In this paper we develop conservative finite-difference schemes (FDS) for the process of femtosecond pulse interaction with semiconductor. This process is described by the set of 2D dimensionless differential equations concerning concentrations of both free electrons and ionized donors, and potential of electric field, induced by laser pulse and laser beam intensity changing. The electron mobility, electron diffusion, nonlinear dependence of absorption coefficient on semiconductor characteristics are taken into account also.
For the problem under consideration we have constructed and compared two conservative FDS. One of them is based on the well known split-step method, the second one is based on the original two-stage iteration process. We paid the special attention to the 2D Poisson equation solution. This equation is solved by using an additional iteration process. Thus, to solve the problem under consideration it is necessary to achieve a convergence of two iteration processes.
As follows from computer simulation provided by us, the criterion choice for the iteration process convergence can significantly affect on the equations solution accuracy. We used the criterion based on assessment of an absolute and relative error of the solution obtained on iterations. This criterion is also used for Poisson equation solving. However, the iteration convergence criterion, based on discrepancy estimating, is more effective for using in this case.
Computer simulation results showed that the developed conservative FDS on the base of two-stage iteration process is an effective tool for investigation of complicated modes of semiconductor characteristics changing.