§16§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 subsc §16§ript (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. §01§Michael Reisch wurde 1957 im oberschwäbischen Bad Waldsee geboren. Er studierte Physik an der TU München und promovierte am Institut für Physikalische Elektronik der TU Wien. Er war von 1983 bis 1991 für die Siemens AG (Zentrale Forschung und Entwicklung) in München tätig. Seit 1991 ist er als Professor an der FH Kempten vor allem für die Lehrgebiete Werkstoffe der Elektrotechnik sowie Elektronische Bauelemente zuständig. Sein berufliches Hauptinteresse gilt der Physik und Modellierung elektronischer Bauelemente - in seiner Freizeit ist er am liebsten mit Tourenski oder Mountainbike in den Bergen unterwegs. §04§ Ionization.- 2.3 The Boltzmann Equation.- 2.3.1 Collision Term.- 2.3.2 Thermal Equilibrium.- 2.3.3 Limits of Validity.- 2.3.4 Relaxation Times.- 2.4 The Drift-Diffusion Approximation.- 2.4.1 The Relaxation Time Approximation.- 2.4.2 Transport in Low Electric Fields.- 2.5 Hydrodynamic Model.- 2.5.1 Continuity Equation.- 2.5.2 Current Equation.- 2.5.3 Energy Balance Equation.- 2.6 Generation and Recombination.- 2.6.1 Shockley Read Hall Processes.- 2.6.2 Auger Recombination.- 2.6.3 Impact Ionization.- 2.6.4 Interband Tunneling.- 2.7 Heavily Doped Semiconductors.- 2.7.1 Modification of the Band Structure.- 2.7.2 Bandgap Narrowing in Silicon.- 2.8 Silicon Device Modeling in the Drift-Diffusion Approximation.- 2.8.1 Basic Equations of the Drift-Diffusion Approximation.- 2.8.2 Model Equations for Material Parameters.- 2.8.3 Compact Modeling.- 2.9 References.- 3. Physics and Modeling of Bipolar Junction Transistors.- 3.1 The Regional Approach.- 3.1.1 Drift Transistors - Homogeneous-Field §04§ Case.- 3.1.2 Transfer Current in Frequency and Time Domains.- 3.1.3 The Ebers-Moll Model.- 3.1.4 The Charge Control Model.- 3.1.5 Non-Quasi-Static Effects.- 3.2 Transfer Current, Early Effect.- 3.2.1 The Integral Charge Control Relation.- 3.2.2 Forward Operation, Early Voltage.- 3.2.3 Base Charge Partitioning.- 3.3 Emitter-Base Diode, Current Gain.- 3.3.1 Minority-Carrier Transport in Heavily Doped Silicon Emitters.- 3.3.2 Polycrystalline Emitter Contacts.- 3.3.3 Recombination in the Space Charge Layer.- 3.3.4 Reverse-Bias Currents, Breakdown.- 3.4 Base-Collector Diode, Breakdown.- 3.4.1 Multiplication Factor.- 3.4.2 Collector-Emitter Breakdown due to Impact Ionization.- 3.4.3 Punchthrough.- 3.5 Charge Storage, Transit Time.- 3.5.1 Depletion Capacitances.- 3.5.2 Hole Continuity and Cutoff Frequency.- 3.5.3 Forward Transit Time.- 3.6 Series Resistances.- 3.6.1 Emitter Resistance.- 3.6.2 Base Resistance.
