Strong excitonic effects in CuAlO 2 delafossite transparent conductive oxides Robert Laskowski, 1 Niels Egede Christensen, 2 Peter Blaha, 1 and Balan Palanivel 3 1 Institute of Materials Chemistry, Technische Universität Wien, Getreidemarkt 9/165TC, A-1060 Vienna, Austria 2 Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark 3 Department of Physics, Pondicherry Engineering College, Puducherry 605 014, India Received 15 January 2009; revised manuscript received 25 March 2009; published 27 April 2009 The imaginary part of the dielectric function of CuAlO 2 has been calculated including the electron-hole correlation effects within Bethe-Salpeter formalism BSE. In the initial step of the BSE solver the band structure was calculated within density-functional theory plus an orbital field LDA / GGA+ U acting on Cu atoms. We discuss the influence of the strength of the additional orbital field on the band structure, electric field gradients, and the dielectric function. The calculated dielectric function shows very strong electron-hole cor- relation effects manifested with large binding energies of the lowest excitons. The electron-hole pair for the lowest excitations are very strongly localized at a single Cu plane and confined within only a few neighboring shells. DOI: 10.1103/PhysRevB.79.165209 PACS numbers: 71.15.Qe, 71.35.Cc, 78.20.Ci, 78.40.Fy I. INTRODUCTION Delafossite oxides CuMO 2 , where M is a trivalent metal, belong to the rare class of p-type transparent semiconduc- tors. They are relatively well studied, especially CuAlO 2 , which was reported to be p-type conducting by Benko and Koffyberg 1 already 25 years ago. They estimated the hole mobility at rather low level of 1.1  10 -7 m 2 / Vs and from electrochemical measurements a lowest indirect band gap of about 1.65 eV was deduced. The compounds attracted more attention after reporting higher p-type electrical conductivity in thin films of CuAlO 2 by Kawazoe et al. 2 They measured the mobility of holes as high as 10 -3 m 2 / Vs and a conduc- tivity of about 1 S/cm. However in the following work of Yanagi et al. 3 the measured value was reduced to 1.3  10 -4 m 2 / Vs. The delafossite R3 ¯ m unit cell is presented in Fig. 1. It can be viewed as a layered structure, where the Cu cations are linearly coordinated by O and the CuO 2 dumbbells are separated by a layer of edge sharing MO 6 octahedra. Kawazoe et al. proposed 2 that the monopolarity in these compounds results from localization of the holes at the oxygen 2p levels due to strong electronegativity of the oxy- gen atoms. Since the energies of the Cu 3d orbitals are quite close to the O 2p states the strong covalent bonding between Cu and O delocalizes the positive holes. 2,3 At the same time the low-dimensional Cu-O coordination suppresses the inter- action and leads to a large band gap comparing to Cu 2 O for example. The allowed direct and indirect band gaps were estimated from optical transmission spectra at about 3.5 eV and 1.8 eV. 2,3 Several x-ray spectroscopy studies indicate that both the valence and conduction bands result from strong mixing of Cu 3d and O 2p states. 3,4 A detailed study of the electronic structure of CuAlO 2 has been performed by Aston et al. using x-ray photoemission spectroscopy XPS, x-ray emission spectroscopy XES, and x-ray absorption spectroscopy XAS. 4 According to their findings the maxi- mum of the Cu 3d band appears about 2.8 eV below the Fermi level, and the maximum of the O 2p band is located around 5 eV below it. They also showed a relatively good agreement with ab-initio calculations. However the calcu- lated Cu 3d band is too close to the valence-band maximum VBM, its binding energy being only 1.2 eV. The calcu- lated band structure shows a dispersion of the valence bands around the F and L points mainly due to the interaction be- tween Cu d z 2 and O p z states, 5 whereas relatively flat bands around  and Z originate from antibonding Cu-O  states. The series of CuMO 2 delafossites, where M is Al, Ga, or In shows band-gap anomalies. The optically measured gaps are 3.5 eV for CuAlO 2 , 3.6 eV for CuGaO 2 , and 3.9 for CuInO 2 . This trend contradicts observed trends for other group-III containing semiconductors. Using first-principles methods Nie et al. 6 gave a simple explanation of this anomaly. They found that the direct gaps follow the general trend and de- crease within the series, however the region of the Brillouin zone BZ around  is optically inactive. It happens that for CuInO 2 and CuGaO 2 the fundamental gaps are at , whereas the optical allowed transitions start at higher energies around L. The electron-hole correlation can strongly affect the cal- culated optical response of a material. The strength of such effects depends to some extent on the atomic structure of a compound. Layered structures enhance the localization of the electron-hole pairs and lead to a strong electron-hole in- teraction. From a point of view of a band structure, parallel valence and conduction bands lead often to delocalized ex- citons in k space and therefore allows for their real-space localization. Due to their layered structure and their band structure the delafossites are expected to be materials where the electron-hole correlations are rather strong. In this work we explicitly calculate the optical spectra including the electron-hole correlation by solving the Bethe-Salpeter equa- tion BSE. We analyze the lowest excitons in real as well as in k space. Since the electron-electron correlation within the Cu atom is also an interesting issue and certainly affects the band structure of CuAlO 2 , we also analyze it within standard density-functional theory plus an orbital field LDA / GGA + URefs. 7–9 methodology. II. COMPUTATIONAL METHOD The scheme for calculating the optical response including the electron-hole interactions used in this work is based on PHYSICAL REVIEW B 79, 165209 2009 1098-0121/2009/7916/1652097 ©2009 The American Physical Society 165209-1