Single-particle states in spherical Si/SiO$_2$ quantum dots

TL;DR

This paper calculates the energy levels of electrons and holes in spherical silicon quantum dots within silicon dioxide, considering anisotropic effective masses and boundary conditions, to understand their electronic structure.

Contribution

It introduces a detailed multiband effective mass model for spherical Si/SiO2 quantum dots, including anisotropy and boundary conditions, for accurate energy level calculations.

Findings

Calculated ground and excited states for electrons and holes.

Accounted for anisotropic effective mass of electrons in Si.

Used boundary conditions ensuring wave function continuity.

Abstract

We calculate ground and excited electron and hole levels in spherical Si quantum dots inside SiO$_2$ in a multiband effective mass approximation. Luttinger Hamiltonian is used for holes and the strong anisotropy of the conduction electron effective mass in Si is taken into account. As boundary conditions for electron and hole wave functions we use continuity of the wave functions and the velocity density at the boundary of the quantum dots.