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3-dimensions analytical modeling of the optical carriers injection in a semiconductor substrate

In order to be faster and more precise than numerical way in the computation of the photo-induced plasma in semiconductor, we have to use an analytical approach to solve the problem. In this study, we use the Hankel transform to simplify the resolution of the differential equation of second order with non-constant coefficient, known as the diffusion equations. As a result, we obtain the 3-dimensions carrier density based on all the physical parameters of the substrate and of the laser beam and so we are able to study the sensibility to several parameters.