Patent Publication Number: US-2023134688-A1

Title: Plate wave devices with wave confinement structures and fabrication methods

Description:
This application is a continuation of U.S. patent application Ser. No. 16/544,279 filed on Aug. 19, 2019 and issuing as U.S. Pat. No. 11,545,955, which is a continuation of U.S. patent application Ser. No. 14/973,336 filed on Dec. 17, 2015 and issuing as U.S. Pat. No. 10,389,332, which is a continuation of International Patent Application No. PCT/US15/066424 filed on Dec. 17, 2015, which is a non-provisional of U.S. Provisional Patent Application No. 62/093,184 filed on Dec. 17, 2014, and is a non-provisional of U.S. Provisional Patent Application No. 62/093,753 filed on Dec. 18, 2014. The entire contents of the foregoing applications and patent are hereby incorporated by reference as if set forth fully herein. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to electromechanical components utilizing acoustic wave propagation in piezoelectric layers, and in particular to improved plate wave structures and methods for making such structures. Such structures may be used, for example, in radio frequency transmission circuits, sensor systems, signal processing systems, and the like. 
     BACKGROUND 
     Micro-electrical-mechanical system (MEMS) devices come in a variety of types and are utilized across a broad range of applications. One type of MEMS device that may be used in applications such as radio frequency (RF) circuitry is a MEMS vibrating device (also known as a resonator). A MEMS resonator generally includes a vibrating body in which a piezoelectric layer is in contact with one or more conductive layers. Piezoelectric materials acquire a charge when compressed, twisted, or distorted. This property provides a transducer effect between electrical and mechanical oscillations or vibrations. In a MEMS resonator, an acoustic wave may be excited in a piezoelectric layer in the presence of an alternating electric signal, or propagation of an elastic wave in a piezoelectric material may lead to generation of an electrical signal. Changes in the electrical characteristics of the piezoelectric layer may be utilized by circuitry connected to a MEMS resonator device to perform one or more functions. 
     Guided wave resonators include MEMS resonator devices in which an acoustic wave is confined in part of a structure, such as in the piezoelectric layer. Confinement may be provided by reflection at a solid/air interface, or by way of an acoustic mirror (e.g., a stack of layers referred to as a Bragg mirror) capable of reflecting acoustic waves. Such confinement may significantly reduce or avoid dissipation of acoustic radiation in a substrate or other carrier structure. 
     Various types of MEMS resonator devices are known, including devices incorporating interdigital transducer (IDT) electrodes and periodically poled transducers (PPTs) for lateral excitation. Examples of such devices are disclosed in U.S. Pat. Nos. 7,586,239, 7,898,158, and 8,035,280 assigned to RF Micro Devices (Greensboro, N.C., USA), wherein the contents of the foregoing patents are hereby incorporated by reference herein. Devices of these types are structurally similar to film bulk acoustic resonator (FBAR) devices, in that they each embody a suspended piezoelectric membrane. Such devices (including IDT-type devices in particular) are subject to limitations of finger resistivity and power handling due to poor thermal conduction in the structures. Additionally, IDT-type and PPT-type membrane devices may require stringent encapsulation, such as hermetic packaging with a near-vacuum environment. 
     Plate wave (also known as lamb wave) resonator devices are also known, such as described in U.S. Patent Application Publication No. 2010-0327995 A1 to Reinhardt et al. (“Reinhardt”). Compared to surface acoustic wave (SAW) devices, plate wave resonators may be fabricated atop silicon or other substrates and may be more easily integrated into radio frequency circuits. Reinhardt discloses a multi-frequency plate wave type resonator device including a silicon substrate, a stack of deposited layers (e.g., SiOC, SiN, SiO 2 , and Mo) constituting a Bragg mirror, a deposited AlN piezoelectric layer, and a SiN passivation layer. According to Reinhardt, at least one resonator includes a differentiation layer arranged to modify the coupling coefficient of the resonator so as to have a determined useful bandwidth. One limitation of Reinhardt&#39;s teaching is that deposition of AlN piezoelectric material (e.g., via epitaxy) over an underlying material having a very different lattice structure generally precludes formation of single crystal material; instead, lower quality material with some deviation from perfect orientation is typically produced. A further limitation is that Reinhardt&#39;s approach does not appear to be capable of producing resonators of widely different (e.g., octave difference) frequencies on a single substrate. Additionally, in at least certain contexts, it may be cumbersome to produce Bragg mirrors with consistently high reproducibility of layer thicknesses. 
     Accordingly, there is a need for guided wave devices that can be efficiently manufactured. Desirable devices would address thermal conduction and stringent packaging concerns associated with membrane-type devices. There is a further need to provide devices that may incorporate high quality piezoelectric materials. There is a still further need for devices that may enable production of widely different frequencies on a single substrate. 
     SUMMARY 
     The present disclosure provides a micro-electrical-mechanical system (MEMS) guided wave device that utilizes a single crystal piezoelectric layer and at least one guided wave confinement structure configured to confine a laterally excited wave in the single crystal piezoelectric layer. One or multiple guided wave confinement structures may be provided. One guided wave confinement structure may include a Bragg mirror separated from a single crystal piezoelectric layer by a slow wave propagation layer or a temperature compensation layer. Another guided wave confinement structure may include a fast wave propagation material. Single crystal piezoelectric materials (e.g., lithium niobate, lithium tantalate, and the like) may be incorporated in such devices, such as by pre-fabrication followed by bonding to at least one underlying layer of a guided wave device to form a bonded interface. Multiple electrodes arranged in or on the single crystal piezoelectric layer are configured for transduction of a lateral acoustic wave. 
     Embodiments incorporating fast wave propagation materials to provide guided wave confinement may benefit from ease of fabrication as compared to production of Bragg mirrors in certain contexts. One or more Bragg mirrors may be used in certain embodiments, such as may be useful to tailor wave reflection parameters, and as also may be useful in the context of confining very high velocity acoustic waves. Certain embodiments incorporate a fast wave propagation material on or adjacent to one (e.g., a first) surface of a piezoelectric material, and incorporate a Bragg mirror adjacent to another (e.g., a second) surface of the piezoelectric material. 
     Guided wave devices incorporating various electrode configurations disclosed herein include, but are not limited to, single layer coplanar interdigital transducers (IDTs) alone, multiple layer coplanar IDTs alone, IDTs in combination with continuous layer electrodes (e.g., useable as floating electrodes or shorting electrodes to enable launch of asymmetric waves), IDTs at least partially embedded in piezoelectric layers, non-coplanar IDTs, IDTs registered with single crystal piezoelectric layer segments, and periodically poled transducers (PPTs). In certain embodiments, electrodes may be partially embedded in, and/or gaps between various electrodes may be filled in whole or in part with, (i) piezoelectric material, or (ii) slow wave propagation material and/or temperature compensation material. The wavelength A of an acoustic wave transduced by an IDT equals two times the pitch or separation distance between adjacent electrodes (fingers) of opposite polarity, and the wavelength A also equals the separation distance between closest electrodes (fingers) of the same polarity. 
     In certain embodiments, MEMS guided wave devices employ single-sided confinement, in which at least one confinement structure is provided adjacent to a first surface of a single crystal piezoelectric layer, and in which a solid/air interface is provided adjacent to a second opposing surface of the single crystal piezoelectric layer. In other embodiments, MEMS guided wave devices employ double-sided confinement, in which first and second confinement structures are provided proximate to first and second opposing surfaces, respectively, of a single crystal piezoelectric layer. 
     In one aspect, a MEMS guided wave device includes multiple electrodes arranged in or on a single crystal piezoelectric layer and configured for transduction of a lateral acoustic wave in the single crystal piezoelectric layer. At least one guided wave confinement structure includes a Bragg mirror proximate to the piezoelectric layer, wherein the Bragg mirror is configured to confine a laterally excited wave in the single crystal piezoelectric layer, and the Bragg mirror is separated from the single crystal piezoelectric layer by a slow wave propagation layer. In certain embodiments, the Bragg mirror includes at least one group of at least one low impedance layer and at least one high impedance layer, and the at least one low impedance layer is sequentially arranged with the at least one high impedance layer in the at least one group. In certain embodiments, the laterally excited wave in the single crystal piezoelectric layer has a wavelength A, and each guided wave confinement structure of the at least one guided wave confinement structure comprises a thickness of less than 5λ. In certain embodiments, a bonded interface is provided between the single crystal piezoelectric layer and at least one underlying layer of the device (such as a guided wave confinement structure, or a slow wave propagation layer, or a substrate). 
     In certain embodiments, a single crystal piezoelectric layer includes a first surface and a second surface opposing the first surface, the at least one guided wave confinement structure includes a first guided wave confinement structure proximate to the first surface and includes a second guided wave confinement structure proximate to the second surface. In certain embodiments, a first guided wave confinement structure includes a first Bragg mirror, and a second guided wave confinement structure includes either a fast wave propagation material or a second Bragg mirror. In certain embodiments, first and second slow wave propagation layers may be provided, with a first slow wave propagation layer arranged between a first surface of the piezoelectric layer and a first guided wave confinement structure, and with a second slow wave propagation layer arranged between a second surface of the piezoelectric layer and a second guided wave confinement structure. In certain embodiments, at least one (or each) slow wave propagation layer includes a thickness that differs from a thickness of each layer of the at least one guided wave confinement structure. In certain embodiments, multiple electrodes are arranged in at least one slow wave propagation layer and in contact with the single crystal piezoelectric layer. In certain embodiments, a first IDT includes a first group of electrodes of a first polarity and a second group of electrodes of a second polarity opposing the first polarity. In certain embodiments, the second group of electrodes may be arranged in a plurality of recessed regions in the piezoelectric layer and are arranged non-coplanar with the first group of electrodes. In certain embodiments, at least one functional layer may be arranged to at least partially cover at least some electrodes. In certain embodiments, a first interdigital transducer (IDT) is arranged on or in (e.g., at least partially embedded in) a first surface of a piezoelectric layer, optionally in combination with a second IDT arranged on or in a second surface of the piezoelectric layer. In certain embodiments, multiple electrodes and a piezoelectric layer in combination embody a periodically poled transducer (PPT), with at least one slow wave propagation layer provided between the PPT and at least one guided wave confinement structure. 
     In another aspect, a MEMS guided wave device includes multiple electrodes arranged in or on a single crystal piezoelectric layer and configured for transduction of a lateral acoustic wave in the single crystal piezoelectric layer. At least one guided wave confinement structure arranged proximate to the single crystal piezoelectric layer confines a laterally excited wave having a wavelength A in the single crystal piezoelectric layer, wherein each guided wave confinement structure comprises a thickness of less than 5λ. The guided wave device includes at least one of the following features (i) and (ii): (i) the at least one guided wave confinement structure includes a fast wave propagation layer, or (ii) the at least one guided wave confinement structure includes a Bragg mirror, wherein the Bragg mirror is separated from the single crystal piezoelectric layer by a slow wave propagation layer. In certain embodiments, the guided wave device is devoid of contact between the electrodes and at least one (or each) guided wave confinement structure. In certain embodiments, spacing between a guided wave confinement structure and a single crystal piezoelectric layer may be provided with at least one slow wave propagation layer and/or a temperature compensation layer (wherein both utilities may optionally be provided by a single material in appropriate instances), wherein the layer providing such spacing may embody a thickness that differs from a thickness of each layer of the at least one guided wave confinement structure. A bonded interface is preferably arranged between the single crystal piezoelectric layer and at least one underlying layer (such as, but not limited to, (i) a guided wave confinement structure of the at least one guided wave confinement structure or (ii) an optionally provided slow wave propagation layer arranged between the single crystal piezoelectric layer and a guided wave confinement structure of the at least one guided wave confinement structure). 
     In another aspect, a single crystal piezoelectric layer of a MEMS guided wave device includes differing first and second thickness regions, a first group of electrodes arranged on or adjacent to the first thickness region and configured for transduction of a first lateral acoustic wave having a wavelength λ 1  in the first thickness region, and a second group of electrodes arranged on or adjacent to the second thickness region and configured for transduction of a second lateral acoustic wave having a wavelength λ 2  in the second thickness region, wherein λ 1  differs from λ 2 . The device further includes at least one guided wave confinement structure configured to confine the first lateral acoustic wave in the first thickness region, and configured to confine the second lateral acoustic wave in the second thickness region. In certain embodiments, the at least one guided wave confinement structure includes a fast wave propagation material. In certain embodiments, the at least one guided wave confinement structure includes a Bragg mirror with at least one group of at least one low impedance layer and at least one high impedance layer, wherein the at least one low impedance layer is sequentially arranged with the at least one high impedance layer in the at least one group. In certain embodiments, the Bragg mirror is separated from the single crystal piezoelectric layer by a temperature compensation layer. 
     In certain embodiments, the first and second groups of electrodes include first and second IDTs, and/or the first and second groups of electrodes are non-coplanar relative to one another. In certain embodiments, at least one temperature compensation layer is provided between the at least one guided wave confinement structure and at least a portion of the piezoelectric layer. Optionally, a temperature compensation layer may include a first temperature compensation layer thickness proximate to the first thickness region of the piezoelectric layer, and may include a second temperature compensation layer thickness proximate to the second thickness region of the piezoelectric layer. In certain embodiments, a temperature compensation layer may also embody a slow wave propagation material. 
     In certain embodiments, a MEMS guided wave device disclosed herein further includes a carrier substrate having a thickness of greater than 5 times the wavelength λ of a laterally excited wave confined in a single crystal piezoelectric layer, with at least one guided wave confinement structure arranged between the carrier substrate and the piezoelectric layer. In certain embodiments, a MEMS guided wave device is solidly mounted to a carrier substrate, or portions of a MEMS guided wave device may be suspended over a carrier substrate and separated by an intervening cavity. In other embodiments, a MEMS guided wave device as disclosed herein is devoid of a carrier substrate. 
     In another aspect, a MEMS guided wave device includes a segmented single crystal piezoelectric layer with multiple electrodes arranged therein or thereon and configured for transduction of a lateral acoustic wave having a wavelength A in the piezoelectric layer, with the multiple electrodes including a segmented layer of first electrodes. At least one guided wave confinement structure (preferably having a thickness of less than 5λ) is arranged proximate to the segmented piezoelectric layer and configured to confine the lateral acoustic wave in the segmented piezoelectric layer. Additionally, segments of the segmented single crystal piezoelectric layer are substantially registered (e.g., overlapping) with segments of the segmented layer of first electrodes. In certain embodiments, a second electrode (e.g., including a substantially continuous layer, or a discontinuous or segmented layer) is additionally provided, such as along a second surface of the piezoelectric layer that opposes a first surface of the piezoelectric layer in contact with the segmented layer of first electrodes. In certain embodiments, first and second guided wave confinement structures are provided, and gaps between segments of the segmented layer of first electrodes, as well as gaps between segments of the segmented single crystal piezoelectric layer, are filled with a slow wave propagation material and/or a temperature compensation material. In certain embodiments, a layer of slow wave propagation material and/or a temperature compensation material may be provided between (i) the segmented layer of first electrodes and (ii) at least one of the first guided wave confinement structure or the second guided wave confinement structure. 
     In another aspect, a method of fabricating a micro-electrical-mechanical system (MEMS) guided wave device including a single crystal piezoelectric material with different thickness regions is provided. A single crystal piezoelectric layer is locally thinned to define first and second thickness regions that differ in thickness. The locally thinned piezoelectric layer is bonded on or over an underlying layer (e.g., at least one of (i) a fast wave propagation layer; (ii) a Bragg mirror, or (iii) a substrate) to provide an internally bonded interface. Such bonding may be performed using wafer bonding techniques known in the art. First and second groups of electrodes are defined on or adjacent to the first thickness region and the second thickness region, respectively, for transduction of a first lateral acoustic wave having a first wavelength λ 1  in the first thickness region, and for transduction of a second lateral acoustic wave having a second wavelength λ 2  in the second thickness region. In certain embodiments, one or more surfaces of the piezoelectric layer are planarized prior to bonding (e.g., as a bonding preparation step), and/or planarized after bonding (e.g., to adjust thickness of the piezoelectric layer). In certain embodiments, a temperature compensation layer may be provided below the piezoelectric layer, with the temperature compensation layer optionally including a first temperature compensation layer thickness region and a second temperature compensation layer thickness region that differ from one another. In certain embodiments, a temperature compensation material is deposited on or over a surface of at least one of the first thickness region or the second thickness region. 
     In another aspect, any of the foregoing aspects, and/or various separate aspects and features as described herein, may be combined for additional advantage. Any of the various features and elements as disclosed herein may be combined with one or more other disclosed features and elements unless indicated to the contrary herein. 
     Those skilled in the art will appreciate the scope of the present invention and realize additional aspects thereof after reading the following detailed description in association with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings incorporated in and forming a part of this specification illustrate several aspects of the invention, and together with the description serve to explain the principles of the invention. 
         FIG.  1    is a perspective view of a MEMS guided wave device including an IDT and two reflector gratings arranged over a piezoelectric layer, an optional slow wave propagation layer, and a guided wave confinement structure according to one embodiment of the present disclosure. 
         FIG.  2    is a perspective view of a MEMS guided wave device including an IDT arranged over portions of a piezoelectric layer and a guided wave confinement structure suspended between anchors according to one embodiment of the present disclosure. 
         FIG.  3    is a perspective view of a MEMS guided wave device including an IDT arranged over portions of a piezoelectric layer and a guided wave confinement structure suspended by narrow mechanical supports between anchors according to one embodiment of the present disclosure. 
         FIG.  4    is a side cross-sectional view of a MEMS guided wave device including top side electrodes in the form of an IDT arranged over a piezoelectric layer, a slow wave propagation layer, a fast wave propagation layer serving as a one-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  5    is a side cross-sectional view of a MEMS guided wave device including top side electrodes in the form of an IDT arranged over a piezoelectric layer, a slow wave propagation layer, a Bragg mirror serving as a one-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  6    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT arranged on only one face of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second fast wave propagation layers according to one embodiment of the present disclosure. 
         FIG.  7    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT arranged on one face of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second Bragg mirrors according to one embodiment of the present disclosure. 
         FIG.  8    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of first and second IDTs arranged on first and second faces of a piezoelectric layer, respectively, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second fast wave propagation layers according to one embodiment of the present disclosure. 
         FIG.  9    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of first and second IDTs arranged on first and second faces of a piezoelectric layer, respectively, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second Bragg mirrors according to one embodiment of the present disclosure. 
         FIG.  10    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT arranged on only one face of a piezoelectric layer within a slow wave propagation layer, and with one-sided guided wave confinement provided by a fast wave propagation layer according to one embodiment of the present disclosure. 
         FIG.  11    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT arranged on only one face of a piezoelectric layer within a slow wave propagation layer, and with one-sided guided wave confinement provided by a Bragg mirror according to one embodiment of the present disclosure. 
         FIG.  12    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in and extending through the entire thickness of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second fast wave propagation layers according to one embodiment of the present disclosure. 
         FIG.  13    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in and extending through the entire thickness of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, and two-sided guided wave confinement provided by first and second Bragg mirrors according to one embodiment of the present disclosure. 
         FIG.  14    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in a single face of a piezoelectric layer, with a slow wave propagation layer contacting the electrodes and the piezoelectric layer, and one-sided guided wave confinement provided by a fast wave propagation layer according to one embodiment of the present disclosure. 
         FIG.  15    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in a single face of a piezoelectric layer, with a slow wave propagation layer contacting the electrodes and the piezoelectric layer, and one-sided guided wave confinement provided by a Bragg mirror according to one embodiment of the present disclosure. 
         FIG.  16    is a side cross-sectional view of a MEMS guided wave device including a periodically poled transducer (PPT) having electrode layers sandwiching a piezoelectric layer with alternating polarity regions, and further including a slow wave propagation layer, a fast wave propagation layer serving as a one-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  17    is a side cross-sectional view of a MEMS guided wave device including a PPT having electrode layers sandwiching a piezoelectric layer with alternating polarity regions, and further including a slow wave propagation layer, a Bragg mirror serving as a one-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  18    is a side cross-sectional view of a MEMS guided wave device including a PPT having electrode layers sandwiching a piezoelectric layer with alternating polarity regions, and further including slow wave propagation layers sandwiching the PPT, first and second fast wave propagation layers serving as a two-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  19    is a side cross-sectional view of a MEMS guided wave device including a PPT having electrode layers sandwiching a piezoelectric layer with alternating polarity regions, and further including slow wave propagation layers sandwiching the PPT, first and second Bragg mirrors serving as a two-sided guided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  20    is a side cross-sectional view of a MEMS guided wave device including a segmented piezoelectric layer arranged between a continuous electrode and a segmented electrode registered with the piezoelectric layer, with the device including a slow wave propagation layer, a fast wave propagation layer serving as a one-sided wave confinement structure, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  21    is a side cross-sectional view of a MEMS guided wave device including a segmented piezoelectric layer arranged between a continuous electrode and a segmented electrode registered with the piezoelectric layer, with the device including a slow wave propagation layer, including a Bragg mirror serving as a one-sided wave confinement structure, and including a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  22    is a side cross-sectional view of a MEMS guided wave device including a segmented piezoelectric layer arranged between a continuous electrode and a segmented electrode registered with the piezoelectric layer, with the device including slow wave propagation material (i) between the segmented piezoelectric layer and the segmented electrode, and (ii) sandwiching the electrodes, including fast wave propagation layers serving as a two-sided wave confinement structure, and including a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  23    is a side cross-sectional view of a MEMS guided wave device including a segmented piezoelectric layer arranged between a continuous electrode and a segmented electrode registered with the piezoelectric layer, with the device including slow wave propagation material (i) between the segmented piezoelectric layer and the segmented electrode, and (ii) sandwiching the electrodes, including Bragg mirrors serving as a two-sided wave confinement structure, and including a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  24    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in and extending through the entire thickness of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, with two-sided guided wave confinement provided by a fast wave propagation layer arranged below the piezoelectric layer and a Bragg mirror arranged above the piezoelectric layer, and with a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  25    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT embedded in and extending through the entire thickness of a piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, with two-sided guided wave confinement provided by a Bragg mirror arranged below the piezoelectric layer and a fast wave propagation layer arranged above the piezoelectric layer, and with a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  26    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT with certain electrodes deposited in recesses defined in a piezoelectric layer and other electrodes deposited atop the piezoelectric layer, with the device further including a slow wave propagation layer, one-sided guided wave confinement provided by a fast wave propagation layer, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  27    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT with certain electrodes deposited in recesses defined in a piezoelectric layer and other electrodes deposited atop the piezoelectric layer, with the device further including a slow wave propagation layer, one-sided guided wave confinement provided by a Bragg mirror, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  28    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT with certain electrodes deposited in recesses defined in a piezoelectric layer and other electrodes deposited atop the piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, with two-sided guided wave confinement provided by fast wave propagation layers arranged above and below the slow wave propagation layers, and with a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  29    is a side cross-sectional view of a MEMS guided wave device including electrodes in the form of an IDT with certain electrodes deposited in recesses defined in a piezoelectric layer and other electrodes deposited atop the piezoelectric layer, with slow wave propagation layers sandwiching the electrodes and the piezoelectric layer, with two-sided guided wave confinement provided by Bragg mirrors arranged above and below the slow wave propagation layers, and with a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  30    is a side cross-sectional view of subassemblies of a MEMS guided wave device during fabrication, following local thinning of a piezoelectric layer to define first and second thickness regions with a thinner region filled with a temperature compensation material, and prior to wafer bonding of the piezoelectric layer to a subassembly including a temperature compensation layer arranged over a fast wave propagation layer and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  31    is a side cross-sectional view of a MEMS guided wave device produced with the subassemblies illustrated in  FIG.  30   , following wafer bonding, planarization/thinning of an outer surface of the piezoelectric layer, and deposition of substantially coplanar first and second groups of electrodes over first and second thickness regions, respectively, of the piezoelectric layer, according to one embodiment of the present disclosure. 
         FIG.  32    is a side cross-sectional view of subassemblies of a MEMS guided wave device during fabrication, following local thinning of a piezoelectric layer to define first and second thickness regions with a thinner region filled with a temperature compensation material, and prior to wafer bonding of the piezoelectric layer to a subassembly including a temperature compensation layer arranged over a Bragg mirror and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  33    is a side cross-sectional view of a MEMS guided wave device produced with the subassemblies illustrated in  FIG.  32   , following wafer bonding, planarization/thinning of an outer surface of the piezoelectric layer, and deposition of substantially coplanar first and second groups of electrodes over first and second thickness regions, respectively, of the piezoelectric layer, according to one embodiment of the present disclosure 
         FIG.  34    is a side cross-sectional view of a MEMS guided wave device including substantially coplanar first and second groups of electrodes arranged over first and second thickness regions, respectively, of a piezoelectric layer, which is arranged over a temperature compensation layer having first and second temperature compensation layer thicknesses underlying the first and second thickness regions of the piezoelectric layer, respectively, which is arranged over a fast wave propagation layer having first and second fast wave propagation layer thicknesses underlying the first and second temperature compensation layer thickness regions and providing guided wave confinement utility, and which is arranged over a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  35    is a side cross-sectional view of a MEMS guided wave device including non-coplanar first and second groups of electrodes arranged over non-coplanar upper surfaces bounding first and second thickness regions, respectively, of a piezoelectric layer, which is arranged over a temperature compensation layer, a fast wave propagation layer providing one-sided guided wave confinement utility, and a carrier substrate according to one embodiment of the present disclosure. 
         FIG.  36    is a side cross-sectional view of a MEMS guided wave device including non-coplanar first and second groups of electrodes arranged over non-coplanar upper surfaces bounding first and second thickness regions, respectively, of a piezoelectric layer, which is arranged over a temperature compensation layer, a Bragg mirror providing one-sided guided wave confinement utility, and a carrier substrate according to one embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments set forth below represent the necessary information to enable those skilled in the art to practice the invention and illustrate the best mode of practicing the invention. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the invention and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present disclosure. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     Relative terms such as “below” or “above” or “upper” or “lower” or “horizontal” or “vertical” may be used herein to describe a relationship of one element, layer, or region to another element, layer, or region as illustrated in the Figures. It will be understood that these terms and those discussed above are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including” when used herein specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the terms “proximate” and “adjacent” as applied to a specified layer or element refers to a state of being close or near to an other layer or element, and encompass the possible presence of one or more intervening layers or elements without necessarily requiring the specified layer or element to be directly on or directly in contact with the other layer or element unless specified to the contrary herein. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     The present disclosure relates in one aspect to a micro-electrical-mechanical system (MEMS) guided wave device that utilizes a single crystal piezoelectric layer and at least one guided wave confinement structure (e.g., a fast wave propagation layer or a Bragg mirror) configured to confine a laterally excited wave in the single crystal piezoelectric layer. Such confinement may significantly reduce or avoid dissipation of acoustic radiation in a substrate or other carrier structure. The MEMS guided wave device may have dominant lateral vibrations. The single crystal piezoelectric layer may include lithium tantalate or lithium niobate, and may provide vibrating structures with precise sizes and shapes, which may provide high accuracy, and (in at least certain embodiments) may enable fabrication of multiple resonators having different resonant frequencies on a single substrate. 
     Vibrating structures of preferred MEMS guided wave devices described herein are formed of single crystal piezoelectric material and use mechanically efficient MEMS construction. Such vibrating structures may be high-Q, low loss, stable, at a low temperature coefficient of frequency, have a high electromechanical coupling efficient, have high repeatability, and have a low motional impedance. In certain embodiments, a nonstandard (e.g., offcut) crystalline orientation of the single crystal piezoelectric material may be used to provide specific vibrational characteristics, such as a low temperature coefficient of frequency, a high electromechanical coupling coefficient, or both. Since it is extremely difficult to grow single crystal piezoelectric material (e.g., via epitaxy) over non-lattice-matched materials, in preferred embodiments, single crystal piezoelectric materials are pre-fabricated (e.g., by growth of a boule followed by formation of thin wafers), surface finished (e.g., via chemical mechanical planarization (CMP) and polishing to provide near-atomic flatness), and bonded to one or more underlying layers—such as may include a guided wave confinement structure that is optionally overlaid with a layer providing slow wave propagation and/or temperature compensation utility, and that is optionally supported by a carrier substrate. Any suitable wafer bonding technique known in the art may be used, such as may rely on van der Waals bonds, hydrogen bonds, covalent bond, and/or mechanical interlocking. In certain embodiments, direct bonding may be used. In certain embodiments, bonding may include one or more surface activation steps (e.g., plasma treatment, chemical treatment, and/or other treatment methods) followed by application of heat and/or pressure, optionally followed by one or more annealing steps. Such bonding results in formation of a bonded interface between the piezoelectric layer and at least one underlying layer. In certain embodiments, the bonded interface may include at least one intervening layer arranged on at least a portion of (or the entirety of) a surface of the piezoelectric layer. Suitable electrodes may be defined in or on the piezoelectric layer for transduction of at least one lateral acoustic wave therein. One or more additional layers (e.g., one or more layers providing additional (two-sided) guided wave confinement utility, and one or more layers providing slow wave propagation utility) may be further provided over the piezoelectric layer. 
     In certain embodiments, a composite including a single crystal piezoelectric layer, at least one guided wave confinement structure, and electrodes (optionally in combination with one or more additional layers providing slow wave propagation and/or temperature compensation utility as disclosed herein) is solidly mounted to a carrier substrate. In other embodiments, at least a portion of such a composite may be suspended above a carrier substrate with a gap arranged therebetween. According to preferred embodiments, no portion of a piezoelectric layer is suspended on its own in the absence of at least one additional layer as described herein. In this regard, the present disclosure relates to plate-type or quasi-plate-type guided wave devices suitable for lateral wave propagation, as opposed to membrane-type devices. In certain embodiments, devices described herein may be used for propagation of quasi-shear horizontal waves, quasi-longitudinal waves, and/or thickness-extensional (FBAR-type) waves. 
     The terms “fast wave propagation material” or “fast wave propagation layer” refers to a material or layer in which an acoustic wave of interest travels more quickly than in a proximate piezoelectric layer in which the acoustic wave is transduced. Similarly, the terms “slow wave propagation material” or “slow wave propagation layer” refers to a material or layer in which an acoustic wave of interest travels more slowly than in a proximate piezoelectric layer in which the acoustic wave is transduced. Examples of fast wave propagation materials that may be used according to certain embodiments include (but are not limited to) diamond, sapphire, aluminum nitride, silicon carbide, boron nitride, and silicon. An example of a slow wave propagation material that may be used according to certain embodiments includes (but is not limited to) silicon dioxide. 
     Certain embodiments disclosed herein utilize acoustic Bragg mirrors (also known as Bragg reflectors). A Bragg mirror includes at least one group of at least one low impedance layer (e.g., silicon dioxide) and at least one high impedance layer (e.g., tungsten or hafnium dioxide), wherein the at least one low impedance layer is sequentially arranged with the at least one high impedance layer in the at least one group. The number of groups of alternating impedance layers used in a Bragg mirror depends on the total reflection coefficient required. 
     Single crystal piezoelectric layers as disclosed herein preferably include a thickness of no greater than 2 times the wavelength A (more preferably no greater than 1 times the wavelength, or no greater than 0.5 times the wavelength) of a lateral acoustic wave transduced in the piezoelectric layer. As disclosed herein, a guided wave confinement structure arranged proximate to a single crystal piezoelectric layer preferably includes a thickness of less than 5λ (e.g., within a range of 1λ to 5λ). (Within a Bragg mirror, each layer may include a thickness on the order of roughly 0.25λ to 0.5λ.) If provided, any optional slow wave propagation layers may have individual thicknesses in a range of up to about 1λ, and may preferably be less than about 0.5λ or less than about 0.25λ. In certain embodiments, each slow wave propagation layer may have a thickness of less than a thickness of an adjacent single crystal piezoelectric layer. This preferred guided wave confinement structure thickness is to be contrasted with a carrier substrate that may be provided according to certain embodiments, wherein such a carrier substrate preferably includes a thickness of greater than 5λ (or five times the greatest wavelength in embodiments in which multiple resonators of different frequencies are provided in a single guided wave device). In alternative embodiments applicable to any structures described herein, however, a fast layer may have a thickness of greater than 5λ, and may embody a substrate of any necessary or desired thickness. When provided, at least one functional layer (e.g., providing slow wave propagation and/or thermal compensation utility) may desirably have a thickness of no greater than 2λ, and/or a thickness that differs from a thickness of each layer of the at least one guided wave confinement structure. 
     Although lithium niobate and lithium tantalate are particularly preferred piezoelectric materials, in certain embodiments any suitable piezoelectric materials may be used, such as quartz, a piezoceramic, or a deposited piezoelectric material (such as aluminum nitride or zinc oxide). 
     Guided wave devices as disclosed herein may incorporate various combinations of electrode configurations and guided wave confinement structure configurations as illustrated in the drawings and described herein. In certain embodiments, electrodes are arranged symmetrically relative to a center thickness of a piezoelectric layer (e.g., arranged both above and below the piezoelectric layer, or embedded along a plane equidistant between upper and lower surfaces of the piezoelectric layer) for symmetric guided wave excitation. In other embodiments, electrodes are asymmetrically arranged relative to a center thickness of a piezoelectric layer for asymmetric guided wave excitation. In certain embodiments, MEMS guided wave devices as disclosed herein may employ single-sided confinement, in which at least one confinement structure is provided adjacent to a first surface of a single crystal piezoelectric layer, and in which a solid/air interface is provided adjacent to a second opposing surface of the single crystal piezoelectric layer. Single sided confinement may be employed in combination with symmetric or asymmetric excitation. In other embodiments, MEMS guided wave devices as disclosed herein may employ double- or two-sided confinement, in which first and second confinement structures are provided proximate to first and second opposing surfaces, respectively, of a single crystal piezoelectric layer. In certain embodiments, a first guided wave confinement structure is proximate to a first surface of a piezoelectric layer, and a second guided wave confinement structure is proximate to a second surface of the piezoelectric layer. Two-sided confinement may be employed in combination with symmetric or asymmetric excitation. Electrode configurations that may be employed according to certain embodiments include, but are not limited to, single layer coplanar interdigital transducers (IDTs) alone, multiple layer coplanar IDTs alone, IDTs in combination with electrodes along a second surface of a piezoelectric layer (e.g., continuous layer electrodes useable as floating or shorting electrodes, or segmented or discontinuous electrodes), IDTs at least partially embedded in piezoelectric layers, non-coplanar IDTs, IDTs registered with single crystal piezoelectric layer segments, and periodically poled transducers (PPTs). In certain embodiments, electrodes may be partially embedded in, and/or gaps between various electrodes may be filled in whole or in part with, (i) piezoelectric material, or (ii) slow wave propagation material and/or temperature compensation material. 
     For each embodiment involving two-sided confinement disclosed herein, alternative embodiments omitting the second (top) side confinement structure are specifically contemplated. 
     Material that has the potential to become piezoelectric may have a crystalline structure with randomly oriented dipoles. The material becomes piezoelectric by substantially aligning the dipoles to form domains having a substantially uniform dipole orientation, which may be created by poling. Poling may include applying a strong poling electric field to a region of the material to substantially force the dipoles into alignment. When the electric field is removed, much of the alignment remains, thereby providing the piezoelectric properties of the poled material, which is called piezoelectric material. In certain instances, a first set of domains have a nominal domain orientation, and a second set of domains may have an inverted domain (e.g., translated about 180 degrees from the nominal domain). Nominal and inverted domains may be alternately arranged within a periodically poled piezoelectric layer. When such a layer is arranged between first and second electrode layers, the result is a periodically poled transducer. 
     An interdigital transducer includes electrodes with a first conducting section and a second conducting section that are inter-digitally dispersed in or on a surface or layer. IDTs are well known in the art. 
     In certain embodiments, at least one functional layer is arranged to at least partially cover at least some electrodes of a plurality of electrodes. In certain embodiments, at least one functional layer covers one group of electrodes, but does not cover another group of electrodes. A functional layer may modify velocity of a transduced acoustic wave and/or alter temperature compensation properties of a MEMS guided wave device. In certain embodiments, at least one functional layer includes a temperature compensation material or a slow wave propagation material. 
     Although various embodiments disclosed herein include single resonators, it is to be appreciated that any suitable combinations of single or multiple resonators and/or reflector gratings in series and/or in parallel (such as may be embodied in one or more filters) may be provided in a single MEMS guided wave device. In certain embodiments, multiple resonators and/or filters arranged for transduction of acoustic waves of different wavelengths may be provided in a single MEMS guided wave device. 
       FIG.  1    illustrates a MEMS guided wave device  10  according to one embodiment of the present disclosure. The device  10  includes a single crystal piezoelectric layer  12  (such as lithium niobate or lithium tantalate) on which an IDT  18  and two reflector gratings  20  are provided. The single crystal piezoelectric layer  12  is arranged over a guided wave confinement structure  16 , with an optional slow wave propagation layer  14  arranged therebetween. Although not illustrated, an optional carrier substrate may be provided below the guided wave confinement structure  16  in certain embodiments. Both the IDT  18  and the reflector gratings  20  include a number of fingers  24  that are connected to respective bus bars  22 . For the reflector gratings  20 , all fingers  24  connect to each bus bar  22 . For the IDT  18 , alternating fingers  24  connect to different bus bars  22 , as depicted. Notably, actual reflector gratings  20  and IDTs  18  generally include much larger numbers of fingers  24  than illustrated. The number of fingers  24  has been reduced in  FIG.  1    and various accompanying drawings to promote drawing clarity and for ease of explaining the disclosure. 
     The fingers  24  are parallel to one another and aligned in an acoustic region that encompasses the area in which the reflector gratings  20  and the IDT  18  reside. The wave or waves generated when the IDT  18  is excited with electrical signals essentially reside in this acoustic region. Acoustic waves essentially travel perpendicular to the length of the fingers  24 . The guided wave confinement structure  16 , which may include a fast wave propagation layer or a Bragg mirror, serves to confine the wave or waves in the single crystal piezoelectric layer  12 . 
     The operating frequency of the MEMS guided wave device  10  is a function of the pitch (P) representing the spacing between fingers  24  of the IDT  18 , wherein the wavelength λ equals two times the pitch P. Lateral mode devices also have preferred thickness ranges for the piezoelectric layer  12  for efficient excitation of lateral waves. 
     To manufacture the MEMS guided wave device  10 , a single crystal piezoelectric wafer may be prefabricated, and separately the slow wave propagation layer  14  may be deposited on the guided wave confinement structure  16  (which may optionally be supported by a carrier substrate). Adjacent surfaces of the piezoelectric wafer and the slow wave propagation layer  14  are planarized and polished, and then attached to one another via a conventional direct bonding (e.g., wafer bonding) process or other process. One or more bonding promoting layers may optionally be arranged between the respective layers to be bonded. Following bonding, the exposed upper surface of the piezoelectric layer  12  is ground (optionally also planarized) to a desired thickness, and the reflector gratings  20  and the IDT  18  are deposited thereon. 
     In certain embodiments, the slow wave propagation layer  14  may provide thermal compensation utility. The materials used to form the single crystal piezoelectric wafer typically have different thermal coefficients of expansion (TCE) relative to the TCE of materials of the guided wave confinement structure  16 . Once the guided wave confinement structure  16  is created, the piezoelectric layer  12  and the slow wave propagation layer  14  tend to expand and contract in a similar manner as temperature changes. As such, the expansion and contraction forces applied to the guided wave confinement structure  16  by the piezoelectric layer  12  due to temperature changes are substantially countered by opposing forces applied by the intermediately arranged slow wave propagation layer  14 . As a result, the composite structure including the intermediately arranged slow wave propagation layer  14  resists bending or warping as temperature changes, thereby reducing expansion and contraction of the piezoelectric layer  12 , and reducing the effective TCE of the piezoelectric layer  12 . 
     Since providing the slow wave propagation layer  14  between the piezoelectric layer  12  and the guided wave confinement structure  16  reduces the effective TCE of the piezoelectric material, the amount of expansion and contraction along the surface of the piezoelectric layer  12  as temperature changes is reduced. Therefore, the change in spacing, or pitch, between fingers  24  of the IDT  18  and the reflector gratings  20  as temperature changes is reduced, thereby reducing the effective thermal coefficient of frequency (TCF) of the piezoelectric layer  12  to improve overall frequency response of the IDT  18  and the reflector gratings  20  with changes in temperature. 
     A MEMS guided wave structure  10  as illustrated in  FIG.  1    may be solidly mounted to a carrier substrate, or alternatively at least a portion of such a structure may be suspended above a carrier substrate with a gap arranged therebetween. 
       FIG.  2    illustrates a MEMS guided wave device  30  including an IDT  18  arranged over portions of a single crystal piezoelectric layer  12  and a guided wave confinement structure  16  in combination that are elevated above a substrate  28  and suspended between anchors  32 ,  34  according to one embodiment of the present disclosure. A conductive layer  36  is arranged on the piezoelectric layer  12  to form the IDT  18  including electrodes, providing a first conductive section  38  and a second conductive section  40 . The single crystal piezoelectric layer  12  is arranged over the guided wave confinement structure  16 , supported along peripheral portions thereof from below by an insulating layer  26  located over the substrate  28 . A central portion of the insulating layer  26  may be removed by etching (e.g., using vias or other openings (not shown) defined through the substrate  28  or the piezoelectric layer  12  and guided wave confinement structure  16 ), leaving anchors  32 ,  34  laterally bounding a central cavity. The central portions of the guided wave confinement structure  16  and the overlying piezoelectric layer  12  (both in substantially continuous form), together with the IDT  18 , are suspended between the anchors  32 ,  34 . Although not shown, in certain embodiments the MEMS guided wave device  30  may further include a slow wave propagation layer between the single crystal piezoelectric layer  12  and the guided wave confinement structure  16 , which may provide temperature compensation utility. 
       FIG.  3    illustrates a MEMS guided wave device  42  including an IDT  18  arranged over portions of a single crystal piezoelectric layer  12  and a guided wave confinement structure  16  in combination that are elevated above a substrate  28  and suspended by narrowed mechanical supports  44 ,  46  between anchors  32 ,  34  according to one embodiment of the present disclosure. A conductive layer  36  is arranged on the piezoelectric layer  12  to form the IDT  18 , including electrodes providing a first conductive section  38  and a second conductive section  40 . The single crystal piezoelectric layer  12  is arranged over the guided wave confinement structure  16 , supported along peripheral portions thereof from below by an insulating layer  26  located over the substrate  28 . Portions of the insulating layer  26  may be removed by etching, leaving anchors  32 ,  34  laterally bounding a central cavity. Additionally, portions of the single crystal piezoelectric layer  12  and the guided wave confinement structure  16  are removed to leave only the narrowed mechanical supports  44 ,  46  to support central portions of the piezoelectric layer  12  and the guided wave confinement structure  16  (as well as the IDT  18 ) between the anchors  32 ,  34 . Although not shown, in certain embodiments the MEMS guided wave device  42  may further include a slow wave propagation layer between the single crystal piezoelectric layer  12  and the guided wave confinement structure  16 , which may provide temperature compensation utility. 
     Additional MEMS guided wave devices including further electrode configurations and guided wave confinement structure configurations are illustrated in the following figures. Although the following figures illustrate single crystal piezoelectric layers and guided wave confinement structures appearing to be solidly mounted to carrier substrates, it is to be appreciated that in each instance the illustrated single crystal piezoelectric layers and guided wave confinement structures (together with accompanying electrodes) may be devoid of a substrate or suspended above a carrier substrate (such as shown in  FIGS.  2 - 3   ). 
       FIG.  4    illustrates a MEMS guided wave device including alternating top side electrodes  38 ,  40  in the form of an IDT arranged over a single crystal piezoelectric layer  12 , an optional slow wave propagation layer  14 , a fast wave propagation layer serving as a one-sided guided wave confinement structure  16 , and an optional carrier substrate  28  according to one embodiment of the present disclosure. The electrodes  38 ,  40  are disposed solely on a top surface of the piezoelectric layer  12  and are therefore asymmetrically arranged relative to a center of the piezoelectric layer  12 . The guided wave confinement structure  16  and optional slow wave propagation layer  14  may be deposited over the substrate  28 . The MEMS guided wave device may be formed by bonding a prefabricated single crystal piezoelectric wafer over the guided wave confinement structure  16  (e.g., with the slow wave propagation layer  14  therebetween), processing an exposed surface of the piezoelectric wafer to a desired thickness to yield the piezoelectric layer  12 , and depositing the electrodes  38 ,  40  thereon. 
       FIG.  5    illustrates a MEMS guided wave device including alternating top side electrodes  38 ,  40  in the form of an IDT arranged over a single crystal piezoelectric layer  12 , an optional slow wave propagation layer  14 , a Bragg mirror serving as a one-sided guided wave confinement structure  16 , and an optional carrier substrate  28  according to one embodiment of the present disclosure. The device of  FIG.  5    may be fabricated in a manner similar to the device of  FIG.  4   . 
       FIG.  6    illustrates a MEMS guided wave device including alternating electrodes  38 ,  40  in the form of an IDT arranged over one surface of a single crystal piezoelectric layer  12  according to one embodiment of the present disclosure. Optional slow wave propagation layers  14 A,  14 B sandwich the electrodes  38 ,  40  and the piezoelectric layer  12 . A portion of the upper slow wave propagation layer  14 B is arranged to at least partially (and preferably completely) fill gaps  48  between the electrodes  38 ,  40 . Two-sided guided wave confinement is provided by first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B that sandwich the slow wave propagation layers  14 A,  14 B. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrodes  38 ,  40  are disposed solely on one surface of the piezoelectric layer  12  and are therefore asymmetrically arranged relative to a center of the piezoelectric layer  12 . A lower portion of the device of  FIG.  6    may be fabricated in a manner similar to the MEMS guided wave device of  FIG.  4   . After formation of the electrodes  38 ,  40 , the optional second slow wave propagation layer  14 B is deposited over the piezoelectric layer  12  and the electrodes  38 ,  40 , and the second guided wave confinement structure  16 B is deposited over the second slow wave propagation layer  14 B. 
       FIG.  7    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  6   , except that first and second Bragg mirrors are used instead of first and second fast wave propagation layers  16 A,  16 B. Fabrication of the device of  FIG.  7    is substantially similar to fabrication of the device of  FIG.  6   . Although  FIGS.  6  and  7    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure may be omitted. 
       FIG.  8    illustrates a MEMS guided wave device including alternating electrodes  38 A,  40 A in the form of a first IDT arranged on the lower surface of a single crystal piezoelectric layer  12  and alternating top side electrodes  38 B,  40 B in the form of a second IDT arranged on the upper surface of the piezoelectric layer  12 , according to one embodiment of the present disclosure. Optional slow wave propagation layers  14 A,  14 B sandwich the electrodes  38 A,  40 A,  38 B,  40 B and the piezoelectric layer  12 , with portions of the slow wave propagation layers  14 A,  14 B being arranged to at least partially (and preferably completely) fill gaps  48 A,  48 B between the electrodes  38 A,  40 A,  38 B,  40 B. The electrodes  38 A,  40 A,  38 B,  40 B are symmetrically arranged relative to a center of the piezoelectric layer  12 . Two-sided guided wave confinement is provided by first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B that sandwich the slow wave propagation layers  14 A,  14 B. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. To fabricate the MEMS guided wave device of  FIG.  8   , a lower subassembly including the substrate  28 , the first guided wave confinement structure  16 A, and the first slow wave propagation layer  14 A is produced. Recesses may be defined (e.g., via etching) in an upper surface of the first slow wave propagation layer  14 A, and metal may be deposited in the recesses to form the lower electrodes  38 A,  40 A. Following planarization and polishing of the first slow wave propagation layer  14 A and lower electrodes  38 A,  40 A, a prefabricated single crystal piezoelectric wafer may be directly bonded to the lower subassembly and processed (e.g., via grinding and polishing) to a desired thickness to form the piezoelectric layer  12 . Thereafter, the upper electrodes  38 B,  40 B may be deposited on the piezoelectric layer  12 , followed by deposition of the second slow wave propagation layer  14 B and the second guided wave confinement structure  16 B. 
       FIG.  9    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  8   , except that first and second Bragg mirrors are used instead of first and second fast wave propagation layers as the first and second guided wave confinement structures  16 A,  16 B. Fabrication of the device of  FIG.  9    is substantially similar to fabrication of the device of  FIG.  8   . Although  FIGS.  8  and  9    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure  16 B may be omitted, optionally in combination with omission of the second slow wave propagation layer  14 B. 
     Although  FIGS.  8  and  9    illustrate two IDTs in phase (wherein electrodes of corresponding types (e.g.,  38 A,  38 B or  40 A,  40 B) are aligned with one another on opposite faces of the piezoelectric layer  12 , such that positive overlies positive and negative overlies negative), in alternate embodiments, IDTs may be arranged out of phase, with electrodes of opposing types (e.g.,  38 A,  40 B or  40 A,  38 B) being aligned with one another on opposite faces of the piezoelectric layer  12 , such that positive overlies negative, and vice-versa. This modification may be applied to any embodiments disclosed herein in which multiple IDTs are arranged on or adjacent to opposing faces of a piezoelectric layer. 
       FIG.  10    illustrates a MEMS guided wave device including alternating electrodes  38 ,  40  in the form of an IDT arranged on the lower surface of a single crystal piezoelectric layer  12  according to one embodiment of the present disclosure. An optional slow wave propagation layer  14 , a fast wave propagation layer serving as a one-sided guided wave confinement structure  16 , and an optional carrier substrate  28  are arranged under the electrodes  38 ,  40  and the piezoelectric layer  12 . The electrodes  38 ,  40  are disposed solely on a bottom surface of the piezoelectric layer  12  and are therefore asymmetrically arranged relative to a center of the piezoelectric layer  12 . The guided wave confinement structure  16  and optional slow wave propagation layer  14  may be deposited over the substrate  28 . A portion of the slow wave propagation layer  14  is arranged to at least partially (and preferably completely) fill gaps  48  between the electrodes  38 ,  40 . To fabricate the MEMS guided wave device of  FIG.  10   , a lower subassembly including the substrate  28 , the guided wave confinement structure  16 , and the slow wave propagation layer  14  is produced. Recesses may be defined (e.g., via etching) in an upper surface of the slow wave propagation layer  14 , and metal may be deposited in the recesses to form the electrodes  38 ,  40 . Following planarization and polishing of the slow wave propagation layer  14  and the electrodes  38 ,  40 , a prefabricated single crystal piezoelectric wafer may be directly bonded to the lower subassembly and processed (e.g., via grinding and polishing) to a desired thickness to form the piezoelectric layer  12 . Alternatively, the electrodes  38 ,  40  may be patterned on the single crystal piezoelectric wafer, the slow wave propagation layer  14  may be deposited over the electrodes, and after planarizing the slow wave propagation layer  14  is may be bonded to the substrate  28 . 
       FIG.  11    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  10   , except that a Bragg mirror is used instead of a fast wave propagation layer as a guided wave confinement structure  16 . Fabrication of the device of  FIG.  11    is substantially similar to fabrication of the device of  FIG.  10   . 
       FIG.  12    illustrates a MEMS guided wave device including electrodes  38 ,  40  in the form of an IDT embedded in and extending through the entire thickness of a piezoelectric layer  12 , with slow wave propagation layers  14 A,  14 B sandwiching the electrodes  38 ,  40  and the piezoelectric layer  12 . Two sided guided wave confinement is provided by first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B that sandwich the slow wave propagation layers  14 A,  14 B. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrodes  38 ,  40  are symmetrically arranged relative to a center thickness of the piezoelectric layer  12 . To fabricate the MEMS guided wave device of  FIG.  12   , a lower subassembly including the substrate  28 , the first guided wave confinement structure  16 A, and the first slow wave propagation layer  14 A is produced. Following planarization and polishing of the first slow wave propagation layer  14 A, a prefabricated single crystal piezoelectric wafer may be directly bonded to the lower subassembly. Thereafter, apertures or recesses may be defined in the piezoelectric wafer by any suitable technique, such as ion milling, and metal may be deposited (e.g., via evaporative deposition) in the apertures or recesses to form electrodes  38 ,  40 . The piezoelectric wafer and deposited electrodes may then be processed (e.g., via grinding and polishing) to a desired thickness that exposes the electrodes  38 ,  40  to form a piezoelectric layer  12  with electrodes  38 ,  40  extending through the entire thickness thereof. Thereafter, the second slow wave propagation layer  14 B and the second guided wave confinement structure  16 B may be sequentially deposited over the piezoelectric layer  12 . 
       FIG.  13    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  12   , except that first and second Bragg mirrors are used instead of first and second fast wave propagation layers as the first and second guided wave confinement structures  16 A,  16 B. Fabrication of the device of  FIG.  13    is substantially similar to fabrication of the device of  FIG.  12   . Although  FIGS.  12  and  13    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure  16 B may be omitted, optionally in combination with omission of the second slow wave propagation layer  14 B. 
       FIG.  14    illustrates a MEMS guided wave device including electrodes  38 ,  40  in the form of an IDT embedded in a lower face of a single crystal piezoelectric layer  12 , with an optional slow wave propagation layer  14  contacting the electrodes  38 ,  40  and the piezoelectric layer  12 , and one sided guided wave confinement provided by a fast wave propagation layer serving as a guided wave confinement structure  16  according to one embodiment of the present disclosure. The electrodes  38 ,  40  are asymmetrically arranged relative to a center of the piezoelectric layer  12 , and gaps  52  between the electrodes  38 ,  40  are filled with piezoelectric material. To fabricate the MEMS guided wave device of  FIG.  14   , the guided wave confinement structure  16  and optional slow wave propagation layer  14  may be deposited over a substrate  28  to form a lower subassembly. Separately, recesses may be defined in a surface of a single crystal piezoelectric wafer by any suitable technique, such as photolithographic etching, and metal may be deposited in the recesses to form electrodes  38 ,  40 . The piezoelectric wafer surface containing the deposited electrode material may be planarized and polished and directly bonded to a planarized and polished surface of the slow wave propagation layer  14 . Thereafter, the exposed upper surface of the piezoelectric wafer may be processed (e.g., via grinding) to a desired thickness to yield the piezoelectric layer  12  with electrodes  38 ,  40  recessed in a lower portion thereof. 
       FIG.  15    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  14   , except that a Bragg mirror is used instead of a fast wave propagation layer as a guided wave confinement structure  16 . Fabrication of the device of  FIG.  15    is substantially similar to fabrication of the device of  FIG.  14   . 
       FIG.  16    illustrates a MEMS guided wave device including a PPT  58  having electrode layers  54 ,  56  sandwiching a piezoelectric layer with alternating polarity piezoelectric regions  12 A,  12 B, and further including an optional slow wave propagation layer  14 , a fast wave propagation layer serving as a one-sided guided wave confinement structure  16 , and an optional carrier substrate  28  according to one embodiment of the present disclosure. The electrode layers  54 ,  56  are symmetrically arranged relative to a center of the piezoelectric layer consisting of the alternating polarity piezoelectric regions  12 A,  12 B. To fabricate the MEMS guided wave device of  FIG.  16   , the guided wave confinement structure  16 , the optional slow wave propagation layer  14 , and the first electrode layer  54  may be deposited over the substrate  28  to form a lower subassembly. A piezoelectric wafer may be directly bonded to the lower subassembly, preceded and optionally followed with appropriate planarization and/or polishing steps. In certain embodiments, alternating polarity piezoelectric regions  12 A,  12 B may be defined (e.g., via liquid cell poling or e-beam writing) prior to bonding; in other embodiments, the alternating polarity piezoelectric regions  12 A,  12 B may be defined after bonding is complete. Thereafter, the second electrode layer  56  may be deposited over the alternating polarity piezoelectric regions  12 A,  12 B to form the PPT  58 . Examples of PPT structures and PPT fabrication techniques are disclosed in U.S. Pat. No. 7,898,158, which is hereby incorporated by reference herein. 
       FIG.  17    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  16   , except that a Bragg mirror is used instead of a fast wave propagation layer as a guided wave confinement structure  16 . Fabrication of the device of  FIG.  17    is substantially similar to fabrication of the device of  FIG.  16   . 
       FIG.  18    illustrates a MEMS guided wave device with a PPT similar to the device of  FIG.  16   , but with addition of double sided confinement. The device of  FIG.  18    includes a PPT  58  having electrode layers  54 ,  56  sandwiching a piezoelectric layer with alternating polarity piezoelectric regions  12 A,  12 B, and further including optional slow wave propagation layers  14 A,  14 B sandwiching the PPT  58 . Additionally, first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B provide two-sided confinement. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrode layers  54 ,  56  are symmetrically arranged relative to a center thickness of the piezoelectric layer. Fabrication of a lower portion of the MEMS guided wave device of  FIG.  18    proceeds according to the steps employed in fabricating the device of  FIG.  16   , with the additional steps of depositing the second slow wave propagation layer  14 B and the second guided wave confinement structure  16 B over the PPT  58 . 
       FIG.  19    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  18   , except that Bragg mirrors are used instead of fast wave propagation layers as the first and second guided wave confinement structures  16 A,  16 B. Fabrication of the device of  FIG.  19    is substantially similar to fabrication of the device of  FIG.  18   . 
       FIG.  20    illustrates a MEMS guided wave device including a segmented single crystal piezoelectric layer  72  arranged between a continuous electrode layer  64  and a segmented electrode layer  66  including electrode segments substantially registered with segments of the piezoelectric layer  72 . The device includes an optional slow wave propagation layer  14 , including a fast wave propagation layer serving as a one-sided wave confinement structure  16 , and including an optional carrier substrate  28  according to one embodiment of the present disclosure. Segmentation of the segmented piezoelectric layer  72  and segmentation of the segmented electrode  66  yields gaps  68  between the segmented structures, and such segmentation is preferably performed after the MEMS guided wave device is formed to facilitate registration of the respective features. The electrode layers  64 ,  66  are asymmetrically arranged relative to a center of the segmented piezoelectric layer  72 . To fabricate the MEMS guided wave device of  FIG.  20   , the guided wave confinement structure  16 , the optional slow wave propagation layer  14 , and the continuous electrode layer  64  may be deposited over the substrate  28  to form a lower subassembly. Thereafter, an appropriately planarized and polished piezoelectric wafer is bonded to the lower subassembly. An upper surface of the piezoelectric layer may be thinned and polished, followed by deposition of an upper electrode layer. Thereafter, apertures may be formed in the upper electrode layer and the piezoelectric layer (e.g., via one or more photolithographic etching steps) to form segments of the segmented electrode layer  66  that are substantially registered with segments of the segmented piezoelectric layer  72 . The guided wave device of  FIG.  20    may be used to generate a mixed wave that includes a vertical component as well as a transverse component. 
       FIG.  21    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  20   , except that a Bragg mirror is used instead of a fast wave propagation layer as a guided wave confinement structure  16 . Fabrication of the device of  FIG.  21    is substantially similar to fabrication of the device of  FIG.  20   . 
     In alternate embodiments, the MEMS guided wave devices of  FIGS.  20  and  21    may be modified to at least partially fill (e.g., flush-fill in certain instances) gaps  68  between segments of the segmented electrode layer  66  and the segmented piezoelectric layer  72 . Additionally, or alternatively, in certain embodiments the MEMS guided wave devices of  FIGS.  20  and  21    may be modified to replace the continuous electrode layer  64  with a (second) segmented electrode layer, to thereby provide symmetric arrangement between the electrodes and a center thickness of the piezoelectric layer. 
       FIG.  22    illustrates a MEMS guided wave device with a continuous electrode layer  64  and a segmented electrode layer  66  including electrode segments substantially registered with segments of the piezoelectric layer  72  similar to the device of  FIG.  21   , but with addition of double sided confinement. The device of  FIG.  22    includes a segmented single crystal piezoelectric layer  72  arranged between a continuous electrode layer  64  and a segmented electrode layer  66  including segments substantially registered with segments of the piezoelectric layer  72 , with the device including optional slow wave propagation layers  14 A,  14 B sandwiching the electrode layers  64 ,  66  and the piezoelectric layer  72 , and with gaps  68  between respective segments of the segmented electrode layer  66  and the segmented piezoelectric layer  72  being at least partially filled (preferably completely filled) with slow wave propagation material of the second slow wave propagation layer  14 B. Additionally, first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B provide two-sided confinement. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrode layers  64 ,  66  are asymmetrically arranged relative to a center thickness of the piezoelectric layer  72 . Fabrication of a lower portion of the MEMS guided wave device of  FIG.  22    proceeds according to the steps employed in fabricating the device of  FIG.  20   , with the additional steps of depositing the second slow wave propagation layer  14 B over and between the segmented electrode layer  66  and the segmented piezoelectric layer  72 , followed by depositing the second guided wave confinement structure  16 B over the second slow wave propagation layer  14 B. 
       FIG.  23    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  22   , except that Bragg mirrors are used instead of fast wave propagation layers as the first and second guided wave confinement structures  16 A,  16 B. Fabrication of the device of  FIG.  23    is substantially similar to fabrication of the device of  FIG.  22   . Although  FIGS.  22  and  23    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure  16 B may be omitted, optionally in combination with omission of the second slow wave propagation layer  14 B. Additionally, although  FIGS.  20  to  23    illustrate a continuous electrode layer  64 , in alternative embodiments, such layers  64  may be replaced with discontinuous (e.g., segmented) electrodes. 
       FIGS.  24  and  25    illustrate MEMS guided wave devices substantially similar to the devices of  FIGS.  12  and  13   , except that double sided confinement is provided by guided wave confinement structures  16 A,  16 B of mixed types.  FIG.  24    illustrates a MEMS guided wave device including electrodes  38 ,  40  in the form of an IDT embedded in and extending through the entire thickness of a single crystal piezoelectric layer  12 , with slow wave propagation layers  14 A,  14 B sandwiching the electrodes  38 ,  40  and the piezoelectric layer  12 . Two sided guided wave confinement is provided by a fast wave propagation layer serving as first guided wave confinement structure  16 A arranged below the piezoelectric layer  12 , and by a Bragg mirror serving as a second guided wave confinement structure  16 B arranged above the piezoelectric layer  12 . Slow wave propagation layers  14 A,  14 B are additionally provided between the respective guided wave confinement structures  16 A,  16 B and the piezoelectric layer  12 . An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrodes  38 ,  40  are symmetrically arranged relative to a center thickness of the piezoelectric layer  12 .  FIG.  25    is substantially similar to  FIG.  24   , except that two sided guided wave confinement is provided by a Bragg mirror serving as first guided wave confinement structure  16 A arranged below the piezoelectric layer  12 , and by a fast wave propagation layer serving as a second guided wave confinement structure  16 B arranged above the piezoelectric layer  12 . Fabrication of the MEMS guided wave devices is substantially similar to the fabrication steps described in connection with  FIGS.  12  and  13   , followed by deposition of a second slow wave propagation layer  14 B and a second guided wave confinement structure  16 B over the piezoelectric layer  12 . Although  FIGS.  24  and  25    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure  16 B may be omitted, optionally in combination with omission of the second slow wave propagation layer  14 B. 
     Although specific embodiments with two sided confinement illustrated in the drawings may include first and second (e.g., lower and upper) guided wave confinement structures of the same type (e.g., both being fast wave propagation layers or both being Bragg mirrors), it is specifically contemplated that any embodiments illustrated herein may be modified to include guided wave confinement structures  16 A,  16 B of mixed types. For example, a Bragg mirror may be provided below a piezoelectric layer and a fast wave propagation layer may be provided above a piezoelectric layer, or vice-versa, to provide two sided confinement. 
     In certain embodiments, electrodes may be arranged along different planes on surfaces of a piezoelectric layer, with one group of electrodes arranged within recesses defined in the piezoelectric layer. By recessing alternate electrodes, the periodicity can be reduced by half, thereby enabling higher operating frequencies. Additionally, by bringing electrodes of opposing polarity very close to one another, stronger acoustic wave excitation may be possible. If depth of the recesses defined in the piezoelectric layer is controlled, then spurious response may be controlled. In certain embodiments, some or all electrodes alternately defined on an upper surface and in recesses of a piezoelectric layer may be at least partially covered with functional layer (e.g., a temperature compensation material or a slow wave propagation material) having either a planar or an undulating top surface. In certain embodiments, such a functional material may provide temperature compensation utility. MEMS guided wave confinement devices including non-coplanar electrodes incorporating recessed electrodes are described in connection with  FIGS.  26  to  29   . 
       FIG.  26    illustrates a MEMS guided wave device including a piezoelectric layer  12  defining multiple recesses  74 , with electrodes  38 ,  40  in the form of an IDT deposited on the piezoelectric layer  12 . A first group of electrodes  38  is arranged on an uppermost surface of the piezoelectric layer  12 , and a second group of electrodes  40  is arranged in the recesses  74 , such that the first group of electrodes  38  is non-coplanar with the second group of electrodes  40 . The MEMS guided wave device of  FIG.  26    further includes an optional slow wave propagation layer  14  below the piezoelectric layer  12 , and fast wave propagation layer serving as a one sided guided wave confinement structure  16 . An optional substrate  28  is disposed under the guided wave confinement structure  16 . The electrodes  38 ,  40  are asymmetrically arranged relative to a center thickness of the piezoelectric layer  12 . To fabricate the MEMS guided wave device of  FIG.  26   , a lower subassembly including the substrate  28 , the guided wave confinement structure  16 , and the slow wave propagation layer  14  may be produced by sequential deposition steps. Following planarization and polishing of the slow wave propagation layer  14 , a prefabricated single crystal piezoelectric wafer may be directly bonded to the lower subassembly. The piezoelectric wafer may be processed (e.g., via grinding and polishing) to a desired thickness. Thereafter, recesses may be defined in the piezoelectric wafer by any suitable technique, such as ion milling, and metal may be deposited (e.g., via evaporative deposition) to form recessed electrodes  40  and non-recessed electrodes  38 . 
       FIG.  27    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  26   , except that a Bragg mirror is used instead of a fast wave propagation layer as a guided wave confinement structure  16 . Fabrication of the device of  FIG.  27    is substantially similar to fabrication of the device of  FIG.  26   . 
       FIGS.  28  and  29    illustrate MEMS guided wave devices similar to the devices of  FIGS.  26  and  27   , but with addition of double sided confinement. 
     The MEMS guided wave device of  FIG.  28    includes a piezoelectric layer  12  defining multiple recesses  74 , with electrodes  38 ,  40  in the form of an IDT deposited on the piezoelectric layer  12 . A first group of electrodes  38  is arranged on a bulk upper surface of the piezoelectric layer  12 , and a second group of electrodes  40  is arranged in the recesses  74 , such that the first group of electrodes  38  is non-coplanar with the second group of electrodes  40 . Optional slow wave propagation layers  14 A,  14 B sandwich the piezoelectric layer  12  and the electrodes  38 ,  40 , with portions of the second slow wave propagation layer  14 B further filling gaps  68  above electrodes  40  and between electrodes  38 . Additionally, first and second fast wave propagation layers serving as first and second guided wave confinement structures  16 A,  16 B provide two-sided confinement and sandwich the slow wave propagation layers  14 A,  14 B. An optional substrate  28  is disposed under the first guided wave confinement structure  16 A. The electrodes  38 ,  40  are asymmetrically arranged relative to a center thickness of the piezoelectric layer  12 . Fabrication of a lower portion of the MEMS guided wave device of  FIG.  28    proceeds according to the steps employed in fabricating the device of  FIG.  26   , with the additional steps of depositing the second slow wave propagation layer  14 B and the second guided wave confinement structure  16 B over the electrodes  38 ,  40  and the piezoelectric layer  12 . 
       FIG.  29    illustrates a MEMS guided wave device substantially similar to the device of  FIG.  28   , except that Bragg mirrors are used instead of fast wave propagation layers as the first and second guided wave confinement structures  16 A,  16 B. Fabrication of the device of  FIG.  29    is substantially similar to fabrication of the device of  FIG.  28   . Although  FIGS.  28  and  29    depict MEMS guided wave devices with two-sided confinement, in alternative embodiments the second (top) side confinement structure  16 B may be omitted, optionally in combination with omission of the second slow wave propagation layer  14 B. 
     In alternate embodiments, the MEMS guided wave devices of  FIGS.  28  and  29    may be modified to include mixed types of guided wave confinement structures  16 A,  16 B, such as a Bragg mirror arranged below a piezoelectric layer and a fast wave propagation layer arranged above a piezoelectric layer, or vice-versa. 
     In certain embodiments, a MEMS guided wave device includes differing first and second thickness regions, a first group of electrodes arranged on or adjacent to the first thickness region and configured for transduction of a first lateral acoustic wave having a wavelength λ 1  in the first thickness region, and a second group of electrodes arranged on or adjacent to the second thickness region and configured for transduction of a second lateral acoustic wave having a wavelength λ 2  in the second thickness region, wherein λ 1  differs from λ 2 . At least one guided wave confinement structure is configured to confine the first lateral acoustic wave in the first thickness region, and configured to confine the second lateral acoustic wave in the second thickness region. In this manner, multiple resonators of a single device may be used for transduction of multiple widely different (e.g., octave difference) frequencies. Examples of multi-frequency MEMS guided wave devices are illustrated in  FIGS.  30 - 36   . 
       FIG.  30    illustrates subassemblies of a MEMS guided wave device during fabrication, following local thinning of a piezoelectric layer  82  prior to direct bonding of the piezoelectric layer to an underlying layer. In  FIG.  30   , a lower subassembly includes a substrate  28 , a fast wave propagation layer serving as a guided wave confinement structure  16  arranged over the substrate  28 , and a temperature compensation layer  14  arranged over the guided wave confinement structure  16 . An upper subassembly includes a piezoelectric wafer that has been locally thinned (e.g., via an appropriate technique such as ion milling or etching) to yield first and second thickness regions, wherein a thinner of the two regions is filled with a temperature compensation material  84 . After formation of the lower and upper subassemblies, mating surfaces may be processed (e.g., via planarization and polishing) and directly bonded. Thereafter, thickness of the piezoelectric layer  82  may be adjusted by grinding and polishing the upper surface, and electrodes may be deposited over the piezoelectric layer. 
       FIG.  31    illustrates a MEMS guided wave device produced with the subassemblies illustrated in  FIG.  30   , following wafer bonding, planarization/thinning of an outer surface of the piezoelectric layer (to yield a first thickness region  82 - 1  and a second thickness region  82 - 2  of the piezoelectric layer) and deposition of electrodes  38 - 1 ,  40 - 1 ,  38 - 2 ,  40 - 2  over the piezoelectric layer. A first group of electrodes  38 - 1 ,  40 - 1  (e.g., forming a first IDT) is arranged over the first thickness region  82 - 1 , and a second group of electrodes  38 - 2 ,  40 - 2  (e.g., forming a second IDT) is arranged over the second thickness region  82 - 2 , with all electrodes  38 - 1 ,  40 - 1 ,  38 - 2 ,  40 - 2  being substantially coplanar and arranged to asymmetric guided wave excitation. As shown in  FIG.  31   , a periodicity (or spacing) of electrodes within the first group of electrodes  38 - 1 ,  40 - 1  preferably differs from a periodicity of electrodes within the second group of electrodes  38 - 2 ,  40 - 2 . Through addition of the temperature compensation material  84  of the upper subassembly (shown in  FIG.  30   ) to the temperature compensation layer  14  of the lower subassembly, the resulting MEMS guided wave device includes a first temperature compensation layer thickness region  14 - 1  and a second temperature compensation layer thickness region  14 - 2 , wherein each such region  14 - 1 ,  14 - 2  has a different thickness. In operation of the MEMS guided wave device of  FIG.  31   , laterally excited waves are stimulated in the first and second thickness regions  82 - 1 ,  82 - 2  of the piezoelectric layer using the first group of electrodes  38 - 1 ,  40 - 1  and the second group of electrodes  38 - 2 ,  40 - 2 , respectively, and the guided wave confinement structure  16  (i.e., fast wave propagation layer) serves to confine the laterally excited waves in the first and second thickness regions  82 - 1 ,  82 - 2 . 
       FIGS.  32  and  33    are substantially similar to  FIGS.  30  and  31   , except that a Bragg mirror is provided instead of a fast wave propagation layer as the guided wave confinement structure  16 . Fabrication of the MEMS guided wave confinement structure of  FIG.  33    is substantially similar to the fabrication steps described in connection with the MEMS guided wave confinement structure of  FIG.  31   , except for replacement of the fast wave propagation layer with a Bragg mirror to serve as the guided wave confinement structure  16 . 
       FIG.  34    illustrates a MEMS guided wave device including first and second thickness regions  82 - 1 ,  82 - 2  of a piezoelectric layer that are overlaid with a first group of electrodes  38 - 1 ,  40 - 1  and a second group of electrodes  38 - 2 ,  40 - 2 , respectively. Each group of electrodes  38 - 1 ,  40 - 1 ,  38 - 2 ,  40 - 2  is substantially coplanar. The first and second thickness regions  82 - 1 ,  82 - 2  of the piezoelectric layer overlie a temperature compensation layer including a first temperature compensation layer thickness region  14 - 1  and a second temperature compensation layer thickness region  14 - 2 . Thereunder, a guided wave confinement structure  16  in the form of a fast wave propagation material including a first guided wave confinement thickness region  16 - 1  and a second guided wave confinement thickness region  16 - 2  is provided. The guided wave confinement structure  16  may optionally be supported by an underlying substrate  28 . Ultimately, the first group of electrodes  38 - 1 ,  40 - 1  (e.g., forming a first IDT) is arranged over a first thickness region  82 - 1  of the piezoelectric layer, a first temperature compensation layer thickness region  14 - 1 , and a first guided wave confinement thickness region  16 - 1 . Similarly, the second group of electrodes  38 - 2 ,  40 - 2  (e.g., forming a second IDT) is arranged over a second thickness region  82 - 2  of the piezoelectric layer, a second temperature compensation layer thickness region  14 - 2 , and a second guided wave confinement thickness region  16 - 2 . In this manner, wave propagation characteristics, temperature compensation characteristics, and guided wave confinement characteristics may be selected for each of the first group of electrodes  38 - 1 ,  40 - 1  and the second group of electrodes  38 - 2 ,  40 - 2 . 
     The MEMS guided wave device of  FIG.  34    may be fabricated from multiple subassemblies. A lower subassembly may be formed by depositing a guided wave confinement structure (e.g., a fast wave propagation material) on a substrate  28 , followed by locally thinning the guided wave confinement structure, depositing a temperature compensation material in the locally thinned area, and depositing further temperature compensation material over the entire surface. An upper subassembly may be formed by locally thinning a prefabricated piezoelectric wafer, and depositing temperature compensation material in the locally thinned area. After appropriate planarization and polishing of mating surfaces of the respective subassemblies, the upper and lower subassemblies may be directly bonded to one another. Thereafter, thickness of the piezoelectric layer  82  may be adjusted by grinding and polishing, and groups of electrodes  38 - 1 ,  40 - 1 ,  38 - 2 ,  40 - 2  may be deposited on an upper surface thereof. 
       FIGS.  35  and  36    illustrate MEMS guided wave devices in which a piezoelectric layer includes different thickness regions with non-coplanar top surfaces over which different groups of electrodes are arranged. Referring to  FIG.  35   , a MEMS guided wave device includes first and second thickness regions  82 - 1 ,  82 - 2  of a piezoelectric layer that are overlaid with a first group of electrodes  38 - 1 ,  40 - 1  (e.g., forming a first IDT) and a second group of electrodes  38 - 2 ,  40 - 2  (e.g., forming a second IDT), respectively. Top surfaces of the first and second thickness regions  82 - 1 ,  82 - 2  are non-coplanar, such that the first group of electrodes  38 - 1 ,  40 - 1  is non-coplanar with the second group of electrodes  38 - 2 ,  40 - 2 . The first and second thickness regions  82 - 1 ,  82 - 2  of the piezoelectric layer overlie a temperature compensation layer  14 . Thereunder, a guided wave confinement structure  16  in the form of a fast wave propagation material is provided. The guided wave confinement structure  16  may optionally be supported by an underlying substrate  28 . The MEMS guided wave device of  FIG.  35    may be fabricated depositing a guided wave confinement structure  16  (e.g., a fast wave propagation material) on a substrate  28 , and depositing a temperature compensation layer  14  over guided wave confinement structure  16 . After appropriate planarization and polishing of a mating surface of the temperature compensation layer  14  and a mating surface of a prefabricated piezoelectric wafer, such surfaces may be directly bonded. Thereafter, the piezoelectric wafer may be locally thinned, such as by ion milling, to define the first and second thickness regions  82 - 1 ,  82 - 2 , and groups of electrodes  38 - 1 ,  40 - 1  and  38 - 2 ,  40 - 2  may be deposited thereon. 
     Thus, a method of fabricating a micro-electrical-mechanical system (MEMS) guided wave device including a single crystal piezoelectric material with different thickness regions includes local thinning of a single crystal piezoelectric layer to define first and second thickness regions that differ in thickness. The locally thinned piezoelectric layer is bonded on or over an underlying layer (e.g., at least one of (i) a fast wave propagation layer; (ii) a Bragg mirror, or (iii) a substrate) to provide an internally bonded interface. Such bonding may be performed using wafer bonding techniques known in the art. First and second groups of electrodes are defined on or adjacent to the first thickness region and the second thickness region, respectively, for transduction of a first lateral acoustic wave having a first wavelength λ 1  in the first thickness region, and for transduction of a second lateral acoustic wave having a second wavelength λ 2  in the second thickness region. One or more surfaces of the piezoelectric layer may be planarized prior to bonding (e.g., as a bonding preparation step), and/or planarized after bonding (e.g., to adjust thickness of the piezoelectric layer). Preferably, a temperature compensation layer may be provided below the piezoelectric layer, wherein in certain embodiments, the temperature compensation layer may include a first temperature compensation layer thickness region and a second temperature compensation layer thickness that differ from one another. In certain embodiments, additional temperature compensation material may be deposited on or over a surface of at least one of the first thickness region or the second thickness region. 
     Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow. Any of the various features and elements as disclosed herein may be combined with one or more other disclosed features and elements unless indicated to the contrary herein.