elastic wave elements

Abstract

The present invention provides an electromechanical coupling coefficient K of a vibration mode at a lower phase velocity side than the main vibration in a rotated Y-cut crystal substrate with a rotation angle based on a specific Euler angle. 2 An elastic wave device is disclosed that has a smaller amplitude than a main vibration, has its primary and secondary temperature coefficients substantially set to zero, and furthermore, has a third-order temperature coefficient closer to zero. The device comprises a crystal substrate cut at a rotation angle defined by right-handed Euler angles (φ, θ, Ψ); and at least one comb-shaped excitation electrode that excites a plate wave from the crystal substrate. The crystal substrate is cut at a rotation angle within the range of φ = 0±2°, θ = 17.5° to 19.5°, and Ψ = 0±2°. The plate wave selects a vibration mode with a phase velocity within the range of 3500 to 4000 m / s. When the thickness of the crystal substrate is H and the wavelength of the plate wave is λ, the normalized plate thickness H / λ is set within the range of 1.5 < H / λ < 2.0.

Description

Technical Field

[0001] The present application relates to an elastic wave element used as a high-frequency oscillation source in computers, communication equipment, and the like. Background Art

[0002] Currently, AT-cut crystal resonators are often used as oscillation sources for various electronic devices, particularly those used as wireless reference signals. When used at high frequencies, these resonators are multiplied to a desired frequency using a phase-locked loop (PLL). Furthermore, when a high-frequency, low-noise signal is required, surface acoustic wave (SAW) devices utilizing surface acoustic waves are sometimes used directly as oscillation sources.

[0003] AT-cut crystal resonators are used as oscillation sources in many electronic devices because they maintain stable frequency characteristics over a wide temperature range. However, their use as high-frequency oscillation sources requires high-precision processing technologies, such as reducing thickness and improving flatness.

[0004] Surface acoustic waves, on the other hand, utilize longitudinal or transverse waves generated on the surface of a piezoelectric (quartz) substrate. Their frequency is proportional to their phase velocity and inversely proportional to their wavelength. A surface acoustic wave device utilizing these waves employs an excitation electrode formed on the surface of a quartz substrate cut at a predetermined angle, with multiple electrode fingers arranged in a comb shape. A predetermined oscillation frequency is achieved by adjusting the thickness of the excitation electrode and the spacing between the electrode fingers.

[0005] The piezoelectric device disclosed in Patent Document 1 utilizes elastic wave modes generated in a rotated Y-cut crystal substrate and has a structure having comb-shaped excitation electrodes on the surface of the crystal substrate and a frequency adjustment thin film on the back surface.

[0006] Patent Documents 2 and 3 disclose oscillators for oscillating elastic waves. In particular, the oscillator disclosed in Patent Document 3 exhibits a cubic curve having an inflection point at approximately 25°C in frequency-temperature characteristics.

[0007] Patent Document 4 discloses a high-frequency oscillator constructed using a rotated Y-cut crystal substrate defined by Euler angles.

[0008] Patent Document 5 discloses an elastic wave device in which the thickness of a crystal substrate cut at predetermined Euler angles and the thickness of an electrode film formed on the crystal substrate are determined.

[0009]

Prior art literature

[0010] [Patent Literature]

[0011] [Patent Document 1] Japanese Patent Application Laid-Open No. 57-68925

[0012] [Patent Document 2] Japanese Patent Application Laid-Open No. 2003-258596

[0013] [Patent Document 3] Japanese Patent No. 4465464

[0014] [Patent Document 4] Japanese Patent No. 4306668

[0015] [Patent Document 5] Japanese Patent No. 5563378 Summary of the Invention

[0016] [Problems to be solved by the invention]

[0017] While AT-cut crystal resonators have high oscillation frequency accuracy, they can also generate phase noise and jitter due to temporal signal shifts and fluctuations when multiplying to a desired frequency. Surface acoustic wave devices, on the other hand, can directly oscillate at high frequencies, so phase noise and jitter are less of a concern. However, their oscillation frequency accuracy can be improved compared to AT-cut crystal resonators.

[0018] Conventional oscillators utilizing plate waves, as described in Patent Documents 1 to 4, are cut at a predetermined rotation angle expressed as Euler angles. In the oscillators described in Patent Documents 2 and 3, the cutting angle of the crystal substrate is determined by the rotation angles of two axes, resulting in problems with ease of manufacture and variations in frequency-temperature characteristics. Furthermore, the oscillators disclosed in Patent Documents 2 to 4 have a structure in which comb-shaped excitation electrodes are arranged on the surface of the piezoelectric substrate, and no thin film or other device for frequency adjustment is provided on the back of the crystal substrate.

[0019] On the other hand, in the case of elastic wave elements using plate waves, we know that the vibration waves (plate waves) generated here are vibration modes formed by the coupling of transverse waves and longitudinal waves, and there are multiple vibration modes due to the degree of coupling between transverse waves and longitudinal waves. The vibration modes under this plate wave are different from the previous Rayleigh waves. In addition to the vibration modes that are expected to be used as elastic wave elements (hereinafter referred to as main vibrations), there are sometimes vibration modes with different phase velocities (hereinafter referred to as unwanted vibrations). The conversion efficiency of the electrical signal in this unwanted vibration to mechanical vibration (hereinafter referred to as the electromechanical coupling coefficient K) is the same as that of the plate wave. 2) is large, and when the signs of the main vibration and the reflection coefficient are equal, the quality factor of the unwanted vibration in the elastic wave element may be greater than 2, and the equivalent series resistance R1 may be lower than the equivalent series resistance R1 of the main vibration. Furthermore, the quality factor (Figure of Merit) is the Q value of the elastic wave element divided by the capacitance ratio γ, and represents the intensity of the vibration of the mechanical elastic wave element when viewed from the electrical terminals. This can cause abnormal oscillation during oscillation in the oscillation circuit. Furthermore, in commonly used Colpitts oscillation circuits, abnormal oscillation may occur if the unwanted vibration described above is at a lower frequency than the main vibration.

[0020] In the elastic wave element described in Patent Document 5, the primary and secondary temperature coefficients can be brought close to zero by specifying the Euler angles and the thickness of the crystal substrate. However, there is a limit to how close the third-order temperature coefficient can be to zero within the Euler angle range described above. In such an elastic wave element, the electromechanical coupling coefficient K is higher at lower frequencies than the main vibration. 2 Therefore, the Colpitts oscillation circuit has a problem of oscillating in a vibration mode at a lower frequency than the main vibration.

[0021] Therefore, the object of the present application is to provide an electromechanical coupling coefficient K of a vibration mode at a lower phase velocity side than the main vibration in a rotated Y-cut crystal substrate with a rotation angle based on a specific Euler angle. 2 An elastic wave element that is smaller than the main vibration and has a third-order temperature coefficient closer to zero, while setting the first- and second-order temperature coefficients of the main vibration to approximately zero.

[0022] Another object of the present application is to provide an elastic wave element that can directly oscillate at a high frequency, achieve an oscillation frequency accuracy superior to that of an AT-cut oscillator over a wide temperature range, and prevent abnormal oscillation caused by unnecessary vibration.

[0023]

Technical means to solve the problem

[0024] The elastic wave device disclosed in the present application comprises: a crystal substrate cut from a crystal having three-dimensional crystal orientations consisting of an X-axis, a Y-axis, and a Z-axis, with the Y-axis and the Z-axis rotated about the X-axis, the cut being cut at a rotation angle defined by right-handed Euler angles (φ, θ, Ψ); and at least one comb-shaped excitation electrode for exciting the crystal substrate to generate plate waves, wherein:

[0025] The crystal substrate is cut within the range of a rotation angle of φ = 0±2°, θ = 17.5° to 19.5°, and Ψ = 0±2°. The plate wave selects a vibration mode with a phase velocity in the range of 3500 to 4000 m / s. When the plate thickness of the crystal substrate is set to H and the wavelength of the plate wave is set to λ, the standardized plate thickness H / λ is in the range of 1.5<H / λ<2.0.

[0026] Here, the so-called standardized (also called normalized) thickness H / λ is defined for the purpose of regulating the H dimension independently of the design frequency (=λ) by dividing the crystal substrate's thickness H (unit: m) by the wavelength λ (unit: m). This is hereinafter referred to as the standardized thickness H / λ. The same applies to the standardized excitation electrode film thickness Hs / λ and the standardized back electrode film thickness Hb / λ, described later.

[0027] Effects of the Invention

[0028] The elastic wave element disclosed in this application is constructed from a quartz crystal substrate cut using right-handed Euler angles (φ = 0±2°, θ = 17.5° to 19.5°, Ψ = 0±2°) at a previously unspecified rotation angle θ. By selecting a plate wave with a phase velocity set within the range of 3500 to 4000 m / s and a standardized plate thickness H / λ within the range of 1.5 < H / λ < 2.0, the first-order temperature coefficient α, second-order temperature coefficient β, and third-order temperature coefficient γ, respectively, can be made close to zero when Taylor expansion is performed at 25°C. The Taylor expansion formula for the relationship between α, β, and γ and the frequency deviation Δf / f is shown below.

[0029] Δf / f=α(t-t0)+β(t-t0) 2 +γ(t-t0) 3

[0030] t0: reference temperature

[0031] This improves the accuracy of the oscillation frequency over a wider range than conventional elastic wave devices and AT-cut oscillators, and enables high-frequency oscillation with the fundamental wave. Furthermore, an elastic wave device with excellent frequency characteristics, low phase noise and jitter, is obtained. Furthermore, with this configuration, the electromechanical coupling coefficient K of all unwanted vibrations with a phase velocity V lower than that of the primary vibration can be reduced to 2 This is achieved by minimizing the frequency difference compared to the main vibration. This improves the accuracy of the oscillation frequency over a wider range than conventional elastic wave resonators and AT-cut oscillators, and suppresses abnormal oscillations caused by unwanted vibrations. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1This is a perspective view showing the appearance of an elastic wave device according to one embodiment of the present application.

[0033] Figure 2 For illustration purposes Figure 1 The right-hand Euler angle coordinate diagram of the cutting angle of the elastic wave element is shown.

[0034] Figure 3 To express Figure 1 Graph showing the dispersion of phase velocity V in vibration modes of multiple plate waves generated in the elastic wave element.

[0035] Figure 4 This is a graph showing the relationship between the rotation angle θ and the primary temperature coefficient α obtained by calculation for each normalized plate thickness H / λ.

[0036] Figure 5 This is a graph showing the relationship between the rotation angle θ and the quadratic temperature coefficient β obtained by calculation for each normalized plate thickness H / λ.

[0037] Figure 6 This is a graph showing the relationship between the rotation angle θ and the third-order temperature coefficient γ obtained by calculation for each normalized plate thickness H / λ.

[0038] Figure 7 This is a graph showing the relationship between the standardized plate thickness H / λ and the primary temperature coefficient α obtained by calculation for each standardized excitation electrode film thickness Hs / λ.

[0039] Figure 8 This is a graph showing the relationship between the standardized plate thickness H / λ and the quadratic temperature coefficient β obtained by calculation for each standardized excitation electrode film thickness Hs / λ.

[0040] Figure 9 This is a graph showing the relationship between the standardized plate thickness H / λ and the third-order temperature coefficient γ obtained by calculation for each standardized excitation electrode film thickness Hs / λ.

[0041] Figure 10 It is a graph showing the relationship between phase velocity V and admittance Y.

[0042] Figure 11 This is a table showing the phase velocity V in each vibration mode using calculated and experimental values.

[0043] Figure 12 This is a graph showing the relationship between the normalized plate thickness H / λ and the primary temperature coefficient α, obtained through calculation and experiment, for each rotation angle θ.

[0044] Figure 13 This is a graph showing the relationship between the normalized plate thickness H / λ and the quadratic temperature coefficient β for each rotation angle θ, obtained through calculation and experiment.

[0045] Figure 14This is a graph showing the relationship between the normalized plate thickness H / λ and the third-order temperature coefficient γ for each rotation angle θ, obtained through calculation and experiment.

[0046] Figure 15 This is a graph comparing the relationship between the standardized plate thickness H / λ and the primary temperature coefficient α using calculated values ​​and experimental values ​​for each standardized excitation electrode film thickness Hs / λ.

[0047] Figure 16 This is a graph comparing the relationship between the standardized plate thickness H / λ and the quadratic temperature coefficient β using calculated and experimental values ​​for each standardized excitation electrode film thickness Hs / λ.

[0048] Figure 17 This is a graph comparing the relationship between the standardized plate thickness H / λ and the third-order temperature coefficient γ using calculated values ​​and experimental values ​​for each standardized excitation electrode film thickness Hs / λ.

[0049] Figure 18 : is a graph showing actual measurement data as an example of the combination of α, β=0.

[0050] Figure 19 It is a perspective view showing the appearance of an elastic wave device in another embodiment. DETAILED DESCRIPTION

[0051] Hereinafter, an embodiment of the elastic wave element disclosed in this application will be described with reference to the accompanying drawings. Figure 1 As shown, the acoustic wave device 11 of this embodiment includes a thin plate-shaped crystal substrate 12 , an excitation electrode 13 formed on a front surface 12 a of the crystal substrate 12 , and a back surface electrode 14 formed on a back surface 12 b of the crystal substrate 12 .

[0052] The crystal substrate 12 is cut from a crystal having three-dimensional crystal orientations consisting of X, Y, and Z axes, with the Y and Z axes rotated about the X axis. The rotated Y axis is referred to as the Y′ axis, and the rotated Z axis is referred to as the Z′ axis.

[0053] The crystal substrate 12 is cut to a predetermined thickness using right-handed Euler angles (φ = 0 ± 2°, θ = 17.5° to 19.5°, Ψ = 0 ± 2°). Furthermore, due to the crystal symmetry of the crystal substrate, the differential values ​​of φ and Ψ for α, β, and γ at a predetermined rotation angle θ of φ or Ψ = 0 become zero. Therefore, if φ = 0 ± 2° and Ψ = 0 ± 2°, the change in the frequency-temperature characteristics is minimal. Regarding the permissible range of Euler angles, a range of ± 2.0° has little effect on the frequency-temperature characteristics, as also described in Patent Document 3.

[0054] The excitation electrodes 13 are composed of a pair of comb-shaped excitation electrodes 15 and 16. These comb-shaped excitation electrodes 15 and 16 include base electrode portions 15a and 16a extending parallel to each other along the longitudinal direction of the crystal substrate 12, and a plurality of electrode fingers 15b and 16b extending from one side of each base electrode portion 15a and 16a in opposing longitudinal directions. The excitation electrodes 13 are configured so that the electrode fingers 15b extending from one base electrode portion 15a and the electrode fingers 16b extending from the other base electrode portion 16a do not contact each other. The distance (pitch) between the electrode fingers 15b and 16b is set based on the wavelength λ of the plate wave to be excited. Furthermore, the pitch is approximately λ / 2 relative to the wavelength λ. By applying voltages with different polarities to the comb-shaped excitation electrodes 15 and 16, the excitation electrodes 13 generate an alternating electric field between adjacent electrode fingers, thereby exciting the plate wave within the crystal substrate 12.

[0055] The crystal substrate 12 is formed thin by rotating Y-cutting to a thickness H that is approximately the same as the wavelength λ of the plate wave to be excited. The thickness H is adjusted based on the relationship between the thickness of the excitation electrode 13 and the back electrode 14 so that the main vibration satisfies the specified frequency-temperature characteristics. At the same time, the electromechanical coupling coefficient K of the unwanted vibration at a lower phase velocity than the main vibration is set to 2 Smaller than the main vibration.

[0056] like Figure 1 As shown, the excitation electrode 13 is a metal film primarily composed of gold (Au) or aluminum (Al) formed approximately in the center of the surface 12a of the crystal substrate 12, formed to a predetermined thickness. Furthermore, reflectors (not shown) may be provided on either side of the excitation electrode 13 in its longitudinal direction. The provision of these reflectors allows the plate waves excited by the excitation electrode 13 to be confined between the reflectors, resulting in greater resonance.

[0057] The back electrode 14 is formed on the back side 12b of the crystal substrate 12, which is opposite to the excitation electrode 13. The back electrode 14 is formed by forming a metal material such as Au or a dielectric material into a film having a predetermined thickness on the back side 12b of the crystal substrate 12. In addition to Au, the metal material may be Al, Ta, Cu, etc., and the dielectric material may be SiO2, ZnO, Ta2O5, etc. The back electrode 14 formed of such a material can be used to fine-tune the oscillation frequency by changing its thickness, and the third-order temperature characteristics are maintained during the main vibration through the relationship with the plate thickness H and the thickness of the excitation electrode 13.

[0058] Figure 2A right-handed Euler angle coordinate system (φ, θ, Ψ) is shown. Here, φ represents the rotation angle about the Z axis, θ represents the rotation angle about the X' axis (the axis obtained by rotating the X axis by φ about the Z axis), and Ψ represents the rotation angle about the Z" axis (the axis obtained by rotating the Z axis by θ about the X' axis). Furthermore, a crystal substrate represented by Euler angles (φ = 0°, θ = 0°, Ψ = 0°) is a rotated Z-cut substrate having a principal surface perpendicular to the crystal's Z axis (optical axis). This coordinate system is used in various analyses of acoustic wave element 11. Figure 3 For the plate wave propagating in the crystal substrate 12 cut at the Euler angle (φ=0°, θ=19.5°, Ψ=0°), dispersion curves are shown under the conditions of the standardized excitation electrode film thickness (Hs / λ)=0 represented by the wavelength λ and the thickness Hs of the comb-shaped excitation electrode, and the standardized back electrode film thickness (Hb / λ)=0 represented by the wavelength λ and the thickness Hb of the back electrode.

[0059] Figure 3 The horizontal axis is set as the product of the wave number k and the plate thickness H, showing the dispersion curve of the plate wave formed by the coupling of longitudinal waves, fast shear waves, slow shear waves, and electromagnetic waves. The plate wave is a wave formed by the complex coupling of these waves. There are numerous various vibration modes, ranging from fast vibration modes with a phase velocity V of more than 10,000 m / s to slow vibration modes of about 3,000 m / s. In the elastic wave element disclosed in this application, the electromechanical coupling coefficient K is selected from the multiple vibration modes. 2 The vibration mode is large and satisfies the specified frequency-temperature characteristics. Figure 3 In the figure, the vibration modes used in this application are shown as solid lines, and the unnecessary vibration modes are shown as dotted lines. In this application, the vibration modes selected are those with a phase velocity V of 3500 to 4500 m / s at 5.0 to 7.5 kh, which are shown as solid lines. The selected vibration modes are counted from the side with the lower phase velocity V in the plate wave vibration, and the electromechanical coupling coefficient K is 2 The vibration mode that reaches the maximum value is also the first vibration mode whose quality factor reaches 2 or more, starting from the side with the lower phase velocity V in the plate wave vibration. The electromechanical coupling coefficient K of all vibration modes with a phase velocity V slower than the above vibration mode is 2 Since it is 0.02% or less, which is extremely small, the quality factor of the vibration mode appearing at a side where the phase velocity V is lower than that of the main vibration will not be greater than 2.

[0060] Figures 4 to 6These are graphs showing the frequency-temperature characteristics (1st-order temperature coefficient α, 2nd-order temperature coefficient β, 3rd-order temperature coefficient γ) of the vibration mode used in this application, and the relationship between the rotation angle θ and H / λ for the plate wave propagating in the crystal substrate specified by the Euler angle (0°, θ, 0°) and the standardized plate thickness (H / λ). The curves shown in these graphs are the values ​​calculated by setting θ to the range of 16° to 21° under the three conditions of H / λ being 1.63, 1.70, and 1.77. In addition, Hs / λ is set to 0.0027, and Au is used as the electrode material. As shown in FIG. Figure 4 As shown in the figure, when H / λ=1.7, α becomes approximately zero near θ=18.3, as shown in the figure. Figure 5 and Figure 6 As shown in the figure, β and γ are approximately zero in the entire range of θ. Therefore, it can be seen that the rotation angle θ only affects α and has almost no effect on β and γ.

[0061] Figures 7 to 9 In this paper, using a crystal substrate with Euler angles (0°, 18.5°, 0°), the relationship between the frequency-temperature characteristics (primary temperature coefficient α, secondary temperature coefficient β, and tertiary temperature coefficient γ) of the elastic wave element when Hs / λ was changed was calculated for each Hs / λ. Hs / λ was set using Au at five conditions: 0.0013, 0.0026, 0.0039, 0.0052, and 0.0065. Figure 7 As shown in FIG, α corresponding to Hs / λ under the above five conditions becomes approximately zero at around H / λ=1.65 to 1.75. Figure 8 As shown in , β is distributed around zero in the range of H / λ from 1.5 to 1.8. Figure 9 As shown in , γ is approximately zero when H / λ is in the range of 1.5 to 2.0. Figure 8 and Figure 9 In the figure, significant sudden increases and decreases are observed near the lower and upper limits of H / λ. This is due to coupling with adjacent vibration modes, causing H / λ to vary due to Hs / λ. Within this range, the frequency-temperature characteristics of the elastic wave element tend to vary significantly during manufacturing, making it less desirable for production. Therefore, based on the calculation results above, setting H / λ to a range of 1.5 to 2.0, corresponding to the five conditions for Hs / λ, can satisfy the specified frequency-temperature characteristics.

[0062] Figure 10 The present invention shows an example of the admittance Y characteristics of an elastic wave element constructed with 300 pairs (600 electrodes) of comb-shaped excitation electrodes, with Euler angles (0°, 19.5°, 0°), H / λ = 1.7, Hs / λ = 0.00266, and no back electrode serving as a weight for frequency adjustment. Figure 11The phase velocity V of the elastic wave element is compared with the calculated value for the vibration mode in which the waveform is observed. It is found that the phase velocity V is roughly consistent, and sufficient analytical accuracy is obtained. Figure 10 and Figure 11 As is clear, all the unwanted vibrations on the lower speed side compared to the main vibration are extremely small at the excitation level. In addition to the main vibration, the mode with a larger waveform is located near the phase velocity V = 5700m / s (vibration mode 3). In this vibration mode, the electromechanical coupling coefficient K 2 It is smaller than the main vibration, the equivalent series resistance R1 is higher than the main vibration, and the frequency is higher than the main vibration, so it has no effect on the oscillation in the oscillation circuit.

[0063] Figures 12 to 14 The relationship between α, β, and γ was compared between calculated and experimental values ​​when Au was used as the electrode material, Hs / λ = 0.00266, and an acoustic wave device was constructed without a back electrode. The relationship between α, β, and γ was varied under four conditions: θ = 18.5, 19.5, 20.0, and 20.5. Figure 12 As shown in , H / λ at 4θ is approximately zero when it is about 1.5. Figure 13 As shown in the figure, the curves for θ = 18.5, 19.5, 20.0, and 20.5 are roughly overlapped, and are approximately zero in the range of H / λ from 1.6 to 1.7. The experimental values ​​also show the same tendency. Figure 14 As shown in the figure, the curves of θ = 18.5, 19.5, 20.0, and 20.5 are roughly overlapped, and are approximately zero in the range of H / λ from 1.3 to 2.0. The experimental value is slightly larger than the calculated value, but is about 0.3×10 -10 = 0, which is extremely small. Corresponding to each θ, β, and γ have little change, so only α can be significantly corrected. Therefore, to meet the specified frequency-temperature characteristics, it is sufficient to set α = 0 by correcting the cutting angle at H / λ with β = 0. Therefore, if Figures 12 to 14 As shown, by setting θ = 18.5 and H / λ = 1.67, an acoustic wave element meeting the specified frequency-temperature characteristics is obtained. However, these conditions apply when using Au as the electrode material and setting Hs / λ = 0.00266. The optimal combination of α = β = 0 must be selected based on the electrode material and Hs / λ. Furthermore, Cr was used as the contact metal below the Au electrode in the experiment. However, the thickness of Cr is extremely thin, so it does not affect the verification of the frequency-temperature characteristics. Alternatively, nickel (Ni), titanium (Ti), or alloys thereof can be used as the contact metal.

[0064] Figures 15 to 17The calculated values ​​and experimental values ​​were compared for the relationship between α, β, and γ when Au was used as the electrode material and H / λ was changed at Hs / λ=0.00266 and 0.00532. Figures 15 to 17 , α and β vary according to Hs / λ, but γ varies minimally. Therefore, as previously mentioned, by correcting θ so that α = 0 at H / λ where β = 0 according to Hs / λ, α = β = 0 can be achieved while maintaining a small γ, thus satisfying the specified frequency-temperature characteristics.

[0065] As described above, the elastic wave device disclosed in this application has been confirmed to be capable of oscillating a high-frequency fundamental wave and to have frequency-temperature characteristics comparable to or better than those of an AT-cut crystal resonator. Furthermore, the electromechanical coupling coefficient K for all unwanted vibrations with a phase velocity V lower than the primary vibration used in this application is 2 is less than 0.02, which is extremely small. Figure 10 As shown, the equivalent series resistance R1 of the unwanted vibration is extremely high, and the quality factor does not exceed 2. This prevents oscillation errors caused by unwanted vibrations at lower frequencies than the main vibration, a problem with typical Lamb waves. Consequently, a frequency characteristic adjustment circuit (such as an LC filter) is unnecessary in the oscillation circuit, allowing the use of simple circuits such as standard Colpitts oscillation circuits. Figure 18 This example shows the best results for the frequency-temperature characteristics of an elastic wave element. The manufacturing conditions were Euler angles (0°, 18.33°, 0°), H / λ = 1.696, Hs / λ = 0.0027, and Hb / λ = 0.0002. The resulting elastic wave element achieved α = 0.03×10 -6 β=0.08×10 -8 ,γ=0.32×10 -10 The frequency-temperature characteristics of the Figure 18 The value of Hb / λ is specified as the actual manufacturing condition, but Figure 17 Previously, it was confirmed that frequency-temperature characteristics comparable to those obtained when Hb / λ=0 could be obtained by applying various conditions such as the Euler angles (φ, θ, Ψ) of the crystal substrate, phase velocity V, H / λ, and Hs / λ.

[0066] also, Figure 1 The reflector is omitted in the figure, but it is also possible to set the size of the crystal substrate 12 in such a way that the plate wave of wavelength λ generates standing waves at the two end faces in the long direction of the crystal substrate 12 to obtain a larger resonance. For example, it is possible to Figure 19 As shown in (a) of FIG. 1 , the length of the crystal substrate 12 in the X-axis direction is set to an integer N times the wavelength λ, or as shown in FIG. Figure 19As shown in (b), the number of electrode fingers on the opposite side is reduced and the length of the crystal substrate 12 in the X-axis direction is set to (N - 0.5 times) relative to the wavelength λ, thereby increasing resonance. The crystal substrate 12 is close to the Z-plate, and the propagation direction of the plate wave is parallel to the X-axis. Therefore, when generating standing waves with the two end faces of the crystal substrate 12 as the boundary, the end faces become the +X and -X planes of the crystal. These planes are the most vertical and stable side faces during etching and stamping, thus forming approximately vertical reflection planes, thereby generating stable standing waves.

[0067] The vibration mode of the plate wave disclosed in this application is the lowest frequency mode among the vibration modes with a quality factor exceeding 2. The Euler angles, H / λ, and Hs / λ are set in such a way that α, β, and γ are approximately zero. Therefore, a standard Colpitts oscillation circuit can be used for stable oscillation. In addition, as mentioned above, the electromechanical coupling coefficient K of all unwanted vibrations with a phase velocity V lower than the main vibration used in this application is 2 The value is extremely small, less than 0.02, achieving excellent frequency characteristics with low phase noise and jitter over a wide temperature range. Generally speaking, a quality factor of 2 or greater becomes inductive, enabling oscillation using a Colpitts oscillation circuit. However, a quality factor of less than 2 prevents the reactance component from becoming positive, meaning it becomes inductive, making oscillation using a Colpitts oscillation circuit impossible.

[0068] In the process of manufacturing the elastic wave element 11 disclosed in this application, the condition that the quality factor of the main vibration is greater than 2 and the quality factor of the unnecessary vibration is less than 2 is set. Under this condition, the thickness of the crystal substrate and the thickness of the back electrode are determined. As a result, the oscillation caused by the unnecessary vibration is effectively suppressed, thereby obtaining more stable oscillation characteristics.

[0069] In addition, the plate wave is a vibration mode formed by coupling of transverse wave and longitudinal wave. According to the coupling degree of the transverse wave and longitudinal wave, there is Figure 3 The vibration modes of such plate waves are different from those of conventional Rayleigh waves. In addition to the required main vibration, there are sometimes differences in phase velocity and electromechanical coupling coefficient K. 2 Larger vibration mode (unwanted vibration). When the acoustic wave element is constructed so that the reflection coefficients of the main vibration and the unwanted vibration have the same sign, the equivalent series resistance R1 of the unwanted vibration may be lower than the equivalent series resistance R1 of the main vibration mode. This may cause abnormal oscillation during oscillation in the oscillation circuit.

[0070] However, if Figure 11 As shown, the vibration mode (S3) of the plate wave selected in the elastic wave element disclosed in this application has the largest electromechanical coupling coefficient K among multiple vibration modes.2 The electromechanical coupling coefficient K of the vibration mode with the largest phase velocity V and lower than the selected vibration mode 2 (X) is in K 2 >K 2 Therefore, it is possible to suppress abnormal oscillation during oscillation by the oscillation circuit.

[0071] Explanation of symbols

[0072] α…1st order temperature coefficient

[0073] β…Second-order temperature coefficient

[0074] γ…3rd order temperature coefficient

[0075] λ…wavelength

[0076] V…Phase velocity

[0077] Y…admittance

[0078] H / λ…standardized plate thickness

[0079] Hs / λ…standardized excitation electrode film thickness

[0080] Hb / λ…standardized back electrode thickness

[0081] 11…Elastic wave element

[0082] 12…Crystal substrate

[0083] 13…Excitation electrode

[0084] 14…Back electrode

[0085] 15, 16…comb-shaped excitation electrode

[0086] 15a, 16a...base electrode portion

[0087] 15b, 16b…electrode fingers.

Claims

1. An elastic wave device comprising: a crystal substrate cut from a quartz crystal having three-dimensional crystal orientations defined by an X-axis, a Y-axis, and a Z-axis, with the Y-axis and the Z-axis rotated about the X-axis, the rotation angle being defined by right-handed Euler angles (φ, θ, Ψ); and at least one comb-shaped excitation electrode for exciting the crystal substrate to generate plate waves. This elastic wave element is characterized in that The rotation angle specified by the right-hand Euler angles (φ, θ, Ψ) is within the range of φ = 0 ± 2°, θ = 17.5° to 19.5°, and Ψ = 0 ± 2°. The plate wave selects a vibration mode with a phase velocity in the range of 3500 to 4000 m / s. When the plate thickness of the crystal substrate is denoted as H and the wavelength of the plate wave is denoted as λ, the normalized plate thickness H / λ is in the range of 1.5<H / λ<2.

0.

2. The elastic wave element according to claim 1, wherein The at least one comb-shaped excitation electrode for exciting the crystal substrate is provided on the front surface side of the crystal substrate, and a back surface electrode for frequency adjustment is provided on the back surface side of the crystal substrate.

3. The elastic wave element according to claim 2, wherein: When the film thickness of the at least one comb-shaped excitation electrode is Hs and the wavelength of the plate wave is λ, the film thickness of the at least one comb-shaped excitation electrode is normalized to a range of 0.0013<Hs / λ<0.0065.

4. The elastic wave element according to claim 1, wherein The selected vibration mode of the plate wave is the lowest frequency among the vibration modes of the plurality of plate waves having a quality factor greater than 2.

5. The elastic wave element according to claim 1, wherein The selected vibration mode has the largest electromechanical coupling coefficient among multiple vibration modes with a phase velocity in the range of 3500 to 4000 m / s, and has a larger electromechanical coupling coefficient than the vibration mode of the plate wave with a phase velocity lower than that of the selected vibration mode.

6. The elastic wave element according to claim 2, wherein The at least one comb-shaped excitation electrode is a metal film mainly composed of Au or Al.

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