Temperature dependence of band gaps in semiconductors: Electron-phonon interaction

Abstract

We have theoretically investigated, by ab initio techniques, the phonon properties of several semiconductors with chalcopyrite structure. Comparison with experiments has led us to distinguish between materials with d electrons in the valence band (e.g., CuGaS 2 , AgGaS 2 ) and those without d electrons (e.g., ZnSnAs 2 ). The former exhibit a rather peculiar nonmonotonic temperature dependence of the energy gap which, so far, has resisted cogent theoretical description. We analyze this nonmonotonic temperature dependence by fitting two Bose-Einstein oscillators with weights of opposite sign leading to an increase at low temperatures and a decrease at higher temperatures and find that the energy of the former correlates well with characteristic peaks in the phonon density of states associated with low-energy vibrations of the d-electron elements. We hope that this work will encourage theoretical investigations of the electron-phonon interaction in this direction, especially of the current ab initio type.

Temperature-dependent optical spectra of single-crystal (CH3NH3)PbBr3 cleaved in ultrahigh vacuum

“…The band gap increases slightly with temperature below 200 K, and decreases at higher temperatures. This behavior has been observed for other semiconductors [76] including CsPbBr 3 [75], and can be understood within the BoseEinstein model [77]: …”

Anomalous Temperature Dependence of the Band Gap in Black Phosphorus

“…In the first case, the gap increases at low temperatures and decreases for high temperatures. 12,13 In the second case, instead, the gap continuously increases with temperature. This is the case of some perovskites, 14 Copper halides 15 and lead chalcogenides.…”

Thermal evolution of the band edges of 6H-SiC: X-ray methods compared to the optical band gap

“…Thermally induced changes of the band structure and explicitly in the band gap of semiconductors arise from a trivial thermal expansion effect plus a direct e-ph interaction effect [13]. It is known from a wealth of experimental and theoretical results (for example [14,15]) that band gap temperature dependencies can be split in two regions: usually a quadratic or cubic dependence on temperature in the cryogenic region and a strong (nearly) linear temperature dependence above the Debye temperature. Although calculations of the temperaturedependence of the gaps based on semi-empirical e-ph interaction have appeared in the literature, the band gap energies and the linear temperature dependence are not completely reliable.…”