D I S S E R T A T I O N

Mixed-Mode Device Simulation

ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik

von

Klaus-Tibor Grasser


Gablenzgasse 97/51
A-1150 Wien, Österreich
Matr. Nr. 8826125
geboren am 28. April 1970 in Wien

Wien, im Mai 1999

To Isabella and Caroline

• Kurzfassung
• Abstract
• Acknowledgment
• Contents
• List of Symbols
• List of Figures
• 1. Introduction
• 2. Circuit Equations
  • 2.1 Nodal Approach
  • 2.2 Modified Nodal Approach
  • 2.3 Constitutive Relation Formulation
    • 2.3.1 Thermal Simulation
    • 2.3.2 Time Discretization
    • 2.3.3 Devices
      • 2.3.3.1 Conductor
      • 2.3.3.2 Resistor
      • 2.3.3.3 Linear Capacitor
      • 2.3.3.4 Non-linear Capacitor
      • 2.3.3.5 Linear Inductor
      • 2.3.3.6 Current Source
      • 2.3.3.7 Voltage Source
      • 2.3.3.8 Voltage Controlled Current Source
      • 2.3.3.9 Current Controlled Current Source
      • 2.3.3.10 Voltage Controlled Voltage Source
      • 2.3.3.11 Current Controlled Voltage Source
      • 2.3.3.12 Gyrator
      • 2.3.3.13 Power Monitor
      • 2.3.3.14 Distributed Device
• 3. Device Equations
  • 3.1 Sets of Partial Differential Equations
    • 3.1.1 The Basic Semiconductor Equations
    • 3.1.2 The Drift-Diffusion Transport Model
    • 3.1.3 The Hydrodynamic Transport Model
    • 3.1.4 The Lattice Heat Flow Equation
    • 3.1.5 The Constant Quasi-Fermi Potential Approximation
  • 3.2 Physical Parameters
    • 3.2.1 Mobility Model
    • 3.2.2 Energy Relaxation Time
    • 3.2.3 Consistent Physical Parameters
    • 3.2.4 Velocity Overshoot
    • 3.2.5 Low-Field Mobility Reconsidered
  • 3.3 Examples
    • 3.3.1 Homogeneous Semiconductor
    • 3.3.2 Gummel's Pentagon
    • 3.3.3 NMOS Transistors
    • 3.3.4 PMOS Transistor
• 4. Simulator Coupling
  • 4.1 The Two-Level Newton Algorithm
    • 4.1.1 Calculation of Conductances
    • 4.1.2 Modified Two-Level Newton Algorithm
  • 4.2 The Quasi Full-Newton Algorithm
  • 4.3 The Full-Newton Algorithm
• 5. Contacts and Boundaries
  • 5.1 Quantities, Segments, Boundaries, and Interfaces
  • 5.2 Equation Assembly
  • 5.3 Interfaces
    • 5.3.1 Neumann Type (Explicit Flux)
    • 5.3.2 Dirichlet Type (Implicit Flux)
  • 5.4 Boundaries
    • 5.4.1 Neumann Type
    • 5.4.2 Dirichlet Type
  • 5.5 Contact Model
  • 5.6 Contact Voltage Variable
  • 5.7 Example
  • 5.8 Mixed-Mode
  • 5.9 Thermal Simulation
• 6. Convergence and Damping
  • 6.1 Device Equation Damping Schemes
  • 6.2 Circuit Equation Damping Schemes
    • 6.2.1 Source Stepping
    • 6.2.2 Pseudo-Transient Method
    • 6.2.3 Global Damping Strategy
    • 6.2.4 Local Limiting
    • 6.2.5 The New Method
  • 6.3 Examples
    • 6.3.1 Output Stage of an OpAmp
    • 6.3.2 CML Inverter
    • 6.3.3 CMOS Inverter
• 7. Simulation Results
  • 7.1 Devices
    • 7.1.1 MOS Transistors
    • 7.1.2 Silicon-Germanium HBT
  • 7.2 Five-Stage CMOS Ring Oscillator
  • 7.3 Five-Stage CML Ring Oscillator
  • 7.4 Thermal Analysis of an Emitter-Coupled Pair
  • 7.5 Complete OpAmp $\mu$A709
• 8. Outlook
• A. Thermal Equivalents
• B. Device Model Implementation
  • B1. The Class MmxDevice
  • B2. Real Device Classes
• C. Overview of the Input Deck Programming Language
• D. Iteration Schemes in MINIMOS-NT
  • D1. Iteration Blocks
    • D1.1 Equations and Quantities
      • D1.1.1 Segment and Device Specific Selection
    • D1.2 Termination Criterion
    • D1.3 Failure Criterion
    • D1.4 Enter Criterion
    • D1.5 Damping Scheme
    • D1.6 Full versus Partial System Matrix
• Bibliography
• Curriculum Vitae
• About this document ...