Adaptive ILU Preconditioning Strategies in Semiconductor Process Modeling

Jun Zhang

Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046

and

Anand L. Pardhanani and Graham F. Carey

CFD Laboratory, WRW 301
University of Texas at Austin
Austin, Texas 78712


Abstract

Preconditioning strategies based on incomplete factorization using thresholding with dual dropping (ILUT) are investigated for iterative solution of sparse linear systems arising in semiconductor dopant diffusion modeling. Of particular interest are questions associated with selection and adaption of threshold parameters with spatial resolution, timestep in the adaptive ODE integrator and the problem physics. It is shown that the convergence rate of the preconditioned iterative solvers is severely affected by the time steps used in adaptive ODE integrator. Thus the accuracy and quality of the ILU preconditioner have to be adaptively adjusted so that iterative convergence is achieved and the overall computation cost is kept low.

Adaptive ILU preconditioners are compared with a fixed block Jacobi preconditioner and a direct band solver in terms of robustness and total simulation cost. A few ILU adaptive preconditioning strategies are discussed and their performance is compared.