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Conductivity Limits in CuAlO2 from Screened-Hybrid Density Functional Theory David O. Scanlon* and Graeme W. Watson* School of Chemistry and CRANN, Trinity College Dublin, Dublin 2, Ireland
ABSTRACT CuAlO2 is a prototypical delafossite p-type transparent conducting oxide (TCO). Despite this, many fundamental questions about its band structure and conductivity remain unanswered. We utilize the screened hybrid exchange functional (HSE06) to investigate defects in CuAlO2 and find that copper vacancies and copper on aluminum antisites will dominate under Cu-poor/Al-poor conditions. Our calculated transitions levels are deep in the band gap, consistent with experimental findings, and we identify the likely defect levels that are often mistaken as indirect band gaps. Finally, we critically discuss delafossite oxides as TCO materials. SECTION Electron Transport, Optical and Electronic Devices, Hard Matter
ransparent conducting oxides (TCOs) currently play an important role in a wide range of optoelectronic devices including solar cells, flat-panel displays, electrochromic mirrors and windows, touch-panel controls, and so forth.1 The development of functional p-n junctions using only these TCO materials would open the possibility of transparent electronics, encompassing transparent diodes and transistors, and is a major research challenge for materials scientists.2 While the majority of the high performance TCOs used in applications are n-type (e.g., SnO2, In2O3, ZnO), the development of p-type TCOs has proved substantially more challenging. In 1997, a study by Hosono and co-workers first reported simultaneous p-type conductivity and optical transparency in thin films of CuAlO2 (CAO), which crystallizes in the delafossite structure.3 Subsequently, p-type TCO ability has been discovered in many other delafossites (CuMO2, M = B, Cr, Sc, Y, In, Ga)4 and in SrCu2O2.5 Although CAO is by far the most studied of the delafossite materials, some critical questions about the band structure and conductivity of this material remain unanswered. The transparency of the group 13 (B, Al, Ga, In) delafossites is made possible by forbidden transitions at the Γ and Z points, with allowed transitions only occurring at the F and L points.6 Thus the optically allowed direct band gap (Edir g ) for CAO is at the L point.7 Experimentally, the optical band gap of CAO has been reported in the range 3.3-4.2 eV;3,7,8 however, the main source of controversy in the literature has been the positioning of the indirect band gap (Eind g ), with different 8,9 It has studies proposing Eind g in the range 1.65-2.99 eV. values in the recently been postulated that the reported Eind g range 1.65-2.10 eV are not Eind g values at all, but are actually signals from defects.8,9 The absorptions commonly attributed to these Eind g values possess optical absorption coefficients that are in excess of 2 orders of magnitude larger than typical indirect absorption edges.8 Most theoretical studies predict the Eind g to be much less than 1 eV smaller than that of
10 the Edir and not ∼1.40-1.85 eV smaller as some g at L, experiments have observed. The source of hole carriers in CAO, and indeed the conductivity mechanism itself is also a matter of much debate. Many theoretical studies have been undertaken to understand defects and conductivity in delafossite materials.11,12 However, in all of these studies, the generalized gradient approximation (GGA) or local density approximation (LDA) methodologies have been used, which have been shown to be unable to accurately model p-type defects in CuI-based materials.13 In all cases, Cu vacancies (VCu) were reported to be the defect with the lowest formation energy, and therefore linked to any intrinsic conductivity in these systems.11,12 Tellingly, these GGA/LDA studies11,12 found that the formation energies of VCu in these systems was spontaneous (ΔHf(D,0) < 0 eV), with transition levels (TLs) inside the valence band, indicating degenerate semiconducting behavior. This is clearly at variance with experimental observations that delafossite materials conduct through activated polaronic hopping mechanisms,14-16 or through activated band conduction from a deep TL 700 meV above the valence band maximum (VBM).9 The general consensus from both experiment and theory has been that VCu is the dominant defect, followed by oxygen interstitials, Oi.11,12 Intriguingly, Mason and co-workers have postulated that the defect responsible for conductivity at high temperature in CAO is not VCu, but a defect cluster of an Al on a 00 00 15 Cu site bound to two oxygen interstitials, [Al•• Cu þ 2Oi ] . This defect has never been investigated theoretically. In this letter, we present a hybrid density functional theory (DFT) examination of the electronic structure and energetics of intrinsic defects in CAO. We report (i) the dominant defects under all growth condition are CuAl and VCu, and not
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Received Date: August 17, 2010 Accepted Date: October 18, 2010 Published on Web Date: October 21, 2010
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Figure 1. HSE calculated band structure of rhombohedral CuAlO2. 00
00 [Al•• Cu þ 2Oi ] , (ii) we find deep TLs for all p-type defects, consistent with the experimentally known activated conductivity, and (iii) we identify the defect that gives rise to the signals often mistaken as the Eind g of CAO. The limitations of CuI-based oxides for TCO applications are outlined, and the future of p-type TCOs is discussed. Thermodynamic Stability of CuAlO2. Varying the chemical potentials, μi (see eq 1, Theoretical Section), relates to varying the partial pressures experimentally. They can thus be used to set the different conditions under which CAO may form, and determine the optimum conditions for defect formation, within the global constraint of the calculated enthalpy of 2 the host, in this instance CAO: μCu þ μAl þ 2μO = ΔHCuAlO = f -8.92 eV. To avoid precipitation into solid elemental Cu, Al, and O2 gas, we also require μCu e 0, μAl e 0, and μO e 0. The chemical potentials are further constrained by the decomposition of CAO into binary compounds: μCu þμO e ΔHCuO = f 2O =-1.55 eV and 2μAl þ3μO e -1.40 eV, 2 μCu þμO e ΔHCu f 2O3 = -16.09 eV, and the competing ternary phase ΔHAl f 2O4 CuAl2O4: μCu þ2μAl þ4μO e ΔHCuAl =-16.74 eV. Previous f DFT defect studies of the delafossites have failed to take the formation of CuO into account, meaning their Cu-poor regimes were probably for an unphysical composition.11,12,17 Following the approach of Walsh et al.,18 the phase diagram for CAO was computed, taking into account the limitations caused by formation of the binary phases (see Supporting Information for more details). In this instance, we explicitly consider one environment, Cu-poor/Al-poor, which yields chemical potentials of μAl = -6.46, μO = -1.06, and μCu = -0.34, which the most favorable for p-type defect formation (see Supporting Information). Band Structure Features. The HSE06 calculated band structure is shown in Figure 1, and possesses features consistent with previous theoretical bandstructures.19 The conduction band minimum (CBM) occurs at the Γ point, with the VBM situated at F. The Edir g at the L point is 4.08 eV, while the dir corresponding Eind g is 3.52 eV. Therefore our calculated Eg is within the experimental range of optical band gaps, and is consistent with previous HSE06 calculations.10 The differind ence between the Edir g and Eg is only 0.56 eV. It has been noted previously that as the level of theory utilized to ind compute the band gap of CAO is increased, Edir g - Eg 10 decreases. Our HSE06 calculated results, in agreement
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Figure 2. HSE06 calculated formation energies for intrinsic defects in CuAlO2 as a function of Fermi energy under Cu-poor/ Al-poor conditions. The solid dots denote the TLs ε(q/q0 ) .
with previous theory results, indicate that the absorption signals assumed to be Eind g in the range 1.65-2.10 eV are unlikely to be a property of stoichiometric CAO, and may stem from defect signals. Defect Energetics and Ionization Levels. A plot of formation energy as a function of Fermi-level position is shown in Figure 2 for all intrinsic defects in the Cu-poor/Al-poor regime. The first point to note is that the formation energy of VCu and the CuAl antisite are substantially lower in energy than all other defects, with the CuAl being slightly more energetically favorable. The (0/-1) TL for VCu at 0.68 eV is in excellent agreement with the experimentally reported TL of 0.70 eV,9 and is a significant improvement on previous GGA/LDATLs (-0.33 eV and -0.40 eV).11,12 Oi and VAl are much higher in energy, and possess deeper TLs than VCu, indicating that they will not play a major role 0 in any conductivity. The formation energy of the 00 0 [Al•• Cu þ 2Oi ] defect complex as proposed by Mason and coworkers15 is 6.06 eV, and its (0/-1) TL is 1.83 eV above the VBM, meaning it is unlikely to ever be a source of conductivity in CAO. The formation energies of compensating n-type defects are also very high, with VO being stable only in the neutral and þ2 charge states (making it a negative U-type defect), with the (þ2/0) TL being very deep (2.70 eV below the CBM). Cui has a large formation energy with relatively deep (þ1/0) TL, and the formation energy of the AlCu antisite is extremely high in energy. These results indicate that p-type defects will dominate under Cu-poor/Al-poor conditions, and indeed under all growth conditions (see Supporting Information). We have also calculated the optical (vertical) transition levels (OTLs) for the native p-type defects as outlined in refs 20 and 21. The calculated (0/-1) OTL for VCu is found to be 0.87 eV, with the (0/-1) OTL for CuAl being 1.73 eV (for all the HSE06 calculated OTLs, see Supporting Information). The Eind g signals reported in experiment in the range 1.65-2.10 eV are thus likely caused by the (0/-1) OTL of the CuAl. In addition, the weak absorptions noted in the most recent study by Tate et al.9 at 0.85 and 1.75 eV, and in the study by Pellicer-Porres et al.8 at 0.9 and 1.8 eV, are in excellent agreement with the (0/-1) OTL of VCu and the (0/-1) OTL for CuAl.
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The most promising approach to develop high-performance p-type TCOs would appear to be to explore the rich chemistry of layered oxychalcogenides.26,27 These materials are composed of layers of [Cu2S2]2- sandwiched between layers of ionic metal oxides.26 To date oxychalcogenides have shown great promise, displaying large mobilities (e.g., (Cu2S2)(Sr3Sc2O5), 150 cm2 V-1 s-1),28 and having the ability to become degenerate semiconductors when doped (e.g., LaCuOSe:Mg).29 The challenge remains to engineer a layered oxychalcogenide with sufficient p-type conductivity and transparency to equal the performance of the n-type TCOs. Summary. We have shown that CuAl and VCu formation 0will 00 0 dominate the conductivity of CAO, and not [Al•• Cu þ 2Oi ] as had previously been proposed. The TLs of all p-type defects are found to be deep in the band gap, consistent with experiment, with our calculated TL for VCu at 0.68 eV being in excellent agreement with a recent experimental report of an acceptor level at 0.70 eV.9 We have identified that the indirect band gaps in the 1.65-2.10 eV range, reported from optical experiments, are most likely due to the (0/-1) OTL for CuAl. CAO will always be dominated by deep defect levels, meaning that high performance p-type CAO will not be achievable. This is expected to be general for all CuI-based delafossites.
Figure 3. Structure and spin density of VCu in CAO. Yellow, red, and green spheres represent Cu, O, and Al, respectively. The vacancy position is indicated with a pink sphere. The blue isosurface is shown at 0.05 e Å-3.
Polaronic? While many studies have suggested that delafossite oxides conduct via a polaronic hopping mechanism,14-16 a recent study by Tate et al. reported that p-type conductivity in CAO is governed by band conduction, with the holes thermally activated from acceptor levels 700 meV above the VBM.9 This study was carried out on single-crystals of CAO, without the influence of grain boundaries and strain effects of the previous thin film and bulk measurements.9 While a direct clarification of the conductivity mechanism is beyond the scope of this study, we can investigate the nature of geometry and electronic structure of VCu in CAO, and find out whether it causes a polaronic distortion. Upon formation of a VCu, the two oxygen atoms that made up the O-Cu-O dumbbell are left under-coordinated and move away from the vacancy by 0.05 Å while the six Cu ions surrounding the vacancy move inward by ∼0.01 Å, as shown in Figure 3. These small perturbations of the geometry are atypical of the large distortions usually associated with small polarons.22 Analysis of the associated spin density of the hole state (Figure 3) shows that the excess spin is localized mainly on the six Cu atoms neighboring the vacancy with d orbital character, which is indicative of a reasonably localized polaron. Conductivity Limits in Delafossite Oxides. Transport in delafossite materials such as CAO will likely be dominated by deep defect levels, and therefore will never realize the high figure of merit performances needed to rival their n-type counterparts. The conductivities of these p-type TCOs are on average 3 orders of magnitude lower than their high performance n-type counterparts,23 and the majority of the delafossites possess indirect band gaps, which limit their efficiency in optoelectronic devices.24 It is becoming increasingly clear that materials based on Cu-O mixing at the VBM will not produce degenerate semiconductors, unless strategies to mix other cations with states that will resonate near the VBM and enhance conductivity can be found.25 CuCrO2:Mg displays the highest conductivity of all the delafossites, possibly due to favorable mixing of Cr d states with the Cu and O states in the VBM;25 however, the conductivity is still ∼2 orders of magnitude below that of the standard n-type TCOs.
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THEORETICAL SECTION We employ the screened hybrid DFT approach of Heyd, Scuseria, and Ernzerhof (HSE06)30 as implemented in the VASP code31 containing a value of exact nonlocal exchange, R, of 25%, and screening paramater of ω=0.11 bohr-1. BeyondLDA/GGA methods such as HSE06 have been shown to be necessary for describing p-type defects in CuI-based materials,32 with the HSE formalism being proven to result in structural and band gap data in better agreement with experiment than standard DFT functionals.33-38 Interactions between the cores (Cu:[Ar], Al:[Ne], and O:[He]) and the valence electrons were described using the projector augmented wave (PAW) method.39 A planewave cutoff of 500 eV and k-point sampling of 8 8 8 for rhombohedral CuAlO2 were used, and the structure was deemed to be converged when the forces on all the atoms were less than 0.01 eV Å-1. Defects were calculated in a 331 (108 atom) expansion of the 12 atom hexagonal representation of the rhombohedral unit cell, and all calculations were spin polarized. The formation enthalpy of a defect with charge state q is given by X ni ðEi þ μi Þ þ qðEFermi þ εHVBM Þ ΔHf ðD, qÞ ¼ ðED, q - EH Þ þ i
þ Ealign ½q
ð1Þ
EH is the total energy of the stoichiometric host supercell, and ED,q is the total energy of the defective cell. Elemental reference energies, Ei, were obtained from calculations on the constituent elements in their standard states, i.e., Cu(s), Al(s), and O2(g), and n is the number of atoms formally added to or taken away from an external reservoir. EFermi ranges from the VBM (EFermi = 0 eV) to the CBM (EFermi = 3.52 eV). εH VBM is the VBM eigenvalue of the host bulk. Ealign[q] is the correction that (i) accounts for the proper alignment of the VBM between the
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bulk and the defective supercells and (ii) corrections for the finite-size-cell effects in the calculations of charged impurities, as outlined by Freysoldt et al.40 The thermodynamic transition (ionization) levels (TLs) of a given defect, εD(q/q0 ), are equal to the Fermi-level for which charge states q and q0 have equal energy: εD ðq=q0 Þ ¼
ΔH f ðD, qÞ- ΔH f ðD, q0 Þ q0 - q
(11) (12)
(13)
ð2Þ
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SUPPORTING INFORMATION AVAILABLE A detailed analysis of the chemical potential limits of CuAlO2 and the effect of different growth environments on defect formation in this material, together with information on the calculated OTLs. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
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Corresponding Author: *To whom correspondence should be addressed. E-mail: scanloda@ tcd.ie (D.O.S.);
[email protected] (G.W.W.).
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ACKNOWLEDGMENT The authors would like to express their appreciation to C. G. Van de Walle for access to the sxdefectalign code. This work was supported by Science Foundation Ireland through the Principal Investigators Programme (PI Grant Numbers 06/IN.1/I92 and 06/IN.1/I92/EC07). Calculations were performed on the IITAC and Lonsdale supercomputers as maintained by TCHPC, and the Stokes supercomputer as maintained by ICHEC.
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