Impact of high-order anharmonicity and nitrogen vacancy defects on the thermal conductivity of MoSi 2 N 4

Accurately determining the thermal transport properties of the two-dimensional material ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ is essential for its application in micro- and nanoscale semiconductor devices. To date, substantial discrepancy persists between theoretical prediction and experimental measurement of the thermal conductivity ${\ensuremath{\kappa}}_{L}$ of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$, with the underlying physical mechanisms remaining unclear. In this work, the intrinsic ${\ensuremath{\kappa}}_{L}$ of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ is accurately determined by using the neuroevolutionary potential combined with the phonon Boltzmann transport equation (BTE). Taking the temperature-dependent interatomic force constants extracted from effective harmonic model as the inputs, the room-temperature ${\ensuremath{\kappa}}_{L}$ of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ calculated by the BTE method (approximately $351.84\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$) exhibits remarkable consistency with results obtained from a homogeneous nonequilibrium molecular-dynamics method (approximately $343.04\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$). These results underscore the critical influence of higher-order phonon scattering and temperature renormalization of force constants on the intrinsic ${\ensuremath{\kappa}}_{\ensuremath{\iota}}$ of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$. Our calculations also demonstrate that the thermal transport performance of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ could be evidently suppressed by nitrogen vacancy. As for the ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ sample with 0.02% randomly distributed N vacancy, the ${\ensuremath{\kappa}}_{L}$ could be decreased to approximately $175\ifmmode\pm\else\textpm\fi{}8.96\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, which provides a plausible explanation for the discrepancy between theoretical predictions and experimental measurements (approximately $173\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$). Interestingly, compared to the internal N vacancy, the surface N vacancy exhibits particularly pronounced effect in suppressing the ${\ensuremath{\kappa}}_{L}$ of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$. Such a phenomenon is primarily attributed to significant modifications of the symmetry of the charge density distribution and the geometric environment induced by the surface N vacancy, which weaken Si-N bond interactions and amplify the vibrational motion of Si atoms, thereby enhancing the phonon anharmonicity. This work offers valuable insights into the thermal transport properties of the ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ family and serves as a case study for exemplifying the use of machine-learning interatomic potentials to investigate the impact of low-concentration disordered vacancy defects on the thermal conductivity of materials.