In this study, the phonon thermal transport in monolayer C3N under biaxial strains ranging from 0% to 10% has been investigated using first-principles calculations based on the Boltzmann transport equation. It is found that the thermal conductivity κ of C3N shows a nonmonotonic up-and-down behavior in response to tensile strain, and the maximum κ occurs at a strain of 6%. Interestingly, the thermal conductivity of monolayer C3N shows a remarkable high strain tunability, as its value at 6% strain is about 13.2 times higher than the value of κ in an unstrained monolayer. A mode-by-mode phonon level analysis shows that a competition between different phonon properties is responsible for such variations in the thermal conductivity. We found that the decrease in group velocity of the transverse acoustic, longitudinal acoustic, and optical modes as well as the increase in the three-phonon phase space of all the acoustic modes tend to reduce the thermal conductivity with strain. However, the group velocity of the z-direction acoustic mode and the Grüneisen parameter of all acoustic modes change in the direction of increasing the phonon lifetime and the thermal conductivity with increasing strain. Upon stretching, the change in the Grüneisen parameter and the phonon lifetime of the acoustic modes is found to be drastically higher than the change in other properties. The competition between these opposite effects leads to the up-and-down behavior of the thermal conductivity in C3N.

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