Extended Data Fig. 1: Theoretical thermal properties based on Bruggeman model calculations.

a, k of PDMS composites with varying AlN particle fillings. b, R_eff of PDMS composites in relation to BLT within a sandwiched interface structure. Only when the BLT is 1–2 micrometres, very adjacent to the particle diameter, does R_eff of PDMS composites filled with highly thermally conductive inorganics fall within the narrow range of 0.1–1 mm² K/W. Achieving such a property at a high particle content poses a significant challenge using current material engineering strategies. c, k of modified LMs with varying filling of AlN particles. The particle diameter used for this illustration is 30 μm. A significant increase in the k of AlN-modified LMs is observed only when the interfacial thermal resistance between AlN and LM reaches values on the order of magnitude of 10⁻⁹ m² K/W. This places stringent demands on manipulating the metal–dielectric heterointerface within the two-phase mixtures. R_eff of modified LMs in a sandwiched interface structure as a function of BLT with different AlN particle sizes: (d) 1 µm; (e) 5 µm; (f) 30 µm; (g) 80 µm. AlN particles with diameters ranging from 1 to 30 µm are likely to enable LMs to achieve an effective R_eff on the order of magnitude of 0.1 mm² K/W. This achievement requires particular regulation of the LM–AlN heterointerface and exceptional thixotropy and adaptability to rough surfaces (low BLT and R_c).