Fast simulation code for heating, phase changes and dopant diffusion in silicon laser processing using the alternating direction explicit (ADE) method

Abstract

Enhancements to our existing finite-differences code for the simulation of laser heating, melting and evaporation of silicon are presented. The Knudsen evaporation model has been added to the previously used enthalpy-based model in order to simulate laser pulses with pulse lengths down to a few nanoseconds. Fick’s diffusion law has also been incorporated allowing laser doping by dopant diffusion in silicon melt to be described. Finally, the basic equations for the alternating direction explicit method (ADE) have been adapted to consider nonlinear temperature-enthalpy relations, thus including affects due to phase changes. This improved the simulation speed by up to factor of 100 compared to standard explicit and implicit time integration methods. Details of the ADE algorithm and numerical stability issues are presented in this paper. Validation of the code is presented by comparing to different integration methods and to experimental results. The final code successfully simulates melting, evaporation and dopant diffusion by multiple laser pulses in three dimensions in an acceptable computing time.