JP2003046368A - Surface acoustic wave device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a surface acoustic wave device that has excellent temperature characteristics and can increase the operating frequency without decreasing a factor h/λ. SOLUTION: The cutting angle of the surface of a crystal substrate 1 and the propagation direction are selected within the Euler's angle (0, θ=100 to 150, 0), the IDT(Inter-Digital Transducer) normalized electrode film thickness h/λ is selected to be 0.02 or more, and a pseudo longitudinal wave leakage surface acoustic wave to propagate in parallel with the +X axis is stimulated on the crystal substrate 1.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a surface acoustic wave device, and more particularly to a frequency selection filter in a mobile phone or the like, an oscillator in a keyless entry system or the like,
It is suitable to be applied to a resonator or the like.

[0002]

2. Description of the Related Art A surface acoustic wave device is a circuit element that converts an electric signal into a surface wave and performs signal processing, and is widely used as a filter, a resonator and the like. Usually, an electrode made of a conductive film called an IDT electrode is provided on an elastic substrate (piezoelectric substrate) having a piezoelectric property to convert an electric signal into a surface wave and vice versa.

The characteristic of the surface acoustic wave device depends on the propagation characteristic of the surface acoustic wave propagating through the piezoelectric substrate. Particularly, in order to cope with the high frequency of the surface acoustic wave device, the propagation velocity of the surface acoustic wave is high. A piezoelectric substrate having a high speed is required. In addition, a surface acoustic wave device having stable characteristics with respect to changes in temperature is required for some applications. Quartz is known as a single crystal substrate material having excellent temperature characteristics.

The surface acoustic wave used in the surface acoustic wave device is a Rayleigh wave.
Alternatively, leaky surface acoustic waves are mainly used. The Rayleigh wave is a surface wave propagating on the surface of the elastic body and propagates without radiating its energy inside the piezoelectric substrate, that is, theoretically without propagation loss.
An example of a surface acoustic wave device using Rayleigh waves is an ST-cut crystal having a propagation velocity of 3150 m / sec.

There are three kinds of volume waves (bulk waves) of "slow transverse wave", "fast transverse wave", and "longitudinal wave" in the piezoelectric substrate, and this Rayleigh wave is slower than "slow transverse wave". It propagates at a phase velocity. The leaky surface acoustic wave is a surface acoustic wave that propagates while radiating energy in the depth direction of the elastic body, and can be used at a special cutting angle and propagation direction. For example, if the phase velocity is 3900 m / sec, L
ST-cut quartz is known. This leaky surface acoustic wave propagates at a phase velocity between "slow transverse wave" and "fast transverse wave".

As described above, the quartz substrate has an advantage that the temperature characteristics are good, but when Rayleigh waves and leaky surface acoustic waves are used, the phase velocity is small and it is suitable for high frequency surface acoustic wave devices. Was not considered a suitable material. However, by setting the surface wave propagation direction at 90 ° with the propagation direction of the ST-cut crystal, an STW (Surface) having a relatively large phase velocity is used while using the crystal.
It is known that Transverse Wave can be used. For example, the 1995 Japan Society for the Promotion of Science Industry-Academia Collaborative Research Support Project Implementation Report 132-137, "Hig
hPerformance GHz Range Su
rface Transverse Wave Res
onnt Devices. Application
s to Low Noise Microwave
Oscillators and Communica
In the “tion System”, the phase velocity of STW is
It is 1.6 times that of conventional ST-cut crystals.

Further, Japanese Unexamined Patent Publication No. 10-233645 discloses a method of improving temperature characteristics by using tantalum or tungsten as an electrode material of a surface acoustic wave device using STW. Further, in recent years, by developing the theory of leaky surface acoustic waves, most of the displacements on the substrate surface are composed of longitudinal wave components, and two transverse wave components are radiated into the piezoelectric substrate as bulk waves while ”And“ longitudinal wave ”, a series of pseudo-longitudinal wave type leaky surface acoustic waves propagating at high phase velocities.

In Japanese Patent Laid-Open No. 6-112763, in lithium tetraborate, the propagation speed is 5000 m / sec-7.
It has been clarified that a pseudo longitudinal wave type leaky surface acoustic wave having a large propagation loss of 500 m / sec and a low propagation loss can be used. In addition, even in the quartz substrate, 1999 IEEE ULT
RASONICS SYMPOSIUM 321-324
Page "Study of Propagation of
Quasi-longitudinal Leaky
Surface Acoustic Wave Pr
Opagating on Y-Rotated Cu
In “t Quartz Substrates” (hereinafter referred to as Reference 1), a pseudo longitudinal wave type leaky surface acoustic wave is used, and the Euler angles (0 °, 155.25 °, 42 °) of 2 are used.
When the shaft is rotated, the delay time temperature coefficient TCD is 0.508.
It has been revealed to be ppm / ° C.

Further, 2000FCS, Kansas
MO USA June7-9, 2000 "ANALY
SIS OF VELOCITY PSEUDO-SU
RFACE ACOUSTIC WAVES (HVPS
AW) IN QUARTZPERIODIC STR
UCTURES WITH ELECTRODEFIN
GERS "(hereinafter referred to as Reference 2) uses a pseudo-longitudinal-wave type leaky surface acoustic wave, and when the standardized film thickness h / λ of the IDT electrode is 0.0125 in uniaxial rotation, it depends on the frequency. It has been revealed that the temperature change exhibits a cubic curve.

[0010]

However, the ST-cut quartz crystal using Rayleigh waves and the LST-cut quartz crystal using leaky surface acoustic waves have excellent temperature characteristics, but the phase velocity is at most 4000 m / sec. However, it is not suitable for higher frequency. For example, with this phase velocity, 1G
In order to target a signal frequency of Hz or higher, an electrode width and an electrode interval of 1 μm or less are required. Also, IDT
Regarding the electrode film thickness h, if the signal frequency of 1 GHz or more is targeted, the ST-cut quartz crystal
NICALREPORT OF IEICE. US99
-20 (1999-06) pp. 37-42 "Frequency-Temperature Characteristic Analysis of Surface Acoustic Waves Using Finite Element Method", IDT standardized electrode film thickness h where the vertex temperature is near room temperature.
Since / λ is about 0.03, the IDT electrode film thickness h is 9
It must be 45 Å or less.

Further, in the case of the LST cut crystal, as described in JP-A-2-194714, I
Since it is necessary to set the DT standardized electrode film thickness h / λ = 0.005 ± 0.001, it is necessary to form the IDT electrode film thickness h thinner than ST. Therefore, in the method using the Rayleigh wave or the leaky surface acoustic wave, when the signal frequency of 1 GHz or higher is targeted, there is a problem that the manufacturing yield of the IDT electrode is reduced and the manufacturing of the surface acoustic wave device becomes difficult.

In the method using STW, the phase velocity is larger than that in ST cut crystal or LST cut crystal,
Frequency change is 1 in the temperature range of -30 ℃ to 60 ℃
It becomes 30 ppm, and there is a problem that the frequency-temperature characteristic deteriorates as compared with the ST-cut crystal and the LST-cut crystal.
Here, in the method described in JP-A-10-233645, by using tantalum or tungsten, which has a higher density than aluminum, as an electrode material, the frequency temperature characteristic can be improved, but the electrical resistance loss is large. Therefore, there is a problem that the phase velocity is greatly reduced.

The method of utilizing a pseudo longitudinal wave type leaky surface acoustic wave by using lithium tetraborate as a substrate material can utilize a large phase velocity, but is inferior in temperature stability to quartz. There's a problem. For example, JP-A-8-1
According to Japanese Patent No. 25488, the frequency change in the temperature range of −20 ° C. to 80 ° C. is about 600 ppm, which is very bad as compared with the ST cut crystal and the LST cut crystal.

Lithium tetraborate has the problems that it is expensive and inferior in stability as compared with quartz. Further, in the case of utilizing the pseudo-longitudinal wave type leaky surface acoustic wave, since the method of Reference 1 uses the biaxial rotation cut angle, the difference between the phase velocity direction in which the surface acoustic wave propagates and the group velocity direction is expressed. It is necessary to consider the power flow angle, which is an angle, and there is a problem that high rotation angle accuracy is required.

In the method of Document 2, the frequency change with temperature exhibits a cubic curve by specifying the relationship between the uniaxial rotation cut angle of the crystal and the normalized film thickness h / λ of the IDT electrode. . However, in the method of Reference 2, since the normalized film thickness h / λ of the IDT electrode is as thin as 0.0125, it is assumed that 1G
In order to target high frequencies of Hz or higher, it is necessary to reduce the electrode width and the electrode interval, and when the phase velocity is 5730 m / sec, the IDT electrode film thickness is 716.
Å Must be formed very thin. Therefore, there is a problem that the electric resistance loss increases and the Q value decreases.

Further, since the reflectance per reflector becomes small, it is necessary to increase the number of pairs of reflectors, which causes a problem that the size of the device becomes large. Further, in the manufacturing process, there is a problem that the manufacturing yield is lowered due to peeling of the electrodes during the wire bonder. Therefore, an object of the present invention is to provide a surface acoustic wave device having excellent temperature characteristics and capable of increasing the operating frequency without decreasing h / λ.

[0017]

In order to solve the above-mentioned problems, according to the surface acoustic wave device of the first aspect, the Euler angle is cut out in the range of (0, θ = 100 to 150,0). A quartz substrate and an IDT electrode having an IDT standardized electrode film thickness h / λ of 0.02 or more and exciting a pseudo longitudinal wave type leaky surface acoustic wave on the main surface of the quartz substrate. And

This makes it possible to generate a pseudo-longitudinal-wave type leaky surface acoustic wave using a uniaxial rotation-cut quartz substrate, so that the surface acoustic wave is easy to manage in manufacturing and stable. The device can be provided at low cost. Further, since the pseudo-longitudinal-wave type leaky surface acoustic wave having a large phase velocity is used, the electrode width and the electrode interval can be increased as compared with the case where the Rayleigh wave or the leaky wave is used. Therefore, even when the size of the IDT standardized electrode film thickness h / λ is limited, it is possible to allow the IDT electrode film thickness h to have a margin as compared with the case of using the Rayleigh wave or the leaky wave. It is possible to suppress an increase in electrical resistance loss and prevent the Q value from decreasing, and it is possible to prevent electrode separation during wire bonding and facilitate high-frequency operation. .

Further, since the IDT standardized electrode film thickness h / λ is set to 0.02 or more, it is possible to increase the IDT electrode film thickness h even when operating at a high frequency, and one reflector is used. The reflectance can be increased to reduce the size of the device, and the peeling of the electrode can be prevented to improve the manufacturing yield. Further, according to the surface acoustic wave device of claim 2, when the Euler angle is combined with the crystal substrate cut out in the range of (0, θ = 140 to 150, 0) and the θ, the temperature change of the frequency. Shows a cubic curve, an IDT standardized electrode film thickness h / λ is specified, and an IDT electrode for exciting a pseudo longitudinal wave type leaky surface acoustic wave is provided on the main surface of the quartz substrate. To do.

As a result, even when the pseudo longitudinal wave type leaky surface acoustic wave is used, the frequency temperature deviation can be set to a small value, and the IDT standardized electrode film thickness h / λ can be easily increased. It becomes possible to do 1GH
A surface acoustic wave device that can stably operate at z or higher can be provided at low cost. Further, according to the surface acoustic wave device of the third aspect, θ = 128 + 444 × (h / λ) ± 4.

As a result, θ and the IDT standardized electrode film thickness h
By simply specifying the relationship with / λ, the frequency temperature deviation can be reduced, and a surface acoustic wave device with good temperature characteristics can be provided without complicating the manufacturing process. Further, according to the surface acoustic wave device of claim 4, the θ = 142.4 ° and h / λ = 0.0275, or the θ = 143.5 ° and h / λ = 0. .0
3 or the above θ = 144.1 ° and h / λ =
It is characterized by being 0.0425.

As a result, θ and the IDT standardized electrode film thickness h
By simply setting / λ to a specific value, the frequency temperature deviation can be reduced, and a surface acoustic wave device having good temperature characteristics can be easily provided without complicating the manufacturing process.

[0023]

BEST MODE FOR CARRYING OUT THE INVENTION A surface acoustic wave device according to an embodiment of the present invention will be described below with reference to the drawings. 1A is a perspective view showing a schematic configuration of a surface acoustic wave device according to a first embodiment of the present invention, and FIG. 1B is a sectional view taken along line AA of FIG. 1A. is there.

In FIG. 1, an IDT electrode 2 and reflector electrodes 3a and 3b are formed on the main surface of a quartz substrate 1. Note that P is the pitch of the IDT electrodes 2 and λ is the ID
T wavelength, h is the thickness of the IDT electrode 2, and the IDT wavelength λ
Is twice the pitch P of the IDT electrodes 2. Here, the crystal substrate 1 is set such that the cut-out angle and the propagation direction of the surface thereof fall within the Euler angle (0, θ = 100 to 150, 0) range. That is, in the uniaxial rotation Y plate cut, θ is set to fall within the range of 100 to 150 °.

The IDT electrode 2 excites a pseudo longitudinal wave type leaky surface acoustic wave propagating on the quartz substrate 1 in parallel with the + X axis, and the IDT standardized electrode film thickness h / λ is 0.02 or more. Is set. The IDT standardized electrode film thickness h / λ is I
The DT electrode film thickness h is standardized by the IDT wavelength λ. The reflector electrodes 3a and 3b reflect and resonate the pseudo longitudinal wave type leaky surface acoustic wave generated on the surface of the quartz substrate 1.

As a result, it is possible to use a pseudo-longitudinal wave type leaky surface acoustic wave having a high phase velocity of 5700 m / sec or more, even if quartz is used, and it is advantageous to form an electrode even for higher frequency. Can be done. Also, cheap,
Quartz crystal that is highly stable and has excellent temperature characteristics can be used as a substrate material, and since pseudo-longitudinal wave type leaky surface acoustic waves propagating in the x-axis direction on a rotating Y plate are used, manufacturing control is required. It is possible to provide a surface acoustic wave device that can be facilitated and operates stably at low cost.

The IDT standardized electrode film thickness h / λ is 0.
Since it is set to be 02 or more, the film thickness h of the IDT electrode can be increased, the electric resistance loss can be reduced, and the Q value can be increased. In addition, since the IDT standardized electrode film thickness h / λ is sufficiently thick, if the pseudo frequency wave type leaky surface acoustic wave is used for a signal frequency of 1 GHz, the IDT electrode film thickness h is set to 1140Å. The manufacturing process can be advantageously performed.

Further, since the reflectance of the reflector can be increased and the logarithm of the reflector can be reduced,
The device can be downsized. Also, when using a wire bonder, IDT
It is possible to suppress a decrease in manufacturing yield such as electrode peeling due to the thin electrode film thickness h, and to facilitate the manufacturing process.

FIG. 2 is a view showing the slicing direction of the crystal substrate of the surface acoustic wave device according to the first embodiment of the present invention.
In FIG. 2, the cutting plane M is displayed with a first rotation angle φ rotated about the Z axis with the counterclockwise direction being positive, and a second rotation angle θ rotated about the X axis with the counterclockwise direction being positive. Then, when the third rotation angle Ψ rotated about the Z axis after rotation with the counterclockwise direction being positive is the surface propagation direction in the plane of the substrate, it is expressed as (φ, θ, Ψ) in the Euler angle display. .

FIG. 3 is a diagram showing the relationship between the electromechanical coupling coefficient and the Euler angle θ of the surface acoustic wave device according to the first embodiment of the present invention. In the first embodiment, considering the elastic constant, the piezoelectric constant, the dielectric constant, the density, and the linear expansion coefficient of quartz, the pseudo-longitudinal wave type leakage in the rotating Y plate cut with the Euler angle of (0, θ, 0). The phase velocity of the surface acoustic wave is Ca
It was analyzed by a SAW characteristic simulation based on the formulation of mpbell and the like. Then, the electromechanical coupling coefficient k ^ 2 is obtained by using the following equation (1) based on the phase velocity obtained by the SAW characteristic simulation.
Was calculated.

K ^ 2 = 2 · (Vpo−Vps) / Vpo (1) However, Vpo and Vps are the phase velocities of the electrical opening and the electrical shorting of the substrate surface, respectively. In FIG.
In the range of 100 to 150 degrees, electromechanical coupling coefficient k
It can be seen that ^ 2 becomes 0 or more. Therefore, θ is 100
By setting the range from 150 degrees to 150 degrees, it is possible to configure a surface acoustic wave device using a pseudo longitudinal wave type leaky surface acoustic wave having a large phase velocity.

Further, this crystal substrate is a rotary Y plate cut, and the crystal substrate surface can be produced by uniaxially cutting around the X axis in parallel with the X axis, which facilitates manufacturing control. Is. Thus, according to the first embodiment described above,
The cut-out angle and the propagation direction of the surface of the quartz substrate are specified by Euler angles (0,100 to 150,0), and the pseudo longitudinal wave type leaky surface acoustic wave having a phase velocity of 5700 m / sec or more can be used.

Therefore, even when the surface acoustic wave device is operated at a high frequency, it is advantageous in forming electrodes. For example, in the case of targeting a signal frequency of 1 GHz, an electrode width and an electrode interval of 1 μm or less are required in an ST cut crystal using a Rayleigh wave and an LST cut crystal using a leaky surface acoustic wave. When the corrugated leaky surface acoustic wave is used, the electrode width and the electrode interval are 1.425 μm.

Further, since quartz is used as the substrate material, it is inexpensive, highly stable and has excellent temperature characteristics, and in order to utilize the pseudo longitudinal wave type leaky surface acoustic wave propagating in the X axis direction on the rotating Y plate. The manufacturing control becomes easy. Further, since the IDT standardized electrode film thickness h / λ is set to 0.02 or more, the IDT electrode film thickness h can be increased. For example, when the signal frequency of 1 GHz is targeted and the normalized film thickness h / λ of the IDT electrode is 0.0125, the ID is
While the T electrode film thickness is extremely thin at 716Å,
When the normalized film thickness of the T electrode h / λ = 0.02, ID
The T electrode film thickness h can be set to 1140Å.

Therefore, the electrical resistance loss can be reduced and the Q value can be increased, and the reflectance per reflector can be increased to downsize the device. Further, in the case of the wire bonder, it is possible to suppress a decrease in manufacturing yield such as electrode peeling due to a thin electrode film thickness, and to facilitate the manufacturing process. 4, 5 and 6 are diagrams showing the temperature dependence of the frequency temperature deviation in the surface acoustic wave device according to the second embodiment of the present invention.

FIGS. 4, 5 and 6 show the results of analyzing the frequency temperature characteristics of the pseudo longitudinal wave type leaky surface acoustic wave at Euler angles of (0,135-150,0) by the finite element method. In addition, IDT is added to the above constants.
It is analyzed in consideration of the electrode film thickness. Where θ
And the IDT standardized film thickness h / λ, a temperature of 25
An example of frequency-temperature characteristics when the center frequency is the frequency at ℃ is shown.

That is, in FIG. 4A, θ = 142.4.
And h / λ = 0.0275 (P
1) and FIG. 4B, θ = 142.4 ° and h / λ
= 0.0425 (P2), FIG. 5 (a) is θ = 143.5 °, and h / λ = 0.03 is set (P3), FIG. 5 (b) is θ = 143 ° and h /
When λ = 0.015 (P4), FIG. 6 (a) is θ = 144.1 °, and h / λ = 0.0425 is set (P5), FIG. 6 (b) is θ = 144.1 °,
Moreover, the case where h / λ is set to 0.0225 (P6) is shown.

P1 in FIG. 4 (a), P3 in FIG. 5 (a), and P5 in FIG. 6 (a) are operating temperature ranges from -40.degree.
It exhibits a third-order temperature characteristic over 0 ° C, and the frequency deviation is small. On the other hand, P2 of FIG. 4B, P4 of FIG.
P6 in (b) is operating temperature range from -40 ° C to 90
At ℃, the frequency deviation becomes very large. FIG. 7 shows h / in the surface acoustic wave device according to the second embodiment of the present invention.
It is a figure which shows the relationship between (lambda) and the Euler angle (theta).

In FIG. 7, θ is 140 ≦ θ ≦ 150
And the IDT standardized film thickness h / λ is in the range of 0.02 or more, and θ and the IDT standardized film thickness h / λ are (2) below.
It was confirmed that the pseudo-longitudinal-wave type leaky surface acoustic wave having a good temperature characteristic can be used in the range satisfying the formula. θ = 128 + 444 × (h / λ) ± 4 (2) Here, P1 in FIG. 4A, P3 in FIG. 5A, and FIG.
P5 of (a) is within this range, and P5 of FIG.
2, P4 in FIG. 5 (b) and P6 in FIG. 6 (b) are outside this range.

As described above, according to the above-described second embodiment, when a crystal substrate cut out with Euler angles in the range of (0, θ = 140 to 150, 0) is used and combined with θ, the frequency As the temperature change shows a cubic curve, IDT
The normalized electrode film thickness h / λ is specified. Therefore, the frequency temperature deviation can be set to a small value, and the IDT standardized electrode film thickness h / λ can be easily increased, and the surface acoustic wave that can stably operate at 1 GHz or higher. The device can be provided at low cost.

Here, when the IDT standardized electrode film thickness h / λ is 0.02 or more, it is preferable to specify the combination of the IDT standardized electrode film thickness h / λ and θ as in the formula (2). , Further, θ = 142.4 °, and h / λ = 0.
0275 or θ = 143.5 ° and h / λ =
0.03 or θ = 144.1 ° and h / λ =
It is preferably set to 0.042. However, θ is ±
The error range includes a range of 15 minutes and an IDT electrode film thickness h of ± 100Å.

[0042]

As described above, according to the present invention,
A quasi-longitudinal-wave type leaky surface acoustic wave can be generated using a uniaxial rotation-cut quartz substrate, and therefore a surface acoustic wave device that is easy to manage in manufacturing, inexpensive, and stable is provided. be able to. Further, since the pseudo-longitudinal-wave type leaky surface acoustic wave having a large phase velocity is used, the electrode width and the electrode interval can be increased as compared with the case where the Rayleigh wave or the leaky wave is used. Therefore, even when the size of the IDT standardized electrode film thickness h / λ is limited, it is possible to allow the IDT electrode film thickness h to have a margin as compared with the case of using the Rayleigh wave or the leaky wave. It is possible to suppress an increase in electrical resistance loss and prevent the Q value from decreasing, and it is possible to prevent electrode separation during wire bonding and facilitate high-frequency operation. .

Further, since the IDT standardized electrode film thickness h / λ is set to 0.02 or more, it is possible to increase the IDT electrode film thickness h even when operating at a high frequency, and one reflector is used. The reflectance can be increased to reduce the size of the device, and the peeling of the electrode can be prevented to improve the manufacturing yield.

[Brief description of drawings]

FIG. 1 (a) is a perspective view showing a schematic configuration of a surface acoustic wave device according to a first embodiment of the present invention, and FIG. 1 (b) is a sectional view taken along line AA of FIG. 1 (a). FIG.

FIG. 2 is a diagram showing a cutout direction of a crystal substrate of the surface acoustic wave device according to the first embodiment of the present invention.

FIG. 3 is a diagram showing a relationship between an electromechanical coupling coefficient and an Euler angle θ of the surface acoustic wave device according to the first embodiment of the present invention.

FIG. 4 is a diagram showing temperature dependence of frequency temperature deviation in a surface acoustic wave device according to a second embodiment of the present invention.

FIG. 5 is a diagram showing temperature dependence of frequency temperature deviation in the surface acoustic wave device according to the second embodiment of the present invention.

FIG. 6 is a diagram showing temperature dependence of frequency temperature deviation in the surface acoustic wave device according to the second embodiment of the present invention.

FIG. 7 is a diagram showing a relationship between h / λ and an Euler angle θ in the surface acoustic wave device according to the second embodiment of the present invention.

[Explanation of symbols]

1 Crystal substrate 2 IDT electrodes 3a, 3b Reflector electrode

Claims (4)

[Claims] 1. An Euler angle of (0, θ = 100 to 15)
A quartz substrate cut out in the range of (0, 0) and an IDT standardized electrode film thickness h / λ are set to 0.02 or more, and a pseudo longitudinal wave type leaky surface acoustic wave is excited on the main surface of the quartz substrate. A surface acoustic wave device comprising: 2. The Euler angle is (0, θ = 140 to 15)
When the crystal substrate cut out in the range of (0, 0) is combined with the above θ, the IDT standardized electrode film thickness h / λ is specified so that the temperature change of frequency shows a cubic curve, A surface acoustic wave device comprising: an IDT electrode for exciting a pseudo-longitudinal-wave type leaky surface acoustic wave on the main surface thereof. 3. The surface acoustic wave device according to claim 1, wherein θ = 128 + 444 × (h / λ) ± 4. 4. The angle θ = 142.4 ° and h / λ =
0.0275 or the above θ = 143.5 °, and
4. The surface acoustic wave device according to claim 3, wherein h / λ = 0.03, or θ = 144.1 ° and h / λ = 0.0425.