Charles M. Reinke

Reduction in the thermal conductivity of single crystalline silicon by phononic crystal patterning.

Phononic crystals (PnCs) are the acoustic wave equivalent of photonic crystals, where a periodic array of scattering inclusions located in a homogeneous host material causes certain frequencies to be completely reflected by the structure. In conjunction with creating a phononic band gap, anomalous dispersion accompanied by a large reduction in phonon group velocities can lead to a massive reduction in silicon thermal conductivity. We measured the cross plane thermal conductivity of a series of single crystalline silicon PnCs using time domain thermoreflectance. The measured values are over an order of magnitude lower than those obtained for bulk Si (from 148 W m(-1) K(-1) to as low as 6.8 W m(-1) K(-1)). The measured thermal conductivity is much smaller than that predicted by only accounting for boundary scattering at the interfaces of the PnC lattice, indicating that coherent phononic effects are causing an additional reduction to the cross plane thermal conductivity.

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.

Phononic crystals operating in the gigahertz range with extremely wide band gaps

Phononic crystals have numerous potential applications including use as filters and oscillators in communications systems and as acoustic isolators for resonant sensors such as gyroscopes. These applications are based on the ability of phononic crystals to exhibit elastic band gaps, frequency bands where the propagation of acoustic waves is forbidden. Here, we focus on solid-solid phononic crystals (solid inclusions in a solid matrix), since they typically exhibit wider band gaps than those observed with air-solid phononic crystals (air inclusions in a solid matrix). We present a micromachined solid-solid phononic crystal operating at 1.4 GHz center frequency with an ultrawide 800 MHz band gap.

Nonlinear finite-difference time-domain method for the simulation of anisotropic, /spl chi//sup (2)/, and /spl chi//sup (3)/ optical effects

A two-dimensional (2-D) finite-difference time-domain (FDTD) code for the study of nonlinear optical phenomena, in which both the slowly varying and the rapidly varying components of the electromagnetic fields are considered, has been developed. The algorithm solves vectorial Maxwells equations for all field components and uses the nonlinear constitutive relation in matrix form as the equations required to describe the nonlinear system. The stability of the code is discussed and its effectiveness is demonstrated through the simulations of self-phase modulation (SPM) and second-harmonic generation (SHG). The authors also show that the combination of nonlinear effects with PCs can result in a significant improvement in device size and integrability, using the example of a Mach-Zehnder interferometer (MZI).

Realization of optimal bandgaps in solid-solid, solid-air, and hybrid solid-air-solid phononic crystal slabs

We investigate the optimal conditions for bandgap formation in square-lattice phononic crystal (PnC) slabs composed of a solid matrix with solid or air inclusions. To ensure sufficient impedance mismatch (key for bandgap formation) and fabrication amenability, silicon and silica were chosen as candidate matrix materials with either air or tungsten inclusions. Solid-solid PnCs were found to exhibit larger bandgaps while relaxing the topological constraints as compared to solid-air PnCs for all but the largest filling fractions. We also demonstrate a hybridized lattice incorporating both air and solid inclusions in the matrix that further relaxes the constraints for realizing wide bandgaps.

Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique

Recent work has demonstrated that nanostructuring of a semiconductor material to form a phononic crystal (PnC) can significantly reduce its thermal conductivity. In this paper, we present a classical method that combines atomic-level information with the application of Bloch theory at the continuum level for the prediction of the thermal conductivity of finite-thickness PnCs with unit cells sized in the micron scale. Lattice dynamics calculations are done at the bulk material level, and the plane-wave expansion method is implemented at the macrosale PnC unit cell level. The combination of the lattice dynamics-based and continuum mechanics-based dispersion information is then used in the Callaway-Holland model to calculate the thermal transport properties of the PnC. We demonstrate that this hybrid approach provides both accurate and efficient predictions of the thermal conductivity.

A new method for the calculation of the dispersion of nonperiodic photonic crystal waveguides

We present a new method for the calculation of the dispersion diagrams of general nonuniform waveguides. The method is based on the spatial Fourier transform (SFT) of the electromagnetic field distribution along the guiding direction. We demonstrate the validity and robustness of the SFT technique using several test cases. As an application, we apply the method to analyze the dispersion of biperiodic photonic crystal waveguides and show that the guiding bandwidths of these waveguides can be significantly enhanced by a proper choice of the two distinctive spatial periods of the biperiodic waveguides.

Silicon carbide phononic crystal cavities for micromechanical resonators

This paper demonstrates silicon carbide phononic crystal cavities for RF and microwave micromechanical resonators. We demonstrate design, fabrication, and characterization of Silicon Carbide/air phononic crystals used as Bragg acoustic mirrors to confine energy in a lateral SiC cavity. Aluminum nitride transducers drive and sense SiC overtone cavities in the 2–3GHz range with ƒxQ products exceeding 3×1013 in air. This approach enables decoupling of the piezoelectric AlN material from the SiC cavity, resulting in high Q resonators at microwave frequencies. The SiC cavities are fabricated in a CMOS-compatible process, enabling integration with wirelesss communication systems.

Effects of release holes on microscale solid-solid phononic crystals

Solid–solid phononic crystals exhibit wider band gaps than those observed with air–solid phononic crystals. For micromachined phononic crystal devices it is advantageous to release the phononic crystal to avoid propagation losses. In a solid–solid phononic crystal operating in the low megahertz range, due to the large lattice constant, it is necessary to place release holes in the center of the inclusions to release devices from the substrate while minimizing the effect the release hole has on the band gap. In this report, we investigate the effect of release holes on phononic band gaps and highlight the need for careful design. It was determined that release holes of radius rair holes/rinclusion=0.26 can reliably release a phononic crystal membrane composed of W inclusions in SiO2 without significantly compromising the phononic band gap.

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.