Three-dimensional analyses of photo-modulated reflectivity for transparent film/opaque substrate structures

For a structure consisting of a transparent film deposited on an opaque substrate radiated by a modulated focused laser beam, a 3-D model is established to calculate the temperature distributions. Then based on 3-D thermoelastic displacements and dielectric constants depended on the temperature of the bilayer structure, the photo-modulated reflectivity of the structure is calculated by using FEM method. As an example, the modulated reflectance variations with the modulation frequency of the optical beam and the thermal conductivity of the film in ZnO/Si bilayer structures are also obtained.