Exciton–LO-phonon couplings in spherical semiconductor microcrystallites

Exciton–LO-phonon couplings in ${\mathrm{CdS}}_{\mathit{x}}$ ${\mathrm{Se}}_{1\mathrm{-}\mathit{x}}$ semiconductor microcrystallites (x=0.12±0.05) are investigated by measuring the temperature dependence of the width and energy of excitons by electroabsorption. The LO phonons are shown semiquantitatively to contribute to the experimentally obtained temperaure dependencies of the width and energy of excitons. The dependence of the coupling constant (the Huang-Rhys parameter) on the radius of microcrystallites is calculated for CdSe and GaAs microcrystallites. The phonon confinement effects are considered with ‘‘free-standing’’ and ‘‘rigid’’-boundary conditions. As for the exciton state, nonparabolicity of the conduction band and the valence-band mixing are considered in order to obtain a precise exciton wave function, which is crucially important in calculating the Huang-Rhys parameter in a microcrystallite. The exciton–confined-optical-phonon interaction Hamiltonian is constructed for a microcrystallite. It is found that the Huang-Rhys parameters have a minimum at a radius of 70 Å for CdSe and 270 Å for GaAs microcrystallites. The size dependence of the Huang-Rhys parameter is also calculated for a microcrystallite with an extra charge at the spherical-particle center. The lowest (s,${\mathit{S}}_{3/2}$) state in the trapped state is found to have small transition probability and g values of 1 in CdSe (R=30 Å) and 0.01 in GaAs (R=100 Å). The higher states are found to have larger transition probability and g values of 0.7 in CdSe (R=30 Å) and 0.01 in GaAs (R=100 Å). These results suggest that large g values observed experimentally in CdS and CdSe microcrystallites originate from extrinsic effects such as the presence of charged point defects inside the microcrystallite.