Polymorph engineering of CuMO2 (M = Al, Ga, Sc, Y) semiconductors for solar energy applications: from delafossite to wurtzite

Structure–property relationships in Cu-based ternary oxides are explored using first-principles materials modelling.

In the delafossite structure each Cu atom is linearly coordinated with two O atoms, forming O-Cu-O dumbbells parallel to the c axis; see Fig. 1(a). O atoms in these O-Cu-O units are also each coordinated to three Al atoms, oriented such that Al-centred octahedra form AlO 2 layers which lie parallel to the ab plane. Alternative layer stackings are possible, resulting in a hexagonal (space group P6 3 /mmc) or rhombohedral (space group R3mh) unit cell (Kö hler & Jansen, 1986).
In 2014, however, CuGaO 2 crystallizing in the orthorhombic -NaFeO 2 structure was reported (Fig. 1b) and was shown to possess an optical band gap of $ 1.5 eV (Omata et al., 2014). The synthesis was achieved by an ion exchange process starting from a -NaFeO 2 precursor. This direct gap material possesses a band gap that would indicate a maximum efficiency of $ 33% according to the Shockley-Queisser detailed balance limit (Shockley & Queisser, 1961). A small band gap oxide absorber has long been sought after by the photovoltaic community (Lee et al., 2014).
In this paper we investigate computationally the geometry, stability and electronic structure of a family of -NaFeO 2 structured CuMO 2 (M = Al, Ga, In, Sc, Y, La) using a screened hybrid-density functional theory approach. We demonstrate: (i) -CuGaO 2 is an indirect band gap semiconductor with a 1.0 eV fundamental band gap, (ii) the optical band gaps of these -CuMO 2 compounds is greater than their fundamental band gaps due to a very weak onset of absorption and (iii) the tetrahedral coordination of the Cu ions leads to a reduced mixing between the Cu 3d states and the O 2p states at upper valence band, producing a localized valence band maximum (VBM) of Cu 3d states. The implications of this unusual electronic structure compared with delafossite oxides is discussed.

Computational methods
All total energy and electronic structure calculations were performed within density functional theory (DFT) and peri-odic boundary conditions as implemented in the code VASP (Kresse & Furthmü ller, 1996). Interactions between the core and valence electrons were described within the projector augmented wave method (Kresse & Joubert, 1999). The calculations were performed using the PBE (Perdew et al., 1996) exchange-correlation functional augmented with 25% screened non-local Hartree-Fock electron exchange, producing the hybrid HSE06 functional (Krukau et al., 2006). HSE06 has been successfully utilized to reproduce improved structural and band gap data compared with 'standard' local and semi-local DFT exchange-correlation functionals for many oxide semiconductors Scanlon et al., 2011;Scanlon & Watson, 2011a,b;Allen et al., 2010;Henderson et al., 2011). Here the primary role of the Hartee-Fock exchange is the cancellation of the artificial self-interaction that arises from the mean-field treatment of the Coulomb interaction between electrons.
A planewave cutoff of 750 eV and a k-point sampling of 6 Â 6 Â 6 for the 12 atom unit cell of -CuGaO 2 were used, with the ionic forces converged to less than 0.01 eV Å À1 . The optical transition matrix elements, calculated following Fermi's golden rule, were used to construct the imaginary dielectric function and the corresponding optical absorption spectrum (Gajdoš et al., 2006).

Crystal structure
The calculated structural data for -CuM III O 2 is displayed in Table 1. The equilibrium structure for -CuGaO 2 is in excellent agreement with that of the recent experimental report (Omata et al., 2014). For the rest of the family the data looks reasonable, except for -CuYO 2 , -CuInO 2 and -CuLaO 2 . All seven materials crystallize in the space group Pna2 1 , but due to the large cationic radius of Y, In and La the oxygen coordination sites in these systems deviate significantly from tetrahedral. In -CuYO 2 and -CuLaO 2 the O atoms remain four-coordinate, but close to a pyramidal coordination. In the case of -CuInO 2 , upon relaxation the system is spontaneously distorted to form linear O-Cu-O dumbells, as shown in Fig. 1(c). Similar coordination is seen in other Cu Ienergy materials Table 1 DFT/HSE06 calculated lattice parameters and bond lengths in -CuM III O 2 (M = Al, Ga, In, Sc, Y, La), and energy difference between the delafossite and phases.
A positive number indicates that the phase is less stable than the delafossite phase. System
containing oxides such as Cu 2 O, PbCu 2 O 2 and SrCu 2 O 2 (Godinho et al., 2008(Godinho et al., , 2010Modreanu et al., 2007;Nolan, 2008;Scanlon & Watson, 2011a). We have also calculated the difference in enthalpy between the delafossite and -CuM III O 2 , as shown in Table 1. In each case the delafossite is more stable than the -CuM III O 2 structure, although this is not necessarily a barrier to the formation of the -CuM III O 2 phase, as the synthesis method (ion exchange) is kinetically limited rather than thermodynamically controlled.

Electronic structure
The calculated electronic band structures for -CuAlO 2 , -CuGaO 2 , -CuScO 2 and -CuYO 2 crystal structures are displayed in Fig. 2. For the Group 13 series, the band gap trend is Al > Ga < In, and for the Group 3 series the band gap trend is Sc > Y < La. In both cases In and La can be considered outliers. The reducing band gap down the groups is initially maintained, similar to the case of the Group 3 and 15 delafossites (Huda et al., 2009a). For all cases, the conduction band minimum (CBM) shows reasonable dispersion in reciprocal space, with the VBM being extremely flat (high hole effective mass). Localized flat bands appear for 1 eV below the VBM, and then a 2 eV gap appears to 4 eV of more localized electronic states.
Analysis of the partial electronic densities of states (Fig. 3) reveals that the upper valence band is dominated by Cu 3d states, with little mixing between the O 2p and Cu 3d states. In fact, the O 2p states are separated from the Cu 3d states by $ 2 eV. This is not consistent with the chemical bonding of the delafossite structured CuMO 2 materials (Wei et al., 1992). The conduction bands are dominated by M III s states for the Group 3 and 13 cations. This is unusual, as the M d states dominate the lower conduction band for the delafossite-structured CuScO 2 and CuYO 2 .

Optical response
We have further calculated the optical absorption spectra, in the single-particle regime using Fermi's Golden rule, with the results presented in Fig. 4. For all materials, the optical band gap is considerably larger than the fundamental electronic band gap. The simulated optical band gap for -CuGaO 2 is $ 1.5 eV, in excellent agreement with the experimental measurements (Omata et al., 2014). To understand the differences between the fundamental indirect band gap and the direct allowed optical band gap, we have analysed the transition matrix elements for the allowed valence to conduction band transitions. Transitions from the VBM to CBM at the À point (k = 0,0,0) are dipole allowed; however, they are negligible until $ 0.5 eV higher in energy. This is due to the change in angular momentum of the bands (from d to metal s character orbitals). -CuGaO 2 has the smallest band gap with -CuAlO 2 possessing the largest optical band gap of $ 2.5 eV.

Discussion and conclusion
The vastly different electronic structures exhibited by the delafossite and wurtzite materials can be explained by considering the role of the coordination of the Cu states in these systems. Cu I has the d 10 electronic configuration. The isolated ion is well known to have low lying d 9 s 1 excited states, which can mix into the ground state in a crystal environment if the site symmetry allows (Orgel, 1958). The common linear coordination preference of the cuprous ion has long been attributed to 3dz 2 À s hybridization, which compensates for a low coordination number. In the delafossite structure, there is effective energetic and spatial overlap of the O 2p and Cu 3dz 2 + s hybrid orbitals, resulting in large valence band dispersion and light hole masses.
In the tetrahedrally coordinated phases, the same mixing is not achievable. The stronger anion field around the Cu atoms destabilizes the 3d band, which is split off in energy from the O 2p states. The result is a localized valence band with a large hole effective mass. Since the delafossites are known to be good p-type semiconductors, and the conduction band dispersion of wurtzite structured materials is likely to give rise to effective n-type conductivity, their combination could be used to form all-oxide p-n junctions. Such heterojunctions may be formed of one chemical composition in two structural forms.
These new insights into the electronic structure of -CuGaO 2 and related materials, however, are not entirely promising for the future use of this material for solar cell applications. The large difference in the electronic and optical band gaps will limit the open circuit voltage, and the localized states at the valence band maximum will likely limit carrier transport and collection. It is possible that the electronic structure could be tuned by alloying with -CuAlO 2 (the combination of different sizes on the M III site could make the weak transitions from the valence to conduction bands stronger, as was proposed previously for delafossite alloys; Huda et al., 2009b). Furthermore, the high dispersion in the conduction bands emphasizes the possibly of robust n-type conductivity, if a suitable n-type dopant was found.
In summary, polymorph engineering can produce unexpected effects in the electronic structure of multi-component materials. The kinetic control of crystallization products may reveal new phases with novel properties from well known materials systems.

Figure 3
The hybrid DFT (HSE06) calculated electronic density of states for (upper panel) -CuAlO 2 and (lower panel) -CuGaO 2 . The atomic components are obtained by projecting the periodic wavefunctions onto atom-centred spherical harmonics.