Fast Modeling of 3D-Optical Carriers Injection and Permittivity in 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 coefficients, known as the diffusion equations. As a result, we obtain the 3-Dimension carrier density based on all the physical parameters of the substrate and of the laser beam. We are thus able to study the sensibility to optical power and then to compute the complex dielectric constant of the photo-induced plasma.