By: A. R. Hayyu, A. Azhar, and M. A. Majidi
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Almost in all first-principles or modeling calculations of semiconductors that do not take into account electron-electron (e-e) interactions the resulting band gap is too much underestimated as compared to experimental data. Most conventional semiconductors, such as Ge, Si, or GaAs, may be classified into non-correlated systems or weakly correlated systems in which e-e interactions do not play any significant role. For such semiconductors, their band gaps may be insensitive to temperature change. Meanwhile, in semiconductors containing transition metal elements having d orbitals in their valence and/or conduction band(s), which we consider as strongly correlated semiconductors, e-e interactions may play a more significant role. To remedy this problem, e-e interactions need to be incorporated.
We hypothesize that such kind of semiconductors would have band structures, including their band gaps, being rather sensitive to temperature change due to e-e interactions. We construct the model Hamiltonian through tight-binding approximation incorporating e-e interactions in the self energy. We solve the model within GW method.
The GW self-consistent calculation is performed numerically in the Matsubara frequency domain. Then, we do analytic continuation using Pade approximant to obtain the retarded Green function defined in the real frequency domain. Using this retarded Green function, in principle, we can calculate and analyze the density of states (DOS) at various temperatures for short-ranged as well as long-ranged repulsive Coulomb interactions. However, in this paper we only present our calculation results for short-range interactions.
Our results qualitatively confirm that e-e interactions tend to increase the semiconductor band gap, and the correlation effects become stronger as we decrease temperature. It also show that the correlation effects become stronger as temperature is decreased, which reflect in the fact that the band gap increases and chemical potential shifts to a higher energy due to the presence of e-e repulsive interactions.