Laser-induced temperature profiles in complex substrates

Scanning CW laser-induced temperature rise in anistropic and multilayer substrates has been investigated by simplifying and solving the dynamic heat equation. It is found that the heat equation in anisotropic media can be simplified to a heat equation in isotropic media by coordinate transformation. The anisotropy of the media can then be reflected by heat source transformation. In multilayer substrate with periodic structures, the substrate can be equivalent to a homogeneous substrate with anisotropic thermal conductivity, if the dimension of the periodic structure is much smaller than the laser spot size. The laser-induced temperature rise can then be obtained by solving the three-dimensional heat equation with the different thermal conductivities in directions parallel and perpendicular to the layer structure. Analytical models were derived to calculate the scanning laser-induced temperature rise in anisotropic and multilayer substrates.