Quantum confinement effect in silicon quantum-well layers

Abstract

The electronic states and optical transition properties of silicon quantum-well layers embedded by ${\mathrm{SiO}}_{2}$ layers are studied by the empirical pseudopotential homojunction model. The energy bands, wave functions, and the optical transition matrix elements are obtained for layers of thickness from 1 to 6 nm, and three oriented directions (001), (110), and (111). It is found that for Si layers in the (001) direction the energy gap is pseudodirect, for those in the (111) direction the energy gap is indirect, while for those in the (110) direction the energy gap is pseudodirect or indirect for a thickness smaller or larger than 3 nm, respectively. The optical transition matrix elements are smaller than that of direct transition, and increase with decreasing layer thickness. When the thickness of a layer is smaller than 2 nm, the Si QW layers have larger transition matrix elements. It is caused by mixing of bulk $X$ states with the ${\ensuremath{\Gamma}}_{1}$ state. The calculated results are compared with experimental results.