QUANTUM CONFINEMENT EFFECTS IN SEMICONDUCTOR NANOPARTICLES: A FIRST-PRINCIPLES STUDY OF ELECTRONIC AND OPTICAL PROPERTIES

Abstract

When the diameter of a semiconductor particle falls below the Bohr diameter of its exciton, the optical gap and the spectrum of electronic levels depend on particle size, and the material can be tuned across the visible and near-infrared range without changing its composition. In this article we study confinement in spherical nanoparticles of CdS, CdSe, CdTe, ZnSe and InP by solving the quantum-mechanical envelope-function problem directly. Single-particle states are obtained for a finite spherical well with an energy-dependent effective mass and a Ben Daniel–Duke boundary condition, and the electron–hole Coulomb attraction is added to first order from the computed wavefunctions. No atomistic calculation was performed. The inputs are bulk band-edge parameters from the literature, and only two quantities were chosen with reference to experiment: a barrier height of 2 eV and the use of static screening, both selected against one published CdSe sizing curve. For CdSe the lowest transition moves from 1.83 eV (676 nm) at 8 nm to 2.73 eV (455 nm) at 2 nm. At 4 nm the electron and hole confinement energies are 0.30 and 0.15 eV and the Coulomb term lowers the transition by 0.11 eV, or 24% of the confinement energy. Treating the barrier as infinite overestimates the size-induced shift by 68 to 86% between 3 and 6 nm, because about 4% of the electron density of a 4 nm particle lies outside it. Against the experimental curve the model has a root-mean-square deviation of 47 meV, with errors below 43 meV up to a diameter of 3.3 nm and an underestimate of up to 73 meV between 5.6 and 7 nm. The spectral sensitivity reaches 41 nm per nm of diameter for CdSe at 4 nm, so a 5% size dispersion alone broadens the lowest transition by about 19 nm. We state which conclusions this level of theory can support, give a reporting checklist, and outline the atomistic first-principles calculations that would test the remaining discrepancies.