Two-dimensional concentration dependent diffusion

The concentration dependent diffusion problem is studied in two dimensions for a variety of cases relevant to the fabrication of narrow-channel MOS transistors. A method for solving the partial differential equation is presented which allowed the solutions to be computed on an available minicomputer. This method enables analytic transformations to be exploited which improve the accuracy of the solutions and increase the speed of computation. The simulations demonstrate that there are three principal nonlinear effects: (i) a large translation of the diffusion front, (ii) a marked steepening of the front itself, and (iii) a very noticeable decrease in the ratio of the lateral to vertical diffusions. The ratio of the lateral to vertical diffusion as predicted by the model is compared with physical values experimentally determined using a scanning electron microscope.