Numerical simulation of vertical temperature distribution in heterogeneous multilayer structure with Mathematica

Temperature distributions produced by a scanning cw Nd:YAG (1.06 μm) laser beam in a heterogeneous multilayer structure (poly-Si/SiO2/Si) are calculated using Mathematica. A solution to the nonlinear heat equations including temperature-dependent thermal parameters is solved numerically for the temperature distributions of the heterogeneous multilayer structure. We present the linear temperature distributions of multilayer along the full depth of structure as a function of normalized thickness of the structure. This calculation scheme could cover a wide range of calculation of the temperature distribution produced by a scanning heat source in the heterogeneous multilayer structure.