Deep vs shallow nature of oxygen vacancies and consequent $n$-type carrier concentrations in transparent conducting oxides

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Deep vs shallow nature of oxygen vacancies and consequent $n$ -type carrier concentrations in transparent conducting oxides

J. Buckeridge, C. R. A. Catlow, M. R. Farrow, A. J. Logsdail, D. O. Scanlon, T. W. Keal, P. Sherwood, S. M. Woodley, A. A. Sokol, and A. Walsh

Phys. Rev. Materials 2, 054604 – Published 25 May 2018

Abstract

The source of $n$ -type conductivity in undoped transparent conducting oxides has been a topic of debate for several decades. The point defect of most interest in this respect is the oxygen vacancy, but there are many conflicting reports on the shallow versus deep nature of its related electronic states. Here, using a hybrid quantum mechanical/molecular mechanical embedded cluster approach, we have computed formation and ionization energies of oxygen vacancies in three representative transparent conducting oxides: ${In}_{2} O_{3}, {SnO}_{2}$ , and ZnO. We find that, in all three systems, oxygen vacancies form well-localized, compact donors. We demonstrate, however, that such compactness does not preclude the possibility of these states being shallow in nature, by considering the energetic balance between the vacancy binding electrons that are in localized orbitals or in effective-mass-like diffuse orbitals. Our results show that, thermodynamically, oxygen vacancies in bulk ${In}_{2} O_{3}$ introduce states above the conduction band minimum that contribute significantly to the observed conductivity properties of undoped samples. For ZnO and ${SnO}_{2}$ , the states are deep, and our calculated ionization energies agree well with thermochemical and optical experiments. Our computed equilibrium defect and carrier concentrations, however, demonstrate that these deep states may nevertheless lead to significant intrinsic $n$ -type conductivity under reducing conditions at elevated temperatures. Our study indicates the importance of oxygen vacancies in relation to intrinsic carrier concentrations not only in ${In}_{2} O_{3}$ , but also in ${SnO}_{2}$ and ZnO.

Received 1 February 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.054604

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Point defects Semiconductors

Oxides

Hybrid functionals

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Buckeridge^1,*, C. R. A. Catlow¹, M. R. Farrow¹, A. J. Logsdail², D. O. Scanlon^1,3,4, T. W. Keal⁵, P. Sherwood⁵, S. M. Woodley¹, A. A. Sokol^1,†, and A. Walsh^6,‡

¹University College London, Kathleen Lonsdale Materials Chemistry, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, United Kingdom
²Cardiff Catalysis Institute, School of Chemistry, Cardiff University, Cardiff CF10 3AT, United Kingdom
³Thomas Young Centre, University College London, Gower Street, London WC1E 6BT, United Kingdom
⁴Diamond Light Source Ltd., Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
⁵Scientific Computing Department, STFC, Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, United Kingdom
⁶Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom

^*j.buckeridge@ucl.ac.uk
^†a.sokol@ucl.ac.uk
^‡a.walsh@imperial.ac.uk

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Vol. 2, Iss. 5 — May 2018

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Images

Figure 1
Formation energies as a function of Fermi energy relative to the valence band maximum (VBM) of oxygen vacancies in (a) ZnO, (b) ${SnO}_{2}$ , and (c) ${In}_{2} O_{3}$ , shown for O-rich and O-poor conditions. Results are given for three hybrid density functionals: BB1k (black), B97-2 (red), and PBE0 (blue). A vertical dashed line is placed at the position of the conduction band minimum for each system (derived from the experimental band gap; see the main text for details). The slopes indicate the charge states; a transition occurs where the slope of a line changes. For ZnO, the B97-2 result lies almost entirely below the PBE0 result.
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Figure 2
The calculated molecular orbital associated with the defect level introduced by a neutral oxygen vacancy in (a) ZnO, (b) ${SnO}_{2}$ , and (c) ${In}_{2} O_{3}$ , determined using the BB1k functional. Oxygen ions are represented by red, In by brown, Sn by darker gray, and Zn by lighter gray spheres. The molecular orbitals are indicated by yellow (positive) and purple (negative) isosurfaces of densities (in atomic units) 0.1, 0.08 and 0.06 (in the cases of ${In}_{2} O_{3}$ and ZnO, the highest density isosurfaces are visible on the ions surrounding the vacancy).
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Figure 3
Cartoon depicting a ‘compact’ neutral oxygen vacancy donor, with two electrons trapped in the vacancy, and a ‘diffuse’ donor, where one of the bound electrons is of the effective-mass type. $r$ indicates the approximate extent of the wave function $ψ$ , which is represented by the blue lines. The black line represents the shape of the electrostatic potential.
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Figure 4
Calculated defect $([V_{O}]$ , green line) and electron $(n_{0}$ , red line) and hole $(p_{0}$ , blue line) carrier concentrations as a function of temperature $T$ for ${SnO}_{2}$ , determined using the PBE0, B97-2, and BB1k hybid density functionals, under O-poor and O-rich conditions. The insets show the self-consistent Fermi energy $E_{F}$ (black line) as a function of $T$ , relative to the conduction band minimum.
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Figure 5
Calculated defect $([V_{O}]$ , green line) and electron $(n_{0}$ , red line) and hole $(p_{0}$ , blue line) carrier concentrations as a function of temperature $T$ for ZnO, determined using the PBE0, B97-2, and BB1k hybid density functionals, under O-poor and O-rich conditions. The insets show the self-consistent Fermi energy $E_{F}$ (black line) as a function of $T$ , relative to the conduction band minimum.
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Figure 6
Calculated defect $([V_{O}]$ , green line) and electron $(n_{0}$ , red line) and hole $(p_{0}$ , blue line) carrier concentrations as a function of temperature $T$ for ${In}_{2} O_{3}$ , determined using the PBE0, B97-2, and BB1k hybid density functionals, under O-poor and O-rich conditions. The insets show the self-consistent Fermi energy $E_{F}$ (black line) as a function of $T$ , relative to the conduction band minimum.
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