Electronic states in quantum films

Department of Physics, Peking University - Beijing 100871, PRC

Received: 3 June 2003
Accepted: 13 October 2003

Abstract

Exact and general results on the electronic states in quantum films bounded at and —here is the only primitive lattice vector out of the film plane, is the bottom boundary and N₃ is a positive integer indicating the thickness of the film— are presented. In many interesting cases, such as in face-center cubic (001) and (110) films, the energies of most electronic states in the film can be analytically obtained from the corresponding energy band structure of the bulk: For each energy band of the bulk and each wave vector in the film plane, there are N_3-1 electronic states in the film whose energy is dependent on the film thickness N₃ but not on the film boundary and maps the energy band of the bulk exactly, and there is one electronic state whose energy is dependent on but not on N₃ and is above or at the highest energy in that energy band with that . This approach can be further extended to obtain exact and general results on electronic states in quantum wires and quantum dots.