Enhanced Reduction of Thermal Conductivity in Amorphous Silicon Nitride-Containing Phononic Crystals Fabricated Using Directed Self-Assembly of Block Copolymers.

Studies have demonstrated that the thermal conductivity (κ) of crystalline semiconductor materials can be reduced by phonon scattering in periodic nanostructures formed using templates fabricated from self-assembled block copolymers (BCPs). Compared to crystalline materials, the heat transport mechanisms in amorphous inorganic materials differ significantly and have been explored far less extensively. However, thermal management of amorphous inorganic solids is crucial for a broad range of semiconductor devices. Here we present the fabrication of freestanding amorphous silicon nitride (SiNx) membranes for studying κ in an amorphous solid. To form a periodic nanostructure, directed self-assembly of cylinder-forming BCPs is used to pattern in the SiNx highly ordered, hexagonally close packed nanopores with pitch and neck width down to 37.5 and 12 nm, respectively. The κ of the nanoporous SiNx membranes is 60% smaller than the classically predicted value based on just the membrane porosity. In comparison, holes with much larger neck widths and pitches patterned by e-beam lithography lead to only a slight reduction in κ, which is closer to the classical porosity-based prediction. These results demonstrate that κ of amorphous SiNx can be reduced by introducing periodic nanostructures that behave as a phononic crystal, where the relationship between the smallest dimension of the nanostructure and the length scale of the mean-free paths of the dominant, heat-carrying phonons is critical. Additionally, changing the orientation of the hexagonal array of nanopores relative to the primary direction of heat flow has a smaller impact on amorphous SiNx than was previously observed in silicon.