A discretization scheme that allows coarse grid-spacing in finite-difference process simulation

Abstract

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>