Size-quantization of carriers in quasi-zero-dimensional structures

A theory of size-quantization of carriers in a small semiconductor sphere is developed under the conditions when the polarization interaction is dominant. The energy spectrum of carriers in the small semiconductor sphere and its dependences on the radius of the sphere, on the effective mass of carriers, and on the relative permittivity are studied. It is shown that there is a threshold radius of the sphere for the formation of local states of carriers