JP6596310B2 - Piezoelectric sensor, sensor system, and piezoelectric element - Google Patents

Description

  The present invention relates to a piezoelectric sensor including a piezoelectric body, a sensor system, and a piezoelectric element.

  A conventional typical piezoelectric element used for a piezoelectric sensor has a structure as shown in FIGS. 17 is a top view of a conventional typical piezoelectric element, and FIG. 18 is a cross-sectional view of the conventional typical piezoelectric element cut along line AA shown in FIG.

  The conventional typical piezoelectric element shown in FIGS. 17 and 18 includes a substrate 101, a lower electrode 102, a piezoelectric layer 103, and an upper electrode 104.

  The substrate 101 is processed into a shape in which the cantilever 101B extends from the main body 101A. A lower electrode 102, a piezoelectric layer 103, and an upper electrode 104 are stacked in that order on the cantilever 101B.

  When bending stress acts on the cantilever 101B with such a structure, electric charges are generated in the piezoelectric layer 103, the piezoelectric layer 103 is polarized, and a voltage is generated between the lower electrode 102 and the upper electrode 104.

  And it can utilize as a piezoelectric sensor by connecting an active circuit and taking out a voltage signal or a current signal from a piezoelectric element.

J0ng Cheol Park, 2 others, “Modeling and Characterization of Piezoelectric d33-Mode MEMS Energy Harvester”, JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, October 2010, Vol. 19, No. 5, p. 1215-1222

  However, the piezoelectric sensor using the conventional typical piezoelectric element shown in FIGS. 17 and 18 has a problem that a high output cannot be obtained. In view of the above situation, an object of the present invention is to provide a high-output piezoelectric sensor, a sensor system including the piezoelectric sensor, and a piezoelectric element that can be used for the piezoelectric sensor.

In order to achieve the above object, a piezoelectric sensor according to the present invention includes a first electrode, a second electrode, and a piezoelectric layer, and the first electrode and the second electrode according to a d ₃₃ mode displacement of the piezoelectric layer. And a piezoelectric element that generates a voltage between them and an active circuit whose input terminal is connected to the first electrode (first configuration).

  In the piezoelectric sensor having the first configuration, the piezoelectric element includes a cantilever, the piezoelectric layer is formed on the cantilever, and the first electrode and the second electrode are formed on the piezoelectric layer. A configuration (second configuration) may be used.

  In the piezoelectric sensor having the second configuration, each of the first electrode and the second electrode is a comb-like electrode, and is arranged so as to mesh with each other, and each comb of the first electrode and the second electrode is arranged. You may make it the structure (3rd structure) formed so that it might extend in the direction which cross | intersects the longitudinal direction of the said cantilever.

In the piezoelectric sensor having the second or third configuration, the piezoelectric layer is a first piezoelectric layer, the piezoelectric element further includes a second piezoelectric layer, and the first piezoelectric layer and the second piezoelectric layer. The first electrode and the second electrode are sandwiched by the piezoelectric layer, and the first and second piezoelectric layers are displaced between the first electrode and the second electrode by the d ₃₃ mode displacement of the first piezoelectric layer and the second piezoelectric layer. Alternatively, a configuration in which a voltage is generated (fourth configuration) may be used.

  In the piezoelectric sensor having the fourth configuration, the layer thickness of the second piezoelectric layer may be greater than the layer thickness of the first piezoelectric layer (fifth configuration).

  In the piezoelectric sensor having any one of the second to fifth configurations, the piezoelectric element may further include a weight (sixth configuration) provided on a free end side of the cantilever.

  In order to achieve the above object, a sensor system according to the present invention includes the piezoelectric sensor having any one of the first to sixth configurations, and an analog signal processing circuit that processes an analog output signal of the piezoelectric sensor. The configuration (seventh configuration) is assumed.

  In the sensor system having the seventh configuration, the active circuit and the analog signal processing circuit may be integrated (eighth configuration).

Sensor system is the configuration of the seventh or eighth, further comprising a housing for accommodating the piezoelectric sensor, the piezoelectric sensor is a piezoelectric sensor which is configured either the second to sixth, wherein You may make it the structure (9th structure) by which the opening is provided in the part facing the said cantilever of a housing | casing.

In order to achieve the above object, a piezoelectric element according to the present invention includes a first electrode, a second electrode, a first piezoelectric layer, a second piezoelectric layer, and a cantilever, and the first piezoelectric body on the cantilever. A layer is formed, and the first electrode and the second electrode are formed on the first piezoelectric layer, and the first electrode and the second electrode are formed by the first piezoelectric layer and the second piezoelectric layer. Is configured such that a voltage is generated between the first electrode and the second electrode by the d ₃₃ mode displacement of the first piezoelectric layer and the second piezoelectric layer (tenth configuration). .

  In the piezoelectric element having the tenth configuration, the layer thickness of the second piezoelectric layer may be greater than the layer thickness of the first piezoelectric layer (an eleventh configuration).

  ADVANTAGE OF THE INVENTION According to this invention, the high output piezoelectric sensor, the sensor system provided with the said piezoelectric sensor, and the piezoelectric element which can be utilized for the said piezoelectric sensor can be provided.

Diagram showing deformation of piezoelectric body when force is applied Top view of a piezoelectric element included in the piezoelectric sensor according to the first embodiment Sectional drawing of the piezoelectric element with which the piezoelectric sensor which concerns on 1st Embodiment is provided Top view of a piezoelectric element included in a piezoelectric sensor according to a second embodiment Sectional drawing of the piezoelectric element with which the piezoelectric sensor which concerns on 2nd Embodiment is provided Diagram showing a configuration example of a sensor system The figure which shows an example of the impedance conversion circuit The figure which shows the other example of an impedance conversion circuit The figure which shows the other structural example of a sensor system The figure which shows the other example of an IV conversion circuit Schematic perspective view of sensor system It is a schematic longitudinal cross-sectional view of a sensor system. It is a schematic longitudinal cross-sectional view of the modification of a sensor system. It is a schematic longitudinal cross-sectional view of the modification of a sensor system. Sectional drawing of the piezoelectric element which concerns on the modification of 1st Embodiment. Sectional drawing of the piezoelectric element which concerns on the modification of 1st Embodiment. Top view of a piezoelectric element according to a modification of the first embodiment Top view of a typical conventional piezoelectric element Sectional view of a typical conventional piezoelectric element

<Displacement mode of piezoelectric body>
The present inventors have focused on the displacement mode of the piezoelectric body and studied the structure of a piezoelectric element suitable for a high output piezoelectric sensor.

  Here, the displacement mode of the piezoelectric body will be described with reference to FIG. In addition, the dotted line in FIG. 1 has shown the external shape of the piezoelectric material P1 when force is not acting. When the tensile force F1 acts on the piezoelectric body P1, contraction E1 occurs in a direction perpendicular to the tensile force F1, and elongation E2 occurs in a direction parallel to the tensile force F1. On the other hand, when the compression force F2 acts on the piezoelectric body P1, the expansion E3 is generated in the direction perpendicular to the compression force F2, and the contraction E4 is generated in the direction parallel to the compression force F2.

Perpendicular stretch the force F (F1 or F2) which acts on the piezoelectric P1 (shrinkage E1 or elongation E3) by generated in the piezoelectric element P1 charge Q ₁ or charge Q ₁ generated in the piezoelectric element P1 by the displacement of the d ₃₁ mode Can be expressed by the following equation (1) using the piezoelectric constant d ₃₁ of the d ₃₁ mode.
Q ₁ = d ₃₁ × F (1)

Further, the charge Q ₂ generated in the piezoelectric body P 1 by expansion / contraction (extension E 2 or contraction E 4) parallel to the force F (F 1 or F 2) acting on the piezoelectric body P 1, that is, the charge generated in the piezoelectric body P 1 due to the d ₃₃ mode displacement. Q ₂ can be expressed by the following equation (2) using the piezoelectric constant d ₃₃ of the d ₃₃ mode.
Q ₂ = d ₃₃ × F (2)

The charge Q ₂ generated by the displacement in the same direction as the force F is better generated than the charge Q ₁ generated by the displacement in the direction different from the force F. For example, the piezoelectric constant d ₃₃ is about twice the piezoelectric constant d ₃₁ .

The piezoelectric element has a capacitor structure including a pair of electrodes and a piezoelectric body interposed between the electrodes. For this reason, the voltage V generated between the pair of electrodes can be expressed as the following equation (3). However, Q is a charge generated in the piezoelectric body, and C is a capacitance of the piezoelectric body.
V = Q / C (3)

Here, the conventional typical piezoelectric element shown in FIGS. 17 and 18 will be considered. When bending stress acts on the cantilever 101B, a force parallel to the longitudinal direction of the cantilever 101B acts on the piezoelectric layer 103. A voltage proportional to the charge generated in the piezoelectric layer 103 due to expansion and contraction perpendicular to the force acting on the piezoelectric layer 103 is generated between the lower electrode 102 and the upper electrode 104. That is, the conventional typical piezoelectric element shown in FIGS. 17 and 18 has a structure using the d ₃₁ mode.

Therefore, by using the d ₃₃ mode in the piezoelectric element, the charge Q and thus the voltage V in the above equation (3) can be made larger than the conventional typical piezoelectric element shown in FIGS. In addition, in the conventional typical piezoelectric element shown in FIGS. 17 and 18, in order to reduce the capacitance in the above equation (3), it is necessary to increase the thickness of the piezoelectric layer 103. Significant reduction was difficult.

Accordingly, the present inventors have adopted a structure in which a voltage is generated between a pair of electrodes by the displacement of the d ₃₃ mode of the piezoelectric body as a structure of the piezoelectric element, and the piezoelectric element having the structure is applied to the piezoelectric sensor. We decided to increase the output of the pressure sensor.

An example of a piezoelectric element using the d ₃₃ mode is disclosed in Non-Patent Document 1. However, in Non-Patent Document 1, since a piezoelectric element using the d ₃₃ mode is used as an energy harvester, the piezoelectric element using the d ₃₃ mode is simply connected to a load (passive element), and the piezoelectric element using the d ₃₃ mode is used. Only the output of the element is consumed by the load. In this way, it is not practical to apply the piezoelectric element to the power generation device in view of the power density disclosed in Non-Patent Document 1. That is, Non-Patent Document 1 does not show any practical application example of the piezoelectric element using the d ₃₃ mode.

<First Embodiment>
The piezoelectric sensor according to the first embodiment includes a piezoelectric element 11 shown in FIGS. 2 and 3, and an active circuit (not shown in FIGS. 2 and 3) whose input end is connected to the first electrode 1 of the piezoelectric element 11. ,have.

  2 is a top view of the piezoelectric element 11, and FIG. 3 is a cross-sectional view of the piezoelectric element 11 cut along line AA shown in FIG. The piezoelectric element 11 includes a first electrode 1, a second electrode 2, a piezoelectric layer 3, and a substrate 4.

  The substrate 4 is processed into a shape in which the cantilever 4B extends from the main body 4A. The piezoelectric layer 3 is formed on the cantilever 4 </ b> B, and the first electrode 1 and the second electrode 2 are formed on the piezoelectric layer 3. A part of the piezoelectric layer 3 extends to the main body 4A beyond the cantilever 4B, and a part of the first electrode 1 and a part of the second electrode 2 extend beyond the piezoelectric layer 3 to the main body 4A. It extends to a portion where the piezoelectric layer 3 is not formed.

  Each of the first electrode 1 and the second electrode 2 is a comb-like electrode. The 1st electrode 1 and the 2nd electrode 2 are arrange | positioned so that it may mutually mesh | engage, ie, the comb of the other electrode is located between the combs of one electrode. Further, in order to maximize the voltage generated between the first electrode 1 and the second electrode 2, the first electrode 1 and the second electrode 2 are each composed of a cantilever in which each comb of the first electrode 1 and the second electrode 2 is a cantilever. It is formed to extend in a direction substantially orthogonal to the longitudinal direction of 4B.

  As an example of the size of each part of the piezoelectric element 11, the longitudinal length L1 of the substrate 1 (see FIG. 2) is 1 mm at the maximum, and the width L2 of each comb of the first electrode 1 and the second electrode 2 (see FIG. 2) is the maximum. A design in which the distance L3 (see FIG. 2) between adjacent combs is 10 μm at the maximum is 10 μm.

The arrangement and shape of the first electrode 1 and the second electrode 2 are not limited to this embodiment, and a voltage is generated between the first electrode 1 and the second electrode 2 due to the displacement of the d ₃₃ mode of the piezoelectric layer 3. Any arrangement and shape may be used.

The piezoelectric sensor according to the present embodiment described above includes the piezoelectric element 11 having a structure in which a voltage is generated between the first electrode 1 and the second electrode 2 by the displacement of the d ₃₃ mode of the piezoelectric layer 3. Therefore, high output can be achieved.

Second Embodiment
The piezoelectric sensor according to the second embodiment includes a piezoelectric element 12 shown in FIGS. 4 and 5, and an active circuit (not shown in FIGS. 4 and 5) whose input end is connected to the first electrode 1 of the piezoelectric element 12. ,have.

  4 is a top view of the piezoelectric element 12, and FIG. 5 is a cross-sectional view of the piezoelectric element 12 cut along line AA shown in FIG. 4 and 5, the same parts as those in FIGS. 2 and 3 are denoted by the same reference numerals, and detailed description thereof is omitted.

  The piezoelectric element 12 has a configuration in which a piezoelectric layer 5 is added to the piezoelectric element 11 used in the first embodiment.

The piezoelectric element 12 has a structure in which the first electrode 1 and the second electrode 2 are sandwiched between the piezoelectric layer 3 and the piezoelectric layer 5. In the piezoelectric element 12, a voltage is generated between the first electrode 1 and the second electrode 2 by the displacement of the d ₃₃ mode of the piezoelectric layers 3 and 5.

  Since the piezoelectric layer 3 has a portion in contact with the cantilever 4B that is influenced by the restraint by the cantilever 4B, it is considered that the polarization direction is not easily aligned when a force parallel to the longitudinal direction of the cantilever 4B is applied. On the other hand, since the piezoelectric layer 5 is not in contact with the cantilever 4B and is not restrained by the cantilever 4B, it is considered that the polarization directions are easily aligned when a force parallel to the longitudinal direction of the cantilever 4B is applied.

Therefore, further increase in output of the piezoelectric sensor can be expected by providing the piezoelectric layer 5 in the piezoelectric element. Furthermore, by increasing than the thickness of the piezoelectric layer 3 the layer thickness of the piezoelectric layer 5, by d ₃₃ mode of the displacement of the piezoelectric layer 3 the generation of charges due to d ₃₃ mode of the displacement of the piezoelectric layer 5 Since it can dominate the generation of electric charge, it can be expected that the output of the piezoelectric sensor will be higher.

  Since the generated electric charge and the inter-electrode voltage of the piezoelectric element 12 are larger than those of the piezoelectric element 11 used in the first embodiment, there is a possibility of application to other than the piezoelectric sensor. That is, the application range of the piezoelectric element 12 and a piezoelectric element having a structure similar to this (electrode sandwiching structure by a piezoelectric body) is not limited to the present embodiment, that is, the piezoelectric sensor.

The piezoelectric sensor according to this embodiment described above includes the piezoelectric element 12 having a structure in which a voltage is generated between the first electrode 1 and the second electrode 2 by the displacement of the d ₃₃ mode of the piezoelectric layers 3 and 5. Therefore, high output can be achieved.

<Sensor system>
A sensor system can be obtained by combining the above-described piezoelectric sensor and an analog signal processing circuit that processes an analog output signal of the piezoelectric sensor.

  FIG. 6 is a diagram illustrating a configuration example of the sensor system. The sensor system shown in FIG. 6 is a microphone that includes a piezoelectric element 11, an impedance conversion circuit 13 that is an active circuit, a gain amplifier 14, an analog filter 15, and an A / D converter 16.

  The piezoelectric element is constituted by the piezoelectric element 11 and the impedance conversion circuit 13. The gain amplifier 14 amplifies the output of the piezoelectric sensor (output of the impedance conversion circuit 13). The analog filter 15 removes or suppresses unnecessary band components from the output (amplified signal) of the gain amplifier 14. The A / D converter 16 converts the output (analog signal) of the analog filter 15 into a digital signal.

  The output (digital signal) of the A / D converter 16 is sent to, for example, a DSP (Digital Signal Processor) (not shown) and subjected to speech recognition processing, speech compression processing, and the like.

  Here, the impedance conversion circuit 13, the gain amplifier 14, the analog filter 15, and the A / D converter 16 are integrated in one ASIC (Application Specific Integrated Circuit) 17, but the present invention is not limited to this.

  FIG. 7 is a diagram illustrating a configuration example of the impedance conversion circuit 13. In the configuration example of FIG. 7, the impedance conversion circuit 13 is an open drain circuit configured by a pull-up resistor R1 and an NMOS transistor Q1, and the first electrode 1 of the piezoelectric element 11 is the gate of the NMOS transistor Q1 (impedance conversion circuit). 13 input terminals).

  FIG. 8 is a diagram illustrating a configuration example of the impedance conversion circuit 13. In the configuration example of FIG. 8, the impedance conversion circuit 13 is a buffer amplifier configured by an operational amplifier A1, and the first electrode 1 of the piezoelectric element 11 is a non-inverting input terminal of the operational amplifier A1 (input terminal of the impedance conversion circuit 13). It is connected to the.

  FIG. 9 is a diagram showing another configuration example of the sensor system. In FIG. 9, the same parts as those in FIG. 6 are denoted by the same reference numerals, and detailed description thereof is omitted. The sensor system shown in FIG. 9 has a configuration in which the impedance conversion circuit 13 is replaced with a charge amplifier 18 in the sensor system shown in FIG. Here, the charge amplifier 18, the gain amplifier 14, the analog filter 15, and the A / D converter 16 are integrated in one ASIC 19, but the present invention is not limited to this.

  FIG. 10 is a diagram illustrating a configuration example of the charge amplifier 18. In the configuration example of FIG. 10, the charge amplifier 18 includes an operational amplifier A2, and a parallel circuit of a capacitor C1 and a resistor R2 provided between a non-inverting input terminal and an output terminal of the operational amplifier A2, and includes a piezoelectric element. 11 first electrodes 1 are connected to the non-inverting input terminal (input terminal of the charge amplifier 18) of the operational amplifier A2.

  Although the sensor system described above has a configuration including the piezoelectric element 11, it is naturally possible to use the piezoelectric element 12 instead of the piezoelectric element 11.

  A schematic structural example of the above-described sensor system will be described by taking the sensor system shown in FIG. 6 as an example.

  FIG. 11 is a schematic perspective view of the sensor system. The sensor system includes a housing 20. The housing 20 includes a base portion 20A and a cover portion 20B that covers the base portion 20A. An opening (acoustic hole) 20 </ b> C for introducing sound pressure into the housing 20 is formed in the cover portion 20 </ b> B.

  FIG. 12 is a schematic longitudinal sectional view of the sensor system. The opening (acoustic hole) 20C is formed in a portion of the cover portion 20B that faces the cantilever 4B. Thereby, the cantilever 5B is easily deformed by the sound pressure introduced into the housing 20 from the opening (acoustic hole) 20C, so that the sensitivity of the piezoelectric sensor is improved.

  A terminal of the ASIC 17 (terminal connected to the input terminal of the impedance conversion circuit 13) and the end of the first electrode 1 are electrically connected by a bonding wire 21. Further, the terminal of the ASIC 17 (terminal connected to the output terminal of the A / D converter 16) and the wiring pattern disposed in the base portion 20A are electrically connected by a bonding wire 21 '.

  The wiring pattern disposed in the base portion 20A is electrically connected to a through hole formed in the base portion 20A, and an electrical contact (terminal) is connected to the bottom surface of the base portion 20A by the through hole of the base portion 20A. Provided.

  Unlike the structure example described above, an opening (acoustic hole) 2 may be formed in a portion of the base portion 20A facing the cantilever 4B as shown in FIG. 13A. Further, unlike the above-described structural example, a piezoelectric element may be placed on the ASIC 17 as shown in FIG. 13B. Further, the shapes of the base portion 20A and the cover portion 20B are not limited to the above-described structural examples. For example, the base portion 20A may have a box shape without a lid, and the cover portion 20B may have a lid shape (plate shape).

<Other variations>
The configuration of the present invention can be variously modified within the scope of the present invention in addition to the above embodiment.

  For example, as a modification of the first embodiment, the shape of the substrate 4 may be changed as shown in FIG. 14 to provide a weight 4C on the free end side of the cantilever 4B.

  Further, as shown in FIG. 15, a weight 22 may be formed by a member different from the substrate 4 and provided on the free end side of the cantilever 4B. In this case, for example, the weight forming process and the electrode forming process may be executed in the same process by using the weight 22 as the same material as the first electrode 1 and the second electrode 2 at the time of manufacture.

  By providing the weight in this manner, the amount of deformation when the cantilever 5B is deformed is increased, so that the sensitivity of the piezoelectric sensor is improved. It should be noted that modifications similar to these modifications can be applied to the second embodiment.

  Further, for example, as a modification of the first embodiment, paying attention to the fact that the deformation of the cantilever 5B is large on the fixed end side, the first electrode 1 and the second electrode 2 are moved from the fixed end of the cantilever 5B as shown in FIG. The cantilever 5B may have a shape that extends to a length half the length a / 2 of the longitudinal length a. That is, the first electrode 1 and the second electrode 2 are not formed on the free end half of the cantilever 5B. The same modification as this modification can be applied to the second embodiment.

  In the above description, the microphone is taken as an application of the piezoelectric sensor, but the application of the piezoelectric sensor is not limited to this. For example, the piezoelectric sensor functions as an ultrasonic sensor by changing the detection target of the piezoelectric sensor from an audible sound to an ultrasonic wave. By adopting a system in which this ultrasonic sensor and ultrasonic transmitter are combined, it can be applied to, for example, a distance measuring device, an ultrasonic diagnostic device, and the like.

  As described above, the above embodiments are examples in all respects and should not be considered to be restrictive, and the technical scope of the present invention is not the description of the above embodiments, but the claims. It is to be understood that all changes that come within the scope of the claims, are equivalent in meaning to the claims, and fall within the scope of the claims.

  The present invention can be applied to, for example, a microphone, an ultrasonic diagnostic apparatus, and a distance measuring apparatus.

DESCRIPTION OF SYMBOLS 1 1st electrode 2 2nd electrode 3, 5 Piezoelectric layer 4 Board | substrate 4A Main body part 4B Cantilever 4C Weight 11,12 Piezoelectric element 13 Impedance conversion circuit 14 Gain amplifier 15 Analog filter 16 A / D converter 17, 19 ASIC
18 Charge amplifier 20 Housing 20A Base part 20B Cover part 20C Opening 21, 21 'Bonding wire

Claims (7)

A piezoelectric element comprising a first electrode, a second electrode, and a piezoelectric layer, wherein a voltage is generated between the first electrode and the second electrode by displacement of a d ₃₃ mode of the piezoelectric layer;
Possess an active circuit whose input terminal is connected to the first electrode,
The piezoelectric element includes a cantilever,
The piezoelectric layer is formed on the cantilever, and the first electrode and the second electrode are formed on the piezoelectric layer,
The piezoelectric layer is a first piezoelectric layer;
The piezoelectric element further includes a second piezoelectric layer,
The first electrode and the second electrode are sandwiched between the first piezoelectric layer and the second piezoelectric layer,
A voltage is generated between the first electrode and the second electrode by the d ₃₃ mode displacement of the first piezoelectric layer and the second piezoelectric layer ,
The piezoelectric sensor according to claim 1, wherein a thickness of the second piezoelectric layer is larger than a thickness of the first piezoelectric layer . Each of the first electrode and the second electrode is a comb-like electrode, and is arranged so as to mesh with each other, and each comb of the first electrode and the second electrode extends in a direction intersecting with a longitudinal direction of the cantilever. The piezoelectric sensor according to claim 1 , which is formed as described above. The piezoelectric sensor according to claim 1, wherein the piezoelectric element further includes a weight provided on a free end side of the cantilever . The piezoelectric sensor according to any one of claims 1 to 3 ,
An analog signal processing circuit for processing an analog output signal of the piezoelectric sensor. The sensor system according to claim 4 , wherein the active circuit and the analog signal processing circuit are integrated. A housing that houses the piezoelectric sensor ;
It said piezoelectric sensor is a piezoelectric sensor according to any one of claims 1 to 3, according to claim 4 or claim 5 opening is provided in a portion facing the cantilever of the housing Sensor system. A first electrode, a second electrode, a first piezoelectric layer, a second piezoelectric layer, and a cantilever;
The first piezoelectric layer is formed on the cantilever, the first electrode and the second electrode are formed on the first piezoelectric layer;
The first electrode and the second electrode are sandwiched between the first piezoelectric layer and the second piezoelectric layer,
A voltage is generated between the first electrode and the second electrode by the d ₃₃ mode displacement of the first piezoelectric layer and the second piezoelectric layer ,
The piezoelectric element according to claim 1, wherein a thickness of the second piezoelectric layer is greater than a thickness of the first piezoelectric layer .

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