PHYSICAL REVIEW B 90, 115150 (2014) Electronic structure calculations of delafossite Cu-based transparent conducting oxides Cu MO 2 ( M = B,Al,Ga,In) by quasiparticle self-consistent GW approximation and Tran-Blaha’s modified Becke-Johnson exchange potential Abdulmutta Thatribud and Teparksorn Pengpan Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90110, Thailand (Received 14 May 2014; revised manuscript received 10 September 2014; published 26 September 2014) In this work, band gaps of the delafossite Cu-based transparent conducting oxides CuMO 2 (M = B,Al,Ga,In) are calculated by density functional theory (DFT) implemented with many-body perturbation theory (MBPT) based on quasiparticle self-consistent GW approximation (QPscGW) and with Tran-Blaha’s modified Becke- Johnson functional (DFT-TB09). Their band gaps are explicitly improved from DFT within local density approximation (LDA). Their optical absorption spectra are also calculated by solving Bethe-Salpeter equation (BSE) that includes the electron-hole correlation effect; they show strong excitonic peaks. DOI: 10.1103/PhysRevB.90.115150 PACS number(s): 71.15.Mb, 71.15.Qe, 71.20.−b, 78.20.−e I. INTRODUCTION Transparent conducting oxides (TCOs) are extensively studied as materials for transparent electrodes in flat-panel displays to photovoltaic devices [1] due to their dual properties, electrical conductivity and optical transparency [2–4]. They are semiconductors having an optical band gap of more than 3 eV, where visible photons cannot excite electrons from the valence edge to a conduction band. Most TCOs that were initially discovered are the n-type ones, such as SnO 2 , In 2 O 3 , ZnO, Ga 2 O 3 , CdO, and others, which are now commercialized and used in many modern devices [5]. The first p-type TCO being discovered was NiO, exhibiting a visible light transmission of 40% and an electrical conductivity of 1 S cm −1 [6]. However, the TCOs that are used in technological applications should have a visible light transmittance of more than 80%. Kawazoe et al. [7] noticed that the obstruction of the p-type TCO is due to its highly localized electrons of oxide ions in the valence band upper edge [8]. The first key to reduce such a strong localization is to use cations such as Cu 1+ , Ag 1+ , and Au 1+ that have an electronic configuration of d 10 s 0 . The energy in the d 10 closed shell electrons of these cations is the highest and is expected to overlap with that in the 2p electrons of the oxide ions. The second key is to select an oxide ion that can enhance the covalency in the bonding between the cation and oxide ion. The third key is to enlarge the direct band gap by weakening the interaction between the d 10 -d 10 closed shell electrons. As a result, a thin film of CuAlO 2 was proposed as the p-type TCO candidate with an optical direct band gap of about 3.5 eV, visible light transmission of 80%, and electrical conductivity of up to 1 S cm −1 at room temperature [7]. Other p-type Cu-based TCOs, like CuGaO 2 [9] and Ca- doped CuInO 2 [10], were later fabricated with optical direct band gaps of about 3.6 and 3.9 eV and electrical conductivities of about 6.3×10 −2 and 2.8×10 −3 S · cm −1 , respectively. The latest p-type Cu-based TCO was a CuBO 2 thin film having an optical direct band gap of 4.5 eV and a remarkable electrical conductivity of 1.65 S cm −1 at room temperature [11]. Since there was a contradiction between experimental and calculated lattice constants [12], recent experiments of crystalline powder CuBO 2 still confirmed Snure and Tiwari’s lattice constants but with an optical direct band gap of 3.46–3.6 eV [13–15], about 1 eV less than the one reported by Snure and Tiwari [11]. All p-type Cu-based TCOs have delafossite structure with a general chemical composition of CuMO 2 [16]. Typical M 3+ cations are either p-block metal cations such as B, Al, Ga, In, or transition metal cations such as Cr, Fe, Co, or others. The M 3+ cation is located in the distorted edge-shared octahedron. The MO 6 groups generally form a layer that possesses hexagonal symmetry. Both, Cu 1+ and MO 6 , can be arranged in layers so that a duplicate of the three-layer stacks gives the 3R (R ¯ 3m) rhombohedral structure and that a duplicate of the two-layer stacks gives the 2H (P 6 3 /mmc) hexagonal structure. Despite having more layers, the 3R primitive unit cell has three times fewer atoms. In the 2H conventional unit cell there are two Cu 1+ cations; each of them is linearly coordinated to two oxygen ions. The interatomic distance between the nearest neighbor Cu 1+ cations in the 2H structure is relatively small, around 2.8–3.0 ˚ A. In all our calculations, we used the 3R unit cell with atoms placed at the Wyckoff positions Cu 1+ (1a) (0,0,0), M 2+ (1b) (1/2,1/2,1/2), and O 2− (2c) ±(u,u,u), where u is an internal parameter. In this work, we present first-principles calculations on electronic and optical properties of CuMO 2 (M = B, Al, Ga, In) by density functional theory within local density approximation (DFT-LDA), many-body perturbation theory based on GW approximations [17–19], and DFT within Tran- Blaha’s modified Becke-Johnson exchange potential (DFT- TB09) [20]. It is well known that the electronic structure calcu- lation of solids based on DFT-LDA yields accurate prediction for the lattice parameters and atomic positions. However, the calculated band gaps of insulators and semiconductors within DFT-LDA are underestimated by about 50% or more from their photoemission experimental values due to the incorrect treatment of the exchange-correlation potential. The failure to predict the correct band gaps by DFT-LDA can be handled by the many-body perturbation theory based on Hedin’s GW method, which has been successful in describing exited-state properties of solids [21–25]. The key for this success is to represent the exchange-correlation potential v xc acting on an excited electron by the electron’s self-energy  [26]. We present two approximation approaches in calculating , the one-shot G 0 W 0 and the quasiparticle self-consistent GW (QPscGW) according to Faleev et al.’s scheme [27–29]. For a comparison purpose with the GW methods, we also did band- structure calculations by the Tran and Blaha’s method (TB09) 1098-0121/2014/90(11)/115150(14) 115150-1 ©2014 American Physical Society