Strain and stress relationships for optical phonon modes in monoclinic crystals with \u3ci\u3eβ\u3c/i\u3e-Ga\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e3\u3c/sub\u3e as an example

Strain-stress relationships for physical properties are of interest for heteroepitaxial material systems, where strain and stress are inherent due to thermal expansion and lattice mismatch. We report linear perturbation theory strain and stress relationships for optical phonon modes in monoclinic crystals for strain and stress situations which maintain the monoclinic symmetry of the crystal. By using symmetry group analysis and phonon frequencies obtained under various deformation scenarios from density-functional perturbation theory calculations on β-Ga2O3, we obtain four strain and four stress potential parameters for each phonon mode. We demonstrate that these parameters are sufficient to describe the frequency shift of the modes regardless of the stress or strain pattern which maintain the monoclinic symmetry of the crystal. The deformation potentials can be used together with experimentally determined phonon frequency parameters from Raman or infrared spectroscopy to evaluate the state of strain or stress of β-Ga2O3, for example, in epitaxial heterostructures