Temperature profile of a silicon-on-insulator multilayer structure in silicon recrystallization with incoherent light source

A one-dimensional distribution of the temperature and the heat source in the SOI (silicon-on-insulator) multilayer structure illuminated by tungsten lamps from both sides was obtained by solving the heat equation in steady state on a finite difference grid using a successive over-relaxation method. The heat source distribution was obtained by considering such features as spectral components of the light source, multiple reflection at the internal interfaces, temperature and frequency dependence of the light absorption coefficient, etc. The front and back surface temperatures, which are boundary conditions for the heat equation, were derived from a requirement that they satisfy the radiation conditions. The radiation flux as well as the conduction flux was considered in modeling the thermal behavior at the internal interfaces. Since the temperature and the heat source profiles are strongly dependent upon each other, the calculation of each profile was iterated using the updated profile of the other until they were consistent with each other.