Quasilinear formulation with a simple remeshing scheme for the finite element based simulation of dopant diffusion in silicon

The weighted residual formulation of the finite-element method is used to solve the nonlinear diffusion equation which describes dopant diffusion. Discretisation in the time domain is carried out using the Crank-Nicolson implicit scheme. A remeshing scheme based on a continuity criterion obtained by comparing the concentration values of adjacent nodes is used to introduce or eliminate nodes in the spatial domain as the diffusion proceeds in time. This scheme which uses an average diffusivity across each element has been successfully applied to the simulation of As diffusion in Si, and overcomes the oscillation and instability which would otherwise occur if a uniform mesh with the same number of nodes were used.