Anisotropic polaron localization and spontaneous symmetry breaking: Comparison of cation-site acceptors in GaN and ZnO

Y. Y. Sun, Tesfaye A. Abtew, Peihong Zhang, and S. B. Zhang

Phys. Rev. B 90, 165301 – Published 3 October 2014

Abstract

The behavior of cation substitutional hole doping in GaN and ZnO is investigated using hybrid density functional calculations. Our results reveal that Mg substitution for Ga $({Mg}_{Ga})$ in GaN can assume three different configurations. Two of the configurations are characterized by the formation of defect-bound small polaron (i.e., a large structural distortion accompanied by hole localization on one of the neighboring N atoms). The third one has a relatively small but significant distortion that is characterized by highly anisotropic polaron localization. In this third configuration, ${Mg}_{Ga}$ exhibits both effective-mass-like and noneffective-mass-like characters. In contrast, a similar defect in ZnO, ${Li}_{Zn}$ , cannot sustain the anisotropic polaron in the hybrid functional calculation, but undergoes spontaneous breaking of a mirror symmetry through a mechanism driven by the hole localization. Finally, using ${Na}_{Zn}$ in ZnO as an example, we show that the deep acceptor levels of the small-polaron defects could be made shallower by applying compressive strain to the material.

Received 20 February 2014
Revised 18 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.165301

Authors & Affiliations

Y. Y. Sun¹, Tesfaye A. Abtew², Peihong Zhang², and S. B. Zhang¹

¹Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
²Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA

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Vol. 90, Iss. 16 — 15 October 2014

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Images

Figure 1
Schematic showing the structural distortion of the cation dopant $(D_{C})$ defect in ZnO or GaN. The structure shown is the nondistorted structure in the pseudo- $T_{d}$ symmetry, which is the structure of these defects in the negatively charged state. The blue arrows show possible directions of the displacement of the dopant atom in the neutral state, which lead to distorted structures. (a) Axial distortion along $A_{1} \to D_{C}$ maintaining the $C_{3 v}$ symmetry as in the wurtzite structure. (b) Nonaxial distortion along $A_{2} \to D_{C}$ , which lowers the symmetry to $C_{s}$ . If starting from a real $T_{d}$ symmetry as in the zinc-blende structure, this distortion is equivalent to that in (a). For this reason, this distortion can be considered as a pseudo- $C_{3 v}$ distortion. (c) Distortion along the direction bisecting the $A_{1} − D_{C} − A_{2}$ angle, which also lowers the symmetry to $C_{s}$ . Similarly, we name this distortion pseudo- $C_{2 v}$ because this distortion will lead to the $C_{2 v}$ symmetry if starting from a real $T_{d}$ symmetry.
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Figure 2
Charge density of the acceptor state (i.e., the lowest unoccupied state of the minority spin at the $Γ$ point) of ${Mg}_{Ga}^{0}$ in GaN in the (a) $C_{3 v}$ , (b) pseudo- $C_{3 v}$ , and (c) pseudo- $C_{2 v}$ configuration. The upper panels show the view along the $c$ axis (or the [0001] direction). The lower panels show the view along the $[11 \bar{2} 0]$ direction. The plots were obtained from calculations using the 300-atom supercell.
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Figure 3
Band structure of ${Mg}_{Ga}^{0}$ in GaN in the pseudo- $C_{2 v}$ configuration. Only the minority-spin component is shown because it contains the acceptor state discussed in the text. The acceptor state is highlighted in red. The plots are shown for the three orthogonal directions labeled in Fig. 2. The dashed lines indicate the highest occupied energy level, which is taken to be zero in the plot.
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Figure 4
The total energy of the ${Li}_{Zn}^{0}$ and ${Na}_{Zn}^{0}$ defects in the pseudo- $C_{2 v}$ configuration as a function of the displacement $d$ of the Li or Na atom, as illustrated in the inset, and the mixing parameter $α$ used in the HSE hybrid functional. The dashed line in the inset shows the mirror symmetry that is broken by the displacement.
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Figure 5
The (0/ $-)$ transition energies of ${Na}_{Zn}$ in ZnO as a function of the change in cell volume $(V)$ . $V_{0}$ denotes the unit cell volume at ambient condition. The transition energies were obtained by using the 96-atom supercell. A Madelung correction of 0.22 eV, which represents the upper limit of the correction, was applied and the actual transition energies should be shallower.
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