Effective uniaxial dielectric function tensor and optical phonons in (201)-oriented β-Ga2O3 films with equally distributed sixfold-rotation domains - Mock, Alyssa; Richter, Steffen; Papamichail, Alexis; Stanishev, Vallery ; 0000-0002-7626-1181; Ghezellou, Misagh; Ul-Hassan, Jawad; Popp, Andreas; Bin Anooz, Saud; Gogova, Daniela; Ranga, Praneeth; Krishnamoorthy, Sriram; Korlacki, Rafal; et al. (Physical Review Applied, 2024)
Monoclinic β-Ga2O3 films grown on c-plane sapphire have been shown to exhibit six (201 ¯ )-oriented domains, which are equally spaced by rotation around the surface normal and equally sized by volume that render the film optical response effectively uniaxial. We derive and discuss an optical model suitable for ellipsometry data analysis of such films. We model mid- and far-infrared ellipsometry data from undoped and electrically insulating films with an effective uniaxial dielectric tensor based on projections of all phonon modes within the rotation domains parallel and perpendicular to the sample normal, i.e., to the reciprocal lattice vector g201 ¯ . Two effective response functions are described by the model, and found sufficient to calculate ellipsometry data that best match measured ellipsometry data from a representative film. We propose to render either effective dielectric functions, or inverse effective dielectric functions, each separately for electric field directions parallel and perpendicular to g201 ¯ , by sums of Lorentz oscillators, which permit determination of either sets of transverse optical phonon-mode parameters, or sets of longitudinal optical phonon-mode parameters, respectively. Transverse optical modes common to both dielectric functions can be traced back to single-crystal modes with Bu character, while modes with Au character appear only within the dielectric function for polarization perpendicular to the sample surface. The thereby obtained parameter sets reveal all phonon modes anticipated from averaging over the sixfoldrotation domains of single crystal β-Ga2O3, but with slightly shifted transverse optical, and completely different longitudinal optical phonon modes. Structural analysis of the film revealed virtually strain-free material. We suggest small crystal grains and high density of grain boundaries as a possible origin for the observed transverse optical phonon-frequency shifts with respect to bulk material. The differences in longitudinal optical modes here compared to the bulk are hypothesized to be caused by averaging of the electric-field-induced polarization over many long-range ordered rotation domains. Our model can be useful for future analysis of free charge-carrier properties using infrared ellipsometry on multiple domain films of monoclinic structure β-Ga2O3.