Insights into strain dependent lattice thermal conductivity of <b> <i>α</i> </b>- and <b> <i>κ</i> </b>-Ga2O3

α- and κ-Ga2O3 are promising candidates for high-performance devices such as high-power electronics, but the low thermal conductivity (TC) severely hinders its application. Strain inevitably exists in practical Ga2O3-based devices due to the mismatch of lattice structure and thermal expansion brought by heteroepitaxial growth, and it significantly influences the thermal properties of α- and κ-Ga2O3. By employing first-principles calculations and the phonon Boltzmann transport equation, we have studied the TC at the induced strain and optimized strain axis in free states and 16 different strain states. The TC at the induced strain and optimized strain axis generally decreases with increasing strain. Under −4% XZ-axes biaxial compressive strain, the kzz of α-Ga2O3 can increase to ∼1.7 times its original value, while under −2% XY-axes biaxial compressive strain, the kxx of κ-Ga2O3 can increase to 2.8 times its original value. The improvement of thermal transport properties is attributed to the increase in phonon group velocity and relaxation time caused by the phonon hardening and decrease in three-phonon scattering channels, respectively. However, we observed an exception: under +4% X-axis tensile strain, kyy of α-Ga2O3 increased by 1.1 times. Moreover, atomic bond analysis revealed that under XY-direction strain, the ICOHP values for α-Ga2O3 are −3.94 eV (at −4% strain), −3.76 eV (unstrained state), and −3.63 eV (+4% strain). This discovery elucidates the origin of phonon hardening under compressive strain, indicating that strengthened bonds enhance phonon transport. This study provides essential insights into the mechanisms of α- and κ-Ga2O3 TC under different strains.