Dielectric tensor of monoclinic Ga$_2$O$_3$ single crystals in the spectral range $0.5 - 8.5\,$eV

The dielectric tensor of $\beta$-Ga$_2$O$_3$ was determined by generalized spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to $8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to $|\varepsilon_{xz} | \approx 0.30 $ and cannot be neglected. Even in the transparent spectral range where it is quite small ($|\varepsilon_{xz} | < 0.02 $) it causes a rotation of the dielectric axes around the symmetry axis of up to $20^\circ$.