Abstract:
A substrate defining a cavity comprising a wide, shallow first portion and a narrow, deep second portion is provided. The first portion of the cavity extends into the substrate from the front side of the substrate and is filled with sacrificial material. The second portion extends deeper into the substrate from the first portion. A device structure is fabricated over the sacrificial material. A release etchant is introduced from the back side of the substrate via the second portion of the cavity to remove from the first portion of the cavity the sacrificial material underlying the device structure. Removing from the first portion of the cavity the sacrificial material underlying the device structure by introducing the release etchant from the back side of the substrate via the second portion of the cavity allows the release etch to be performed without exposing the device structure to the release etchant. This allows the device structure to incorporate materials that have a low etch selectivity with respect to the sacrificial material.

Description:
RELATED APPLICATION  
       [0001]     This application is related to U.S. patent application Ser. No. 10/XXX,XXX of John D. Larson III entitled Stacked Bulk Acoustic Resonator Band-Pass Filter with Controllable Pass Bandwidth (Agilent Docket No. 10030669), filed on the filing date of this application and incorporated into this application by reference. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     Transformers are used in many types of electronic device to perform such functions as transforming impedances, linking single-ended circuitry with balanced circuitry or vice versa and providing electrical isolation. However, not all transformers have all of these properties. For example, an auto-transformer does not provide electrical isolation.  
         [0003]     Transformers operating at audio and radio frequencies up to VHF are commonly built as coupled primary and secondary windings around a high permeability core. The core contains the magnetic flux and increases the coupling between the windings. A transformer operable in this frequency range can also be realized using an optical-coupler. An opto-coupler used in this mode is referred to in the art as an opto-isolator.  
         [0004]     In transformers based on coupled windings or opto-couplers, the input electrical signal is converted to a different form (i.e., a magnetic flux or photons) that interacts with an appropriate transforming structure (i.e., another winding or a light detector), and is re-constituted as an electrical signal at the output. For example, an opto-coupler converts an input electrical signal to photons using a light-emitting diode. The photons pass through an optical fiber or free space that provides isolation. A photodiode illuminated by the photons generates an output electrical signal from the photon stream. The output electrical signal is a replica of the input electrical signal  
         [0005]     At UHF and microwave frequencies, coil-based transformers become impractical due to such factors as losses in the core, losses in the windings, capacitance between the windings, and a difficulty to make them small enough to prevent wavelength-related problems. Transformers for such frequencies are based on quarter-wavelength transmission lines, e.g., Marchand type, series input/parallel output connected lines, etc. Transformers also exist that are based on micro-machined coupled coils sets and are small enough that wavelength effects are unimportant. However such transformers have issues with high insertion loss.  
         [0006]     All the transformers just described for use at UHF and microwave frequencies have dimensions that make them less desirable for use in modem miniature, high-density applications such as cellular telephones. Such transformers also tend to be high in cost because they are not capable of being manufactured by a batch process and because they are essentially an off-chip solution. Moreover, although such transformers typically have a bandwidth that is acceptable for use in cellular telephones, they typically have an insertion loss greater than 1 dB, which is too high.  
         [0007]     Opto-couplers are not used at UHF and microwave frequencies due to the junction capacitance of the input LED, non-linearities inherent in the photodetector and insufficient isolation to give good common mode rejection.  
         [0008]     What is needed, therefore, is a transformer capable of providing one or more of the following attributes at electrical frequencies in the range from UHF to microwave: impedance transformation, coupling between balanced and unbalanced circuits and electrical isolation. What is also needed is such a transformer that has a low insertion loss, a bandwidth sufficient to accommodate the frequency range of cellular telephone RF signals, for example, a size smaller than transformers currently used in cellular telephones and a low manufacturing cost.  
       SUMMARY OF THE INVENTION  
       [0009]     In a first aspect, the invention provides an acoustically-coupled transformer that comprises a stacked bulk acoustic resonator (SBAR) that has a stacked pair of film bulk acoustic resonators (FBARs) and an acoustic decoupler between the FBARs. Each of the FBARs has opposed planar electrodes and a layer of piezoelectric material between the electrodes. The acoustically-coupled transformer additionally comprises first terminals electrically connected to the electrodes of one of the FBARs and second terminals electrically connected to the electrodes of the other of the FBARs. The acoustically-coupled transformer has a 1:1 impedance transformation ratio, is capable of linking single-ended circuitry with balanced circuitry or vice versa and provides electrical isolation between primary and secondary.  
         [0010]     In one embodiment, the acoustic decoupler includes a layer of acoustic decoupling material having an acoustic impedance less than that of the other materials of the FBARs. In another embodiment, the acoustic decoupler includes a Bragg structure.  
         [0011]     In a second aspect, the invention provides an acoustically-coupled transformer that has a first stacked bulk acoustic resonator (SBAR) and a second SBAR. Each SBAR has a stacked pair of film bulk acoustic resonators (FBARs) and an acoustic decoupler between the FBARs. Each of the FBARs has opposed planar electrodes and a layer of piezoelectric material between the electrodes. The acoustically-coupled transformer additionally has a first electrical circuit connecting one of the FBARs of the first SBAR to one of the FBARs of the second SBAR and a second electrical circuit connecting the other of the FBARs of the first SBAR to the other of the FBARs of the second SBAR. All embodiments of the acoustically-coupled transformer are capable of linking single-ended circuitry with balanced circuitry or vice versa, and provides electrical isolation between primary and secondary.  
         [0012]     Some embodiments of the acoustically-coupled transformer in accordance with the invention are inherently electrically balanced and have a higher common-mode rejection ratio than the above-described embodiment having the single SBAR. In such embodiments, the first electrical circuit electrically connects one of the FBARs of the first SBAR either in anti-parallel or in series with one of the FBARs of the second SBAR, and the second electrical circuit electrically connects the other of the FBARs of the first SBAR either in anti-parallel or in series with the other of the FBARs of the second SBAR. An embodiment of the acoustically-coupled transformer in which the first electrical circuit connects the respective FBARs in anti-parallel and the second electrical circuit connects the respective FBARs in anti-parallel has a 1:1 impedance transformation ratio between the first electrical circuit and the second electrical circuit and vice versa. An embodiment in which the first electrical circuit connects the respective FBARs in series and the second electrical circuit connects the respective FBARs in series also has a 1:1 impedance transformation ratio between the first electrical circuit and the second electrical circuit and vice versa. However, the impedances are higher than the embodiment in which the FBARs are connected in anti-parallel. An embodiment of the acoustically-coupled transformer in which the first electrical circuit connects the respective FBARs in anti-parallel and the second electrical circuit connects the respective FBARs in series has a 1:4 impedance transformation ratio between the first electrical circuit and the second electrical circuit and a 4:1 impedance transformation ratio between the second electrical circuit and the first electrical circuit. An embodiment of the acoustically-coupled transformer in which the first electrical circuit connects the respective FBARs in series and the second electrical circuit connects the respective FBARs in anti-parallel has a 4:1 impedance transformation ratio between the first electrical circuit and the second electrical circuit and a 1:4 impedance transformation ratio between the second electrical circuit and the first electrical circuit.  
         [0013]     Other embodiments of the acoustically-coupled transformer in accordance with the invention are electrically unbalanced and can be used in applications in which a high common-mode rejection ratio is less important. In such embodiments, the first electrical circuit electrically connects one of the FBARs of the first SBAR either in parallel or in anti-series with one of the FBARs of the second SBAR, and the second electrical circuit electrically connects the other of the FBARs of the first SBAR either in parallel or in anti-series with the other of the FBARs of the second SBAR.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]      FIG. 1A  is a plan view of an example of a first embodiment of a thin-film acoustically-coupled transformer in accordance with the invention  
         [0015]      FIGS. 1B and 1C  are cross-sectional views of the thin-film acoustically-coupled transformer along section lines  1 B- 1 B and  1 C- 1 C, respectively, in  FIG. 1A .  
         [0016]      FIG. 1D  is an enlarged cross-sectional view of part of the acoustically-coupled transformer shown in  FIG. 1A  along the section line  1 B- 1 B showing a first embodiment of the acoustic decoupler.  
         [0017]      FIG. 1E  is an enlarged cross-sectional view of part of the acoustically-coupled transformer shown in  FIG. 1A  along the section line  1 B- 1 B showing a second embodiment of the acoustic decoupler.  
         [0018]      FIG. 2 a  graph showing how the calculated frequency response of embodiments of the thin-film acoustically-coupled transformer shown in  FIGS. 1A-1C  depends on the acoustic impedance of the acoustic decoupling material.  
         [0019]      FIG. 3A  is a plan view of an example of a second embodiment of a thin-film acoustically-coupled transformer in accordance with the invention  
         [0020]      FIGS. 3B and 3C  are cross-sectional views of the thin-film acoustically-coupled transformer along section lines  3 B- 3 B and  3 C- 3 C, respectively, in  FIG. 1A .  
         [0021]      FIGS. 4A through 4D  are schematic drawings showing the electrical circuits of electrically balanced embodiments of the thin-film acoustically-coupled transformer shown in  FIGS. 3A-3C .  
         [0022]      FIGS. 4E through 4H  are schematic drawings showing the electrical circuits of electrically unbalanced embodiments of the thin-film acoustically-coupled transformer shown in  FIGS. 3A-3C .  
         [0023]      FIGS. 5A-5J  are plan views illustrating a process for making a thin-film acoustically-coupled transformer in accordance with the invention.  
         [0024]      FIGS. 5K-5S  are cross-sectional views along the section lines  5 K- 5 K,  5 L- 5 L,  5 M- 5 M,  5 N- 5 N,  50 - 50 ,  5 P- 5 P,  5 Q- 5 Q,  5 R- 5 R,  5 S- 5 S and  5 T- 5 T in  FIGS. 5A-5J , respectively.  
     
    
     DETAILED DESCRIPTION  
       [0025]      FIGS. 1A, 1B  and  1 C show a plan view and two cross-sectional views, respectively, of a first embodiment  100  of a thin-film acoustically-coupled transformer in accordance with the invention. Transformer  100  has a 1:1 impedance transformation ratio, is capable of linking single-ended circuitry with balanced circuitry or vice versa and provides electrical isolation between primary and secondary.  
         [0026]     Transformer  100  is composed of a stacked bulk acoustic resonator (SBAR)  106 , first terminals  132  and  134  and second terminals  136  and  138 . SBAR  106  is composed of a stacked pair of film bulk acoustic resonators (FBARs)  110  and  120  and an acoustic decoupler  130  between them. In the example shown, FBAR  120  is stacked atop FBAR  110 . FBAR  110  is composed of opposed planar electrodes  112  and  114  and a layer of piezoelectric material  116  between the electrodes. FBAR  120  is composed of opposed planar electrodes  122  and  124  and a layer of piezoelectric material  126  between the electrodes. Acoustic decoupler  130  is located between electrode  114  of FBAR  110  and electrode  122  of FBAR  120 . The acoustic decoupler controls the coupling of acoustic energy between FBARs  110  and  120 .  
         [0027]     In the example shown, first terminals  132  and  134  are structured as bonding pads electrically connected by electrical traces  133  and  135 , respectively, to electrodes  112  and  114 , respectively, of FBAR  110 . Also in the example shown, second terminals  136  and  138  are structured as bonding pads electrically connected by electrical traces  137  and  139 , respectively, to electrodes  122  and  124 , respectively, of FBAR  120 . In an embodiment, first terminals  132  and  134  constitute the primary terminals and the second terminals  136  and  138  constitute the secondary terminals of thin-film acoustically-coupled transformer  100 . In an alternative embodiment, first terminals  132  and  134  constitute the secondary terminals and second terminals  136  and  138  constitute the primary terminals of thin-film acoustically-coupled transformer  100 .  
         [0028]     In the example shown, SBAR  106  is suspended over a cavity  104  defined in a substrate  102 . Suspending the SBAR over a cavity allows the FBARs of the SBAR to resonate mechanically. Other suspension schemes that allow the FBARs to resonate mechanically are possible. For example, the SBAR can be located over a mismatched acoustic Bragg reflector (not shown) formed in or on substrate  102 , as disclosed by Lakin in U.S. Pat. No. 6,107,721, the disclosure of which is incorporated into this disclosure by reference.  
         [0029]     FBARs are disclosed by Ruby et al. in U.S. Pat. No. 5,587,620 entitled Tunable Thin Film Acoustic Resonators and Method of Making Same, now assigned to the assignee of this disclosure and incorporated in this disclosure by reference. Ruby&#39;s disclosure also discloses a stacked film bulk acoustic resonator (SBAR) composed of two layers of piezoelectric material interleaved with three planar electrodes. Ruby&#39;s SBAR can be regarded as being composed of a stacked pair of FBARs in which one electrode is common to both FBARs, and will be referred to as a common-electrode SBAR. The common electrode renders the common-electrode SBAR incapable of linking balanced to unbalanced circuits and vice versa and of providing electrical isolation between primary and secondary. Moreover, the common electrode SBAR exhibits an extremely narrow pass bandwidth that makes it unsuitable for use in most applications. The narrow pass bandwidth is the result of the common electrode, which over couples acoustic energy between the FBARs.  
         [0030]     As noted above, in transformer  100  in accordance with the invention, acoustic decoupler  130  controls the coupling of acoustic energy between stacked FBARs  110  and  120  and additionally electrically isolates FBAR  110  from FBAR  120 . The electrical isolation provided by acoustic decoupler  130  enables transformer  100  to link balanced to unbalanced circuits and vice versa and provides electrical isolation between primary and secondary. The acoustic coupling provided by acoustic decoupler  130  is substantially less than the acoustic coupling between the FBARs in the common electrode SBAR referred to above. As a result, FBARs  110  and  120  are not over coupled, and transformer  100  has a relatively flat response in the pass band, as will be described below with reference to  FIG. 2 .  
         [0031]     The embodiment of the acoustic decoupler  130  shown in  FIGS. 1A-1C  is a first embodiment composed of layer  131  of acoustic decoupling material located between the electrodes  114  and  122  of FBARs  110  and  120 , respectively.  FIG. 1D  is an enlarged view showing this first embodiment of the acoustic decoupler in more detail. Important properties of the acoustic decoupling material of layer  131  that constitutes acoustic decoupler  130  are an acoustic impedance less than that of the materials of FBARs  110 ,  120 , a high electrical resistivity, a low dielectric permittivity and a nominal thickness that is an odd integral multiple of one quarter of the wavelength in the acoustic decoupling material of an acoustic wave having a frequency equal to the center frequency of the pass band of acoustically-coupled transformer  100 .  
         [0032]     The acoustic decoupling material of acoustic decoupler  130  has an acoustic impedance less that of the materials of FBARs  110  and  120  and substantially greater than that of air. The acoustic impedance of a material is the ratio of stress to particle velocity in the material and is measured in Rayleighs, abbreviated as rayl. The materials of the FBARs are typically aluminum nitride (AlN) as the material of piezoelectric layers  116 ,  126  and molybdenum (Mo) as the material of electrodes  112 ,  114 ,  122  and  124 . The acoustic impedances of the materials of the FBARs are typically greater than 30 Mrayl (35 Mrayl for AlN and 63 Mrayl for Mo) and the acoustic impedance of air is about 1 krayl. In embodiments of transformer  100  in which the materials of FBARs  110 ,  120  are as stated above, materials with an acoustic impedance in the range from about 2 Mrayl to about 16 Mrayl work well as the acoustic coupling material of acoustic decoupler  130 .  
         [0033]      FIG. 2  is a graph showing how the calculated frequency response of thin-film acoustically-coupled transformer  100  depends on the acoustic impedance of the acoustic decoupling material of layer  131  that constitutes the first embodiment of acoustic decoupler  130 . The embodiment illustrated has a center frequency of about 1,900 MHz. Calculated frequency responses for embodiments in which the acoustic decoupling material of the acoustic decoupler has acoustic impedances of about 4 Mrayl (polyimide-curve  140 ), 8 Mrayl (curve  142 ) and 16 Mrayl (curve  144 ) are shown. It can be seen that the bandwidth of transformer  100  increases with increasing acoustic impedance of the acoustic decoupling material. In the embodiment in which the acoustic impedance is 16 Mrayl, the resonances of the FBARs are over coupled, which causes the characteristic double peak in the pass band response.  
         [0034]     The embodiment of acoustic decoupler  130  shown in  FIGS. 1B, 1C  and  1 D is composed of layer  131  of acoustic decoupling material with a nominal thickness equal to one quarter of the wavelength in the acoustic decoupling material of an acoustic wave having a frequency equal to the center frequency of the transformer&#39;s pass band, i.e., t≈λ n /4, where t is the thickness of the layer  131  of acoustic decoupling material that constitutes acoustic decoupler  130  and λ n  is the wavelength in the acoustic decoupling material of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  100 . A thickness of layer  131  within approximately ±10% of the nominal thickness can alternatively be used. A thickness outside this range can alternatively be used with some degradation in performance. However, the thickness of layer  131  should differ significantly from. 0λ n  at one extreme and λ n /2 at the other extreme.  
         [0035]     More generally, the first embodiment of acoustic decoupler  130  shown in  FIG. 1D  is composed of layer  131  of acoustic decoupling material with a nominal thickness equal to an odd integral multiple of one quarter of the wavelength in the acoustic decoupling material of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  100 , i.e., t≈(2m+1)λ n /4, where t and λ n  are as defined above and m is an integer equal to or greater than zero. In this case, a thickness of layer  131  that differs from the nominal thickness by approximately ±10% of λ n /4 can alternatively be used. A thickness tolerance outside this range can be used with some degradation in performance, but the thickness of layer  131  should differ significantly from an integral multiple of λ n /2.  
         [0036]     Many plastic materials have acoustic impedances in the range stated above and can be applied in layers of uniform thickness in the thickness ranges stated above. Such plastic materials are therefore potentially suitable for use as the acoustic decoupling material of layer  131  of acoustic decoupler  130 . However, the acoustic decoupling material must also be capable of withstanding the temperatures of the fabrication operations performed after layer  131  of acoustic decoupling material has been deposited on electrode  114  to form acoustic decoupler  130 . As will be described in more detail below, in practical embodiments of thin-film acoustically-coupled transformer  100 , electrodes  122  and  124  and piezoelectric layer  126  are deposited by sputtering after layer  131  has been deposited. Temperatures as high as 300° C. are reached during these deposition processes. Thus, a plastic that remains stable at such temperatures is used as the acoustic decoupling material.  
         [0037]     Plastic materials typically have a very high acoustical attenuation per unit length compared with the other materials of FBARs  110  and  120 . However, since the above-described embodiment of acoustic decoupler  130  is composed of layer  131  of plastic acoustic decoupling material typically less than 1 μm thick, the acoustic attenuation introduced by layer  131  is typically negligible.  
         [0038]     In one embodiment, a polyimide is used as the acoustic decoupling material of layer  131 . Polyimide is sold under the trademark Kapton® by E. I. du Pont de Nemours and Company. In such embodiment, acoustic decoupler  130  is composed of layer  131  of polyimide applied to electrode  114  by spin coating. Polyimide has an acoustic impedance of about 4 Mrayl. In another embodiment, a poly(para-xylylene) is used as the acoustic decoupling material of layer  131 . In such embodiment, acoustic decoupler  130  is composed of layer  131  of poly(para-xylylene) applied to electrode  114  by vacuum deposition. Poly(para-xylylene) is also known in the art as parylene. The dimer precursor di-para-xylylene from which parylene is made and equipment for performing vacuum deposition of layers of parylene are available from many suppliers. Parylene has an acoustic impedance of about 2.8 Mrayl.  
         [0039]     In an alternative embodiment, the acoustic decoupling material of layer  131  constituting acoustic decoupler  130  has an acoustic impedance substantially greater than the materials of FBARs  110  and  120 . No materials having this property are known at this time, but such materials may become available in future, or lower acoustic impedance FBAR materials may become available in future. The thickness of layer  131  of such high acoustic impedance acoustic decoupling material is as described above.  
         [0040]      FIG. 1E  is an enlarged view of part of thin-film acoustically-coupled transformer  100  showing a second embodiment of acoustic decoupler  130  that incorporates a Bragg structure  161 . Bragg structure  161  is composed of a low acoustic impedance Bragg element  163  sandwiched between high acoustic impedance Bragg elements  165  and  167 . Low acoustic impedance Bragg element  163  is a layer of a low acoustic impedance material whereas high acoustic impedance Bragg elements  165  and  167  are each a layer of high acoustic impedance material. The acoustic impedances of the Bragg elements are characterized as “low” and “high” with respect to one another and additionally with respect to the acoustic impedance of the piezoelectric material of layers  116  and  126 . At least one of the Bragg elements additionally has a high electrical resistivity and a low dielectric permittivity to provide electrical isolation between input and output of transformer  100 .  
         [0041]     Each of the layers constituting Bragg elements  161 ,  163  and  165  has a nominal thickness equal to an odd integral multiple of one quarter of the wavelength in the material the layer of an acoustic wave having a frequency equal to the center frequency of transformer  100 . Layers that differ from the nominal thickness by approximately ±10% of one quarter of the wavelength can alternatively be used. A thickness tolerance outside this range can be used with some degradation in performance, but the thickness of the layers should differ significantly from an integral multiple of one-half of the wavelength.  
         [0042]     In an embodiment, low acoustic impedance Bragg element  163  is a layer of silicon dioxide (SiO 2 ), which has an acoustic impedance of about 13 Mrayl, and each of the high acoustic impedance Bragg elements  165  and  167  is a layer of the same material as electrodes  114  and  122 , respectively, i.e., molybdenum, which has an acoustic impedance of about  63  Mrayl. Using the same material for high acoustic impedance Bragg elements  165  and  167  and electrodes  114  and  122 , respectively, of FBARs  110  and  120 , respectively, allows high acoustic impedance Bragg elements  165  and  167  additionally to serve as electrodes  114  and  122 , respectively.  
         [0043]     In an example, high acoustic impedance Bragg elements  165  and  167  have a nominal thickness equal to one quarter of the wavelength in molybdenum of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  100 , and low acoustic impedance Bragg element  163  had a nominal thickness equal to three quarters of the wavelength in SiO 2  of an acoustic wave having a frequency equal to the center frequency of the pass band of the transformer. Using a three-quarter wavelength-thick layer of SiO 2  instead of a one-quarter wavelength thick layer of SiO 2  as low acoustic impedance Bragg element  163  reduces the capacitance between FBARs  110  and  120 .  
         [0044]     In embodiments in which the acoustic impedance difference between high acoustic impedance Bragg elements  165  and  167  and low acoustic impedance Bragg element  163  is relatively low, Bragg structure  161  may be composed of more than one (e.g., n) low acoustic impedance Bragg element interleaved with a corresponding number (i.e., n+1) of high acoustic impedance Bragg elements. Only one of the Bragg elements need be insulating. For example, the Bragg structure may be composed of two low acoustic impedance Bragg element interleaved with three high acoustic impedance Bragg elements.  
         [0045]     Wafer-scale fabrication is used to fabricate thin-film acoustically-coupled transformers similar to thin-film acoustically-coupled transformer  100  thousands at a time. Wafer-scale fabrication makes each thin-film acoustically-coupled transformer inexpensive to fabricate. Thin-film acoustically-coupled transformer  100  can be made using a fabrication method similar to that to be described below with reference to  FIGS. 5A-5T . Accordingly, a method of fabricating thin-film acoustically-coupled transformer  100  will not be separately described.  
         [0046]     Referring again to  FIGS. 1A-1C , to use thin-film acoustically-coupled transformer  100 , electrical connections are made to first terminals  132  and  134  electrically connected to electrodes  112  and  114 , respectively, as shown in  FIGS. 1A and 1B  and electrical connections are additionally made to second terminals  136  and  138  electrically connected to electrodes  122  and  124 , respectively, as shown in  FIGS. 1A and 1C . The electrical connections to first terminals  132  and  134  provide electrical connections to the primary of thin-film acoustically-coupled transformer  100  and the electrical connections to second terminals  136  and  138  provide electrical connections to the secondary of thin-film acoustically-coupled transformer  100 . In an alternative embodiment, the electrical connections to second terminals  136  and  138  provide electrical connections to the primary of thin-film acoustically-coupled transformer  100  and the electrical connections to first terminals  132  and  134  provide electrical connections to the secondary of thin-film acoustically-coupled transformer  100 .  
         [0047]     In operation of thin-film acoustically-coupled transformer  100 , an input electrical signal applied to first terminals  132  and  134 , which constitute the primary terminals of thin-film acoustically-coupled transformer  100 , establishes a voltage difference between electrodes  112  and  114  of FBAR  110 . The voltage difference between electrodes  112  and  114  mechanically deforms FBAR  110  at the frequency of the input electrical signal. Depending on the frequency of the input electrical signal, acoustic decoupler  130  couples all or part of the acoustic energy resulting from the mechanical deformation of FBAR  110  to FBAR  120 . The acoustic energy received from FBAR  110  mechanically deforms FBAR  120  at the frequency of the input electrical signal. The mechanical deformation of FBAR  120  generates a voltage difference between electrodes  122  and  124  at the frequency of the input electrical signal. The voltage difference is output at second terminals  136  and  138 , which constitute the secondary terminals of transformer  100 , as an output electrical signal. Piezoelectricity is a linear effect, so the amplitude and phase of the input electrical signal applied to the first terminals is preserved in the output electrical signal output at the second terminals.  
         [0048]     An embodiment of thin-film acoustically-coupled transformer  100  in which second terminals  136  and  138  constitute the primary terminals and first terminals  132  and  134  constitute the secondary terminals operates similarly, except acoustic energy propagates through acoustic decoupler  130  from FBAR  120  to FBAR  110 .  
         [0049]     As noted above, thin-film acoustically-coupled transformer  100  provides a 1:1 impedance transformation ratio, is capable of linking single-ended circuitry with balanced circuitry or vice versa and provides electrical isolation between primary and secondary. However, the capacitance between electrode  112  and substrate  102  differs from that between electrode  114  and the substrate. As a result, thin-film acoustically-coupled transformer  100  is not perfectly balanced electrically and can have an insufficient common-mode rejection ratio (CMRR) for certain applications.  
         [0050]      FIGS. 3A-3C  show a plan view and two cross-sectional views, respectively, of a second embodiment  200  of a thin-film acoustically-coupled transformer in accordance with the invention. Acoustically-coupled transformer  200  is capable of linking single-ended circuitry with balanced circuitry or vice versa, provides electrical isolation between primary and secondary. Some embodiments of transformer  200  are electrically balanced, and therefore have a high common-mode rejection ratio: other embodiments are electrically unbalanced and have a lower common-mode rejection ratio. Acoustically-coupled transformer  200  has an impedance transformation ratio of 1:1, 1:4 or 4:1 depending on the configurations of the electrical circuits that form part of the transformer.  
         [0051]     Acoustically-coupled transformer  200  is composed of two stacked bulk acoustic resonators (SBARs)  206  and  208 . Each SBAR is composed of a stacked pair of film bulk acoustic resonators (FBARs) and an acoustic decoupler between the FBARs. Transformer  200  is additionally composed of an electrical circuit that connects one of the FBARs of SBAR  206  to one of the FBARs of SBAR  208 , and an electrical circuit that connects the other of the FBARs of SBAR  206  to the other of the FBARs of SBAR  208 .  
         [0052]     SBAR  206  is composed of a stacked pair of FBARs  210  and  220  and an acoustic decoupler  230  between them. SBAR  208  is composed of a stacked pair of FBARs  250  and  260  and an acoustic decoupler  270  between them. In the example shown, FBAR  220  is stacked atop FBAR  210  and FBAR  260  is stacked atop FBAR  250 . FBAR  210  is composed of opposed planar electrodes  212  and  214  and a layer of piezoelectric material  216  between the electrodes. FBAR  220  is composed of opposed planar electrodes  222  and  224  and a layer of piezoelectric material  226  between the electrodes. FBAR  250  is composed of opposed planar electrodes  252  and  254  and a layer of piezoelectric material  256  between the electrodes. FBAR  260  is composed of opposed planar electrodes  262  and  264  and a layer of piezoelectric material  266  between the electrodes.  
         [0053]     As noted above, an electrical circuit connects one of the FBARs of SBAR  206  to one of the FBARs of SBAR  208 , and an electrical circuit connects the other of the FBARs of SBAR  206  to the other of the FBARs of SBAR  206 . Each electrical circuit electrically connects the respective FBARs in any one of a parallel, a series, an anti-parallel and an anti-series configuration. Of the sixteen possible combinations of the parallel, series, anti-parallel and anti-series electrical circuit configurations, only eight produce a working transformer. The combination of electrical circuit configurations connecting the FBARs determines whether the transformer is electrically balanced (high common-mode rejection ratio) or electrically unbalanced, and determines the impedance transformation ratio of the transformer, i.e., 1:1, 1:4 or 4:1. The possible combinations of electrical circuit configurations are summarized in Table 1 below:  
                                                             TABLE 1                                   Parallel   Series   Anti-par.   Anti-series                                        Parallel   U 1:1   X   X   U 1:4           Series   X   B 1:1   B 4:1   X           Anti-par.   X   B 1:4   B 1:1   X           Anti-series   U 4:1   X   X   U 1:1                      
 
         [0054]     In Table 1, the row captions indicate the configuration of one of the electrical circuits, e.g., electrical circuit  245  described below with reference to  FIG. 4C , the column captions indicate the configuration of the other of the electrical circuits, e.g., electrical circuit  246  described with reference to  FIG. 4C , B denotes that the transformer is electrically balanced, U denotes that the transformer is unbalanced, and X denotes a non-functioning transformer. The impedance transformation ratio shown is the impedance transformation from electrical terminals connected to the electrical circuit indicated by the row caption to electrical terminals connected to the electrical circuit indicated by the column caption.  
         [0055]     The electrical circuits shown in Table 1 are subject to the constraint that an electrical circuit may only connect the electrodes of FBARs at the same level as one another in SBARs  206  and  208 , i.e., one of the electrical circuits may only connect the electrodes of FBARs  210  and  250  and the other of the electrical circuits may only connect the electrodes of FBARs  220  and  260 . Table 1 additionally assumes that the c-axes of piezoelectric layers  216 ,  226 ,  256  and  266  are all oriented in the same direction. More electrical circuits are possible in embodiments not subject to the constraint, e.g., in embodiments in which an electrical circuit is allowed to connect the electrodes of FBARs  210  and  260  and the electrodes of FBARs  220  and  250 , and/or the assumption.  
         [0056]     Before the electrical circuits interconnecting the FBARs are described in detail, the terms anti-parallel, parallel, anti-series and series as applied to the electrical circuits connecting the electrodes of FBARs of different SBARs will be defined. An FBAR is a polarity-dependent device. A voltage of a given polarity applied between the electrodes of the FBAR will cause the FBAR to contract mechanically while the same voltage of the opposite polarity will cause the FBAR to expand mechanically by the same amount. Similarly, a mechanical stress applied to the FBAR that causes the FBAR to contract mechanically will generate a voltage of the given polarity between the electrodes of the FBAR whereas a mechanical stress that causes the FBAR to expand mechanically will generate a voltage of the opposite polarity between the electrodes of the FBAR.  
         [0057]     Referring to  FIGS. 4A-4D , in acoustically-coupled transformer  200 , the electrodes of the FBARs that an electrical circuit connects in parallel are at the same level in the respective SBARs. A signal applied to the FBARs connected in parallel produces signals of the same phase across the FBARs. The FBARs therefore expand and contract in phase, and generate acoustic energy in phase. On the other hand, electrodes of the FBARs that an electrical circuit connects in anti-parallel are at different levels in the respective SBARs. A signal applied to FBARs connected in anti-parallel produces signals of the opposite phases across the FBARs. The FBARs therefore expand and contract in antiphase, and generate acoustic energy in antiphase.  
         [0058]     The electrodes of the FBARs that an electrical circuit connects in series are at the same level in the respective SBARs. A signal applied to the FBARs connected in series produces signals of opposite phases across the FBARs. The FBARs expand and contract in antiphase, and generate acoustic energy in antiphase. On the other hand, the electrodes of the FBARs that an electrical circuit connects in anti-series are at different levels in the respective SBARs. A signal applied to the FBARs connected in anti-series produces signals of the same phase across the FBARs. The FBARs expand and contract in phase and generate acoustic energy in phase.  
         [0059]     FBARs receiving acoustic energy that causes them to expand and contract in phase generate signals in phase. Connecting FBARs that generate signals in phase in parallel produces a signal level equal to that across the individual FBARs and an impedance of one-half the characteristic impedance of the individual FBARs. Connecting such FBARs in anti-series produces a signal level of twice that across the individual FBARs and an impedance of twice the characteristic impedance of the individual FBARs. However, connecting FBARs that generate signals in phase in anti-parallel or in series causes the signals to cancel. FBARs receiving acoustic energy that causes them to expand and contract in antiphase generate signals in antiphase. Connecting FBARs that generate signals in antiphase in antiparallel produces a signal equal in level to that across the individual FBARs and an impedance of one-half the characteristic impedance of the individual FBARs. Connecting such FBARs in series produces a signal of twice the level of that across the individual FBARs and an impedance of twice the characteristic impedance of the individual FBARs. However, connecting FBARs that generate signals in antiphase in parallel or in antiseries causes the signals to cancel. The transformers indicated in Table 1 as being non-functional are transformers in which the FBARs that receive acoustic energy generate signals that cancel.  
         [0060]      FIGS. 4A and 4B  schematically illustrate two configurations of electrical circuits that connect the FBARs  210  and  220  of SBAR  206  and the FBARs  250  and  260  of SBAR  208  in anti-parallel or in series, respectively, to form respective electrically-balanced embodiments of an acoustically-coupled transformer having a 1:1 impedance transformation ratio.  
         [0061]      FIG. 4A  shows an electrical circuit  241  electrically connecting one of the FBARs of SBAR  206  in anti-parallel with one of the FBARs of SBAR  208  and to first terminals F and an electrical circuit  242  electrically connecting the other of the FBARs of SBAR- 206  in anti-parallel with the other of the FBARs of SBAR  208  and to second terminals S. In the example shown, the electrical circuit  241  electrically connects FBAR  220  of SBAR  206  in anti-parallel with FBAR  260  of SBAR  208  and to first terminals F, and electrical circuit  242  electrically connects FBAR  210  of SBAR  206  in anti-parallel with FBAR  250  of SBAR  208  and to second terminals S.  
         [0062]     Specifically, electrical circuit  241  electrically connects electrode  222  of FBAR  220  to electrode  264  of FBAR  260  and to one of the first terminals F and additionally electrically connects electrode  224  of FBAR  220  to electrode  262  of FBAR  260  and to the other of the first terminals F. Electrical circuit  242  electrically connects electrode  214  of FBAR  210  to electrode  252  of FBAR  250  and to one of the second terminals S and additionally electrically connects electrode  212  of FBAR  210  to electrode  254  of FBAR  250  and to the other of the second terminals S.  
         [0063]     Electrical circuit  241  electrically connects FBARs  220  and  260  in anti-parallel so that an input electrical signal applied to the first terminals F is applied equally but in antiphase to FBARs  220  and  260 . Electrical circuit  241  electrically connects FBARs  220  and  260  in anti-parallel in the sense that an electrical signal applied to first terminals F that causes FBAR  220  to contract mechanically additionally causes FBAR  260  to expand mechanically by the same amount, and vice versa. The acoustic energy generated by FBAR  260  is therefore in antiphase with the acoustic energy generated by FBAR  220 . Consequently, the acoustic energy received by FBAR  250  from FBAR  260  is in antiphase with the acoustic energy received by FBAR  210  from FBAR  220 , and the signal between electrodes  214  and  212  is in antiphase with the signal between electrodes  254  and  252 . Electrical circuit  242  connects FBARs  210  and  250  in anti-parallel, so that the signal output to the second terminals S is in phase with the signal between electrodes  214  and  212  and also with the signal between electrodes  254  and  252 . As a result, the signal between second terminals S is the same as the signal across either of FBARs  210  and  250 .  
         [0064]     Substantially the same capacitance exists between each of the first terminals F and substrate  202 . Each first terminal has connected to it one electrode closer to the substrate and one electrode further from the substrate. In the example shown, one first terminal has electrode  222  closer to the substrate and electrode  264  further from the substrate connected to it and the other first terminal has electrode  262  closer to the substrate and electrode  224  further from the substrate connected to it. Moreover, substantially the same capacitance exists between each of the second terminals S and substrate  202 . Each second terminal has connected to it one electrode closer to the substrate and one electrode further from the substrate. In the example shown, one second terminal has electrode  212  closer to the substrate and electrode  254  further from the substrate connected to it and the other second terminal has electrode  252  closer to the substrate and electrode  214  further from the substrate connected to it. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4A  is electrically balanced and, as a result, has a common-mode rejection ratio sufficiently high for many more applications than the thin-film acoustically-coupled transformer  100  described above with reference to  FIGS. 1A-1C .  
         [0065]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4A  has a 1:1 impedance transformation ratio. First terminals F may serve as the primary terminals or the secondary terminals of the transformer and second terminals P may serve as the secondary terminals or the primary terminals, respectively, of the transformer. An input electrical signal applied to the primary terminals is output at substantially the same level at the secondary terminals. In a typical embodiment in which all of the FBARs  210 ,  220 ,  250  and  260  have a similar characteristic impedance, the impedance seen at the primary terminals and at the secondary terminals is that of two FBARs in parallel, i.e., one half of the typical characteristic impedance of a single FBAR. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4A  is suitable for use in relatively low characteristic impedance applications.  
         [0066]      FIG. 4B  schematically shows an electrical circuit  243  electrically connecting one of the FBARs of SBAR  206  and one of the FBARs of SBAR  208  in series between first terminals F and an electrical circuit  244  electrically connecting the other of the FBARs of SBAR  206  and the other of the FBARs of SBAR  208  in series between second terminals S. In the example shown in  FIG. 4B , electrical circuit  243  electrically connects FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in series between first terminals F, and electrical circuit  244  electrically connects FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in series between second terminals S.  
         [0067]     Specifically, electrical circuit  243  electrically connects electrode  222  of FBAR  220  to electrode  262  of FBAR  260  and additionally electrically connects electrode  224  of FBAR  220  to one of the first terminals F and electrically connects electrode  264  of FBAR  260  to the other of the first terminals F. In a variation, electrical circuit  243  electrically connects electrode  224  of FBAR  220  to electrode  264  of FBAR  260  and additionally electrically connects electrode  222  of FBAR  220  and electrode  262  of FBAR  260  to first terminals F. Electrical circuit  244  electrically connects electrode  212  of FBAR  210  to electrode  252  of FBAR  250  and additionally electrically connects electrode  214  of FBAR  210  to one of the second terminals S and additionally electrically connects electrode  254  of FBAR  250  to the other of the second terminals S. In a variation, electrical circuit  244  electrically connects electrode  214  of FBAR  210  to electrode  254  of FBAR  250  and additionally electrically connects electrode  212  of FBAR  210  and electrode  252  of FBAR  250  to second terminals S.  
         [0068]     Electrical circuit  243  electrically connecting FBARs  220  and  260  in series divides an input electrical signal applied to the first terminals F approximately equally between FBARs  220  and  260 . FBARs  220  and  260  are connected in series in the sense that an electrical signal applied to first terminals F that causes FBAR  220  to contract mechanically causes FBAR  260  to expand mechanically by the same amount, and vice versa. The acoustic energy generated by FBAR  260  is therefore in antiphase with the acoustic energy generated by FBAR  220 . The acoustic energy received by FBAR  250  from FBAR  260  is in antiphase with the acoustic energy received by FBAR  210  from FBAR  220  and the signal on electrode  254  is in antiphase with the signal on electrode  214 . Electrical circuit  244  electrically connects FBARs  210  and  250  in series so that the signal at second terminals S is twice the signal across either of FBARs  210  and  250 .  
         [0069]     Substantially the same capacitance exists between each of the first terminals F and substrate  202 . Electrodes  224  and  264  connected to the first terminals are at the same distance from the substrate. Moreover, substantially the same capacitance exists between each of the second terminals S and substrate  202 . Electrodes  214  and  254  connected to the second terminals are at the same distance from the substrate. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4B  is electrically balanced and, as a result, has a common-mode rejection ratio sufficiently high for many more applications than the thin-film acoustically-coupled transformer  100  described above with reference to  FIGS. 1A-1C .  
         [0070]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4B  has a 1:1 impedance transformation ratio. First terminals F may serve as the primary terminals or the secondary terminals of the transformer and second terminals P may serve as the secondary terminals or the primary terminals, respectively, of the transformer. An input electrical signal applied to the primary terminals is output at substantially the same level at the secondary terminals. In a typical embodiment in which all of the FBARs  210 ,  220 ,  250  and  260  have a similar characteristic impedance, the impedance seen at the primary terminals and at the secondary terminals is that of two FBARs in series, i.e., twice the typical characteristic impedance of a single FBAR. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4B  is suitable for use in higher characteristic impedance applications than that shown in  FIG. 4A .  
         [0071]      FIGS. 4C and 4D  schematically illustrate two configurations of electrical circuits that connect the FBARs  210  and  220  of SBAR  206  and the FBARs  250  and  260  of SBAR  208  in anti-parallel and in series to form respective embodiments of an acoustically-coupled transformer having a 1:4 or 4:1 impedance transformation ratio.  FIG. 4C  shows an electrical circuit  245  electrically connecting one of the FBARs of SBAR  206  in anti-parallel with one of the FBARs of SBAR  208  and to first terminals F and an electrical circuit  246  electrically connecting the other of the FBARs of SBAR  206  and the other of the FBARs of SBAR  208  in series between second terminals S. In the example shown, the electrical circuit  245  electrically connects FBAR  220  of SBAR  206  in anti-parallel with FBAR  260  of SBAR  208  and to first terminals P, and electrical circuit  246  electrically connects FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in series between second terminals S.  
         [0072]     Specifically, electrical circuit  245  electrically connects electrode  222  of FBAR  220  to electrode  264  of FBAR  260  and to one of the first terminals F, and additionally electrically connects electrode  224  of FBAR  220  to electrode  262  of FBAR  260  and to the other of the first terminals F. Electrical circuit  246  electrically connects electrode  214  of FBAR  210  to electrode  254  of FBAR  250  and additionally electrically connects electrode  212  of FBAR  210  to one of the second terminals S and electrode  252  of FBAR  250  to the other of the second terminals S. In a variation, electrical circuit  246  electrically connects electrode  212  of FBAR  210  to electrode  252  of FBAR  250  and additionally electrically connects electrode  214  of FBAR  210  and electrode  254  of FBAR  250  to second terminals S.  
         [0073]     Electrical circuit  245  electrically connects FBARs  220  and  260  in anti-parallel so that an input electrical signal applied to the first terminals F is applied equally but in antiphase to FBARs  220  and  260 . Electrical circuit  245  electrically connects FBARs  220  and  260  in anti-parallel in the sense that an electrical signal applied to first terminals F that causes FBAR  220  to contract mechanically additionally causes FBAR  260  to expand mechanically by the same amount, and vice versa. The acoustic energy generated by FBAR  260  is therefore in antiphase with the acoustic energy generated by FBAR  220 . Consequently, the acoustic energy received by FBAR  250  from FBAR  260  is in antiphase with the acoustic energy received by FBAR  210  from FBAR  220 , and the signal on electrode  252  is in antiphase with the signal on electrode  212 . Electrical circuit  246  connects FBARs  210  and  250  in series so that the voltage difference between second terminals S is twice the voltage across either of FBARs  210  and  250 .  
         [0074]     Substantially the same capacitance exists between each of the first terminals F and substrate  202 . Each first terminal has connected to it one electrode closer to the substrate and one electrode further from the substrate. In the example shown, one first terminal has electrode  222  closer to the substrate and electrode  264  further from the substrate connected to it and the other first terminal has electrode  262  closer to the substrate and electrode  224  further from the substrate connected to it. Moreover, substantially the same capacitance exists between each of the second terminals S and substrate  202 . Electrodes  212  and  252  connected to the second terminals are at the same distance from the substrate. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4C  is electrically balanced and, as a result, has a common-mode rejection ratio sufficiently high for many more applications than the thin-film acoustically-coupled transformer  100  described above with reference to  FIGS. 1A-1C .  
         [0075]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4C  is a step-up transformer when first terminals F serve as primary terminals and second terminals S serve as secondary terminals. A signal applied to the primary terminals is output at twice the level at the secondary terminals. Also, in a typical embodiment in which all of the FBARs  210 ,  220 ,  250  and  260  have a similar characteristic impedance, the impedance seen at the primary terminals is that of two FBARs in parallel, i.e., one half of the typical characteristic impedance of a single FBAR, whereas the impedance seen at the secondary terminals is that of two FBARs in series, i.e., twice the typical characteristic impedance of a single FBAR. Thus, the embodiment of thin-film acoustically-coupled transformer  200  illustrated in  FIG. 4C  has a 1:4 primary-to-secondary impedance ratio.  
         [0076]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4C  is a step-down transformer when first terminals F serve as secondary terminals and second terminals S serve as primary terminals. In this case, the signal output at the secondary terminals is one-half the level of the input electrical signal applied to the primary terminals, and the primary-to-secondary impedance ratio is 4:1.  
         [0077]      FIG. 4D  schematically shows an electrical circuit  247  electrically connecting FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in series between first terminals F, and an electrical circuit  248  electrically connecting FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in anti-parallel and to second terminals S.  
         [0078]     Specifically, electrical circuit  247  electrically connects electrode  222  of FBAR  220  to electrode  262  of FBAR  260  and additionally electrically connects electrode  224  of FBAR  220  and electrode  264  of FBAR  260  to first terminals F. Electrical circuit  248  electrically connects electrode  212  of FBAR  210  to electrode  254  of FBAR  250  and to one of the second terminals S, and additionally electrically connects electrode  214  of FBAR  210  to electrode  252  of FBAR  250  and to the other of the second terminals S. In a variation, electrical circuit  247  electrically connects electrode  224  of FBAR  220  to electrode  264  of FBAR  260  and additionally electrically connects electrode  222  of FBAR  220  and electrode  262  of FBAR  260  to first terminals F.  
         [0079]     Electrical circuit  247  electrically connecting FBARs  220  and  260  in series divides an input electrical signal applied to the first terminals F approximately equally between FBARs  220  and  260 . FBARs  220  and  260  are connected in series in the sense that an electrical signal applied to first terminals F that causes FBAR  220  to contract mechanically causes FBAR  260  to expand mechanically by the same amount, and vice versa. The acoustic energy generated by FBAR  260  is therefore in antiphase with the acoustic energy generated by FBAR  220 . The acoustic energy received by FBAR  250  from FBAR  260  is in antiphase with the acoustic energy received by FBAR  210  from FBAR  220  and the voltage between electrodes  252  and  254  is in antiphase with the voltage between electrodes  212  and  214 . Electrical circuit  248  electrically connects FBARs  210  and  250  in anti-parallel, so that the signal output at the second terminals S is in phase with the signal across electrodes  214  and  212  and also with the signal across electrodes  254  and  252 . As a result, the signal at second terminals S is equal in level to the signal across either of FBARs  210  and  250 , and is equal to one-half the level of the input electrical signal applied to first terminals F.  
         [0080]     Substantially the same capacitance exists between each of the first terminals F and substrate  202 . Electrodes  224  and  264  connected to the first terminals are the at same distance from the substrate. Moreover, substantially the same capacitance exists between each of the second terminals S and substrate  202 . Each second terminal has connected to it one electrode closer to the substrate and one electrode further from the substrate. In the example shown, one second terminal has electrode  212  closer to the substrate and electrode  254  further from the substrate connected to it and the other second terminal has electrode  252  closer to the substrate and electrode  214  further from the substrate connected to it. Thus, the embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4D  is electrically balanced and, as a result, has a common-mode rejection ratio sufficiently high for many more applications than the thin-film acoustically-coupled transformer  100  described above with reference to  FIGS. 1A-1C .  
         [0081]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4D  is a step-down transformer when first terminals F serve as primary terminals and second terminals S serve as secondary terminals. The signal level output at the secondary terminals is one-half that of the input electrical signal applied to the primary terminals. Also, in a typical embodiment in which all of the FBARs  210 ,  220 ,  250  and  260  have a similar characteristic impedance, the impedance seen at the primary terminals is that of two FBARs in series, i.e., twice the typical characteristic impedance of a single FBAR, whereas the impedance seen at the secondary terminals is that of two FBARs in parallel, i.e., one-half of the typical characteristic impedance of a single FBAR. Thus, the embodiment of thin-film acoustically-coupled transformer  200  illustrated in  FIG. 4D  has a 4:1 primary-to-secondary impedance ratio.  
         [0082]     The embodiment of thin-film acoustically-coupled transformer  200  shown in  FIG. 4D  is a step-up transformer when first terminals F serve as secondary terminals and second terminals S serve as primary terminals. In this case, the signal level output at the secondary terminals is twice that of the input electrical signal applied to the primary terminals, and the primary-to-secondary impedance ratio is 1:4.  
         [0083]     In applications in which a low common mode rejection ratio is unimportant, electrical circuits interconnecting the FBARs can be different from those just described.  FIG. 4E  shows an embodiment of an acoustically-coupled transformer with a 1:1 impedance transformation ratio in which an electrical circuit  341  connects FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in parallel and to first terminals F, and an electrical circuit  342  electrically connects FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in parallel and to second terminals S.  
         [0084]      FIG. 4F  shows an embodiment of an acoustically-coupled transformer with a 1:1 impedance transformation ratio in which an electrical circuit  343  connects FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in anti-series between first terminals F, and an electrical circuit  344  connects FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in anti-series between second terminals S.  
         [0085]      FIG. 4G  shows an embodiment of an acoustically-coupled transformer in which an electrical circuit  345  electrically connects FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in parallel and to first terminals F, and an electrical circuit  346  electrically connects FBAR  210  of SBAR  206  and FBAR  250  of SBAR  208  in anti-series between second terminals S. This embodiment has a 1:4 impedance transformation ratio when first terminals F serve as primary terminals and second terminals S serve as secondary terminals, or a 4:1 impedance transformation ratio when second terminals S serve as the primary terminals and first terminals F serve as the secondary terminals.  
         [0086]      FIG. 4H  shows an embodiment of an acoustically-coupled transformer in which electrical circuit  347  electrically connects FBAR  220  of SBAR  206  and FBAR  260  of SBAR  208  in anti-series between first terminals F, and an electrical circuit  348  electrically connects FBAR  210  of SBAR- 206  and FBAR  250  of SBAR  208  in parallel and to second terminals S. This embodiment has a 4:1 impedance transformation ratio when first terminals F serve as primary terminals and second terminals S serve as secondary terminals, or a 1:4 impedance transformation ratio when second terminals S serve as the primary terminals and first terminals F serve as the secondary terminals.  
         [0087]     The electrical configuration of the embodiment of the thin-film acoustically-coupled transformer  200  shown in  FIGS. 3A-3C  is similar to that shown in  FIG. 4C . A bonding pad  282  and a bonding pad  284  constitute the first terminals of thin-film acoustically-coupled transformer  200 . An interconnection pad  236 , an electrical trace  237  extending from electrode  222  to interconnection pad  236  ( FIG. 5G ), an interconnection pad  278  in electrical contact with interconnection pad  236  and an electrical trace  279  extending from electrode  264  to interconnection pad  278  constitute the part of electrical circuit  245  ( FIG. 4C ) that electrically connects electrode  222  of FBAR  220  to electrode  264  of FBAR  260 . An interconnection pad  238 , an electrical trace  239  extending from-electrode  224  to interconnection pad  238 , an interconnection pad  276  in electrical contact with interconnection pad  238  and an electrical trace  277  extending from electrode  262  to interconnection pad  276  ( FIG. 5G ) constitute the part of electrical circuit  245  ( FIG. 4C ) that electrically connects electrode  224  of FBAR  220  to electrode  262  of FBAR  260 . An electrical trace  283  that extends between electrode  222  and bonding pad  282  and an electrical trace  285  that extends between electrode  264  and bonding pad  284  ( FIG. 5G ) constitute the part of electrical circuit  245  that connects FBARs  220  and  260  connected in anti-parallel to the first terminals provided by bonding pads  282  and  284 .  
         [0088]     In an alternative embodiment, bonding pads  282  and  284  and traces  283  and  285  are omitted and interconnection pads  238  and  278  are configured as bonding pads and provide the first terminals of thin-film acoustically-coupled transformer  200 .  
         [0089]     Bonding pad  232  and bonding pad  272  constitute the second terminals of thin-film acoustically-coupled transformer  200 . An electrical trace  235  that extends between electrode  214  and electrode  254  ( FIG. 5E ) constitutes the part of electrical circuit  246  ( FIG. 4C ) that connects FBAR  210  and FBAR  250  in series. An electrical trace  233  that extends between electrode  212  and bonding pad  232  and an electrical trace  273  that extends between electrode  252  and bonding pad  272  ( FIG. 5C ) constitutes the part of electrical circuit  246  that connects FBAR  210  and FBAR  250  to the second terminals provided by bonding pads  232  and  272 .  
         [0090]     In thin-film acoustically-coupled transformer  200 , acoustic decoupler  230  is located between FBARs  210  and  220 , specifically, between electrodes  214  and  222 . Acoustic decoupler  230  controls the coupling of acoustic energy between FBARs  210  and  220 . Additionally, acoustic decoupler  270  is located between FBARs  250  and  260 , specifically, between electrodes  254  and  262 . Acoustic decoupler  270  controls the coupling of acoustic energy between FBARs  250  and  260 . Acoustic decoupler  230  couples less acoustic energy between the FBARs  210  and  220  than would be coupled if the FBARs were in direct contact with one another. Acoustic decoupler  270  couples less acoustic energy between the FBARs  250  and  260  than would be coupled if the FBARs were in direct contact with one another. The coupling of acoustic energy defined by acoustic decouplers  230  and  270  determines the pass bandwidth of thin-film acoustically-coupled transformer  200 .  
         [0091]     In the embodiment shown in  FIGS. 3A-3C , acoustic decouplers  230  and  270  are respective parts of a layer  231  of acoustic decoupling material. Important properties of the acoustic decoupling material of layer  231  are an acoustic impedance less than that of FBARs  210 ,  220 ,  250  and  260 , a nominal thickness that is an odd integral multiple of one quarter of the wavelength in the acoustic decoupling material of an acoustic wave having a frequency equal to the center frequency of the pass band of the transformer  200 , and a high electrical resistivity and low dielectric permittivity to provide electrical isolation between the primary and secondary of the transformer. The materials and other properties of layer  231  are similar to those described above with reference to  FIGS. 1A-1D  and  FIG. 2 . Therefore, layer  231  that provides acoustic decouplers  230  and  270  will not be further described here. In another embodiment (not shown), acoustic decouplers  230  and  270  each include a Bragg structure similar to Bragg structure  161  described above with reference to  FIG. 1E . Acoustic decouplers  230  and  270  may alternatively share a common Bragg structure in a manner similar to the way in which the embodiments of acoustic couplers  230  and  270  shown in  FIGS. 3A-3C  share a common layer  231 .  
         [0092]     SBAR  206  and SBARs  208  are located adjacent one another suspended over a cavity  204  defined in a substrate  202 . Suspending the SBARs over a cavity allows the stacked FBARs in each SBAR to resonate mechanically. Other suspension schemes that allow the stacked FBARs to resonate mechanically are possible. For example, the SBARs can be located over a mismatched acoustic Bragg reflector (not shown) formed in or on substrate  202 , as disclosed by the above-mentioned U.S. Pat. No. 6,107,721 of Lakin.  
         [0093]     Thousands of thin-film acoustically-coupled transformers similar to thin-film acoustically-coupled transformer  200  are fabricated at a time by wafer-scale fabrication. Such wafer-scale fabrication makes the thin-film acoustically-coupled transformers inexpensive to fabricate. An exemplary fabrication method will be described next with reference to the plan views of  FIGS. 5A-5J  and the cross-sectional views of  FIGS. 5K-5T . As noted above, the fabrication method can also be used to make the thin-film acoustically-coupled transformer  100  described above with reference to  FIGS. 1A-1C .  
         [0094]     A wafer of single-crystal silicon is provided. A portion of the wafer constitutes, for each transformer being fabricated, a substrate corresponding to the substrate  202  of transformer  200 .  FIGS. 5A-5J  and  FIGS. 5K-5T  illustrate and the following description describes the fabrication of transformer  200  in and on a portion of the wafer. As transformer  200  is fabricated, the remaining transformers on the wafer are similarly fabricated.  
         [0095]     The portion of the wafer that constitutes substrate  202  of transformer  200  is selectively wet etched to form cavity  204 , as shown in  FIGS. 5A and 5K .  
         [0096]     A layer of fill material (not shown) is deposited on the surface of the wafer with a thickness sufficient to fill the cavities. The surface of the wafer is then planarized to leave the cavity filled with the fill material.  FIGS. 5B and 5L  show cavity  204  in substrate  202  filled with fill material  205 .  
         [0097]     In an embodiment, the fill material was phosphosilicate glass (PSG) and was deposited using conventional low-pressure chemical vapor deposition (LPCVD). The fill material may alternatively be deposited by sputtering, or by spin coating.  
         [0098]     A layer of metal is deposited on the surface of the wafer and the fill material. The metal is patterned to define electrode  212 , bonding pad  232 , an electrical trace  233  extending between electrode  212  and bonding pad  232 , electrode  252 , bonding pad  272  and an electrical trace  273  extending between electrode  212  and bonding pad  272 , as shown in  FIGS. 5C and 5M . Electrode  212  and electrode  252  typically have an irregular shape in a plane parallel to the major surface of the wafer. An irregular shape minimizes lateral modes in FBAR  210  and FBAR  250  ( FIG. 3A ) of which the electrodes form part, as described in U.S. Pat. No. 6,215,375 of Larson III et al., the disclosure of which is incorporated into this disclosure by reference. Electrode  212  and electrode  252  are located to expose part of the surface of fill material  205  so that the fill material can later be removed by etching, as will be described below.  
         [0099]     The metal layers in which electrodes  212 ,  214 ,  222 ,  224 ,  252 ,  254 ,  262  and  264  are defined are patterned such that, in respective planes parallel to the major surface of the wafer, electrodes  212  and  214  of FBAR  210  have the same shape, size, orientation and position, electrodes  222  and  224  of FBAR  220  have the same shape, size, orientation and position, electrodes  252  and  254  of FBAR  250  have the same shape, size, orientation and position and electrodes  262  and  264  of FBAR  260  have the same shape, size, orientation and position. Typically, electrodes  214  and  222  additionally have the same shape, size, orientation and position and electrodes  254  and  262  additionally have the same shape, size, orientation and position.  
         [0100]     In an embodiment, the metal deposited to form electrode  212 , bonding pad  232 , trace  233 , electrode  252 , bonding pad  272  and trace  273  was molybdenum. The molybdenum was deposited with a thickness of about 440 nm by sputtering, and was patterned by dry etching to define pentagonal electrodes each with an area of about 26,000 square tim. Other refractory metals such as tungsten, niobium and titanium may alternatively be used as the material of electrodes  212  and  252 , bonding pads  232  and  272  and traces  233  and  273 . The electrodes, bonding pads and traces may alternatively comprise layers of more than one material.  
         [0101]     A layer of piezoelectric material is deposited and is patterned to define a piezoelectric layer  217  that provides piezoelectric layer  216  of FBAR  210  and piezoelectric layer  256  of FBAR  250 , as shown in  FIGS. 5D and 5N . Piezoelectric layer  217  is patterned to expose part of the surface of fill material  205  and bonding pads  232  and  272 . Piezoelectric layer  217  is additionally patterned to define windows  219  that provide access to additional parts of the surface of the fill material.  
         [0102]     In an embodiment, the piezoelectric material deposited to form piezoelectric layer  217  was aluminum nitride and was deposited with a thickness of about 780 nm by sputtering. The piezoelectric material was patterned by wet etching in potassium hydroxide or by chlorine-based dry etching. Alternative materials for piezoelectric layer  217  include zinc oxide and lead zirconium titanate.  
         [0103]     A layer of metal is deposited and is patterned to define electrode  214 , electrode  254  and electrical trace  235  extending between electrode  214  and electrode  254 , as shown in  FIGS. 5E and 5O .  
         [0104]     In an embodiment, the metal deposited to form electrode  214 , electrode  254  and trace  235  was molybdenum. The molybdenum was deposited with a thickness of about 440 nm by sputtering, and was patterned by dry etching. Other refractory metals may alternatively be used as the material of electrodes  214  and  254  and trace  235 . The electrodes and trace may alternatively comprise layers of more than one material.  
         [0105]     A layer of acoustic decoupling material is then deposited and is patterned to define an acoustic decoupling layer  231  that provides acoustic decoupler  230  and acoustic decoupler  270 , as shown in  FIGS. 5F and 5P . Acoustic decoupling layer  231  is shaped to cover at least electrode  214  and electrode  254 , and is additionally shaped to expose part of the surface of fill material  205  and bonding pads  232  and  272 . Acoustic decoupling layer  231  is additionally patterned to define windows  219  that provide access to additional parts of the surface of the fill material.  
         [0106]     In an embodiment, the acoustic decoupling material was polyimide with a thickness of about 750 nm, i.e., three quarters of the center frequency wavelength in the polyimide. The polyimide was deposited to form acoustic decoupling layer  231  by spin coating, and was patterned by photolithography. Polyimide is photosensitive so that no photoresist is needed. As noted above, other plastic materials can be used as the acoustic decoupling material. The acoustic decoupling material can be deposited by methods other than spin coating.  
         [0107]     In an embodiment in which the material of the acoustic decoupling layer  231  was polyimide, after deposition and patterning of the polyimide, the wafer was baked at about 300° C. before further processing was performed. The bake evaporates volatile constituents of the polyimide and prevents the evaporation of such volatile constituents during subsequent processing from causing separation of subsequently-deposited layers.  
         [0108]     A layer of metal is deposited and is patterned to define electrode  222 , interconnection pad  236 , electrical trace  237  extending from electrode  222  to interconnection pad  236 , bonding pad  282  and electrical trace  283  extending from electrode  222  to bonding pad  282 , as shown in  FIGS. 5G and 5Q . The patterning also defines in the layer of metal electrode  262 , interconnection pad  276  and electrical trace  277  extending from electrode  262  to interconnection pad  276 , also as shown in  FIGS. 5G and 5Q .  
         [0109]     In an embodiment, the metal deposited to form electrodes  222  and  262 , bonding pad  282 , interconnection pads  236  and  276  and electrical traces  237 ,  277  and  283  was molybdenum. The molybdenum was deposited with a thickness of about 440 nm by sputtering, and was patterned by dry etching. Other refractory metals may alternatively be used as the material of electrodes  222  and  262 , pads  236 ,  276  and  282  and electrical traces  237 ,  277  and  283 . The electrodes, bonding pads and traces may alternatively comprise layers of more than one material.  
         [0110]     A layer of piezoelectric material is deposited and is patterned to define piezoelectric layer  227  that provides piezoelectric layer  226  of FBAR  220  and piezoelectric layer  266  of FBAR  260 . Piezoelectric layer  227  is shaped to expose pads  232 ,  236 ,  272 ,  276  and  282  and to expose part of the surface of fill material  205  as shown in  FIGS. 5H and 5R . Piezoelectric layer  227  is additionally patterned to define the windows  219  that provide access to additional parts of the surface of the fill material.  
         [0111]     In an embodiment, the piezoelectric material deposited to form piezoelectric layer  227  was aluminum nitride and was deposited with a thickness of about 780 nm by sputtering. The piezoelectric material was patterned by wet etching in potassium hydroxide or by chlorine-based dry etching. Alternative materials for piezoelectric layer  227  include zinc oxide and lead zirconium titanate.  
         [0112]     A layer of metal is deposited and is patterned to define electrode  224 , interconnection pad  238  and electrical trace  239  extending from electrode  224  to interconnection pad  238 , as shown in  FIGS. 5I and 5S . Interconnection pad  238  is located in electrical contact with interconnection pad  276  to provide the part of electrical circuit  245  ( FIG. 4C ) that connects electrodes  224  and  262 . The patterning also defines in the layer of metal electrode  264 , interconnection pad  278 , electrical trace  279  extending from electrode  264  to interconnection pad  278 , bonding pad  284  and electrical trace  285  extending from electrode  264  to bonding pad  284 , also as shown in  FIGS. 5I and 5S . Interconnection pad  278  is located in electrical contact with interconnection pad  236  to provide the part of electrical circuit  245  ( FIG. 4C ) that connects electrodes  222  and  264 . As noted above, bonding pads  282  and  284  and electrical traces  283  and  285  may be omitted if reliable electrical connections can be made to stacked interconnection pads  236  and  278  and to stacked interconnection pads  276  and  238 .  
         [0113]     In an embodiment, the metal deposited to form electrodes  224  and  264 , pads  238 ,  278  and  284  and electrical traces  237 ,  279  and  285  was molybdenum. The molybdenum was deposited with a thickness of about 440 nm by sputtering, and was patterned by dry etching. Other refractory metals such may alternatively be used as the material of electrodes  224  and  264 , pads  238 ,  278  and  284  and electrical traces  237 ,  279  and  285 . The electrodes, pads and traces may alternatively comprise layers of more than one material.  
         [0114]     The wafer is then isotropically wet etched to remove fill material  205  from cavity  204 . As noted above, portions of the surface of fill material  205  remain exposed through, for example, windows  219 . The etch process leaves thin-film acoustically-coupled transformer  200  suspended over cavity  204 , as shown in  FIGS. 5J and 5T .  
         [0115]     In an embodiment, the etchant used to remove fill material  205  was dilute hydrofluoric acid.  
         [0116]     A gold protective layer is deposited on the exposed surfaces of pads  232 ,  238 ,  272 ,  278 ,  282  and  284 .  
         [0117]     The wafer is then divided into individual transformers, including transformer  200 . Each transformer is then mounted in a package and electrical connections are made between bonding pads  232 ,  272 ,  282  and  284  of the transformer and pads that are part of the package.  
         [0118]     A process similar to that described may be used to fabricate embodiments of thin-film acoustically-coupled transformer  200  in which the FBARs are electrically connected as shown in  FIGS. 4B-4H .  
         [0119]     In use, bonding pad  282  electrically connected to electrodes  222  and  264  and bonding pad  284  electrically connected to electrodes  224  and  262  provide the first terminals of the transformer  200 , and bonding pad  232  electrically connected to electrode  212  and bonding pad  272  electrically connected to electrode  252  provide the second terminals of transformer  200 . In one embodiment, the first terminals provide the primary terminals and the second terminals provide the secondary terminals of thin-film acoustically-coupled transformer  200 . In another embodiment, the first terminals provide the secondary terminals and the second terminals provide the primary terminals of thin-film acoustically-coupled transformer  200 .  
         [0120]     An embodiment of thin-film acoustically-coupled transformer  200  in which acoustic decoupler  130  incorporates a Bragg structure similar to that described above with reference to  FIG. 1E  is made by a process similar to that described above. The process differs as follows:  
         [0121]     After a layer  217  of piezoelectric material is deposited and patterned ( FIGS. 5D and 5N ), a layer of metal is deposited and is patterned to define a high acoustic impedance Bragg element incorporating electrodes  214  and  254  and additionally to define electrical trace  235  extending between the electrodes, in a manner similar to that shown in  FIGS. 5E and 5O . The high acoustic impedance Bragg element is similar to high acoustic impedance Bragg element  165  shown in  FIG. 1E . The layer of metal is deposited with a nominal thickness equal to an odd, integral multiple of one quarter of the wavelength in the metal of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  200 .  
         [0122]     In an embodiment, the metal deposited to form the high acoustic impedance Bragg element incorporating electrodes  214  and  254  is molybdenum. The molybdenum is deposited with a thickness of about 820 nm (one-quarter wavelength in Mo) by sputtering, and is patterned by dry etching. Other refractory metals may alternatively be used as the material of the high acoustic impedance Bragg element incorporating electrodes  214  and  254 . The high acoustic impedance Bragg element may alternatively comprise layers of more than one metal.  
         [0123]     A layer of low acoustic impedance material is then deposited and is patterned to define a low acoustic impedance Bragg element in a manner similar to that shown in  FIGS. 5F and 5P . The layer of low acoustic impedance material is deposited with a nominal thickness equal to an odd, integral multiple of one quarter of the wavelength in the low acoustic impedance material of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  200 . The low acoustic impedance Bragg element is shaped to cover at least the high acoustic impedance Bragg element, and is additionally shaped to expose part of the surface of fill material  205  and bonding pads  232  and  272 . The layer of low acoustic impedance material is additionally patterned to define windows that provide access to additional parts of the surface of the fill material.  
         [0124]     In an embodiment, the low acoustic impedance material is SiO 2  with a thickness of about 790 nm. The SiO 2  is deposited by sputtering, and is patterned by etching. Other low acoustic impedance material that can be used as the material of low acoustic impedance Bragg element include phosphosilicate glass (PSG), titanium dioxide and magnesium fluoride. The low acoustic impedance material can alternatively be deposited by methods other than sputtering.  
         [0125]     A layer of metal is deposited and is patterned to define a high acoustic impedance Bragg element incorporating electrodes  222  and  262 . The layer of metal is additionally patterned to define an interconnection pad  236 , an electrical trace  237  extending from electrode  222  to interconnection pad  236 , a bonding pad  282 , an electrical trace  283  extending from electrode  222  to bonding pad  282 , an interconnection pad  276  and an electrical trace  277  extending from electrode  262  to interconnection pad  276  in a manner similar to that shown in  FIGS. 7G and 7Q . The layer of metal is deposited with a nominal thickness equal to an odd, integral multiple of one quarter of the wavelength in the metal of an acoustic wave having a frequency equal to the center frequency of the pass band of transformer  200 .  
         [0126]     In an embodiment, the metal deposited to form a high acoustic impedance Bragg element incorporating electrodes  222  and  262  is molybdenum. The molybdenum is deposited with a thickness of about 820 nm (one-quarter wavelength in Mo) by sputtering, and is patterned by dry etching. Other refractory metals may alternatively be used as the material of the high acoustic impedance Bragg element incorporating electrodes  222  and  262  and its associated pads and electrical traces. The high acoustic impedance Bragg element, pads and electrical traces may alternatively comprise layers of more than one material.  
         [0127]     A layer of piezoelectric material is then deposited and is patterned to define piezoelectric layer  227 , as described above, and the process continues as described above to complete fabrication of transformer  200 .  
         [0128]     This disclosure describes the invention in detail using illustrative embodiments. However, the invention defined by the appended claims is not limited to the precise embodiments described.