Effect of the Surface on the Electron Quantum Size Levels and Electron g-Factor in Spherical Semiconductor Nanocrystals

TL;DR

This paper investigates how the surface of spherical semiconductor nanocrystals influences electron energy levels and g-factors, revealing surface-induced spin-orbit effects and magnetic moments through an eight-band effective mass model.

Contribution

It introduces a boundary condition model for surface effects on electron states and determines the surface parameter from experimental g-factor data in CdSe nanocrystals.

Findings

Surface induces spin-orbit splitting in conduction band states.

Surface contributes to nonzero Zeeman splitting of energy levels.

Determined surface boundary parameter from g-factor size dependence.

Abstract

The structure of the electron quantum size levels in spherical nanocrystals is studied in the framework of an eight--band effective mass model at zero and weak magnetic fields. The effect of the nanocrystal surface is modeled through the boundary condition imposed on the envelope wave function at the surface. We show that the spin--orbit splitting of the valence band leads to the surface--induced spin--orbit splitting of the excited conduction band states and to the additional surface--induced magnetic moment for electrons in bare nanocrystals. This additional magnetic moment manifests itself in a nonzero surface contribution to the linear Zeeman splitting of all quantum size energy levels including the ground 1S electron state. The fitting of the size dependence of the ground state electron g factor in CdSe nanocrystals has allowed us to determine the appropriate surface parameter of the boundary conditions. The structure of the excited electron states is considered in the limits of weak and strong magnetic fields.