Thermal conductivity anisotropy in holey silicon nanostructures and its impact on thermoelectric cooling

Artificial nanostructures have improved prospects of thermoelectric systems by enabling selective scattering of phonons and demonstrating significant thermal conductivity reductions. While the low thermal conductivity provides necessary temperature gradients for thermoelectric conversion, the heat generation is detrimental to electronic systems where high thermal conductivity are preferred. The contrasting needs of thermal conductivity are evident in thermoelectric cooling systems, which call for a fundamental breakthrough. Here we show a silicon nanostructure with vertically etched holes, or holey silicon, uniquely combines the low thermal conductivity in the in-plane direction and the high thermal conductivity in the cross-plane direction, and that the anisotropy is ideal for lateral thermoelectric cooling. The low in-plane thermal conductivity due to substantial phonon boundary scattering in small necks sustains large temperature gradients for lateral Peltier junctions. The high cross-plane thermal conductivity due to persistent long-wavelength phonons effectively dissipates heat from a hot spot to the on-chip cooling system. Our scaling analysis based on spectral phonon properties captures the anisotropic size effects in holey silicon and predicts the thermal conductivity anisotropy ratio up to 20. Our numerical simulations demonstrate the thermoelectric cooling effectiveness of holey silicon is at least 30% greater than that of high-thermal-conductivity bulk silicon and 400% greater than that of low-thermal-conductivity chalcogenides; these results contrast with the conventional perception preferring either high or low thermal conductivity materials. The thermal conductivity anisotropy is even more favorable in laterally confined systems and will provide effective thermal management solutions for advanced electronics.