Quantum size level structure of narrow-gap semiconductor nanocrystals: Effect of band coupling

We study the size dependence of electron and hole quantum size levels in spherical semiconductor nanocrystals. An analytical theory of the quantum size levels within a spherical eight-band Pidgeon and Brown model has been developed, which takes into account both the coupling of conduction and valence bands and the complex structure of the valence band in nanocrystals with an infinite potential barrier. We show that in narrow gap semiconductors band mixing must always be taken into account and that it may be important even in wide gap semiconductors, because the mixing is governed by the square root of the ratio of the quantization energy to the energy gap. The strength of the coupling also depends on the ratio of the contributions of remote bands to the effective masses of the electron and the light hole. As a result level structure is very sensitive, in general, to the energy band parameters. The calculated level structure for narrow gap InSb, moderate gap CdTe, and wide gap CdS nanocrystals are presented.