Simulation of implantation and diffusion of profiles made with a focused ion-beam implanter

A method is presented by which two-dimensional profiles made with a focused ion-beam implanter are quickly and easily calculated. Advantage is taken of the Gaussian nature of the beam and its interaction with the target to represent the dose versus position as a sum of Gaussian functions spaced along the beam path. The vertical profile, taken either from measured data or from a one-dimensional simulation, is also fit to a sum of Gaussian functions. With this form, and assuming uniform diffusivity, subsequent diffusion steps can be modeled as a simple increase in the standard deviation of the Gaussian functions-eliminating the need to step in time. A method for satisfying the boundary condition at the surface and for modeling a variable oxide thickness on this surface is also demonstrated.