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

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 toward the QD surfaces with high electron densities and large radii and when solvated by a high dielectric medium. (ii) The maximum density of the conduction-band electrons depends strongly on the dielectric strength of the solvent and the electron affinity and dielectric strength of the QD material. (iii) Fermi-level energies stabilize with charge-balancing cations in close proximity to the QD surface.