A Hybrid Quantum-Classical Model of Electrostatics in Multiply Charged Quantum Dots

Abstract

We present a general model for describing the properties of excess electrons in multiply charged quantum dots (QDs). Key factors governing Fermi-level energies and electron density distributions are investigated by treating carrier densities, charge compensation, and various material and dielectric medium properties as independently tunable parameters. Electronic interactions are described using a mean-field electrostatic potential calculable through Gauss's Law by treating the quantum dot as a sphere of uniform charge density. This classical approximation modifies the Particle in a Sphere'' Schrodinger equation for a square well potential and reproduces the broken degeneracy and Fermi-level energies expected from experiment and first-principles methods. Several important implications emerge from this model: (i) Excess electron density drifts substantially towards the QD surfaces with high electron densities and large radii, and when solvated by a high dielectric medium. (ii) The maximum density of condu...