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 beta-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 beta-Ga2O3, for example, in epitaxial heterostructures.
Funding Agencies|National Science FoundationNational Science Foundation (NSF) [DMR 1808715]; Air Force Office of Scientific ResearchUnited States Department of DefenseAir Force Office of Scientific Research (AFOSR) [FA9550-18-1-0360]; Nebraska Materials Research Science and Engineering Center [DMR 1420645]; Swedish Governmental Agency for Innovation Systems (VINNOVA) under the Competence Center Program [2016-05190]; Swedish Research Council VR Award [2016-00889]; Swedish Foundation for Strategic Research Grants [RIF14-055, EM16-0024]; Knut and Alice-Wallenberg FoundationKnut & Alice Wallenberg Foundation; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University, Faculty Grant SFO Mat LiU [2009-00971]; University of Nebraska Foundation; J. A. Woollam Foundation; NRC Research Associateship award at the U.S. Naval Research Laboratory; Nebraska Research Initiative