Drew F. Goettler

Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature

Large reductions in the thermal conductivity of thin silicon membranes have been demonstrated in various porous structures. However, the role of coherent boundary scattering in such structures has become a matter of some debate. Here we report on the first experimental observation of coherent phonon boundary scattering at room temperature in 2D phononic crystals formed by the introduction of air holes in a silicon matrix with minimum feature sizes >100 nm. To delaminate incoherent from coherent boundary scattering, phononic crystals with a fixed minimum feature size, differing only in unit cell geometry, were fabricated. A suspended island technique was used to measure the thermal conductivity. We introduce a hybrid thermal conductivity model that accounts for partially coherent and partially incoherent phonon boundary scattering. We observe excellent agreement between this model and experimental data, and the results suggest that significant room temperature coherent phonon boundary scattering occurs.

Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators

High-Q (quality factor) resonators are a versatile class of components for radio frequency micro-electromechanical systems . Phononic crystals provide a promising method of producing these resonators. In this article, we present a theoretical study of the Q factor of a cavity resonator in a two-dimensional phononic crystal comprised of tungsten rods in a silicon matrix. One can optimize the Q of a phononic crystal resonator by varying the number of inclusions or the cavity harmonic number. We conclude that using higher harmonics marginally increases Q while increasing crystal length via additional inclusions causes Q to increase by orders of magnitude. Incorporating loss into the model shows that the silicon material limit on Q is achievable using a two-dimensional phononic crystal design with a reasonable length. With five layers of inclusions on either side of the cavity, the material limit on Q is achieved, regardless of the harmonic number.

Effects of flexural and extensional excitation modes on the transmission spectrum of phononic crystals operating at gigahertz frequencies

Phononic crystals (PnCs) are a class of materials that are capable of manipulating elastodynamic waves. Much of the research on PnCs, both theoretical and experimental, focus on studying the transmission spectrum of PnCs in an effort to characterize and engineer their phononic band gaps. Although most studies have shown acceptable agreement between the theoretical and experimental bandgaps, perfect matches are elusive. A framework is presented wherein two and three dimensional harmonic finite element analyses are utilized to study their mechanical behavior for the purpose of more accurately predicting the spectral properties of PnCs. Discussions on a Harmonic Finite Elements Analysis formulation of a perfectly matched layer absorbing boundary and how reflections from absorbing boundaries can be inferred via standing wave ratios are provided. Comparisons between 2D and 3D analyses are presented that show the less computationally intensive 2D models are equally accurate under certain conditions. Finally, it...

Ultra high frequency (UHF) phononic crystal devices operating in mobile communication bands

Recently phononic crystal slabs operating in the very high frequency (VHF) range have been reported and have gained interest for RF signal processing. This paper reports phononic crystal slabs and devices operating in the commonly used GSM-850 and GSM-900 cellular phone bands, representing nearly an order of magnitude increase in operating frequency compared to the state-of-the-art. Phononic crystals centered at 943 MHz are formed by arranging 1.4 µm diameter W rods in a square lattice with a pitch of 2.5 µm inside a 1.85 µm thick suspended SiO2 membrane. The resulting phononic crystal has a bandgap width of 416 MHz or 44% and a maximum bandgap depth of 35 dB. Waveguide devices formed by placing defects in the phononic lattice have also been realized with propagation frequencies of 780 and 1060 MHz.

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.

Thermal conductivity manipulation in single crystal silicon via lithographycally defined phononic crystals

The thermal conductivity of single crystal silicon was engineered to be as low as 32.6W/mK using lithographically defined phononic crystals (PnCs), which is only one quarter of bulk silicon thermal conductivity [1]. Specifically sub-micron through-holes were periodically patterned in 500nm-thick silicon layers effectively enhancing both coherent and incoherent phonon scattering and resulting in as large as a 37% reduction in thermal conductivity beyond the contributions of the thin-film and volume reduction effects. The demonstrated method uses conventional lithography-based technologies that are directly applicable to diverse micro/nano-scale devices, leading to potential performance improvements where heat management is important.

Manipulation of thermal phonons: a phononic crystal route to High-ZT thermoelectrics

Phononic crystals (PnCs) are acoustic devices composed of a periodic arrangement of scattering centers embedded in a homogeneous background matrix with a lattice spacing on the order of the acoustic wavelength. When properly designed, a superposition of Bragg and Mie resonant scattering in the crystal results in the opening of a frequency gap over which there can be no propagation of elastic waves in the crystal, regardless of direction. In a fashion reminiscent of photonic lattices, PnC patterning results in a controllable redistribution of the phononic density of states. This property makes PnCs a particularly attractive platform for manipulating phonon propagation. In this communication, we discuss the profound physical implications this has on the creation of novel thermal phenomena, including the alteration of the heat capacity and thermal conductivity of materials, resulting in high-ZT materials and highly-efficient thermoelectric cooling and energy harvesting.

The effect of stiffness and mass on coupled oscillations in a phononic crystal

Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers. The stiffness of the tethers and the mass of the oscillator are varied and their influences on the bandgap formation are deduced. This analysis is reinforced by conducting numerical simulations to examine the modes bounding the bandgap and highlighting the effect of the above parameters. The analysis presented here not only sheds light on the origins of gap formation, but also allows one to define design rules for wide phononic gaps and maximum gap-to-midgap ratios.

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.

Micro and nano fabricated phononic crystals: technology and applications

With the application of microfabrication techniques, phononic crystals have been transformed over the past decade: from hand assembled millimeter-to-meter scale crystals consisting of metal balls in water or epoxy, to precisely machined crystals with sub-micron features operating at frequencies in excess of 1 GHz. This paper reviews the contributions of Sandia National Laboratories to micro and nano scale phononic crystal devices including: the integration of piezoelectric transducers, the choice of phononic crystal materials, phononic crystal design, and the application of phononic crystals to radio frequency and thermal management applications.