Effect of Release Holes on Micro-scale Solid-solid Phononic Crystals

Solid-solid phononic crystals (solid inclusions in a solid matrix) exhibit wider bandgaps than those observed with airsolid phononic crystals (air inclusions in a solid matrix). In a solid-solid phononic crystal operating in the low MHz range, it is essential to place release holes in the center of the inclusions to release devices from the substrate. It is necessary to release, and therefore suspend the phononic crystal to avoid propagation losses through the substrate. In this report we investigate the effect of release holes on phononic bandgaps and highlight the need for careful design to avoid compromising the phononic bandgap. Studying release issues for solid-solid phononic crystals is essential for the successful fabrication of such devices. INTRODUCTION Phononic crystals (PnCs) are composite structures where inclusions (cylindrical or otherwise) are periodically placed in a host medium (matrix). The periodicity of the structure causes Bragg and Mie scattering, resulting in a frequency range over which propagation of elastic waves is forbidden, known as a phononic bandgap (PnBG). PnCs have potential use in many applications, including communications where the suppression of noise and having a high signal-to-noise (SNR) ratio are essential to the operation of any filter. With rejection of up to 30dB over a large range of frequencies exhibited by a properly-designed PnC [1], the bandgap frequency range can be manipulated to allow only desired signals to transmit in a controlled filtering process [2-5]. Such a feature can be explored further to perform multiplexing and other functions, leading to the possibility of acoustic-logic-based devices. Furthermore, PnCs have also been used in liquid sensing [6] where peak shifts in the transmission of waves within the liquid in a cavity can be correlated with the acoustic properties of the material, leading to the identification the liquid. Other devices based on phononic crystals such as waveguides [7-10], structures for acoustic collimation [11], focusing [12] and negative refraction [13-14], have also been demonstrated. PnCs based on solid inclusions in a solid matrix (called herein solid-solid PnCs) exhibit wider bandgaps [1,15] as compared to air-solid (air inclusions in a solid matrix) PnCs [16]. In a solid-solid PnC operating in the low MHz range, it is necessary to place release holes in the phononic crystal membrane to release devices from the substrate. The release holes are placed in the center of the inclusion so that the effect of the hole on the propagating wave is minimized, as the solid inclusion partially masks the release hole. It is necessary to release, and therefore suspend, the PnC to avoid propagation losses through the substrate. Releasing solid-solid PnCs is more difficult than air-solid PnCs because in the solid-solid case the inclusion is filled with the solid material preventing the undercutting etchant from reaching the sacrificial layer. Because a large hole radius is needed to create a wide bandgap in air-solid PnCs [15], releasing air-solid PnCs is much easier than releasing solid-solid PnCs since the etchant can travel through the void inclusions. Release holes in solid-solid PnCs have the same function of allowing the etchant to reach the sacrificial layer and suspend the PnC membrane. However, placing release holes in the center of the solid inclusions in a solid-solid PnC can interfere with a propagating wave, which partially penetrates through the inclusion and is scattered again at the inclusion-air interface, causing a disruption to the observed bandgap as compared with a PnC having no release holes. In this report we theoretically study the effects of introducing release holes on the propagation of elastic waves