Effect of Thermal Deformation on the Quasiparticle Gap and Exciton Binding Energies in Semiconductor Quantum Dots

Spectroscopic properties of semiconductor nanoparticles (NPs) exhibit strong dependence on NP shape and size. At finite temperatures, the NPs exists in an ensemble of structures and inclusion of these structures is essential for accurate theoretical investigation of the optical properties of these materials. However, performing ensemble-averaged calculations using conventional electronic structure theories prohibitive because of steep computational cost. In this work, we present a random matrix based statistical mechanical procedure for ensemble-averaged calculations of optical properties of semiconductor NPs. This approach is based on deriving an effective fluctuating potential for the NPs to account for the thermal fluctuations in the system. The method was applied to a series of CdSe quantum dots (Cd₂₀Se₂₀-Cd₂₀₀Se₂₀₀) and was used for calculation of ensemble-averaged excitonic properties including quasiparticle gap, optical gap, exciton binding energies, and electron-hole recombination probabilities. The results from these calculations highlight the importance of ensemble averaging and demonstrate the limitations of using a single optimized NP structure for computational prediction of optical properties of NPs.