Zhang Yiming, Wang Ziyu, Xi Jinyang, Yang Jiong
Materials Genome Institute, Shanghai University, 99 Shangda Road, Shanghai 200444, People's Republic of China.
J Phys Condens Matter. 2020 Aug 31;32(47). doi: 10.1088/1361-648X/aba45d.
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 gapsall decrease as temperatureincreases, 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 ofs 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.
带隙的温度依赖性是半导体最基本的特性之一，对许多应用都有重要影响。有限温度下带隙的重整化是由于晶格膨胀和声子诱导的原子振动。在这项工作中，我们应用最近发展的电子-声子重整化（EPR）方法来研究一些经典共价（金刚石、硅和碳化硅）和离子半导体（氧化镁和氯化钠）中随温度变化的带隙。考虑了有限温度下晶格膨胀和声子诱导的原子振动的贡献。结果表明，所有带隙都随温度升高而减小，这与实验和其他理论研究一致（例如，从0K到1500K，金刚石的减小约为0.451eV，氧化镁的减小约为1.148eV）。由于晶格膨胀弱得多，因此所研究的共价化合物的带隙温度依赖性比离子化合物弱。零点运动效应在轻原子半导体（如金刚石，减小约0.437eV）的带隙中影响更大，这是由于原子位移较大。通过将EPR效应分解为各自的声子模式，发现高频光学声子振动在共价和离子化合物的带隙温度依赖性中起主导作用。我们的工作为晶格动力学引起的带隙温度依赖性提供了基本认识。
