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 $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ single-crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and $\left(\overline{2}01\right)$, are investigated by generalized spectroscopic ellipsometry within infrared and far-infrared spectral regions. We determine the frequency dependence of 4 independent $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ 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 $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$. 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 $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ 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 $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$.

• Received 28 December 2015
• Revised 18 February 2016

DOI:https://doi.org/10.1103/PhysRevB.93.125209