Binding and Recombination Energies of Quasi-One-Dimensional Excitonic Complexes in Ellipsoidal Quantum Dot

David B Hayrapetyan

doi:10.3390/foundations2010015

Abstract

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate character, all excitonic complexes are considered quasi-one-dimensional. As in such a system, the analytical solution does not exist for the many-particle problem, it is solved by the variational method. The trial variation functions based on the one-particle wave functions are used to construct the wavefunctions for the excitonic complexes. The energy spectrum, binding, and recombination energies dependent on the geometrical parameters of the ellipsoidal quantum dots are calculated for the excitons, negative and positive trions, and biexcitons. The radiative lifetime of exciton complexes in ellipsoid is estimated.

Highlights

In quantum dots (QD), optically generated excitonic complexes can exist in different states: neutral monoexciton X, negatively charged exciton X− (2e − h), positively charged exciton X+ (e − 2h), biexciton XX (2e − 2h), etc.Investigation of the excitonic complexes of semiconductor QDs, where the parameters can be tuned in a wide range, are of importance both from the point of view of fundamental and applied physics
The energy of the positive trion is close to the exciton energy, and the energy of the negative trion is close to the biexciton energy
The regularity, that the negative trion energy is higher than the energy of the positive trion, is because X − consists of two electrons and one hole and X + consists of two holes and one electron

Summary

Introduction

In quantum dots (QD), optically generated excitonic complexes can exist in different states: neutral monoexciton X (one electron and one hole e − h), negatively charged exciton X− (2e − h), positively charged exciton X+ (e − 2h), biexciton XX (2e − 2h), etc.Investigation of the excitonic complexes of semiconductor QDs, where the parameters can be tuned in a wide range, are of importance both from the point of view of fundamental and applied physics. The investigation of excitonic complexes in bulk semiconductors is difficult to achieve experimentally; the reason for this is the small value of the binding energy [1,2,3,4,5] This problem does not arise in the semiconductor nanostructures, in QDs because of the effects of size quantization [6,7,8,9,10]. Biexciton and trion states in quantum nanostructures with different shapes and geometries need to be theoretically and experimentally investigated The realization of these complexes in QDs can be applied for the development of quantum information processes. The theoretical and experimental investigation of these structures is an actual problem, due to the application of these structures in many areas of novel technologies

Methods

Results

Conclusion