SIMULATION OF THE P-I-N-STRUCTURES CHARACTERISTICS INTERACTING WITH HIGH-FREQUENCY ELECTROMAGNETIC RADIATION BY PERTURBATION THEORY METHODS - Moroz, I. P. (Computer Science and Applied Mathematics, 2023)
The mathematical model is proposed for the electron-hole plasma characteristics predicting of the active region (i-region) of p-i-n structures, taking into account the effect of the displacement current (induced by an external microwave electromagnetic field) on the formation of a space charge. The model is based on a singularly perturbed nonlinear boundary value problem for the system of the electron-hole current continuity equations and Poisson’s (the Poisson’s equation contains a naturally formed small parameter). The model nonlinear boundary value problem is reduced to a recurrent sequence of linear boundary value problems for determining of the electron-hole plasma concentrations and the electric potential distributions in the i-region by using asymptotic methods, in particular, the boundary layer method and complex amplitudes. The proposed mathematical model feature is that it reflects the role of the boundary layer in the p-i-n structure contact zones in the formation of a space charge and takes into account the effect of a displacement current caused by microwave radiation. An algorithm for predicting the charge carrier concentrations distribution in the electron-hole plasma is constructed. It is shown that an extraneous microwave field entails an additional increase in the stationary concentration of electrons and holes in the active region, against which the plasma concentration fluctuates at the microwave field frequency (the appearance of higher harmonics is not taken into account in the model). The effect of the growth of the concentration stationary component is more pronounced in the zones of p-i-, n-i-contacts. The proposed mathematical model and the developed algorithm for analyzing the problem posed are important for developers of microwave electronics semiconductor elements, in particular, p-i-n structures used for switching powerful electromagnetic fields and as protective devices for the input paths of radio engineering systems.