" has been overlooked during copy-editing and proof-reading. If you find a mistake please let me know. Michael Reisch Kempten, December 2002 Notation It is intended here to use the most widely employed notation, in cases where the standard textbook notation is different from the SPICE notation, the latter is used. In order to make formulas more readable, model parameters represented in SPICE by a series of capital letters are written here as one capital letter with the rest in the form of a subscript (e.g. XCJC is used here instead of the XCJC used in the SPICE input). Concerning the use of lower-case and capital letters, the following rules are applied: • Time-dependent large-signal quantities are represented by lower-case let­ ters. The variables 't, v and p therefore denote time-dependent current, voltage and power values.

1. An Introductory Survey.- 1.1 History.- 1.2 Devices, Circuits, Compact Models.- 1.3 Semiconductors.- 1.4 PN Junctions.- 1.5 Bipolar Transistor Principles.- 1.6 Elementary Large-Signal Models.- 1.7 Elementary Small-Signal Models.- 1.8 Noise Modeling.- 1.9 Orders of Magnitude.- 1.10 References.- 2. Semiconductor Physics Required for Bipolar-Transistor Modeling.- 2.1 Band Structure.- 2.2 Thermal Equilibrium.- 2.3 The Boltzmann Equation.- 2.4 The Drift-Diffusion Approximation.- 2.5 Hydrodynamic Model.- 2.6 Generation and Recombination.- 2.7 Heavily Doped Semiconductors.- 2.8 Silicon Device Modeling in the Drift-Diffusion Approximation.- 2.9 References.- 3. Physics and Modeling of Bipolar Junction Transistors.- 3.1 The Regional Approach.- 3.2 Transfer Current, Early Effect.- 3.3 Emitter-Base Diode, Current Gain.- 3.4 Base-Collector Diode, Breakdown.- 3.5 Charge Storage, Transit Time.- 3.6 Series Resistances.- 3.7 High-Level Injection.- 3.8 The Gummel-Poon Model.- 3.9 Small-Signal Description.- 3.10 Figures of Merit.- 3.11 Temperature Dependences, Self-Heating.- 3.12 Parameter Extraction — DC Measurements.- 3.13 Parameter Extraction — AC Measurements.- 3.14 The VBIC Model.- 3.15 The HICUM Model.- 3.16 The MEXTRAM Model.- 3.17 References.- 4. Physics and Modeling of Heterojunction Bipolar Transistors.- 4.1 Heterojunctions.- 4.2 Heterojunction Bipolar Transistors.- 4.3 Silicon-Based Semiconductor Hctorostructures.- 4.4 SiGe HBTs.- 4.5 Compound Semiconductor HBTs.- 4.6 References.- 5. Noise Modeling.- 5.1 Noise in Semiconductors.- 5.2 Transport Theory of Noise.- 5.3 Noise of pn Junctions.- 5.4 Noise Generated by the Transfer Current.- 5.5 High-Frequency Noise Equivalent Circuit.- 5.6 Noise Figure.- 5.7 Low-Frequency Noise.- 5.8 References.- 6. Basic CircuitConfigurations.- 6.1 Common-Emitter Configuration.- 6.2 Common-Collector Configuration.- 6.3 Common-Base Configuration.- 6.4 The Diode-Connected Bipolar Transistor.- 6.5 Current Sources and Active Loads.- 6.6 Differential Amplifiers.- 6.7 Analog Multipliers.- 6.8 Two-Transistor Amplifier Stages.- 6.9 Bandgap References.- 6.10 Digital Circuits.- 6.11 References.- 7. Process Integration.- 7.1 Fabrication of Integrated npn Transistors.- 7.2 Passive Components.- 7.3 PNP Transistors.- 7.4 Reliability.- 7.5 References.- 8. Applications.- 8.1 Emitter-Coupled Logic.- 8.2 High-Speed Optical Transmission Systems.- 8.3 RF Microelectronics.- 8.4 BiCMOS.- 8.5 References.- A. Linear and Nonlinear Response.- A.1 Linear Response.- A.1.1 Step Response, Elmore Delay.- A.2 Nonlinear Systems Without Memory.- A.2.1 Harmonic Distortion, Gain Compression.- A.2.2 Intermodulation Distortion.- A.3 Nonlinear Systems with Memory.- A.3.1 Volterra Series.- A.4 References.- B. Linear Two-Ports, s-Parameters.- B.1 Indefinite Admittance Matrix.- B.2 Terminated Two-Ports.- B.2.1 Input and Output Impedance.- B.2.2 Voltage and Current Gain.- B.2.3 Power Gain.- B.2.4 Stability.- B.2.5 Incident and Reflected Power.- B.3 S-Parameters.- B.3.1 Relations between s-Parameters and Two-Port Parameters.- B.3.2 Matching and Power Gain.- B.4 References.- C. PN Junctions: Details.- C.1 Boundary Conditions at PN Junctions.- C.2 Epitaxial Diode.- C.3 Minority-Carrier Transport in Heavily Doped Emitter Regions.- C.4 High-Frequency Diode Admittance.- C.5 References.- D. Bipolar Transistor: Details.- D.1 Drift Transistor.- D.1.1 Electron Transport Through the Base Region.- D.1.3 Excess Phase.- D.1.4 Collector Transit Time.- D.1.5 Small-Signal Analysis.- D.2 Quasi-Thrce-Dimensional Computations of the Base Resistance.- D.3Generation of Model Parameters from Layout Data.- D.4 Generalization of the Gummol Transfer Current Relation to Arbitrary Geometries.- D.5 Definition of Series Resistances Within the Integral Charge Control Relation.- D.6 Multiplication Factor.- D.7 References.- E. Noise: Details.- E.1 Some Statistics.- E.1.1 Stochastic Variables, Correlation.- E.1.2 Ensemble Average, Distribution Function.- E.1.3 Spectral Density.- E.1.4 Carson Theorem, Shot Noise.- E.2 Velocity Fluctuations and Diffusion.- E.3 Thermodynamics and Noise.- E.4 Generation-Recombination Noise.- E.5 McWorther Model of 1/f Noise.- E.6 Short-Base Diode with Metal Contact.- E.7 Short-Base Diode with Polysilicon Contact.- E.8 Equivalent-Circuit Representation of Transfer Current Noise.- E.9 References.- F. Overtemperature Developed During Electrostatic Discharges.- F.1 Thermal Conductivity.- F.2 Transient Overtemperature During a Short Pulse.- F.3 References.