Theoretical upper limits of the thermal conductivity of Si3N4

Silicon nitride (Si3N4) is a promising substrate for high-power electronics due to its superior mechanical properties and potential outstanding thermal conductivity (κ). As experiments keep pushing the upper limit of κ of Si3N4, it is believed that it can reach 450 W/mK, similar to SiC, based on classical models and molecular dynamics simulations. In this work, we reveal from first principles that the theoretical κ upper limits of β-Si3N4 are only 169 and 57 W/mK along the c and a axes at room temperature, respectively. Those of α-Si3N4 are about 116 and 87 W/mK, respectively. The predicted temperature-dependent κ matches well with the highest available experimental data, which supports the accuracy of our calculations, and suggests that the κ upper limit of Si3N4 has already been reached in the experiment. Compared to other promising semiconductors (e.g., SiC, AlN, and GaN), Si3N4 has a much lower κ than expected even though the chemical bonding and mechanical strengths are close or even stronger. We find the underlying reason is that Si3N4 has much lower phonon lifetimes and mean free paths (<0.5 μm) due to the larger three-phonon scattering phase space and stronger anharmonicity. Interestingly, we find that the larger unit cell (with more basis atoms) that leads to a smaller fraction of acoustic phonons is not the reason for lower κ. Grain size-dependent κ indicates that the grain boundary scattering plays a negligible role in most experimental samples. This work clarifies the theoretical κ upper limits of Si3N4 and can guide experimental research.