Excited states of an electron-hole pair in spherical quantum dots and their optical properties

The energy-level structure of a correlated electron-hole pair confined in spherical quantum dots and their optical properties are theoretically investigated. An efficient method of numerical calculation is presented for the eigenvalue problem of the excited states of the electron-hole pair with an arbitrary total angular momentum, which employs the Hylleraas coordinate system and a correlated-basis-set expansion. It is shown that the picture of exciton confinement holds generally when the dot radius is several times larger than the effective Bohr radius of the exciton, but the amount of blue shift in the excited states of the relative motion is larger than that in the lowest S-like state. In addition to the one-photon absorption spectra, the excited-state absorption and the two-photon absorption spectra are investigated. The calculated spectra show good agreements with those observed in CuCl nanocrystals.