Self-Consistent Calculations of the Ground State and the Capacitance of a 3D Si/SiO₂ Quantum Dot

Abstract

We perform self-consistent electronic structure calculations in the framework of inhomogeneously and anisotropically scaled local density functional theory of a fully 3D modeled Si/SiO₂ quantum dot. Electrons are laterally confined in the semiconductor/ oxide heterojunction by a metallic gate atop of the device. Total charge densities, total free energies, chemical potentials for different numbers of electrons in the dot, and the differential capacitances for various dot sizes are calculated. We observe shell filling effects in the differential capacitance. The magic-numbers are governed by the six valley bandstructure of silicon, which leads to four fold degenerated single particle levels in the dot.