Numerical study of the effect of surface recombination on nonlinear and phase distortions arising during the restoration of the optical signal shape

V. Ya. Grishaev ; S. M. Muryumin ; E. V. Nikishin

Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 2, pp. 215-227

Résumé

The photoconductivity kinetics of a resistor with homogeneous generation of electrons and holes in thickness is investigated. Calculations are carried out for an $n$-type semiconductor. The cases of linear and quadratic volumetric recombination are considered. The mathematical model of the process includes a non-linear parabolic partial differential equation. The cause of its non-linearity is quadratic recombination. Boundary conditions of the 3rd kind are used, thus allowing to examine the surface recombination of nonequilibrium charge carriers. This latter phenomenon makes it necessary to take into account the diffusion term when writing kinetic equations describing the distribution of electrons and holes. The model neglects the volumetric charge. In described circumstances it is possible to use the integration of the photocurrent flowing through the resistor to obtain the dependence of the light intensity on time for small optical pulse durations: $T \max{(\tau_n, \tau_p)}$. Here $T$ is the pulse duration, $\tau_n$ and $\tau_p$ are the lifetimes of electrons and holes, respectively. Nonlinear distortions in this case are mainly associated with the appearance of the second and the third harmonics of the Fourier series expansion of the function that determines the photocurrent dependence on time. To "restore" the optical pulse, the operation of differentiating the photocurrent can be used. Nonlinear and phase distortions are small when the condition $T \max{(\tau_n, \tau_p)}$ is met. Proposed methods make it possible to expand the range of optical pulse durations ($T$) in which its "recovery" is possible. In the vicinity of the region defined by the equality $T\approx \max{(\tau_n, \tau_p)}$, nonlinear and phase distortions are significant.

Détail

Keywords: mathematical model, non-linear parabolic equation, recombination mechanisms, kinetics of photoconductivity, nonlinear distortions, frequency distortions, phase distortions, pulse recovery.