Realization of a 33 GHz phononic crystal fabricated in a freestanding membrane

Phononic crystals (PnCs) are man-made structures with periodically varying material properties such as density, ρ, and elastic modulus, E. Periodic variations of the material properties with nanoscale characteristic dimensions yield PnCs that operate at frequencies above 10 GHz, allowing for the manipulation of thermal properties. In this article, a 2D simple cubic lattice PnC operating at 33 GHz is reported. The PnC is created by nanofabrication with a focused ion beam. A freestanding membrane of silicon is ion milled to create a simple cubic array of 32 nm diameter holes that are subsequently backfilled with tungsten to create inclusions at a spacing of 100 nm. Simulations are used to predict the operating frequency of the PnC. Additional modeling shows that milling a freestanding membrane has a unique characteristic; the exit via has a conical shape, or trumpet-like appearance

Phonon manipulation with phononic crystals.

In this work, we demonstrated engineered modification of propagation of thermal phonons, i.e. at THz frequencies, using phononic crystals. This work combined theoretical work at Sandia National Laboratories, the University of New Mexico, the University of Colorado Boulder, and Carnegie Mellon University; the MESA fabrication facilities at Sandia; and the microfabrication facilities at UNM to produce world-leading control of phonon propagation in silicon at frequencies up to 3 THz. These efforts culminated in a dramatic reduction in the thermal conductivity of silicon using phononic crystals by a factor of almost 30 as compared with the bulk value, and about 6 as compared with an unpatterned slab of the same thickness. This work represents a revolutionary advance in the engineering of thermoelectric materials for optimal, high-ZT performance. We have demonstrated the significant reduction of the thermal conductivity of silicon using phononic crystal structuring using MEMS-compatible fabrication techniques and in a planar platform that is amenable to integration with typical microelectronic systems. The measured reduction in thermal conductivity as compared to bulk silicon was about a factor of 20 in the cross-plane direction [26], and a factor of 6 in the in-plane direction. Since the electrical conductivity was only reduced by a corresponding factor of about 3 due to the removal of conductive material (i.e., porosity), and the Seebeck coefficient should remain constant as an intrinsic material property, this corresponds to an effective enhancement in ZT by a factor of 2. Given the number of papers in literature devoted to only a small, incremental change in ZT, the ability to boost the ZT of a material by a factor of 2 simply by reducing thermal conductivity is groundbreaking. The results in this work were obtained using silicon, a material that has benefitted from enormous interest in the microelectronics industry and that has a fairly large thermoelectric power factor. In addition, the techniques and scientific understanding developed in the research can be applied to a wide range of materials, with the caveat that the thermal conductivity of such a material be dominated by phonon, rather than electron, transport. In particular, this includes several thermoelectric materials with attractive properties at elevated temperatures (i.e., greater than room temperature), such as silicon germanium and silicon carbide. It is reasonable that phononic crystal patterning could be used for high-temperature thermoelectric devices using such materials, with applications in energy scavenging via waste-heat recovery and thermoelectric cooling for high-performance microelectronic circuits. The only part of the ZT picture missing in this work was the experimental measurement of the Seebeck coefficient of our phononic crystal devices. While a first-order approximation indicates that the Seebeck coefficient should not change significantly from that of bulk silicon, we were not able to actually verify this assumption within the timeframe of the project. Additionally, with regards to future high-temperature applications of this technology, we plan to measure the thermal conductivity reduction factor of our phononic crystals as elevated temperatures to confirm that it does not diminish, given that the nominal thermal conductivity of most semiconductors, including silicon, decreases with temperature above room temperature. We hope to have the opportunity to address these concerns and further advance the state-of-the-art of thermoelectric materials in future projects