Exact calculation of single-electron states in Si-nanocrystal embedded in SiO2

TL;DR

This paper provides an exact calculation method for single-electron states in Si-SiO2 quantum dots, accounting for material properties and validating approximate methods for many-electron systems.

Contribution

It introduces a precise approach to compute single-electron energies in realistic quantum dots, including material-dependent effective masses, and verifies approximate methods.

Findings

Energy levels shift by tens to hundreds of meV compared to simplified models.

The exact calculation improves understanding of electronic structure in Si nanocrystals.

Validation of approximate methods for many-electron systems using exact single-electron results.

Abstract

We present an exact calculation of the single-electron energies and wave-functions for any bound state in a realistic Si-SiO2 spherical quantum dot, including the material dependence of the electron effective mass. The influence of dot radius, confinement barrier potential and barrier-to-dot electron mass ratio on the electronic structure is investigated in detail. The results show that the energy structure shifts down from some tens to some hundreds meV compared to that obtained in the simplified model where the change in effective mass is neglected. Our exact single-electron calculation is finally used to verify the accuracy of the results obtained from a numerical approximate method developed to treat many-electron systems.