DFT-1/2 and shell DFT-1/2 methods: electronic structure calculation for semiconductors at LDA complexity

It is known that the Kohn-Sham eigenvalues do not characterize experimental excitation energies directly, and the band gap of a semiconductor is typically underestimated by local density approximation (LDA) of density functional theory (DFT). An embarrassing situation is that one usually uses LDA+Ufor strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals orGW. In spite of the state-of-the-art meta-generalized gradient approximation functionals like TB-mBJ and SCAN, methods with LDA-level complexity to rectify the semiconductor band gaps are in high demand. DFT-1/2 stands as a feasible approach and has been more widely used in recent years. In this work we give a detailed derivation of the Slater half occupation technique, and review the assumptions made by DFT-1/2 in semiconductor band structure calculations. In particular, the self-energy potential approach is verified through mathematical derivations. The aims, features and principles of shell DFT-1/2 for covalent semiconductors are also accounted for in great detail. Other developments of DFT-1/2 including conduction band correction, DFT+A-1/2, empirical formula for the self-energy potential cutoff radius, etc, are further reviewed. The relations of DFT-1/2 to hybrid functional, sX-LDA,GW, self-interaction correction, scissor's operator as well as DFT+Uare explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.