Contrasting temperature dependence of the band gap in CH3NH3PbX3 ( X = I , Br , Cl ): Insight from lattice dilation and electron-phonon coupling

Although hybrid halide perovskites ( MAPbX3, MA = CH3NH3 and X = I , Br , Cl ) have been ubiquitously explored from the photovoltaic perspective, there are still a few unanswered questions which require a more fundamental understanding. One such unsettled issue is the puzzling behavior of the band gap. Unlike conventional semiconductors, MAPbX3 ( X = I , Br ) is found to show a blueshift (increase) in the band gap ( Eg ) with increasing temperature ( T ) , while MAPbCl3 shows an unusual redshift (decrease). In order to understand this, we performed a detailed T-dependent study of electronic, optical, and structural properties of MAPbX3 combined with the state-of-the-art first-principles calculations. With increasing T , two dominant mechanisms which come into play are lattice dilation and electron-phonon coupling (EPC). The former (latter) is responsible for an increase (decrease) in Eg. We found that lattice dilation effect dominates in MAPbX3 ( X = I , Br ) , causing an enhancement in Eg. EPC involves various contributions, of which the interaction of charge carriers with the longitudinal optical phonon mode via Fröhlich interaction is the most dominant one at room temperature. We quantify this contribution using Fröhlich's theory of large polarons and show that the Eg correction due to this effect in MAPbCl3 is almost double as compared to MAPbBr3 and thus explain the reduction in Eg for the former.