Anisotropy, phonon modes, and free charge carrier parameters in monoclinic beta-gallium oxide single crystals

We derive a dielectric function tensor model approach to render the optical response of monoclinic and triclinic symmetry materials with multiple uncoupled infrared and far-infrared active modes. We apply our model approach to monoclinic beta-Ga2O3 single-crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and ((2) over bar 01), are investigated by generalized spectroscopic ellipsometry within infrared and far-infrared spectral regions. We determine the frequency dependence of 4 independent beta-Ga2O3 Cartesian dielectric function tensor elements by matching large sets of experimental data using a point-by-point data inversion approach. From matching our monoclinic model to the obtained 4 dielectric function tensor components, we determine all infrared and far-infrared active transverse optic phonon modes with A(u) and B-u symmetry, and their eigenvectors within the monoclinic lattice. We find excellent agreement between our model results and results of density functional theory calculations. We derive and discuss the frequencies of longitudinal optical phonons in beta-Ga2O3. We derive and report density and anisotropic mobility parameters of the free charge carriers within the tin-doped crystals. We discuss the occurrence of longitudinal phonon plasmon coupled modes in beta-Ga2O3 and provide their frequencies and eigenvectors. We also discuss and present monoclinic dielectric constants for static electric fields and frequencies above the reststrahlen range, and we provide a generalization of the Lyddane-Sachs-Teller relation for monoclinic lattices with infrared and far-infrared active modes. We find that the generalized Lyddane-Sachs-Teller relation is fulfilled excellently for beta-Ga2O3.Funding Agencies|National Science Foundation (NSF) through the Center for Nanohybrid Functional Materials [EPS-1004094]; Nebraska Materials Research Science and Engineering Center [DMR-1420645]; Swedish Research Council (VR) [2013-5580, 2010-3848]; Swedish Governmental Agency for Innovation Systems (VINNOVA) under the VINNMER international qualification program [2011-03486, 2014-04712]; Swedish Foundation for Strategic Research (SSF) [FFL12-0181, RIF14-055]; Linkoping Linnaeus Initiative on Nanoscale Functional Materials (LiLiNFM) - VR; University of Nebraska-Lincoln; J. A. Woollam Co., Inc.; J. A. Woollam Foundation; [CMMI 1337856]; [EAR 1521428]