Delafossite α-CuGaO2 and Wurtzite β-CuGaO2 - ACS Publications

20 Jul 2016 - ABSTRACT: The electronic structures of delafossite α-CuGaO2 and wurtzite β-. CuGaO2 were calculated based on density functional theory...
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First-Principles Study of CuGaO2 Polymorphs: Delafossite α‑CuGaO2 and Wurtzite β‑CuGaO2 Issei Suzuki,† Hiraku Nagatani,† Masao Kita,‡ Yuki Iguchi,§ Chiyuki Sato,§ Hiroshi Yanagi,§ Naoki Ohashi,∥ and Takahisa Omata*,⊥ †

Division of Material and Manufacturing Science, Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan Department of Mechanical Engineering, National Institute of Technology, Toyama College, Toyama 939-8630, Japan § Interdisciplinary Graduate School of Medical & Engineering Material Science and Technology, University of Yamanashi, Kofu, Yamanashi 400-8510, Japan ∥ National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan ⊥ Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira, Aoba-ku, Sendai 980-8577, Japan ‡

S Supporting Information *

ABSTRACT: The electronic structures of delafossite α-CuGaO2 and wurtzite βCuGaO2 were calculated based on density functional theory using the local density approximation functional including the Hubbard correction (LDA+U). The differences in the electronic structure and physical properties between the two polymorphs were investigated in terms of their crystal structures. Three major structural features were found to influence the electronic structure. The first feature is the atomic arrangements of cations. In the conduction band of α-CuGaO2 with a layered structure of Cu2O and Ga2O3, Cu and Ga states do not mix well; the lower part of the conduction band mainly consists of Cu 4s and 4p states, and the upper part consists of Ga 4s and 4p states. By contrast, in β-CuGaO2, which is composed of CuO4 and GaO4 tetrahedra, Cu and Ga states are well-mixed. The second feature is the coordination environment of Cu atoms; the breaking of degeneracy of Cu 3d orbitals is determined by the crystal field. Dispersion of the Cu 3d valence band of β-CuGaO2, in which Cu atoms are tetrahedrally coordinated to oxygen atoms, is smaller than those in α-CuGaO2, in which Cu atoms are linearly coordinated to oxygen atoms; this results in a larger absorption coefficient and larger hole effective mass in β-CuGaO2 than in α-CuGaO2. The interatomic distance between Cu atomsthe third featurealso influences the dispersion of the Cu 3d valence band (i.e., the effective hole mass); the effective hole mass decreases with decreasing interatomic distance between Cu atoms in each structure. The results obtained are valuable for understanding the physical properties of oxide semiconductors containing monovalent copper and silver.

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INTRODUCTION

sixfold and octahedral coordination to O atoms in this structure. Numerous studies on delafossite-type oxide semiconductors, such as α-CuGaO2,1 α-CuInO2,2 and α-AgGaO2,3 have been reported since Kawazoe et al. discovered p-type electrical conduction and transparency to visible light in thin films of delafossite α-CuAlO2.4 The second structure is the wurtzite-derived β-NaFeO2-type structure (space group: Pna21), in which the monovalent and trivalent cations alternately occupy the cation site of the wurtzite-type structure, as shown in Figure 1b; both the monovalent and trivalent cations have fourfold and tetrahedral coordination to O atoms in this structure. Examples of oxide semiconductors that adopt this structure are β-LiGaO2,5 β-AgGaO2,3,6 β-AgAlO2,7 and βCuGaO2;8 the energy band gaps of these materials cover a wide proportion of the light spectrum from near-infrared to ultraviolet.9

I III

Ternary A B O2 oxide semiconductors occur with one of two typical types of crystal structure. One is the delafossite-type structure (space group: R3̅m), which consists of AI2O and BIII2O3 layers, as shown in Figure 1a; the monovalent cation has twofold and linear coordination, and the trivalent cation has

Figure 1. Schematic illustration of the crystal structures of (a) delafossite α-AIBIIIO2 and (b) wurtzite-derived β-AIBIIIO2. © XXXX American Chemical Society

Received: April 28, 2016

A

DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Both α-CuGaO2 and β-CuGaO2 exhibit p-type electrical conduction; however, their optical properties are distinctly different despite their identical compositions. α-CuGaO2 exhibits optical transparency to visible light and is therefore expected to be suitable as a p-type, transparent electrode.10−12 By contrast, β-CuGaO2 possesses a direct, narrow band gap in the near-infrared region. The band gap of this material (1.47 eV) corresponds to the energy required to achieve the theoretical maximum conversion efficiency of single-junction solar cells; therefore, β-CuGaO2 is expected to be suitable as a thin-film solar-cell absorber.8 In this study, we investigated the electronic structures of αand β-CuGaO2 by first-principles calculations based on density functional theory (DFT) using the local density approximation functional including the Hubbard correction (LDA+U). We investigated the differences in the electronic structures and physical properties (band gap, absorption coefficient, and effective masses of electrons and holes) of the two polymorphs in terms of their crystal structures.

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weighted by a one-electron ionization cross section for Ag Lα X-rays18 and spectral broadening of the instrumental resolution of 0.5 eV.

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RESULTS AND DISCUSSION Hubbard Correction. As we previously reported,19 the appropriate Hubbard correction U for the LDA+U calculation of β-CuGaO2 was determined to be U = 5−7 eV, because the calculated crystal structure and valence-band structure using values within this range reproduced well the experimentally obtained crystal structure and valence-band XPS spectrum. In the case of α-CuGaO2, the calculated lattice parameters were only slightly dependent on U (Figure S1 in the Supporting Information), whereas the lattice parameters and fractional coordinates of the atoms in β-CuGaO2 after geometry optimization were strongly dependent on U.19 This is because all atoms in α-CuGaO2 occupy highly symmetric special equivalent positions, and only the z-coordinate of O atoms is capable of being optimized,20 whereas all atoms occupy low-symmetry general equivalent positions in βCuGaO2, and all coordinates of the atoms are capable of being optimized. Because the calculation for α-CuGaO2 reproduced well the experimentally observed lattice parameters for U = 0−12 eV (Figure S1 in the Supporting Information), we determined the appropriate value of U for α-CuGaO2 based on the reproducibility of the valence-band electronic structure. The valence-band XPS spectra of α-CuGaO2 calculated using LDA+U are shown in Figure 2 together with the experimentally

EXPERIMENTAL SECTION

Sample Preparation. α-CuGaO2 powder was prepared by conventional solid-state reaction between Cu2O and Ga2O3 at 1100 °C for 24 h under N2 flow.1 β-CuGaO2 powder was prepared by ionexchange of Na+ ions in the β-NaGaO2 precursor with Cu+ ions in CuCl, similar to the process described in a previous report.8 The powdered samples were sintered by spark plasma sintering (SPS). For α-CuGaO2, SPS was performed at 900 °C for 5 min in Ar atmosphere under application of a uniaxial pressure of 100 MPa using a carbon die with an inner diameter of 10 mm. For β-CuGaO2, SPS was performed at 400 °C for 5 min under vacuum and a uniaxial pressure of 1 GPa using a carbide die with an inner diameter of 5 mm. The densities of the obtained compacts of α- and β-CuGaO2 were 80% of their theoretical densities. X-ray Photoelectron Spectroscopy. X-ray photoelectron spectroscopy (XPS) spectra of sintered samples were recorded using a photoemission spectrometer with a hemispherical electron analyzer (Axis Ultra DLD, Kratos Analytical, U.K.) at room temperature. Monochromatic Ag Lα X-ray radiation (hν = 2984.2 eV) was used as the excitation source to obtain information about the bulk material. The mean free path of valence electrons with 3 keV kinetic energy was calculated as ∼5 nm for both samples,13 implying a total probe depth of at least 10 nm. The total resolution, which was evaluated from the Fermi edge of the Au films, was ∼0.5 eV. The binding energy of the system was calibrated using the Au 4f7/2 core level at 84.0 eV of the Au film sputtered on a portion of the sample surface. Computational Method. All calculations based on DFT were performed using LDA+U14 as implemented in the CASTEP code.15 The norm-conserving pseudopotentials16 generated with OPIUM17 were used for the valence electrons of Cu 3d, 4s, and 4p; Ga 3d, 4s, and 4p; and O 2s and 2p. For Cu 3d electrons, the Hubbard correction U was varied from 0 to 12 eV at 1 eV intervals to determine an appropriate value based on the reproducibility of the experimentally observed crystal structure and valence-band XPS spectra. Brillouinzone sampling was performed with a 10 × 10 × 10 and 5 × 4 × 5 kpoint mesh for α- and β-CuGaO2, respectively. The plane-wave cutoff energy was set at 880 eV for all calculations. Geometry optimization for α- and β-CuGaO2 was performed with imposed rhombohedral symmetry with the space group R3̅m and orthorhombic symmetry with the space group Pna21, respectively. The convergence conditions of the geometry optimization were as follows: the energy convergence tolerance was 5.0 × 10−6 eV atom−1, the maximum ionic displacement tolerance was 5.0 × 10−4 Å, the maximum force tolerance was 1.0 × 10−2 eV Å−1, and the maximum stress tolerance was 2.0 × 10−2 GPa. The calculated XPS spectra were generated from the cross-sectionweighted density of states (DOS), which is the sum of the atomically projected partial density of states (PDOS) with each contribution

Figure 2. Simulated XPS spectra of α-CuGaO2 calculated with (a) LDA and (b−d) LDA+U. The experimentally obtained spectrum is shown in panel (e). The green line represents the contribution of the Cu 3d state.

observed spectra. In the calculated XPS spectrum for LDA without U (Figure 2a), the main band, where the Cu 3d contribution is significant, appeared at ca. −1.9 eV; its position is ∼0.8 eV higher energy than that experimentally observed (ca. −2.7 eV; Figure 2e). When U was introduced into the LDA calculation and its value was increased, the energy of the main band shifted to lower energies with a concomitant increase in the width of the Cu 3d main band, which is similar to the results of previous calculations for β-CuGaO219 and Cu2O.21 Consequently, the calculated energy of the Cu 3d main band and its spectral shape closely matched the experimentally observed spectrum when U was set at 3 or 4 eV (Figure 2b,c). When U was increased further to 5 eV, the energy of the main band became too low, and the Cu 3d main band was extremely broadened. The crystal structure of α-CuGaO2 obtained by B

DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry geometry optimization with U = 3−4 eV reproduced well the experimentally observed structure,22 as summarized in Table 1. Thus, we conclude that the appropriate value of U is 3−4 eV in the case of the LDA+U calculations for α-CuGaO2. Table 1. Structural Parameters of α-CuGaO2 Obtained by Geometry Optimization with LDA+U for U = 4 eV and the Experimentally Obtained Results a0 (Å) c0 (Å) volume (Å3) Cu−O (Å) Ga−O (Å) a

calculated

observeda

difference

3.010 17.362 136.2 1.871 2.016

2.977 17.171 131.8 1.848 1.996

+1.1% +1.1% +3.3% +1.2% +1.0%

Reference 22.

The appropriate values of U for α- and β-CuGaO2 are not identical. In the case of Cu2O, where Cu atoms are twofold and linearly coordinated to O atoms, as they are in α-CuGaO2, we determined the appropriate value of U to be 3−4 eV (Figure S2 in the Supporting Information), which is the same as for αCuGaO2. Because the value of U corresponding to the on-site Coulomb interaction of shallow Cu 3d electrons should be dependent on the local structure (e.g., the number of bonds, bond lengths, and bond angles) the appropriate value of U varies between the two polymorphs. The appropriate values of U determined for α-CuGaO2 (3−4 eV) and β-CuGaO2 (5−7 eV) are characteristic for twofold and linear coordination, and fourfold and tetrahedral coordination of Cu atoms, respectively. Because U corrects the self-interaction error of Cu 3d electrons, larger U indicates the higher localization nature of Cu 3d electrons. Thus, the larger U for β-phase than α-phase indicates that the Cu 3d electrons in β-phase are highly localized as compared to that in α-phase; this situation is consistent with the calculation that the dispersion of Cu 3d band in valence band of β-CuGaO2 is smaller than that of α-CuGaO2 (Figure 3). The previously reported appropriate values of U for Cu2O (5−6 eV)23,24 and α-CuAlO2 (5.2 eV)25 are almost identical with our values, although a slight difference that probably comes from the difference in computational code or pseudopotentials remains. The calculated total energy of β-CuGaO2 was larger than that of α-CuGaO2 over the entire U range (0−12 eV) employed in the present study (Figure S3 in the Supporting Information). Specifically, the difference between the β- and α-phases was 42.2 kJ mol−1 under U = 4 eV and 36.0 kJ mol−1 under U = 6 eV. This indicates that β-CuGaO2 is more unstable than αCuGaO2. We previously reported that β-CuGaO2 irreversibly transforms into α-CuGaO2 above 460 °C in an Ar atmosphere, which indicates that β-CuGaO2 is a metastable phase, in contrast to α-CuGaO2, and has a transformation heat of −31.97 kJ mol−1, as obtained using differential scanning calorimetry.26 The results obtained in our calculation are consistent with the results of the thermal analysis; the difference in the calculated total energies between the two polymorphs reproduced well the experimentally obtained transformation heat even though the experimentally obtained value involves kinetics effects. We employed LDA+U calculations with U = 4 eV for αCuGaO2 based on the results detailed above and with U = 6 eV for β-CuGaO2 (the value for the β-form is similar to that used in our previous study19), because these values are most appropriate for reproducing the crystal structures and valence-

Figure 3. Electronic band structure of α-CuGaO2 and β-CuGaO2 calculated with LDA+U with the optimized Hubbard correction U. (a,c) Band structure along the symmetry line; the horizontal axis was standardized with respect to the length of each k-vector. (b, d) Corresponding total and partial DOS.

band electronic structures. In the following section, we discuss in detail the electronic and physical properties of these polymorphs. Electronic Structures of CuGaO2 Polymorphs. The E−k diagrams and total and partial DOS of α- and β-CuGaO2 are shown in Figure 3. The E−k diagrams indicate that α-CuGaO2 is an indirect semiconductor and that β-CuGaO2 is a direct semiconductor. This result is similar to that of previous calculations,27,28,8,19 and this is one of the major differences in the electronic structure between the two polymorphs. In Table 2, the calculated band gaps for the two polymorphs are Table 2. Calculated and Experimentally Obtained Band Gaps of α- and β-CuGaO2 materials

transition

type

α-CuGaO2

F−Γ Γ−Γ L−L F−F Γ−Γ

allowed indirect forbidden directa

β-CuGaO2 a

C

calculated (eV)

observed (eV)

1.20 2.02 3.49 3.77 0.23

2.55b −

allowed directa allowed direct

3.75b 1.47c

Reference 28. bReference 29. cReference 8. DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry summarized together with the experimentally determined values. Although the calculation underestimated the energy band gaps, the order of energies of respective gaps agrees well with the experimentally obtained result29,8 and is consistent with previously reported calculations.27,19 Upon analysis of the electronic structure of the conduction band of α- and βCuGaO2 in Figure 3b,d, we find a difference in mixing levels of Cu and Ga orbitals. In α-CuGaO2, electronic states derived from Cu and Ga atoms, which mainly appeared at ∼3.7 and ∼5.7 eV, respectively, do not mix, as schematically illustrated in Figure 4a. In delafossite α-CuGaO2, Cu and Ga atoms are not

Figure 5. Two-dimensional electron-density contour plot of the LDA +U calculation of (a) α-CuGaO2 with U = 4 eV corresponding to the higher-energy region of the valence band (E−EVBM = −2.45 to 0 eV) and the lower-energy region of the valence band (E−EVBM = −6.82 to −2.81 eV) and (b) β-CuGaO2 with U = 6 eV corresponding to the higher-energy region of the valence band (band I; EVBM = −2.16 to 0 eV) and the lower-energy region of the valence band (band II; EVBM = −5.66 to −2.96 eV).

Figure 4. Schematic illustration of the electronic states near the band edge of (a) α-CuGaO2 and (b) β-CuGaO2.

mixed, but Cu2O and Ga2O3 layers are alternately stacked, as indicated in Figure 1a. This structural feature results in poorly mixed electronic states of Cu and Ga atoms. In contrast to αCuGaO2, the conduction band of β-CuGaO2 is composed of well-mixed states of Cu and Ga atoms, where Cu 4s and 4p and Ga 4s and 4p contribute almost equally, as shown in Figure 3d. In β-CuGaO2, both Cu and Ga atoms are fourfold and tetrahedrally coordinated to O atoms and occupy almost equivalent cation sites in the wurtzite structure. This structural feature results in well-mixed conduction band electronic states of Cu and Ga atoms. In the valence band, the distributions of DOS in the two polymorphs are substantially different; specifically, the Cu 3d valence band of α-CuGaO2 is highly dispersed and appears to be single broad band indicated as band I (0 to −6 eV) in Figure 3b, whereas the dispersion of the Cu 3d valence band in βCuGaO2 is very small, and the band split into two parts indicated as band I′ (0 to −2 eV) and band II′ (−3.5 to −6 eV) in Figure 3d. The two-dimensional electron-density contour plots of the valence bands of the two polymorphs are shown in Figure 5. In the higher-energy region of band I for α-CuGaO2 (Figure 5a), nodes are observed between the Cu and O atoms, indicating that this energy region corresponds to the antibonding states of Cu 3d and O 2p orbitals. By contrast, the high-electron-density region around Cu and O atoms is connected in the lower-energy region of band I for α-CuGaO2; therefore, the lower-energy region of band I can be attributed to the bonding states of Cu 3d and O 2p orbitals. In β-CuGaO2 (Figure 5b), the higher- (band I′) and lower- (band II′) energy regions of the valence band correspond to the antibonding and bonding states of Cu 3d and O 2p orbitals, respectively, which

is similar to the case for α-CuGaO2; however, there is large energy splitting between the antibonding and bonding states in β-CuGaO2 (−2 to −3.5 eV, as observed in Figure 3c,d) because of the small dispersion of Cu 3d valence band. According to crystal-field theory,30 the Cu 3d orbitals in delafossite α-CuGaO2, where Cu atoms are twofold and linearly coordinated to O atoms, split into three levels of a nondegenerate σg+ state at +1.03Δ, doubly degenerated πg states at +0.11Δ, and doubly degenerated δg states at −0.63Δ, as shown in Figure 6a. Such characteristic feature of Cu 3d orbitals in delafossite-type oxides was also reported in previous calculation.27 Conversely, the Cu 3d orbitals in β-CuGaO2, where Cu atoms are fourfold and tetrahedrally coordinated to O atoms, split into triply degenerated t2 states at +0.18Δ′ and doubly degenerated e states at −0.27Δ′30 (Figure 6b). These

Figure 6. Schematic illustration of the crystal-field splitting of the 3d orbital of Cu atoms with (a) twofold and linear coordination and (b) fourfold and tetrahedral coordination. D

DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

CuGaO2 and β-CuGaO2 make them promising for applications as transparent electrodes and solar-cell absorbers, respectively. The band dispersion near the conduction-band minimum in α-CuGaO2 is almost the same as that observed for β-CuGaO2 in Figure 3a,c (note: the horizontal axes in Figure 3a,c were normalized with respect to the length of each k-vector, which allows the band dispersions to be compared for the two polymorphs). As shown in Table 3, the electron effective

results indicate the degeneracy of Cu 3d orbitals are highly resolved in α-CuGaO2 (i.e., Cu 3d orbitals are distributed across a broad energy range, in contrast to wurtzite βCuGaO2). Therefore, the difference in the dispersion of the Cu 3d band in the valence band between the two polymorphs is attributed to differences in the local structures surrounding Cu atoms. Accordingly, the energy splitting between −2 and −3.5 eV in β-CuGaO2 is attributable to energy splitting between bonding t2 states and antibonding e states, and the high DOS from −2 to −3 eV in α-CuGaO2 is attributable to the overlap of the bonding σg+ state and the antibonding δg states. The DOS near the valence-band maximum of α-CuGaO2 is ∼2 states eV−1 unit cell−1 (∼0.04 states eV−1 Å−3), which is smaller than that of β-CuGaO2 (∼20 states eV−1 unit cell−1; that is, ∼0.1 states eV−1 Å−3). This also comes from the difference in the local structures surrounding Cu atoms in these polymorphs; the top of the valence band in delafossite αCuGaO2 consists of the nondegenerate antibonding σg+* state, whereas that in wurtzite β-CuGaO2 consists of triply degenerate antibonding t2* states, according to the crystal-field theory. Physical Properties Expected from the Electronic Band Structure. As described in the previous section, the electronic structures of delafossite α-CuGaO2 and wurtzite βCuGaO2 reflect the characteristics of their crystal structures. In this section, we discuss the relationship between the electronic structure and physical properties. The calculated absorption spectra of polycrystalline α- and β-CuGaO2 are shown in Figure 7. The direct and allowed energy band gaps of α- and β-

Table 3. Effective Masses (in units of free electron mass, m0) of Electrons and Holes for α- and β-CuGaO2 electron material α-CuGaO2 (U = 4 eV)

β-CuGaO2 b (U = 6 eV)

hole

direction

me*/m0

directiona

mh*/m0

Γ→F Γ→Z Γ→L Γ→X Γ→Y Γ→Z Γ→R

0.44 0.34 0.44 0.21 0.21 0.21 0.21

F→Γ F→L F→Z Γ→X Γ→Y Γ→Z Γ→R

0.41 1.7 0.49 5.1 1.7 4.9 2.7

a

The k-vectors of Γ→F, Γ→Z, Γ→L, F→L, and F→Z in α-CuGaO2 correspond to the (110), (111), (010), (100), and (001) directions of the primitive cell (rhombohedral unit cell) in real space, respectively. The k-vectors of Γ→X, Γ→Y, Γ→Z, and Γ→R in β-CuGaO2 correspond to the (010), (100), (001), and (111) directions in real space, respectively. bReference 19. a

masses of α- and β-CuGaO2, which were calculated by the parabolic approximation, are almost identical and are similar to those in typical n-type oxide semiconductors such as ZnO (me*/m0 = 0.28)31 and In2O3 (me*/m0 = 0.35)32. Moreover, they do not depend on whether the conduction-band minimum consists of mostly Cu 4s orbitals and well-mixed Cu and Ga 4s orbitals. As described in the previous section, the band dispersion in the valence band in β-CuGaO2 is smaller than that of αCuGaO2 (Figure 3a,c) because of differences in the local structure surrounding Cu atoms. This has a direct effect on the effective hole masses, mh*/m0, of the two polymorphs: mh*/m0 in β-CuGaO2 is calculated to be in the range of 1.7−5.1, which is several times larger for α-CuGaO2 (mh*/m0 = 0.41−1.7). The hole effective mass (i.e., delocalization of holes in Cu 3d states) should also be dependent on the Cu−Cu distance because the electronic states near the valence-band maximum are composed mainly of Cu 3d antibonding states between Cu 3d and O 2p orbitals. In Figure 8, the smallest values of the calculated effective hole masses of delafossite α-CuBO2 (B = Al, Ga, In)27,33 and wurtzite β-AgB′O2 (B′ = Al, Ga)34 are plotted as a function of interatomic distance of the monovalent metallic atoms. The effective hole mass systematically increases with increasing interatomic distance in both α-CuBO2 and β-AgB′O2 systems. Therefore, it can be expected that the large effective mass of holes in wurtzite β-CuGaO2 can be reduced by substitution of Ga with Al.

Figure 7. Calculated absorption coefficients of polycrystalline αCuGaO2 (U = 4 eV) and β-CuGaO2 (U = 6 eV). The calculated direct and allowed energy band gaps of α-CuGaO2 and β-CuGaO2 were rigidly shifted to the experimentally measured direct band gap.

CuGaO2 were rigidly shifted to the experimental values;29,8 the L−L transition that was calculated to be 3.49 eV was set to 3.75 eV for α-CuGaO2, and the Γ−Γ transition that was calculated to be 0.23 eV was set to 1.47 eV for β-CuGaO2. α-CuGaO2 is an indirect semiconductor; the first direct but optically forbidden transition at the Γ-point28 was shifted to 2.40 eV when the direct and allowed band gap at the L-point was set to 3.75 eV. Therefore, the absorption coefficient increased gradually above the forbidden band gap of 2.40 eV and reached 5 × 104 cm−1 at 3.95 eV, which is 0.2 eV above the energy of the direct and allowed band gap. Conversely, β-CuGaO2 is a direct semiconductor and possesses a large DOS near the valence-band maximum; therefore, the absorption coefficient increased abruptly above the band gap, reaching 1.1 × 105 cm−1 at 1.67 eV. The absorption coefficient of α-CuGaO2 near the direct and allowed band gap (5 × 104 cm−1) is slightly smaller than that of β-CuGaO2 (1.1 × 105 cm−1) because the DOS near the valence-band maximum of α-CuGaO2 is smaller than that of β-CuGaO2. These optical-absorption characteristics of α-

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CONCLUSIONS In this study, we calculated the electronic structures of α- and β-CuGaO2 using LDA+U functional. The most appropriate values of the Hubbard correction U, determined as those that yielded the most reproducible valence-band XPS spectra and crystal structures, were 3−4 and 5−7 eV for the α- and β-forms, respectively. We analyzed the electronic structures and optical E

DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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Article

AUTHOR INFORMATION

Corresponding Author

*Phone: +81-22-217-5832. Fax: +81-22-217-5832. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by a Grant-in-Aid for Scientific Research of Challenging Exploratory Research (Grant No. 25630283), Grant-in-Aid for Scientific Research (B) (Grant No. 26289239) and Grant-in-Aid for JSPS Fellows (Grant No. 26763). We thank Prof. F. Oba, Tokyo Institute of Technology, for his valuable comments.

Figure 8. Relationship between the interatomic distances between monovalent metallic atoms and the smallest values of calculated hole effective masses of delafossite α-CuBO2 (B = Al, Ga, In) (blue), wurtzite β-AgB′O2 (B′ = Al, Ga) (red), and β-CuGaO2 (black). aref 33, bthis work, cref 27, and dref 34. The interatomic distances between monovalent metallic atoms were determined from the reported crystal structures obtained by geometry optimization, with the exception of βAgB′O2, the detailed crystal structure of which was not described in ref 34; therefore, the interatomic distances of β-AgB′O2 in this figure were based on experimentally obtained crystal structures.6,7

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and electrical properties obtained from the calculations in terms of structural features of the two polymorphs. We identified three major features of the crystal structure that have significant influence on the electronic structures of the CuGaO2 polymorphs. The first feature is the atomic arrangement of Cu and Ga atoms in the crystal structure; αCuGaO2 possesses a layered structure composed of Cu2O and Ga2O3 layers, whereas Cu and Ga atoms are atomically mixed in β-CuGaO2. Therefore, Cu and Ga states do not mix well in the conduction band of α-CuGaO2, whereas they are wellmixed in β-CuGaO2. The second feature is the coordination environment of Cu atoms that determines the breaking of degeneracy of Cu 3d orbitals. This has a significant impact on the dispersion of the Cu 3d valence band. The dispersion of the Cu 3d valence band is larger in α-CuGaO2, in which Cu atoms are twofold and linearly coordinated to O atoms, than in βCuGaO2, in which Cu atoms are fourfold and tetrahedrally coordinated to O atoms. Such a difference in valence-band dispersion results in a larger absorption coefficient and larger hole effective mass in β-CuGaO2. In addition to the coordination environment of Cu atoms, we found that the interatomic distance between Cu atoms has an impact on the dispersion of the Cu 3d valence band (i.e., the effective hole mass); the effective hole mass decreases with decreasing interatomic distance between Cu atoms. Therefore, we suggest that the large effective mass of holes in wurtzite β-CuGaO2 can be reduced by substitution of Ga with Al.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01012. Variation of calculated lattice parameters of α-CuGaO2, appropriate values of the Hubbard correction U for Cu2O calculations with LDA+U, and calculated total energies of α- and β-CuGaO2. (PDF) F

DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

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DOI: 10.1021/acs.inorgchem.6b01012 Inorg. Chem. XXXX, XXX, XXX−XXX