Ab initio description of lattice dynamics in oxide semiconductors

Abstract

As non-toxic and sustainable materials the system of binary oxide semiconductors Cu2O, Cu4O3, and CuO is in the focus of current research, e.g., for solar-cell applications. The objective of this work is to analyse the vibrational and Raman spectroscopic properties of these binary semiconductors using ab initio methods (density functional theory).The phonon dispersions of polar semiconductors display a splitting in frequency of the longitudinal optical (LO) and transversal optical (TO) infrared active modes (LO-TO splitting) in the limit of vanishing phonon wave vector. This traces back to long-ranged dipole-dipole interactions present in these crystals. The theoretical treatment of these interactions requires the usage of certain correction schemes for the dynamical matrices. Two methods implementing these corrections [Phys. Rev. B 55, 10355 (1997) (Gonze s method); J. Phys.: Condens. Matter 22, 202201 (2010) (Wang s method)] are employed. Gonze s method, which is traditionally in the framework of density function perturbation theory, is shown to be applicable together with the real space method. Both correction schemes are compared using the insulator CaF2 as test system. The evolution of the phonon frequencies of the modes showing LO-TO splitting close to the Brillouin zone centre in many cases is better described by Gonze s method. Wang s method, on the contrary, can introduce artificial features in the phonon dispersion.The phonon dispersion and derived quantities of all three copper oxide phases are calculated and compared to experiment. It becomes particularly clear that the corrections following Gonze s method are necessary to obtain agreement with experimentally determined phonon dispersions. Good agreement with experiment is obtained for the vibrational contributions to the specific heat and the entropy. Based on Gonze s method the velocities of sound are calculated along several directions also yielding good accordance with experiment.The focus of the Raman spectroscopy investigations is on Cu4O3 and CuO. Cu4O3 is not too extensively studied theoretically as well as experimentally, and for CuO different crystal structures must be considered for room temperature (RT) and low temperatures (LT) (below 213 K). While group theory predicts three Raman active modes for CuO at RT additional modes appear in the experimental LT Raman spectrum [Phys. Rev. B 52, R13130 (1995)]. The appearance of the extra Raman active modes can be explained by a local symmetry lowering of the atomic positions compared to the RT structure owing to a change in the antiferromagnetic ordering. Additional measured Raman active modes can be identified in the calculations; more extra modes are calculated than measured, while each of those not visible in experiment shows a small intensity in the calculated Raman spectrum. Additionally, a rather different behaviour of the Raman intensities of the modes common to both the RT and the LT structures as a function of the laser energy is found. For Cu4O3 the dependence of the Raman intensities on the crystal orientation and the chosen polarisations are investigated in detail. Particularly, the totally symmetric A1g mode has noteworthy angular intensity dependence since it depends on the relative phase of the complex-valued Raman tensor elements. The effect of hydrostatic pressure is also studied showing that the frequencies of the Raman active modes are very sensitive to the exerted pressure.