Electronic Structure of the Carrier System in Small Semiconductor Particles

We clarify characteristics of the electronic structure of the carrier system in small semiconductor particles, and investigate the size dependence of this electronic structure with the doping level fixed. We assume spherical doped semiconductor particles in an insulating medium or in the vacuum, and calculate the carrier density distribution and the effective one-particle potential self-consistently. Irrespective of the particle size, a prominent peak appears right inside the carrier-deficient surface layer in the carrier density profile. With increase of the size, the density oscillation inside the prominent peak becomes less and less conspicuous, which reduced to nearly constant density to tend toward charge neutrality. The remarkable variation of the potential bending with increasing size depends on where the probability density of newly occupied carrier states is concentrated. This potential variation often entails the intersection of two close energy levels with different concentration features in their probability density distribution