Effects of finite spin-orbit splitting on optical properties of spherical semiconductor quantum dots

The multiband envelope-function formalism-of which a convenient, analytical formulation is presented-is used to investigate the energies and wave functions of valence-band levels in spherical nanocrystallites of several III-V and II-VI compound semiconductors with finite spin-orbit splitting energy Delta. Interband absorption spectra are deduced. A significant influence of the split-off band is found even in cases where Delta is large, as for CdTe. In fact, Delta is not a decisive criterion for the strength of couplings; Luttinger parameters play a major role. Numerical results are presented for size-distributed crystallites of various binaries (CdTe, CdSe, CdS, GaAs, InP). These are analyzed in terms of the accuracy of measuring the sizes from absorption spectra by using a fitting procedure, and of performing size-selective excitation of photoluminescence. It is also found that optical transitions between the ground valence- and conduction-band levels may be forbidden, due to incompatible symmetries. Calculations neglecting the influence of the split-off band are unable to account for this property, which strongly affects photoluminescence mechanisms.