Abstract
Two-dimensional and three-dimensional mathematical models of diffusion and cathodoluminescence of excitons in single-crystal gallium nitride excited by a pulsating sharply focused electron beam in a homogeneous semiconductor material are compared. The correctness of these models has been carried out, estimates have been obtained to evaluate the effect of errors in the initial data on the distribution of the diffusing excitons and the cathodoluminescence intensity.
Highlights
Registration of informative signals excited in a semiconductor target and comparison of experimental data with a mathematical model of this phenomenon make it possible to identify semiconductor parameters that are very difficult or even impossible to determine by other methods
The need for the study is due to the insufficient knowledge of the physical phenomenon under consideration: there are only a few publications devoted to studies of the correctness of mathematical models used in electron beam technologies [1,2,3,4]
A mathematically correct study of mathematical models of physical phenomena arising from the interaction of electron beams with semiconductor objects and described by differential equations of heat and mass transfer with partial derivatives has practically not
Summary
Registration of informative signals excited in a semiconductor target and comparison of experimental data with a mathematical model of this phenomenon make it possible to identify semiconductor parameters that are very difficult or even impossible to determine by other methods. It can be said that previously the task of modelling diffusion (and subsequent radiative recombination with the release of cathodoluminescent (CL) radiation from a semiconductor) for the process under consideration was to a certain extent semiquantitative It was solved only when using the model of energy losses by primary lowenergy electrons in the target in the form of a two-dimensional normal Gaussian distribution, which is a rather rough approximation that describes the available experimental data on energy losses in a condensed matter only qualitatively [5, 6]. The solution to the problems of identifying the electrophysical parameters of semiconductors is largely determined by the correctness of the used mathematical models, which is the subject of consideration in this paper as applied to the diffusion of nonequilibrium minority charge carriers (MCC) or excitons generated by the electron beam and their subsequent radiative recombination
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