The authors point out that modern numerical process simulators are becoming increasingly complicated in both physical models and domain shape. Grid generation is difficult for these simulators because of the inherently transient nature of the problems being solved. Here, adaptive grid refinement is considered for use in solving diffusion problems. Higher order approximations to the discretized diffusion flux are also studied. Several methods of both adaptive grid refinement and discretization are investigated and compared in terms of CPU time and final discretization error. All the methods are directly applied to the one-dimensional version of SUPREM-IV.>

The central processing unit requirements of two-dimensional numerical process simulation require much larger typical grid spacings than those used in one-dimensional simulations. With these larger grid spacings, the discretization error in diffusion simulation can have a large effect on the final simulated profile. This discretization error is analyzed and a first-order correction is applied and compared to the standard discretization method. Results show that this correction allows for a significant increase in the allowed grid spacing. As a typical example, implantation and subsequent diffusion of arsenic into silicon was modeled with different grid spacings using the SUPREM-IV program (and all its default diffusion parameters) in a one-dimensional mode. In all cases, the total dose of the implant was a constant, and differences in the implantation profile width (due to the different grid spacings) were small enough to have no significant effect on the final diffused profiles. It is seen that the standard method overestimates the amount of diffusion. The proposed method shows much better agreement between the coarse and fine grids.>

The addition of a mobility model to a finite-element simulator was found to create a convergence problem identified with the addition of positive terms to the off-diagonal elements in the solution matrix. Fast convergence rates were recovered by carefully adjusting the solution matrix such that the off-diagonal elements in question were all nonpositive.>