Coulomb correlations in an electron-hole semiconductor plasma in the vicinity of a quantum dot

Abstract

The paper considers coulomb correlations in electron-hole plasma of semiconductor heterostructures.As a heterostructure, a material based on a solid solution was chosen.As the potential that simulates the heterolayer, one-dimensional parabolic potential is taken.Unlike the commonly used heterolayer potential in the form of a rectangular well, a one-dimensional parabolic potential is chosen in the article.In the framework of this approximation, the Coulomb interaction of an electron and a hole in an exciton was considered as a perturbation.This choice of potential modeling a heterolayer has the following advantages:firstly, it allows us to abandon numerical calculations, replacing them with analytic studies;secondly, since the oscillatory potential grows indefinitely, the Coulomb interaction between the quasiparticles of the electron-hole plasma is small, in comparison with the heterolayer potential, which allows one to take it into account in the framework of perturbation theory.The wave functions of the electron-hole pair for the ground s-state are obtained and with their help the exciton binding energy is calculated as a function of the thickness of the heterolayer.In the framework of perturbation theory, the wave functions of the electron-hole pair (exciton) are obtained, and the main state of the exciton corresponding to the zero orbital momentum of the pair of quasiparticles (the s state of the exciton) is considered in the article.The calculations are performed for the ground state of the exciton corresponding to the s-state of the orbital motion of the electron and hole and zero vibronic numbers.The vibronic quantum numbers corresponding to the motion of an electron and a hole in a direction perpendicular to the heterolayerare also taken to be zero.Such a limit corresponds to a minimum of the exciton energy, i.e. its state of exciton.With the help of the found wave functions, the probability distribution of detection of the electron and hole at a distance ρ is obtained and analyzed as a function of the dimensionless coordinate ξ.With the help of the obtained wave functions, the binding energy of the ground state of the exciton is calculated as a function of the thickness of the heterolayer.The expressions obtained can be generalized to excitons with nonzero orbital quantum numbers.