Confinement Characterization of a 2-Electron Quantum Dot

TL;DR

This paper solves the Schrödinger equation for two electrons in a parabolic quantum dot, clarifying how the confinement potential influences system energy and aiding in device parameter validation.

Contribution

It introduces a parameterization method that separates confinement strength from effective mass, improving characterization of quantum dot systems.

Findings

Explicit solution for two-electron quantum dot energy levels

Enhanced understanding of confinement potential effects

Improved validation of effective mass assumptions in devices

Abstract

The time independent Schoedinger equation for two electrons confined in a parabolic external potential is solved. Developing this solution in terms of a dimensionless variable it is demonstrated that parameterization of the strength of the confining potential separate from the effective mass assumption greatly clarifies the functional dependence of the system energy on the system parameters. The determination of the strength of the external confinement and validation of the effective mass assumption in real devices is greatly improved by characterizing the strength of the confining potential separate from the effective mass.