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

Abstract

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+U for strongly correlated materials with rectified band gaps, but for non-strongly-correlated semiconductors one has to resort to expensive methods like hybrid functionals or GW. In spite of the state-of-the-art meta-GGA functionals like TB09 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+U are explained. Applications, issues and limitations of DFT-1/2 are comprehensively included in this review.

In Quest of Low‐Leakage Dynamic Random Access Memory Enabled by Doped TiO2 Dielectrics

“…[68,71,74,75] However, it was discovered that the band gap of rutile TiO 2 does not increase monotonously with U, showing a maximum at some critical U value but an even larger U would reduce the band gap. [75] This is consistent with the argument that the oxygen 2p orbitals should be corrected and methods like LDA+U d +U p [67] or LDA+U-1/2 [76] are more proper. Due to the efficiency of LDA+U, there have been some works discussing the interfaces between rutile TiO 2 and the electrode.…”

From NaGa(IO3)3F to NaGa(IO3)2F2 and NaGa(IO3)4: The Effects of Chemical Substitution between F– Anions and IO3– Groups on the Structures and Properties of Gallium Iodates

“…In general, the band gap calculated by this method is 30%∼50% lower than the experimental result. 66,67 The total and partial density of states analyses reveal that the upper portion of the valence bands (VBs) in compounds 1 and 2 primarily composed of O 2p and I 5s5p orbitals, while the bottom of the conduction bands (CBs) region is mostly filled with O 2p and I 5p orbitals (Figure 6c,d). These findings suggest that the IO 3 units play a predominant role in the optical properties of compounds 1 and 2.…”

Two-Dimensional AMgB (A = Na, K; B = P, As, Sb, Bi) with Promising Optoelectronic and Thermoelectric Performances

“…The Perdew–Burke–Ernzerhof (PBE) functional was implemented for the exchange-correlation energy. While GGA could yield satisfactory total energies as well as reasonable atomic structures, it is well known that the incomplete cancellation of electron self-interaction error leads to inaccurate band gaps for semiconductors. − Hence, the screened exchange Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional was further employed in electronic band structure calculations . Furthermore, for compounds with heavy elements (such as As, Sb, and Bi), the spin–orbit coupling (SOC) effect was involved in the electronic band structure calculations.…”