First-Principles Treatment of Photoluminescence in Semiconductors

A comparison of two first-principles methodologies, (1) molecular dynamics (MD) sampling and (2) time integration along progression of subsequently occupied excited states for computing emission spectra of semiconductors at different levels of accuracy is presented. Photoluminescence (PL) linewidth broadening is calculated to account for the motion of ionic positions. (1) In the MD sampling method, excited state lifetimes are assumed to be very short due to quick cascade thermalization, leading to intense PL peaks in semiconductors at transition energies corresponding to the bandgap energy of the materials, according to Kasha's rule. Nuclear motion is modeled via adiabatic MD within VASP software. During MD, electronic orbital energies fluctuate through time according to electron–phonon coupling terms. A sampling of possible radiative transition energies along the MD trajectory contributes to PL line width inhomogeneous broadening σ1. Optically allowed transitions along fluctuating transition energies found at each MD time step model the emission spectra. (2) In the time integration method, nonadiabatic dynamics of a photoexcitation provides details of cascade thermalization and allows description of several channels of emission from long-lived intermediate states, taking into account non-radiative pathways, providing possible exceptions from Kasha's rule and demonstrating relatively small PL line broadening σ2, so that σ1 ≫ σ2. PL spectra calculated using different methods are applied to nanostructured TiO2 semiconducting materials in different quantum confinement regimes, showing optical gap narrowing due to confinement. Ti(OH)4, which is a precursor in TiO2 synthesis, wet TiO2 ⟨001⟩ nanowire (NW), and TiO2 anatase thin film models are presented and compared with experimental PL results. Computed time-integrated PL spectra for the TiO2 ⟨001⟩ NW accurately describe the relevant PL energy and, when used in conjunction with the MD sampling PL method, provide the realistic PL line width.