ACOUSTIC WAVE DEVICE

Abstract

An acoustic wave device includes a support substrate, a quartz-crystal layer provided directly or indirectly on the support substrate, a piezoelectric layer on the quartz-crystal layer, and an IDT electrode on the piezoelectric layer. When λ represents a wavelength defined by an electrode finger pitch of the IDT electrode, a thickness of the quartz-crystal layer is about 0.2λ or more and about 0.4λ or less, and the piezoelectric layer has a thickness smaller than the thickness of the quartz-crystal layer.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an acoustic wave device.

2. Description of the Related Art

Acoustic wave devices have been widely used in, for example, filters of cellular phones. International Publication No. 2018/164211 discloses an example of a multiplexer in which an acoustic wave filter including an acoustic wave device is used. The acoustic wave device described in International Publication No. 2018/164211 includes an IDT (Interdigital Transducer) electrode disposed on a multilayer substrate. The multilayer substrate includes a silicon substrate, a silicon oxide layer, and a piezoelectric body that are stacked in this order. In the multiplexer, adjustment is performed so that a frequency of a higher-order mode is positioned outside a pass band of the acoustic wave filter.

SUMMARY OF THE INVENTION

However, the acoustic wave device described in International Publication No. 2018/164211 has difficulty in sufficiently suppressing a ripple itself due to the higher-order mode.

Preferred embodiments of the present invention provide acoustic wave devices each being capable of suppressing a higher-order mode in a wide band.

An acoustic wave device according to a preferred embodiment of the present disclosure includes a support substrate, a silicon oxide layer provided directly or indirectly on the support substrate and having crystallinity, a piezoelectric layer on the silicon oxide layer having crystallinity, and an IDT electrode on the piezoelectric layer. When A represents a wavelength defined by an electrode finger pitch of the IDT electrode, a thickness of the silicon oxide layer having crystallinity is about 0.2λ or more and about 0.4λ or less, and the piezoelectric layer has a thickness smaller than the thickness of the silicon oxide layer having crystallinity.

With the acoustic wave devices according to preferred embodiments of the present disclosure, a higher-order mode can be suppressed in a wide band.

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.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front sectional view of a portion of an acoustic wave device according to a first preferred embodiment of the present invention.

FIG. 2 is a plan view of the acoustic wave device according to the first preferred embodiment of the present invention.

FIG. 3 illustrates the phase characteristics of an acoustic wave device having the configuration of the first preferred embodiment of the present invention and the phase characteristics of an acoustic wave device of a comparative example.

FIG. 4 illustrates the relationship between the thickness of a quartz-crystal layer and the phase of a higher-order mode.

FIG. 5 is an enlarged view of FIG. 4.

FIG. 6 illustrates the relationship between φ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of lithium tantalate of a piezoelectric layer, and the phase of a Rayleigh wave.

FIG. 7 illustrates the relationship between θ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the Rayleigh wave.

FIG. 8 illustrates the relationship between ψ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the Rayleigh wave.

FIG. 9 illustrates the relationship between φ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of a higher-order mode.

FIG. 10 illustrates the relationship between θ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the higher-order mode.

FIG. 11 illustrates the relationship between ψ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the higher-order mode.

FIG. 12 illustrates the relationship between φ_q in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave.

FIG. 13 illustrates the relationship between θ_q in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave.

FIG. 14 illustrates the relationship between ψ_q in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave.

FIG. 15 illustrates the ranges of φ_q and θ_q in the azimuthal angles of the quartz-crystal layer, in which the Rayleigh wave can be suppressed.

FIG. 16 is a front sectional view of the vicinity of a pair of electrode fingers in a modification of the first preferred embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the present invention will be clarified through the description of specific preferred embodiments thereof, with reference to the drawings.

Note that preferred embodiments in the present description are examples, and the configurations in the different preferred embodiments can be partially replaced from one to another or combined with one another.

FIG. 1 is a front sectional view of a portion of an acoustic wave device according to a first preferred embodiment of the present disclosure. FIG. 2 is a plan view of the acoustic wave device according to the first preferred embodiment. Note that FIG. 1 is a sectional view taken along line I-I in FIG. 2. In FIG. 2, illustration of a protective film, which will be described later, is omitted.

As FIG. 1 illustrates, an acoustic wave device 1 includes a multilayer substrate 6. The multilayer substrate 6 includes a support substrate 2, a quartz-crystal layer 4, and a piezoelectric layer 5. More specifically, the quartz-crystal layer 4 is disposed on the support substrate 2. The piezoelectric layer 5 is disposed on the quartz-crystal layer 4.

In the present preferred embodiment, the support substrate 2 is a silicon substrate. However, the material for the support substrate 2 is not limited to the above-described material. The quartz-crystal layer 4 corresponds to a silicon oxide layer having crystallinity in the present disclosure. More specifically, the quartz-crystal layer 4 is a monocrystalline quartz-crystal layer in the present preferred embodiment. However, a layer corresponding to the quartz-crystal layer 4 may be any silicon oxide layer having crystallinity. In the present description, such a silicon oxide layer having crystallinity is regarded as equivalent to a silicon oxide layer having anisotropy in the material constants thereof. Examples of the silicon oxide layer having crystallinity include a silicon oxide layer having no piezoelectricity. Note that such a state of having anisotropy in the material constants means that anisotropy is exhibited in at least one of the elastic constant, the permittivity, the piezoelectric constant, the coefficient of linear expansion, and the thermal conductivity. The silicon oxide layer having crystallinity may contain a crystal phase of, for example, tridymite, cristobalite, or coesite. When, inside the silicon oxide layer having crystallinity, the percentage of orientation in a specific direction is about 50% or more, the silicon oxide layer having crystallinity exhibits physical properties similar to those of quartz crystal and exhibits Euler angle dependence as with quartz crystal. Thus, when the silicon oxide layer having crystallinity is used, effects similar to those exhibited when quartz crystal is used are also obtained even when the silicon oxide layer having crystallinity is not quartz crystal. The crystallinity of the silicon oxide can be evaluated by using the following methods. That is, for analyzing the crystal structure, there can be used an X-ray diffraction method, electron diffraction, electron backscattered diffraction (EBSD: Electron BackScatter Diffraction), an Automated Crystal Orientation Mapping-TEM method (ACOM-TEM method), or a synchrotron radiation diffraction method enabling analysis on a very minute structure.

In the present preferred embodiment, the piezoelectric layer 5 is a lithium tantalate (LiTaO3) layer. However, the material for the piezoelectric layer 5 is not limited to the above-described material. Examples of the material for the piezoelectric layer 5 include lithium niobate.

Here, in the piezoelectric layer 5, (XLT, YLT, ZLT) represent the crystallographic axes, and (φLT, θLT, ψLT) represent the azimuthal angles, and, in the quartz-crystal layer 4, (Xq, Yq, Zq) represent the crystallographic axes, and (φq, θq, ψq) represent the azimuthal angles. In the present preferred embodiment, the piezoelectric layer 5 and the quartz-crystal layer 4 are stacked so that, when (φLT, θLT, ψLT) are (0°, 0°, 0°), and (φq, θq, ψq) are (0°, 0°, 0°), (XLT, YLT, ZLT) coincide with (Xq, Yq, Zq). Note that, in the present description, the azimuthal angles are given in Euler angle notation.

An IDT electrode 7 is disposed on the piezoelectric layer 5. An alternating voltage is applied to the IDT electrode 7, and an acoustic wave is thereby excited. As FIG. 2 illustrates, a pair of reflectors 8A and 8B is disposed on the piezoelectric layer 5 on both sides, in a propagation direction of an acoustic wave, of the IDT electrode 7. As described above, the acoustic wave device 1 of the present preferred embodiment is a surface acoustic wave resonator. Note that the acoustic wave devices according to the present disclosure are not limited thereto and may be, for example, a filter device including plural surface acoustic wave resonators or a multiplexer.

As FIG. 2 illustrates, the IDT electrode 7 includes a first busbar 16, a second busbar 17, plural first electrode fingers 18, and plural second electrode fingers 19. The first busbar 16 and the second busbar 17 face one another. One end of each of the first electrode fingers 18 is connected to the first busbar 16. One end of each of the second electrode fingers 19 is connected to the second busbar 17. The plural first electrode fingers 18 and the plural second electrode fingers 19 interdigitate with one another.

Each of the IDT electrode 7 and the reflectors 8A and 8B may include a multilayer metal film or a single-layer metal film.

Here, when λ represents a wavelength defined by the electrode finger pitch of the IDT electrode 7, the thickness of the quartz-crystal layer 4 is about 0.2λ or more and about 0.4λ or less, for example. Moreover, the piezoelectric layer 5 has a thickness smaller than the thickness of the quartz-crystal layer 4. Note that the electrode finger pitch refers to a distance between the centers of adjacent ones of the electrode fingers. Specifically, the electrode finger pitch refers to a distance between the center points, in the propagation direction of the acoustic wave, of adjacent ones of the electrode fingers.

Referring back to FIG. 1, a protective film 9 is disposed on the piezoelectric layer 5 so as to cover the IDT electrode 7. The IDT electrode 7 is hardly broken with the protective film 9. As for the protective film 9, an appropriate dielectric can be used. For example, when silicon oxide is used for the protective film 9, a temperature coefficient of frequency (TCF) can be increased. When silicon nitride is used for the protective film 9, a frequency can be easily adjusted through adjustment of the thickness of the protective film 9. However, the protective film 9 is not necessarily disposed.

Some of the unique features of the present preferred embodiment include, in the multilayer substrate 6, the support substrate 2, the quartz-crystal layer 4, and the piezoelectric layer 5 are stacked, the quartz-crystal layer 4 has a thickness of about 0.2λ or more and about 0.4λ or less, and the piezoelectric layer 5 has a thickness smaller than the thickness of the quartz-crystal layer 4. However, as described above, a layer corresponding to the quartz-crystal layer 4 may be the silicon oxide layer having crystallinity. With the configuration, a higher-order mode can be suppressed in a wide band. Such suppression of a higher-order mode in a wide band will be demonstrated below through comparison between the present preferred embodiment and a comparative example. Note that the comparative example differs from the present preferred embodiment in that a multilayer substrate has no quartz-crystal layer. More specifically, the multilayer substrate of the comparative example is a multilayer body including a support substrate, a silicon nitride film, a silicon oxide film, and a piezoelectric layer.

The phase characteristics of an acoustic wave device having the configuration of the present preferred embodiment and the phase characteristics of an acoustic wave device of the comparative example were measured. The design parameters of the acoustic wave device having the configuration of the present preferred embodiment are as follows.

Support substrate 2; material . . . Si

Quartz-crystal layer 4; material . . . monocrystalline SiO2, thickness . . . 600 nm, azimuthal angles (φq, θq, ψq) . . . (45°, 90°, 90°)

Piezoelectric layer 5; material . . . LiTaO3, thickness . . . 400 nm, cut angle . . . 40° Y

IDT electrode 7; material . . . Ti/AlCu/Ti, thickness 12 nm/100 nm/4 nm

Wavelength λ of IDT electrode 7; 2 μm

FIG. 3 illustrates the phase characteristics of the acoustic wave device having the configuration of the first preferred embodiment and the phase characteristics of the acoustic wave device of the comparative example.

From FIG. 3, it is clear that, in the comparative example, a large spurious emission due to a higher-order mode occurs in the vicinity of the frequency indicated by arrow A. Specifically, at the frequency indicated by arrow A, the phase of the higher-order mode in the comparative example is 40 deg. In contrast, in the first preferred embodiment, the higher-order mode in the vicinity of the frequency indicated by arrow A is suppressed. Moreover, it is clear that, in the first preferred embodiment, the higher-order mode is suppressed to less than about −80 deg. in a wide band.

In addition, in the comparative example, a large spurious emission due to a Rayleigh wave occurs at the frequency indicated by arrow B. In contrast, it is clear that, in the first preferred embodiment, such a Rayleigh wave can also be suppressed.

Moreover, it will be demonstrated below that the higher-order mode can be suppressed by the quartz-crystal layer having a thickness of about 0.2λ or more and about 0.4λ or less. In the acoustic wave device having a multilayer substrate whose layer configuration is similar to that of the first preferred embodiment, the phase of the higher-order mode was measured while the thickness of the quartz-crystal layer was changed. The thickness of the quartz-crystal layer was changed in a range of about 200 nm or more and about 1300 nm or less in increments of about 100 nm, for example. Note that, because the wavelength λ is defined as about 2 μm, the thickness of the quartz-crystal layer varies in a range of about 0.1λ or more and about 0.65λ or less in increments of about 0.05λ, for example.

FIG. 4 illustrates the relationship between the thickness of the quartz-crystal layer and the phase of the higher-order mode. FIG. 5 is an enlarged view of FIG. 4.

From FIG. 4 and FIG. 5, it is clear that, when the thickness of the quartz-crystal layer is less than about 0.2λ and is more than about 0.4λ, the values of the phase of the higher-order mode are larger than about −70 deg, for example. In contrast, it is clear that, when the thickness of the quartz-crystal layer is about 0.2λ or more and about 0.4λ or less as in the first preferred embodiment, the higher-order mode is suppressed to less than about −70 deg, for example. Thus, in the first preferred embodiment, the higher-order mode can be effectively suppressed. In addition, when the thickness of the quartz-crystal layer is about 0.2λ or more and about 0.4λ or less, for example, the piezoelectric layer has a thickness smaller than the thickness of the quartz-crystal layer.

As described above, in the first preferred embodiment, in addition to the higher-order mode, the Rayleigh wave can also be suppressed. The study conducted by the inventors of the present application has revealed that, when the cut angle of the piezoelectric body of the piezoelectric layer 5 is changed, the azimuthal angles of the quartz-crystal layer 4 at which the Rayleigh wave can be suppressed are also changed. At this point, there was obtained the relationship between the cut angle of the piezoelectric body of the piezoelectric layer 5 and the azimuthal angles of the quartz-crystal layer 4; and the phase of the Rayleigh wave. Note that, regarding the azimuthal angles of the quartz-crystal layer 4, φq, θq, and ψq in (φq, 10°, 0°), (0°, θq, 0°), and (0°, 10°, ψq) were changed. The cut angle of lithium tantalate of the piezoelectric layer 5 was about 30° Y, about 50° Y, or about 70° Y.

FIG. 6 illustrates the relationship between φq in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 6 illustrates, when the cut angle is about 30° Y, the Rayleigh wave is effectively suppressed in the ranges of about 10°≤φq≤about 45°, about 80°≤φq≤about 105°, and about 130° ≤φq≤about 165°. Note that, here, such a state of effectively suppressing the Rayleigh wave refers to a state where values of the phase of the Rayleigh wave are within the range from the minimum value of the phase of the Rayleigh wave to a value about 40 deg. larger than the minimum value. Except where specifically noted, the same applies to the following description. When the cut angle is about 50° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤φq≤about 25° and about 95°≤φq≤about 145°. When the cut angle is 70° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤φq≤about 15° and about 100°≤φq≤about 135°, for example.

FIG. 7 illustrates the relationship between θq in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 7 illustrates, when the cut angle is about 30° Y, the Rayleigh wave is effectively suppressed in the ranges of about 15°≤θq≤about 35° and about 75°≤θq≤about 115°. When the cut angle is about 50° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤θq≤about 25° and about 110°≤θq≤about 180°, for example. When the cut angle is about 70° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤θq≤about 15° and about 160°≤θq≤about 180°, for example.

FIG. 8 illustrates the relationship between ψq in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the Rayleigh wave.

As FIG. 8 illustrates, when the cut angle is about 30° Y, the Rayleigh wave is effectively suppressed in the ranges of about 10°≤ψq≤about 40°, about 70° ψq about 100°, and about 145° ≤ψq≤about 180°, for example. When the cut angle is about 50° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤ψq≤about 25° and about 90°≤ψq≤about 150°, for example. When the cut angle is about 70° Y, the Rayleigh wave is effectively suppressed in the ranges of about 0°≤ψq≤about 20° and about 100°≤ψq≤about 140°, for example.

In the above-described comparative example, as FIG. 3 illustrates, the phase of the higher-order mode is 40 deg. In contrast, with the configuration of the multilayer substrate 6 in the first preferred embodiment, the higher-order mode can be suppressed even when φq, θq, and ψq in the azimuthal angles of the quartz-crystal layer 4 are changed. Such suppression of the higher-order mode will be demonstrated below. Note that the measurement of the phase of the higher-order mode was conducted under conditions similar to the conditions under which the relationships in FIGS. 6 to 8 were obtained.

FIG. 9 illustrates the relationship between φq in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the higher-order mode. FIG. 10 illustrates the relationship between θ_q in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the higher-order mode. FIG. 11 illustrates the relationship between ψq in the azimuthal angles of the quartz-crystal layer, the cut angle of the lithium tantalate of the piezoelectric layer, and the phase of the higher-order mode.

From FIG. 9, it is clear that, regardless of φq in the azimuthal angles of the quartz-crystal layer 4, the higher-order mode can be suppressed to less than about 40 deg., more specifically, less than about −30 deg, for example. Similarly, from FIG. 10 and FIG. 11, it is clear that, regardless of θq and ψq, the higher-order mode can be further suppressed than in the above-described comparative example.

As described above, the higher-order mode can be suppressed in the first preferred embodiment. Moreover, the Rayleigh wave can also be effectively suppressed through adjustment of the azimuthal angles of the quartz-crystal layer 4.

At this point, it was confirmed that the phase of the Rayleigh wave has low dependency on the thickness of the quartz-crystal layer 4. More specifically, the phase of the Rayleigh wave was measured in each of the cases of about 0.2λ, about 0.3λ, and about 0.4λ in thicknesses of the quartz-crystal layer 4, while an azimuthal angle was changed. Note that, regarding the azimuthal angles of the quartz-crystal layer 4, φq, θq, and ψq in (φq, 120°, 90°, (70°, θq, 90°), and (70°, 120°, ψq) were changed.

FIG. 12 illustrates the relationship between φq in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave. FIG. 13 illustrates the relationship between θq in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave. FIG. 14 illustrates the relationship between ψ₄ in the azimuthal angles of the quartz-crystal layer, the thickness of the quartz-crystal layer, and the phase of the Rayleigh wave.

From FIG. 12, it is clear that, when the thickness of the quartz-crystal layer 4 is about 0.2λ or more and about 0.4λ or less, the relationship between: φq in the azimuthal angles of the quartz-crystal layer 4; and the phase of the Rayleigh wave does not vary greatly. Similarly, from FIG. 13 and FIG. 14, it is clear that, when the thickness of the quartz-crystal layer 4 is about 0.2λ or more and about 0.4λ or less, the relationships between: ϵq and ψq in the azimuthal angles of the quartz-crystal layer 4; and the phase of the Rayleigh wave do not vary greatly.

Examples of the relationship between an azimuthal angle of the quartz-crystal layer 4, the cut angle of the lithium tantalate of the piezoelectric layer 5, and the phase of the Rayleigh wave are given above. The relationship will be further detailed below.

FIG. 15 illustrates the ranges of φq and θq in the azimuthal angles of the quartz-crystal layer, in which the Rayleigh wave can be suppressed. Note that the ranges in FIG. 15 are each a range when ψq in the azimuthal angles of the quartz-crystal layer 4 is about 0°, and the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 30° Y.

When the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 30° Y, the Rayleigh wave can be effectively suppressed in the ranges of (φq, θq, 0°) represented by the hatched areas in FIG. 15. The relationship is given in Table 1. Here, it has been clear that, when the cut angle is about 20° Y or more and less than about 40° Y, for example, the Rayleigh wave can also be suppressed in ranges of the azimuthal angles, similar to the ranges of the azimuthal angles in the case of about 30° Y in cut angle. Thus, in Table 1, the case where the cut angle is about 20° Y or more and less than about 40° Y is given, for example. Moreover, the Rayleigh wave can also be suppressed in a similar manner within the range of about ±5° or ±10° of each of φq, θq, and ψq, for example. Thus, the range of about ±5° or ±10° of each of φq, θq, and ψq is given in the tables in the present description, for example.

Similarly, the ranges of φq and θq in which the Rayleigh wave can be suppressed were obtained while the cut angle of the lithium tantalate of the piezoelectric layer 5 and ψq in the azimuthal angles of the quartz-crystal layer 4 were changed. The results therefrom are given in Tables 2 to 10.

The Rayleigh wave can be suppressed when the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 20° Y or more and less than about 40° Y and if φq, θq, and ψq in the azimuthal angles of the quartz-crystal layer 4 are in any one of the combinations in Tables 1 to 10. Note that the quartz-crystal layer 4 is a monocrystalline quartz-crystal layer.

TABLE 1
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	15 ≤ θq ≤ 35	−10 ≤ ψq < 10
2	−5 ≤ φq < 5	75 ≤ θq ≤ 135	−10 ≤ ψq < 10
3	5 ≤ φq < 15	5 ≤ θq ≤ 35	−10 ≤ ψq < 10
4	5 ≤ φq < 15	65 ≤ θq ≤ 115	−10 ≤ ψq < 10
5	15 ≤ φq < 25	5 ≤ θq ≤ 35	−10 ≤ ψq < 10
6	15 ≤ φq < 25	65 ≤ θq ≤ 105	−10 ≤ ψq < 10
7	15 ≤ φq < 25	175 ≤ θq ≤ 185	−10 ≤ ψq < 10
8	25 ≤ φq < 35	−5 ≤ θq ≤ 105	−10 ≤ ψq < 10
9	25 ≤ φq < 35	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
10	35 ≤ φq < 45	−5 ≤ θq ≤ 105	−10 ≤ ψq < 10
11	35 ≤ φq < 45	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
12	45 ≤ φq < 55	25 ≤ θq ≤ 95	−10 ≤ ψq < 10
13	45 ≤ φq < 55	145 ≤ θq ≤ 175	−10 ≤ ψq < 10
14	55 ≤ φq < 65	25 ≤ θq ≤ 95	−10 ≤ ψq < 10
15	55 ≤ φq < 65	145 ≤ θq ≤ 175	−10 ≤ ψq < 10
16	65 ≤ φq < 75	25 ≤ θq ≤ 95	−10 ≤ ψq < 10
17	65 ≤ φq < 75	145 ≤ θq ≤ 175	−10 ≤ ψq < 10
18	75 ≤ φq < 85	−5 ≤ θq ≤ 95	−10 ≤ ψq < 10
19	75 ≤ φq < 85	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
20	85 ≤ φq < 95	−5 ≤ θq ≤ 45	−10 ≤ ψq < 10
21	85 ≤ φq < 95	55 ≤ θq ≤ 105	−10 ≤ ψq < 10
22	85 ≤ φq < 95	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
23	95 ≤ φq < 105	−5 ≤ θq ≤ 35	−10 ≤ ψq < 10
24	95 ≤ φq < 105	65 ≤ θq ≤ 115	−10 ≤ ψq < 10
25	105 ≤ φq < 115	15 ≤ θq ≤ 35	−10 ≤ ψq < 10
26	105 ≤ φq < 115	75 ≤ θq ≤ 125	−10 ≤ ψq < 10
27	115 ≤ φq < 125	15 ≤ θq ≤ 35	−10 ≤ ψq < 10
28	115 ≤ φq < 125	75 ≤ θq ≤ 135	−10 ≤ ψq < 10
29	125 ≤ φq < 135	5 ≤ θq ≤ 35	−10 ≤ ψq < 10
30	125 ≤ φq < 135	65 ≤ θq ≤ 115	−10 ≤ ψq < 10
31	135 ≤ φq < 145	5 ≤ θq ≤ 35	−10 ≤ ψq < 10
32	135 ≤ φq < 145	65 ≤ θq ≤ 105	−10 ≤ ψq < 10
33	135 ≤ φq < 145	175 ≤ θq ≤ 185	−10 ≤ ψq < 10
34	145 ≤ φq < 155	−5 ≤ θq ≤ 105	−10 ≤ ψq < 10
35	145 ≤ φq < 155	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
36	155 ≤ φq < 165	−5 ≤ θq ≤ 105	−10 ≤ ψq < 10
37	155 ≤ φq < 165	155 ≤ θq ≤ 185	−10 ≤ ψq < 10
38	165 ≤ φq < 175	25 ≤ θq ≤ 95	−10 ≤ ψq < 10
39	165 ≤ φq < 175	145 ≤ θq ≤ 175	−10 ≤ ψq < 10
40	175 ≤ φq ≤ 185	25 ≤ θq ≤ 95	−10 ≤ ψq < 10
41	175 ≤ φq ≤ 185	145 ≤ θq ≤ 175	−10 ≤ ψq < 10

TABLE 2
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	5 ≤ θq ≤ 35	10 ≤ ψq < 30
2	−5 ≤ φq < 5	65 ≤ θq ≤ 145	10 ≤ ψq < 30
3	5 ≤ φq < 15	−5 ≤ θq ≤ 145	10 ≤ ψq < 30
4	15 ≤ φq < 25	−5 ≤ θq ≤ 135	10 ≤ ψq < 30
5	25 ≤ φq < 35	25 ≤ θq ≤ 135	10 ≤ ψq < 30
6	35 ≤ φq < 45	25 ≤ θq ≤ 125	10 ≤ ψq < 30
7	35 ≤ φq < 45	175 ≤ θq ≤ 185	10 ≤ ψq < 30
8	45 ≤ φq < 55	25 ≤ θq ≤ 105	10 ≤ ψq < 30
9	45 ≤ φq < 55	165 ≤ θq ≤ 185	10 ≤ ψq < 30
10	55 ≤ φq < 65	−5 ≤ θq ≤ 105	10 ≤ ψq < 30
11	55 ≤ φq < 65	155 ≤ θq ≤ 185	10 ≤ ψq < 30
12	65 ≤ φq < 75	−5 ≤ θq ≤ 105	10 ≤ ψq < 30
13	65 ≤ φq < 75	145 ≤ θq ≤ 175	10 ≤ ψq < 30
14	75 ≤ φq < 85	−5 ≤ θq ≤ 45	10 ≤ ψq < 30
15	75 ≤ φq < 85	75 ≤ θq ≤ 95	10 ≤ ψq < 30
16	75 ≤ φq < 85	145 ≤ θq ≤ 165	10 ≤ ψq < 30
17	85 ≤ φq < 95	15 ≤ θq ≤ 35	10 ≤ ψq < 30
18	85 ≤ φq < 95	75 ≤ θq ≤ 95	10 ≤ ψq < 30
19	85 ≤ φq < 95	145 ≤ θq ≤ 175	10 ≤ ψq < 30
20	95 ≤ φq < 105	15 ≤ θq ≤ 35	10 ≤ ψq < 30
21	95 ≤ φq < 105	65 ≤ θq ≤ 95	10 ≤ ψq < 30
22	95 ≤ φq < 105	145 ≤ θq ≤ 185	10 ≤ ψq < 30
23	105 ≤ φq < 115	15 ≤ θq ≤ 35	10 ≤ ψq < 30
24	105 ≤ φq < 115	65 ≤ θq ≤ 95	10 ≤ ψq < 30
25	105 ≤ φq < 115	145 ≤ θq ≤ 185	10 ≤ ψq < 30
26	115 ≤ φq < 125	5 ≤ θq ≤ 35	10 ≤ ψq < 30
27	115 ≤ φq < 125	65 ≤ θq ≤ 145	10 ≤ ψq < 30
28	125 ≤ φq < 135	−5 ≤ θq ≤ 145	10 ≤ ψq < 30
29	135 ≤ φq < 145	−5 ≤ θq ≤ 135	10 ≤ ψq < 30
30	145 ≤ φq < 155	25 ≤ θq ≤ 135	10 ≤ ψq < 30
31	155 ≤ φq < 165	25 ≤ θq ≤ 115	10 ≤ ψq < 30
32	155 ≤ φq < 165	175 ≤ θq ≤ 185	10 ≤ ψq < 30
33	165 ≤ φq < 175	25 ≤ θq ≤ 105	10 ≤ ψq < 30
34	165 ≤ φq < 175	165 ≤ θq ≤ 185	10 ≤ ψq < 30
35	175 ≤ φq ≤ 185	−5 ≤ θq ≤ 105	10 ≤ ψq < 30
36	175 ≤ φq ≤ 185	155 ≤ θq ≤ 185	10 ≤ ψq < 30

TABLE 3
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 85	30 ≤ ψq < 50
2	−5 ≤ φq < 5	125 ≤ θq ≤ 185	30 ≤ ψq < 50
3	5 ≤ φq < 15	25 ≤ θq ≤ 75	30 ≤ ψq < 50
4	5 ≤ φq < 15	125 ≤ θq ≤ 185	30 ≤ ψq < 50
5	15 ≤ φq < 25	25 ≤ θq ≤ 55	30 ≤ ψq < 50
6	15 ≤ φq < 25	65 ≤ θq ≤ 85	30 ≤ ψq < 50
7	15 ≤ φq < 25	125 ≤ θq ≤ 155	30 ≤ ψq < 50
8	25 ≤ φq < 35	15 ≤ θq ≤ 55	30 ≤ ψq < 50
9	25 ≤ φq < 35	115 ≤ θq ≤ 145	30 ≤ ψq < 50
10	35 ≤ φq < 45	−5 ≤ θq ≤ 45	30 ≤ ψq < 50
11	35 ≤ φq < 45	75 ≤ θq ≤ 145	30 ≤ ψq < 50
12	45 ≤ φq < 55	−5 ≤ θq ≤ 65	30 ≤ ψq < 50
13	45 ≤ φq < 55	75 ≤ θq ≤ 135	30 ≤ ψq < 50
14	55 ≤ φq < 65	−5 ≤ θq ≤ 65	30 ≤ ψq < 50
15	55 ≤ φq < 65	85 ≤ θq ≤ 135	30 ≤ ψq < 50
16	55 ≤ φq < 65	175 ≤ θq ≤ 185	30 ≤ ψq < 50
17	65 ≤ φq < 75	15 ≤ θq ≤ 45	30 ≤ ψq < 50
18	65 ≤ φq < 75	75 ≤ θq ≤ 115	30 ≤ ψq < 50
19	65 ≤ φq < 75	155 ≤ θq ≤ 185	30 ≤ ψq < 50
20	75 ≤ φq < 85	15 ≤ θq ≤ 45	30 ≤ ψq < 50
21	75 ≤ φq < 85	75 ≤ θq ≤ 105	30 ≤ ψq < 50
22	75 ≤ φq < 85	145 ≤ θq ≤ 185	30 ≤ ψq < 50
23	85 ≤ φq < 95	15 ≤ θq ≤ 45	30 ≤ ψq < 50
24	85 ≤ φq < 95	55 ≤ θq ≤ 95	30 ≤ ψq < 50
25	85 ≤ φq < 95	145 ≤ θq ≤ 165	30 ≤ ψq < 50
26	95 ≤ φq < 105	5 ≤ θq ≤ 95	30 ≤ ψq < 50
27	95 ≤ φq < 105	145 ≤ θq ≤ 165	30 ≤ ψq < 50
28	105 ≤ φq < 115	−5 ≤ θq ≤ 85	30 ≤ ψq < 50
29	105 ≤ φq < 115	135 ≤ θq ≤ 175	30 ≤ ψq < 50
30	115 ≤ φq < 125	−5 ≤ θq ≤ 85	30 ≤ ψq < 50
31	115 ≤ φq < 125	125 ≤ θq ≤ 185	30 ≤ ψq < 50
32	125 ≤ φq < 135	25 ≤ θq ≤ 75	30 ≤ ψq < 50
33	125 ≤ φq < 135	125 ≤ θq ≤ 185	30 ≤ ψq < 50
34	135 ≤ φq < 145	25 ≤ θq ≤ 55	30 ≤ ψq < 50
35	135 ≤ φq < 145	65 ≤ θq ≤ 85	30 ≤ ψq < 50
36	135 ≤ φq < 145	125 ≤ θq ≤ 155	30 ≤ ψq < 50
37	145 ≤ φq < 155	15 ≤ θq ≤ 55	30 ≤ ψq < 50
38	145 ≤ φq < 155	65 ≤ θq ≤ 75	30 ≤ ψq < 50
39	145 ≤ φq < 155	115 ≤ θq ≤ 145	30 ≤ ψq < 50
40	155 ≤ φq < 165	−5 ≤ θq ≤ 45	30 ≤ ψq < 50
41	155 ≤ φq < 165	75 ≤ θq ≤ 145	30 ≤ ψq < 50
42	165 ≤ φq < 175	−5 ≤ θq ≤ 65	30 ≤ ψq < 50
43	165 ≤ φq < 175	75 ≤ θq ≤ 135	30 ≤ ψq < 50
44	175 ≤ φq ≤ 185	−5 ≤ θq ≤ 65	30 ≤ ψq < 50
45	175 ≤ φq ≤ 185	85 ≤ θq ≤ 135	30 ≤ ψq < 50
46	175 ≤ φq ≤ 185	175 ≤ θq ≤ 185	30 ≤ ψq < 50

TABLE 4
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	25 ≤ θq ≤ 65	50 ≤ ψq < 70
2	−5 ≤ φq < 5	125 ≤ θq ≤ 165	50 ≤ ψq < 70
3	5 ≤ φq < 15	15 ≤ θq ≤ 65	50 ≤ ψq < 70
4	5 ≤ φq < 15	105 ≤ θq ≤ 165	50 ≤ ψq < 70
5	15 ≤ φq < 25	−5 ≤ θq ≤ 65	50 ≤ ψq < 70
6	15 ≤ φq < 25	75 ≤ θq ≤ 185	50 ≤ ψq < 70
7	25 ≤ φq < 35	−5 ≤ θq ≤ 185	50 ≤ ψq < 70
8	35 ≤ φq < 45	−5 ≤ θq ≤ 175	50 ≤ ψq < 70
9	45 ≤ φq < 55	25 ≤ θq ≤ 85	50 ≤ ψq < 70
10	45 ≤ φq < 55	95 ≤ θq ≤ 145	50 ≤ ψq < 70
11	55 ≤ φq < 65	25 ≤ θq ≤ 65	50 ≤ ψq < 70
12	55 ≤ φq < 65	75 ≤ θq ≤ 145	50 ≤ ψq < 70
13	65 ≤ φq < 75	15 ≤ θq ≤ 135	50 ≤ ψq < 70
14	75 ≤ φq < 85	5 ≤ θq ≤ 125	50 ≤ ψq < 70
15	75 ≤ φq < 85	175 ≤ θq ≤ 185	50 ≤ ψq < 70
16	85 ≤ φq < 95	−5 ≤ θq ≤ 105	50 ≤ ψq < 70
17	85 ≤ φq < 95	145 ≤ θq ≤ 185	50 ≤ ψq < 70
18	95 ≤ φq < 105	−5 ≤ θq ≤ 85	50 ≤ ψq < 70
19	95 ≤ φq < 105	135 ≤ θq ≤ 185	50 ≤ ψq < 70
20	105 ≤ φq < 115	25 ≤ θq ≤ 75	50 ≤ ψq < 70
21	105 ≤ φq < 115	125 ≤ θq ≤ 165	50 ≤ ψq < 70
22	115 ≤ φq < 125	25 ≤ θq ≤ 65	50 ≤ ψq < 70
23	115 ≤ φq < 125	125 ≤ θq ≤ 165	50 ≤ ψq < 70
24	125 ≤ φq < 135	15 ≤ θq ≤ 65	50 ≤ ψq < 70
25	125 ≤ φq < 135	105 ≤ θq ≤ 165	50 ≤ ψq < 70
26	135 ≤ φq < 145	−5 ≤ θq ≤ 65	50 ≤ ψq < 70
27	135 ≤ φq < 145	75 ≤ θq ≤ 185	50 ≤ ψq < 70
28	145 ≤ φq < 155	−5 ≤ θq ≤ 185	50 ≤ ψq < 70
29	155 ≤ φq < 165	−5 ≤ θq ≤ 175	50 ≤ ψq < 70
30	165 ≤ φq < 175	25 ≤ θq ≤ 85	50 ≤ ψq < 70
31	165 ≤ φq < 175	95 ≤ θq ≤ 145	50 ≤ ψq < 70
32	175 ≤ φq ≤ 185	25 ≤ θq ≤ 145	50 ≤ ψq < 70

TABLE 5
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 95	70 ≤ ψq < 90
2	−5 ≤ φq < 5	105 ≤ θq ≤ 185	70 ≤ ψq < 90
3	5 ≤ φq < 15	−5 ≤ θq ≤ 165	70 ≤ ψq < 90
4	15 ≤ φq < 25	−5 ≤ θq ≤ 155	70 ≤ ψq < 90
5	25 ≤ φq < 35	35 ≤ θq ≤ 165	70 ≤ ψq < 90
6	35 ≤ φq < 45	35 ≤ θq ≤ 185	70 ≤ ψq < 90
7	45 ≤ φq < 55	25 ≤ θq ≤ 185	70 ≤ ψq < 90
8	55 ≤ φq < 65	5 ≤ θq ≤ 175	70 ≤ ψq < 90
9	65 ≤ φq < 75	−5 ≤ θq ≤ 145	70 ≤ ψq < 90
10	75 ≤ φq < 85	−5 ≤ θq ≤ 135	70 ≤ ψq < 90
11	85 ≤ φq < 95	25 ≤ θq ≤ 135	70 ≤ ψq < 90
12	95 ≤ φq < 105	25 ≤ θq ≤ 155	70 ≤ ψq < 90
13	95 ≤ φq < 105	175 ≤ θq ≤ 185	70 ≤ ψq < 90
14	105 ≤ φq < 115	15 ≤ θq ≤ 95	70 ≤ ψq < 90
15	105 ≤ φq < 115	105 ≤ θq ≤ 185	70 ≤ ψq < 90
16	115 ≤ φq < 125	−5 ≤ θq ≤ 95	70 ≤ ψq < 90
17	115 ≤ φq < 125	105 ≤ θq ≤ 185	70 ≤ ψq < 90
18	125 ≤ φq < 135	−5 ≤ θq ≤ 165	70 ≤ ψq < 90
19	135 ≤ φq < 145	−5 ≤ θq ≤ 155	70 ≤ ψq < 90
20	145 ≤ φq < 155	35 ≤ θq ≤ 165	70 ≤ ψq < 90
21	155 ≤ φq < 165	35 ≤ θq ≤ 185	70 ≤ ψq < 90
22	165 ≤ φq < 175	25 ≤ θq ≤ 185	70 ≤ ψq < 90
23	175 ≤ φq ≤ 185	5 ≤ θq ≤ 175	70 ≤ ψq < 90

TABLE 6
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 5	90 ≤ ψq < 110
2	−5 ≤ φq < 5	15 ≤ θq ≤ 185	90 ≤ ψq < 110
3	5 ≤ φq < 15	25 ≤ θq ≤ 185	90 ≤ ψq < 110
4	15 ≤ φq < 25	35 ≤ θq ≤ 185	90 ≤ ψq < 110
5	25 ≤ φq < 35	45 ≤ θq ≤ 155	90 ≤ ψq < 110
6	35 ≤ φq < 45	5 ≤ θq ≤ 15	90 ≤ ψq < 110
7	35 ≤ φq < 45	25 ≤ θq ≤ 155	90 ≤ ψq < 110
8	45 ≤ φq < 55	−5 ≤ θq ≤ 165	90 ≤ ψq < 110
9	55 ≤ φq < 65	−5 ≤ θq ≤ 75	90 ≤ ψq < 110
10	55 ≤ φq < 65	95 ≤ θq ≤ 185	90 ≤ ψq < 110
11	65 ≤ φq < 75	15 ≤ θq ≤ 185	90 ≤ ψq < 110
12	75 ≤ φq < 85	25 ≤ θq ≤ 175	90 ≤ ψq < 110
13	85 ≤ φq < 95	15 ≤ θq ≤ 155	90 ≤ ψq < 110
14	95 ≤ φq < 105	−5 ≤ θq ≤ 145	90 ≤ ψq < 110
15	105 ≤ φq < 115	−5 ≤ θq ≤ 155	90 ≤ ψq < 110
16	115 ≤ φq < 125	−5 ≤ θq ≤ 5	90 ≤ ψq < 110
17	115 ≤ φq < 125	15 ≤ θq ≤ 185	90 ≤ ψq < 110
18	125 ≤ φq < 135	25 ≤ θq ≤ 185	90 ≤ ψq < 110
19	135 ≤ φq < 145	35 ≤ θq ≤ 185	90 ≤ ψq < 110
20	145 ≤ φq < 155	45 ≤ θq ≤ 155	90 ≤ ψq < 110
21	155 ≤ φq < 165	5 ≤ θq ≤ 15	90 ≤ ψq < 110
22	155 ≤ φq < 165	25 ≤ θq ≤ 155	90 ≤ ψq < 110
23	165 ≤ φq < 175	−5 ≤ θq ≤ 165	90 ≤ ψq < 110
24	175 ≤ φq ≤ 185	−5 ≤ θq ≤ 75	90 ≤ ψq < 110
25	175 ≤ φq ≤ 185	95 ≤ θq ≤ 185	90 ≤ ψq < 110

TABLE 7
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	35 ≤ θq ≤ 95	110 ≤ ψq < 130
2	−5 ≤ φq < 5	105 ≤ θq ≤ 155	110 ≤ ψq < 130
3	5 ≤ φq < 15	45 ≤ θq ≤ 165	110 ≤ ψq < 130
4	15 ≤ φq < 25	45 ≤ θq ≤ 185	110 ≤ ψq < 130
5	25 ≤ φq < 35	−5 ≤ θq ≤ 35	110 ≤ ψq < 130
6	25 ≤ φq < 35	65 ≤ θq ≤ 185	110 ≤ ψq < 130
7	35 ≤ φq < 45	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
8	35 ≤ φq < 45	85 ≤ θq ≤ 185	110 ≤ ψq < 130
9	45 ≤ φq < 55	15 ≤ θq ≤ 45	110 ≤ ψq < 130
10	45 ≤ φq < 55	105 ≤ θq ≤ 155	110 ≤ ψq < 130
11	55 ≤ φq < 65	15 ≤ θq ≤ 55	110 ≤ ψq < 130
12	55 ≤ φq < 65	115 ≤ θq ≤ 155	110 ≤ ψq < 130
13	65 ≤ φq < 75	5 ≤ θq ≤ 65	110 ≤ ψq < 130
14	65 ≤ φq < 75	125 ≤ θq ≤ 165	110 ≤ ψq < 130
15	75 ≤ φq < 85	−5 ≤ θq ≤ 75	110 ≤ ψq < 130
16	75 ≤ φq < 85	125 ≤ θq ≤ 185	110 ≤ ψq < 130
17	85 ≤ φq < 95	−5 ≤ θq ≤ 185	110 ≤ ψq < 130
18	95 ≤ φq < 105	−5 ≤ θq ≤ 5	110 ≤ ψq < 130
19	95 ≤ φq < 105	15 ≤ θq ≤ 85	110 ≤ ψq < 130
20	95 ≤ φq < 105	95 ≤ θq ≤ 175	110 ≤ ψq < 130
21	105 ≤ φq < 115	25 ≤ θq ≤ 155	110 ≤ ψq < 130
22	115 ≤ φq < 125	35 ≤ θq ≤ 95	110 ≤ ψq < 130
23	115 ≤ φq < 125	105 ≤ θq ≤ 155	110 ≤ ψq < 130
24	125 ≤ φq < 135	45 ≤ θq ≤ 165	110 ≤ ψq < 130
25	135 ≤ φq < 145	45 ≤ θq ≤ 185	110 ≤ ψq < 130
26	145 ≤ φq < 155	−5 ≤ θq ≤ 35	110 ≤ ψq < 130
27	145 ≤ φq < 155	65 ≤ θq ≤ 185	110 ≤ ψq < 130
28	155 ≤ φq < 165	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
29	155 ≤ φq < 165	85 ≤ θq ≤ 185	110 ≤ ψq < 130
30	165 ≤ φq < 175	15 ≤ θq ≤ 45	110 ≤ ψq < 130
31	165 ≤ φq < 175	105 ≤ θq ≤ 155	110 ≤ ψq < 130
32	175 ≤ φq ≤ 185	15 ≤ θq ≤ 55	110 ≤ ψq < 130
33	175 ≤ φq ≤ 185	115 ≤ θq ≤ 155	110 ≤ ψq < 130

TABLE 8
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	45 ≤ θq ≤ 105	130 ≤ ψq < 150
2	−5 ≤ φq < 5	115 ≤ θq ≤ 175	130 ≤ ψq < 150
3	5 ≤ φq < 15	−5 ≤ θq ≤ 25	130 ≤ ψq < 150
4	5 ≤ φq < 15	65 ≤ θq ≤ 105	130 ≤ ψq < 150
5	5 ≤ φq < 15	125 ≤ θq ≤ 165	130 ≤ ψq < 150
6	15 ≤ φq < 25	−5 ≤ θq ≤ 35	130 ≤ ψq < 150
7	15 ≤ φq < 25	65 ≤ θq ≤ 105	130 ≤ ψq < 150
8	15 ≤ φq < 25	135 ≤ θq ≤ 165	130 ≤ ψq < 150
9	25 ≤ φq < 35	5 ≤ θq ≤ 35	130 ≤ ψq < 150
10	25 ≤ φq < 35	75 ≤ θq ≤ 115	130 ≤ ψq < 150
11	25 ≤ φq < 35	135 ≤ θq ≤ 165	130 ≤ ψq < 150
12	35 ≤ φq < 45	15 ≤ θq ≤ 35	130 ≤ ψq < 150
13	35 ≤ φq < 45	85 ≤ θq ≤ 125	130 ≤ ψq < 150
14	35 ≤ φq < 45	145 ≤ θq ≤ 185	130 ≤ ψq < 150
15	45 ≤ φq < 55	5 ≤ θq ≤ 45	130 ≤ ψq < 150
16	45 ≤ φq < 55	95 ≤ θq ≤ 185	130 ≤ ψq < 150
17	55 ≤ φq < 65	−5 ≤ θq ≤ 45	130 ≤ ψq < 150
18	55 ≤ φq < 65	95 ≤ θq ≤ 145	130 ≤ ψq < 150
19	55 ≤ φq < 65	165 ≤ θq ≤ 185	130 ≤ ψq < 150
20	65 ≤ φq < 75	−5 ≤ θq ≤ 55	130 ≤ ψq < 150
21	65 ≤ φq < 75	105 ≤ θq ≤ 155	130 ≤ ψq < 150
22	75 ≤ φq < 85	−5 ≤ θq ≤ 5	130 ≤ ψq < 150
23	75 ≤ φq < 85	15 ≤ θq ≤ 55	130 ≤ ψq < 150
24	75 ≤ φq < 85	65 ≤ θq ≤ 85	130 ≤ ψq < 150
25	75 ≤ φq < 85	95 ≤ θq ≤ 105	130 ≤ ψq < 150
26	75 ≤ φq < 85	115 ≤ θq ≤ 155	130 ≤ ψq < 150
27	85 ≤ φq < 95	35 ≤ θq ≤ 65	130 ≤ ψq < 150
28	85 ≤ φq < 95	85 ≤ θq ≤ 95	130 ≤ ψq < 150
29	85 ≤ φq < 95	115 ≤ θq ≤ 125	130 ≤ ψq < 150
30	85 ≤ φq < 95	135 ≤ θq ≤ 165	130 ≤ ψq < 150
31	95 ≤ φq < 105	35 ≤ θq ≤ 95	130 ≤ ψq < 150
32	95 ≤ φq < 105	115 ≤ θq ≤ 185	130 ≤ ψq < 150
33	105 ≤ φq < 115	45 ≤ θq ≤ 95	130 ≤ ψq < 150
34	105 ≤ φq < 115	135 ≤ θq ≤ 185	130 ≤ ψq < 150
35	115 ≤ φq < 125	45 ≤ θq ≤ 105	130 ≤ ψq < 150
36	115 ≤ φq < 125	115 ≤ θq ≤ 175	130 ≤ ψq < 150
37	125 ≤ φq < 135	−5 ≤ θq ≤ 25	130 ≤ ψq < 150
38	125 ≤ φq < 135	65 ≤ θq ≤ 105	130 ≤ ψq < 150
39	125 ≤ φq < 135	125 ≤ θq ≤ 165	130 ≤ ψq < 150
40	135 ≤ φq < 145	−5 ≤ θq ≤ 35	130 ≤ ψq < 150
41	135 ≤ φq < 145	65 ≤ θq ≤ 105	130 ≤ ψq < 150
42	135 ≤ φq < 145	135 ≤ θq ≤ 165	130 ≤ ψq < 150
43	145 ≤ φq < 155	5 ≤ θq ≤ 35	130 ≤ ψq < 150
44	145 ≤ φq < 155	75 ≤ θq ≤ 115	130 ≤ ψq < 150
45	145 ≤ φq < 155	135 ≤ θq ≤ 165	130 ≤ ψq < 150
46	155 ≤ φq < 165	15 ≤ θq ≤ 35	130 ≤ ψq < 150
47	155 ≤ φq < 165	85 ≤ θq ≤ 125	130 ≤ ψq < 150
48	155 ≤ φq < 165	145 ≤ θq ≤ 185	130 ≤ ψq < 150
49	165 ≤ φq < 175	5 ≤ θq ≤ 45	130 ≤ ψq < 150
50	165 ≤ φq < 175	95 ≤ θq ≤ 185	130 ≤ ψq < 150
51	175 ≤ φq ≤ 185	−5 ≤ θq ≤ 45	130 ≤ ψq < 150
52	175 ≤ φq ≤ 185	95 ≤ θq ≤ 145	130 ≤ ψq < 150
53	175 ≤ φq ≤ 185	165 ≤ θq ≤ 185	130 ≤ ψq < 150

TABLE 9
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
2	−5 ≤ φq < 5	75 ≤ θq ≤ 185	150 ≤ ψq < 170
3	5 ≤ φq < 15	5 ≤ θq ≤ 35	150 ≤ ψq < 170
4	5 ≤ φq < 15	75 ≤ θq ≤ 185	150 ≤ ψq < 170
5	15 ≤ φq < 25	5 ≤ θq ≤ 35	150 ≤ ψq < 170
6	15 ≤ φq < 25	75 ≤ θq ≤ 105	150 ≤ ψq < 170
7	15 ≤ φq < 25	135 ≤ θq ≤ 175	150 ≤ ψq < 170
8	25 ≤ φq < 35	5 ≤ θq ≤ 35	150 ≤ ψq < 170
9	25 ≤ φq < 35	75 ≤ θq ≤ 105	150 ≤ ψq < 170
10	25 ≤ φq < 35	145 ≤ θq ≤ 165	150 ≤ ψq < 170
11	35 ≤ φq < 45	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
12	35 ≤ φq < 45	85 ≤ θq ≤ 115	150 ≤ ψq < 170
13	35 ≤ φq < 45	145 ≤ θq ≤ 165	150 ≤ ψq < 170
14	45 ≤ φq < 55	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
15	45 ≤ φq < 55	85 ≤ θq ≤ 115	150 ≤ ψq < 170
16	45 ≤ φq < 55	145 ≤ θq ≤ 165	150 ≤ ψq < 170
17	55 ≤ φq < 65	−5 ≤ θq ≤ 5	150 ≤ ψq < 170
18	55 ≤ φq < 65	65 ≤ θq ≤ 115	150 ≤ ψq < 170
19	55 ≤ φq < 65	145 ≤ θq ≤ 185	150 ≤ ψq < 170
20	65 ≤ φq < 75	45 ≤ θq ≤ 125	150 ≤ ψq < 170
21	65 ≤ φq < 75	155 ≤ θq ≤ 185	150 ≤ ψq < 170
22	75 ≤ φq < 85	45 ≤ θq ≤ 145	150 ≤ ψq < 170
23	75 ≤ φq < 85	155 ≤ θq ≤ 185	150 ≤ ψq < 170
24	85 ≤ φq < 95	45 ≤ θq ≤ 155	150 ≤ ψq < 170
25	95 ≤ φq < 105	65 ≤ θq ≤ 155	150 ≤ ψq < 170
26	105 ≤ φq < 115	−5 ≤ θq ≤ 15	150 ≤ ψq < 170
27	105 ≤ φq < 115	75 ≤ θq ≤ 165	150 ≤ ψq < 170
28	115 ≤ φq < 125	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
29	115 ≤ φq < 125	75 ≤ θq ≤ 185	150 ≤ ψq < 170
30	125 ≤ φq < 135	5 ≤ θq ≤ 35	150 ≤ ψq < 170
31	125 ≤ φq < 135	75 ≤ θq ≤ 185	150 ≤ ψq < 170
32	135 ≤ φq < 145	5 ≤ θq ≤ 35	150 ≤ ψq < 170
33	135 ≤ φq < 145	75 ≤ θq ≤ 105	150 ≤ ψq < 170
34	135 ≤ φq < 145	135 ≤ θq ≤ 175	150 ≤ ψq < 170
35	145 ≤ φq < 155	5 ≤ θq ≤ 35	150 ≤ ψq < 170
36	145 ≤ φq < 155	75 ≤ θq ≤ 105	150 ≤ ψq < 170
37	145 ≤ φq < 155	145 ≤ θq ≤ 165	150 ≤ ψq < 170
38	155 ≤ φq < 165	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
39	155 ≤ φq < 165	85 ≤ θq ≤ 115	150 ≤ ψq < 170
40	155 ≤ φq < 165	145 ≤ θq ≤ 165	150 ≤ ψq < 170
41	165 ≤ φq < 175	−5 ≤ θq ≤ 35	150 ≤ ψq < 170
42	165 ≤ φq < 175	85 ≤ θq ≤ 115	150 ≤ ψq < 170
43	165 ≤ φq < 175	145 ≤ θq ≤ 165	150 ≤ ψq < 170
44	175 ≤ φq ≤ 185	−5 ≤ θq ≤ 5	150 ≤ ψq < 170
45	175 ≤ φq ≤ 185	55 ≤ θq ≤ 115	150 ≤ ψq < 170
46	175 ≤ φq ≤ 185	145 ≤ θq ≤ 185	150 ≤ ψq < 170

TABLE 10
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	5 ≤ θq ≤ 35	170 ≤ ψq ≤ 190
2	−5 ≤ φq < 5	85 ≤ θq ≤ 155	170 ≤ ψq ≤ 190
3	5 ≤ φq < 15	5 ≤ θq ≤ 35	170 ≤ ψq ≤ 190
4	5 ≤ φq < 15	85 ≤ θq ≤ 155	170 ≤ ψq ≤ 190
5	15 ≤ φq < 25	−5 ≤ θq ≤ 25	170 ≤ ψq ≤ 190
6	15 ≤ φq < 25	75 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
7	25 ≤ φq < 35	−5 ≤ θq ≤ 25	170 ≤ ψq ≤ 190
8	25 ≤ φq < 35	75 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
9	35 ≤ φq < 45	−5 ≤ θq ≤ 5	170 ≤ ψq ≤ 190
10	35 ≤ φq < 45	75 ≤ θq ≤ 115	170 ≤ ψq ≤ 190
11	35 ≤ φq < 45	145 ≤ θq ≤ 175	170 ≤ ψq ≤ 190
12	45 ≤ φq < 55	65 ≤ θq ≤ 115	170 ≤ ψq ≤ 190
13	45 ≤ φq < 55	145 ≤ θq ≤ 175	170 ≤ ψq ≤ 190
14	55 ≤ φq < 65	45 ≤ θq ≤ 105	170 ≤ ψq ≤ 190
15	55 ≤ φq < 65	145 ≤ θq ≤ 165	170 ≤ ψq ≤ 190
16	65 ≤ φq < 75	55 ≤ θq ≤ 105	170 ≤ ψq ≤ 190
17	65 ≤ φq < 75	145 ≤ θq ≤ 165	170 ≤ ψq ≤ 190
18	75 ≤ φq < 85	65 ≤ θq ≤ 115	170 ≤ ψq ≤ 190
19	75 ≤ φq < 85	145 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
20	85 ≤ φq < 95	−5 ≤ θq ≤ 25	170 ≤ ψq ≤ 190
21	85 ≤ φq < 95	75 ≤ θq ≤ 125	170 ≤ ψq ≤ 190
22	85 ≤ φq < 95	135 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
23	105 ≤ φq ≤ 115	5 ≤ θq ≤ 35	170 ≤ ψq ≤ 190

On the other hand, it has been clear that the Rayleigh wave can be suppressed when the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 40° Y or more and about 90° Y or less, in similar ranges of the azimuthal angles of the quartz-crystal layer 4, for example. Thus, in Tables 11 to 20, there are given the ranges of the azimuthal angles in which the Rayleigh wave can be suppressed when the cut angle is about 40° Y or more and about 90° Y or less, for example.

The Rayleigh wave can be suppressed when the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 40° Y or more and about 90° Y or less and if φ_q, θ_q, and ψ_q in the azimuthal angles of the quartz-crystal layer 4 are in any one of the combinations in Tables 11 to 20, for example. Note that the quartz-crystal layer 4 is a monocrystalline quartz-crystal layer.

TABLE 11
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 25	−10 ≤ ψq < 10
2	−5 ≤ φq < 5	105 ≤ θq ≤ 185	−10 ≤ ψq < 10
3	5 ≤ φq < 15	−5 ≤ θq ≤ 25	−10 ≤ ψq < 10
4	5 ≤ φq < 15	105 ≤ θq ≤ 185	−10 ≤ ψq < 10
5	15 ≤ φq < 25	−5 ≤ θq ≤ 15	−10 ≤ ψq < 10
6	15 ≤ φq < 25	95 ≤ θq ≤ 185	−10 ≤ ψq < 10
7	25 ≤ φq < 35	95 ≤ θq ≤ 175	−10 ≤ ψq < 10
8	35 ≤ φq < 45	95 ≤ θq ≤ 165	−10 ≤ ψq < 10
9	45 ≤ φq < 55	95 ≤ θq ≤ 155	−10 ≤ ψq < 10
10	55 ≤ φq < 65	95 ≤ θq ≤ 155	−10 ≤ ψq < 10
11	65 ≤ φq < 75	95 ≤ θq ≤ 155	−10 ≤ ψq < 10
12	75 ≤ φq < 85	95 ≤ θq ≤ 165	−10 ≤ ψq < 10
13	85 ≤ φq < 95	95 ≤ θq ≤ 175	−10 ≤ ψq < 10
14	95 ≤ φq < 105	−5 ≤ θq ≤ 15	−10 ≤ ψq < 10
15	95 ≤ φq < 105	95 ≤ θq ≤ 185	−10 ≤ ψq < 10
16	105 ≤ φq < 115	−5 ≤ θq ≤ 25	−10 ≤ ψq < 10
17	105 ≤ φq < 115	95 ≤ θq ≤ 185	−10 ≤ ψq < 10
18	115 ≤ φq < 125	−5 ≤ θq ≤ 25	−10 ≤ ψq < 10
19	115 ≤ φq < 125	105 ≤ θq ≤ 185	−10 ≤ ψq < 10
20	125 ≤ φq < 135	−5 ≤ θq ≤ 25	−10 ≤ ψq < 10
21	125 ≤ φq < 135	105 ≤ θq ≤ 185	−10 ≤ ψq < 10
22	135 ≤ φq < 145	−5 ≤ θq ≤ 15	−10 ≤ ψq < 10
23	135 ≤ φq < 145	95 ≤ θq ≤ 185	−10 ≤ ψq < 10
24	145 ≤ φq < 155	95 ≤ θq ≤ 175	−10 ≤ ψq < 10
25	155 ≤ φq < 165	95 ≤ θq ≤ 165	−10 ≤ ψq < 10
26	165 ≤ φq < 175	95 ≤ θq ≤ 155	−10 ≤ ψq < 10
27	175 ≤ φq < 185	95 ≤ θq ≤ 155	−10 ≤ ψq < 10

TABLE 12
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 15	10 ≤ ψq < 30
2	−5 ≤ φq < 5	95 ≤ θq ≤ 185	10 ≤ ψq < 30
3	5 ≤ φq < 15	115 ≤ θq ≤ 185	10 ≤ ψq < 30
4	15 ≤ φq < 25	105 ≤ θq ≤ 115	10 ≤ ψq < 30
5	15 ≤ φq < 25	125 ≤ θq ≤ 185	10 ≤ ψq < 30
6	25 ≤ φq < 35	115 ≤ θq ≤ 185	10 ≤ ψq < 30
7	35 ≤ φq < 45	105 ≤ θq ≤ 185	10 ≤ ψq < 30
8	45 ≤ φq < 55	95 ≤ θq ≤ 175	10 ≤ ψq < 30
9	55 ≤ φq < 65	95 ≤ θq ≤ 165	10 ≤ ψq < 30
10	65 ≤ φq < 75	95 ≤ θq ≤ 155	10 ≤ ψq < 30
11	75 ≤ φq < 85	−5 ≤ θq ≤ 25	10 ≤ ψq < 30
12	75 ≤ φq < 85	95 ≤ θq ≤ 155	10 ≤ ψq < 30
13	85 ≤ φq < 95	−5 ≤ θq ≤ 25	10 ≤ ψq < 30
14	85 ≤ φq < 95	95 ≤ θq ≤ 155	10 ≤ ψq < 30
15	95 ≤ φq < 105	−5 ≤ θq ≤ 25	10 ≤ ψq < 30
16	95 ≤ φq < 105	95 ≤ θq ≤ 155	10 ≤ ψq < 30
17	105 ≤ φq < 115	−5 ≤ θq ≤ 25	10 ≤ ψq < 30
18	105 ≤ φq < 115	95 ≤ θq ≤ 175	10 ≤ ψq < 30
19	115 ≤ φq < 125	−5 ≤ θq ≤ 15	10 ≤ ψq < 30
20	115 ≤ φq < 125	95 ≤ θq ≤ 185	10 ≤ ψq < 30
21	125 ≤ φq < 135	115 ≤ θq ≤ 185	10 ≤ ψq < 30
22	135 ≤ φq < 145	105 ≤ θq ≤ 115	10 ≤ ψq < 30
23	135 ≤ φq < 145	125 ≤ θq ≤ 185	10 ≤ ψq < 30
24	145 ≤ φq < 155	115 ≤ θq ≤ 185	10 ≤ ψq < 30
25	155 ≤ φq < 165	105 ≤ θq ≤ 185	10 ≤ ψq < 30
26	165 ≤ φq < 175	95 ≤ θq ≤ 175	10 ≤ ψq < 30
27	175 ≤ φq < 185	95 ≤ θq ≤ 165	10 ≤ ψq < 30

TABLE 13
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	75 ≤ θq ≤ 105	30 ≤ ψq < 50
2	−5 ≤ φq < 5	115 ≤ θq ≤ 155	30 ≤ ψq < 50
3	5 ≤ φq < 15	65 ≤ θq ≤ 95	30 ≤ ψq < 50
4	5 ≤ φq < 15	115 ≤ θq ≤ 175	30 ≤ ψq < 50
5	15 ≤ φq < 25	65 ≤ θq ≤ 75	30 ≤ ψq < 50
6	15 ≤ φq < 25	145 ≤ θq ≤ 185	30 ≤ ψq < 50
7	25 ≤ φq < 35	55 ≤ θq ≤ 65	30 ≤ ψq < 50
8	25 ≤ φq < 35	135 ≤ θq ≤ 185	30 ≤ ψq < 50
9	35 ≤ φq < 45	135 ≤ θq ≤ 185	30 ≤ ψq < 50
10	45 ≤ φq < 55	125 ≤ θq ≤ 185	30 ≤ ψq < 50
11	55 ≤ φq < 65	−5 ≤ θq ≤ 25	30 ≤ ψq < 50
12	55 ≤ φq < 65	115 ≤ θq ≤ 185	30 ≤ ψq < 50
13	65 ≤ φq < 75	−5 ≤ θq ≤ 35	30 ≤ ψq < 50
14	65 ≤ φq < 75	115 ≤ θq ≤ 175	30 ≤ ψq < 50
15	75 ≤ φq < 85	−5 ≤ θq ≤ 25	30 ≤ ψq < 50
16	75 ≤ φq < 85	95 ≤ θq ≤ 165	30 ≤ ψq < 50
17	85 ≤ φq < 95	−5 ≤ θq ≤ 25	30 ≤ ψq < 50
18	85 ≤ φq < 95	95 ≤ θq ≤ 155	30 ≤ ψq < 50
19	95 ≤ φq < 105	−5 ≤ θq ≤ 15	30 ≤ ψq < 50
20	95 ≤ φq < 105	85 ≤ θq ≤ 155	30 ≤ ψq < 50
21	105 ≤ φq < 115	85 ≤ θq ≤ 145	30 ≤ ψq < 50
22	115 ≤ φq < 125	75 ≤ θq ≤ 105	30 ≤ ψq < 50
23	115 ≤ φq < 125	115 ≤ θq ≤ 155	30 ≤ ψq < 50
24	125 ≤ φq < 135	65 ≤ θq ≤ 95	30 ≤ ψq < 50
25	125 ≤ φq < 135	115 ≤ θq ≤ 175	30 ≤ ψq < 50
26	135 ≤ φq < 145	65 ≤ θq ≤ 75	30 ≤ ψq < 50
27	135 ≤ φq < 145	145 ≤ θq ≤ 185	30 ≤ ψq < 50
28	145 ≤ φq < 155	55 ≤ θq ≤ 65	30 ≤ ψq < 50
29	145 ≤ φq < 155	135 ≤ θq ≤ 185	30 ≤ ψq < 50
30	155 ≤ φq < 165	135 ≤ θq ≤ 185	30 ≤ ψq < 50
31	165 ≤ φq < 175	125 ≤ θq ≤ 185	30 ≤ ψq < 50
32	175 ≤ φq < 185	−5 ≤ θq ≤ 25	30 ≤ ψq < 50
33	175 ≤ φq < 185	115 ≤ θq ≤ 185	30 ≤ ψq < 50

TABLE 14
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	55 ≤ θq ≤ 135	50 ≤ ψq < 70
2	5 ≤ φq < 15	55 ≤ θq ≤ 135	50 ≤ ψq < 70
3	15 ≤ φq < 25	45 ≤ θq ≤ 115	50 ≤ ψq < 70
4	25 ≤ φq < 35	45 ≤ θq ≤ 85	50 ≤ ψq < 70
5	25 ≤ φq < 35	165 ≤ θq ≤ 175	50 ≤ ψq < 70
6	35 ≤ φq < 45	−5 ≤ θq ≤ 65	50 ≤ ψq < 70
7	35 ≤ φq < 45	145 ≤ θq ≤ 185	50 ≤ ψq < 70
8	45 ≤ φq < 55	−5 ≤ θq ≤ 45	50 ≤ ψq < 70
9	45 ≤ φq < 55	135 ≤ θq ≤ 185	50 ≤ ψq < 70
10	55 ≤ φq < 65	−5 ≤ θq ≤ 35	50 ≤ ψq < 70
11	55 ≤ φq < 65	125 ≤ θq ≤ 185	50 ≤ ψq < 70
12	65 ≤ φq < 75	−5 ≤ θq ≤ 35	50 ≤ ψq < 70
13	65 ≤ φq < 75	125 ≤ θq ≤ 185	50 ≤ ψq < 70
14	75 ≤ φq < 85	−5 ≤ θq ≤ 25	50 ≤ ψq < 70
15	75 ≤ φq < 85	115 ≤ θq ≤ 185	50 ≤ ψq < 70
16	85 ≤ φq < 95	95 ≤ θq ≤ 175	50 ≤ ψq < 70
17	95 ≤ φq < 105	75 ≤ θq ≤ 155	50 ≤ ψq < 70
18	105 ≤ φq < 115	65 ≤ θq ≤ 145	50 ≤ ψq < 70
19	115 ≤ φq < 125	65 ≤ θq ≤ 135	50 ≤ ψq < 70
20	125 ≤ φq < 135	55 ≤ θq ≤ 135	50 ≤ ψq < 70
21	135 ≤ φq < 145	45 ≤ θq ≤ 115	50 ≤ ψq < 70
22	145 ≤ φq < 155	45 ≤ θq ≤ 85	50 ≤ ψq < 70
23	145 ≤ φq < 155	165 ≤ θq ≤ 175	50 ≤ ψq < 70
24	155 ≤ φq < 165	−5 ≤ θq ≤ 65	50 ≤ ψq < 70
25	155 ≤ φq < 165	145 ≤ θq ≤ 185	50 ≤ ψq < 70
26	165 ≤ φq < 175	−5 ≤ θq ≤ 45	50 ≤ ψq < 70
27	165 ≤ φq < 175	135 ≤ θq ≤ 185	50 ≤ ψq < 70
28	175 ≤ φq < 185	−5 ≤ θq ≤ 35	50 ≤ ψq < 70
29	175 ≤ φq < 185	125 ≤ θq ≤ 185	50 ≤ ψq < 70

TABLE 15
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	55 ≤ θq ≤ 135	70 ≤ ψq < 90
2	5 ≤ φq < 15	25 ≤ θq ≤ 35	70 ≤ ψq < 90
3	5 ≤ φq < 15	45 ≤ θq ≤ 135	70 ≤ ψq < 90
4	15 ≤ φq < 25	−5 ≤ θq ≤ 115	70 ≤ ψq < 90
5	25 ≤ φq < 35	−5 ≤ θq ≤ 65	70 ≤ ψq < 90
6	35 ≤ φq < 45	−5 ≤ θq ≤ 55	70 ≤ ψq < 90
7	45 ≤ φq < 55	−5 ≤ θq ≤ 45	70 ≤ ψq < 90
8	55 ≤ φq < 65	−5 ≤ θq ≤ 35	70 ≤ ψq < 90
9	55 ≤ φq < 65	135 ≤ θq ≤ 185	70 ≤ ψq < 90
10	65 ≤ φq < 75	125 ≤ θq ≤ 185	70 ≤ ψq < 90
11	75 ≤ φq < 85	115 ≤ θq ≤ 185	70 ≤ ψq < 90
12	85 ≤ φq < 95	85 ≤ θq ≤ 185	70 ≤ ψq < 90
13	95 ≤ φq < 105	65 ≤ θq ≤ 185	70 ≤ ψq < 90
14	105 ≤ φq < 115	55 ≤ θq ≤ 175	70 ≤ ψq < 90
15	115 ≤ φq < 125	55 ≤ θq ≤ 135	70 ≤ ψq < 90
16	125 ≤ φq < 135	25 ≤ θq ≤ 35	70 ≤ ψq < 90
17	125 ≤ φq < 135	45 ≤ θq ≤ 135	70 ≤ ψq < 90
18	135 ≤ φq < 145	−5 ≤ θq ≤ 115	70 ≤ ψq < 90
19	135 ≤ φq < 145	125 ≤ θq ≤ 135	70 ≤ ψq < 90
20	145 ≤ φq < 155	−5 ≤ θq ≤ 65	70 ≤ ψq < 90
21	155 ≤ φq < 165	−5 ≤ θq ≤ 55	70 ≤ ψq < 90
22	165 ≤ φq < 175	−5 ≤ θq ≤ 45	70 ≤ ψq < 90
23	175 ≤ φq < 185	−5 ≤ θq ≤ 35	70 ≤ ψq < 90
24	175 ≤ φq < 185	135 ≤ θq ≤ 185	70 ≤ ψq < 90

TABLE 16
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 45	90 ≤ ψq < 110
2	−5 ≤ φq < 5	135 ≤ θq ≤ 185	90 ≤ ψq < 110
3	5 ≤ φq < 15	−5 ≤ θq ≤ 45	90 ≤ ψq < 110
4	5 ≤ φq < 15	165 ≤ θq ≤ 175	90 ≤ ψq < 110
5	15 ≤ φq < 25	−5 ≤ θq ≤ 65	90 ≤ ψq < 110
6	25 ≤ φq < 35	−5 ≤ θq ≤ 65	90 ≤ ψq < 110
7	35 ≤ φq < 45	−5 ≤ θq ≤ 75	90 ≤ ψq < 110
8	45 ≤ φq < 55	15 ≤ θq ≤ 115	90 ≤ ψq < 110
9	45 ≤ φq < 55	175 ≤ θq ≤ 185	90 ≤ ψq < 110
10	55 ≤ φq < 65	35 ≤ θq ≤ 125	90 ≤ ψq < 110
11	65 ≤ φq < 75	55 ≤ θq ≤ 145	90 ≤ ψq < 110
12	75 ≤ φq < 85	55 ≤ θq ≤ 185	90 ≤ ψq < 110
13	85 ≤ φq < 95	65 ≤ θq ≤ 185	90 ≤ ψq < 110
14	95 ≤ φq < 105	85 ≤ θq ≤ 105	90 ≤ ψq < 110
15	95 ≤ φq < 105	115 ≤ θq ≤ 185	90 ≤ ψq < 110
16	105 ≤ φq < 115	125 ≤ θq ≤ 185	90 ≤ ψq < 110
17	115 ≤ φq < 125	−5 ≤ θq ≤ 45	90 ≤ ψq < 110
18	115 ≤ φq < 125	135 ≤ θq ≤ 185	90 ≤ ψq < 110
19	125 ≤ φq < 135	−5 ≤ θq ≤ 45	90 ≤ ψq < 110
20	125 ≤ φq < 135	165 ≤ θq ≤ 175	90 ≤ ψq < 110
21	135 ≤ φq < 145	−5 ≤ θq ≤ 65	90 ≤ ψq < 110
22	145 ≤ φq < 155	−5 ≤ θq ≤ 65	90 ≤ ψq < 110
23	155 ≤ φq < 165	−5 ≤ θq ≤ 75	90 ≤ ψq < 110
24	165 ≤ φq < 175	15 ≤ θq ≤ 115	90 ≤ ψq < 110
25	175 ≤ φq < 185	35 ≤ θq ≤ 125	90 ≤ ψq < 110

TABLE 17
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
2	−5 ≤ φq < 5	145 ≤ θq ≤ 185	110 ≤ ψq < 130
3	5 ≤ φq < 15	−5 ≤ θq ≤ 55	110 ≤ ψq < 130
4	5 ≤ φq < 15	145 ≤ θq ≤ 185	110 ≤ ψq < 130
5	15 ≤ φq < 25	−5 ≤ θq ≤ 55	110 ≤ ψq < 130
6	15 ≤ φq < 25	155 ≤ θq ≤ 185	110 ≤ ψq < 130
7	25 ≤ φq < 35	5 ≤ θq ≤ 75	110 ≤ ψq < 130
8	35 ≤ φq < 45	25 ≤ θq ≤ 95	110 ≤ ψq < 130
9	45 ≤ φq < 55	35 ≤ θq ≤ 105	110 ≤ ψq < 130
10	55 ≤ φq < 65	35 ≤ θq ≤ 125	110 ≤ ψq < 130
11	65 ≤ φq < 75	45 ≤ θq ≤ 125	110 ≤ ψq < 130
12	75 ≤ φq < 85	45 ≤ θq ≤ 135	110 ≤ ψq < 130
13	85 ≤ φq < 95	5 ≤ θq ≤ 25	110 ≤ ψq < 130
14	85 ≤ φq < 95	85 ≤ θq ≤ 155	110 ≤ ψq < 130
15	95 ≤ φq < 105	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
16	95 ≤ φq < 105	105 ≤ θq ≤ 185	110 ≤ ψq < 130
17	105 ≤ φq < 115	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
18	105 ≤ φq < 115	135 ≤ θq ≤ 185	110 ≤ ψq < 130
19	115 ≤ φq < 125	−5 ≤ θq ≤ 45	110 ≤ ψq < 130
20	115 ≤ φq < 125	145 ≤ θq ≤ 185	110 ≤ ψq < 130
21	125 ≤ φq < 135	−5 ≤ θq ≤ 55	110 ≤ ψq < 130
22	125 ≤ φq < 135	145 ≤ θq ≤ 185	110 ≤ ψq < 130
23	135 ≤ φq < 145	−5 ≤ θq ≤ 55	110 ≤ ψq < 130
24	135 ≤ φq < 145	155 ≤ θq ≤ 185	110 ≤ ψq < 130
25	145 ≤ φq < 155	5 ≤ θq ≤ 75	110 ≤ ψq < 130
26	155 ≤ φq < 165	25 ≤ θq ≤ 95	110 ≤ ψq < 130
27	165 ≤ φq < 175	35 ≤ θq ≤ 105	110 ≤ ψq < 130
28	175 ≤ φq < 185	35 ≤ θq ≤ 125	110 ≤ ψq < 130

TABLE 18
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	−5 ≤ θq ≤ 65	130 ≤ ψq < 150
2	−5 ≤ φq < 5	155 ≤ θq ≤ 185	130 ≤ ψq < 150
3	5 ≤ φq < 15	5 ≤ θq ≤ 65	130 ≤ ψq < 150
4	5 ≤ φq < 15	145 ≤ θq ≤ 185	130 ≤ ψq < 150
5	15 ≤ φq < 25	15 ≤ θq ≤ 75	130 ≤ ψq < 150
6	15 ≤ φq < 25	145 ≤ θq ≤ 185	130 ≤ ψq < 150
7	25 ≤ φq < 35	25 ≤ θq ≤ 85	130 ≤ ψq < 150
8	25 ≤ φq < 35	155 ≤ θq ≤ 185	130 ≤ ψq < 150
9	35 ≤ φq < 45	25 ≤ θq ≤ 95	130 ≤ ψq < 150
10	35 ≤ φq < 45	165 ≤ θq ≤ 185	130 ≤ ψq < 150
11	45 ≤ φq < 55	35 ≤ θq ≤ 95	130 ≤ ψq < 150
12	55 ≤ φq < 65	25 ≤ θq ≤ 105	130 ≤ ψq < 150
13	65 ≤ φq < 75	5 ≤ θq ≤ 65	130 ≤ ψq < 150
14	65 ≤ φq < 75	85 ≤ θq ≤ 115	130 ≤ ψq < 150
15	75 ≤ φq < 85	−5 ≤ θq ≤ 55	130 ≤ ψq < 150
16	75 ≤ φq < 85	75 ≤ θq ≤ 85	130 ≤ ψq < 150
17	75 ≤ φq < 85	105 ≤ θq ≤ 125	130 ≤ ψq < 150
18	85 ≤ φq < 95	−5 ≤ θq ≤ 55	130 ≤ ψq < 150
19	85 ≤ φq < 95	105 ≤ θq ≤ 115	130 ≤ ψq < 150
20	95 ≤ φq < 105	−5 ≤ θq ≤ 45	130 ≤ ψq < 150
21	105 ≤ φq < 115	−5 ≤ θq ≤ 55	130 ≤ ψq < 150
22	115 ≤ φq < 125	−5 ≤ θq ≤ 65	130 ≤ ψq < 150
23	115 ≤ φq < 125	155 ≤ θq ≤ 185	130 ≤ ψq < 150
24	125 ≤ φq < 135	5 ≤ θq ≤ 65	130 ≤ ψq < 150
25	125 ≤ φq < 135	145 ≤ θq ≤ 185	130 ≤ ψq < 150
26	135 ≤ φq < 145	15 ≤ θq ≤ 75	130 ≤ ψq < 150
27	135 ≤ φq < 145	145 ≤ θq ≤ 185	130 ≤ ψq < 150
28	145 ≤ φq < 155	25 ≤ θq ≤ 85	130 ≤ ψq < 150
29	145 ≤ φq < 155	155 ≤ θq ≤ 185	130 ≤ ψq < 150
30	155 ≤ φq < 165	25 ≤ θq ≤ 95	130 ≤ ψq < 150
31	155 ≤ φq < 165	165 ≤ θq ≤ 185	130 ≤ ψq < 150
32	165 ≤ φq < 175	35 ≤ θq ≤ 95	130 ≤ ψq < 150
33	175 ≤ φq < 185	25 ≤ θq ≤ 105	130 ≤ ψq < 150

TABLE 19
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	15 ≤ θq ≤ 85	150 ≤ ψq < 170
2	5 ≤ φq < 15	25 ≤ θq ≤ 85	150 ≤ ψq < 170
3	15 ≤ φq < 25	25 ≤ θq ≤ 85	150 ≤ ψq < 170
4	15 ≤ φq < 25	165 ≤ θq ≤ 185	150 ≤ ψq < 170
5	25 ≤ φq < 35	25 ≤ θq ≤ 85	150 ≤ ψq < 170
6	25 ≤ φq < 35	155 ≤ θq ≤ 185	150 ≤ ψq < 170
7	35 ≤ φq < 45	25 ≤ θq ≤ 85	150 ≤ ψq < 170
8	35 ≤ φq < 45	155 ≤ θq ≤ 185	150 ≤ ψq < 170
9	45 ≤ φq < 55	5 ≤ θq ≤ 85	150 ≤ ψq < 170
10	45 ≤ φq < 55	155 ≤ θq ≤ 185	150 ≤ ψq < 170
11	55 ≤ φq < 65	−5 ≤ θq ≤ 85	150 ≤ ψq < 170
12	55 ≤ φq < 65	165 ≤ θq ≤ 185	150 ≤ ψq < 170
13	65 ≤ φq < 75	−5 ≤ θq ≤ 85	150 ≤ ψq < 170
14	75 ≤ φq < 85	−5 ≤ θq ≤ 75	150 ≤ ψq < 170
15	85 ≤ φq < 95	−5 ≤ θq ≤ 65	150 ≤ ψq < 170
16	95 ≤ φq < 105	−5 ≤ θq ≤ 75	150 ≤ ψq < 170
17	105 ≤ φq < 115	5 ≤ θq ≤ 75	150 ≤ ψq < 170
18	115 ≤ φq < 125	15 ≤ θq ≤ 85	150 ≤ ψq < 170
19	125 ≤ φq < 135	25 ≤ θq ≤ 85	150 ≤ ψq < 170
20	135 ≤ φq < 145	25 ≤ θq ≤ 85	150 ≤ ψq < 170
21	135 ≤ φq < 145	165 ≤ θq ≤ 185	150 ≤ ψq < 170
22	145 ≤ φq < 155	25 ≤ θq ≤ 85	150 ≤ ψq < 170
23	145 ≤ φq < 155	155 ≤ θq ≤ 185	150 ≤ ψq < 170
24	155 ≤ φq < 165	25 ≤ θq ≤ 85	150 ≤ ψq < 170
25	155 ≤ φq < 165	155 ≤ θq ≤ 185	150 ≤ ψq < 170
26	165 ≤ φq < 175	5 ≤ θq ≤ 85	150 ≤ ψq < 170
27	165 ≤ φq < 175	155 ≤ θq ≤ 185	150 ≤ ψq < 170
28	175 ≤ φq < 185	−5 ≤ θq ≤ 85	150 ≤ ψq < 170
29	175 ≤ φq < 185	165 ≤ θq ≤ 185	150 ≤ ψq < 170

TABLE 20
	φq	θq	ψq
CONDITION	RANGE[°]	RANGE[°]	RANGE[°]
1	−5 ≤ φq < 5	25 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
2	5 ≤ φq < 15	25 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
3	15 ≤ φq < 25	15 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
4	25 ≤ φq < 35	5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
5	35 ≤ φq < 45	−5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
6	35 ≤ φq < 45	165 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
7	45 ≤ φq < 55	−5 ≤ θq ≤ 75	170 ≤ ψq ≤ 190
8	45 ≤ φq < 55	155 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
9	55 ≤ φq < 65	−5 ≤ θq ≤ 75	170 ≤ ψq ≤ 190
10	55 ≤ φq < 65	155 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
11	65 ≤ φq < 75	−5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
12	65 ≤ φq < 75	155 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
13	75 ≤ φq < 85	−5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
14	75 ≤ φq < 85	165 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
15	85 ≤ φq < 95	5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
16	95 ≤ φq < 105	15 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
17	105 ≤ φq < 115	25 ≤ θq ≤ 45	170 ≤ ψq ≤ 190
18	105 ≤ φq < 115	55 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
19	115 ≤ φq < 125	25 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
20	125 ≤ φq < 135	25 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
21	135 ≤ φq < 145	15 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
22	145 ≤ φq < 155	5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
23	155 ≤ φq < 165	−5 ≤ θq ≤ 85	170 ≤ ψq ≤ 190
24	155 ≤ φq < 165	165 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
25	165 ≤ φq < 175	−5 ≤ θq ≤ 75	170 ≤ ψq ≤ 190
26	165 ≤ φq < 175	155 ≤ θq ≤ 185	170 ≤ ψq ≤ 190
27	175 ≤ φq < 185	−5 ≤ θq ≤ 75	170 ≤ ψq ≤ 190
28	175 ≤ φq < 185	155 ≤ θq ≤ 185	170 ≤ ψq ≤ 190

In Tables 1 to 20, there are given the combinations of φ_q, θ_q, and ψ_q in the azimuthal angles of the quartz-crystal layer 4 when the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 20° Y or more and about 90° Y or less, for example. As described above, a relative bandwidth can be sufficiently widened when the cut angle of the lithium tantalate of the piezoelectric layer 5 is about 20° Y or more and about 90° Y or less, for example.

As FIG. 1 illustrates, in the multilayer substrate 6 in the first preferred embodiment, the quartz-crystal layer 4 is directly disposed on the support substrate 2. Note that the quartz-crystal layer 4 may be indirectly disposed on the support substrate 2 with another layer interposed therebetween.

FIG. 16 is a front sectional view of the vicinity of a pair of electrode fingers in a modification of the first preferred embodiment.

A multilayer substrate 26 in the present modification includes an intermediate layer 23 disposed between the support substrate 2 and the quartz-crystal layer 4. Examples of the material for the intermediate layer 23 include a dielectric of silicon oxide, silicon nitride, or silicon oxynitride. Note that the intermediate layer 23 may be a multilayer body. In such a case, for example, the intermediate layer 23 includes at least a first layer and a second layer. Examples of the material for each of the layers of the intermediate layer 23 include a dielectric of silicon oxide, silicon nitride, or silicon oxynitride.

In the present modification, the higher-order mode can also be suppressed in a wide band as in the first preferred embodiment.

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.

Claims

1. An acoustic wave device comprising: a support substrate;a silicon oxide layer provided directly or indirectly on the support substrate and having crystallinity;a piezoelectric layer on the silicon oxide layer having crystallinity; andan IDT electrode on the piezoelectric layer; whereinwhen λ represents a wavelength defined by an electrode finger pitch of the IDT electrode, a thickness of the silicon oxide layer having crystallinity is about 0.2λ or more and about 0.4λ or less; andthe piezoelectric layer has a thickness smaller than the thickness of the silicon oxide layer having crystallinity.

2. The acoustic wave device according to claim 1, wherein the silicon oxide layer having crystallinity is a quartz-crystal layer.

3. The acoustic wave device according to claim 1, wherein the support substrate is a silicon substrate.

4. The acoustic wave device according to claim 1, wherein the piezoelectric layer is a lithium tantalate layer; anda cut angle of lithium tantalate of the piezoelectric layer is about 20° Y or more and about 90° Y or less.

5. The acoustic wave device according to claim 4, wherein the cut angle of the lithium tantalate of the piezoelectric layer is about 20° Y or more and less than about 40° Y;the silicon oxide layer having crystallinity is a monocrystalline quartz-crystal layer; andwhen (φq, θq, ψq) represent azimuthal angles of the monocrystalline quartz-crystal layer, the angles φq, θq, and ψq are in any one of combinations in Tables 1 to 10:

6. The acoustic wave device according to claim 4, wherein the cut angle of the lithium tantalate of the piezoelectric layer is about 40° Y or more and about 90° Y or less;

7. The acoustic wave device according to claim 1, further comprising an intermediate layer between the support substrate and the silicon oxide layer having crystallinity.

8. The acoustic wave device according to claim 1, further comprising a protective film provided on the piezoelectric layer to cover the IDT electrode.

9. The acoustic wave device according to claim 8, wherein the protective film includes silicon oxide or silicon nitride.

10. The acoustic wave device according to claim 7, wherein the intermediate layer includes silicon oxide, silicon nitride, or silicon oxynitride.

11. The acoustic wave device according to claim 7, wherein the intermediate layer includes at least a first layer and a second layer.