Temperature distributions produced in a two-layer structure by a scanning cw laser or electron beam

We derive the Green’s function solution to the heat equation for a two-layer structure and describe how to extend the technique to derive the Green’s function for N-layer structures. The Green’s function is applied to the interaction of a two-layer structure with scanning circular energy beams. The mathematics necessary to reduce the resultant solutions from a quintuple integral to a double integral are presented. Numerical integration of the remaining integrals leads to temperature profiles generated during laser irradiation of two-layer structures. These profiles are shown to reduce, in the appropriate limits, to previously reported profiles for the single-material case. Normalized linear temperature profiles as well as actual temperature profiles for silicon on sapphire are presented and discussed.