Investigation of exciton ground state in quantum dots via Hamiltonian diagonalization method

Abstract

We analyze the electron-hole (exciton) ground state associated with the first peak in the optical absorption spectra of semiconductor quantum dots. We assume the effective mass approximation and a dot radius R on the order of the exciton Bohr radius aB. A Hamiltonian diagonalization method which accounts for the exciton’s kinetic, direct Coulomb, and surface polarization energies is used. We obtain a representation of the exciton ground-state wavefunction and a value for its energy using a basis set consisting of only three composite infinite spherical well wavefunctions. We discuss the precision obtained by this basis set by comparing with results from a much more extended basis set. Our results are used to predict the radius-dependent energy of the first peak in visible-light absorption spectra for CdSe quantum dots. Our analysis accurately describes the experimental data for dots with radii in the range aB<R<2aB. We discuss why our model breaks down for smaller radii.