MEMS device using topologically protected localized interface states

Abstract

Provided herein are localized interface-state MEMS devices including a suspended elastic waveguide having a first periodic structure including corrugated elements and a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave; a second periodic structure including corrugated elements and a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and first and second antisymmetric lamb waves counter-propagate, and a topological interface between the first periodic structure and the second periodic structure configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric lamb waves and first and second antisymmetric lamb waves at the topological interface, wherein the destructive interference creates a third localized state.

Description

[0001] TITLE:

[0002] MEMS DEVICE USING TOPOLOGICALLY PROTECTED LOCALIZED INTERFACE STATES

[0003] CROSS REFERENCE TO RELATED APPLICATIONS

[0004] This application claims the priority of U.S. Provisional Application No. 63 / 654,888 filed 31 May 2024 and titled “MEMS Resonator Using Topologically Protected Fano Resonance,” the entirety of which is hereby incorporated by reference.

[0005] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0006] This invention was made with government support under Grant No. ECCS-2034948 awarded by the National Science Foundation. The government has certain rights in the invention.

[0007] BACKGROUND

[0008] A variety of scientific fields, including proteomics and spintronics, have created a new demand for on-chip devices capable of sensing parameters localized within a few tens of micrometers. Nano and microelectromechanical systems (NEMS / MEMS) are extensively employed for monitoring parameters that exert uniform forces over hundreds of micrometers or more, such as acceleration, pressure, and magnetic fields. However, they can show significantly degraded sensing performance when targeting more localized parameters, like the mass of a single cell.

[0009] Emerging needs in proteomics have created a necessity to sense parameters localized within a few tens of micrometers or less. This is crucial for studying biological processes at a single-cell scale [1-7], identifying protein biomarkers associated with specific diseases [8-12] achieving atomic-scale resolutions in mass spectrometry [13-19], and more; similar needs have emerged even in other fields of study

[0020] , For instance, being able to sense spin waves transduced in strongly localized regions

[0021] can lead to higher bit densities and improved energy efficiency in high-frequency spintronic memory devices. Similarly, highly localized acoustic modes of vibration in piezoelectric films can provide a path toward robust Quantum State Transfer (QST) between remote superconducting qubits

[0022] and their successful readout. Over the past fifteen years, nano and microelectromechanical systems (NEMS / MEMS) have been extensively utilized for sensing parameters (magnetic field [23- 25], acceleration [26-29], pressure [30-36], etc.) that exert nearly uniform forces across hundreds of micrometers along their frequency-setting dimension. However, these devices are significantly limited in their ability to monitor parameters localized within a few tens of micrometers or less (i.e., in their ability to achieve a high “spatial sensing resolution"). In fact, to enable high responsivity in such scenarios, the size of current NEMS / MEMS must be shrunk to confine their mode of vibration within an area matching closely the one where the targeted parameter exerts its force. However, shrinking the size of the current MEMS / NEMS, particularly along their frequency-setting dimension, results in a notable reduction of their quality factor (Q) and dynamic range

[0014] , which inevitably impacts the achievable sensing performance

[0037] ,

[0010] Several physical phenomena have been exploited to enhance the spatial sensing resolution of NEMS / MEMS while preserving a high-quality factor. These include internal resonance [38-40], phase-synchronization [41-43], phonon-cavity [44-47], and mode localization [48-50], Most of these phenomena originate from the nonlinear interaction between multiple mechanical modes. As a result, they necessitate precise control of these modes’ driving conditions. Harnessing these phenomena also requires the use of amplitude read-out schemes, which are inherently more susceptible to accuracy degradations caused by electrical noise than the frequency read-out schemes typically used for linear NEMS / MEMS

[0051] .

[0011] Piezoelectric microelectromechanical bulk acoustic wave (B AW) sensors are widely used across a range of applications, from inertial to chemical sensing. These devices typically rely on the resonance frequency of a Lamb mode as the readout parameter, making them well suited for detecting parameters of interest (Pols) that act over the entire vibrating structure. However, this approach is less effective for monitoring localized Pols. To address this limitation, prior efforts have focused on miniaturizing BAW sensors. While miniaturization enhances responsivity to localized Pols, it often comes at the cost of a degraded limit of detection.

[0012] In recent years, the demand for chip-scale sensing technologies capable of monitoring parameters localized within tens of micrometers or less has grown across several scientific fields. In proteomics, for instance, this need has emerged from the ability to detect certain cancer cells at an early stage by monitoring their mass, as well as from the necessity to understand how these cells evolve over time by tracking dynamic changes in their protein expression. Similarly, the rise of spintronics has created opportunities to enhance the bit density and power efficiency of memory devices by replacing highly dissipative charge currents with localized, high-frequency magnons. This has driven a demand for on-chip sensing technologies capable of accurately reading the spin of such magnons. Additionally, the development of chip-scale, uncooled infrared (IR) cameras with smaller pixel dimensions has been a constant goal in the last twenty years to enhance security, surveillance, biological imaging, chemical sensing, and environmental monitoring.

[0013] Microelectromechanical systems (MEMS) have steadily gained popularity over the past few decades, playing key roles in commercial radiofrequency front-ends, as well as in numerous available systems for sensing and timing applications. Among the available MEMS based sensors, piezoelectric bulk-acoustic-wave (BAW) sensors are currently the preferred choice when targeting sensing applications simultaneously demanding high performance, compact form factors, and good resilience to shock and vibration. These devices typically exploit the detuning (A) exerted by their targeted sensing parameter on the resonance frequency of a piezoelectrically actuated mode of vibration (typically a Lamb mode) as the read-out parameter. However, since the mechanical energy transduced by the current BAW sensors is distributed across nearly their entire suspended volume, these sensors quickly become ineffective when tasked with detecting highly localized parameters of interest. In fact, in this scenario, any perturbation that the sensing parameter exerts on the typical BAW sensors’ elastic or mass properties only affects a very small portion of the area where the mechanical energy is stored (e.g., as shown in Fig. 11 A), effectively leading to only marginal A values. Furthermore, attempts to shrink the active region of BAW sensors along their frequency-setting dimension often lead to a degradation in the quality factor (Q) of these devices, along with stronger nonlinearities. Stronger nonlinearities effectively reduce the maximum electrical power (Pmax) that BAW sensors can tolerate before bifurcations in the electromechanical response occur, imposing a significant constraint on the achievable limit of detection (LoD), which is the minimum strength of the parameter of interest that can be reliably measured. That is, a trade-off exists for current BAW sensors prevents the achievement of higher responsivity to localized parameters without degrading the limit of detection.

[0014] SUMMARY OF THE INVENTION

[0015] The methods and techniques described herein present localized interface-state MEMS devices that leverage the destructive interference of two topological radiofrequency (RF) counter-propagating wave modes along a Su-Schrieffer-Heeger (SSH) interface of a suspended elastic waveguide, such as, for example, a topologically modified piezoelectric Aluminum Scandium Nitride (AlScN) bilayer. In addition to sensing applications, the localized interface-state MEMS devices described herein present opportunities for further applications, including achieving more stable frequency sources for communication and timing applications.

[0016] Also presented herein is a new class of BAW sensors, referred to as topologically enhanced BAW (tBAW) sensors. As described herein, tBAW sensors incorporate localized interface-state MEMS devices to exploit topological elastic properties in order to activate localized modes of vibration never previously used by BAW sensors. These modes, known as interface states (ISs), emerge at the interface between one dimensional (ID) periodic structures with identical elastic dispersion but distinct topological phases (i.e., different Zak phases). ISs are stationary (i.e., non-propagating) modes.

[0017] This makes them suitable for sensing, which can be implemented by monitoring the detuning of their resonance frequency induced by the targeted parameter of interest, as is commonly done in current BAW sensors. Such tBAW sensors can be particularly useful in connection with localized Pols, wherein the tBAW sensors represent the first instance of a BAW sensor capable of overcoming the intrinsic trade-off between responsivity (R) and limit of detection (LoD) by leveraging topological interface states (IS).

[0018] The effectiveness of this approach was tested by sensing infrared (IR) power emitted by a laser with a 5 pm x 5 pm beam size, focused on the interface where the IS is transduced. Experimental results show that harnessing ISs yields significantly higher responsivity to IR power and an improved limit of detection compared to conventional Lamb modes. These findings pave the way for the deployment of BAW sensors in emerging applications requiring to monitor localized parameters, such as in proteomics and spintronics.

[0019] In one aspect, a localized interface-state MEMS device is provided. The localized interface-state MEMS device includes a suspended elastic waveguide. The suspended elastic waveguide includes a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate. The suspended elastic waveguide also includes a piezoelectric material layer disposed on top of the bottom electrode layer. The suspended elastic waveguide also includes first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer. The suspended elastic waveguide also includes a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements. The localized interface-state MEMS device also includes a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave. The localized interface-state MEMS device also includes a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-prop agate. The localized interface-state MEMS device also includes a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface, wherein the destructive interference creates a third localized state.

[0020] In some embodiments, the first periodic structure includes one or more first unit cells having a width a and two corrugated elements separated along a frequency-setting direction of the suspended elastic waveguide by a distance A, the two corrugated elements positioned between two upper electrodes. In some embodiments, the second periodic structure includes one or more second unit cells having a width a and two corrugated elements separated along the frequency-setting direction of the suspended elastic waveguide by a distance a — A, the two corrugated elements having an upper electrode positioned therebetween. In some embodiments, the first periodic structure includes an interface first unit cell encompassing a first upper electrode and half of a second upper electrode along the frequency-setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode. In some embodiments, the second periodic structure includes an interface second unit cell adjacent and connected to the interface first unit cell, opposite along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface. In some embodiments, the first periodic structure includes one or more non-interface first unit cells, each adjacent and connected to at least one of the interface first unit cell and / or non-interface first unit cells and encompassing half of an upper electrode shared with the at least one adjacent interface first unit cell and / or non-interface first unit cells along the frequency-setting dimension of the suspended elastic waveguide. In some embodiments, the second periodic structure includes one or more noninterface second unit cells adjacent and connected to the interface second unit cell and / or non-interface second unit cells along the frequency-setting dimension of the suspended elastic waveguide.

[0021] In some embodiments, the topological interface is an elastic Su-Schrieffer-Heeger (SSH) interface. In some embodiments, the first and second localized states have distinct Zak phases. In some embodiments, the first and second localized states have different wavenumbers. In some embodiments, the third localized state exhibits a quality factor greater than or equal to 10,000. In some embodiments, the topological interface includes an interface first unit cell of the first periodic structure encompassing a first upper electrode and half of a second upper electrode along the frequency-setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode. In some embodiments, the topological interface includes an interface second unit cell of the second periodic structure adjacent and connected to the interface first unit cell along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface. In some embodiments, the first periodic structure further comprises a plurality of adjacent non-interface first unit cells extending away from the interface first unit cell along the frequency-setting direction of the suspended elastic waveguide. In some embodiments, the second periodic structure further comprises a plurality of adjacent noninterface second unit cells extending away from the interface second unit cell along the frequency-setting direction of the suspended elastic waveguide. In some embodiments, an active region of the MEMS device in the third localized state is confined by the first and second periodic structures to the topological interface, a portion of the non-interface first unit cells most proximate to the topological interface, and a portion of the non-interface second unit cells most proximate to the topological interface along the frequency-setting direction of the suspended elastic waveguide. In some embodiments, the active region has a width along the frequency-setting direction of the suspended elastic waveguide between about 16pm and about 58 pm. In some embodiments, an upper electrode of the first periodic structure forming a first electrical port and an upper electrode of the second periodic structure forming a second electrical port for excitation of one or more of the first, second, and third localized states. In some embodiments, one or more additional upper electrodes of the first and second periodic structures are grounded. In some embodiments, the localized interface-state MEMS device is sensitive to a parameter of interest. In some embodiments, two of the upper electrodes of the first and second periodic structures are configured to transduce and read an electrical transmission of the localized interface-state MEMS device and wherein all other upper electrodes of the first and second periodic structures are not grounded. In some embodiments, the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof. In some embodiments, the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof. In some embodiments, the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest. In some embodiments, the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof. In some embodiments, the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof. In some embodiments, the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal.

[0022] In some embodiments, the localized interface-state MEMS device is a Bulk Acoustic Wave (BAW) sensor. In some embodiments, the piezoelectric material layer comprises aluminum scandium nitride (AlScN), lithium niobate (LiNbCE or LN), aluminum chromium nitride (AlCrN), lead zirconate titanate (PZT), lithium tantalate (LiTaCE), gallium nitride (GaN), aluminum nitride (AIN), or combinations thereof. In some embodiments, the corrugated elements comprise an insulating layer, a metallic layer, or combinations thereof. In some embodiments, a temperature coefficient of Young’s Modulus of the corrugated elements and a temperature coefficient of Young’s Modulus of the piezoelectric material layer are either both positive or both negative. In some embodiments, the upper electrodes and the bottom electrode layer each comprise one or more of platinum, aluminum, tungsten chromium, copper, gold, silver, titanium, or combinations thereof. In some embodiments, the substrate comprises silicon, sapphire, silicon carbide, or combinations thereof. In some embodiments, the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least one anchor connecting the first end to the substrate and at least one anchor connecting the second end to the substrate. In some embodiments, the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least two anchors connecting the first end to the substrate and at least two anchors connecting the second end to the substrate.

[0023] In another aspect, a method of producing localized topological states in a MEMS device is provided. The method includes providing a localized interface-state MEMS device. The localized interface-state MEMS device includes a suspended elastic waveguide. The suspended elastic waveguide includes a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate. The suspended elastic waveguide also includes a piezoelectric material layer disposed on top of the bottom electrode layer. The suspended elastic waveguide also includes first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer. The suspended elastic waveguide also includes a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements. The localized interface-state MEMS device also includes a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave. The localized interface-state MEMS device also includes a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-prop agate. The localized interface-state MEMS device also includes a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface. The method also includes causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface. The method also includes creating, by the destructive interference at the topological interface, a third localized state.

[0024] In some embodiments, the method also includes confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency-setting direction of the suspended elastic waveguide. In some embodiments, the topological interface is an elastic Su-Schrieffer-Heeger (SSH) interface. In some embodiments, the first and second localized states have distinct Zak phases. In some embodiments, the first and second localized states have different wavenumbers.

[0025] In an additional aspect, a method of detecting a presence, absence, or change of a parameter of interest is provided. The method includes providing a localized interface-state MEMS device. The localized interface-state MEMS device includes a suspended elastic waveguide. The suspended elastic waveguide includes a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate. The suspended elastic waveguide also includes a piezoelectric material layer disposed on top of the bottom electrode layer. The suspended elastic waveguide also includes first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer. The suspended elastic waveguide also includes a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements. The localized interface-state MEMS device also includes a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave. The localized interface-state MEMS device also includes a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate. The localized interface-state MEMS device also includes a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface. The method also includes exposing the localized interface-state MEMS device to the parameter of interest. The method also includes exciting, by the exposure of the localized interface-state MEMS device to the parameter of interest, the localized interface-state MEMS device to produce the counter-propagating first and second symmetric and first and second antisymmetric lamb waves. The method also includes causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface. The method also includes creating, by the destructive interference at the topological interface, a third localized state.

[0026] In some embodiments, the method also includes confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency-setting direction of the suspended elastic waveguide. In some embodiments, the step of exposing the localized interface-state MEMS device to the parameter of interest further comprises exposing at least a portion of the active region to the parameter of interest. In some embodiments, the method also includes transducing and reading, via two upper electrodes of the first and second periodic structures an electrical transmission of the localized interfacestate MEMS device. In some embodiments, other upper electrodes of the first and second periodic structures are not grounded. In some embodiments, the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof. In some embodiments, the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof. In some embodiments, the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest. In some embodiments, the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof. In some embodiments, the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof. In some embodiments, the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal.

[0027] Additional features and aspects of the technology include the following:

[0028] 1. A localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, a piezoelectric material layer disposed on top of the bottom electrode layer, first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, and a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements; a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave; a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate; and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface, wherein the destructive interference creates a third localized state.

[0029] 2. The localized interface-state MEMS device of feature 1, wherein: the first periodic structure includes one or more first unit cells having a width a and two corrugated elements separated along a frequency-setting direction of the suspended elastic waveguide by a distance A, the two corrugated elements positioned between two upper electrodes; and the second periodic structure includes one or more second unit cells having a width a and two corrugated elements separated along the frequency-setting direction of the suspended elastic waveguide by a distance a — A, the two corrugated elements having an upper electrode positioned therebetween.

[0030] 3. The localized interface-state MEMS device of feature 2, wherein the first periodic structure includes an interface first unit cell encompassing a first upper electrode and half of a second upper electrode along the frequency-setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode.

[0031] 4. The localized interface-state MEMS device of feature 3, wherein the second periodic structure includes an interface second unit cell adjacent and connected to the interface first unit cell, opposite along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface.

[0032] 5. The localized interface-state MEMS device of feature 4, wherein the first periodic structure includes one or more non-interface first unit cells, each adjacent and connected to at least one of the interface first unit cell and / or non-interface first unit cells and encompassing half of an upper electrode shared with the at least one adjacent interface first unit cell and / or non-interface first unit cells along the frequency-setting dimension of the suspended elastic waveguide.

[0033] 6. The localized interface-state MEMS device of any of features 4-5, wherein the second periodic structure includes one or more non-interface second unit cells adjacent and connected to the interface second unit cell and / or non-interface second unit cells along the frequencysetting dimension of the suspended elastic waveguide.

[0034] 7. The localized interface-state MEMS device of any of features 1-6, wherein the topological interface is an elastic Su-Schrieffer-Heeger (SSH) interface.

[0035] 8. The localized interface-state MEMS device of any of features 1-7, wherein the first and second localized states have distinct Zak phases.

[0036] 9. The localized interface-state MEMS device of any of features 1-8, wherein the first and second localized states have different wavenumbers.

[0037] 10. The localized interface-state MEMS device of any of features 1-9, wherein the third localized state exhibits a quality factor greater than or equal to 10,000.

[0038] 11. The localized interface-state MEMS device of any of features 1-10, wherein the topological interface comprises: an interface first unit cell of the first periodic structure encompassing a first upper electrode and half of a second upper electrode along the frequency -setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode; and an interface second unit cell of the second periodic structure adjacent and connected to the interface first unit cell along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface.

[0039] 12. The localized interface-state MEMS device of feature 11, wherein: the first periodic structure further comprises a plurality of adjacent non-interface first unit cells extending away from the interface first unit cell along the frequency-setting direction of the suspended elastic waveguide; and the second periodic structure further comprises a plurality of adjacent non-interface second unit cells extending away from the interface second unit cell along the frequency-setting direction of the suspended elastic waveguide.

[0040] 13. The localized interface-state MEMS device of feature 12, wherein an active region of the MEMS device in the third localized state is confined by the first and second periodic structures to the topological interface, a portion of the non-interface first unit cells most proximate to the topological interface, and a portion of the non-interface second unit cells most proximate to the topological interface along the frequency -setting direction of the suspended elastic waveguide.

[0041] 14. The localized interface-state MEMS device of feature 13, wherein the active region has a width along the frequency-setting direction of the suspended elastic waveguide between about 16pm and about 58pm.

[0042] 15. The localized interface-state MEMS device of any of features 13-14, wherein an upper electrode of the first periodic structure forming a first electrical port and an upper electrode of the second periodic structure forming a second electrical port for excitation of one or more of the first, second, and third localized states.

[0043] 16. The localized interface-state MEMS device of feature 15, wherein one or more additional upper electrodes of the first and second periodic structures are grounded.

[0044] 17. The localized interface-state MEMS device of any of features 13-16, wherein the localized interface-state MEMS device is sensitive to a parameter of interest.

[0045] 18. The localized interface-state MEMS device of feature 17, wherein two of the upper electrodes of the first and second periodic structures are configured to transduce and read an electrical transmission of the localized interface-state MEMS device and wherein all other upper electrodes of the first and second periodic structures are not grounded.

[0046] 19. The localized interface-state MEMS device of any of features 17-18, wherein the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof.

[0047] 20. The localized interface-state MEMS device of feature 19, wherein the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof.

[0048] 21. The localized interface-state MEMS device of any of features 19-20, wherein the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest. 22. The sensing circuit of feature 21, wherein the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof.

[0049] 23. The sensing circuit of feature 21 , wherein the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof.

[0050] 24. The localized interface-state MEMS device of any of features 19-20, wherein the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal.

[0051] 25. The localized interface-state MEMS device of any of features 17-24, wherein the localized interface-state MEMS device is a Bulk Acoustic Wave (BAW) sensor.

[0052] 26. The localized interface-state MEMS device of any of features 1-25, wherein the piezoelectric material layer comprises aluminum scandium nitride (AlScN), lithium niobate (LiNbCE or LN), aluminum chromium nitride (AlCrN), lead zirconate titanate (PZT), lithium tantalate (LiTaCE), gallium nitride (GaN), aluminum nitride (AIN), or combinations thereof.

[0053] 27. The localized interface-state MEMS device of any of features 1-26, wherein the corrugated elements comprise an insulating layer, a metallic layer, or combinations thereof.

[0054] 28. The localized interface-state MEMS device of any of features 1-27, wherein a temperature coefficient of Young’s Modulus of the corrugated elements and a temperature coefficient of Young’s Modulus of the piezoelectric material layer are either both positive or both negative.

[0055] 29. The localized interface-state MEMS device of any of features 1-28, wherein the upper electrodes and the bottom electrode layer each comprise one or more of platinum, aluminum, tungsten chromium, copper, gold, silver, titanium, or combinations thereof.

[0056] 30. The localized interface-state MEMS device of any of features 1-29, wherein the substrate comprises silicon, sapphire, silicon carbide, or combinations thereof.

[0057] 31. The localized interface-state MEMS device of any of features 1-30, wherein the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least one anchor connecting the first end to the substrate and at least one anchor connecting the second end to the substrate.

[0058] 32. The localized interface-state MEMS device of any of features 1-31, wherein the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least two anchors connecting the first end to the substrate and at least two anchors connecting the second end to the substrate.

[0059] 33. A method of producing localized topological states in a MEMS device comprising: providing a localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, and a piezoelectric material layer disposed on top of the bottom electrode layer; first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, and a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements, a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave, a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate, and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; and creating, by the destructive interference at the topological interface, a third localized state.

[0060] 34. The method of feature 33, further comprising confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency -setting direction of the suspended elastic waveguide.

[0061] 35. The method of any of features 33-34, wherein the topological interface is an elastic Su- Schrieffer-Heeger (SSH) interface.

[0062] 36. The method of any of features 33-35, wherein the first and second localized states have distinct Zak phases.

[0063] 37. The method of any of features 33-36, wherein the first and second localized states have different wavenumbers.

[0064] 38. A method of detecting a presence, absence, or change of a parameter of interest comprising: providing a localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, and a piezoelectric material layer disposed on top of the bottom electrode layer; first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, and a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements, a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave, a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate, and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; exposing the localized interface-state MEMS device to the parameter of interest; exciting, by the exposure of the localized interface-state MEMS device to the parameter of interest, the localized interface-state MEMS device to produce the counter-propagating first and second symmetric and first and second antisymmetric lamb waves; causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; and creating, by the destructive interference at the topological interface, a third localized state.

[0065] 39. The method of feature 38, further comprising confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency -setting direction of the suspended elastic waveguide.

[0066] 40. The method of any of features 38-39, wherein the step of exposing the localized interface-state MEMS device to the parameter of interest further comprises exposing at least a portion of the active region to the parameter of interest.

[0067] 41. The method of any of features 38-40, further comprising transducing and reading, via two upper electrodes of the first and second periodic structures an electrical transmission of the localized interface-state MEMS device. 42. The method of feature 41, wherein other upper electrodes of the first and second periodic structures are not grounded.

[0068] 43. The method of any of features 38-42, wherein the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof.

[0069] 44. The method of feature 43, wherein the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof.

[0070] 45. The method of any of features 43-44, wherein the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest.

[0071] 46. The method of feature 45, wherein the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof.

[0072] 47. The method of feature 45, wherein the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof.

[0073] 48. The method of any of features 43-44, wherein the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0075] FIG. 1 A illustrates a Fano resonance, wherein the dark and bright states have very different lifetimes. Specifically, as shown, the bright state approaches a continuum state and the dark mode is a localized state.

[0076] FIG. IB illustrates interference of two topologically protected localized states, labeled State 1 and State 2 in accordance with various embodiments, wherein the localized states exhibit a strong wave localization achieved by leveraging the interference between the two states (State 1 and State 2).

[0077] FIGS. 2 A and 2B are 3D renderings illustrating the interference between State 1 and State 2 produced by coupling, at a topological interface, counterpropagating symmetric (SO) (red) and antisymmetric (AO) (blue) Lamb waves each with distinct Zak phases.

[0078] FIG. 3 illustrates confinement of modal energy of the first localized state (State 1) and the second localized state (State 2) around a same interface, wherein States 1 and 2 interfere to generate a localized interference state (State 3).

[0079] FIG. 4A illustrates a Su-Schrieffer-Heeger (SSH) first unit cell Cl of a localized interface-state MEMS device in accordance with various embodiments.

[0080] FIG. 4B illustrates a SSH second unit cell Cl’of the localized interface-state MEMS device in accordance with various embodiments.

[0081] FIG. 4C illustrates wave dispersion of Cl and Cl’ of FIGS. 4A and 4B. As shown, rods of each periodic structure cause a spatial symmetry breaking, which creates a strong coupling between S and A modes. As a result, a non-trivial bandgap opens, which is populated by topologically protected interface states.

[0082] FIG. 5A illustrates a localized interface-state MEMS device comprising a SSH supercell having a first periodic structure including the SSH first unit cell Cl of FIG. 4 A interfaced with a second periodic structure including the SSH second unit cell Cl’ of FIG. 4B, wherein Cl and Cl’ share the same periodicity a, but have corrugated elements separated by A and a-A respectively.

[0083] FIG. 5B illustrates wave coupling, in one-dimensional wave propagation, as achieved by breaking horizontal spatial symmetry of the localized interface-state MEMS device. Specifically, by corrugating one side of the surface of an elastic plate. This structure is then combined with an elastic version of the SSH model, where an interface is encountered between two periodic structures (Cl and Cl’). The unit cells of each structure share the same periodicity a, but have corrugated elements separated by A and a-A respectively. This creates two distinct topological states in the bandgap, localized around the same interface, each of the two states with distinct Zak phases and different wavenumbers, which are shown as a 2D Fast Fourier Transform of wavefield as taken from numerical simulations. Because the two states have mixed polarization, they can interfere to generate an interface state.

[0084] FIG. 5C is a scanning electron microscope (SEM) image of a prototype localized interface-state MEMS device using Aluminum Scandium Nitride as a piezoelectric material, Silicon Oxide to form the periodic corrugations of Cl and Cl ’, and Aluminum strips to form the electrical ports.

[0085] FIG. 5D illustrates experimental electrical transmission of the MEMS device shown, expressed in terms of the S21 scattering parameter, showing the existence of two interface states that lie within a complete bandgap. At their destructive interference (fs), strong localization is achieved, as well as a quality factor (Q) > 10000, which is a record high Q for MEMS devices using AlScN films as piezoelectric layers.

[0086] FIG. 6A is a spring-mass model wherein chain 1 models the propagation of antisymmetric Ao waves while chain 2 models the propagation of symmetric So waves.

[0087] FIG. 6B illustrates dispersion curves for the model of FIG. 6A, showing that, when the chains are disconnected, no coupling occurs and band crossing is observed.

[0088] FIG. 6C is a spring-mass model wherein elastic connections are introduced to couple the two chains of FIG. 6 A.

[0089] FIG. 6D illustrates dispersion curves for the model of FIG. 6C, showing that, when the chains are coupled, a complete bandgap is opened, wherein distinct Zak phases guarantee the existence of non-trivial topological states.

[0090] FIG. 6E is a spring-mass model wherein an interface is introduced between the initial chain of FIG. 6C, having stiffness kl-k2, k3-k4, and its mirrored counterpart, k2-kl, k4-k3.

[0091] FIG. 6F illustrates a supercell dispersion analysis for the model of FIG. 6E, showing that introduction of the interface enables two topological states, wherein a color map of the dispersion curves shows the relative polarization of the waves, with blue points corresponding to vertical (out-of-plane) polarization, while red refers to horizontal (in-plane) polarization (the Ao and So waves).

[0092] FIG. 7A illustrates measured displacement magnitude for an experimental displacement field of a midsection of the localized interface-state MEMS device of FIG. 5C while operating at a first frequency / i corresponding to a first topologically protected localized state (State 1).

[0093] FIG. 7B illustrates measured displacement magnitude for an experimental displacement field of the midsection of the localized interface-state MEMS device of FIG. 5C while operating at a third frequency fi, corresponding to a localized interference state (State 3).

[0094] FIG. 7C illustrates measured displacement magnitude for an experimental displacement field of a midsection of the localized interface-state MEMS device of FIG. 5C while operating at a second frequency fz corresponding to a second topologically protected localized state (State 2).

[0095] FIG. 7D illustrates localization of the modal energy of States 1-3 based on the measured displacement magnitude of FIGS. 7A-7C, wherein State 1 is localized within an effective cavity width, calculated along a frequency setting dimension of the prototype MEMS device, of 27pm, State 2 is localized within an effective cavity width of 58pm, and State 3 is localized within an effective cavity width of 16pm.

[0096] FIG. 8 illustrates the finite element method (FEM) calculated frequency distribution of the device transmission (S21, in blue) of the prototype localized interface-state MEMS device, together with a trend of the normalized quality factor term associated to anchor losses (in red) vs. frequency. The inset shows a detailed view of the measured S21 around fi, together with an analytical fitting line quantifying the MEMS device’s Q at fi. The prototype localized interface-state MEMS device was electrically tested by probing its input and output ports through two RF GSG probes and by using a Vector Network Analyzer (VNA).

[0097] FIG. 9A illustrates a comparison of the Q achieved by the prototype localized interface-state MEMS device with the Q achieved by state-of-the-art AlScN devices.

[0098] FIG. 9B illustrates Q vs. resonant cavity size in the frequency-setting direction as measured for the prototype localized interface-state MEMS device compared with the Q vs. frequency-setting size of the same state-of-the-art AlScN devices used for comparison in FIG. 9A. As shown, the prototype localized interface-state MEMS device not only shows a superior quality factor, but also overcomes the previously strict correlation of Q with the effective size of the resonant cavity in AlScN MEMS devices. As such, the Q achieved by the prototype localized interface-state MEMS device is about 2 orders of magnitude higher conventional AlScN devices with the same frequency-setting size of the resonant cavity.

[0099] FIG. 10 illustrates experimental electrical transmission, expressed in terms of the S21 scattering parameter, of a prototype localized interface-state MEMS device, wherein S21 has been measured a) at room temperature in air, b) at room temperature in vacuum, and c) at cryogenic temperatures.

[0100] FIG. 11 A illustrates an active area of a conventional bulk acoustic wave (BAW) infrared sensor being exposed to a highly localized infrared signal. As shown, the localized infrared signal only perturbs a small portion of the active area of the BAW sensor and, accordingly, results in only a marginal detuning (A) effect. Such marginal A can reduce response signal strength below a limit of detection (LoD) of the BAW sensor, preventing detection or accurate measurement of the infrared signal.

[0101] FIG. 1 IB illustrates an active area of a topologically enhanced BAW (tBAW) infrared sensor incorporating a localized interface-state MEMS device being exposed to the same highly localized infrared signal. The tBAW sensor is only active in a small portion of its overall area located within a few unit cells of a localized interface wherein interface state vibration modes are generated. As shown, because the highly localized active area of the tBAW sensor is much smaller than the overall area of the conventional BAW sensor, the localized infrared signal perturbs a much larger portion of the active area, generating a much higher A.

[0102] FIG. 12A illustrates a SSH first unit cell UC1 of a tBAW sensor incorporating a localized interface-state MEMS device in accordance with various embodiments.

[0103] FIG. 12B illustrates a SSH second unit cell UC2 of the tBAW sensor incorporating the localized interface-state MEMS device in accordance with various embodiments.

[0104] FIG. 12C illustrates the tBAW sensor incorporating the localized interface-state MEMS device comprising a SSH supercell having a first periodic structure including the SSH first unit cell UC1 of FIG. 12A interfaced with a second periodic structure including the SSH second unit cell UC2 of FIG. 12B, wherein UC1 and UC2 share the same periodicity a, but have corrugated elements separated by 5 and a-5 respectively.

[0105] FIG. 13 illustrates wave dispersion of UC1 and UC2 of FIGS. 12A and 12B. As shown, rods of each periodic structure cause a spatial symmetry breaking, which creates a strong coupling between S and A modes. As a result, a non-trivial bandgap opens, which is populated by topologically protected interface states.

[0106] FIG. 14 illustrates a supercell dispersion analysis for a prototype tBAW sensor, illustrated in FIG. 20A, showing that introduction of the interface enables two topological states, wherein a color map of the extracted supercell dispersion shows the relative polarization of the waves. FIG. 15 illustrates experimental electrical transmission of the prototype tBAW sensor, expressed in terms of the S21 scattering parameter, showing the existence of two interface states (State 1 and State 2) that lie within a complete bandgap. At their destructive interference (State 3), strong localization is achieved. Also shown is a high-order lamb mode (LM-1) having modal energy distributed across the entire suspended elastic waveguide.

[0107] FIG. 16 illustrates measured displacement magnitude for an experimental displacement field of a midsection of the prototype tBAW sensor while operating in a first topologically protected localized state (State 1).

[0108] FIG. 17 illustrates measured displacement magnitude for an experimental displacement field of a midsection of the prototype tBAW sensor while operating in a second topologically protected localized state (State 2).

[0109] FIG. 18 illustrates measured displacement magnitude for an experimental displacement field of the midsection of the prototype tBAW sensor while operating in a localized interference state (State 3).

[0110] FIG. 19 illustrates measured displacement magnitude for an experimental displacement field of the prototype tBAW sensor while operating in LM-1.

[0111] FIG. 20A illustrates a schematic of an experimental setup used to test the prototype tBAW sensor.

[0112] FIG. 20B illustrates a detail view of laser spot positioning during testing of the prototype tBAW sensor using the setup of FIG. 20 A.

[0113] FIG. 21 illustrates A / vs. distance from the interface of the prototype tBAW sensor as measured using the experimental setup of FIG. 20 A for States 1-3 and LM-1.

[0114] FIG. 22 illustrates an iterative Multiphysics finite element analysis (FEA) simulation framework for estimating infrared power absorbed by the prototype tBAW sensor.

[0115] FIG. 23 illustrates a schematic of an interferometric setup for measuring at-resonance out-of-plane displacements of the prototype tBAW sensor to determine a thermomechanical limit of detection (LoDtm) for the prototype tBAW sensor for each mode of interest (e.g., State 1, State 2, State 3, and LM-1 as tested).

[0116] DETAILED DESCRIPTION OF THE INVENTION

[0117] The methods and techniques described herein present localized interface-state MEMS devices that leverage the destructive interference of two topological radiofrequency (RF) counter-propagating wave modes along a Su-Schrieffer-Heeger (SSH) interface of a suspended elastic waveguide (such as, for example, a topologically modified piezoelectric Aluminum Scandium Nitride (AlScN) bilayer). In addition to sensing applications, the localized interface-state MEMS devices described herein present opportunities for further applications, including achieving more stable frequency sources for communication and timing applications.

[0118] Localized Interface- State MEMS Devices

[0119] As described herein, both a strong mode localization and a high-quality factor can be simultaneously achieved in a MEMS device operating in a linear regime by leveraging the destructive interference of two topologically protected states. This interference is achieved by leveraging a unique design strategy based on the creation of a SSH interface supporting counter-propagating symmetric So and antisymmetric Ao Lamb waves

[0052] , The counter propagation of the So and Ao waves is key to the ultimate high Q factors obtained and is achieved along the topological SSH interface by breaking the spatial symmetry of an elastic layer, i.e. by corrugating the upper surface of the AlScN layer. This creates two localized states in a one-dimensional wave propagation problem but without using in-plane symmetry breaking which would be the usual approach to create topological states in acoustics or elasticity [53, 54], These states, hereinafter State 1 and State 2 and shown, for example, in Figs. 1 A and 3, show comparable lifetimes. Also, they are both localized around an interface, which marks a significant difference between the dark and bright states that form a Fano resonance (see Fig. IB, wherein the bright state approaches a continuum state and the dark state is a localized state) [55, 56],

[0120] The interference between State 1 and State 2 is described by coupling counterpropagating symmetric So and antisymmetric Ao Lamb waves

[0052] at a topological interface in an elastic waveguide (Figs. 2A and 2B). To verify the generation of States 1 and 2 a prototype MEMS device operating in the radiofrequency range was built that uses a piezoelectric Aluminum Scandium Nitride (AlScN) layer (see Fig. 5C). This device reconstructs an elastic version of the SSH model

[0057] , where an interface is encountered between two periodic structures referred to as Cl and CL. The unit cells of each structure share the same periodicity a, but have corrugated elements separated by A and a-A, respectively. This creates two topological interface states with distinct Zak phases and different wavenumbers, as shown in the numerically computed dispersion curves reported in Fig. 5B.

[0121] It is also shown (see e.g., Figs. 5D, 7B, 7D) that the interaction between State 1 and State 2 creates an interference state (State 3) even more localized than both State 1 and State 2. In fact, the majority of the energy stored by the device when transducing State 3 is confined within 16pm along the frequency setting dimension. The stronger localization of State 3 enables a significant reduction in radiation losses (also known as anchor losses for NEMS / MEMS devices

[0058] ) towards the surrounding silicon substrate. As a result, State 3 exhibits a Q substantially higher than States 1 & 2.

[0122] The Q factor of AlScN resonators is usually affected by various dissipation mechanisms, including thermoelastic damping

[0059] , interfacial losses

[0060] , ohmic losses, and anchor losses

[0061] , The anchor losses-caused by acoustic energy leaking into the resonator’s surroundings-are dominant when the effective cavity size of AlScN resonators is reduced along the frequency-setting dimension

[0062] , and this effective size reduction is initially suggestive of similar leakage in the MEMS device reported in this work. Previous studies have attempted to mitigate anchor losses in AlScN resonators by using reflectors [63,64], however it is notable that the AlScN device reported here demonstrates a Q at the resonance frequency of State 3 (Fig. 5D) that is five times higher or more than any previously reported device made from a thin AlScN film. An additional advantage of the MEMS device is that States 1-3 exist within a topologically protected bandgap; this provides immunity to the typical defects [65, 66] relaxing required tolerances for the microfabrication of chip-scale devices.

[0123] Topological Characteristics

[0124] Referring now to Figs. 4A-4C, and 5A-5D, a localized interface-state MEMS device 500 includes a suspended elastic waveguide 501 having a first periodic structure 525 including at least one first unit cell (CT) 400, a second periodic structure 575 having at least one distinct second unit cell (Cl) 450, and an interface 550 between the periodic structures 525, 575. The suspended elastic waveguide 500 includes an electrode layer 401 and a piezoelectric layer 403 forming a bilayer plate. The first and second periodic structures 525, 575 and their constituent unit cells (CT 400 and Cl 450) are each comprised of a plurality of corrugated rods 405 and upper electrodes 407 formed on the piezoelectric layer 403. In some embodiments, as shown in FIG. 5 A, an upper electrode 407 of each of the first and second periodic structures 525, 575 can form first and second electrical ports 503, 507 and one or more other upper electrodes 407 can be grounded via ground 505. Although not shown, in some embodiments one or more upper electrodes 407 may not be grounded and may instead be left floating.

[0125] In some embodiments, the electrode layer 401 can be formed from any suitable material including, for example, metallic layers such as, but not limited to, platinum, aluminum, tungsten chromium, copper, gold, silver, titanium, or combinations thereof and the piezoelectric layer 403 can be formed from any suitable material including, for example, aluminum scandium nitride (AlScN), lithium niobate (LiNbCE or LN), aluminum chromium nitride (AlCrN), lead zirconate titanate (PZT), lithium tantalate (LiTaCh), gallium nitride (GaN), aluminum nitride (AIN), or combinations thereof. The corrugated rods 405 can be formed from any suitable material including, for example, silicon dioxide (SiCh) or other insulating materials, a metallic layer, or combinations thereof. The upper electrodes 407 can be formed from any suitable material including, for example, metals such as aluminum, platinum, tungsten chromium, copper, gold, silver, titanium, or combinations thereof and can be any suitable size (e.g., 100 nm -thick Al metallic strips as shown).

[0126] As shown in Figs. 4 A, 4B, and 5 A, CL 400 and Cl 450 can have the same periodicity a, but the position of their corrugated rods 405 is shifted by an amount equal to a-A and A respectively, as shown in Figs. 4A and 4B. This structure, when the first and second periodic structures 525, 550 are interfaced 550, forms an elastic version of the SSH-model. This structure, as shown at least, for example, in Figs. 4C and 5B, uses the rods 405 of each periodic structure 525, 575 to cause a spatial symmetry breaking, which creates a strong coupling between S and A modes (see Figs. 2A-2B). As a result, a non-trivial bandgap opens, which is populated by topologically protected interface states.

[0127] The upper electrodes 407 used to form first and second electrical ports 503, 507, in some embodiments, can be used to piezoelectrically excite the device. In some embodiments, the ports 503, 507 can advantageously be upper electrodes 407 positioned near the interface 550 of Cl 450 and CL 400 to ensure strong enough piezoelectric transduction efficiency to successfully validate the presence of States 1-3 from the extraction of the localized interfacestate MEMS device’s 500 electrical scattering parameters (S-parameters). As noted above, other, grounded upper electrodes 407 have been inserted across the device to preserve the same dispersion characteristics for all unit cells 400, 450.

[0128] As best shown in Figs. 5C and 7A-7C, four anchors 507 are used to support the fabricated device after its structural release (after the removal of the silicon underneath the device to generate a suspension). A Scanned Electron Microscope (SEM) picture of a fabricated prototype of the localized interface-state MEMS device 500 is shown in Fig. 5C.

[0129] Measured electrical transmission of the localized interface-state MEMS device 500 is reported via its S21 scattering parameter as shown in Fig. 5D.

[0130] Physical Principles

[0131] The So-Ao counter-propagating wave mode conversion of the localized interface-state MEMS device 500, illustrated visually in Figs. 2A-2B, can be conceptually idealized by coupling two distinct elastic waveguides supporting So and Ao wave modes, as usually done to describe wave locking

[0067] ,

[0132] Referring now to Figs. 6A-6F, the creation of topological interface states via such counter propagating wave mode conversion can be analytically described using a spring-mass model. As shown, both waveguides can be modeled as independent periodic chains (Fig. 6A) including a set of masses and springs (mi, m2, ki, k2 and m3, nu, 1<3, k4 respectively). These chains mimic the propagation of the Ao and So wave modes when no coupling between them occurs. The solution to the wave-equation for the system in Fig. 6A can be found by solving the time-independent Schrodinger equation for any possible Bloch state: 0)

[0133] In Eq. (1), EKnidentifies a time-independent eigenvalue relative to the wavevector K for a specific propagating nth mode. Similarly, \i / jKn) denotes the solution to the wave equation for the nth mode and wavevector K.

[0134] The solution of Eq. (1) for the independent chains in Fig. 6A is shown in Fig. 6B in terms of dispersion curves relating frequency and wavenumber. In order to model the coupling between the Ao wave and the So wave in the structure, connecting springs can be added between the two chains, as shown in Fig. 6C. The resulting dispersion curves are reported in Fig. 6D, where a complete bandgap appears due to the coupling of the two modes.

[0135] Next, the case where an SSH model is reconstructed from the two chains described in Figs. 6A and 6C is examined. To do so, each chain in Fig. 6C is connected with a mirrored version forming the Cl’ structure (Fig. 6E). The calculation of the Zak phase

[0068] for both Cl and Cl’ allows verification that non trivial interface states localized at the common interface exist, and that these states are topologically protected, being the bandgaps of Cl and Cl’ endowed with distinct Zak phases.

[0136] The dispersion curves of the supercell, reported in Fig. 6F for the system shown in Fig. 6E clearly demonstrate the existence of two interface states inside the topological bandgap. As both states have mixed polarizations and store their entire elastic energy within few unit cells around the same interface discontinuity, they can interfere. As a result, an interference state arises, as expected from the analysis of the spring-mass chain system shown in Fig. 6E. The modal characteristics of the interference state have been investigated both numerically and experimentally for the prototype MEMS device described herein as described below. The electrical response of the localized interface-state MEMS device 500 was characterized by measuring its S21 transmission from 60 MHz to 110 MHz using a Vector Network Analyzer. The device’s S21 trend shows two peaks and one notch in its electrical transmission (i.e., in its S21). The two peaks correspond to States 1 and 2 while the notch corresponds to State 3. From measured S21 vs. frequency trend, the Q value of State 3 was extracted. The Q of State 3 was found to be higher than 10,000, as shown in Fig. 5D. The localization of States 1-3 was characterized by direct measurement of the reported device’s displacement through a high-frequency vibrometer as shown in Figs. 7A-7D. The measured displacement for State 3 was found to be localized within an effective cavity width (d, calculated along the frequency setting dimension) of 16pm. Such a d value was attained by identifying the width of the region around the interface characterized by displacement

[0137] 1 magnitudes higher than where l-lmaxis the maximum displacement and e is the

[0138] Neper number. In turn, States 1,2 exhibit a lower Q (approximately 700) and show a more spread modal energy distribution with State 1 being more localized (effective cavity width of 27 m) than State 2 (effective cavity width of 58pm). These findings have been confirmed numerically through additional Finite Element Method (FEM) simulations as shown in the FEM simulated cross-sectional mode shapes of the total displacement for States 1-3 Figs. 7A- 7D.

[0139] The strong localization of State 3 allows an exceptionally high-Q, because the leakage of elastic energy into the surrounding silicon substrate is minimized. To confirm this outcome, the device’s response was simulated through FEM, extracting its S21 trend at various frequencies (see Fig. 8) as well as the trend of its Q term (Qai) associated to anchor losses. FEM simulations further confirm the presence of States 1,3. Also, they show a significant enhancement in the simulated Qaivalue for frequencies approaching the resonance frequency of State 3 (fs), as shown in Fig. 8.

[0140] Fabrication

[0141] The fabrication process of the prototype localized interface-state MEMS device 500 started with the deposition of an AlN / Pt / AlScN stack, implemented by reactive co-sputtering in the same multi-target chamber, without breaking the vacuum. Then, the AlN / Pt / AlScN stack was etched to form “release windows". This step provided direct access to silicon, which was required to be able to etch the silicon under the device through a XeF2 isotropic etching step (ensuring its suspension). Wet-etching of AlScN was then processed to create vias, allowing electrical grounding of the bottom Pt layer. Then a 2pm-thick SiCE layer was sputtered and patterned via plasma-enhanced chemical vapor deposition (PECVD) to form the surface corrugations, which have the longest dimension along the out-of-plane direction (along the anchors’ direction). Etching of the SiCL layer to form the corrugations was implemented through a reactive ion etching (RIE) step. The Al strips were then formed by sputtering and patterning a 150 nm-thick aluminum (Al) layer.

[0142] Finally, a 300 nm-thick gold (Au) layer was deposited through evaporation to cover the vias, routing lines and probing pads, ensuring lower ohmic losses.

[0143] Analysis

[0144] Localized interface-state MEMS devices (e.g., topological microacoustic devices using a topologically enhanced AlScN thin-film suspended elastic waveguide as shown and described herein) have been described above. These devices leverage the interaction of two interface states with hybrid polarizations and comparable localization properties, allowing the generation of an interference state simultaneously exhibiting a strong mode-localization and a high quality factor.

[0145] Fig. 9A compares the Q achieved at fi, by the described prototype localized interfacestate MEMS device with the Q value of other recent AlScN thin-film MEMS devices operating in the RF range. As shown, the prototype localized interface-state MEMS device described herein achieves a quality factor exceeding anything reported previously for AlScN MEMS devices by a factor of at least 5x.

[0146] Furthermore, Fig. 9B illustrates a trend of the measured Q value vs. size of the active region (where the modal energy is confined along the frequency setting dimension, i.e., d) for the prototype localized interface-state MEMS device and each one of the AlScN MEMS devices compared in Fig. 9A. The d values for all the devices listed in Fig. 9B have been extracted from reported mode shape distributions. As shown, a reduction in Q typically occurs for devices showing a lower d value. However, the localized interface-state MEMS device described herein overcomes this limitation by exhibiting a Q value more than one order of magnitude higher than other AlScN MEMS devices with comparable d values. Due to its record high Q, the localized interface-state MEMS device described herein has applicability for achieving MEMS sensors with a lower limit-of-detection (LoD). In fact, the minimum LoD of any MEMS / NEMS sensors is constrained by thermomechanical noise- induced fluctuations of their resonance frequency [37,69,70], These fluctuations decrease inversely with Q, which underscores the importance of achieving a higher Q in order to improve the achievable LoD. Furthermore, the high-Q achieved by the localized interfacestate MEMS device described herein at fi, also creates a path to achieve ultra-stable MEMS- based frequency synthesizers for timing and frequency conversion

[0071] , which can be manufactured with conventional semiconductor processes.

[0147] FIG. 10 illustrates experimental electrical transmission, expressed in terms of the S21 scattering parameter, of a different prototype localized interface-state MEMS device, wherein S21 has been measured a) at room temperature in air, b) at room temperature in vacuum, and c) at cryogenic temperatures. As shown and as reported in Table 1, the most constrained response (and thus highest Q) occurs at the interference state (State 3) of the cryogenically cooled case, showing the impact of temperature on results.

[0148] Table 1: Q-Factor in Variable Environments for Each State of Interest

[0149] Topologically Enhanced Bulk Acoustic Wave Sensors

[0150] Also presented herein is a new class of BAW sensors, referred to as topologically enhanced BAW (tBAW) sensors. As described herein, tBAW sensors incorporate localized interface-state MEMS devices to exploit topological elastic properties in order to activate localized modes of vibration never previously used by BAW sensors. These modes, known as interface states (ISs), emerge at the interface between ID periodic structures with identical elastic dispersion but distinct topological phases (different Zak phases). ISs are stationary (non-propagating) modes.

[0151] As such, the elastic energy of ISs is localized within a few unit cells from the interface where they are generated, as shown, for example, in Figs. 16-18. In other words, unlike Lamb modes, ISs’ equivalent size of the resonant cavity (Left), is limited to the length of a few unit-cells and not to the entire area of the suspended portion. Such modal energy distribution makes the resonance frequency of ISs more sensitive to Pols acting near the shared boundary of the periodic structures, providing a path towards higher responsivities to localized Pols than what is achievable when exploiting Lamb modes.

[0152] This makes them suitable for sensing, which can be implemented by monitoring the detuning of their resonance frequency induced by the targeted parameter of interest, as is commonly done in current B AW sensors. Such tB AW sensors can be particularly useful in connection with localized Pols, wherein the tB AW sensors represent the first instance of a BAW sensor capable of overcoming the intrinsic trade-off between responsivity (R) and limit of detection (LoD) by leveraging the ISs.

[0153] Importantly, the localized modal energy distribution of ISs is not achieved by downscaling the suspended volume of the BAW, which is the only viable approach when exploiting Lamb modes. Instead, the modal energy localization emerges from the dispersion of the two periodic structures, which show a complete stopband at the ISs’ resonance frequency. This allows suppression of acoustic energy leakage (also known as ’’anchor losses”) and enables superior Q values regardless of the small Leff value. Furthermore, since the strain energy density rapidly decays away from the interface between the two periodic structures, almost no energy reaches their outer lateral edges. This allows to connect such edges to the surrounding silicon without causing a Q degradation.

[0154] This anchoring approach ensures improved heat flow (lower thermal resistance, Rth) from the suspended elastic waveguide to the surrounding silicon substrate, allowing tBAW sensors to sustain higher electrical driving powers and achieve greater elastic energy — a fundamental requirement for minimizing the LoD. It is noted that using wide lateral anchors along the frequency-setting dimension typically destroys the resonance response of conventional BAW devices to a point that no resonance can be detected electrically. The performance enhancements brought by using ISs collectively contribute to the achievement of reduced levels of thermomechanical noise-driven frequency fluctuations (Afn). Both the reduction of Afnand the increase in responsivity attained by exploiting ISs rather than Lamb modes contribute in enabling an improved LoD compared to what is achievable when exploiting Lamb modes.

[0155] In order to study the application of ISs to sensing applications, a prototype tBAW sensor using ISs was built a microfabricated radiofrequency (RF) AlScN tBAW sensor operating at ~ 80MHz. This device has been used to sense infrared (IR) power at a ~ 1.55pm wavelength, emitted by a laser with a 5 pm diameter circular beam size. The design and fundamental electromechanical characteristics of the fabricated prototype tBAW sensor are described below along with testing and demonstration of its application for IR-sensing, providing evidence of enhanced performance due to mode localization. The demonstration is achieved by comparing the device’s IR sensing response when leveraging an IS or a Lamb mode. Through both a Finite Element Method (FEM) simulation framework developed in this work and experimental results, it is shown that leveraging an IS allows the incident IR power to manipulate more efficiently the device’s effective stiffness than exploiting a Lamb mode. Next, the device’s elastic energy is evaluated at the maximum driving power that can be used before the on-set of bifurcations (operating points with marginal stability) in its electromechanical response. Using this energy and the maximum measured responsivity, the thermomechanical noise-limited LoD (LoDtm) is calculated. This value is then used, along with the measured responsivity alone, to benchmark the device’s IR sensing performance against previously reported bulk acoustic wave (B AW) IR sensors.

[0156] Although shown and described herein as being used for IR sensing, it will be apparent in view of this disclosure that tBAW sensors incorporating localized interface-state MEMS devices to exploit the advantages of ISs can be used in accordance with the sensing of any Pol, including, for example, one or more of a physical or electrical parameter, including, for example, one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration, presence, or absence of a chemical agent including, for example, one or more of gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, or combinations thereof, concentration, presence, or absence of a biological agent, including one or more of a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, or combinations thereof.

[0157] Topological Characteristics

[0158] As shown in Figs. 12A-12C, the prototype tBAW sensor 1200 includes a grounded bottom metal layer 1201 (e.g., Pt as shown), a piezoelectric layer 1203 (e.g., an AlScN thin- film as shown) on the grounded bottom layer 1201, upper electrodes 1207 (e.g., Al strips as shown) formed on the piezoelectric layer 1203, and corrugated rods 1205 (e.g., thick SiCh rods as shown) having a longer size along the out-of-plane dimension than along the frequency-determining dimension. For the IR application, the bottom metal layer 1201 is electrically grounded while all the upper electrodes 1207 are left floating, with the exception of two upper electrodes 1207 used to transduce and read the device’s electrical transmission (represented by its S21 scattering parameter). The prototype tBAW sensor 1200 includes a first periodic structure 1225 including nine first unit-cells (UC1) 1210, a second periodic structure 1275 including nine second unit-cells (UC2) 1220, and an interface 1250 therebetween.

[0159] The first and second unit cells UC1 1210, UC2 1220 share dispersion characteristics and periodicity a, but have corrugated elements separated by 5 and a-5 respectively, which results in UC1 1210, UC2 1220 having different Zak phases.

[0160] An overlapping numerically calculated band diagram for the first and second periodic structures 1225, 1275 is shown in Fig. 13, showing the existence of a complete bandgap between 70.97 MHz and 83.59 MHZ. This is possible because cascading two ID periodic structures with identical dispersion properties but different Zak phases creates the conditions for the existence of topologically protected ISs in the surfaces’ bandgaps.

[0161] These ISs exhibit properties that Lamb modes do not. One of these properties is a strong mode localization, which makes ISs’ elastic energy squeezed around the boundary between the two periodic surfaces. When looking specifically at the tBAW sensor reported in this work, two ISs (’’State 1” and ’’State 2”) are generated at frequencies fi and f2. Such ISs have hybrid polarizations, incorporating both symmetric and antisymmetric components. This leads to the generation of a third topological state (’’State 3”) — an interference state — at a frequency (fs) at which the device exhibits minimal strain energy. The existence of the three states can be verified by numerically extracting the supercell dispersion relative to the tBAW sensor as shown in Fig. 14. The three states can be also identified from the device’s measured scattering parameters and, specifically, from the S21 response as shown in Fig. 15.

[0162] In this regard, the tBAW sensor described herein also shows an additional mode (LM- 1) in its S21, close to the three topological states. LM-1 is a high-order Lamb mode, thereby having elastic energy distributed across its entire suspended volume. FEA was used to visualize the modal energy distributions of States 1,2,3 and LM-1 (see Figs. 16-19). Evidently, the elastic energy of LM-1 is distributed across the entire suspended elastic waveguide, unlike States 1,2,3 that have their elastic energy constrained around the interface 1250.

[0163] Enhanced sensing performance through topological mode localization.

[0164] The resonance frequency of any BAW device can be expressed as fes= where ce^ is the phase velocity of the exploited mode of vibration and is its wavelength. Regardless of the specific mode employed, ce^ can be estimated as yjEe^ / pe^^ where Ee^ and peff are the mode’s effective Young’s modulus and effective mass density, respectively. These effective parameters represent weighted averages of the Young’s modulus and mass density of all materials across the BAW device’s cross-section, with the weights determined by the amount of elastic energy each layer stores in the active region at resonance.

[0165] When a BAW device is exposed to a sensing parameter, both Ee^ and peff may vary due to the perturbation induced by the parameter. The magnitude of this variation depends on the strength of the sensing parameter and the spatial extent over which it acts. For instance, an analyte deposited on top of a BAW device used as a mass sensor typically induces a change in peff (changes in Young’s modulus are negligible) whose extent depends on the analyte’s mass density, as well as on the ratio (Aratio) between the area of the device perturbed by the analyte and the total area of the device’s active region (assuming for simplicity the elastic energy equally spread across the active region). In other words, in this example, the resonance frequency shift induced by the analyte is proportional to Aratio, highlighting the need for a higher Aratioto enhance the responsivity of the BAW device to mass changes.

[0166] A similar conclusion can be drawn when looking at BAW devices used for infrared (IR) sensing. These devices absorb a portion of the IR power emitted by a laser and focused onto their surface within a defined spot. This leads to a temperature change that is maximized within the spot area. The local absorption of IR power and the corresponding increase of temperature cause a change in Ee^ because the Young’s modulus of each material is inherently characterized by a temperature dependence. The extent to which Ee^ changes in the presence of IR power is proportional to the ratio between spot size and the overall area of the active region (referred to as Aratiosimilar to the previous example). In other words, the responsivity (R) of the BAW device used for infrared sensing, defined as the ratio between the frequency shift inducted by the IR power and the amount of IR power that is absorbed, is ultimately proportional to Aratio.

[0167] This suggests that enhanced responsivity to IR power can be achieved by reducing the size of the active region to better match the spot size. Increasing Aratiorequires reducing the area wherein a BAW device stores its mechanical energy at resonance. For existing BAW devices, this implies reducing the size of their suspended portion, which is typically where the great majority of the elastic energy is stored. This is currently done by targeting lower order Lamb modes or by exciting higher frequency (i.e., shorter-wavelength) Lamb modes. Pursuing these approaches generally comes with degraded electromechanical performance, specifically in reductions of Q due to higher anchor losses (for both approaches) or higher thermoelastic dissipations (for the second approach). Narrower anchors can help mitigate the increase in anchor losses caused by miniaturization, but at the cost of reducing Pmax due to a diminished ability to dissipate heat generated during the motion. It is noted that nonlinearities in BAW sensors primarily arise from thermal effects, specifically from changes in the Young’s modulus of their forming layers as a result of temperature (T) increases caused by mechanical and ohmic losses. Thermal nonlinearities in BAW devices are typically characterized using a Duffing coefficient, which captures the degree of softening that these devices experience for large displacements in the membrane. Reductions of Q and Pmax, along with the increase of T , collectively contribute to larger levels of thermomechanical noise-driven frequency fluctuations, degrading BAW sensors’ ultimate LoD value. In practice, miniaturizing an existing BAW sensor to enhance the responsivity to a targeted parameter of interest leads to a degradation in LoD. The performance trade-off observed in current BAW sensors arises from the need to miniaturize their size to enhance responsivity. However, this miniaturization adversely affects their thermal behavior, making them more susceptible to nonlinearities at lower strain levels (i.e., under lower electrical driving power), and generally leads to lower Q values. tB AW sensors address the need for larger Aratio in a different manner. Instead of pursuing a miniaturization of the suspended volume, tBAWs leverage the intrinsic mode localization of ISs. This allows squeezing of the elastic energy into an effective area spanning only a few unit cells in either direction from the common interface boundary between the two periodic surfaces without having to downsize their suspended region or to excite higher frequency modes. This prevents Q-degradations. Also, tBAWs’ periodic surfaces also act as lateral anchors, which makes it possible to largely improve the heat flow (thus to lower Rth) and, consequently, to enhance Pmax and reduce the temperature reached in the active region for any applied driving power. In other words, tBAW sensors’ topological properties add a degree of freedom in the design of BAW sensors that allows tBAWs to simultaneously achieve high responsivities and high LoDs.

[0168] The advantage of tBAW sensors becomes clear by comparing Figs. 11 A and 1 IB. Fig. 11 A illustrates an active area 1100 of a conventional bulk acoustic wave (BAW) infrared sensor being exposed to a highly localized infrared signal 1125. As shown, the localized infrared signal 1125 only perturbs a small portion of the active area of the BAW sensor and, accordingly, results in only a marginal detuning (A) effect. Such marginal A can reduce response signal strength below a limit of detection (LoD) of the BAW sensor, preventing detection or accurate measurement of the infrared signal. By contrast, Fig. 1 IB illustrates an active area 1150 of a topologically enhanced BAW (tBAW) infrared sensor incorporating a localized interface-state MEMS device. As can be seen, the tBAW sensor is being exposed to the same highly localized infrared signal 1125 as the conventional BAW of Fig. 11 A. In addition, although not shown, the overall suspended area of the tBAW is identical to that of the conventional BAW. However, because the tBAW sensor is only active in a small, localized portion (located within a few unit cells of the interface) of its overall suspended area, the localized infrared signal 1125 perturbs a much larger portion of the active area 1150, generating a much higher A.

[0169] Experimental Results

[0170] To experimentally demonstrate the impact of the topological properties on the sensing performance of the tBAW sensor 1200, the tBAW sensor’s response in an infrared (IR) sensing experiment. Specifically, the tBAW sensor was validated by exposing it to IR radiation focused onto a spot significantly smaller than the total suspended elastic waveguide area. To fairly assess the advantage of using Iss over conventional Lamb modes, the responsivity and limit of detection achieved in the IR sensing experiment was evaluated when leveraging each one of the device’s ISs or LM-1. The existence of LM-1 is convenient for testing purposes since it permits a direct comparison of the sensing performance achievable by ISs and Lamb modes within the same fabricated device, avoiding inaccuracies originated from testing ISs and Lamb waves on separate devices. Also, it ensures that any observed enhancement in the ISs’ performance over LM-1 can be attributed solely to differences in their modal energy distributions.

[0171] These experiments were designed to address two main goals: (i) demonstrate that States 1,2,3 have a higher responsivity to IR power than LM-1, and (ii) that the higher responsivity also effectively comes with lower Afnand, consequently, a lower LoD. The steps taken to achieve each one of these goals, is described below, including presentation of the experimental setups used for both evaluations and the corresponding measured results.

[0172] Responsivity extraction for tBAWs’ ISs and a Lamb mode

[0173] To experimentally demonstrate that States 1,2,3 have a higher responsivity to IR power than LM-1, the tBAW sensor was wirebonded on a Printed-Circuit-Board. Then, an optical set-up including an IR laser with a 1.55pm wavelength and having a circular beam spot of 5 pm in diameter was assembled. The tBAW sensor 1200 was placed at a close distance (35mm) under the laser, on a stage movable by using micro-manipulators. The total IR power emitted by the laser was measured by using a power meter (1.466mW ). The tBAW sensor’s two ports were connected to a vector network analyzer to extract the resonance frequency shift (A) produced by the activation of the laser, for different positions of the spot size across the device’s suspended area and for all modes of vibration under consideration.

[0174] A schematic representation of the set-up used in the experiments for the extraction of the A values is shown in Fig. 20A. In the measurements, the controllable stage was used to shift the position of the laser spot along the device’s width (the frequency-setting direction (x) for all modes under investigation) and extract the corresponding A at each configured position and for all modes of vibration investigated.

[0175] During this extraction, the stage was moved along the x-direction while keeping the laser spot at the same position along the y-direction (at half of the total length of the suspended area). A schematic representation of the position of the laser spot during this experiment is shown in Fig. 20B. The extracted A values for all experiments are reported in Fig. 21, which shows that States 1,2, and 3 can exhibit A value four times higher than LM-1. Furthermore, the highest A values were attained by States 3 at the interface between the tBAW sensor’s periodic structures. This behavior is expected, as this location corresponds to the region where most of the elastic energy is concentrated, owing to the strong mode localization exhibited by topological interface states (ISs). In contrast, LM-1 displays A values that are significantly less sensitive to the position of the laser spot.

[0176] While computing A is sufficient to demonstrate that States 1,2,3 are indeed more responsive to IR power than LM-1, the evaluation of the responsivity for all these modes requires knowing the amount of IR power that the device absorbs. In this regard, while FEA shows that a peak in absorption is expected at 1.54pm, which is close to the wavelength of a Fabry -Perot resonance, estimating the IR power absorbed by the tBAW sensor under study is more challenging than for conventional BAW sensors used for IR sensing. In fact, the thick SiCL rods (whose thickness is higher than the IR wavelength) are expected to produce significant amounts of scattering and surface wave excitation when a laser is used to shine IR power from the device’s top side, introducing uncertainties in the actual value of absorbed IR power.

[0177] Therefore, to estimate the absorbed IR power, an iterative Multiphysics FEA simulation framework was developed. The process begins by assuming an initial value for the IR power absorbed within the laser spot. Based on this value, the framework calculates the resulting spatial temperature distribution across the entire volume of the device. It then updates the elastic coefficients of all device layers in a spatially distributed manner, using the FEA calculated temperature profile and the temperature coefficient of the Young’s modulus (TCE) for each layer. Subsequently, a piezoelectric structural mechanics simulation is performed to compute the resulting A value based on the temperature-altered elastic properties. If the simulated A does not align with the experimentally measured value, the simulation is repeated with a revised assumption for the absorbed IR power. This iterative procedure continues until the simulated and measured A values closely match, yielding an accurate estimate of the IR power absorbed during the experiment (see Fig. 22 for a schematic overview of the simulation steps implemented in the FEA framework).

[0178] This FEA-based approach estimated the IR power absorbed by the device to be ~ 55pW . To further confirm the validity of the simulation routine, it was verified that the A values produced when placing the tBAW sensor on a temperature controlled plate match closely the corresponding values simulated using the simulation routine.

[0179] Given the calculated value for the absorbed IR power, the maximum responsivity that the tBAW sensor exhibits can be quantified. This can be found by dividing the measured maximum A value for each mode to the value of absorbed IR power. As expected, State 2 exhibits the highest responsivity of 962Hz / pW as shown in Table 2.

[0180] Table 2: Responsivity for Each State of Interest

[0181] It is noted that, although an IR sensing experiment was used to demonstrate the influence of the tBAW sensors’ topological properties on the sensing performance of localized parameters, the tBAW design described herein has not been optimized for maximum responsivity to IR power. In this regard, refinements to its design could lead to even higher responsivity, such as reducing the device’s length, optimizing the unit-cell geometry and the number of unit cells in its periodic structures, and adopting a different material to form the rods — one with a TCE having the same sign as that of AlScN. This last modification would allow an increase in the device’s temperature coefficient of frequency (TCF) and, consequently, its responsivity to IR power.

[0182] LoDtm Extraction for tBAW ISs and LM-1

[0183] After extracting the responsivity of the reported tBAW sensor to incident IR power, its thermomechanical limit of detection was evaluated, denoted as LoDtm. For any MEMS resonant sensor system, LoDtmcorresponds to the minimum detectable signal when assuming thermomechanical noise as the only noise source in the system. As such, LoDtmprovides a reliable metric to assess the intrinsic sensing resolution achievable by MEMS devices. The

[0184] LoDtm value of the reported tBAW sensor can be quantified for each one of its analyzed modes of vibration by using Eq. (1), where R denotes the device’s responsivity:

[0185] Efncan be evaluated by using Eq. (2). In Eq. (2), Ethrepresents the average thermal energy in the device’s active region, while Ecis a critical energy threshold. Specifically, Eccorresponds to the kinetic energy of the device operating at resonance and driven with the maximum allowable power which ensures accurate sensing without triggering bifurcations in the electromechanical response.

[0186] To determine Pmaxfor each vibration mode, the input power at the actuation port of the MEMS device was incrementally increased until the onset of a bifurcation was detected in the measured S21 vs. frequency trend. Accurate estimation of Ethrequires knowledge of the average temperature (Tave) across the device’s active region when the device is driven by an input power equal to Pmaxsee Eq. (2)). Also, this evaluation must be carried out over the maximum usable measurement bandwidth (BWm), typically defined as the inverse of the device’s thermal time constant. Both Taveand BWmwere computed using the developed FEA framework, as discussed in Fig. 22.

[0187] Estimating Ecnecessitates evaluating the at-resonance kinetic energy stored by the device at Pmax(see Eq. (2)), which requires knowing the device’s modal mass and total displacement magnitude for each analyzed mode of vibration. To achieve this, displacement measurements were performed using an interferometric setup as shown in Fig. 23. These measurements evaluated the at-resonance out-of-plane displacement for each mode of interest, averaged across multiple points along the device’s length. Since the setup does not resolve in-plane displacements, FEA simulations were used to estimate their magnitudes. Specifically, the same in-plane to out-of-plane displacement ratios observed in simulations were assumed, allowing inference of in-plane displacements from measured out-of-plane values. The modal mass required for the evaluation of Ecwas extracted from the FEA model.

[0188] LoDtm values computed for each one of the topological states, as well as for LM-1, are reported in Table 3, which also lists the Pmaxvalues for each mode, as well as the calculated thermomechanical noise given the simulated average temperature across the device’s active region when considering all the electrical power absorbed by the device being dissipated into heat. No nonlinearities were observed in the measured S21 response for State 3 at the applicable maximum driving power Pmax, drive=23dBm. For this reason, the Pmaxvalue for State 3 was assumed to be equal to maximum driving power.

[0189] Table 3: Thermomechanical Limit of Detection for Each State of Interest

[0190] Additional features and advantages of tBAW sensors

[0191] Described herein is the first BAW sensor that leverages topological phenomena (tBAW) to produce localized interface states and interference states to reduce Ley without reducing suspended volume. Specifically, the tBAW sensors disclosed herein can transduce three distinct topological states (States 1-3), all included in the bandgap of two periodic surfaces used to reconstruct the SSH model in an elastic framework.

[0192] The tBAW sensors disclosed herein can be used to sense highly localized Pols, including, as tested, IR power emitted by a laser with a 5 pm x 5 pm beam width. This is possible because the strong localization of the topological states significantly enhances the device’s responsivity to IR power compared to the typically used modes, which distribute energy across the entire suspended elastic waveguide. Among the three topological states, the state exhibiting the highest spatial confinement delivers the greatest responsivity. Crucially, the enhancement in responsivity brought by topology does not compromise the device’s intrinsic limit of detection set by thermomechanical noise, a trade-off typically encountered when reducing conventional BAW sensors’ dimensions to achieve highly localized sensing. On the contrary, it is shown that the most localized topological state not only offers the highest responsivity but also achieves the lowest LoDtm. Thus, as established by this disclosure, topological ISs can be harnessed to address longstanding limitations in the miniaturization and performance of BAW sensors targeting highly localized Pols.

[0193] As used herein, "consisting essentially of allows the inclusion of materials or steps that do not materially affect the basic and novel characteristics of the claim. Any recitation herein of the term "comprising", particularly in a description of components of a composition or in a description of elements of a device, can be exchanged with "consisting essentially of' or "consisting of'.

[0194] While the present invention has been described in conjunction with certain preferred embodiments, one of ordinary skill, after reading the foregoing specification, will be able to effect various changes, substitutions of equivalents, and other alterations to the compositions and methods set forth herein.

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Claims

CLAIMSWhat is claimed is:

1. A localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, a piezoelectric material layer disposed on top of the bottom electrode layer, first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, and a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements; a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave; a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate; and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface, wherein the destructive interference creates a third localized state.

2. The localized interface-state MEMS device of claim 1, wherein: the first periodic structure includes one or more first unit cells having a width a and two corrugated elements separated along a frequency-setting direction of the suspended elasticwaveguide by a distance A, the two corrugated elements positioned between two upper electrodes; and the second periodic structure includes one or more second unit cells having a width a and two corrugated elements separated along the frequency-setting direction of the suspended elastic waveguide by a distance a — A, the two corrugated elements having an upper electrode positioned therebetween.

3. The localized interface-state MEMS device of claim 2, wherein the first periodic structure includes an interface first unit cell encompassing a first upper electrode and half of a second upper electrode along the frequency-setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode.

4. The localized interface-state MEMS device of claim 3, wherein the second periodic structure includes an interface second unit cell adjacent and connected to the interface first unit cell, opposite along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface.

5. The localized interface-state MEMS device of claim 4, wherein the first periodic structure includes one or more non-interface first unit cells, each adjacent and connected to at least one of the interface first unit cell and / or non-interface first unit cells and encompassing half of an upper electrode shared with the at least one adjacent interface first unit cell and / or non-interface first unit cells along the frequency-setting dimension of the suspended elastic waveguide.

6. The localized interface-state MEMS device of claim 4, wherein the second periodic structure includes one or more non-interface second unit cells adjacent and connected to the interface second unit cell and / or non-interface second unit cells along the frequency-setting dimension of the suspended elastic waveguide.

7. The localized interface-state MEMS device of claim 1, wherein the topological interface is an elastic Su-Schrieffer-Heeger (SSH) interface.

8. The localized interface-state MEMS device of claim 1, wherein the first and second localized states have distinct Zak phases.

9. The localized interface-state MEMS device of claim 1, wherein the first and second localized states have different wavenumbers.

10. The localized interface-state MEMS device of claim 1, wherein the third localized state exhibits a quality factor greater than or equal to 10,000.

11. The localized interface-state MEMS device of claim 1, wherein the topological interface comprises: an interface first unit cell of the first periodic structure encompassing a first upper electrode and half of a second upper electrode along the frequency -setting direction of the suspended elastic waveguide, wherein the first upper electrode having a width equal to half of a width of the second upper electrode; and an interface second unit cell of the second periodic structure adjacent and connected to the interface first unit cell along the frequency-setting dimension of the suspended elastic waveguide to form the topological interface.

12. The localized interface-state MEMS device of claim 11, wherein: the first periodic structure further comprises a plurality of adjacent non-interface first unit cells extending away from the interface first unit cell along the frequency-setting direction of the suspended elastic waveguide; and the second periodic structure further comprises a plurality of adjacent non-interface second unit cells extending away from the interface second unit cell along the frequency-setting direction of the suspended elastic waveguide.

13. The localized interface-state MEMS device of claim 12, wherein an active region of the MEMS device in the third localized state is confined by the first and second periodic structures to the topological interface, a portion of the non-interface first unit cells most proximate to the topological interface, and a portion of the non-interface second unit cells most proximate to the topological interface along the frequency-setting direction of the suspended elastic waveguide.

14. The localized interface-state MEMS device of claim 13, wherein the active region has a width along the frequency-setting direction of the suspended elastic waveguide between about 16pm and about 58pm.

15. The localized interface-state MEMS device of claim 13, wherein an upper electrode of the first periodic structure forming a first electrical port and an upper electrode of the second periodic structure forming a second electrical port for excitation of one or more of the first, second, and third localized states.

16. The localized interface-state MEMS device of claim 15, wherein one or more additional upper electrodes of the first and second periodic structures are grounded.

17. The localized interface-state MEMS device of claim 13, wherein the localized interface-state MEMS device is sensitive to a parameter of interest.

18. The localized interface-state MEMS device of claim 17, wherein two of the upper electrodes of the first and second periodic structures are configured to transduce and read an electrical transmission of the localized interface-state MEMS device and wherein all other upper electrodes of the first and second periodic structures are not grounded.

19. The localized interface-state MEMS device of claim 17, wherein the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof.

20. The localized interface-state MEMS device of claim 19, wherein the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal, current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof.

21. The localized interface-state MEMS device of claim 19, wherein the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest.

22. The sensing circuit of claim 21, wherein the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-born pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof.

23. The sensing circuit of claim 21, wherein the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof.

24. The localized interface-state MEMS device of claim 19, wherein the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal.

25. The localized interface-state MEMS device of claim 17, wherein the localized interface-state MEMS device is a Bulk Acoustic Wave (BAW) sensor.

26. The localized interface-state MEMS device of claim 1, wherein the piezoelectric material layer comprises aluminum scandium nitride (AlScN), lithium niobate (LiNbCE or LN), aluminum chromium nitride (AlCrN), lead zirconate titanate (PZT), lithium tantalate (LiTaCE), gallium nitride (GaN), aluminum nitride (AIN), or combinations thereof.

27. The localized interface-state MEMS device of claim 1 , wherein the corrugated elements comprise an insulating layer, a metallic layer, or combinations thereof.

28. The localized interface-state MEMS device of claim 1, wherein a temperature coefficient of Young’s Modulus of the corrugated elements and a temperature coefficient of Young’s Modulus of the piezoelectric material layer are either both positive or both negative.

29. The localized interface-state MEMS device of claim 1, wherein the upper electrodes and the bottom electrode layer each comprise one or more of platinum, aluminum, tungsten chromium, copper, gold, silver, titanium, or combinations thereof.

30. The localized interface-state MEMS device of claim 1, wherein the substrate comprises silicon, sapphire, silicon carbide, or combinations thereof.

31. The localized interface-state MEMS device of claim 1, wherein the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least one anchor connecting the first end to the substrate and at least one anchor connecting the second end to the substrate.

32. The localized interface-state MEMS device of claim 1, wherein the suspended elastic waveguide includes a first end and a second end and the suspended elastic waveguide is suspended over the cavity by at least two anchors connecting the first end to the substrate and at least two anchors connecting the second end to the substrate.

33. A method of producing localized topological states in a MEMS device comprising: providing a localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, and a piezoelectric material layer disposed on top of the bottom electrode layer; first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, anda plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements, a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave, a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate, and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; and creating, by the destructive interference at the topological interface, a third localized state.

34. The method of claim 33, further comprising confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency -setting direction of the suspended elastic waveguide.

35. The method of claim 33, wherein the topological interface is an elastic Su-Schrieffer- Heeger (SSH) interface.

36. The method of claim 33, wherein the first and second localized states have distinct Zak phases.

37. The method of claim 33, wherein the first and second localized states have different wavenumbers.

38. A method of detecting a presence, absence, or change of a parameter of interest comprising: providing a localized interface-state MEMS device comprising: a suspended elastic waveguide comprising: a bottom electrode layer, the bottom electrode layer suspended over a cavity in a substrate, and a piezoelectric material layer disposed on top of the bottom electrode layer; first and second arrays of corrugated elements patterned on top of the piezoelectric material layer, each of the corrugated elements having a long axis substantially perpendicular to a plane of the piezoelectric material layer and positioned to alter a dispersion of symmetric and antisymmetric Lamb modes of the piezoelectric material layer, and a plurality of upper electrodes, each upper electrode disposed on the piezoelectric material layer between two corrugated elements of the first and / or second array of corrugated elements, a first periodic structure of the suspended elastic waveguide including the first array of corrugated elements and having a first localized state supporting a first symmetric lamb wave and a first antisymmetric lamb wave, a second periodic structure of the suspended elastic waveguide including the second array of corrugated elements and having a second localized state supporting a second symmetric lamb wave and a second antisymmetric lamb wave, wherein the first and second symmetric lamb waves and the first and second antisymmetric lamb waves counter-propagate, and a topological interface between the first periodic structure and the second periodic structure, the topological interface configured to break a spatial symmetry of the suspended elastic waveguide to create the first and second localized states and cause destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; exposing the localized interface-state MEMS device to the parameter of interest;exciting, by the exposure of the localized interface-state MEMS device to the parameter of interest, the localized interface-state MEMS device to produce the counter-propagating first and second symmetric and first and second antisymmetric lamb waves; causing destructive interference between the counter-propagating first and second symmetric and first and second antisymmetric lamb waves at the topological interface; and creating, by the destructive interference at the topological interface, a third localized state.

39. The method of claim 38, further comprising confining, by the first and second periodic structures, an active region of the localized interface-state MEMS device in the third localized state to the topological interface and a portion of each of the first and second periodic structures most proximate to the topological interface along a frequency -setting direction of the suspended elastic waveguide.

40. The method of claim 38, wherein the step of exposing the localized interface-state MEMS device to the parameter of interest further comprises exposing at least a portion of the active region to the parameter of interest.

41. The method of claim 38, further comprising transducing and reading, via two upper electrodes of the first and second periodic structures an electrical transmission of the localized interface-state MEMS device.

42. The method of claim 41, wherein other upper electrodes of the first and second periodic structures are not grounded.

43. The method of claim 38, wherein the parameter of interest includes one or more of a physical parameter, an electrical parameter, a chemical agent, a biological agent, or combinations thereof.

44. The method of claim 43, wherein the parameter of interest includes one or more of mass, acceleration, pressure, transduced spin waves, vibration frequency, vibration intensity, temperature, humidity, radiation concentration, radiation energy, radiation intensity, radiation type, acoustic frequency, acoustic intensity, acoustic power, acoustic phase, photonic intensity, photonic frequency, photonic phase, photonic polarization, voltage of an electrical signal,current of an electrical signal, power of an electrical signal, frequency of an electrical signal, magnetic field, concentration of a chemical agent, presence or absence of a chemical agent, concentration of a biological agent, presence or absence of a biological agent, or combinations thereof.

45. The method of claim 43, wherein the localized interface-state MEMS device is a mass sensor and an effective mass density of the localized interface-state MEMS device is changed by perturbation of the active region by an analyte of interest.

46. The method of claim 45, wherein the analyte is a chemical agent selected from a gas, a toxin, a volatile organic compound, an atmospheric or water-bom pollutant, a vehicle emission, an emission of an animal or human, soil moisture, a pharmaceutical agent or formulation ingredient, a polymer, and combinations thereof.

47. The method of claim 45, wherein the analyte is a biological agent selected from a bacterium, a virus, a viral vector, a cell, an exosome, an extracellular vesicle, a cellular organelle or cell fragment, an antibody, a protein, a glycoprotein, a nucleic acid, an antigen, a tumor antigen, a sugar, an oligosaccharide, a polysaccharide, a lipid, a glycolipid, a sphingolipid, a vaccine, and combinations thereof.

48. The method of claim 43, wherein the localized interface-state MEMS device is an infrared sensor and an effective Young’s modulus of the localized interface-state MEMS device is changed by a temperature change in the active region caused by infrared power absorbed from exposure of the active region to a received infrared signal.

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