Temperature evolutions in silicon induced by a scanned cw laser, pulsed laser, or an electron beam

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Abstract
A self-consistent time procedure for solving a nonlinear heat diffusion equation is proposed. This paper addresses three-dimensional time dependent heat equations with nonlinear sources and diffusivity. The semianalytical model of the static regime is thereby extended to transient treatment. The advantage of this method is that it allows handling of nonlinearity in the heat diffusion equation, while keeping calculations simple. The method may be applied to either a cw laser beam or a pulsed beam. In the latter case, the method applies for any spot size, since the problem remains three-dimensional. Different deposited energy pentrations are reviewed, among them the Gaussian-shaped deposited energy corresponding to the case of the scanned electron beam. Using this method, temperatures are calculated and compared with the high speed melting isotherm for silicon under cw laser irradiation.