Numerical integral method for diffusion modeling

• Published in: IEEE transactions on computer-aided design of integrated circuits and systems Vol. 10; no. 9; pp. 1110 - 1124
• Main Authors: Tian, X., Strojwas, A.J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.1991; Institute of Electrical and Electronics Engineers
• Subjects: Analytical models; Applied sciences; Computational modeling; Electronics; Exact sciences and technology; Finite difference methods; Fusion power generation; Impurities; Integral equations; Large scale integration; Mathematical model; Nonlinear equations; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Very large scale integration; Diffusion process; VLSI circuit; Numerical integration; Computer simulation; Algorithm; Implementation
• ISSN: 0278-0070; 1937-4151
• DOI: 10.1109/43.85757

The authors present a numerically efficient mathematical approach, the numerical integral method, for diffusion modeling. This method extends the boundary integral methods to solve linear and nonlinear diffusion problems with physically based diffusivity models to account for concentration-dependent effects, oxidizing ambient effects, electric field effects, etc. The algorithm for solving nonlinear diffusion problems and its implementation in a computer program are described. Results from example problems are shown. This new numerical method provides the potential for achieving a diffusion simulation which is computationally efficient, numerically stable, and sufficiently accurate in an engineering environment. Such an efficient and yet accurate diffusion simulation is especially important in statistical simulation of VLSI processes.< >