Band alignment of semiconductors and insulators using dielectric-dependent hybrid functionals: Toward high-throughput evaluation

Yoyo Hinuma, Yu Kumagai, Isao Tanaka, and Fumiyasu Oba

Phys. Rev. B 95, 075302 – Published 3 February 2017

Abstract

The band alignment of prototypical semiconductors and insulators is investigated using first-principles calculations. A dielectric-dependent hybrid functional, where the nonlocal Fock exchange mixing is set at the reciprocal of the static electronic dielectric constant and the exchange correlation is otherwise treated as in the Perdew-Burke-Ernzerhof (PBE0) hybrid functional, is used as well as the Heyd-Scuseria-Ernzerhof (HSE06) hybrid and PBE semilocal functionals. In addition, these hybrid functionals are applied non-self-consistently to accelerate calculations. The systems considered include C and Si in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, InP, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, MgO in the rocksalt structure, and GaN and ZnO in the wurtzite structure. Surface band positions with respect to the vacuum level, i.e., ionization potentials and electron affinities, and band offsets at selected zinc-blende heterointerfaces are evaluated as well as band gaps. The non-self-consistent approach speeds up hybrid functional calculations by an order of magnitude, while it is shown using HSE06 that the resultant band gaps and surface band positions are similar to the self-consistent results. The dielectric-dependent hybrid functional improves the band gaps and surface band positions of wide-gap systems over HSE06. The interfacial band offsets are predicted with a similar degree of precision. Overall, the performance of the dielectric-dependent hybrid functional is comparable to the $G W_{0}$ approximation based on many-body perturbation theory in the prediction of band gaps and alignments for most systems. The present results demonstrate that the dielectric-dependent hybrid functional, particularly when applied non-self-consistently, is promising for applications to systematic calculations or high-throughput screening that demand both computational efficiency and sufficient accuracy.

Received 17 December 2016

DOI:https://doi.org/10.1103/PhysRevB.95.075302

Physics Subject Headings (PhySH)

Band gap Electronic structure Semiconductors Surface & interfacial phenomena

High-throughput calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yoyo Hinuma^1,2, Yu Kumagai^3,4,*, Isao Tanaka^1,2, and Fumiyasu Oba^2,3,5,†

¹Department of Materials Science and Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
²Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan
³Materials Research Center for Element Strategy, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan
⁴PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi 332-0012, Japan
⁵Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan

^*yuuukuma@gmail.com
^†oba@msl.titech.ac.jp

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Vol. 95, Iss. 7 — 15 February 2017

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Images

Figure 1
Differences in the band gap, CBM, VBM, and macroscopically averaged slab electrostatic potential between self-consistent and non-self-consistent HSE06 calculations using the identical bulk and surface cells. The plotted energy differences correspond to the values from the self-consistent calculations with respect to those from the non-self-consistent calculations. The CBM, VBM, and slab electrostatic potential are measured with respect to the vacuum level. Note that the electrostatic potential is determined using HSE06 in the self-consistent approach while it is treated at the PBE level in the non-self-consistent case.
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Figure 2
Band structures of (a) and (b) Si and (c) and (d) ZnO obtained using self-consistent (sc) and non-self-consistent (nsc) HSE06 calculations. The origin of the energy is set at the valence band maximum. Band paths reported in Ref. [62] are used.
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Figure 3
Differences in the charge density of surface slab models between self-consistent and non-self-consistent HSE06 calculations for (a) BN, (b) MgO, and (c) ZnO. The values from the self-consistent calculations with respect to those from the non-self-consistent calculations are plotted on planes perpendicular to the surfaces. Note that the charge density is determined using HSE06 in the self-consistent approach while it is treated at the PBE level in the non-self-consistent case.
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Figure 4
Band gaps obtained using various approximations compared with reported $G W_{0}$ @PBE and experimental values. Here nsc-hybrid( $ɛ_{\infty}^{PBE - RPA}$ ) and nsc-hybrid( $ɛ_{\infty}^{PBE 0}$ ) denote non-self-consistent dielectric-dependent hybrid functionals with static electronic dielectric constants obtained using PBE(+ $U$ ) with the RPA and PBE0 with local-field effects, respectively. The $G W_{0}$ @PBE and experimental values are taken from Ref. [28].
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Figure 5
(a) CBM and (b) VBM with respect to the vacuum level (negatives of the EA and IP, respectively) obtained using various approximations compared with reported $G W_{0}$ @PBE and experimental values. Here nsc-hybrid( $ɛ_{\infty}^{PBE - RPA}$ ) and nsc-hybrid( $ɛ_{\infty}^{PBE 0}$ ) denote non-self-consistent dielectric-dependent hybrid functionals with static electronic dielectric constants obtained using PBE(+ $U$ ) with the RPA and PBE0 with local-field effects, respectively. The $G W_{0}$ @PBE values are taken from Ref. [28]. The experimental values are for the nonpolar surfaces identical to those considered in the present study [66, 67]; an exception is GaN, for which experimental values for polar {0001} surfaces are shown. The experimental CBM is estimated by adding a reported experimental band gap to the VBM (see Table 2).
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