CN114105082A

CN114105082A - Piezoelectric micromechanical ultrasonic transducer and manufacturing method thereof

Info

Publication number: CN114105082A
Application number: CN202010881346.2A
Authority: CN
Inventors: 钱优; 拉奇许·库玛; 夏佳杰
Original assignee: Vanguard International Semiconductor Corp
Current assignee: Vanguard International Semiconductor Corp
Priority date: 2020-08-27
Filing date: 2020-08-27
Publication date: 2022-03-01

Abstract

A piezoelectric micromachined ultrasonic transducer includes a substrate, a membrane layer, and a sacrificial layer. The substrate has a cavity penetrating through the substrate. The membrane is disposed over the cavity and includes a first piezoelectric layer, a bottom electrode, a top electrode, and a second piezoelectric layer. The first piezoelectric layer is disposed on the cavity and includes an anchor portion, wherein the anchor portion of the first piezoelectric layer directly contacts the substrate. A top electrode and a bottom electrode are disposed on the first piezoelectric layer. The second piezoelectric layer is disposed between the bottom electrode and the top electrode. The sacrificial layer is disposed between the substrate and the first piezoelectric layer, and a vertical projection of the sacrificial layer does not overlap a vertical projection of a portion of the membrane layer disposed directly above the cavity.

Description

Piezoelectric micromechanical ultrasonic transducer and manufacturing method thereof

[ technical field ] A method for producing a semiconductor device

The present invention relates to the field of Micro Electro Mechanical Systems (MEMS), and more particularly, to a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) and a method for manufacturing the same.

[ background of the invention ]

Micro mechanical transducers (MUTs) have been extensively studied over the past several decades and have become an important component in various consumer electronics products, such as fingerprint sensors, proximity sensors, and gesture sensors. Generally, MUTs can be divided into two broad categories, for example, Capacitive Micromachined Ultrasonic Transducers (CMUTs) and Piezoelectric Micromachined Ultrasonic Transducers (PMUTs). For a typical piezoelectric micromachined ultrasonic transducer, the piezoelectric micromachined ultrasonic transducer includes a membrane layer formed by an elastic material, an electrode and a piezoelectric material, and the membrane layer is disposed on a cavity serving as an acoustic wave resonator to improve the acoustic performance of the piezoelectric micromachined ultrasonic transducer. During the operation of the piezoelectric micromachined ultrasonic transducer, the ultrasonic wave generated by the vibration of the membrane layer is transmitted from the piezoelectric micromachined ultrasonic transducer to the target object, and then the piezoelectric micromachined ultrasonic transducer can detect the reflected acoustic wave generated after the ultrasonic wave strikes the target object.

Typically, piezoelectric micromachined ultrasonic transducers operate at the membrane's flexural resonance frequency, which can be determined by choosing the correct materials, membrane dimensions and thickness. Therefore, good matching of the resonant frequencies of the individual piezoelectric micromachined ultrasonic transducers is a necessary condition for proper operation. In order to tune the bending resonance frequency of the membrane, the membrane disposed over the cavity typically includes a flexible layer having a desired flexibility, the flexible layer is disposed on the bottom of the membrane, and the electrodes and the piezoelectric layer of the membrane are typically disposed on the flexible layer. However, there are limitations to the material of the elastic layer and its fabrication process, since the quality of the piezoelectric layer in the membrane layer is very sensitive to the surface texture of the layer below it (e.g., the elastic layer). Therefore, even though the film layer may be fabricated as a structure including an elastic layer, it is difficult to freely adjust the resonance frequency of the PMUT.

Accordingly, there is a need to provide an improved PMUT and method of making the same that addresses the problems encountered in conventional PMUTs.

[ summary of the invention ]

Accordingly, there is a need for an improved PMUT and method for making the same that can arbitrarily control the elasticity of the PMUT membrane.

According to an embodiment of the present invention, a PMUT includes a substrate, a film layer, and a sacrificial layer. The substrate has a cavity penetrating through the substrate. The membrane layer is disposed over the cavity and includes a first piezoelectric layer, a bottom electrode, a top electrode, and a second piezoelectric layer. The first piezoelectric layer is disposed over the cavity and includes an anchor portion, wherein the anchor portion of the first piezoelectric layer is in direct contact with the substrate. A bottom electrode is disposed over the first piezoelectric layer. The top electrode is disposed over the bottom electrode. The second piezoelectric layer is disposed between the bottom electrode and the top electrode. A sacrificial layer is disposed between the substrate and the first piezoelectric layer, wherein a vertical projection of the sacrificial layer does not overlap a partial vertical projection of a film layer disposed directly above the cavity.

According to another embodiment of the present invention, a method of fabricating a PMUT is disclosed, comprising the following steps. First, a substrate is provided, and a sacrificial layer is formed on the substrate, wherein the sacrificial layer includes at least one hole exposing the substrate. Then, a piezoelectric layer is formed in the at least one hole and on the sacrificial layer. Thereafter, a cavity is formed through the substrate to expose a portion of the sacrificial layer. Thereafter, the piezoelectric layer is used as an etch stop structure to remove the portion of the sacrificial layer exposed from the cavity.

According to an embodiment of the present invention, the elastic layer may not be disposed between the substrate and the film layer, but may be disposed at an upper portion of the film layer. Therefore, the crystallinity of the piezoelectric layer in the membrane layer is no longer affected by the elastic layer, and the elasticity of the membrane layer in the PMUT can be freely adjusted.

[ description of the drawings ]

For the following to be more readily understood, reference is made to the drawings and to the detailed description thereof, when read in conjunction with the appended drawings. Through the embodiments herein and with reference to the accompanying drawings, the embodiments of the present invention are explained in detail and the operation principle of the embodiments of the present invention is illustrated. Furthermore, for purposes of clarity, the various features in the drawings may not be to scale and the dimensions of some of the features in some drawings may be exaggerated or minimized.

Fig. 1 is a schematic top view of a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) depicted in accordance with an embodiment of the present invention.

Fig. 2 is a schematic cross-sectional view taken along a line a-a' of fig. 1 according to an embodiment of the present invention.

Fig. 3 is a schematic cross-sectional view illustrating a sacrificial layer formed on a substrate according to an embodiment of the invention.

Fig. 4 is a schematic cross-sectional view after a layer is formed on a substrate.

Fig. 5 is a schematic cross-sectional view after forming an elastic layer on a film layer.

Fig. 6 is a schematic cross-sectional view illustrating a through-substrate cavity formed according to an embodiment of the invention.

Fig. 7 is a flow chart illustrating a method of fabricating a PMUT according to an embodiment of the present invention.

[ detailed description ] embodiments

The present invention provides several different embodiments, which can be used to implement different features of the present invention. For simplicity of illustration, examples of specific components and arrangements are also described. These examples are provided for the purpose of illustration only and are not intended to be limiting in any way. For example, the following description of the first feature being formed over or on the second feature may refer to the first feature being in direct contact with the second feature, or to the second feature being in the presence of other features, such that the first feature is not in direct contact with the second feature. Moreover, various embodiments of the present invention may use repeated reference characters and/or written notation. These repeated reference characters and notations are used to make the description more concise and unambiguous and are not used to indicate any relationship between the different embodiments and/or configurations.

In addition, for spatially related descriptive words mentioned in the present invention, for example: the use of "under", "lower", "under", "over", "under", "top", "bottom" and the like in describing, for purposes of convenience, the relative relationship of one element or feature to another element(s) or feature in the drawings. In addition to the orientations shown in the drawings, these spatially relative terms are also used to describe possible orientations of the semiconductor device during use and operation. With respect to the swinging direction of the semiconductor device (rotated 90 degrees or other orientations), the spatially relative descriptions for describing the swinging direction should be interpreted in a similar manner.

Although the present invention has been described using terms such as first, second, third, etc. to describe various elements, components, regions, layers and/or sections, it should be understood that such elements, components, regions, layers and/or sections should not be limited by such terms. These terms are only used to distinguish one element, component, region, layer and/or block from another element, component, region, layer and/or block, and do not denote any order or importance, nor do they denote any order or importance, unless otherwise indicated. Thus, a first element, component, region, layer or block discussed below could be termed a second element, component, region, layer or block without departing from the scope of embodiments of the present invention.

The term "about" or "substantially" as used herein generally means within 20%, preferably within 10%, and more preferably within 5%, or within 3%, or within 2%, or within 1%, or within 0.5% of a given value or range. It should be noted that the numerical ranges, amounts, values and percentages provided in the specification are approximate numbers, i.e., the meaning of "about" or "substantially" may still be implied without specifically stating "about" or "substantially".

Particular steps or block levels in the steps/processes described below are exemplary. The particular steps or block hierarchies in the steps/flows described below may be rearranged as a matter of design preference. Further, some blocks may be integrated or deleted. Furthermore, the method claims below list corresponding elements of the different blocks in a simple order, and the method claims should not be limited to the specific steps or block hierarchy described above.

Although the invention is described below by way of specific embodiments, the inventive principles of this disclosure are defined by the claims of this application and may therefore also be applied to embodiments not specifically described in this specification. Moreover, specific details are not set forth in the description so as not to obscure the spirit of the invention, and such details are not set forth in the description to be within the knowledge of a person of ordinary skill in the art.

Fig. 1 is a schematic top view of a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) depicted in accordance with an embodiment of the present invention. Referring to fig. 1, a Piezoelectric Micromachined Ultrasonic Transducer (PMUT)100 includes at least a substrate 102, a cavity 120 formed through the substrate 102, an etch stop structure (not depicted) disposed along an opening of the cavity 120, a film layer (not depicted) (e.g., a multilayer structure) disposed on the cavity 120, and an elastic layer 142 disposed on the film layer and separated from the cavity 120. According to an embodiment of the present invention, the etch stop structure disposed along the opening of the cavity 120 may be a ring-shaped structure protruding from the bottom surface of the film layer, so that the film layer may be attached to the substrate 102. The shape of the etching stop structure is not limited to this, and the etching stop structure may be a polygon or an arc disposed along the opening of the cavity 120. The first and

second contact pads

114 and 116 disposed on opposite sides may be electrically coupled to the electrodes of the film layer, respectively. In addition, to avoid unnecessary parasitic capacitance between the first contact pad 114 and the second contact pad 116, the sizes of the first contact pad 114 and the second contact pad 116 may be reduced as much as possible, but are not limited thereto. According to an embodiment of the invention, the first contact pad 114 and the second contact pad 116 may be disposed on the same side of the film layer 106 or anywhere as long as the first contact pad 114 and the second contact pad 116 may be electrically coupled to the electrodes of the film layer. Additional conductive traces (not shown) may be disposed on the substrate 102 and electrically coupled to the first and

second contact pads

114, 116 to transmit electrical signals into or out of the film layers. During operation of the PMUT 100, the membrane layer may generate vibrations when sound waves apply an acoustic pressure to the membrane layer or an electrical signal is applied to the membrane layer. By using the etch stop structure, the size and location of the film above the cavity 120 may be precisely defined, regardless of the size and location of the cavity 120 below the film. Therefore, the uniformity of the resonance frequency of each PUMT 100 can be effectively increased.

FIG. 2 is a cross-sectional view along line A-A' of FIG. 1 according to one embodiment of the disclosure. Referring to fig. 2, the etch stop structure may be a portion of the first piezoelectric layer 132 anchored to the substrate 102 and in direct contact with the cavity 120, which may be referred to as an "anchor" of the first piezoelectric layer 132. The opening O of the cavity 120 on the top surface 102A of the substrate 102 can be considered to be sealed by the first piezoelectric layer 132. Substrate 102 may be a semiconductor substrate, such as a bulk silicon substrate, but is not limited thereto. The substrate 102 may be monocrystalline silicon, polycrystalline silicon, amorphous silicon, glass, a ceramic material, or other suitable material. According to an embodiment of the invention, the substrate 102 may be an SOI substrate. The sacrificial layer 124 may be disposed between the substrate 102 and the first piezoelectric layer 132, and the composition of the sacrificial layer 124 may be different from the composition of the substrate 102 and the first piezoelectric layer 132. In the case where the composition of the substrate 102 includes a semiconductor material, such as silicon, the sacrificial layer 124 may be, for example, silicon oxide (SiO)_x) Or silicon dioxide (SiO)₂) The dielectric layer of (2). Furthermore, according to another embodiment of the present invention, most of the sacrificial layer 124 may be omitted to increase the contact area between the first piezoelectric layer 132 and the substrate 102. A membrane layer 106, for example a multilayer structure comprising a bottom electrode 134, a second piezoelectric layer 136 and a top electrode 138, may be disposed on the first piezoelectric layer 132. A portion of the film 106 may be disposed over the cavity 120, with the cavity 120 including an edge 120e proximate the film 106. According to an embodiment of the present invention, the vertical projection of the sacrificial layer 124 may not overlap the vertical projection of the film 106 disposed directly above the cavity 120. The bottom electrode 134 and the top electrode 138 of the PMUT 100 may be electrically coupled to the first contact pad 114 and the second contact pad 116, respectively. An optional passivation layer 140 may further be disposed on the film layer 106, and may be comprised of a dielectric layer. An elastic layer having a desired elasticity (elasticity) may be disposed on the selective passivation layer 140 so that when an acoustic wave or an electric signal is applied to the PMUAt T100, the membrane layer 106 may vibrate at a specific frequency. It should be noted that the mechanical behavior of the film layer 106 is dominated primarily by the elastic layer 142, since the elasticity of the elastic layer 142 is higher than the elasticity of other layers below the elastic layer 142.

In order to enable a person skilled in the art to practice the invention, a method of fabricating a piezoelectric micromachined ultrasonic transducer is further described below. In addition, since the piezoelectric micromachined ultrasonic transducer can be fabricated through a standard CMOS process, related electronic components, such as field effect transistors, amplifiers, and integrated circuits, can also be fabricated through the same CMOS process on the same substrate of the piezoelectric micromachined ultrasonic transducer.

FIG. 3 is a cross-sectional view of a substrate after forming a sacrificial layer thereon according to one embodiment of the invention. Fig. 7 is a flowchart illustrating a method for fabricating a piezoelectric micromachined ultrasonic transducer according to an embodiment of the present invention. Referring to fig. 3, in step 202 of the method 200, a substrate 102 is provided, and the substrate 102 may be selected from a semiconductor substrate or an insulating substrate according to different requirements. According to an embodiment of the invention, the substrate 102 may be a monocrystalline silicon substrate. Then, in step 204, a sacrificial layer 124 is deposited on the top surface 102A of the substrate 102. There may be at least two holes 126 in the sacrificial layer 124 such that portions of the substrate 102 may be exposed from the bottom of the holes 126. Since the position of the holes 126 can be precisely defined by photolithography, the distance between two holes 126 can be precisely controlled. It should be noted that in subsequent processes, some layers may be deposited on the sacrificial layer 124, and in order to increase the electrical performance or crystallinity of these layers, the angle θ 1 between the sidewall 126S of the sacrificial layer 124 and the top surface 102A of the substrate 102 should be set within a range of 10 ° -40 °, such as 10 °, 20 °, 30 °, or 40 °, but not limited thereto.

Fig. 4 is a schematic cross-sectional view after a layer is formed on a substrate. In step 206, the first piezoelectric layer 132 may be deposited on the substrate 102 and filled into the holes 126 of the sacrificial layer 124. The first piezoelectric layer 132 may be made of an insulating material, such as aluminum nitride (AlN), scandium-doped aluminum nitride (ScAlN), lead zirconate titanate (PZT), zinc oxide (ZnO), polyvinylidene fluoride (pvdf)Ethylene (PVDF), lead manganese niobate-lead titanate (PMN-PT), but is not limited thereto. According to an embodiment of the present invention, the first piezoelectric layer 132 may also be used as a seed layer for a layer subsequently deposited on the first piezoelectric layer 132. In addition, the surface texture of the first piezoelectric layer 132 may affect the crystallinity of some layers deposited thereon. Thereafter, a bottom electrode 134, a second piezoelectric layer 136, a top electrode 138, and a passivation layer 140 may be sequentially deposited on the first piezoelectric layer 132. The bottom electrode 134 and the top electrode 138 may be the same or different materials composed of molybdenum (Mo), titanium (Ti), aluminum (Al), or platinum (Pt), but are not limited thereto. The second piezoelectric layer 136 may be composed of, but not limited to, aluminum nitride (AlN), scandium-doped aluminum nitride (ScAlN), lead zirconate titanate (PZT), zinc oxide (ZnO), polyvinylidene fluoride (PVDF), lead niobate-lead titanate (PMN-PT). The passivation layer 140 may be a selective layer made of an insulating material, such as SiO₂SiON or AlN, but not limited thereto. In addition, the material of the second piezoelectric layer 136 may be the same as the material of the first piezoelectric layer 132. In addition, a plurality of grooves may be formed on the surface of the passivation layer 140, and each groove may have an angle θ 2 of 5 ° to 35 ° between the sidewall 140S of the passivation layer 140 and the top surface 140A of the passivation layer 140. Holes may be formed in the film layer 106 to expose the bottom electrode 134 and the top electrode 138, respectively, and then contact pads, i.e., the first contact pad 114 and the second contact pad 116, may be filled into each hole. As such, the first contact pad 114 may be electrically coupled to the bottom electrode 134, while the second contact pad 116 may be electrically coupled to the top electrode 138.

Fig. 5 is a schematic cross-sectional view after an elastic layer is formed on a film layer. Referring to fig. 5, a layer having a desired elasticity may be deposited on the film layer 106 and then patterned to form an elastic layer 142 separated from the first and

second contact pads

114 and 116. The elastic layer 142 may be composed of a material having suitable elasticity, such as crystalline silicon (c-Si), amorphous silicon (a-Si), silicon-rich nitride (SiN)_x) Silicon carbide (SiC), molybdenum (Mo), titanium (Ti), aluminum (Al), or platinum (Pt), but is not limited thereto. Since the elastic layer 142 is not disposed under the second piezoelectric layer 136, the junction of the second piezoelectric layer 136The crystallinity is no longer affected by the surface texture of the elastic layer 142.

FIG. 6 is a cross-sectional view of a substrate after forming a cavity through the substrate according to an embodiment of the invention. Referring to fig. 6, in step 208, the cavity 120 is formed by etching the back side of the substrate 102 to penetrate the substrate 102. Accordingly, a portion of the bottom surface of the sacrificial layer 124 may be exposed from the cavity 120. The cavity 120 may have an opening O at the front side of the substrate 102, the opening O being defined by an edge 120e of the cavity 120 adjacent to the membrane layer 106, and the length defined by the opening O may be less than the distance D defined by the anchor portion of the first piezoelectric layer 132. Since the distance D used to define the position of the membrane layer in the PMUT is mainly determined by the anchor of the first piezoelectric layer 132, the position and size of the membrane layer of the PMUT do not change even if the position or size of the opening O is slightly shifted.

Thereafter, in step 210, an etching process is performed to remove the sacrificial layer 124 exposed from the cavity 120 by using the first piezoelectric layer 132 as an etching stop structure. When the composition of the sacrificial layer 124 is silicon oxide, the etchant may be gaseous hydrofluoric acid (Vapor HF, VHF). In the process of removing the sacrificial layer 124 exposed from the cavity 120, since the etching selection ratio of the sacrificial layer 124 to the first piezoelectric layer 132 is greater than 10, only the sacrificial layer 124 in direct contact with the etchant may be removed. Furthermore, since the anchor portion of the first piezoelectric layer 132 may prevent the etchant from reaching the remaining portion of the sacrificial layer 124, the remaining portion of the sacrificial layer may be prevented from being removed during the etching process. As a result, a structure as shown in fig. 2 can be obtained.

According to embodiments of the present invention, the elastic layer is not disposed between the substrate and the film layer, but is disposed on the top surface of the film layer. Therefore, the crystallinity of the piezoelectric layer in the membrane layer is no longer affected by the surface texture of the elastic layer, and the overall elasticity of the membrane layer of the PMUT can be freely adjusted.

The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made within the scope of the claims of the present invention should be covered by the present invention.

[ notation ] to show

100 … Piezoelectric Micromachined Ultrasonic Transducer (PMUT)

102 … base plate

102A … top surface

102B … bottom surface

106 … film layer

114 … first contact pad

116 … second contact pad

120 … cavity

Edge of 120e …

124 … sacrificial layer

126 … holes

126S … side wall

132 … first piezoelectric layer

134 … bottom electrode

136 … second piezoelectric layer

138 … Top electrode

140 … passivation layer

140A … top surface

140S … side wall

142 … elastic layer

200 … method

202 … step

204 … step

206 … step

208 … step

210 … step

Distance D …

O … opening

Angle theta 1 …

Angle theta 2 …

Claims

1. A piezoelectric micromachined ultrasonic transducer, comprising:

a substrate including a cavity penetrating the substrate;

a membrane disposed over the cavity, the membrane comprising:

a first piezoelectric layer disposed on the cavity, the first piezoelectric layer including an anchoring portion, wherein the anchoring portion of the first piezoelectric layer directly contacts the substrate;

a bottom electrode disposed on the first piezoelectric layer;

a top electrode disposed on the bottom electrode; and

a second piezoelectric layer disposed between the bottom electrode and the top electrode; and

a sacrificial layer disposed between the substrate and the first piezoelectric layer, wherein a vertical projection of the sacrificial layer does not overlap a partial vertical projection of the film disposed directly above the cavity.

2. The piezoelectric micromachined ultrasonic transducer of claim 1, wherein an opening of the cavity is adjacent to the membrane.

3. The piezoelectric micromachined ultrasonic transducer of claim 1, wherein the anchor portion of the first piezoelectric layer directly contacting the substrate is disposed along an opening of the cavity, the anchor portion comprising an annular, polygonal, or arcuate structure.

4. The piezoelectric micromachined ultrasonic transducer of claim 1, further comprising an interface between an end of the sacrificial layer and the first piezoelectric layer, wherein an angle between the interface and the top surface of the substrate is between 10 ° and 40 °.

5. The piezoelectric micromachined ultrasonic transducer of claim 1, wherein an etch selectivity ratio of the sacrificial layer to the first piezoelectric layer is greater than 10 when using gaseous hydrofluoric acid as an etchant.

6. The piezoelectric micromachined ultrasonic transducer of claim 5, wherein the material of the first piezoelectric layer is the same as the material of the second piezoelectric layer.

7. The piezoelectric micromachined ultrasonic transducer of claim 6, wherein the first piezoelectric layer directly contacts the bottom electrode.

8. The piezoelectric micromachined ultrasonic transducer of claim 5, further comprising an elastic layer disposed on the membrane layer.

9. The piezoelectric micromachined ultrasonic transducer of claim 8, further comprising at least one contact pad disposed on the sacrificial layer and separated from the elastic layer.

10. The piezoelectric micromachined ultrasonic transducer of claim 8, further comprising a passivation layer disposed between the membrane layer and the elastic layer.

11. A method of fabricating a piezoelectric micromachined ultrasonic transducer, comprising:

providing a substrate;

forming a sacrificial layer on the substrate, wherein the sacrificial layer comprises at least one hole exposing the substrate;

forming a piezoelectric layer in the at least one hole and on the sacrificial layer;

forming a cavity penetrating through the substrate to expose a portion of the sacrificial layer; and

the portion of the sacrificial layer exposed from the cavity is removed using the piezoelectric layer as an etch stop structure.

12. The method of fabricating a piezoelectric micromachined ultrasonic transducer according to claim 11, wherein an angle between a sidewall of the at least one hole and the top surface of the substrate is between 10 ° and 40 °.

13. The method of claim 11, wherein the piezoelectric layer includes an anchor portion directly contacting the substrate.

14. The method of fabricating a piezoelectric micromachined ultrasonic transducer of claim 11, further comprising:

forming a plurality of layers on the piezoelectric layer and the sacrificial layer prior to the step of forming the cavity through the substrate, wherein the layers include:

a bottom electrode;

a top electrode disposed on the bottom electrode; and

another piezoelectric layer disposed between the bottom electrode and the top electrode.

15. The method of fabricating a piezoelectric micromachined ultrasonic transducer according to claim 14, further comprising forming an elastic layer on the layers.

16. The method of claim 15, further comprising forming at least one contact pad disposed on the layers and electrically coupled to one of the top electrode or the bottom electrode, wherein the elastic layer is separated from the at least one contact pad.

17. The method of fabricating a piezoelectric micromachined ultrasonic transducer according to claim 11, wherein when the step of removing the portion of the sacrificial layer exposed from the cavity is completed, other portions of the sacrificial layer remain on the substrate.

18. The method of fabricating a piezoelectric micromachined ultrasonic transducer according to claim 11, wherein during the step of removing the portion of the sacrificial layer exposed from the cavity, an etch selectivity of the sacrificial layer to the piezoelectric layer is greater than 10.