Semi-analytical modeling and analysis in three dimensions of the optical carrier injection and diffusion in a semiconductor substrate

In order to be faster and more precise than any numerical technique for the computation of the photo-induced plasma in semiconductor, an analytical solution has to be developed. In this paper, the Hankel transform is used to simplify the solution of the differential equation of second order with nonconstant coefficient, known as the diffusion equation. The resulting expression of the three-dimensional (3-D) carrier density includes all the physical parameters of the substrate and the laser beam as well. A parametric study was also feasible using the developed expressions.