On the use of the Galerkin method for mathematical modeling of diffusion of excitons caused by a pulsing electron beam in a semiconductor target.
Stepovich M.A., Seregina E.V., Polyakov A.N., Lyamina O.I.
Some possibilities of using the Galerkin projection method to simulate two-dimensional diffusion of excitons excited by a pulsing electron beam in a semiconductor target are considered. The problem is solved in a cylindrical coordinate system. The wanted concentration of excitons is found in the form of a partial sum of a double Fourier series in the system of modified Laguerre functions. An order-of-magnitude estimate of the discrepancy error corresponding to the approximate solution of the nonstationary equation of their diffusion is obtained. In the simulation, parameters typical of gallium nitride were used.Keywords: Galerkin method, Fourier series, diffusion, semiconductor.
