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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.
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Minimum thermal conductivity in the context of diffuson -mediated thermal transport
A model for the thermal conductivity of bulk solids is proposed in the limit of diffusive transport mediated by diffusons as opposed to phonons. This diffusive thermal conductivity, κ diff , is determined by the average energy of the vibrational density of states, ℏ ω avg , and the number density of atoms, n . Furthermore, κ diff is suggested as an appropriate estimate of the minimum thermal conductivity for complex materials, such that (at high temperatures): . A heuristic finding of this study is that the experimental ω avg is highly correlated with the Debye temperature, allowing κ diff to be estimated from the longitudinal and transverse speeds of sound: . Using this equation to estimate κ min gives values 37% lower than the widely-used Cahill result and 18% lower than the Clarke model for κ min , on average. This model of diffuson-mediated thermal conductivity may thus help explain experimental results of ultralow thermal conductivity.
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- PAR ID:
- 10079408
- Date Published:
- Journal Name:
- Energy & Environmental Science
- Volume:
- 11
- Issue:
- 3
- ISSN:
- 1754-5692
- Page Range / eLocation ID:
- 609 to 616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/c7ee03256k
