Conservative Finite-Difference Scheme and Two-Stage Iteration Process of Its Realization for the 2D Problem of Semiconductor Plasma Generation by Femtosecond Pulse (Communications in Computational Physics, 2018)
In this paper we develop conservative finite-difference schemes (FDS) forthe process of femtosecond pulse interaction with semiconductor. This process is describedby the set of 2D dimensionless differential equations concerning concentrationsof both free electrons and ionized donors, and potential of electric field, inducedby laser pulse and laser beam intensity changing. The electron mobility, electron diffusion,nonlinear dependence of absorption coefficient on semiconductor characteristicsare taken into account also.For the problem under consideration we have constructed and compared two conservativeFDS. One of them is based on the well known split-step method, the secondone is based on the original two-stage iteration process. We paid the special attentionto the 2D Poisson equation solution. This equation is solved by using an additionaliteration process. Thus, to solve the problem under consideration it is necessary toachieve a convergence of two iteration processes.As follows from computer simulation provided by us, the criterion choice for theiteration process convergence can significantly affect on the equations solution accuracy.We used the criterion based on assessment of an absolute and relative error of thesolution obtained on iterations. This criterion is also used for Poisson equation solving.However, the iteration convergence criterion, based on discrepancy estimating, ismore effective for using in this case.Computer simulation results showed that the developed conservative FDS on thebase of two-stage iteration process is an effective tool for investigation of complicatedmodes of semiconductor characteristics changing.