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

Schultz, Zachary M.; Essick, John M.

doi:doi:10.1119/1.2825391

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American Journal of Physics -- March 2008 -- Volume 76, Issue 3, pp. 241

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

Zachary M. Schultz and John M. Essick

Reed College, Department of Physics, Portland, Oregon 97202

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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 a_B. 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 a_B<R<2a_B. We discuss why our model breaks down for smaller radii.