Thickness Dependence of Carrier-Electron States in Doped Semiconductor Films

Abstract

By means of the local-density-functional formalism, we examine the thickness dependence of carrier-electron states in doped semiconductor films with and without surface carrier-depletion layers. The film thickness is varied in a broad range where our carrier system evolves from a virtually semi-infinite (S-I) system to a quasi-two-dimensional (2D) one. The carrier-density distribution near the surface and the level of the chemical potential are found to remain the same as those of the S-I system down to such a small thickness that carrier motion normal to the surfaces is quantized significantly. With further decrease in film thickness, our carrier system evolves from the above S-I-like system into a quasi-2D one differently in the absence and presence of the depletion layers.