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Perovskite gaps ruled by thermal expansion and electron-phonon interaction

In lead halide perovskites, the variation of the fundamental gap with temperature is equally determined by thermal expansion and electron-phonon interaction effects

For all the spectacular developments in lead-halide perovskite-based photovoltaics, there are still several fundamental physical questions that remain a matter of debate. In particular, this is the case of the atypical temperature dependence of the fundamental optical gap of most halide perovskites, for which the gap increases with increasing temperature.

So far, the available literature ascribes such a behavior to a particularly strong electron-phonon renormalization of the band gap, neglecting completely contributions from thermal expansion. However, high pressure experiments performed, for instance, on the archetypal perovskite methylammonium lead tri-iodide (MAPI) yield a negative pressure coefficient for the gap of the tetragonal room-temperature phase, which speaks against the assumption of a negligible gap shift due to thermal expansion.

On the basis of the high pressure results, we show here that for MAPI the temperature-induced gap renormalization due to electron-phonon interaction can only account for about 40% of the total energy shift, thus implying thermal expansion to be more if not as important as electron-phonon coupling. This result possesses general validity, holding also for the structural phases, stable at ambient conditions, of most halide perovskite counterparts. Given the relevance of the electron-phonon interaction for a variety of physical phenomena apart from the temperature dependence of the gap (charge transport, exciton lifetimes, non-radiative relaxation processes, thermoelectric properties, etc.), its correct assessment is fundamental for further scientific and/or technological developments in the field.

Equal Footing of Thermal Expansion and Electron-Phonon Interaction in the Temperature Dependence of Lead Halide Perovskite Band Gaps
Adrián Francisco-López, Bethan Charles, M. Isabel Alonso, Miquel Garriga, Mariano Campoy-Quiles, Mark T. Weller, Alejandro Goñi
J. Phys. Chem. Lett. 10, 2971−2977, 2019
DOI: 10.1021/acs.jpclett.9b00876

Figure: Sketch illustrating the contribution from thermal expansion (TE) and electron-phonon interaction (EP) to the temperature-induced renormalization of the perovskite band gap with temperature (data points).  

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