This disclosure is related to the field of phononic crystals and, in particular, to the use of a phononic crystal with intentionally formed defects as a waveguide, such as may be used to connect two micro-electro mechanical systems (MEMS) resonators.
A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and liquids. In greater detail, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles and can be thought of as a quantized sound wave.
A phononic crystal is an artificial functional composite formed by periodic scatters embedded in a matrix, is designed to control, direct, and manipulate phonons, and is formed by periodic variation of acoustic properties of the material (e.g., elasticity, mass, etc.). A phononic crystal may have a band gap, which effectively prevents phonons of selected ranges of frequencies from being transmitted through the phononic crystal. The formation of such bandgaps is caused by the Bragg scattering phenomenon, meaning that the frequency range of the bandgap is directly proportional to the size of the unit cells of the phononic crystal.
By utilizing a phononic crystal with a band gap, a highly effective waveguide can be created. In particular, a phononic crystal with a band gap that encompasses the frequency of the phonons/waves to be transmitted through the phononic crystal is created so as to have a defect line extend therethrough. The geometric or material properties of the unit cells within the phononic crystal along the defect line are altered so that the frequency of the phonons/waves to be transmitted can in fact pass through those unit cells. Thus, a waveguide results since the phonons/waves to be transmitted propagate along the defect line but cannot propagate through other portions of the phononic crystal.
It is envisioned that the use of such phononic crystal-based waveguides can permit the creation of useful MEMS devices. Certain such devices are disclosed herein.
Disclosed herein is a micro-electro mechanical systems (MEMS) device, including: a phononic crystal body formed from unit cells and having at least one defect line extending through the phononic crystal body, wherein unit cells outside of the at least one defect line have a phononic bandgap, and wherein unit cells inside of the at least one defect line lack a same phononic bandgap as the unit cells outside of the at least one defect line; an input MEMS resonator mechanically coupled to the at least one defect line; and an output MEMS resonator mechanically coupled to the at least one defect line.
Each of the unit cells outside of the at least one defect line may have an identical geometry.
The input MEMS resonator and the output MEMS resonator may have an identical geometry.
The input MEMS resonator may have a natural frequency within the same phononic bandgap possessed by the unit cells outside of the at least one defect line.
The output MEMS resonator may have a natural frequency within the same phononic bandgap possessed by the unit cells outside of the at least one defect line.
The input MEMS resonator and the output MEMS resonator may have different geometries.
The output MEMS resonator may have a natural frequency within the same phononic bandgap possessed by the unit cells outside of the at least one defect line while the input MEMS resonator has a natural frequency outside of the same phononic bandgap possessed by the unit cells outside of the at least one defect line.
The input MEMS resonator and the output MEMS resonator may have different stiffnesses.
The input MEMS resonator and the output MEMS resonator may each exhibit a same natural frequency within the same phononic bandgap possessed by the unit cells outside of the at least one defect line when activated by a same wave type.
The wave type may be a flexural wave, a pressure wave, and/or a shear wave.
At least one suspension spring may be affixed to the phononic crystal body and shaped so as to suspend the phononic crystal body over an underlying substrate.
At least one pair of drive electrodes may be configured to cooperate with the input MEMS resonator to induce a desired mode of vibration in the phononic crystal body to thereby transmit phonons having a frequency within phononic bandgap possessed by the unit cells outside of the at least one defect line through the at least one defect line to the output MEMS resonator.
The desired mode of vibration may be an out-of-plane flexural mode, or may be an in-plane flexural mode.
At least one pair of sense electrodes may be configured to cooperate with the output MEMS resonator to thereby permit differential sensing of transmitted phonons.
The phononic crystal body may have a plurality of intersecting defect lines extending therethrough, and a plurality of additional input MEMS resonators may be mechanically coupled to the plurality of intersecting defect lines.
At least one additional output MEMS resonator may be mechanically coupled to at least one of the plurality of intersecting defect lines.
The input MEMS resonator may be mechanically coupled to a first end of the at least one defect line and the output MEMS resonator may be mechanically coupled to a second end of the at least one defect line.
Also disclosed herein is a method of transmitting phonons, including: actuating at least one pair of drive electrodes associated with an input micro-electro mechanical systems (MEMS) resonator that is mechanically coupled to a phononic crystal body to thereby induce a desired mode of vibration in the input MEMS resonator, resulting in generation of phonons having a frequency within a phononic bandgap possessed by unit cells of the phononic crystal body outside of a defect line formed therein; passing the phonons through the defect line; and detecting the passed phonons at an output MEMS resonator by detecting vibrations induced in the output MEMS resonator by the passed phonons.
The desired mode of vibration may be an out-of-plane flexural mode or an in-plane flexural mode.
The input MEMS resonator and the output MEMS resonator may each exhibit a same natural frequency within the phononic bandgap possessed by the unit cells outside of the defect line when actuated by a same wave type. The wave type may be at least one of a flexural wave, a pressure wave, and a shear wave.
The following disclosure enables a person skilled in the art to make and use the subject matter disclosed herein. The general principles described herein may be applied to embodiments and applications other than those detailed above without departing from the spirit and scope of this disclosure. This disclosure is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed or suggested herein.
Briefly stated, with initial reference to
As will be described below, the input resonator 110 and output resonator 150 may each have the same geometry, and are each of which may be (but may in some configurations not be) configured to exhibit a natural frequency (resonant frequency) within the bandgap of the phononic crystal waveguide 130 when activated by a same wave type (e.g., flexural wave, pressure wave, shear wave, etc.).
Construction of the phononic crystal waveguide 130 itself will first be described, and then specific embodiments and their operation will be described.
Referring now to
The irreducible Brillouin zone for the unit cell 131 is illustrated in
A first embodiment of a MEMS device 100a formed using the unit cell 131 described above is now described with reference to
At each corner of the phononic crystal waveguide 130 is a suspension spring 140, illustratively a straight spring, used to connect the phononic crystal waveguide 130 to an anchoring point 139, the spring suspending the phononic crystal waveguide 130 over a substrate 138. An enlarged overhead view of this arrangement may be observed in
Referring back to
Parallel plate drive electrodes D1, D2 and sense electrodes S1, S2 are affixed to the substrate underlying the phononic crystal waveguide 130 below the defect line 141. In particular, drive electrodes D1, D2 are arranged in a geometry such that they are staggered with respect to one another in a direction along the longitudinal axis of the phononic crystal waveguide 130 extending from the input resonator 110 toward a midpoint of the phononic crystal waveguide 130, and are spaced apart from one another in a direction along the axis of thickness of the phononic crystal waveguide 130 at a properly designed gap. Sense electrodes S1, S2 are likewise arranged in a geometry such that they are staggered with respect to one another along the longitudinal axis of the phononic crystal waveguide 130 extending from the output resonator 150 toward a midpoint of the phononic crystal waveguide 130, and spaced apart from one another along the axis of thickness of the phononic crystal waveguide 130 at a properly designed gap. A diagrammatical side view of the geometry of the drive electrodes D1, D2 and sense electrodes S1, S2 may be observed at the bottom of the graph of
This geometric arrangement of the drive electrodes D1, D2 is such that push-pull electrostatic actuation of the input resonator 110 is assisted by the drive electrodes D1, D2 when excited by a suitable drive signal during operation to cause out-of-plane flexural forces to be applied from the input resonator 110 to the phononic crystal waveguide 130. As illustrated in
A top view of the physical arrangement of the drive electrodes D1, D2 and sense electrodes S1, S2 may also be observed in
It should be appreciated that the input resonator 110 need not impart, or need not solely impart, out-of-plane flexural forces to the phononic crystal waveguide 130 to cause the generation and propagation of corresponding phonons or waves through the defect line 141. For example, in-plane flexural forces may instead be imparted, as shown in
A first set of parallel plate drive electrodes D1, D2 underlies the input resonator 110 on opposite sides of the longitudinal axis of the input resonator 110, are anchored to the substrate 138 by anchors 137, and are spaced apart from the input resonator 110 by a properly designed in-plane gap. Similarly, a first set of parallel plate sense electrodes S1, S2 underlies the output resonator 150 on opposite sides of the longitudinal axis of the output resonator 150, are anchored to the substrate 138 by anchors 137, and are spaced apart from the output resonator 150 by a properly designed in-plane gap. The thickness of the first set of parallel plate drive electrodes D1, D2 is the same as that of the input resonator 110, and the thickness of the first set of parallel plate sense electrodes S1, S2 is the same as that of the output resonator 150. A second set of parallel plate drive electrodes D1, D2 underlies the phononic crystal waveguide 130 on opposite sides of the defect line 141 along the longitudinal axis of the phononic crystal waveguide 130, from the input resonator 110 toward the midpoint of the phononic crystal waveguide 130, with drive electrodes D1, D2 being oriented perpendicularly to the longitudinal axis of the phononic crystal waveguide 130. These drive electrodes D1, D2 are spaced apart from the phononic crystal waveguide 130 by a properly designed in-plane gap and are anchored to the substrate 138 by anchors 137. The thickness of the second set of parallel plate drive electrodes D1, D2 is the same as that of the phononic crystal waveguide 130.
The specific geometry of the placement of these drive electrodes D1, D2 with respect to each other is shown in
A second set of parallel plate sense electrodes S1, S2 underlies the phononic crystal waveguide 130 on opposite sides of the defect line 141 along the longitudinal axis of the phononic crystal waveguide 130, from the output resonator 150 toward the midpoint of the phononic crystal waveguide 130, with sense electrodes S1, S2 being oriented perpendicularly to the longitudinal axis of the phononic crystal waveguide 130. These sense electrodes S1, S2 are spaced apart from the phononic crystal waveguide 130 by a properly designed in-plane gap and are anchored to the substrate 138 by anchors 137. The thickness of the second set of parallel plate sense electrodes S1, S2 is the same as that of the phononic crystal waveguide 130.
The specific geometry of the placement of these sense electrodes S1, S2 with respect to each other is shown in
This geometric arrangement of the drive electrodes D1, D2 is such that push-pull electrostatic actuation of the input resonator 110 is assisted by the drive electrodes D1, D2 when excited by a suitable drive signal during operation to cause in-plane flexural forces to be applied from the input resonator 110 to the phononic crystal waveguide 130. As illustrated in
As can be appreciated, the above embodiments may be combined, and the input resonator and output resonator may be sized and shaped so as to impart both in-plane and out-of-plane flexural forces to the phononic crystal waveguide 130, as shown in
In the instances shown above, the input resonator 110 and output resonator 150 have the same shape, but that need not be so. For example, as shown in
In the instances shown above, the phononic crystal waveguide 130 has a single defect line 141 defined therein, but instead, as shown in
The above described embodiments utilize drive and sense electrodes to contribute to the generation of phonons or waves to be transmitted through the waveguide and to the sensing of those transmitted phonons or waves at the output of the waveguide. However, drive and sense electrodes are not necessary along the phononic crystal waveguide, and all of the above embodiments are functional and commercially useful without the use of drive and sense electrodes in those specific positions, or without the use of drive electrodes in those specific positions but with the use of sense electrodes, or with the use of drive electrodes but without the use of sense electrodes in those specific positions. Sense and drive electrodes placed under and/or about the resonators are sufficient to start the propagation of waves or phonons through the phononic crystal waveguide. It should be appreciated that the imparting of movement to the input resonator may be effectuated other than electrostatically, and that all ways of imparting such movement are within the scope of this disclosure.
Finally, it is clear that modifications and variations may be made to what has been described and illustrated herein, without thereby departing from the scope of this disclosure, as defined in the annexed claims. For example, while the previously described unit cell 131 used to form the phononic waveguides 130 has been described as having specific dimensions and a specific shaped hole 133, other shapes may be used. For example, as shown in
While the disclosure has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be envisioned that do not depart from the scope of the disclosure as disclosed herein. Accordingly, the scope of the disclosure shall be limited only by the attached claims.