Strain and composition dependencies of the near bandgap optical transitions in monoclinic (Al$_x$Ga$_{1-x}$)$_2$O$_3$ alloys with coherent biaxial in-plane strain on (010) Ga$_2$O$_3$

TL;DR

This study combines density functional theory and spectroscopic ellipsometry to analyze how strain and composition affect the near bandgap optical transitions in monoclinic (Al$_x$Ga$_{1-x}$)$_2$O$_3$ alloys, revealing bowing parameters after accounting for strain effects.

Contribution

It introduces a combined DFT and GSE approach to quantify strain and composition effects on optical transitions in (Al$_x$Ga$_{1-x}$)$_2$O$_3$ alloys, providing new insights into their electronic properties.

Findings

Determined bowing parameters for the three lowest band-to-band transitions.

Quantified the role of coherent strain on optical transition energies.

Separated strain effects from alloy composition effects in the energy shifts.

Abstract

The bowing of the energy of the three lowest band-to-band transitions in $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloys was resolved using a combined density functional theory (DFT) and generalized spectroscopic ellipsometry (GSE) approach. The DFT calculations of the electronic band structure of both, $\beta$-Ga$_2$O$_3$ and $\theta$-Al$_2$O$_3$, allow extracting of the linear portion of the energy shift in the alloys, and provide a method for quantifying the role of coherent strain present in the $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ thin films on (010) $\beta$-Ga$_2$O$_3$ substrates. The energies of band-to-band transitions were obtained using the spectroscopic ellipsometry eigenpolarization model approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017)]. After subtracting the effects of strain which also induces additional bowing and after subtraction of the linear portion of the energy shift due to alloying, the bowing parameters associated with the three lowest band-to-band transitions in monoclinic $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ are found.