Towards an Atomistic Picture of Quantum Dots—Simulating Absorption Spectra and Exciton-Phonon Coupling

Understanding the electronic structure of quantum dots (QDs) on an atomistic scale has the potential to drastically improve the performance of nanomaterial devices. Previous density functional theory (DFT) results draw a clear connection between undercoordinated chalcogenide atoms and the existence of deep trap states in II-VI QDs, for example. [1] However, most computational works only consider equilibrium structures at 0 K, which impedes direct comparison with experiment. Even routine measurements such as UV-Vis absorption spectra are not accurately predicted by simple DFT methodologies [2, 3]. Our work seeks to bridge the gap between theory and experiment, to facilitate a better atomistic understanding of QDs.<br/>The Nuclear Ensemble Approach (NEA) [4] is the conventional method for simulating spectra that account for thermal and ensemble averaging. We show that NEA is effective in reproducing experimental results, but is prohibitively expensive for QDs that are beyond the ultrasmall regime.<br/>To address this issue, our group proposes the less resource-intensive Harmonic Approximation (HA) approach, inspired by the independent mode displaced harmonic oscillator model. We assume the electronic potential energy surfaces of QDs to be harmonic, with excited states having the same curvature as the ground state. Absorption spectra for a series of II-VI QDs computed with the equilibrium HA accurately capture homogeneous broadening, at a fraction of the cost of the NEA method. To further include inhomogeneous broadening, we also developed the averaged HA. This technique requires limited sampling from an ab-initio molecular dynamics trajectory and accounts for the thermal expansion of QDs, as well as for some anharmonicity. This method yields highly accurate absorption spectra, at less than 50% of the cost of NEA.<br/>With these results in mind, we hypothesize that the harmonic approximation works sufficiently well for modelling broadening effects in II-VI QD linear spectra. A leading cause of spectral broadening, exciton-phonon coupling, is subsequently investigated using the Huang-Rhys (HR) factor metric. Our findings suggest that low-frequency modes and LO phonons have the strongest coupling to electronic excitations, particularly with surface-localized trap states. Additionally, the degree of surface passivation drastically affects the average HR factor, with higher ligand coverage decreasing the exciton-phonon coupling. This leads to narrower absorption lines and steeper Urbach slopes, suggesting that phonons play a significant role in explaining passivation behavior.<br/>The Harmonic Approximation DFT-based toolbox thus allows users to disentangle homogeneous and inhomogeneous broadening effects in QD absorption spectra across a wide range of temperatures. It also provides qualitative insights into the strength of exciton-phonon coupling and the slope of Urbach spectral tails. These methods could facilitate the more robust computational testing of passivation strategies and their effects on absorption and emission spectra, before experimentally validating them.<br/><br/>[1] - Houtepen, A. J. <i>et al.</i> <i>Chem. Mater.</i> 2017, 29, 752-761.<br/>[2] – Fischer, S. A. <i>et al.</i> <i>Nanoscale</i> 2012, 4, 904-914.<br/>[3] – Del Ben, M.<i> et al.</i> <i>J. Phys. Chem. C</i> 2011, 115, 16782-16796.<br/>[4] – Kossoki, F. <i>et al.</i> <i>JCTC</i> 2018, 14, 3173-3183.