Temperature-dependent bandgap in nanoclusters

Temperature-dependent bandgap in nanoclusters

The wide tunability of the fundamental electronic bandgap by size control is a key attribute of semiconductor nanocrystals, enabling applications spanning from biomedical imaging to optoelectronic devices. At finite temperature, exciton-phonon interactions are shown to exhibit a strong impact on this fundamental property.

In materials at the border between solids and molecules, the temperature-dependence of the bandgap differs significantly from bulk materials. Due to the strong quantum confinement, excitons in nanocrystals are distributed over a spatial region encompassing only a few tens of chemical bonds, leading to a strongly enhanced exciton-phonon coupling. By occupying antibonding states, the presence of the exciton causes a pronounced weakening of the bonds and a strong exciton-induced shift of the phonon spectrum. This shift is enhanced by almost 2 orders of magnitude, compared to the bulk. As a consequence, a drastic enhancement of the temperature-dependent shift of the bandgap is observed, i. e. the photon as the probe medium itself is found to fundamentally affect the material to be studied.

Comparison of computed and measured temperature-dependent band gap for a (CdSe)13 magic-sized nanocluster.

We compute the temperature-dependent band gap as the Gibbs free energy of formation for the electron-hole pair. Entropy contributions are explicitly taken into account. Using constrained density-functional molecular dynamics on the excited state potential energy surface and the principle of maximum entropy, we explore exciton-phonon coupling and compute the change in vibrational entropy associated with the creation of an exciton. Our approach allows for the first time to compute temperature-dependent bandgaps in nanoclusters with quantitative accuracy. We compare our results to spectroscopic measurements for single, monodisperse magic-sized nanoclusters.

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