ABSTRACT
In this chapter we discuss the numerical method used in the simulator. In an iterative method for solving, we start with a guess for the solution (often just the zero vector) and then successively renew this guess, getting closer to the solution at each stage. This iteration is usually performed until it converges to a result and a desired accuracy is achieved. The power of most iterative methods lies in their ability to achieve this convergence ef“ciently. However, two con¤icting issues for a particular iterative method are high speed and
CONTENTS
3.1 Introduction ................................................................................................ 145 3.2 Numerical Solution Methods ................................................................... 146 3.3 Non-Linear Iteration .................................................................................. 146
3.3.1 Newton Iteration ............................................................................ 146 3.3.2 Gummel Iteration ........................................................................... 147 3.3.3 Block Iteration ................................................................................. 148 3.3.4 Combining the Iteration Methods ............................................... 148
3.4 Convergence Criteria for Non-Linear Iterations ................................... 149 3.5 Initial Guess Requirement ........................................................................ 149 3.6 Numerical Method Implementation ....................................................... 150 3.7 Basic Drift Diffusion Calculations .......................................................... 151 3.8 Drift Diffusion Calculations with Lattice Heating ............................... 152 3.9 Energy Balance Calculations .................................................................... 152 3.10 Energy Balance Calculations with Lattice Heating .............................. 152 3.11 Setting the Number of Carriers ............................................................... 153 3.12 Important Parameters of the METHOD Statement ............................... 153
3.12.1 Restrictions on the Choice of METHOD .................................... 154 3.12.2 Pisces-II Compatibility .................................................................. 154
References ............................................................................................................. 154
convergence. Say, for example, to achieve a convergence for an equation a large number of iterations are needed. This will severely affect the speed and hence the time consumed. Conversely, a high-speed solver may not achieve a convergence. In the following sections the different iterative techniques implemented in technology computer aided design (TCAD) to achieve convergence ef“ciently are described in detail.
