Temperature-dependent band gaps in several semiconductors: from the role of electron-phonon renormalization.

Temperature dependence of band gap is one of the most fundamental properties for semiconductors, and has strong influences on many applications. The renormalization of the band gap at finite temperatures is due to the lattice expansion and the phonon-induced atomic vibrations. In this work, we apply the recently-developed electron-phonon renormalization (EPR) method to study the temperature-dependent band gap in some classical covalent (diamond, Si, and SiC) and ionic semiconductors (MgO and NaCl). The contributions from both the lattice expansion and the phonon-induced atomic vibrations at finite temperatures are considered. The results show that the band gapsEgall decrease as temperatureTincreases, consistent with the experiments and other theoretical studies (e.g., from 0 K to 1500 K, the reductions are ~ 0.451 eV for diamond and ~ 1.148 eV for MgO, respectively). The covalent compounds investigated show weaker temperature dependences ofEgs than the ionic compounds, due to the much weaker lattice expansions and therefore low contributions from these. The zero-point motion effect has greater influence on the band gap in semiconductors with light atoms, such as diamond (reduction ~ 0.437 eV), due to larger atomic displacements. By decomposing the EPR effect into respective phonon modes, it is found that the high-frequency optical phonon vibrations dominate the temperature-dependent band gap in both covalent and ionic compounds. Our work provides the fundamental understandings on the temperature-dependent band gaps caused by lattice dynamics.