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

We perform self-consistent electronic structure calculations in the framework ofinhomogeneously and anisotropically scaled local density functional theory of a fully3D 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, andthe differential capacitances for various dot sizes are calculated. We observe shell fillingeffects in the differential capacitance. The magic-numbers are governed by the six valleybandstructure of silicon, which leads to four fold degenerated single particle levels in thedot