THE INFLUENCE OF QUANTUM DOT GEOMETRY ON HOLE ENERGY SPECTRA WITHIN THE FRAMEWORK OF THE LUTTINGER MODEL

Abstract

We present a theoretical study of the hole energy spectra and wave-function spatial distributions in spherical, cubic, and conical GaAs/AlAs quantum dots. The calculations are performed within the four-band Luttinger–Kohn model using a three-dimensional plane- wave expansion method, which allows for the exact analytical evaluation of the Hamiltonian matrix elements via the Fourier transforms of the nanostructure shape functions. We demonstrate that the reduction of spatial confinement symmetry from spherical to cubic and conical geometries alters the energy levels structure by taking off the characteristic four-fold and six-fold degeneracies into lower-symmetry multiplets. Cross-sectional distribution of probability density reveal that the hole states exhibiting distinct S-and P-like characteristics by a mixing of heavy- and light-hole components. Furthermore, a comparative analysis at a constant internal volume shows a blue-shift of the ground state energy confirming that geometric shapes with sharp boundaries minimize the effective carrier volume and significantly enhance quantum confinement.