Hole States in Spherical Quantum Nanoheterosystem with Intermediate Spin-Orbital Interaction

I.V. Bilynskyi,R.Ya. Leshko,H.O. Metsan,I.S. Shevchuk

doi:10.15330/pcss.20.3.227-233

Abstract

The hole energy spectrum has been studied for the spherical semiconductor nanoheterosystem with the cubic symmetry. The exact solutions of the Schrödinger equation for the ground and excited hole states are presented within the framework of the 6-band Luttinger Hamiltonian and the finite gap of bands with the corresponding boundary conditions. Dependence of the holes energies from the radius of the quantum dot has been calculated for the GaAs/AlAs heterostructure. Obtained results where compared with data obtained using the infinite potential well model, as well as the single-band model for heavy and light holes.

Highlights

Significant success has been achieved in the theoretical and experimental studies of nanoheterostructures over the past two decades
There are many theoretical publications concerning the investigation of the spectra of electrons, holes and excitons in quantum dots of different configurations [8,9,10]
Peaks are clearly visible in these spectra in the case of a small change in the quantum dots (QDs) size

Summary

Introduction

Significant success has been achieved in the theoretical and experimental studies of nanoheterostructures over the past two decades. Peaks are clearly visible in these spectra in the case of a small change in the QD size These peaks correspond to interband optical transitions that are related with different electron and hole quantum states. In the study of electronic states often the complex structure of the valence band in semiconductors, that forming the heterosystem [9, 11,12, 15, 16], don’t take into account In these cases, the effective mass approximation were used. The inhomogeneous change in the effective mass of quasiparticles near heterojunctions is taken into account, the so-called single-band approximation These approximations are suitable for electronic states of wide-band crystals forming a heterosystem. The qualitative and quantitative compare obtained results for different models of hole states

The spherical semiconductor nanocrystal with radius

Jz ψ B

All numerical calculations have been obtained for