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

Abstract

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.

Silver content dependent thermal conductivity and thermoelectric properties of electrodeposited antimony telluride thin films

“…In crystalline structures, Umklapp scattering dominates the phonon transport at the temperature range of interest, which shortens the phonon mean free path and leads to a reduction in the thermal conductivity with the temperature. The thermal conductivity of crystalline samples κ C is computed using the Callaway model 44 , which is expressed aswhere the average phonon relaxation time τ is computed combining phonon-grain boundary , film boundaries , phonon-impurity , Umklapp , phonon-carrier , and, in the case of Ag 3.9 Sb 33.6 Te 62.5 films, nanoprecipitate scattering mechanisms as 45–47 , where D is the average grain size , P is the phonon transmission across the grain boundary, t is the thickness of the film, n NP is the nanoprecipitate number density, and Θ is the average nanoprecipitate scattering cross-section, which is estimated using the average nanoinclusion size, and the mass and tensor strength difference with the matrix 17,48 . As detailed at the beginning of this section, the thickness of the film is measured using cross-sectional SEM imaging and the grain size is derived from the XRD spectra.…”

Recent Advances in Thermal Metamaterials and Their Future Applications for Electronics Packaging

“…In recent studies, silicon nanostructures with vertically etched holes, or holey silicon, had demonstrated significant thermalconductivity reductions and anisotropic thermal conductivity in the in-plane and cross-plane directions [56][57][58]. Ren and Lee had shown that the unique thermal-conductivity anisotropy in holey silicon is ideal for thermoelectric cooling (TEC) to address onchip hot spots [59,60]. In the in-plane direction, the neck size dominated phonon boundary scattering reduces the thermal conductivity (k x and k y ), which sustains a large temperature gradient for enhanced thermoelectric effects.…”

“…For 3D packages, thermal metamaterials based on bending or shifting designs could be used to guide the heat efficiently toward heat sinks and facilitate heat dissipation through HBM stacks. Thermal management of 3D stacks could be further addressed by optimal arrangements of TSVs and potential use of silicon-based thermoelectric cooling elements [34,36,37,39,59,61,132,136]. Several studies discussed the potential use of thermal metamaterials for circuit designs [15,19,20,152].…”

Thermally Anisotropic Composites for Improving the Energy Efficiency of Building Envelopes

“…Unlike isotropic materials, the thermal conductivity of anisotropic materials is different in different directions, enabling preferential heat transfer in one direction compared to another. Thermal anisotropy allows heat to dissipate in a preferential direction, and has been investigated for improved heat dissipation and hot spot remediation in electronics [10][11][12][13]. Suszko and El-Genk [11] numerically investigated thermally anisotropic composite heat spreaders comprised of two 0.5 mm thick copper (Cu) laments separated by a thin (0.25-1.0 mm) layer of graphite to achieve in-plane thermal conductivities of 200-325 W/(mK) and cross-plane conductivities of 5-20 W/(mK).…”

“…The composite spreaders were predicted to remove up to 429% higher heat than an all-Cu spreader [11]. Conversely, Ren and Lee [13] utilized the high cross-plane conductivity and low in-plane conductivity of holey silicon nanostructures to achieve improved thermoelectric cooling effectiveness compared to high-thermal conductivity bulk silicon.…”