CN1801612A - Lamb-wave high-frequency resonator - Google Patents

Abstract

A Lamb wave type high frequency resonator. The present invention provides a Lamb wave type high-frequency resonator capable of increasing the frequency, having good frequency-temperature characteristics, and capable of reducing manufacturing costs. A Lamb wave type high frequency resonator (1) has comb-tooth-shaped IDT electrodes (20) for exciting Lamb waves on one main surface of a quartz substrate (10), and the IDT electrodes (20) are formed in accordance with the European standard. When drawing the angle representation mode, the cutting angle of the quartz substrate (10) and the propagation direction of the Lamb wave are (0, θ, 0), and the relationship between the thickness t of the quartz substrate (10) and the wavelength λ is set In the range represented by 0<t/λ≤3, 6 regions are set in this range, and in the first region, the angle θ is set within the range of 132.8 degrees ≤ θ ≤ 178 degrees, t /λ is set within the range of 1.1≦t/λ≦3.

Description

Lamb wave type high frequency resonator

technical field

The present invention relates to a Lamb wave (lamb wave) type high-frequency resonator, in particular to a Lamb wave type with a quartz substrate and a propagation direction represented by Euler angles (0, θ, 0) and composed of IDT electrodes high frequency resonator.

Background technique

Conventionally, high-frequency resonators have been represented by surface acoustic wave devices using Rayleigh waves and SH waves, and Lamb wave resonators using Lamb waves. As their substrates, ST-cut quartz for Rayleigh waves and STW-cut quartz for SH waves are used, and AT-cut quartz is used for high-frequency resonators using Lamb waves.

For example, a Rayleigh-wave type surface acoustic wave element in which IDT (Interdigital Transducer) electrodes are formed in the Z'-axis direction on the surface of a quartz substrate called ST-cut quartz is known (for example, refer to Non-Patent Document 1 ).

In addition, as an SH-type surface acoustic wave element, a surface acoustic wave element that propagates a transverse wave in which the propagation direction of the surface acoustic wave is shifted by 90 degrees from ST-cut quartz, that is, ST-cut quartz, is known (for example, refer to Patent Document 1).

In addition, Lamb wave type high-frequency resonators are also known (see, for example, Non-Patent Document 2 and Patent Document 2): IDT electrodes are formed on the surface of an AT-cut quartz substrate, and bulk waves propagating inside the quartz substrate (Bulk wave) In a resonator using a Lamb wave that is repeatedly reflected and propagated from the upper and lower surfaces of a quartz substrate, the thickness H of the quartz substrate and the wavelength λ of the Lamb wave are represented by 0<2H/λ≤10 .

[Non-Patent Document 1] TECHNIALCALREPORT OF IEICE. US99-20 (199-06) pp. 37-42, "Analysis of the cycle number-temperature characteristics of surface elastic waves using the finite element method", Shigeo Kamito.

[Non-Patent Document 2] The 33rd EM Symposium 2004, pages 93-96, "Substrates for Lamb wave-type surface acoustic wave elements" Nakagawa Kyohiko, Morose Masayuki, and Kakio Shoji.

[Patent Document 1] Japanese Patent Laid-Open No. 10-233645 (pages 3 to 6, FIG. 1 ).

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

According to this Non-Patent Document 1, in the temperature range of -40°C to 90°C, the frequency-temperature variation is about 140ppm, and although a surface acoustic wave device exhibits good frequency-temperature characteristics, it is difficult for a resonator requiring high precision. Can't say enough. In addition, the theoretical value of the phase velocity is about 3100 m/s, and it is difficult to cope with the high frequency band.

Furthermore, according to Patent Document 1, the surface acoustic wave device is an end surface reflection type surface wave device using SH waves, and the frequency-temperature variation is 254 ppm in the temperature range of -40°C to 90°C. ST cut quartz is poor. In addition, using tantalum or tungsten as an electrode material with a density higher than that of aluminum improves the frequency-temperature characteristics, but there are also problems in that the resistance loss increases and the phase velocity decreases.

In addition, according to Patent Document 2, by using an AT-cut quartz substrate whose thickness is 5 wavelengths or less with respect to the wavelength of the elastic wave, the frequency-temperature characteristic is good and suitable for high frequency. However, according to Non-Patent Document 2, the secondary The temperature coefficient performance is the same as that of the above-mentioned ST-cut quartz, and the frequency-temperature characteristic in the temperature range of -40°C to 90°C is about 320ppm. It is not superior to ST-cut quartz, and it cannot be said that it has met the requirements.

Contents of the invention

It is an object of the present invention to provide a Lamb wave type high-frequency resonator capable of high frequency, good frequency-temperature characteristics, and reduced manufacturing cost, with the aim of solving the aforementioned problems.

The Lamb wave type high-frequency resonator of the present invention has comb-tooth-shaped IDT electrodes for exciting Lamb waves on one main surface of the quartz substrate, and is characterized in that the IDT electrodes are formed in terms of Euler angles In this way, the cutting angle of the quartz substrate and the propagation direction of the Lamb wave are (0, θ, 0).

According to the present invention, high frequency can be achieved by using Lamb waves that are repeatedly reflected and propagated on the upper and lower surfaces of the quartz substrate, and the propagation directions of the quartz substrate and Lamb waves are formed with Euler angles (0, θ, 0), Therefore, the cutting angle is simple, the quartz substrate can be easily manufactured, and the manufacturing cost can be reduced.

Also, in the present invention, it is preferable that when the thickness of the quartz substrate is set as t and the wavelength of the Lamb wave is set as λ, the relationship between the thickness t and the wavelength λ is set such that 0<t In the range indicated by /λ≤3.

where t/λ is referred to as the normalized substrate thickness.

The details will be described in the following embodiments. A quartz substrate with Euler angles (0, θ, 0) has a plurality of vibration modes (modes). When the thickness of the quartz substrate increases, the frequency bands of these various modes become close, so that mode combination is easy to occur, but here, the normalized substrate thickness t/λ is set to an appropriate value less than or equal to 3, so that it is difficult to generate modes In combination, a single mode can be selected, and the frequency characteristics are stable and can be used for high frequencies.

Also, it is preferable that the angle θ is within the range represented by 132.8 degrees ≤ θ ≤ 178 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 1.1 ≤ t/λ ≤ 3 within the range indicated.

Also, it is preferable that the angle θ is within the range represented by 4 degrees ≤ θ ≤ 57.5 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 2.08 ≤ t/ In the range indicated by λ≤2.82.

Also, it is preferable that the angle θ is within the range represented by 6 degrees ≤ θ ≤ 33 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 0.975 ≤ t/ In the range indicated by λ≤2.025.

Also, it is preferable that the angle θ is within the range represented by 35 degrees ≤ θ ≤ 47.2 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 0.176 ≤ t/ In the range indicated by λ≤1.925.

Also, it is preferable that the angle θ is within the range represented by 2.7 degrees ≤ θ ≤ 16 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 2.878 ≤ t/ In the range indicated by λ≤3.

Also, it is preferable that the angle θ is within the range represented by 116 degrees ≤ θ ≤ 122.1 degrees, and the relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set to be 0.375 ≤ t/ In the range indicated by λ≤1.06.

The specific situation will be described in the following embodiments. The blue wave is restricted according to the cut-out angle of the quartz substrate and the propagation direction of the elastic wave, that is, the angle θ among the Euler angles (0, θ, 0), the thickness t of the substrate, and the wavelength λ. Frequency-temperature characteristics, frequency band, and excitation stability of M-wave high-frequency resonators. By making them satisfy the aforementioned relational expressions, it is possible to realize the frequency-temperature characteristics of the STW-cut quartz and the ST-cut quartz superior to the aforementioned prior art, and to be able to correspond to a high-frequency band, and to improve the electromechanical coupling indicating the excitation efficiency of the quartz substrate. coefficient (K ² ), it is possible to provide a Lamb wave type high-frequency resonator that is easy to excite and has stable frequency characteristics.

Description of drawings

FIG. 1 is a perspective view showing a schematic configuration of a Lamb wave type high-frequency resonator according to an embodiment of the present invention.

2 is a cross-sectional view showing the Lamb wave type high-frequency resonator according to the embodiment of the present invention along the A-A cross-section in FIG. 1 .

FIG. 3 is an explanatory view showing the cutting orientation of the quartz substrate according to the embodiment of the present invention.

4 is a graph showing part of the relationship between the normalized substrate thickness t/λ and the phase velocity according to the embodiment of the present invention.

5 is a graph showing the relationship between the phase velocity, the angle θ, and the normalized substrate thickness t/λ according to the embodiment of the present invention.

6 is a graph showing the relationship between temperature and frequency temperature deviation according to the embodiment of the present invention.

FIG. 7 is an explanatory diagram showing a region that can be realized by the Lamb wave type high-frequency resonator according to the embodiment of the present invention.

8 is a graph showing the relationship between the Euler angles and the amount of frequency-temperature variation in the first region according to the embodiment of the present invention.

9 is a graph showing the relationship between t/λ in the first region and the amount of frequency-temperature variation according to the embodiment of the present invention.

FIG. 10 is a graph showing the relationship between the Euler angles of the first region and the electromechanical coupling coefficient K ² according to the embodiment of the present invention.

11 is a graph showing the relationship between t/λ in the first region and the electromechanical coupling coefficient K ² according to the embodiment of the present invention.

12 is a graph showing the relationship between the Euler angles and the amount of frequency-temperature variation in the second region according to the embodiment of the present invention.

13 is a graph showing the relationship between t/λ and frequency-temperature variation in the second region according to the embodiment of the present invention.

14 is a graph showing the relationship between the Euler angles and the frequency-temperature variation in the third region according to the embodiment of the present invention.

15 is a graph showing the relationship between t/λ and frequency-temperature variation in the third region according to the embodiment of the present invention.

16 is a graph showing the relationship between the Euler angles and the frequency-temperature variation in the fourth region according to the embodiment of the present invention.

17 is a graph showing the relationship between t/λ and frequency-temperature variation in the fourth region according to the embodiment of the present invention.

18 is a graph showing the relationship between Euler angles and phase velocity in the fourth region according to the embodiment of the present invention.

19 is a graph showing the relationship between t/λ and phase velocity in the fourth region according to the embodiment of the present invention.

20 is a graph showing the relationship between Euler angles, phase velocity, and frequency-temperature variation in the fourth region according to the embodiment of the present invention.

21 is a graph showing the relationship between the Euler angles, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation in the fourth region according to the embodiment of the present invention.

22 is a graph showing the relationship between t/λ, phase velocity, and frequency-temperature variation in the fourth region according to the embodiment of the present invention.

23 is a graph showing the relationship between t/λ, electromechanical coupling coefficient K ² , and frequency-temperature variation in the fourth region according to the embodiment of the present invention.

24 is a graph showing the relationship between the Euler angles and the amount of frequency-temperature variation in the fifth region according to the embodiment of the present invention.

25 is a graph showing the relationship between t/λ and frequency-temperature variation in the fifth region according to the embodiment of the present invention.

FIG. 26 is a graph showing the relationship between the Euler angles and the amount of frequency-temperature variation in the sixth region according to the embodiment of the present invention.

27 is a graph showing the relationship between t/λ and frequency-temperature variation in the sixth region according to the embodiment of the present invention.

28 is a graph showing the relationship between Euler angles, t/λ, and phase velocity in the sixth region according to the embodiment of the present invention.

29 is a graph showing the relationship between t/λ, Euler angles, and phase velocity in the sixth region according to the embodiment of the present invention.

30 is a graph showing the relationship between Euler angles, phase velocity, and frequency-temperature variation in the sixth region according to the embodiment of the present invention.

31 is a graph showing the relationship between Euler angles, electromechanical coupling coefficient K ² , and frequency-temperature variation in the sixth region according to the embodiment of the present invention.

32 is a graph showing the relationship between t/λ, phase velocity, and frequency-temperature variation in the sixth region according to the embodiment of the present invention.

33 is a graph showing the relationship between t/λ, electromechanical coupling coefficient K ² , and frequency-temperature variation in the sixth region according to the embodiment of the present invention.

Symbol Description

1 Lamb wave type high-frequency resonator; 10 quartz substrate; 20 IDT electrode; 21 input IDT electrode; 22 GND IDT electrode; 25, 26 reflector.

Detailed ways

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

1 to 3 show a Lamb wave type high-frequency resonator according to Embodiment 1 of the present invention. Figure 4 and Figure 5 show the relationship between the phase velocity and the normalized substrate thickness t/λ and Euler angle (0, θ, 0), and the relationship between the frequency temperature deviation and the temperature is shown in Figure 6, FIG. 7 is an explanatory view showing a region where the Lamb wave type high-frequency resonator of the present invention can realize. In addition, FIGS. 8 to 11 are graphs showing the characteristics of the first region, FIGS. 12 and 13 are graphs showing the characteristics of the second region, and FIGS. 14 and 15 are graphs showing the characteristics of the third region. 16 to 23 are graphs showing the characteristics of the fourth region, FIGS. 24 and 25 are graphs showing the characteristics of the fifth region, and FIGS. 26 to 33 are graphs showing the characteristics of the sixth region.

(Embodiment 1)

1 and 2 show a Lamb wave type high-frequency resonator according to an embodiment of the present invention. FIG. 1 is a perspective view showing a schematic structure, and FIG. 2 is a cross-sectional view showing a cross section along line A-A of FIG. 1 . In FIGS. 1 and 2 , the Lamb wave type high-frequency resonator 1 is composed of a quartz substrate 10 and a comb-shaped IDT electrode 20 formed on one main surface of the quartz substrate 10 .

The cut-off angle of the surface of the quartz substrate 10 and the propagation direction of the Lamb wave are set within a range represented by Euler angles (0, θ, 0). Regarding the thickness t of the quartz substrate 10 , the normalized substrate thickness t/λ is set within a range represented by 0<t/λ≦3 when the wavelength of the propagated Lamb wave is λ.

The comb-shaped IDT electrode 20 is made of an aluminum electrode, and is formed sequentially on the surface of the quartz substrate 10 in the X-axis direction of the quartz substrate to form a reflector 25, an input IDT electrode 21, a GND (ground) IDT electrode 22, and a reflector. 26.

The input IDT electrode 21 and the GND IDT electrode 22 are formed so that electrode fingers are inserted into each other, for example, the width of the electrode fingers is λ/4, and the width between the electrode fingers is λ/4. Therefore, when the input IDT electrode 21 is described as an example, the pitch between the electrode finger pieces 21A and the electrode finger pieces 21B is set by λ. The electrode fingers of the reflectors 25, 26 are also set according to the same relationship.

The quartz substrate 10 is excited by a drive signal input to the input IDT electrode 21 at a predetermined frequency, and the excited elastic wave propagates in the X-axis direction of the quartz substrate 10 while reflecting in-plane on the front and rear surfaces of the quartz substrate 10 . The elastic waves propagating in this way are called Lamb waves. And the Lamb waves are reflected by the reflectors 25 , 26 . Therefore, the distance between the electrode finger (the left end in the figure) and the reflector 25 at the outer end of the input IDT electrode 21 and the distance between the electrode finger (the right end in the figure) at the outer end of the input IDT electrode 21 and the reflector 26 are set It is set to (1/2)nλ (n is an integer), and is set so that the phase of the reflected wave and the drive signal coincide with each other at a predetermined frequency.

FIG. 3 shows the cutting orientation of the quartz substrate 10 . The quartz substrate 10 is a thin plate made up of a plane with an X axis called an electrical axis, a Y axis called a mechanical axis, and a Z axis called an optical axis. The cutting orientation of the quartz substrate 10 in this embodiment is The Z-axis in the thickness direction is rotated exactly by the angle θ to reach the rotation Y-cut quartz of Z', and the cutting is performed so that the length direction in the figure is the X-axis, the width direction is Y', and the thickness direction is Z'.

Next, the theoretical values of the main parameters related to the present embodiment will be described using graphs showing the relationship with the respective relevant elements.

FIG. 4 is a graph showing part of the relationship between the normalized substrate thickness t/λ and the phase velocity. In FIG. 4 , the horizontal axis represents t/λ, and the vertical axis represents phase velocity (m/s). Here, a Lamb wave type high frequency resonator with Euler angles (0, 140, 0) is exemplified. According to Figure 4, it shows that there are multiple modes in the Lamb wave type high-frequency resonator, and as the normalized substrate thickness t/λ increases, the phase velocity in each mode is collected at a phase velocity of 3000 (m/s ) to 6000 (m/s), especially dense in the range of 5000 (m/s) to 6000 (m/s).

When the modes are dense like this, mode coupling tends to occur, and it is considered that a desired mode cannot be obtained or the phase velocity tends to fluctuate. Therefore, by setting t/λ≦3, it is possible to avoid the range where mode binding is likely to occur.

Furthermore, this graph shows a tendency for the phase velocity to increase as t/λ decreases, and when t/λ≦3, there are many modes with a phase velocity of 6000 (m/s) or more. Since the phase velocity is represented by the product of the frequency and the wavelength, it is shown that this Lamb wave type high-frequency resonator can cope with high frequencies.

Next, the relationship between the phase velocity and the Euler angles (0, θ, 0) will be described.

FIG. 5 is a graph showing the relationship among phase velocity, angle θ, and normalized substrate thickness t/λ. In FIG. 5 , the horizontal axis represents the angle θ, and the vertical axis represents the phase velocity. Here, the normalized substrate thickness t/λ is set to seven kinds of t/λ between 0.5 and 4, and the theoretical value of the phase velocity of each t/λ is shown.

According to Fig. 5, the following trend is shown, that is, when the value of t/λ is less than 0.8, the phase velocity becomes higher as the angle θ becomes larger, and when t/λ is larger than 1.2, as the angle θ becomes larger, the phase The speed becomes lower.

However, regardless of the normalized substrate thickness, when the Euler angles (0, θ, 0) are within the range of the angle θ represented by the curve, it is possible to obtain a phase velocity of 5000 m/s, which is regarded as a limit in the STW type. High phase velocity. In addition, when t/λ is less than or equal to 0.8, a phase velocity of 7000m/s or more, which is regarded as a high-frequency region, can be obtained.

Next, the frequency-temperature characteristics of the Lamb wave type high-frequency resonator of the present embodiment will be described with reference to the drawings.

FIG. 6 is a graph showing the relationship between temperature and resonance frequency. In FIG. 6 , the horizontal axis represents temperature (unit: °C), and the vertical axis represents frequency temperature deviation (unit: ppm) when the frequency at a temperature of 25 °C is taken as the center frequency. Compared with the lamb wave type high-frequency resonator of θ=140 degrees in the present embodiment, the ST-cut quartz (hereinafter abbreviated as ST type) and STW-cut quartz (hereinafter abbreviated as STW type) of the aforementioned prior art are compared. The frequency temperature deviation of Rayleigh wave, SH-type surface acoustic wave elements, and Lamb wave resonators composed of AT-cut quartz (abbreviated as AT-type hereinafter) in the range of -40°C to 90°C.

According to FIG. 6, in the temperature range of -40°C to 90°C, the Lamb wave type high-frequency resonator according to this embodiment (in the figure, Lamb wave (θ=140°)) has a frequency temperature variation of 30ppm, is minimal and shows good frequency-temperature characteristics. In the ST type, STW type, and Lamb wave type high-frequency resonators 1 of this embodiment, the position of the highest frequency (vertex temperature) on the quadratic curve representing the change in the frequency-temperature deviation is located at the standard temperature in the actual use environment It is around 20°C, and in the AT type (Lamb wave (AT cut) in the figure), it is around -25°C. In addition to the large frequency temperature fluctuation, it is also expected that it will be difficult to use.

The frequency temperature deviation and phase of the Lamb wave type high-frequency resonator 1 of this embodiment are controlled by the cut-out angle of the quartz substrate and the angle θ among the Euler angles (0, θ, 0), the substrate thickness t, and the wavelength λ. Speed (frequency band). Here, the theoretically calculated region in which the phase velocity and frequency temperature characteristics that should be realized in the present invention can be obtained is shown.

FIG. 7 is an explanatory view showing a region having characteristics achievable by the Lamb wave type high-frequency resonator of the present invention. The horizontal axis represents the Euler angles, and the vertical axis represents t/λ. A plurality of regions (1st to 6th regions) capable of realizing the following characteristics as the characteristics to be realized in the present invention can be obtained, that is, the phase velocity is 5000m/s , the frequency temperature fluctuation in the range of -40°C to +90°C is smaller than that of STW cut quartz and less than 250ppm, and the electromechanical coupling coefficient (K ² ) indicating the excitation efficiency of the quartz substrate is greater than or equal to 0.02%.

Here, there are different regions in a range where Euler angles or t/λ values are close. For example, there are a second area, a third area, a fourth area, and a fifth area shown in FIG. 7 . It is expected that there is a region where vibration mode bonding is likely to occur at the boundary of these regions, and the second to fifth regions exist independently.

Hereinafter, each of the aforementioned regions will be described with reference to the drawings.

FIG. 8 is a graph showing the relationship between the frequency-temperature variation of the Lamb wave type high-frequency resonator 1 in the first region and the angle θ among the Euler angles (0, θ, 0). In this graph, the present embodiment is exemplified in the case of t/λ=2.2. In FIG. 8 , the horizontal axis represents the angle θ, and the vertical axis represents the amount of frequency temperature variation. In this graph, the frequency temperature fluctuations of the ST type and the STW type are shown for comparison. The frequency temperature fluctuation amount of the ST type is about 140ppm, and the STW type is about 254ppm, which may not necessarily be said to be a satisfactory level.

In the first region, the frequency temperature fluctuation varies with the angle θ. To make it smaller than the STW type, it only needs to be set within the range of 132.8 ≤ θ ≤ 178 degrees. In order to make it smaller than the ST type, just set Set it within the range of 133.5 degrees ≤ θ ≤ 177.5 degrees.

Next, the relationship between the frequency temperature variation in the range of -40°C to 90°C and the thickness of the quartz substrate will be described. As mentioned above, the thickness of the quartz substrate is restricted by the relationship with the frequency of the Lamb wave, so it is expressed as the normalized substrate thickness t/λ.

FIG. 9 is a graph showing the relationship between the amount of frequency temperature variation and the normalized substrate thickness t/λ (hereinafter sometimes abbreviated as t/λ) of the Lamb wave type high-frequency resonator in the first region. In this graph, the present embodiment is exemplified in the case where the angle θ=140 degrees. In FIG. 9 , the horizontal axis represents t/λ, and the vertical axis represents the amount of frequency temperature variation.

The frequency temperature fluctuation varies with t/λ. In this first region, in order to make it smaller than the STW type, it only needs to be set within the range of 1.1≤t/λ≤3. In order to make it smaller than the ST type, as long as It may be set within the range of 1.1≤t/λ≤2.9.

Next, the relationship between the electromechanical coupling coefficient K ² and the angles θ and t/λ of the Lamb wave type high-frequency resonator according to the present embodiment will be described.

FIG. 10 is a graph showing the relationship between the electromechanical coupling coefficient K ² and the angle θ among the Euler angles (0, θ, 0). In FIG. 10 , the horizontal axis represents Euler angles (0, θ, 0), and the vertical axis represents the electromechanical coupling coefficient K ² (unit: %). Here, when t/λ is in the range of 1 to 3, seven types of t/λ values are set, and theoretical values of the electromechanical coupling coefficient K ² at various thicknesses are shown.

In addition, assuming that the phase velocity when the surface of the quartz substrate is electrically opened is Vf, and the phase velocity when the surface of the quartz substrate is electrically short-circuited is Vs, the electromechanical coupling coefficient K ² is expressed as K ² =2(Vf-Vs )/Vf, the larger the value of K ² , the easier it is to excite, which is well known.

FIG. 10 firstly shows that the thinner the thickness t of the quartz substrate, the larger the electromechanical coupling coefficient K ² . Furthermore, it also shows a tendency that the electromechanical coupling coefficient K ² becomes larger as the angle θ becomes smaller. Here, referring to the above-mentioned relationship between the angle θ and the amount of frequency temperature variation (refer to FIG. 8), in the range of the angle θ ranging from 130 degrees to 180 degrees, in each set value of t/λ, there is It is possible to obtain a point of an angle θ that enables the electromechanical coupling coefficient K ² to obtain a value equal to or greater than 0.02%. When the electromechanical coupling coefficient K ² is equal to or greater than 0.02%, the Lamb wave type high-frequency resonator of this embodiment can obtain sufficient excitation characteristics.

Next, the relationship between the electromechanical coupling coefficient K ² and the normalized substrate thickness t/λ of the Lamb wave type high-frequency resonator of this embodiment will be described.

FIG. 11 is a graph showing the relationship between the electromechanical coupling coefficient K ² and t/λ. In FIG. 11 , the horizontal axis represents t/λ, and the vertical axis represents the electromechanical coupling coefficient K ² (unit: %). Here, six angles divided into 10-degree intervals in the range of 130° to 180° are set, and theoretical values of the electromechanical coupling coefficient K ² for each angle θ are shown.

According to FIG. 11 , it first shows that the smaller the angle θ is, the larger the electromechanical coupling coefficient K ² is. Furthermore, it also shows a tendency that the electromechanical coupling coefficient K ² becomes larger as t/λ becomes smaller. Here, referring to the aforementioned relationship between t/λ and frequency-temperature variation (refer to FIG. 9 ), setting the frequency-temperature variation for the range of t/λ is generally better than that of the STW type, that is, 1.1≤t/λ≤3. The range shows that within this range, and within the range of the angle θ of 130 degrees to 180 degrees, there are points where the electromechanical coupling coefficient K ² is equal to or greater than 0.02.

Next, the second area will be described.

12 and 13 are graphs showing the relationship between the frequency temperature variation and the angle θ in Euler angles (0, θ, 0) and the relationship between the frequency temperature variation and t/λ in the second region. Here, the frequency temperature characteristic is better than that of STW cut quartz (the frequency temperature fluctuation is small). The range of θ in the Euler angle (0, θ, 0) is 4 degrees ≤ θ ≤ 57.5 degrees, and the range of t/λ is 2.08 ≤t/λ≤2.82.

Next, the third area will be described.

14 and 15 are graphs showing the relationship between the frequency temperature variation and the angle θ in Euler angles (0, θ, 0) and the relationship between the frequency temperature variation and t/λ in the third region. In the third region, the frequency temperature characteristic is superior to that of STW-cut quartz in the range of θ is 6 degrees ≤ θ ≤ 33 degrees, and the range of t/λ is 0.975 ≤ t/λ ≤ 2.025.

Here, although illustrations and detailed descriptions are omitted, in the second and third regions, there are also phase speeds equal to or greater than 5000 m/s and electromechanical coupling coefficients within the above-mentioned Euler angle and t/λ ranges. Points where K ² is greater than or equal to 0.02.

Next, the fourth region will be described with reference to FIGS. 16 to 23 .

16 and 17 are graphs showing the relationship between the frequency temperature variation and the angle θ in Euler angles (0, θ, 0) and the relationship between the frequency temperature variation and t/λ in the fourth region. In the 4th region, the range of the angle θ at which the frequency temperature characteristic is better than STW-cut quartz is 35 degrees ≤ θ ≤ 47.2 degrees, and the range of t/λ is 0.176 ≤ t/λ ≤ 1.925.

In addition, the respective relationships between the angle θ and t/λ in the fourth region, the phase velocity, the amount of frequency temperature variation, and the electromechanical coupling coefficient K ² will be described in detail.

Fig. 18 shows the relationship between the angle θ and the phase velocity among the Euler angles (0, θ, 0). Here, t/λ is set to six levels within the range of 0.2 to 2.0, and the phase velocity at each t/λ is shown in a graph. According to FIG. 18 , in all cases except t/λ=2.0, at each t/λ, a phase velocity of 5000 m/s or more can be obtained within the angle θ range of 30° to 50°.

Also, FIG. 19 shows the relationship between t/λ and the phase velocity. The angle θ among the Euler angles (0, θ, 0) is set to 5 levels within the range of 30 degrees to 50 degrees, and the phase velocity at each angle θ is shown by a graph. According to FIG. 19 , the deviation of the phase velocity at each angle θ is small, and a phase velocity of 5000 m/s or more can be obtained in most ranges where t/λ is 0.2 to 2.

Next, the relationship between Euler angle, t/λ, phase velocity, frequency temperature variation, and electromechanical coupling coefficient ^K2 will be described.

FIG. 20 shows the relationship between the angle θ among the Euler angles (0, θ, 0), the phase velocity, and the amount of frequency temperature fluctuation. Here, t/λ is set to 1.7. According to FIG. 20 , the range in which the frequency temperature variation is smaller than θ of STW-cut quartz is 35 degrees ≤ θ ≤ 47.2 degrees (see also FIG. 16 ), and a phase velocity of 5000 m/s or more can be obtained within this range.

FIG. 21 shows the relationship between the Euler angles, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation. According to Fig. 21, the frequency temperature variation is less than the range of the angle θ among the Euler angles (0, θ, 0) of the STW-cut quartz is 35 degrees ≤ θ ≤ 47.2 degrees (see also Fig. 16), within this range, the electromechanical The coupling coefficient K2 ^greatly exceeds the benchmark value of 0.02. When the range of the angle θ is 32.5 degrees ≤ θ ≤ 47.2 degrees, the electromechanical coupling coefficient K ² is greater than or equal to 0.03, and when the range of the angle θ is 34.2 degrees ≤ θ ≤ 47.2 degrees, the electromechanical coupling coefficient K ² is greater than or equal to 0.04. When the range of θ is 36 degrees ≤ θ ≤ 47.2 degrees, the electromechanical coupling coefficient K ² is greater than or equal to 0.05.

Fig. 22 shows the relationship between t/λ, phase velocity, frequency and temperature variation. According to Fig. 22, the range in which the frequency temperature variation is smaller than t/λ of STW cut quartz is 0.176≤t/λ≤1.925 (see also Fig. 17), and a phase of 5000m/s or more can be obtained in most of the range speed. Within this t/λ range, the smaller the t/λ, the higher the phase velocity, and a high frequency band can be obtained.

Next, the relationship between t/λ, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation will be described.

FIG. 23 shows the relationship between t/λ, electromechanical coupling coefficient K ² , and frequency-temperature variation. According to Fig. 23, the range in which the frequency temperature variation is smaller than t/λ of STW cut quartz is 0.176≤t/λ≤1.925 (also refer to Fig. 17, 22), and in most of the range, the electromechanical coupling coefficient K ² Values greater than or equal to 0.02 can be obtained. In the range where this t/λ is close to 1, a high region where the electromechanical coupling coefficient K ² is equal to or greater than 0.05 can be obtained.

Next, the fifth area will be described with reference to FIGS. 24 and 25 .

24 and 25 are graphs showing the relationship between the frequency temperature variation and the angle θ in Euler angles (0, θ, 0) and the relationship between the frequency temperature variation and t/λ in the fifth region. In the 5th region, the range of the angle θ at which the frequency-temperature characteristics are better than STW-cut quartz is 2.7 degrees ≤ θ ≤ 16 degrees, and the range of t/λ is 2.878 ≤ t/λ ≤ 3.

Next, the sixth area will be described with reference to FIGS. 26 to 33 .

26 and 27 are graphs showing the relationship between the frequency temperature variation and the angle θ in the Euler angles (0, θ, 0) and the relationship between the frequency temperature variation and t/λ in the sixth region. In the 6th region, the range of the angle θ at which the frequency temperature characteristics are better than STW-cut quartz is 116 degrees ≤ θ ≤ 122.1 degrees, and the range of t/λ is 0.375 ≤ t/λ ≤ 1.06.

In addition, the respective relationships between the angle θ and t/λ in the sixth region, the phase velocity, the amount of frequency temperature variation, and the electromechanical coupling coefficient K ² will be described in detail.

Fig. 28 shows the relationship between the angle θ and the phase velocity among the Euler angles (0, θ, 0). Here, t/λ is set in five levels within the range of 0.2 to 1.2, and the phase velocity at each t/λ is shown by a graph. According to FIG. 28 , at each t/λ, a phase velocity of 5000 m/s or more can be obtained within the range of the angle θ of 110° to 130°.

Also, FIG. 29 shows the relationship between t/λ and the phase velocity. The angle θ of the Euler angle is set in five levels within the range of 110 degrees to 130 degrees, and the phase speed at each angle θ is shown by a graph. According to FIG. 29 , the variation of the phase velocity at each angle θ is small, and a phase velocity of 5000 m/s or more can be obtained within the range of t/λ of 0.2 to 1.2. In the region where t/λ is less than 0.4, extremely high phase velocities can be obtained.

Next, the relationship between Euler angles and t/λ, phase velocity, frequency temperature variation, and electromechanical coupling coefficient ^K2 will be described.

Fig. 30 shows the relationship between the angle θ among the Euler angles (0, θ, 0), the phase velocity, and the amount of frequency temperature fluctuation. According to FIG. 30 , the range in which the frequency temperature variation is smaller than the angle θ of STW-cut quartz is 116 degrees ≤ θ ≤ 122.1 degrees (see also FIG. 26 ), and a phase velocity of 5000 m/s or more can be obtained within this range.

FIG. 31 shows the relationship between the Euler angles, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation. According to Figure 31, the range of the frequency temperature variation less than the angle θ among the Euler angles (0, θ, 0) of the STW-cut quartz is 116 degrees ≤ θ ≤ 122.1 degrees, and within this range the electromechanical coupling coefficient K ² is greater than or equal to 0.05 , greatly exceeding the benchmark value of 0.02, which can be said to be an easy-to-motivate region.

Fig. 32 shows the relationship between t/λ, phase velocity, frequency and temperature variation. According to Fig. 32, the range in which the frequency temperature variation is less than t/λ of STW-cut quartz is 0.375≤t/λ≤1.06 (see also Fig. 17), and a phase of 5000m/s or more can be obtained in most of the range speed. Within this t/λ range, the smaller the t/λ, the higher the phase velocity, and a high frequency band can be obtained.

Next, the relationship between t/λ, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation will be described.

FIG. 33 shows the relationship between t/λ, the electromechanical coupling coefficient K ² , and the amount of frequency-temperature variation. According to Fig. 33, the range in which the frequency temperature variation is less than t/λ of STW cut quartz is 0.375≤t/λ≤1.06 (also refer to Fig. ²⁷ ), and within this range, it is possible to obtain more than A region equal to a value of 0.02. When 0.62≤t/λ≤1.06, the electromechanical coupling coefficient K ² is greater than or equal to 0.03; when 0.67≤t/λ≤1.06, the electromechanical coupling coefficient K ² is greater than or equal to 0.04; when 0.71≤t/λ≤1.06, the electromechanical coupling The coefficient K ² is greater than or equal to 0.05.

Therefore, according to the foregoing embodiment, as shown in FIG. 4 , if the normalized substrate thickness t/λ is set to an appropriate value less than or equal to 3, mode coupling is unlikely to occur, and a stable phase-velocity region can be selected. Mpo effect.

Moreover, according to the graph, by setting the normalized substrate thickness t/λ to be less than or equal to 3, there can be more modes in the high-frequency band with a phase velocity of 5000 m/s or more, and the desired Phase velocity (frequency).

Furthermore, according to this embodiment, it is possible to provide frequency-temperature fluctuations with respect to temperature changes compared with conventional ST-type Rayleigh wave resonators, STW-type SH-wave resonators, and AT-type Lamb wave resonators. Lamb wave type high frequency resonator with small volume and excellent temperature characteristics. In addition, since the peak temperature of the frequency temperature deviation is around 20° C., which is regarded as normal temperature, good temperature characteristics can be obtained in practical use.

In addition, in the above-mentioned first to sixth ranges, the frequency-temperature variation can be made smaller than that of the STW type, and good frequency-temperature characteristics can be obtained. In addition, a high electromechanical coupling coefficient K ² can be set to provide an easy-to-excite Lamb wave type high frequency resonator.

Furthermore, in the present invention, the quartz substrate is formed with Euler angles (0, θ, 0), so the cutting angle is simple, and the width of the angle θ and the normalized substrate thickness t/λ can be set wider, and it is possible to Since desired temperature characteristics and frequency characteristics are selectively set within desired frequency bands, there are effects of ease of manufacture, improvement of yield, and reduction of manufacturing cost.

In each of the aforementioned six regions, the phase velocity in the high-frequency region, good frequency-temperature characteristics, and high electromechanical coupling coefficient K ² can be obtained, especially in the first region, it can be obtained in a wide range to satisfy The range of the angle θ and the range of t/λ among the Euler angles (0, θ, 0) of the above conditions expand the options for manufacturing.

Furthermore, in the fourth region, a high phase velocity (high frequency) region and a high electromechanical coupling coefficient K ² can be obtained, and in the sixth region, a high electromechanical coupling coefficient K ² can be obtained.

In the present invention, as described above, each characteristic is restricted by the angles θ and t/λ of the Euler angles, but in accordance with the target characteristics and manufacturing conditions, in the aforementioned first to sixth regions It can be arbitrarily selected from the range of , and it is possible to provide a Lamb wave type high-frequency resonator having desired good characteristics.

In addition, the present invention is not limited to the foregoing embodiments, and modifications, improvements, and the like within a range in which the object of the present invention can be achieved are also included in the present invention.

For example, in the aforementioned embodiment, the reflectors 25 and 26 are provided, but an end face reflection type structure not having these reflectors may also be employed.

Therefore, according to the above-mentioned embodiments, it is possible to provide a Lamb wave type high-frequency resonator capable of increasing the frequency, having good frequency-temperature characteristics, and capable of reducing manufacturing costs.

Claims (8)

1. A Lamb wave type high-frequency resonator has comb-tooth-shaped IDT electrodes for exciting Lamb waves on one main surface of a quartz substrate, characterized in that, The IDT electrode is formed such that the cut-out angle of the quartz substrate and the propagation direction of the Lamb wave are (0, θ, 0) in Euler angle representation. 2. The Lamb wave type high-frequency resonator according to claim 1, wherein When t is the thickness of the quartz substrate and λ is the wavelength of the Lamb wave, the relationship between the thickness t and the wavelength λ is set within a range represented by 0<t/λ≦3. 3. Lamb wave type high-frequency resonator according to claim 1, is characterized in that, The angle θ is within the range represented by 132.8 degrees ≤ θ ≤ 178 degrees, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 1.1≦t/λ≦3. 4. The Lamb wave type high-frequency resonator according to claim 1 or 2, wherein The angle θ is within the range represented by 4 degrees ≤ θ ≤ 57.5 degrees, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 2.08≦t/λ≦2.82. 5. The Lamb wave type high-frequency resonator according to claim 1 or 2, wherein the angle θ is within the range represented by 6°≤θ≤33°, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 0.975≦t/λ≦2.025. 6. The Lamb wave type high-frequency resonator according to claim 1 or 2, wherein the angle θ is within a range represented by 35 degrees ≤ θ ≤ 47.2 degrees, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 0.176≦t/λ≦1.925. 7. The Lamb wave type high-frequency resonator according to claim 1 or 2, wherein the angle θ is within a range represented by 2.7 degrees≤θ≤16 degrees, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 2.878≦t/λ≦3. 8. The Lamb wave type high-frequency resonator according to claim 1 or 2, wherein the angle θ is within a range represented by 116 degrees ≤ θ ≤ 122.1 degrees, The relationship between the thickness t of the quartz substrate and the wavelength λ of the Lamb wave is set within a range represented by 0.375≦t/λ≦1.06.

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