JP2018033122A - Crystal oscillator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a new excitation electrode structure capable of improving the characteristics of a crystal oscillator oscillating in a thickness-shear mode.SOLUTION: A quartz crystal piece 11 has a thickness in the Y' axial direction of a quartz crystal and the X'-Z' plane of the quartz crystal served as a main surface and includes excitation electrodes 13a and 13b on the front and rear surfaces. When defining an excitation electrode provided on a plus Y' plane as a first excitation electrode 13a and an excitation electrode provided on a minus Y' plane as an excitation second electrode 13b, the second excitation electrode is provided at a position projecting the state of moving the first excitation electrode by a distance dx given by Ttanα in the plus X' direction along the X' axis of the quartz crystal and moving the first electrode excitation by a distance dy given by Ttanβ in the minus Z' direction along the Z' axis of the quartz crystal on the minus Y' plane, to the first excitation electrode.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a crystal resonator that vibrates in a thickness shear mode.

  As a crystal resonator that vibrates in the thickness-shear mode, an AT-cut crystal resonator and a so-called twice-rotation crystal resonator represented by an SC-cut crystal resonator are known. Since these crystal resonators are indispensable electronic components for an advanced information communication society, efforts are being made to improve characteristics from various aspects.

One technique for improving characteristics is a technique that focuses on excitation electrodes provided on both sides of a crystal piece. For example, Patent Document 1 describes a structure in which excitation electrodes provided on both main surfaces of an AT-cut crystal piece are shifted by a predetermined amount in the X-axis direction of the crystal for the purpose of controlling frequency temperature characteristics. Patent Document 2 discloses an excitation electrode on the lower surface side among excitation electrodes provided on the front and back of a quartz piece in a quartz crystal having an SMD structure in which one end of an AT-cut quartz piece is supported by a conductive adhesive. In order to reduce the influence of the conductive adhesive, a structure is described in which it is shifted to a position farther from the conductive adhesive than the excitation electrode on the upper surface side.

WO 98/47226 JP 2014-42084 A

However, the method for improving the characteristics of a crystal resonator focusing on the excitation electrode still has potential.
The present application has been made in view of these points, and therefore the object of this application is to provide a crystal having a novel excitation electrode structure capable of improving the characteristics of a crystal resonator that vibrates in a thickness-slip mode. It is to provide a vibrator.

In order to achieve this object, according to the present invention, in the quartz resonator that includes the excitation electrodes on the front and back of the quartz piece and vibrates in the thickness-slip mode,
The displacement electrode at the edge of the excitation electrode on one side has the same positional relationship as the displacement distribution at the edge of the excitation electrode on the other side, and these excitation electrodes are provided on the front and back sides of the crystal piece. And

In carrying out the present invention, the crystal piece is a crystal piece whose thickness is in the Y′-axis direction of the crystal and whose main surface is the X′-Z ′ plane of the crystal. The excitation electrodes provided on the front and back main surfaces of the crystal piece have the same planar shape and the same size. However, the excitation electrode provided on the plus Y ′ plane is the first excitation electrode, minus Y When the excitation electrode provided on the surface 'is defined as the second excitation electrode, the second excitation electrode is preferably provided at a position satisfying the following relationship with respect to the first excitation electrode.
(1) The first excitation electrode is moved along the X ′ axis of the crystal in the plus X ′ direction by a distance dx given by T · tanα (see FIG. 1).
(2) The first excitation electrode is moved along the Z ′ axis of the crystal in the minus Z ′ direction by a distance dy given by T · tan β (see FIG. 1)
(3) A position where the state moved in (1) and (2) above is projected on the minus Y ′ plane.

  Here, T is the thickness of the crystal piece. Α and β are angles within a predetermined range according to the cut type (SC cut, IT cut, etc.) of the crystal piece. In addition, α is an angle with the Z ′ axis of the crystal piece as a rotation axis (see FIG. 1B), and β is an angle with the X ′ axis of the crystal piece as a rotation axis (FIG. 1 ( C)). In the following description, the positive and negative angles α and β are considered on the plus Z ′ plane and the plus X ′ plane of the crystal piece (FIGS. 1B and 1C), plus counterclockwise plus plus clockwise. Negative. These pluses and minuses determine the displacement direction of the front and back excitation electrodes. Note that the angles α and β are the main vibration (thickness shear vibration in the X ′ direction, so-called C mode) and sub-vibration (Z ′) if the crystal piece is a twice-rotation crystal resonator such as an SC cut. The thickness shear vibration in the direction (so-called B mode) is a different value for each of the C mode and the B mode.

  The X ′ axis and the Z ′ axis are axes generated by rotating the crystal piece with the cutting angles φ and θ with respect to the X axis and the Y axis, which are crystal axes of the crystal. That is, for example, in the case of a crystal piece that performs only one rotation, such as an AT-cut crystal piece, this is the axis after the one rotation, and for example, twice such as an SC cut. In the case of a crystal piece with the rotations φ and θ, the axis after the two rotations. However, the dash “′” does not mean the number of rotations. That is, as in the case of the AT-cut crystal piece, even when the rotation is only about the X axis and not the rotation about the Z axis, a dash symbol “′” is attached here and indicated by X ′, Y ′, Z ′. It is. In the case of the twice-rotated crystal piece, one dash symbol “′” is attached.

The present invention is preferably applied to a flat crystal piece, that is, a crystal piece having a substantially uniform thickness throughout the crystal piece. However, the present invention can also be applied to a plano-convex crystal piece. When the present invention is applied to a plano-convex crystal piece, the thickness T of the crystal piece is the thickness of the thickest part of the crystal piece, and the above (1), (2), (3) Apply the following conditions. When the present invention is applied to a plano-convex type crystal piece, the influence of the curved surface on one side of the crystal piece occurs compared to the case of applying to a flat plate, but the curvature of this curved surface is sufficiently larger than the thickness T of the crystal piece. Since it is large, the effect of the present invention can be obtained even if the above conditions (1) to (3) are applied as they are.
In implementing this invention, the planar shape of the excitation electrode can be arbitrary. However, the planar shape of the excitation electrode is preferably an elliptical shape. Moreover, it is preferable that the elliptical ratio of the elliptical electrode is set within a predetermined range according to the cut type of the crystal piece, and the elliptical electrode is rotated in-plane within the predetermined range with respect to the crystal piece. However, the ellipse in this preferred example is not only a true ellipse in which the sum of distances from two fixed points on one plane is constant, but also a shape that is slightly deformed from a true ellipse. In addition, a substantially ellipse showing the same effect as is included. For example, an ellipse in the present invention includes those that can define the major axis and minor axis even if they are slightly deformed from a true ellipse.
In carrying out the present invention, the thickness of the excitation electrode is reduced toward the end of the excitation electrode on at least one edge of the excitation electrode provided on the front and back of the crystal piece, and a predetermined dimension ( An inclined portion having an inclination width) can be provided.

According to the crystal resonator of the present invention, the front and back excitation electrodes are shifted in a predetermined relationship. Therefore, it is possible to realize a crystal resonator that vibrates with the same displacement distribution at the edges of the front and back excitation electrodes. Therefore, compared to the case where the displacement distributions at the edges of the front and back excitation electrodes are different, generation of unnecessary modes (spurious) at the edges can be easily suppressed, and loss during vibration is less likely to occur. In other words, according to the crystal resonator of the present invention, the excitation electrodes are arranged in a region where there is a vibration displacement distribution (vibration energy) on each of the front and back surfaces of the crystal piece, so that the characteristics of the crystal resonator are improved. Can be planned.

(A), (B), (C) is a figure explaining the structure of the crystal oscillator of 1st Embodiment. It is a figure explaining the simulation conditions in the crystal oscillator of a 1st embodiment. (A), (B) is a figure explaining the simulation result of the crystal oscillator of 1st Embodiment. (A), (B) is a figure following FIG. 3 explaining the simulation result of the crystal resonator of the first embodiment. (A), (B) is a figure following FIG. 4 explaining the simulation result of the crystal resonator of the first embodiment. It is the figure which showed the principal point of the simulation result of the crystal oscillator of 1st Embodiment. (A), (B) is a figure explaining the structure of the crystal oscillator of 2nd Embodiment. (A), (B), (C) is a figure explaining the simulation result of the ellipse ratio of an ellipse electrode. (A), (B), (C) is a figure following FIG. 8 explaining the simulation result of the ellipse ratio of the ellipse electrode. (A), (B), (C) is a figure following FIG. 9 explaining the simulation result of the ellipse ratio of the ellipse electrode. It is the figure which showed the principal point of the simulation result of the ellipse ratio. (A), (B), (C) is a figure explaining the simulation result of the in-plane rotation angle (delta) of an excitation electrode. (A), (B), (C) is a figure following FIG. 12 explaining the simulation result of the in-plane rotation angle δ of the excitation electrode. (A), (B), (C) is a figure following FIG. 13 explaining the simulation result of the in-plane rotation angle δ of the excitation electrode. It is the figure which showed the principal point of the simulation result of in-plane rotation angle (delta). (A), (B) is the figure which showed the structural example of the actual crystal oscillator of this invention. It is a figure explaining the structure of the crystal oscillator of 3rd Embodiment. It is a figure explaining the effect of the crystal oscillator of a 3rd embodiment. It is a figure explaining the structure of the crystal oscillator of 4th Embodiment. It is a figure explaining the effect of the crystal oscillator of a 4th embodiment. It is a figure explaining the effect of the crystal oscillator of a 5th embodiment.

Embodiments of the crystal resonator according to the present invention will be described below with reference to the drawings. It should be noted that the drawings used for the description are merely schematically shown to the extent that the present invention can be understood. Moreover, in each figure used for description, about the same component, it attaches | subjects and shows the same number, The description may be abbreviate | omitted. The shapes, dimensions, materials, etc. described in the following description are merely preferred examples within the scope of the present invention. Therefore, the present invention is not limited only to the following embodiments.

1. First embodiment 1-1. Structure of Crystal Resonator of First Embodiment FIGS. 1A to 1C are explanatory views of the crystal resonator of the first embodiment, particularly focusing on the crystal piece 11. Specifically, FIG. 1A is a plan view of the crystal piece 11, FIG. 1B is a cross-sectional view of the crystal piece 11 along the line P-P in FIG. 1A, and FIG. It is sectional drawing of the crystal piece 11 along the QQ line in FIG.

The crystal resonator of the first embodiment includes a crystal piece 11 and excitation electrodes 13a and 13b provided on the front and back surfaces thereof. The excitation distribution is such that the displacement distribution at the edge of the excitation electrode 13a on one surface of the crystal piece 11 is the same as the displacement distribution at the edge of the excitation electrode 13b on the other surface. Electrodes 13 a and 13 b are provided on the front and back of the crystal piece 11.
The crystal piece 11 is various crystal pieces that vibrate in the thickness-slip mode. Specific examples include an AT-cut crystal piece, an SC-cut crystal piece called a so-called two-time rotating vibrator, an M-SC cut crystal piece, and an IT-cut crystal piece. Detailed simulations and the like in the following description are performed using an M-SC cut crystal piece. The M-SC cut is a rotation of a quartz crystal at a predetermined angle φ in the range of 24 ° ± 1 ° with the Z axis of the crystal as the rotation axis, and 34 ° ± 1 with the X ′ axis generated here as the rotation axis. It is a crystal piece that is cut by rotating at a predetermined angle θ in the range of °. Therefore, the crystal piece 11 is a kind of crystal piece having a thickness in the Y′-axis direction of the crystal and having the X′-Z ′ plane of the crystal as a main surface.

Next, a specific configuration of the excitation electrodes 13a and 13b will be described. The excitation electrodes 13a and 13b have the same planar shape and the same size. Of course, the same planar shape and the same size may be substantially the same, and there may be some differences due to manufacturing accuracy and the like. When the excitation electrode provided on the plus Y ′ surface of the crystal piece 11 is defined as the first excitation electrode 13a and the excitation electrode provided on the minus Y ′ surface of the crystal piece 11 is defined as the second excitation electrode 13b, the second excitation electrode 13a is defined. The excitation electrode 13b is provided at a position that satisfies the following relationships (1), (2), and (3) with respect to the first excitation electrode 13a. In the following formula, T is the thickness of the crystal piece. Further, the angles α and β are predetermined angles described later.
(1) The first excitation electrode 13a is moved in the plus X ′ direction along the X ′ axis of the crystal by a distance dx given by T · tan α (see FIG. 1B).
(2) The first excitation electrode 13a is moved along the Z ′ axis of the crystal in the minus Z ′ direction by a distance dy given by T · tan β (see FIG. 1C).
(3) A position obtained by projecting the state moved in (1) and (2) above onto the minus Y ′ plane (see FIG. 1A).
Therefore, as shown in FIG. 1A, the second excitation electrode 13b viewed from the first excitation electrode 13a is in the plus X ′ direction on the back surface of the crystal piece 11 with respect to the first excitation electrode 13a. And it is provided at a position shifted by a predetermined distance in the minus Z ′ direction.

By setting the angles α and β shown in the above equations (1) and (2) to predetermined angles, the displacement distribution at the edge of the first excitation electrode 13a is changed to the displacement distribution at the edge of the second excitation electrode 13b. It has been found by the simulation based on the finite element method by the inventor of this application that the first and second excitation electrodes can be arranged in the same positional relationship as in FIG. However, it has been found that the angles α and β have appropriate values for each type of crystal piece cut and for each vibration mode to be used. The results are shown in Table 1 below.

1-2. Examination example of angles α and β in the first embodiment Table 1 shows predetermined angles α and β and their allowable ranges. Therefore, a simulation example relating to a point where the angles α and β are preferably within a predetermined range will be described. Since quartz is an anisotropic material, it is known that the direction of the phase velocity of the elastic wave in the medium and the direction of the energy velocity (power flow direction) are different for quartz resonators that vibrate in the thickness-slip mode. Yes. Therefore, it is considered that the vibration displacement of the front and back surfaces of the crystal piece when the crystal resonator vibrates is not at the same position on the front and back surfaces. The inventor according to this application considered that it is not preferable that the excitation electrodes having the same shape and the same size are directly opposed to the crystal piece in such a state on the front and back surfaces of the crystal piece.

Therefore, as shown in FIG. 2, as a simulation model by the finite element method, a model in which the first and second excitation electrodes 13a and 13b having the same planar shape and the same size on the front and back surfaces of the crystal piece 11 is set. Furthermore, the position of the edge of each of the first and second excitation electrodes 13a and 13b, that is, the vibration displacement at various locations along the edge of the excitation electrode was calculated by the finite element method. Furthermore, the vibration displacement was calculated when the position of the second excitation electrode 13b was shifted with respect to the first excitation electrode 13a. As shown in FIG. 2, each position of the edge of the excitation electrode was a position on the edge specified by the angle γ, that is, a position of 0 °, a position of 180 °, and so on.

3, 4 and 5 show the displacement distribution obtained by the above simulation. However, these figures show simulation results when using an M-SC cut crystal piece as the crystal piece and vibrating in the C mode. 3 to 5, the horizontal axis is the position of the edge of the excitation electrode specified by the angle γ, and the vertical axis is the displacement when the crystal piece of the model vibrates. The displacement is shown as a value normalized by the maximum displacement. 3 to 5, the characteristic diagram plotted with ◯ is the edge displacement distribution of the first excitation electrode 13a, and the characteristic diagram plotted with + is the edge displacement distribution of the second excitation electrode 13b. . However, from the results of various simulations conducted by the inventors, it has been found that the angle β in the case of the M-SC cut is preferably around 0.2 °, so the results shown in FIGS. The first and second excitation electrodes when the angle α is different from 35 °, 30 °, 25 °, 20 °, and 15 ° 0 ° under the condition that the angle β is fixed to 0.2 °. An edge displacement distribution is shown.
FIG. 6 is a diagram summarizing the main points of the results of FIGS. 3, 4, and 5. Specifically, for each of the six types of simulations with different angles α, the difference between the displacement distribution at the edge of the first excitation electrode and the displacement distribution at the edge of the second excitation electrode The displacement difference at is shown as an integrated value integrated over the entire edge. Therefore, the smaller this integrated value is, the higher the degree of coincidence of the displacement distributions at the edges of the front and back excitation electrodes is.

Comparing FIGS. 3 to 5 and, as is clear from FIG. 6, the displacement distribution at the edge of the first excitation electrode 13a and the displacement distribution at the edge of the second excitation electrode 13 You can see that it changes when you change. When the angle α is 25 ° (see FIG. 4A), the displacement distribution at the edge of the first excitation electrode 13a and the displacement distribution at the edge of the second excitation electrode most closely match. I understand. From the results of many simulations conducted by the inventors, including this simulation, in the case of M-SC cut and C mode, the angle α = 25 ° and the angle β = 0.2 ° are It was found that the displacement distribution at the edge of the second excitation electrode most closely matched. However, as is apparent from FIG. 6, in consideration of the effect of improving the characteristics of the vibrator, the angle α is preferably −20 to −30 °, that is, α = 25 ± 5 °, and more preferably α = 25. It can be seen that ± 3 is good. Moreover, it was found that β = 0 ± 5 ° is preferable, and β = 0 ± 3 ° is more preferable. From the same simulation results, in the case of M-SC cut and in the B mode, the angles α and β are preferably α = −6 ± 5 ° and β = −17 ± 5 °, more preferably Α = −6 ± 3 ° and β = −6 ± 3 ° were found to be good.

As other crystal pieces, SC cut, IT cut, and AT cut were also simulated in the same manner as described above, and preferable values of the angles α and β were calculated. The results are shown in Table 2 below together with the results of the above M-SC cut.

また、ＳＣカット、ＩＴカット、ＡＴカット各々の角度α、角度βの許容範囲は、シミュレーション結果から、上記の表１に示した通り、各々所定値±５°が良く、より好ましくは所定値±３°が良いことが判明した。

Further, the allowable range of the angle α and the angle β of each of the SC cut, IT cut, and AT cut is preferably a predetermined value ± 5 °, more preferably a predetermined value ± as shown in Table 1 above, from the simulation results. 3 ° proved to be good.

2. Second Embodiment In the first embodiment, the displacement distribution at the edges of the front and back excitation electrodes is obtained by shifting the front and back excitation electrodes in the predetermined positional relationship shown in the above (1) to (3). Could be the same or similar. However, according to further studies by the inventors, the excitation electrodes on the front and back sides are shifted in a predetermined positional relationship, the planar shape of the excitation electrode is an elliptical shape, and the elliptical shape of the elliptical electrode is set according to the cut type of the crystal piece. It has been found that it is preferable to set the ratio within a predetermined range and to rotate the ellipse electrode within the predetermined range with respect to the crystal piece. In this way, although it will be described in detail later, it has been found that the displacement at the edge of the excitation electrode tends to be the same or close to each other at the edge. That is, it has been found that the displacement distribution at the edge of the excitation electrode tends to be flat. This second embodiment is an example.

7A and 7B are explanatory diagrams thereof. In the crystal resonator according to the second embodiment, each of the first excitation electrode 13a and the second excitation electrode 13b provided on the crystal piece 11 has an elliptical planar shape and a predetermined elliptical ratio, and a quartz crystal. It is in-plane rotation within a predetermined angle range with respect to the piece, and is shifted by predetermined relationships (1) to (3) as in the first embodiment.
Here, the ellipse ratio and the in-plane rotation angle are defined as follows. The dimension along the X ′ axis of the crystal piece of the elliptical excitation electrode is defined as a, the dimension along the Z ′ axis is defined as b (FIG. 7A), and the elliptical ratio is defined as a / b. The in-plane rotation angle of the elliptical excitation electrode with respect to the crystal piece is defined as an angle δ with respect to the X ′ axis of the crystal piece (FIG. 7B). However, as shown in FIG. 7 (B), this angle δ is defined as positive on the Y ′ plane with the Y ′ axis as the rotation axis and positive in the clockwise direction and negative in the clockwise direction. To do.
Displacement distributions at the edges of the first and second excitation electrodes 13a and 13b using the finite element method by setting models in which the ellipticity ratio a / b and the in-plane rotation angle δ thus defined are variously set. Were examined as follows.

2-1. Examination of Ellipse Ratio First, the preferred range of the ellipse ratio of the excitation electrode was examined as follows. In the simulation, the crystal piece is M-SC cut, the vibration mode is the fundamental mode of the C mode, and the angles α and β determining the positional relationship between the first excitation electrode 13a and the second excitation electrode 13b. Were set to α = 25.5 ° and β = 0.2 °, the in-plane rotation angle δ of the excitation electrode with respect to the crystal piece was set to δ = −9 °, and the elliptical ratio was variously changed. The simulated elliptic ratios are 1.584, 1.518, 1.452, 1.386, 1.32, 1.254, 1.188, 1.122, and 1.056. When considering 32 as a reference, each elliptical ratio corresponds to that of 20% increase, 15% increase, 10% increase, 5% increase, 5% decrease, 10% decrease, 15% decrease and 20% decrease.

FIGS. 8, 9 and 10 show the displacement distribution at the edge of the excitation electrode obtained by the simulation of the elliptic ratio. 8 to 10, the horizontal axis is the position of the edge of the excitation electrode specified by the angle γ as in the first embodiment, and the vertical axis is the displacement when the crystal piece of the model vibrates. Note that the displacement is indicated by a value normalized by the maximum displacement, as in the first embodiment. In FIGS. 8 to 10, the characteristic diagram plotted with ◯ is the edge displacement distribution of the first excitation electrode 13a, and the characteristic diagram plotted with + is the edge displacement distribution of the second excitation electrode 13b. .
FIG. 11 is a diagram summarizing the main points of the results of FIGS. Specifically, for each of the nine types of simulations with different ellipse ratios, the difference between the displacement distribution at the edge of the first excitation electrode and the displacement distribution at the edge of the second excitation electrode is Regardless, it is the difference between the maximum and minimum values of all displacements. The smaller this difference is, the flatter the displacement distribution at the edges of the front and back excitation electrodes.

First, it is clear from FIGS. 8 to 10 that the edges of the first excitation electrode 13a and the second excitation electrode 13b are obtained by the effect of the first embodiment in which the front and back excitation electrodes are shifted in a predetermined positional relationship. Even if the elliptical ratio is changed, the displacement distribution in FIG. 2 shows the same tendency, that is, both show a substantially sinusoidal displacement distribution. However, comparing FIG. 8 to FIG. 10 and particularly as apparent from FIG. 11, the flatness of each of the displacement distributions at the edges of the first and second excitation electrodes 13 a and 13 b changes the elliptical ratio. It can be seen that changes. That is, it can be seen that the displacement distribution is flattened when the elliptical ratio is 1.32 (see FIG. 9B), and gradually becomes sinusoidal when the elliptical ratio increases or decreases with respect to 1.32. Since it is considered that the flat displacement distribution at the edge of the excitation electrode is preferable for the suppression of unnecessary vibration and the like compared to the case where the displacement is not so, it can be said that the excitation electrode having a predetermined elliptic ratio is useful.

According to the simulation result based on the elliptical ratio of 1.32, in the case of a crystal resonator that vibrates in the C mode and vibrates in the fundamental wave with M-SC cut, the elliptical ratio is 1.32 ± A range of 10% is good, and a range of 1.32 ± 5% is more preferred. According to this simulation procedure, preferred elliptic ratios for M-SC cut 3rd harmonic, 5th harmonic, fundamental wave in B mode, 3rd harmonic, 5th harmonic were also examined. The preferable elliptic ratio at each level determined by these studies is shown in the column of elliptic ratio in Table 3 below. Similarly, preferred elliptical ratios for each of the SC cut, IT cut, and AT cut were determined. These results are shown in the elliptic ratio column of Table 4, Table 5, and Table 6 below. Further, according to the inventors' examination of the simulation results, it was determined that the preferable allowable range of the elliptical ratio of the excitation electrode in each cut type was ± 10%, more preferably ± 5%.

2-2. Examination of In-Plane Rotation Angle of Excitation Electrode with Quartz Piece Next, an appropriate range of the in-plane rotation angle δ with respect to the quartz piece of elliptical excitation electrode will be described.
First, the crystal piece is M-SC cut, the vibration mode is the fundamental mode of the C mode, and the angles α and β that determine the positional relationship between the first excitation electrode 13a and the second excitation electrode 13b are α = The simulation results were as follows under the conditions of 25.5 °, β = 0.2 °, and the ellipticity ratio of 1.32. The angle δ during the simulation is 1 °, −1.5 °, −4 °, −6.5 °, −9 °, −11.5 °, −14 °, −16.5 °, − 19 °. Here, as shown in FIG. 7B, the direction of the angle δ is defined by defining the counterclockwise direction as positive and the clockwise direction as negative with the Y ′ axis as the rotation axis on the plus Y ′ surface of the crystal piece 11. Yes.

12, 13, and 14 show the displacement distribution obtained by the above simulation. 12 to 14, the horizontal axis is the position of the edge of the excitation electrode specified by the angle γ as in the first embodiment, and the vertical axis is the displacement when the model crystal piece vibrates. Note that the displacement is indicated by a value normalized by the maximum displacement, as in the first embodiment. 10 to 12, the characteristic plots plotted with ◯ are the displacement distribution of the edge of the first excitation electrode 13a, and the characteristic plots plotted with + are the displacement distribution of the edge of the second excitation electrode 13b. .
FIG. 15 is a diagram summarizing the main points of the results of FIGS. 12, 13, and 14. Specifically, for each of the nine types of simulations with different in-plane rotation angles δ, the difference between the displacement distribution at the edge of the first excitation electrode and the displacement distribution at the edge of the second excitation electrode is as follows. The difference between the maximum value and the minimum value of all displacements regardless of the front and back is shown. The smaller this difference is, the flatter the displacement distribution at the edges of the front and back excitation electrodes.

As is clear from comparing FIGS. 12 to 14 and from FIG. 15, the displacement distribution at the edges of the first and second excitation electrodes 13a and 13b is an angle that is the direction of the ellipse. It turns out that it changes by changing (delta). That is, in the case of the M-SC cut, the displacement distribution at the edge of each of the first and second excitation electrodes is flatter than the other when δ = −9 °, and both are the same. Thus, it can be seen that when the angle δ increases or decreases from −9 °, the unevenness increases and the difference between the two increases. Accordingly, the angle δ is preferably −9 °, and according to the simulation results of the inventors, it can be determined that the allowable range is ± 5 °, more preferably ± 3 °. In accordance with this simulation procedure, the 3rd harmonic, 5th harmonic in the C mode of M-SC cut, the 3rd harmonic, the 5th harmonic in the B mode of M-SC cut, the SC cut, the IT cut, For each AT cut, a preferred angle δ was determined for each mode and fundamental, third, and fifth harmonics. These results are shown in the column of the ellipse direction in Table 3, Table 4, Table 5, and Table 6 above. In any case, the preferable allowable range of the ellipse direction δ was determined to be ± 5 °, more preferably ± 3 °.

3. Actual Structure Example An actual structure example of the crystal resonator of the above-described embodiment will be described. 16A and 16B are explanatory diagrams thereof.
The structural example shown in FIG. 16A is an example in which the present invention is applied to a lead-type crystal resonator 20 and is a schematic view of the crystal resonator 20 viewed from the side. The crystal unit 20 includes a base 21, a lead 23 provided on the base, and a clip terminal 25 provided at the tip of the lead. The crystal piece 11 is fixed to the clip terminal 25. Specifically, the extraction electrode 15 drawn from the excitation electrodes 13 a and 13 b is provided on the front and back of the crystal piece 11, and the crystal piece 11 is attached to the clip terminal 25 near the end of the extraction electrode 15 with the conductive adhesive 27. It is fixed with. In practice, a cap (not shown) is bonded to the base to seal the crystal piece 11.
The structural example shown in FIG. 16B is an example in which the present invention is applied to a surface-mount type crystal unit 30 and is a schematic view of the crystal unit 30 as viewed from above. The crystal unit 30 includes a ceramic base 31 and a support pad 33 provided on the base. The crystal piece 11 is fixed to the support pad 33. Specifically, the extraction electrode 15 drawn from the excitation electrodes 13 a and 13 b is provided on the front and back of the crystal piece 11, and the crystal piece 11 is attached to the support pad 33 near the end of the extraction electrode 15 with the conductive adhesive 35. It is fixed with. In practice, a lid member (not shown) is joined to the base to seal the crystal piece 11. Further, a mounting terminal (not shown) is provided on the bottom surface of the ceramic base, and the mounting terminal is electrically connected to the support pad.
Of course, these structural examples are preferred examples of the present invention, and other structures may be used.

4). 3rd Embodiment (form which provides an inclination part in the edge part of the electrode for excitation)
In the first and second embodiments described above, the excitation electrodes have substantially the same thickness throughout the entire area. However, providing an inclined portion at the edge of the excitation electrode is more preferable for suppressing unnecessary modes. The third embodiment is an example.
FIG. 17 is an explanatory diagram of the crystal resonator according to the third embodiment. In particular, it is a view focusing on the crystal piece 41 included in the crystal resonator of the third embodiment, where (A) is a plan view of the crystal piece 41, and (B) is an RR line of the crystal piece 40. FIG. In FIG. 17B, the thickness of the excitation electrode is shown enlarged from the actual thickness in order to deepen the understanding of the inclined portions 13ab and 13bb of the excitation electrodes 13a and 13b.

The crystal piece 41 includes main thickness portions 13aa and 13ba formed on the front and back surfaces of the excitation electrodes 13a and 13b with a constant thickness, and portions formed around and in contact with the main thickness portions. It is characterized by having inclined portions 13ab and 13bb formed so that the thickness gradually decreases from the outermost periphery of the excitation electrode to the outermost periphery of the excitation electrode. Note that the constant thicknesses of the main thickness portions 13aa and 13ba allow variations due to unavoidable variations in manufacturing.
In this example, the inclined portion 13ab is composed of four steps. The width from the main thick portion 13aa side to the outermost periphery of the excitation electrode 13a, that is, the inclined width is formed as XA, and the width between the steps is formed as XB. That is, in this example, the width XA is formed to be three times as long as the width XB. The main thickness portion 13aa is formed in YA. The height of each step of the inclined portion 13ab is YB. Therefore, the thickness YA is four times the thickness YB.

The effects of these inclined portions 13ab and 13bb were confirmed by performing the following simulation. That is, as a simulation model of the crystal piece 41, two types of models were prepared: a model using an AT cut crystal piece and a model using an M-SC cut crystal piece. The thicknesses YA of the main thickness portions 13aa and 13ba of the excitation electrodes in these models are 140 nm, the frequency of the main vibration is 26 MHz, and the width XA of the inclined portions 13ab and 13bb is variously changed. Simulation by the element method was performed.
In the crystal resonator, the main vibration (for example, C mode) and the unnecessary vibration which is a vibration which is not designed in design are generated unlike the main vibration. In a crystal resonator that is formed of a quartz material such as AT cut or M-SC cut and vibrates due to thickness shear vibration, the influence of bending vibration is particularly significant as unnecessary vibration. The horizontal axis of the graph of FIG. 18 shows the inclination width normalized by the bending wavelength λ which is the wavelength of this bending vibration. Therefore, the inclination width shown in the graph of FIG. 18 differs in the inclination width dimensions of the inclined portions 13ab and 13bb depending on whether the crystal piece is AT cut or M-SC cut even with the same scale. For example, when the vibration with a vibration frequency of 26 MHz is the main vibration, the bending wavelength λ of the AT cut crystal piece is about 100 μm, and the bending wavelength λ of the M-SC cut crystal piece is about 110 μm. At this time, the actual dimension of the tilt width indicated by “1” in the graph of FIG. 18 is 1 × λ. In the case of the AT cut crystal piece, the tilt width is 1 × λ = about 100 μm, and the M-SC cut crystal piece. In this case, the inclination width is 1 × λ = about 110 μm.

The vertical axis of the graph of FIG. 18 shows the reciprocal of the Q value indicating the loss of vibration energy of the main vibration. The characteristics of the AT-cut crystal piece model are indicated by black circles ●, and the characteristics of the M-SC cut crystal piece model are indicated by black triangles ▲.
As can be seen from FIG. 18, in both models, 1 / Q indicating the loss of vibration energy in the range where the inclination width normalized by the bending wavelength λ is about “0.5” to “3” is 3.0 ×. It is as low as 10-6 (denoted as “3.0E-6” in FIG. 18). That is, it can be seen that the loss of vibration energy is suppressed when the inclination width is formed to be 0.5 to 3 times the bending wavelength λ. In particular, in both models, the 1 / Q magnitude is low and the fluctuation is also small when the slope width normalized by the bending wavelength λ is in the range of “1” to “2.5”. That is, it can be seen that when the inclination width is 1 to 2.5 times the bending wavelength, the loss of vibration energy is more stably reduced.

  The configuration in which the inclined portion is provided at the edge of the excitation electrode is particularly suitable when applied to a crystal piece on a flat plate. In order to improve the characteristics of the crystal resonator, a so-called convex crystal piece in which the thickness of the edge region of the crystal piece itself is thin has been conventionally used. In this way, vibration energy can be confined and unnecessary vibration can be suppressed. However, there is a problem that processing and cost are required to make the quartz crystal into a convex shape. In the case of the third embodiment, the inclined portion of the edge portion of the excitation electrode serves as a convex shape of the crystal piece. Therefore, when the structure of the inclined portion is further added to the configuration of the present invention exemplified in the first and second embodiments in which the front and back excitation electrodes are shifted in a predetermined relationship, the characteristics of the crystal resonator can be improved. Cost can be further reduced.

5). 4th Embodiment (form which provides an inclination part in the edge part of the electrode for single-sided excitation)
In the above-described third embodiment, the structure in which the inclined portion is provided at the edge of each of the front and back excitation electrodes has been described. However, when manufacturing a crystal resonator, the excitation electrode is trimmed with an argon ion beam or the like in order to adjust the vibration frequency. In this trimming process, the inclined portion disappears, which may increase the loss of vibration energy. In order to avoid this, the inclined electrode may not be provided on the excitation electrode on the frequency adjustment surface of the crystal piece, and the inclined portion may be provided only on the excitation electrode on the surface opposite to the frequency adjustment surface. The fourth embodiment is an example.

FIG. 19 is an explanatory diagram of the crystal resonator according to the fourth embodiment. In particular, it is a diagram focusing on the crystal piece 51 included in the crystal resonator of the fourth embodiment, where (A) is a plan view of the crystal piece 51, and (B) is an SS line of the crystal piece 51. FIG. In the case of the fourth embodiment, only the excitation electrode on the side where the frequency of the crystal piece is not adjusted has a structure having an inclined portion at the edge thereof. In the example of FIG. 19, only the excitation electrode 13b of the excitation electrodes 13a and 13b has a structure having a main thick portion 13ba and an inclined portion 13bb. The configuration of the excitation electrode 13b may be the configuration described in the third embodiment. That is, as described in the third embodiment, the excitation electrode 13b includes a main thickness portion 13ba formed with a constant thickness YA2 (YA in the third embodiment), and the main thickness portion 13b. An inclined portion 13bb is formed so that the thickness gradually decreases from a portion formed around the main thickness portion to the outermost periphery of the excitation electrode, and an inclined width XA is 0.5 times the bending wavelength λ. The length is 3 times or less, preferably 1 to 2.5 times. On the other hand, the film thickness of the excitation electrode 13a on the side where no inclined portion is provided is YA1. Details of the structures of the film thicknesses YA1 and YA2 will be described later. The crystal piece 51 is mounted on a crystal resonator container (see, for example, FIG. 16) so that the excitation electrode 13 b side is the frequency unadjusted side.

Next, matters to be noted when implementing the fourth embodiment will be described below with reference to FIG.
FIG. 20 shows the results of analyzing the loss (1 / Q) of main vibration energy in each model by the finite element method by preparing the following three types of simulation models as simulation models. The first of the three types is a model corresponding to the crystal piece 51 of the fourth embodiment, that is, a model in which an inclined portion is provided only on the excitation electrode on one side of the crystal piece. The second model corresponds to the crystal piece 41 of the third embodiment, that is, a model in which inclined portions are provided on the excitation electrodes on both sides of the crystal piece. The third model corresponds to the crystal piece 11 of the first embodiment, that is, a model in which an inclined portion is not provided on the excitation electrode of the crystal piece.

In all models, the quartz material is M-SC cut, the excitation electrodes are all gold (Au), the frequency of the main vibration is 30 MHz (bending wavelength λ is about 95 μm), and the inclination is the model with the inclined part. The width XA is 133 μm (1.4 times the bending wavelength λ). In the graph of FIG. 20, the thickness YA1 of the excitation electrode 13a and the thickness YA2 of the main thickness portion 13ba of the excitation electrode 13b are shown on the horizontal axis in the graph of FIG. In this simulation, the sum of the thickness YA1 and the thickness YA2 is always 280 nm. In FIG. 20, the thickness YA2 increases toward the right side of the graph. Also, the vertical axis of FIG. 20 shows the loss (1 / Q) of vibration energy of the main vibration (for example, C mode). In FIG. 20, the calculation result of the model in which the inclined portion is provided only on one side of the excitation electrode is indicated by a black circle ●, and the calculation result of the model in which the inclination portion is provided on both sides of the excitation electrode is indicated by a black rhombus ◆ The calculation result of the model in which the excitation electrode is not provided with the inclined portion is indicated by a white square □.
The reason why the simulation is performed under the condition that the sum of the thickness YA1 and the thickness YA2 is always 280 nm is to ensure so-called energy confinement in the crystal resonator. That is, it is because it is desired to confirm the effect of the present invention on the premise of securing energy confinement. However, the value of 280 nm is an example corresponding to the size, shape, and frequency of the crystal piece of the embodiment.

As can be seen from FIG. 20, in the model in which the inclined portion is provided only on the single-sided excitation electrode, when the thickness YA1 and the thickness YA2 are 140 nm, 1 / Q indicating the loss of vibration energy is about 5.5. × 10-6 (in the graph of FIG. 20, “× 10-6” is expressed as “E-6”). However, in this model, 1 / Q is reduced by reducing the thickness YA1 of the excitation electrode without the inclined portion and increasing the thickness YA2 of the excitation electrode provided with the inclined portion instead. When the thickness YA1 is 60 nm and the thickness YA2 is 220 nm, 1 / Q is about 3.1 × 10 −6. That is, in the model in which the inclined portion is provided only on the single-sided excitation electrode, the inclined portion is provided only on the single-sided excitation electrode, and the thickness of the excitation electrode not provided with the inclined portion is reduced. It can be seen that the loss of is reduced. On the other hand, in a model in which the excitation electrodes on both sides have inclined portions, even when the thickness YA1 and the thickness YA2 are changed, 1 / Q is about 2.4 × 10 −6 to about 2.6 × 10 −. 6, it is in a flat state, and it is preferable as a characteristic at first glance. However, in the model in which the excitation electrodes on both sides have inclined portions, the inclined portion of the excitation electrode on the frequency adjustment surface side disappears during frequency adjustment, and this characteristic cannot be maintained in the actual product. Further, in a model in which the excitation electrodes on both sides do not have inclined portions, when the thickness YA1 and the thickness YA2 are changed, 1 / Q increases as the thickness YA2 increases, and the thickness YA2 is 220 nm. 1 / Q is about 9.9 × 10 −6. That is, in a model in which the excitation electrodes on both sides do not have inclined portions, an unnecessary mode due to a step at the edge of the excitation electrode occurs as the thickness of YA2 increases, and the loss increases.

The effect of the crystal resonator according to the fourth embodiment occurs for the following reason. In the crystal resonator, the main vibration (for example, C mode) and the unnecessary vibration which is a vibration which is not designed in design are generated unlike the main vibration. In a crystal resonator formed of a crystal piece formed of a crystal material such as AT cut and M-SC cut and vibrated by thickness shear vibration, modes other than the main vibration become unnecessary modes that inhibit the oscillation of the main vibration. . In the unnecessary vibration that is the vibration in the unnecessary mode, it is known that the bending vibration particularly affects the main vibration. In bending vibration, vibration energy is converted into bending vibration mainly at the end of the excitation electrode, which is superimposed on the main vibration, and the bending vibration vibrates throughout the piezoelectric vibrating piece. Vibration energy is absorbed by the adhesive. Such a loss of energy due to bending vibration leads to a loss of vibration energy.
In the crystal resonator according to the fourth embodiment, when both the excitation electrode thicknesses YA1 and YA2 are 140 nm, the excitation electrode 13b has the inclined portion 13bb, but the excitation electrode 13a Since the slope portion is not formed, the influence of the bending vibration on the main vibration is not sufficiently suppressed. Therefore, the loss is as large as the model without the slope portion. However, in the crystal resonator according to the fourth embodiment, 1 / Q decreases as the thickness YA1 of the excitation electrode 13a without the inclined portion decreases, and the loss is reduced when the thickness YA1 is 60 nm. This is close to a model in which inclined portions are provided on the excitation electrodes on both sides. This is presumably because the occurrence of bending vibration is suppressed because the thickness YA1 of the excitation electrode not provided with the inclined portion is reduced, thereby reducing the influence of the step at the electrode end. Therefore, in the case of the fourth embodiment, the thickness YA1 of the excitation electrode 13b not provided with the inclined portion can suppress the induction of the unnecessary mode at the end of the excitation electrode 13b, and can serve as the original conductive film of the electrode. It is preferable that the thickness is as thin as possible on the assumption that the function is obtained. In the thin film technology, it is known that the lower limit range that can be established as a film is a thickness of 60 nm to 100 nm, and considering this, in order to exert the function of the excitation electrode without the inclined portion, The length YA1 is preferably in the range of 60 nm to 100 nm, preferably 60 nm to 80 nm.

Further, in the crystal piece 51 of the fourth embodiment, the vibration energy is confined by forming the excitation electrode with a predetermined thickness instead of the crystal piece 51 being processed such as bevel processing or convex processing. It is preferable to select the thickness YA2 of the excitation electrode not provided with the inclined portion so that the total thickness of the excitation electrodes YA1 and YA2 becomes a film thickness that can confine the vibration energy. Specifically, the total thickness of both excitation electrodes can be determined from a value of several percent with respect to the thickness of the crystal piece in consideration of the size, frequency, etc. of the piezoelectric vibration piece. Choose from 5%.
In the case of the fourth practical form, the effect of the present invention exemplified in the first and second embodiments in which the front and back excitation electrodes are shifted in a predetermined relationship is obtained, and an effect is provided in which an inclined portion is provided in the excitation electrode. And the effect that this inclination part can avoid damaging at the time of frequency adjustment is acquired.

6). Fifth embodiment (a configuration of an inclined portion that takes harmonics into consideration)
In the third embodiment and the fourth embodiment described above, the appropriate value related to the fundamental wave has been described for the inclination width XA that is the length of the inclined portion. On the other hand, as one of the applications of the crystal resonator, there is an application in which signals of two frequencies are simultaneously output from one crystal resonator. For example, International Publication No. 2015/133472 describes taking out a fundamental wave and a harmonic from one crystal piece. In such a case, one frequency can be used as an output signal, and the other frequency can be used as a temperature compensation sensor signal. However, since two frequencies can be obtained by one crystal resonator, It is preferable because the influence of individual differences can be reduced. The fifth embodiment relates to a design that further considers the fundamental wave and the harmonics in the first to fourth embodiments described above.
In the various embodiments of the first to fourth embodiments, the quartz piece of the fifth embodiment has an inclination width when the inclined portion is provided in the excitation electrode with the fundamental wave of the thickness shear vibration. It is not less than 0.84 times and not more than 1.37 times the first bending wavelength, which is the wavelength of bending vibration, and is not less than 2.29 times, 3 times, the second bending wavelength, which is the wavelength of bending vibration at the third harmonic wave of the thickness shear vibration. The length is 71 times or less.

FIG. 21 is a diagram showing a simulation result for explaining the effect of the fifth embodiment. Specifically, FIG. 21 shows a value obtained by normalizing the inclination width of the excitation electrode with the wavelength of the bending vibration, and the vibration model for the simulation model in which the inclined portions are provided on the excitation electrodes on both sides described with reference to FIG. It is the graph which showed the relationship with the loss of energy (1 / Q). In the simulation model, all of the excitation electrodes are made of gold (Au), and the main thickness portion 13aa (frequency: 30 MHz) and the fundamental wave (frequency: 30 MHz) and the third harmonic (frequency: 90 MHz) are assumed. 13B shows the calculation results by simulation when the film thickness YA1 is 100 nm, 140 nm, and 180 nm.

  The horizontal axis of the graph of FIG. 21 indicates the inclination width XA (μm). The vertical axis of the graph of FIG. 21 indicates the reciprocal of the Q value indicating the loss of vibration energy of the main vibration. Further, in FIG. 21, the loss of the crystal piece when the fundamental wave oscillates when the thickness YA of the main thickness part is 100 nm is indicated by a white square □, and the crystal piece when the fundamental wave oscillates when the thickness YA is 140 nm. Loss is indicated by a white triangle Δ, the loss of the crystal piece when the fundamental wave is oscillated when the thickness YA is 180 nm is indicated by a white circle ○, and the thickness YA of the main thick portion is 100 nm and a third harmonic wave The loss of the crystal piece when oscillating is indicated by a black square ■, the loss of the crystal piece when the thickness YA is 140 nm and the third harmonic is oscillated is indicated by a black triangle ▲, and the third harmonic when the thickness YA is 180 nm. The loss of the crystal piece when oscillating is indicated by black circles ●.

  As can be seen from FIG. 21, the relationship between the inclination width of the fundamental wave and the loss of vibration energy (1 / Q) shows a similar tendency regardless of the thickness YA of the main thickness portion, 1 / Q indicating the loss of vibration energy when the inclination width XA is about 30 μm to about 130 μm is 8.0 × 10 −6 (“× 10 −6” is expressed as “E-6” in the graph of FIG. 21) It is lower as below. In addition, regarding the relationship between the tilt width and vibration energy loss (1 / Q) in the third harmonic wave, 1 / Q indicating the loss of vibration energy in the range where the tilt width XA is about 80 μm or more is 4.0 × 10 −6. It is lower as below. From these results, in the range where the inclination width XA where both the vibration energy loss (1 / Q) of the fundamental wave and the third harmonic wave are low is about 80 μm to about 130 μm (range A in FIG. 21), the fundamental wave and 3 Since the loss of vibration energy of both harmonics of the crystal resonator is suppressed, the loss of vibration energy of the crystal resonator when the fundamental wave and the third harmonic are simultaneously oscillated can be suppressed.

  Furthermore, as can be seen from FIG. 21, the fundamental wave is particularly preferable because it is stable at a low 1 / Q indicating a loss of vibration energy when the inclination width XA is in the range of about 40 μm to about 120 μm. The third harmonic wave is particularly preferable because 1 / Q indicating a loss of vibration energy is as low as 3.0 × 10 −6 or less in the range where the inclination width XA is about 100 μm or more. From these results, the fundamental wave and the triple wave are obtained when the slope width XA in which the vibration energy loss (1 / Q) of both the fundamental wave and the triple wave is low is about 100 μm to about 120 μm (range B in FIG. 21). Since the loss of vibration energy in the wave piezoelectric vibrating piece 140 can be particularly suppressed, the loss of vibration energy of the crystal resonator when the fundamental wave and the third harmonic wave are simultaneously oscillated can be particularly suppressed.

7). Other Embodiments In the above description, the crystal resonator according to the present invention has been described. However, the present invention is not limited to the above-described embodiment. For example, in the above-described example, an example of a rectangular crystal piece is shown as the crystal piece. However, the planar shape of the crystal piece may be a square shape, a round shape, or an elliptical shape. In each embodiment, a rectangular crystal piece having a long side in the X ′ direction and a short side in the Z ′ direction is shown. However, the long side and the short side may be reversed. In the case of the first embodiment, the electrode shape may be a square shape or a round shape in plan view. As already described, the crystal piece may be a plano-convex type. Moreover, although the example of 4 steps | paragraphs structure was shown as an inclination part provided in the electrode for excitation, the structure of an inclination part is not restricted to this. For example, the inclined portion may have any other configuration such as a case where the number of steps is different from that illustrated, or a configuration having a slope instead of a step structure. These inclined portions can be formed by the following method, for example. That is, a method of forming a film of each step by a known metal film forming method using a plating frame, a method of applying the patterning of the formed metal film by a photolithographic technique to the film formation of each step, film formation For example, a resist pattern in which a film thickness of a portion to be an inclined portion is thinned is formed on the metal film, and a part of the metal film is processed into an inclined shape by a dry etching method using this pattern as a mask.

11: Crystal piece, 13a: Excitation electrode (first excitation electrode),
13b: Excitation electrode (second excitation electrode), 13aa, 13ba: main thickness part,
13ab, 13bb: inclined part, XA: inclined width (width of inclined part),
15: Lead electrode 20: Lead type crystal resonator, 21: Base, 23: Lead,
25: Clip terminal, 27: Conductive adhesive 30: Surface-mount type crystal unit, 31: Ceramic base,
33: Support pad 35: Conductive adhesive 41: Crystal piece of the third embodiment 51: Crystal piece of the fourth embodiment

  Here, T is the thickness of the crystal piece. Α and β are angles within a predetermined range according to the cut type (SC cut, IT cut, etc.) of the crystal piece. In addition, α is an angle with the Z ′ axis of the crystal piece as a rotation axis (see FIG. 1B), and β is an angle with the X ′ axis of the crystal piece as a rotation axis (FIG. 1 ( C)). In the following description, the positive and negative angles α and β are considered on the plus Z ′ plane and the plus X ′ plane of the crystal piece (FIGS. 1B and 1C), plus counterclockwise plus plus clockwise. Negative. These pluses and minuses determine the displacement direction of the front and back excitation electrodes. Note that the angles α and β are angles in a predetermined range for each of the C mode and the B mode when the crystal piece is a two-time rotation crystal resonator such as an SC cut.

Comparing FIGS. 3 to 5 and, as is clear from FIG. 6, the displacement distribution at the edge of the first excitation electrode 13a and the displacement distribution at the edge of the second excitation electrode 13 You can see that it changes when you change. When the angle α is 25 ° (see FIG. 4A), the displacement distribution at the edge of the first excitation electrode 13a and the displacement distribution at the edge of the second excitation electrode most closely match. I understand. From the results of many simulations conducted by the inventors, including this simulation, in the case of M-SC cut and C mode, the angle α = 25 ° and the angle β = 0.2 ° are It was found that the displacement distribution at the edge of the second excitation electrode most closely matched. However, as is apparent from FIG. 6, in consideration of the effect of improving the characteristics of the vibrator, the angle α is preferably −20 to −30 °, that is, α = 25 ± 5 °, and more preferably α = 25. It can be seen that ± 3 ° is good. Moreover, it was found that β = 0 ± 5 ° is preferable, and β = 0 ± 3 ° is more preferable. From the same simulation results, in the case of M-SC cut and in the B mode, the angles α and β are preferably α = −6 ± 5 ° and β = −17 ± 5 °, more preferably Α = −6 ± 3 ° and β = −6 ± 3 ° were found to be good.

As can be seen from FIG. 21, the relationship between the inclination width of the third harmonic wave and the loss of vibration energy (1 / Q) shows a similar tendency regardless of the thickness YA of the main thickness portion. 1 / Q indicating vibration energy loss in the range of inclination width XA from about 30 μm to about 130 μm is 8.0 × 10 −6 (“× 10 −6” is expressed as “E-6” in the graph of FIG. 21) ) It is as low as below. Further, regarding the relationship between the inclination width and vibration energy loss (1 / Q) in the fundamental wave , 1 / Q indicating vibration energy loss in the range where the inclination width XA is about 80 μm or more is 4.0 × 10 −6 or less. It is low. From these results, in the range where the inclination width XA where both the vibration energy loss (1 / Q) of the fundamental wave and the third harmonic wave are low is about 80 μm to about 130 μm (range A in FIG. 21), the fundamental wave and 3 Since the loss of vibration energy of both harmonics of the crystal resonator is suppressed, the loss of vibration energy of the crystal resonator when the fundamental wave and the third harmonic are simultaneously oscillated can be suppressed.

Furthermore, as can be seen from FIG. 21, the triple wave is particularly preferable because it is stable in a state where 1 / Q indicating a loss of vibration energy is low when the inclination width XA is in the range of about 40 μm to about 120 μm. The fundamental wave is particularly preferable because 1 / Q indicating a loss of vibration energy is as low as 3.0 × 10 −6 or less when the inclination width XA is about 100 μm or more. From these results, the fundamental wave and the triple wave are obtained when the slope width XA in which the vibration energy loss (1 / Q) of both the fundamental wave and the triple wave is low is about 100 μm to about 120 μm (range B in FIG. 21). Since the loss of vibration energy in the piezoelectric wave vibrating piece can be particularly suppressed, the loss of vibration energy of the crystal resonator when the fundamental wave and the third harmonic wave are simultaneously oscillated can be particularly suppressed.

Claims (21)

In the crystal unit that has excitation electrodes on both sides of the crystal piece and vibrates in the thickness-slip mode,
The excitation electrode is provided on the crystal piece so that the displacement distribution at the edge of the excitation electrode on one surface is the same as the displacement distribution at the edge of the excitation electrode on the other surface. Crystal oscillator. The crystal piece is a crystal piece having a thickness in the Y′-axis direction of the crystal and having the X′-Z ′ surface of the crystal as a main surface, and the excitation electrodes provided on the front and back surfaces have the same planar shape and the same size. If the excitation electrode provided on the plus Y ′ plane is defined as the first excitation electrode and the excitation electrode provided on the minus Y ′ plane is defined as the second excitation electrode, the second excitation electrode is used for the first excitation. The crystal resonator according to claim 1, wherein the crystal resonator is provided at a position satisfying the following relationship with respect to the electrode.
(1) Move the first excitation electrode along the X ′ axis of the quartz crystal in the plus X ′ direction by a distance dx given by T · tanα,
(2) Move the first excitation electrode along the Z ′ axis of the crystal in the minus Z ′ direction by a distance dy given by T · tan β,
(3) A position where the state moved in (1) and (2) above is projected on the minus Y ′ plane.
Here, T is the thickness of the crystal piece. Α and β are angles determined in advance according to the cut type of the crystal piece, α is a rotation angle on the plus Z ′ plane, and β is a rotation angle on the plus X ′ plane. The X ′ axis and the Z ′ axis are axes generated at the cutting angle of the crystal piece with respect to the crystal axes X and Y of the crystal. 2. The crystal resonator according to claim 1, wherein the crystal piece is an M-SC cut crystal piece, wherein α is α = 25 ± 5 °, and β is β = 0 ± 5 °. 2. The crystal resonator according to claim 1, wherein the crystal piece is an SC-cut crystal piece, wherein α is α = 25 ± 5 °, and β is β = 1 ± 5 °. 2. The crystal resonator according to claim 1, wherein the crystal piece is an IT cut crystal piece, wherein α is α = 24 ± 5 °, and β is β = 2 ± 5 °. 2. The crystal resonator according to claim 1, wherein the crystal piece is an AT-cut crystal piece, α is α = 0 ± 5 °, and β is β = 4 ± 5 °. The front and back excitation electrodes are electrodes having an elliptical planar shape and a predetermined elliptical ratio, and are arranged at an in-plane rotation angle δ with respect to the crystal piece. The crystal resonator according to any one of the above. The crystal piece is an M-SC cut crystal piece, the α is α = 25 ± 5 °, the β is β = 0 ± 5 °, the elliptical ratio is 1.32 ± 10%, The crystal resonator according to claim 7, wherein the in-plane angle δ is δ = −9 ± 5 °. The crystal piece is an M-SC cut crystal piece, the α is α = 25 ± 5 °, the β is β = 0 ± 5 °, the elliptical ratio is 0.91 ± 10%, The crystal resonator according to claim 7, wherein the in-plane angle δ is δ = −15 ± 5 °. The crystal piece is an M-SC cut crystal piece, the α is α = 25 ± 5 °, the β is β = 0 ± 5 °, the elliptical ratio is 0.93 ± 10%, The crystal resonator according to claim 7, wherein the in-plane angle δ is δ = −10 ± 5 °. The crystal piece is an SC cut crystal piece, the α is α = 25 ± 5 °, the β is β = 1 ± 5 °, the elliptical ratio is 1.32 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −7 ± 5 °. The crystal piece is an SC cut crystal piece, α is α = 25 ± 5 °, β is β = 1 ± 5 °, the elliptical ratio is 0.93 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −17 ± 5 °. The crystal piece is an SC cut crystal piece, the α is α = 25 ± 5 °, the β is β = 1 ± 5 °, the elliptical ratio is 0.95 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −12 ± 5 °. The crystal piece is an IT cut crystal piece, the α is α = 24 ± 5 °, the β is β = 2 ± 5 °, the elliptical ratio is 1.32 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −3 ± 5 °. The crystal piece is an IT cut crystal piece, the α is α = 24 ± 5 °, the β is β = 2 ± 5 °, the elliptical ratio is 0.95 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −38 ± 5 °. The crystal piece is an IT cut crystal piece, the α is α = 24 ± 5 °, the β is β = 2 ± 5 °, the elliptical ratio is 0.98 ± 10%, and the in-plane The crystal resonator according to claim 7, wherein the angle δ is δ = −40 ± 5 °. The excitation electrode gradually decreases in thickness from a main thickness portion formed with a constant thickness and a portion formed around the main thickness portion and in contact with the main thickness portion to an outermost periphery of the excitation electrode. Having an inclined portion formed as follows,
2. The crystal resonator according to claim 1, wherein an inclination width that is a width of the inclined portion is a length that is not less than 0.5 times and not more than 3 times a bending wavelength that is a wavelength of bending vibration that is unnecessary vibration. The excitation electrode gradually decreases in thickness from a main thickness portion formed with a constant thickness and a portion formed around the main thickness portion and in contact with the main thickness portion to an outermost periphery of the excitation electrode. Having an inclined portion formed as follows,
The inclination width, which is the width of the inclined portion, is 0.84 to 1.37 times the first bending wavelength, which is the wavelength of bending vibration in the fundamental wave of thickness shear vibration, and is the third harmonic of thickness shear vibration. 2. The crystal resonator according to claim 1, wherein the crystal resonator has a length that is not less than 2.29 times and not more than 3.71 times the second bending wavelength that is the wavelength of bending vibration.   The quartz crystal according to claim 17 or 18, wherein the inclined portion is provided only on an excitation electrode on a surface opposite to a frequency adjustment surface of the crystal resonator among excitation electrodes provided on the front and back surfaces of the crystal piece. Vibrator.   20. The crystal resonator according to claim 19, wherein the thickness of the excitation electrode on the frequency adjustment surface of the crystal resonator is smaller than the thickness of the main thickness portion of the excitation electrode on the surface opposite to the frequency adjustment surface. .   The crystal unit according to claim 17, wherein the crystal piece is a flat crystal piece.

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