Crystal vibration piece and crystal oscillator

Abstract

To provide a crystal vibration piece having a novel structure capable of suppressing reduction of a frequency variable amount, even in the case of the crystal vibration piece being a crystal vibration piece of AT cut and having peculiar inclined planes in both ends of a crystal in a Z' axis direction, and a crystal oscillator using the same.SOLUTION: A crystal vibration piece 10 comprises a crystal piece 11 of AT cut and electrodes 13 for excitation which are provided on front and rear faces of the crystal piece. Each of the front and rear faces of the crystal piece includes a principal surface part 11a in parallel with an X-Z' plane, which is specified by an X axis and a Z' axis of a crystal, and a first inclined plane 11b which is continued to the principal surface part at an angle θ1 in an end at one side along the Z' axis of the principal surface part. The electrodes for excitation are provided only on an opposed region 11aa where the principal surface parts of the front and rear faces of the crystal piece are opposed. The θ1 is an angle of θ1=3±2 degrees.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a quartz crystal resonator element capable of suppressing a decrease in the amount of frequency variation, and a quartz crystal oscillator using the same. [Background technology]

[0002] In order to cope with the increase in communication traffic in information and communications, it is essential to further increase communication speed. Therefore, there is a demand for higher frequencies for quartz crystal resonator pieces, which are the reference signal sources for information and communications, and for quartz crystal oscillators using such resonator pieces. In order to achieve high frequencies from a quartz crystal resonator that vibrates in thickness shear mode, it is necessary to make the thickness of the vibrating part thinner and thinner. However, when the thickness of the vibrating part is made thinner, the influence of stress on the vibrating part from the support part that supports the piezoelectric resonator becomes an issue.

[0003] To avoid this, for example, Patent Document 1 discloses a quartz crystal vibrating piece having a so-called one-sided frame structure, in which a vibrating part made of a thin piece and a supporting part that is thicker than the vibrating part along one side of the outer circumference of the vibrating part are integrally formed (Claim 1, Figure 1, paragraph 2, etc. of Patent Document 1). In this quartz crystal vibrating piece, the thickness of the supporting part can be made any thickness regardless of the oscillation frequency, so that the thickness of the supporting part can counter the stress of the deformation of the container and prevent fluctuations in the oscillation frequency (Patent Document 1, paragraph 33). In Patent Document 1, the one-sided frame structure is realized by a mechanical processing method (Patent Document 1, paragraphs 21 and 22, Figure 2, etc.). In recent years, the above structure can be realized by photolithography technology. On the other hand, one type of crystal oscillator is a voltage-controlled crystal oscillator (see, for example, Patent Document 2). In this type of crystal oscillator, one or both of the capacitors connected to both ends of the crystal resonator element are capacitive elements whose capacitance changes depending on the voltage, such as varicap diodes, and the frequency of the crystal oscillator is changed by varying this capacitance. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2001-144578 A [Patent Document 2] Japanese Patent Application Publication No. 8-46427 Summary of the Invention [Problem to be solved by the invention]

[0005] As is well known, the smaller the capacitance ratio C0 / C1, defined as the ratio of the series capacitance C1 to the parallel capacitance C0 of the crystal resonator blank, the greater the frequency variation. In the case of a voltage-controlled crystal oscillator, the greater the frequency adjustment range can be, so a smaller capacitance ratio of the crystal resonator blank is preferable. On the other hand, in the case of a quartz crystal resonator element that vibrates in thickness shear mode, the higher the frequency of use, the thinner the thickness, and therefore the larger the parallel capacitance C0. Furthermore, as described in the embodiment section below, some quartz crystal resonator elements manufactured by photolithography have a structure with an inclined surface that becomes thinner toward the end along the Z' axis of the quartz crystal resonator element, a so-called tapered structure, in order to ensure characteristics other than the capacitance ratio, specifically to reduce the influence of unnecessary vibration in the Z' direction. In the case of a quartz crystal resonator element with such a tapered structure, the parallel capacitance C0 becomes even larger due to the influence of the tapered structure and the arrangement of the excitation electrodes, which causes the problem of further increasing the capacitance ratio C0 / C1. This application has been made in consideration of the above points, and therefore the purpose of this application is to provide a quartz crystal vibrating piece having a new structure that can suppress a reduction in the amount of frequency variation, even if the quartz crystal vibrating piece is an AT-cut quartz crystal vibrating piece having unique inclined surfaces on both ends in the Z'-axis direction of the quartz crystal, and a quartz oscillator using the same. [Means for solving the problem]

[0006] In order to achieve this object, the first invention of this application is a quartz crystal vibrating piece comprising an AT-cut quartz crystal piece and excitation electrodes provided on the front and back surfaces of the quartz crystal piece, Each of the front and back surfaces includes a main surface portion parallel to an XZ' plane defined by the X-axis and Z'-axis of the quartz crystal, and a first inclined surface continuous with the main surface portion at an angle θ1 at one end of the main surface portion along the Z'-axis, The excitation electrodes are provided only on the opposing regions of the front and back surfaces of the quartz element where the principal surfaces face each other. However, the Z' axis is an axis defined based on the cutting angle of the AT cut with respect to the Z axis, which is the crystal axis of the quartz, and θ1 is an angle between the first inclined surface and a reference line that is parallel to the principal surfaces and aligned in the Z' direction, and is θ1 = 3±2 degrees.

[0007] The second aspect of the present invention is a crystal oscillator comprising the crystal resonator element of the first aspect of the present invention, a container for mounting the crystal resonator element, and an oscillation circuit for the crystal resonator element. In carrying out the second aspect of the present invention, it is preferable that the crystal oscillator is a voltage variable type. Effect of the Invention

[0008] According to the quartz crystal vibrating piece of this invention, both ends in the Z' direction are formed into a predetermined shape including a first inclined surface, so it is easier to reduce unwanted vibrations compared to cases where this is not the case. Also, because the excitation electrodes are provided only on the front and back surfaces of the quartz crystal vibrating piece, in the areas where the main surfaces face each other, the parallel capacitance can be made smaller compared to cases where this is not the case, so the capacitance ratio can be made smaller. As a result, it is possible to provide a quartz crystal vibrating piece and a quartz crystal oscillator with a novel structure that can reduce characteristic degradation caused by unwanted vibrations and suppress a decrease in the amount of frequency variation. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram illustrating a quartz crystal vibrating piece 10 according to an embodiment. [Diagram 2] FIG. 2 is a diagram for explaining a modified example of the quartz crystal vibrating piece of the present invention. [Diagram 3] FIG. 3 is a diagram for explaining a crystal oscillator 20 according to an embodiment. [Figure 4]FIG. 4 is a diagram for explaining an example of a method for manufacturing the quartz crystal vibrating piece 10 according to the embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, the embodiments of the inventions of this application will be described with reference to the drawings. Note that the drawings used in the description are merely schematic illustrations to the extent that these inventions can be understood. In addition, in the drawings used in the description, similar components are indicated by the same numbers, and their explanation may be omitted. Furthermore, the shapes, materials, etc. described in the following description are merely preferred examples within the scope of this invention. Therefore, each invention is not limited to only the following embodiments.

[0011] 1. Crystal resonator element according to the embodiment 1(A) to 1(C) are diagrams illustrating a quartz crystal vibrating piece 10 according to an embodiment. In particular, FIG. 1(A) is a plan view of the quartz crystal vibrating piece 10, FIG. 1(B) is a side view showing an enlarged side of the quartz crystal vibrating piece 10, and FIG. 1(C) is a cross-sectional view showing an enlarged cross section along line PP in FIG. 1(A). Here, the coordinate axes X, Y', and Z' shown in FIG. 1 are crystal axes defined by the cutting angle of the AT-cut quartz crystal piece with respect to the crystal axes X, Y, and Z of the quartz crystal. Note that the AT-cut quartz crystal piece and the Y' and Z' axes are well-known matters, and are described in, for example, the literature: "Explanation and Application of Quartz Crystal Devices." Japan Quartz Device Industry Association, March 2002, 4th Edition, p. 7, etc., so detailed description will be omitted.

[0012] The quartz crystal vibrating piece 10 of the embodiment includes an AT-cut quartz crystal piece 11 and excitation electrodes 13 provided on the front and back surfaces thereof, and has a structure described below. In the quartz crystal vibrating piece 10, each of the front and back surfaces of the quartz crystal piece 11 includes a main surface 11a parallel to the XZ' plane defined by the X-axis and Z'-axis of the quartz crystal, and a first inclined surface 11b that is continuous with the main surface 11a at an angle θ1 at one end of the main surface 11a along the Z'-axis of the quartz crystal. The excitation electrodes 13 are provided only on the facing regions 11aa of the quartz crystal piece 11 where the main surfaces 11a of the front and back surfaces face each other. Here, the Z' axis is an axis defined based on the cutting angle of the AT cut with respect to the Z axis, which is the crystal axis of quartz, and is typically inclined at about 35 degrees with respect to the Z axis of quartz. Also, θ1 is the angle between the reference line 11x, which is defined as a line parallel to the main surface 11a and along the Z' direction, and the first inclined surface 11b, and is an angle in the range of θ1 = 3 ± 2 degrees.

[0013] In this invention, the excitation electrodes 13 are provided only on the opposing regions 11aa on the front and back of the crystal blank 11 where the principal surfaces 11a face each other, so the parallel capacitance can be made smaller than when the excitation electrodes 13 are provided across the first inclined surface 11b. Note that what is indicated by 13a in Fig. 1(A) is an extraction electrode. The extraction electrode 13a is extracted from the excitation electrodes 13 to one of the short sides of the crystal blank 11. Furthermore, if the angle is θ1=3±2 degrees, even if unwanted vibration occurs along the Z' axis in the quartz crystal vibrating piece 10, the energy of the unwanted vibration is attenuated in the portion inclined at angle θ1, thereby reducing adverse effects on the desired main vibration. The reason for forming the inclined surface of θ=3±2 degrees will be explained in the manufacturing method example section below.

[0014] In addition, it is preferable that the dimension X2 of the excitation electrode 13 along the X-axis of the crystal is longer than the dimension Z2 along the Z' direction. Specifically, it is preferable that the excitation electrode 13 is an ellipse with the long axis along the X-axis of the crystal as shown in FIG. 1(A), or a rectangle in a plan view with the long side along the X-axis direction as shown in FIG. 2(A). If the dimension X2 of the excitation electrode 13 along the X-axis of the crystal is longer than the dimension Z2 along the Z' direction, the area of ​​the excitation electrode can be expanded while suppressing the increase in parallel capacitance. Since the increase in parallel capacitance can be suppressed, the increase in the capacitance ratio can be suppressed and the area of ​​the vibration region can be secured, so the deterioration of the crystal impedance of the crystal vibrating piece can be prevented. Furthermore, when the dimension of first inclined surface 11b projected onto reference line 11x is defined as Z1 and the dimension along the Z' direction of area 11aa facing principal surface 11a of crystal piece 11 is defined as Z2, it is preferable that Z1 / Z2 is 0.30 to 0.45. This is because when Z1 / Z2 is in this range, it is easy to achieve both a sufficient vibration area and the effect of damping unwanted vibrations in the area where first inclined surface 11b is located.

[0015] In the case of the quartz crystal vibrating piece 10 of the embodiment, the quartz crystal piece 11 is provided with a second inclined surface 11c. Specifically, the quartz crystal piece 11 is provided with a second inclined surface 11c that is connected to the first inclined surface 11b and is continuous with the main surface portion 11a on the opposite side of the first inclined surface with an interior angle θ2=43±2 degrees. Moreover, the quartz crystal piece 11 is shaped to be point symmetrical when the rotation axis that passes through the center point O of the quartz crystal piece 11 in the Z' direction and is parallel to the X-axis of the quartz crystal is used as the center of rotation. Therefore, in the case of the quartz crystal vibrating piece 10 of the embodiment, the quartz crystal piece 11 has a convex structure in which both ends along the Z' axis are composed of the first inclined surface 11b and the second inclined surface 11c. With this structure, unwanted vibrations are more effectively attenuated, which is preferable for improving the characteristics of the quartz crystal vibrating piece 10.

[0016] As shown in FIG. 1B, the quartz crystal vibrating piece 10 of the embodiment includes a vibrating portion 11d including an area including an excitation electrode 13, and a supporting portion 11e that is connected to the vibrating portion 11d at one end in the X-axis direction of the quartz crystal and has a thickness (dimension in the Y' direction) greater than that of the vibrating portion 11d, and the vibrating portion 11d and the supporting portion 11e are integrally formed. In addition, the quartz crystal vibrating piece 10 includes an intermediate portion 11f between the vibrating portion 11d and the supporting portion 11e, the thickness of which increases from the vibrating portion 11d toward the supporting portion 11e. In addition, the intermediate portion 11f has an inclined surface 11g. When the interior angle between the inclined surface 11g and the Z' axis of the quartz crystal is defined as θ3, θ3=32±2 degrees.

[0017] In the case of the quartz crystal vibrating piece 10 having the support portion 11e, it has a so-called one-sided frame structure, so that even if the vibrating portion 11d is made thin for high frequencies, the influence of the fixing portion on the vibrating portion 11d when the quartz crystal vibrating piece 10 is fixed to a container (see FIG. 2) with a conductive adhesive or the like can be mitigated, which is preferable for improving the characteristics of the quartz crystal vibrating piece. In addition, if the intermediate portion 11f is provided, the influence of the fixing portion on the vibrating portion 11d can be further mitigated, which is preferable. The angle θ3 between the inclined surface 11g and the Z' axis of the quartz crystal is set to 32±2 degrees because the reproducibility of the angle θ3 is good when the quartz crystal vibrating piece 10 is formed by photolithography and wet etching. In the above embodiment, the quartz crystal vibrating piece 10 is configured with two surfaces, the first inclined surface 11b and the second inclined surface 11c, at both ends along the Z' axis of the quartz crystal, but the present invention can also be applied to a quartz crystal vibrating piece 10 in which both ends along the Z' axis of the quartz crystal are configured with a total of three surfaces, the first inclined surface 11b and the other two inclined surfaces, as shown in Figure 2(B). The angles of these three surfaces can be controlled by devising the manufacturing conditions for the photoetching and wet etching techniques used when forming the quartz crystal vibrating piece 10.

[0018] 2. Crystal oscillator according to embodiment Next, the crystal oscillator of the embodiment will be described. Figures 3(A) to 3(C) are explanatory diagrams. In particular, Figure 3(A) is a plan view of the crystal oscillator 20 of the embodiment, Figure 3(B) is a cross-sectional view taken along line QQ in Figure 3(A), and Figure 3(C) is a block diagram showing an example of an oscillation circuit 23. The crystal oscillator 20 of the embodiment includes the above-mentioned crystal vibrating piece 10, a container 21 in which the crystal vibrating piece 10 is mounted, an oscillator circuit 23 for the crystal vibrating piece 10, a conductive adhesive 25 that connects the crystal vibrating piece 10 to the adhesive pad 21a of the container 21, and a lid member 27 that seals the container 21.

[0019] In this case, the container 21 includes the above-mentioned adhesive pads 21a, a recess 21b that contains the quartz crystal vibrating piece 10, and an external connection terminal 21c provided on the outer bottom surface of the container 21. The adhesive pads 21a and the external connection terminals 21c are electrically connected by via wiring or castellation (not shown). The container 21 can be configured, for example, as a well-known ceramic package. The structure of the container 21 is not limited to the example of FIG. 2, and other suitable structures may be used. For example, the container 21 may have a structure in which a quartz chamber that houses the quartz crystal vibrating piece and an IC chamber that houses the oscillation circuit 23 are separated, for example, a structure in which the quartz chamber and the IC chamber are stacked back to back and the cross section cut in the stacking direction is H-shaped. The oscillator circuit 23 may be of any type depending on the specifications of the crystal oscillator 20. In this embodiment, the oscillator circuit 23 is of a voltage-controlled type. Specifically, The crystal oscillator 20 includes a feedback circuit and a capacitive element 23a whose capacitance can be changed by the control voltage Vc. The crystal oscillator 20 of the embodiment includes a crystal vibrating piece 10 having a structure that can reduce the capacitance ratio. Therefore, a voltage-controlled crystal oscillator with a wide frequency variable range relative to the control voltage Vc can be realized. The oscillation circuit shown in FIG. 3C is an example. Of course, other configurations are also possible, such as further including a capacitive element 23a in the capacitor on the output side of the oscillation circuit.

[0020] 3. Explanation of manufacturing method examples We will now explain an example of a method for manufacturing the quartz crystal vibrating piece 10 of the embodiment, including the fact that the quartz crystal vibrating piece has a tapered structure, in which the thickness of the quartz crystal vibrating piece becomes thinner toward the end of the quartz crystal vibrating piece in order to enhance the energy trapping effect, as explained in the Problems section. Figures 4(A) to (E) are schematic process diagrams for explaining this, in which in particular Figure 4(A) is an overall view of quartz crystal wafer 31, Figures 4(B) and (D) are partially enlarged views of a portion M of quartz crystal wafer 30, and Figures 4(C) and (E) are cross-sectional views taken along lines PP and QQ in Figures 4(B) and (D).

[0021] In order to form a large number of crystal vibrating pieces having a one-sided frame structure, which are crystal vibrating pieces 10 according to the present invention, in a matrix on an AT-cut crystal wafer 31 (FIG. 4(A)), a mask 33 for forming the outer shape of the crystal vibrating pieces is formed (FIG. 4(B)) using a metal film and photoresist on the front and back of the crystal wafer 31. Specifically, the mask 33 for forming the outer shape is formed over each of the following areas of the crystal wafer 31: an area 33a where the crystal vibrating pieces are to be formed, a frame portion 33b that connects the crystal vibrating pieces, and an area 33c where a bridge portion is to be formed that connects the area 33a where the crystal vibrating pieces are to be formed and the frame portion 33b.

[0022] When the quartz crystal wafer 31 on which the mask 33 for forming the outer shape is formed is immersed in a hydrofluoric acid-based etchant for a predetermined time, the areas of the quartz crystal wafer 31 other than the area 33a where the quartz crystal vibrating piece is to be formed, the frame portion 33b, and the bridge portion 33c are dissolved. As a result, the area 33a where the quartz crystal vibrating piece is to be formed becomes a rectangular parallelepiped with the same thickness as the wafer (FIG. 4(C)). Next, a mask 35 for forming the vibrating portion is formed on the quartz wafer 31 (FIG. 4(D)). The mask 35 exposes the area 33a where the quartz vibrating piece is to be formed into the vibrating portion 11d (see also FIG. 1(B)) and covers the other areas, the frame portion 33b, and the bridge portion 33c.

[0023] Next, the quartz crystal wafer 31 with the vibration portion forming mask 35 provided thereon is immersed in a hydrofluoric acid-based etchant for a predetermined time. The predetermined time is the time for the thickness of the region where the vibration portion 11d is to be formed to reach a thickness (thickness indicated by t in FIG. 4(E)) that provides the oscillation frequency required for the quartz crystal vibrating piece. As a result, as shown in FIG. 4(E), a quartz crystal piece 11 is obtained that has a one-sided frame structure in which the vibration portion 11d having a predetermined thickness and the support portion 11e having a thickness thicker than the vibration portion 11d are integrally formed. During the above-mentioned etching for the specified time to form the vibration portion 11d, due to the fact that the etching rate for a hydrofluoric acid-based etchant differs for each crystal axis of the quartz, i.e., due to etching anisotropy, a special shape is formed at both ends of the quartz in the Z'-axis direction of the quartz of the quartz piece 11, having a first inclined surface 11b and a second inclined surface 11c, as described using Figure 1(C), and convex at both ends in the Z'-axis direction. Next, excitation electrodes 13 are formed on each of the quartz crystal pieces 11 on the quartz crystal wafer 31 by known film formation and photoetching techniques. After that, each of the quartz crystal pieces 10 is broken off from the quartz crystal wafer 31 at the bridge portion 33c, thereby forming the quartz crystal piece 10 described with reference to FIG.

[0024] Examples and Comparative Examples (Example) In order to confirm the effect of the present invention, particularly in terms of reducing the capacitance ratio, a number of crystal vibrating pieces 10 were prototyped under the following conditions. The dimension X of the crystal axis of the crystal vibrating piece 10 in the X direction (see FIG. 1; the same applies below) is about 1300 μm, the dimension X1 of the crystal of the vibrating part 11d in the X direction is about 1060 μm, the dimension Z3 of the crystal axis of the crystal vibrating piece 10 in the Z' direction is about 880 μm, the dimension Z2 of the crystal axis of the facing region 11aa in the Z' direction is about 500 μm, the dimension Z1 of the first inclined surface is about 190 μm, the excitation electrode 13 is elliptical, the dimension X2 in the major axis direction is about 640 μm, and the dimension Z2 in the minor axis direction (same as the facing region 11aa) is about 450 μm. The excitation electrode 13 is disposed so that its center point is offset from the center point of the crystal piece 11 by ΔX ≒ 185 μm toward the tip side of the crystal piece 11. The dimension of the support 11e along the X-axis of the crystal is X-X1, and the thickness of the support is about 55 μm. The oscillation frequency of the crystal vibrating piece 10 is about 122 MHz. Therefore, the thickness of the vibrating portion 11d is about 12 μm. In this embodiment, Z1 / Z2=190 / 450≈0.42.

[0025] (Comparative Example) As a comparative example, a quartz crystal vibrating piece was prepared using the same quartz crystal piece as in the example, but with a circular excitation electrode having a diameter of 550 μm. That is, a plurality of quartz crystal vibrating pieces were prepared, each of which had an excitation electrode extending to the first inclined surface 11b. (Measurement results) As characteristics of each of the quartz crystal resonator pieces of the example and the comparative example, the crystal impedance (abbreviated as CI), the parallel capacitance C0, and the series capacitance C1 were measured. The capacitance ratio was calculated from the parallel capacitance C0 and the series capacitance C1. The average CI of the quartz crystal resonator element of the example was 17.4Ω, the average parallel capacitance was 0.96, the average series capacitance was 3.92, and the average capacitance ratio was 245. The average CI of the quartz crystal resonator element of the comparative example was 19.0Ω, the average parallel capacitance was 1.03, the average series capacitance was 3.96, and the average capacitance ratio was 260. In the case of the embodiment, the capacitance ratio can be reduced to 94% and the CI can be reduced to 89% compared to the comparative example. In the embodiment, the excitation electrodes are provided only on the facing region 11aa of the main surface and not on the first inclined surface 11b, so that the increase in parallel capacitance can be suppressed, and as a result, the capacitance ratio can be reduced. Moreover, since the excitation electrodes are provided only on the facing region 11aa of the main surface and not on the first inclined surface 11b, in addition to the unwanted vibration suppression effect due to the convex structure at both ends in the Z' direction of the quartz crystal piece, it is believed that the vibration energy trapping can be further strengthened, and an improvement in CI is obtained. [Explanation of symbols]

[0026] 10: Crystal piece according to an embodiment 11: Crystal piece 11a: Main surface part 11aa: Opposing area of ​​main surface part 11b: First slope part 11c: Second slope part 11e: Support part 11f: Intermediate part 11g: Middle inclined surface 11x: Reference line 13: Excitation electrode 13a: Extraction electrode 20: Crystal oscillator of the embodiment 21: Container 23: Oscillator circuit 23a: Variable capacitance element 25: Conductive adhesive 27: Lid material

Claims

1. A quartz crystal resonator element, The crystal element is an AT-cut crystal piece, and excitation electrodes are provided on the front and back surfaces of the crystal piece. Each of the front and back surfaces includes a main surface portion parallel to an X-Z' plane defined by the X-axis and Z'-axis of the quartz crystal, and a first inclined surface continuous with the main surface portion at an angle θ1 at one end of the main surface portion along the Z'-axis, The quartz crystal vibrating piece is characterized in that the excitation electrodes are provided only on the opposing regions of the front and back surfaces of the quartz crystal piece where the principal surfaces of the quartz crystal piece face each other, where the Z' axis is an axis defined based on the cutting angle of the AT cut with respect to the Z axis, which is the crystal axis of the quartz crystal, and the θ1 is an angle between the first inclined surface and a reference line that is parallel to the principal surfaces and aligned in the Z' direction, and is θ1 = 3 ± 2 degrees.

2. 2. The quartz crystal resonator element according to claim 1, wherein the excitation electrode has a dimension along the X-axis of the quartz crystal that is greater than a dimension along the Z' direction.

3. 2. The quartz crystal resonator element according to claim 1, wherein the excitation electrode has an elliptical shape with its major axis aligned along the X-axis of the quartz crystal.

4. The quartz crystal vibrating piece according to claim 1, characterized in that, when the dimension of the first inclined surface projected onto the reference line is defined as Z1 and the dimension of the opposing region along the Z' direction is defined as Z2, Z1 / Z2 is 0.30 to 0.

45.

5. 2. The quartz crystal piece according to claim 1, further comprising a second inclined surface that is connected to the first inclined surface and is connected to the main surface portion on the opposite side thereof at an interior angle θ2 = 43 ± 2 degrees.

6. 2. The quartz crystal piece according to claim 1, wherein the quartz crystal piece has a shape that is point-symmetrical with respect to a rotation axis that passes through a center point O of the quartz crystal piece in the Z' direction and is parallel to the X-axis.

7. 2. The quartz crystal vibrating piece according to claim 1, further comprising: a vibrating portion including an area having the excitation electrodes; and a supporting portion connected to the vibrating portion at one end in the X-axis direction of the quartz crystal and having a thickness greater than that of the vibrating portion, the supporting portion being integrally formed with the vibrating portion.

8. 2. The quartz crystal vibrating piece according to claim 1, further comprising: a vibrating portion including an area having the excitation electrode; and a supporting portion connected to the vibrating portion at one end in the X-axis direction of the quartz crystal and having a thickness greater than that of the vibrating portion; the vibrating portion and the supporting portion are integrally formed; and an intermediate portion is provided between the vibrating portion and the supporting portion, the thickness of which increases from the vibrating portion toward the supporting portion.

9. The quartz crystal vibrating piece comprises a vibrating section including an area having the excitation electrodes, and a supporting section connected to the vibrating section at one end in the X-axis direction of the quartz crystal and having a thickness greater than that of the vibrating section, and the vibrating section and the supporting section are integrally formed, a middle portion between the vibration portion and the support portion, the middle portion having a thickness that increases from the vibration portion toward the support portion; 2. The quartz crystal vibrating piece according to claim 1, wherein the intermediate portion has an inclined surface extending from the vibrating portion toward the support portion, and when the interior angle formed by the inclined surface and the Z' axis is defined as θ3, θ3 = 32 ± 2 degrees.

10. 10. A crystal oscillator comprising: the crystal resonator piece according to claim 1; a container for mounting the crystal resonator piece; and an oscillation circuit for the crystal resonator piece.

11. 11. The crystal oscillator according to claim 10, wherein the oscillation circuit includes a variable capacitance element, and the crystal oscillator is a voltage-controlled crystal oscillator.

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