Accurate Model of a Vertical Pillar Quantum Dot

TL;DR

This paper presents a precise three-dimensional model of a vertical pillar quantum dot that accurately predicts experimental data, including magnetic field effects, by incorporating device-specific potentials and adjustable parameters.

Contribution

It introduces a comprehensive 3D device-based model with a novel effective 2D approach and detailed numerical methods, improving the accuracy of quantum dot simulations.

Findings

Model explains magnetic field dependent data within 5% accuracy

Numerical procedures enable stable calculations of interaction potentials

Parameter extraction from experimental data is demonstrated

Abstract

An accurate model of a vertical pillar quantum dot is described. The full three dimensional structure of the device containing the dot is taken into account and this leads to an effective two dimensional model in which electrons move in the two lateral dimensions, the confinement is parabolic and the interaction potential is very different from the bare Coulomb potential. The potentials are found from the device structure and a few adjustable parameters. Numerically stable calculation procedures for the interaction potential are detailed and procedures for deriving parameter values from experimental addition energy and chemical potential data are described. The model is able to explain magnetic field dependent addition energy and chemical potential data for an individual dot to an accuracy of about 5%, the accuracy level needed to determine ground state quantum numbers from experimental transport data. Applications to excited state transport data are also described.