Macroscopic vs. microscopic models of circular Quantum Dots

TL;DR

This paper compares macroscopic and microscopic models of electron confinement in circular quantum dots, analyzing their accuracy and the significance of various confinement contributions across different modeling approaches.

Contribution

It provides a systematic comparison of models from 3D Hartree to semiclassical and parameterized approaches for quantum dots.

Findings

2D Hartree calculations are accurate for moderate-sized dots.

Thomas-Fermi approximation is effective for dots with around 50 electrons.

Shikin's parameterization helps quantify contributions to confinement potential.

Abstract

The confinement mechanism of electrons in gated circular quantum dots is studied in a sequence of models, from self-consistent 3D Hartree calculations to the semiclassical model of Shikin et al. Separation of the vertical from transverse confinement allows accurate 2D Hartree calculations. For moderate size dots containing $\sim 50$ electrons, 2D Thomas-Fermi can also be accurate. Finally, a Shikin type parameterization of the electron density allows quantitative study of the importance of the many contributions to the confinement potential.