Patent Application
20200028483
The present invention relates to an elastic wave device including a support substrate made of silicon and to a high-frequency front-end circuit and a communication device including the same.
Various elastic wave devices in which a silicon plate is used as a support substrate have been proposed. For example, Japanese Unexamined Patent Application Publication No. 11-55070 discloses an elastic wave device in which a SiO2 film, a LiTaO3 film, and an interdigital transducer electrode are stacked in this order on a silicon substrate. According to Japanese Unexamined Patent Application Publication No. 11-55070, the film thickness of the LiTaO3 film is about 1λ, where the wavelength of an elastic wave is assumed to be λ.
Regarding the elastic wave device described in Japanese Unexamined Patent Application Publication No. 11-55070, a higher-order mode response may be relatively significant depending on the crystal orientation state of the silicon substrate.
Preferred embodiments of the present invention provide elastic wave devices, high-frequency front-end circuits, and communication devices in which a higher-order mode response is effectively reduced or prevented.
An elastic wave device according to a preferred embodiment of the present invention includes a support substrate made of silicon, a piezoelectric film disposed directly or indirectly on the support substrate, and an interdigital transducer electrode disposed on one surface of the piezoelectric film, wherein a higher-order mode acoustic velocity of propagation through the piezoelectric film is equal or substantially equal to the acoustic velocity Vsi denoted by formula (1) described below or higher than the acoustic velocity Vsi.
V
si=(V1)1/2 (m/sec) formula (1)
In formula (1), V1 is the solution to formula (2) described below.
Ax
3
+Bx
2
+Cx+D=0 formula (2)
In formula (2), A, B, C, and D are values denoted by formulae (2A) to (2D), respectively, described below.
A=−ρ
3 formula (2A)
B=ρ
2(L11+L22+L33) formula (2B)
C=ρ(L212+L232+L312−L11·L33−L22·L33−L11·L22) formula (2C)
D=2·L21·L23·L31+L11·L22·L33−L312·L22−L11·L232−L212·L33 formula (2D)
In each of formula (2A), formula (2B), formula (2C), and formula (2D), ρ represents the density (g/cm3) of silicon and L11, L22, L33, L21, L31, and L23 are values denoted by formulae (3A) to (3F), respectively, described below.
L
11
=c
11
·a
1
2
+c
44
·a
2
2
+c
44
·a
3
2 formula (3A)
L
22
=c
44
·a
1
2
+c
11
·a
2
2
+c
44
·a
3
2 formula (3B)
L
33
=c
44
·a
1
2
+c
44
·a
2
2
+c
11
·a
3
2 formula (3C)
L
21=(c12+c44)·a2·a1 formula (3D)
L
31=(c12+c44)·a1·a3 formula (3E)
L
23=(c44+c12)·a3·a2 formula (3F)
In the formulae (3A) to (3F), each of c11, c12, and c44 is an elastic constant (N/m2) of silicon, and a1, a2, and a3 are values denoted by formulae (4A) to (4C), respectively, described below.
a
1=cos(ϕ)·cos(φ)−sin(ϕ)·cos(θ)·sin(φ) formula (4A)
a
2=sin(ϕ)·cos(φ)+cos(ϕ)·cos(θ)·sin(φ) formula (4B)
a
3=sin(θ)·sin(φ) formula (4C)
In the formulae (4A) to (4C), ϕ, θ, and φ represent ϕ, θ, and φ in the crystal orientation (ϕ,θ,φ) of silicon.
In an elastic wave device according to a preferred embodiment of the present invention, V1 in formula (1) is the solution with the lowest value among the solutions V1, V2, and V3 with respect to formula (2) described above.
In an elastic wave device according to a preferred embodiment of the present invention, the piezoelectric film is made of LiTaO3. In this case, a main mode response has high Q and, further, a higher-order mode response is reduced or prevented.
In an elastic wave device according to a preferred embodiment of the present invention, the film thickness of the piezoelectric film made of LiTaO3 is within the range of about 0.05λ or more and about 3.5λ or less, where the wavelength of the elastic wave, which is determined in accordance with the electrode finger pitch of the interdigital transducer electrode, is λ. In this case, a higher-order mode response is more effectively reduced or prevented. More preferably, the film thickness of the piezoelectric film made of LiTaO3 is about 1.5λ or less. In this case, a higher-order mode response is also more effectively reduced or prevented. Further preferably, the film thickness of the piezoelectric film made of LiTaO3 is about 0.5λ or less. In this case, a higher-order mode response is also more effectively reduced or prevented and, in addition, the Q of a main mode response is more improved.
In an elastic wave device according to a preferred embodiment of the present invention, a dielectric film stacked between the support substrate and the piezoelectric film is further included.
In an elastic wave device according to a preferred embodiment of the present invention, the dielectric film is made of silicon oxide. In this case, the absolute value of the temperature coefficient of resonant frequency TCF is reduced.
In an elastic wave device according to a preferred embodiment of the present invention, the film thickness of the dielectric film made of silicon oxide is about 1.2λ or less, where the wavelength of the elastic wave, which is determined in accordance with the electrode finger pitch of the interdigital transducer electrode, is λ. In this case, a higher-order mode response is more effectively reduced or prevented. More preferably, the film thickness of the dielectric film made of silicon oxide is about 0.6λ or less, where the wavelength of the elastic wave, which is determined in accordance with the electrode finger pitch of the interdigital transducer electrode, is λ. In this case, a higher-order mode response is also more effectively reduced or prevented.
In an elastic wave device according to a preferred embodiment of the present invention, a high acoustic velocity film, which is disposed between the support substrate and the piezoelectric film and through which a bulk wave propagates at an acoustic velocity higher than the acoustic velocity of an elastic wave that propagates through the piezoelectric film, and a low acoustic velocity film, which is stacked on the high acoustic velocity film and through which a bulk wave propagates at an acoustic velocity lower than the acoustic velocity of an elastic wave that propagates through the piezoelectric film, are further provided.
A high-frequency front-end circuit according to a preferred embodiment of the present invention includes the elastic wave device according to a preferred embodiment of the present invention and a power amplifier.
A communication device according to a preferred embodiment of the present invention includes the high-frequency front-end circuit, an RF signal processing circuit, and a base band signal processing circuit.
In elastic wave devices according to preferred embodiments of the present invention, a higher-order mode response is effectively reduced or prevented by selecting a silicon crystal orientation (ϕ,θ,φ) in which the acoustic velocity through the support substrate made of silicon is lower than or equal to the higher-order mode acoustic velocity. In high-frequency front-end circuits and communication devices according to preferred embodiments of the present invention, a higher-order mode response is effectively reduced or prevented by using the above-described elastic wave device.
The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings.
The preferred embodiments according to the present invention will be described below with reference to the drawings so as to clarify the present invention.
It is indicated that each of the preferred embodiments described in the present specification is an exemplification and the configuration may be partly replaced or combined with the configuration of other preferred embodiments.
A LiTaO3 film 4 defining a piezoelectric film is stacked on the SiO2 film 3. That is, the LiTaO3 film 4 is disposed indirectly on the support substrate 2. An interdigital transducer electrode 5 and reflectors 6 and 7 are disposed on the LiTaO3 film 4. As shown in
The interdigital transducer electrode 5 is preferably disposed on the upper surface of the LiTaO3 film 4 but may be disposed on the lower surface.
The dielectric film may be disposed on the interdigital transducer electrode 5.
Preferred embodiments of the present invention were developed by the inventor based on a new discovery that a higher-order mode response increased when the acoustic velocity through the support substrate made of silicon became higher than a higher-order mode acoustic velocity and that a higher-order mode response decreased when the acoustic velocity through the support substrate became lower than or equal to a higher-order mode acoustic velocity.
In this regard, the acoustic velocity through the support substrate made of silicon is denoted by formulae (1) to (4C) described below, and the value of the acoustic velocity changes in accordance with the value of the crystal orientation (ϕ,θ,φ) of silicon.
V
si=(V1)1/2 (m/sec) formula (1)
In formula (1), V1 is the solution to formula (2) described below.
Ax
3
+Bx
2
+Cx+D=0 formula (2)
In formula (2), A, B, C, and D are values denoted by formulae (2A) to (2D), respectively, described below.
A=−ρ
3 formula (2A)
B=ρ
2(L11+L22+L33) formula (2B)
C=ρ(L212+L232+L312−L11·L33−L22·L33−L11·L22) formula (2C)
D=2·L21·L23·L31+L11·L22·L33−L312·L22−L11·L232−L212·L33 formula (2D)
In each of formula (2A), formula (2B), formula (2C), and formula (2D), ρ represents the density (g/cm3) of silicon, and L11, L22, L33, L21, L31, and L23 are values denoted by formulae (3A) to (3F), respectively, described below.
L
11
=c
11
·a
1
2
+c
44
·a
2
2
+c
44
·a
3
2 formula (3A)
L
22
=c
44
·a
1
2
+c
11
·a
2
2
+c
44
·a
3
2 formula (3B)
L
33
=c
44
·a
1
2
+c
44
·a
2
2
+c
11
·a
3
2 formula (3C)
L
21=(c12+c44)·a2·a1 formula (3D)
L
31=(c12+c44)·a1·a3 formula (3E)
L
23=(c44+c12)·a3·a2 formula (3F)
In the formulae (3A) to (3F), each of c11, c12, and c44 is an elastic constant (N/m2) of Si (silicon), and a1, a2, and a3 are values denoted by formulae (4A) to (4C), respectively, described below.
a
1=cos(ϕ)·cos(φ)−sin(ϕ)·cos(θ)·sin(φ) formula (4A)
a
2=sin(ϕ)·cos(φ)+cos(ϕ)·cos(θ)·sin(φ) formula (4B)
a
3=sin(θ)·sin(φ) formula (4C)
In the formulae (4A) to (4C), ϕ, θ, and φ represent ϕ, θ, and φ in the crystal orientation (ϕ,θ,φ) of silicon.
Then, a higher-order mode response is effectively reduced or prevented by selecting the value of a silicon crystal orientation (ϕ,θ,φ) such that a higher-order mode acoustic velocity of propagation through the piezoelectric film becomes equal or substantially equal to the acoustic velocity Vsi through the support substrate made of silicon or higher than the acoustic velocity Vsi through the support substrate made of silicon.
A further feature of the elastic wave device 1 is that the higher-order mode acoustic velocity of propagation through the LiTaO3 film 4 is preferably set to be equal or substantially equal to a slow transverse wave acoustic velocity Vsi denoted by Vsi=(V1)1/2 or to be higher than the acoustic velocity Vsi, where the solution with the lowest value among the solutions V1, V2, and V3 (V1≤V2<V3) with respect to x that satisfies formula (2) described above is assumed to be V1. The slow transverse wave acoustic velocity Vsi of propagation through silicon is (V1)1/2 (m/sec).
Consequently, a higher-order mode response is more effectively reduced or prevented.
The crystal orientation (ϕ,θ,φ) of silicon will be described with reference to
As shown in
Here, Vsi is calculated as the acoustic velocity of the slow transverse wave among silicon bulk waves that propagate in the Xa-direction.
When the crystal orientation (ϕ,θ,φ) of silicon is, for example, (30°,54.7°,45°), the acoustic velocity Vsi determined on the basis of formula (1) is 4,913 (m/sec).
The elastic constants c11, c12, and c44 of Si are values defined as described below.
The strain S and the stress T of an elastic body are in a proportional relationship with each other. This proportional relationship is represented by the following matrix.
The proportionality constant (cij) of this formula is called an elastic constant. The elastic constant cij is determined based on the crystal system to which a solid belongs. For example, regarding silicon, the elastic constant may be expressed by three independent values, as described below, because of the symmetry of the crystal.
Si Elastic Constant (N/m2)
The above-described elastic constants c11, c12, and c44 are elastic constants of Si defined as described above. The elastic constants of Si are c11=1.674E+11 (N/m2), c12=6.523E+10 (N/m2), and c44=7.957E+10 (N/m2) (H. J. McSkimin, et al., “Measurement of the Elastic Constants of Silicon Single Crystals and Their Thermal Constants”, Phys. Rev. Vol. 83, p. 1080(L) (1951)). In addition, the density ρ of silicon is 2,331 (g/cm3).
In the elastic wave device 1, the higher-order mode acoustic velocity is increased so as to become higher than or equal to the acoustic velocity Vsi. Therefore, the higher-order mode is not confined within the portion in which the SiO2 film 3 and the LiTaO3 film 4 are stacked, and the higher-order mode leaks into the support substrate 2 made of Si. Consequently, a higher-order mode response is effectively reduced or prevented.
The higher-order mode acoustic velocity is able to be adjusted in accordance with the film thickness of the low acoustic velocity film, e.g., the SiO2 film.
When the crystal orientation of silicon is rotated in all directions, Vsi in the orientation in which Vsi is minimized is about 4,673 (m/sec), for example. According to
In addition, in the elastic wave device 1, the thickness of the LiTaO3 film 4 is preferably within the range of about 0.05λ or more and about 3.5λ or less, for example, where the wavelength of the elastic wave, which is determined in accordance with the electrode finger pitch of the interdigital transducer electrode 5, is λ. The film thickness is more preferably set to be about 1.5λ or less, and even more preferably to be about 0.5λ or less, for example.
This is because, although the higher-order mode tends to be confined to within the portion in which the SiO2 film 3 and the LiTaO3 film 4 are stacked, as described above, when a structure according to a preferred embodiment of the present invention is applied, the higher-order mode is not readily confined by setting the thickness of the LiTaO3 film 4 to be within the above-described range so as to reduce the thickness of the stacking portion of the SiO2 film 3 and the LiTaO3 film 4.
An example of the elastic wave device according to the above-described preferred embodiment and an elastic wave device of a comparative example were produced. The design parameters were as described below.
An example of an elastic wave device according to a preferred embodiment includes a SiO2 film 3 having a thickness of about 0.337λ, a LiTaO3 film 4 having a thickness of about 0.300λ, an Al interdigital transducer electrode 5 having a thickness of about 0.08λ, and reflectors 6 and 7 disposed on a support substrate 2 composed of silicon with a crystal orientation of (45°,0°,0°), for example. The wavelength λ, which was determined in accordance with the electrode finger pitch of the interdigital transducer electrode was set to be about 1 μm. In the comparative example, an elastic wave device was produced in the same or similar manner as the above-described preferred embodiment except that the crystal orientation of silicon was set to be (0°,0°,0°).
In the above-described elastic wave device, the acoustic velocity through the support substrate 2 was about 4,673 (m/sec), a spurious first higher-order mode acoustic velocity was about 4,673 (m/sec), and a spurious second higher-order mode acoustic velocity was about 5,628 (m/sec), for example.
In the elastic wave device of the comparative example, the acoustic velocity through the support substrate was about 5,844 (m/sec), a first higher-order mode acoustic velocity was about 5,108 (m/sec), and a second higher-order mode acoustic velocity was about 5,588 (m/sec).
In
As described above, in the elastic wave device 1 according to the present preferred embodiment, the higher-order mode acoustic velocities are set to be higher than the acoustic velocity through the support substrate and, therefore, higher-order mode responses are effectively reduced or prevented.
In order to set the higher-order mode acoustic velocity to be higher than the acoustic velocity through the support substrate made of silicon, as described above, the film thickness of the low acoustic velocity film, e.g., a SiO2 film, or the piezoelectric thin film, e.g., a LiTaO3 film, may be changed so as to change the higher-order mode acoustic velocity. Alternatively, the acoustic velocity of a wave that propagates through the support substrate made of silicon may be adjusted by changing the crystal orientation of silicon.
That is, at least one of the higher-order mode acoustic velocity and the acoustic velocity Vsi satisfying formula (1) may be adjusted such that the higher-order mode acoustic velocity of propagation through the piezoelectric film becomes higher than the acoustic velocity Vsi of the wave that propagates through silicon.
In preferred embodiments of the present invention, it is not always necessary that the dielectric film, e.g., the SiO2 film 3, be provided. In that case, the piezoelectric film is disposed directly on the support substrate 2. In this case as well, a higher-order mode response is able to be reduced or prevented by adjusting the acoustic velocity Vsi of a wave that propagates through the support substrate 2 made of silicon such that the higher-order mode acoustic velocity becomes higher than the acoustic velocity Vsi. That is, the above-described acoustic velocity Vsi may be adjusted such that the acoustic velocity Vsi becomes lower than the higher-order mode acoustic velocity by adjusting the crystal orientation of silicon.
In this regard, as described above, it is preferable that a method in which the higher-order mode acoustic velocity is set to be higher than the acoustic velocity Vsi by adjusting the film thickness of the SiO2 film so as to control the higher-order mode acoustic velocity be used. Consequently, a higher-order mode response is able to be more effectively reduced or prevented.
In addition, a dielectric film made of a dielectric other than SiO2 may be used.
Further, as an elastic wave device 21 according to a modified example of a preferred embodiment of the present invention as shown in
In this regard, the first low acoustic velocity film 22 in the elastic wave device 21 may be omitted. That is, the structure in which the high acoustic velocity film 23 and the second low acoustic velocity film 24 are stacked on the support substrate 2 may be provided.
In the above-described preferred embodiment, the one-port elastic wave resonator was described as the elastic wave device 1. However, the elastic wave device according to the present invention is not limited to the one-port elastic wave resonator. The present invention can be widely applied to elastic wave devices having various electrode structures, e.g., a longitudinally coupled resonator-type elastic wave filter.
The material used for the piezoelectric film is not limited to LiTaO3, and materials made of other piezoelectric single crystals, e.g., LiNbO3, or other piezoelectric materials may be used.
The high-frequency front-end circuit 130 includes a quadplexer 101, a receiving switch 113, a sending switch 123, a low noise amplifying circuit 114, and a power amplifying circuit 124. The elastic wave device 1 may preferably define the quadplexer 101 or filters 111, 112, 121, and 122, for example.
The receiving switch 113 is a switch circuit including two selection terminals individually connected to an individual terminal 111A and an individual terminal 121A that are receiving terminals of the quadplexer 101 and a common terminal connected to the low noise amplifying circuit 114.
The sending switch 123 is a switch circuit including two selection terminals individually connected to an individual terminal 112A and an individual terminal 122A that are sending terminals of the quadplexer 101 and a common terminal connected to the power amplifying circuit 124.
Each of the receiving switch 113 and the sending switch 123 connects the common terminal to a signal path corresponding to a predetermined band in accordance with a control signal from a control portion (not shown in the drawing) and is preferably, for example, a SPDT (single pole double throw) switch. The selection terminal connected to the common terminal is not limited to one and may be two or more. That is, the high-frequency front-end circuit 130 may be compatible with carrier aggregation.
The low noise amplifying circuit 114 is a receiving amplifying circuit that amplifies high-frequency signals (i.e., high-frequency received signals), which are received via the antenna element 102, the quadplexer 101, and the receiving switch 113, and output to the RF signal processing circuit 103.
The power amplifying circuit 124 is a sending amplifying circuit that amplifies high-frequency signals (i.e., high-frequency sending signals), which are output from the RF signal processing circuit 103, and outputs to the antenna element 102 via the sending switch 123 and the quadplexer 101.
The RF signal processing circuit 103 subjects high-frequency received signals, which are input from the antenna element 102 through a receiving signal path, to signal processing, e.g., down-conversion, and outputs received signals, which are generated by the signal processing, to the base band signal processing circuit 104. In addition, the RF signal processing circuit 103 subjects sending signals, which are input from the base band signal processing circuit 104, to signal processing, e.g., up-conversion, and outputs high-frequency sending signals, which are generated by the signal processing, to the power amplifying circuit 124. The RF signal processing circuit 103 is preferably, for example, RFIC. The signals processed by the base band signal processing circuit 104 are used as, for example, image signals for image display or voice signals for telephone calls. In this regard, the high-frequency front-end circuit 130 may include other circuit elements between the above-described components.
With the high-frequency front-end circuit 130 and the communication device 140 having the above-described configuration, ripples in a pass band are reduced or prevented by including the quadplexer 101.
The high-frequency front-end circuit 130 may preferably include a quadplexer according to a modified example of the quadplexer 101, instead of the above-described quadplexer 101.
The elastic wave device, the high-frequency front-end circuit, and the communication device according to the preferred embodiments of the present invention have been described with reference to the preferred embodiments and the modified examples thereof. The present invention includes other preferred embodiments that are obtained by combining any components and elements in the above-described preferred embodiments and modified examples, modified examples obtained by applying various modifications, which are conceived by a person skilled in the art, within the scope of the gist of the present invention to the above-described preferred embodiments, and various equipment including the high-frequency front-end circuit or the communication device.
For example, in the above-described preferred embodiments of the present invention and modified examples thereof, the elastic wave device may preferably be the quadplexer or the filter, for example. However, the present invention can also be applied to, for example, multiplexers, e.g., a triplexer in which three filters share an antenna terminal and a hexaplexer in which six filters share an antenna terminal. The multiplexer only needs to include at least two filters.
Further, the multiplexer is not limited to a configuration in which both of the sending filter and the receiving filter are included and may have a configuration in which only the sending filter is included or only the receiving filter is included.
Preferred embodiments of the present invention can be widely used as the multiplexer, which may be applied to a filter and a multiband system, the front-end circuit, and the communication device for communication equipment, e.g., a cellular phone.
The present invention reduces or prevents a higher-order mode that propagates through a piezoelectric film by changing the crystal orientation of a support substrate made of silicon.
Therefore, the higher-order mode described herein refers to any one of modes (types) of waves or a plurality of modes of waves which are generated between about 4,673 m/s and about 5,844 m/s that is the range of the transverse wave acoustic velocity of silicon and which are generated in the higher frequency side than the main mode that propagates through the piezoelectric film.
That is, the higher-order mode that propagates through a piezoelectric film refers to any one of modes (types) of waves or a plurality of modes of waves which are generated in the higher frequency side than the main mode that propagates through the piezoelectric film and which are generated between about 4,673 m/s and about 5,844 m/s that is the range of the transverse wave acoustic velocity of silicon.
For example, when reduction or prevention of the higher-order mode nearest to about 5,844 m/s between about 4,673 m/s and about 5,844 m/s that is the range of the silicon acoustic velocity is intended, this higher-order mode is able to be reduced or prevented by setting the acoustic velocity Vsi to be lower than or equal to this higher-order mode acoustic velocity.
In addition, when reduction or prevention of all higher-order modes between about 4,673 m/s and about 5,844 m/s is intended, all of the above-described higher-order modes are able to be reduced or prevented by setting the acoustic velocity Vsi to be lower than or equal to the higher-order mode acoustic velocity nearest to about 4,673 m/s between about 4,673 m/s and about 5,844 m/s.
When the elastic wave device is a resonator, the main mode that propagates through a piezoelectric film refers to a mode of a wave that has the largest difference between the impedance at a resonant frequency and the impedance at an anti-resonant frequency.
When the elastic wave device is a filter, the main mode that propagates through a piezoelectric film refers to a mode of a wave that is used to provide a pass band of the filter.
Then, the higher-order mode that propagates through a piezoelectric film is able to be specified by simulation of a finite element method. Specifically, the film thickness of the interdigital transducer electrode, the material use for the interdigital transducer electrode, the film thickness of the piezoelectric film, the material used for the piezoelectric film, the film thickness of each intermediate layer of the low acoustic velocity film, the high acoustic velocity film, the material used for each intermediate layer, the thickness of the support substrate, and each parameter of the crystal orientation of the support substrate are specified. Thereafter, harmonic vibration analysis is performed using each parameter and simulation software (FEMTET).
Subsequently, the impedance at each frequency is able to be obtained based on the harmonic vibration analysis.
Therefore, from the results of the harmonic vibration analysis, at least one resonant frequency at which the impedance has the local minimum value and at least one anti-resonant frequency at which the impedance has the local maximum value are able to be specified. Then, among them, the mode of a wave that has the largest difference between the impedance at a resonant frequency and the impedance at an anti-resonant frequency is specified. The mode of the wave is the main mode that propagates through the piezoelectric film.
As a result, a higher-order mode (the mode of a wave which is generated in the higher frequency side than the main mode and which is generated between about 4,673 m/s and about 5,844 m/s that is the range of the silicon acoustic velocity) that propagates through the piezoelectric film is able to be specified on the basis of the above-described main mode.
When a plurality of higher-order modes are specified, the mode which has the velocity higher than the acoustic velocity Vsi and which is nearest to the acoustic velocity Vsi is assumed to be the higher-order mode.
Then, regarding the higher-order mode acoustic velocity, V=f×λ is satisfied, where the higher-order mode acoustic velocity of propagation through the piezoelectric film is denoted as V, the anti-resonant frequency of the higher-order mode that propagates through the piezoelectric film is denoted as f, and the value that is twice the electrode finger pitch of the interdigital transducer electrode is denoted as λ.
Therefore, the higher-order mode acoustic velocity V of propagation through the piezoelectric film is able to be determined by multiplying the anti-resonant frequency f of the higher-order mode that propagates through the piezoelectric film by λ that is twice the electrode finger pitch of the interdigital transducer electrode.
While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2015-178650 | Sep 2015 | JP | national |
This application claims the benefit of priority to Japanese Patent Application No. 2015-178650 filed on Sep. 10, 2015 and is a Continuation Application of PCT Application No. PCT/JP2016/075526 filed on Aug. 31, 2016. The entire contents of each application are hereby incorporated herein by reference.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15879468 | Jan 2018 | US |
| Child | 16583511 | US | |
| Parent | PCT/JP2016/075526 | Aug 2016 | US |
| Child | 15879468 | US |
