Numerical solution of a Stefan-like problem in laser processing of semiconducting alloys

Abstract

A theoretical model of binary alloy melting and solidification induced by pulsed-laser irradiation is formulated using the mass and internal energy balances in the liquid and solid phases. The interface between the solid and liquid phases is modeled as a discontinuity surface where the mass and internal energy balance conditions are expressed, together with the interface response function. Both melting and solidification are considered as nonequilibrium processes. The numerical solution of the mathematical model is performed using the Galerkin finite element method in a 1D approximation and the moving boundary problem is solved by a front-fixing technique. The resulting set of nonlinear algebraic equations is solved by an iterative procedure using the successive approximation approach. In a practical application of the computational model, the phase change processes in a Si–Ge system induced by XeCl excimer laser are simulated. The temperature and concentration fields, and the position and velocity of the phase interface are calculated in dependence on the laser energy density. The results show good agreement with experimental measurements by Slaoui et al. [10]. The model can also provide some data which are difficult to be measured in a direct experiment.