Stress/Strain Effects on Phonon Modes and Phonon Deformation Potentials in Monoclinic <i>β</i>-Ga₂O₃

Strain-induced shifts of phonon energies provide a powerful tool for modeling strain patterns in heterostructures and thin films. In the case β-Ga₂O₃, an emerging wide-bandgap semiconducting oxide, the low symmetry of its monoclinic structure is responsible for the high anisotropy and unusual ordering of phonon modes, while the effects of stress and strain on the phonon properties in general are not yet well understood. We present a rigorous, symmetry-based analysis on how the frequencies of optical phonon modes depend on the components of stress and strain tensors in monoclinic crystals, and we confront it with the results of density functional theory (DFT) calculations involving several distinct deformation scenarios, and the resulting shifts in phonon mode frequencies for β-Ga₂O₃. We derive sets of phonon deformation potential parameters for all phonon modes, including infrared-active (A_u and B_u) and Raman-active (A_g and B_g) modes. Additionally, we discuss how stress affects the order of phonon modes with B_u symmetry.