Dipole Analysis of the Dielectric Function of Colour Dispersive Materials: Application to Monoclinic Ga$_2$O$_3$

TL;DR

This paper introduces a generalized dipole model for analyzing the dielectric function of anisotropic, color dispersive materials, demonstrated on monoclinic Ga$_2$O$_3$, linking electronic transitions to crystal structure and accounting for domain effects.

Contribution

It extends existing models to include anisotropic dipole polarizations and applies this to monoclinic Ga$_2$O$_3$, connecting optical properties with atomic structure.

Findings

Relates electronic transitions to atomic bonds and orbitals.

Shows optical biaxiality reduces to uniaxial in thin films with domains.

Demonstrates the model's applicability to real crystal structures.

Abstract

We apply a generalized model for the determination and analysis of the dielectric function of optically anisotropic materials with colour dispersion to phonon modes and show that it can also be generalized to excitonic polarizabilities and electronic band-band transitions. We take into account that the tensor components of the dielectric function within the cartesian coordinate system are not independent from each other but are rather projections of the polarization of dipoles oscillating along directions defined by the, non-cartesian, crystal symmetry and polarizability. The dielectric function is then composed of a series of oscillators pointing in different directions. The application of this model is exemplarily demonstrated for monoclinic ($\beta$-phase) Ga$_2$O$_3$ bulk single crystals. Using this model, we are able to relate electronic transitions observed in the dielectric function to atomic bond directions and orbitals in the real space crystal structure. For thin films revealing rotational domains we show that the optical biaxiality is reduced to uniaxial optical response.