Vibration piece and vibration device

Abstract

To provide a vibration piece and a vibration device excellent in G-sensitivity characteristics.SOLUTION: A vibration piece 3 is formed of an AT-cut crystal substrate having a surface 31 orthogonal to a Y'-axis. When the length from an excitation electrode 38-side outer edge of a first portion 35 of a slit 34 to the other end in a first direction of the AT-cut crystal substrate is defined as Lx, the length of a second portion 36 as L1, and the length of a third portion 37 as L2, L1 / Lx and L2 / Lx satisfy any one of formula (1) to formula (8).SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a vibrating element and a vibrating device. [Background technology]

[0002] For example, Patent Document 1 discloses a piezoelectric substrate in which a support portion has two beam portions extending from the other end along the free end with the vibration substrate sandwiched therebetween, a first connecting portion connecting the other end of the vibration substrate to the two beam portions, and a second connecting portion connecting the tip ends of the two beam portions extending beyond the free end, and a fixing portion is provided on the second connecting portion. In other words, a U-shaped slit is formed through the outer periphery of the vibration substrate, thereby reducing the transmission of residual stress to the vibration substrate when the fixing portion is bonded to a package substrate via a bonding member. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2012-169890 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the piezoelectric substrate described in Patent Document 1 reduces the influence of support stress by providing a U-shaped slit between the support portion and the vibration substrate, but has the problem that no consideration is given to G sensitivity characteristics. [Means for solving the problem]

[0005] The vibrating piece is made of an AT-cut quartz substrate having a plane orthogonal to the Y' axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating by a predetermined angle around the X axis of an orthogonal coordinate system (X, Y, Z). It includes a support portion provided at one end in a first direction along the X axis, an excitation portion arranged in parallel with the support portion along the first direction and having excitation electrodes disposed on the plane, and a slit having an opening on the plane. The slit is provided between the support portion and the excitation electrodes and includes a first portion extending along a second direction intersecting the first direction, a second portion connected to one end of the first portion in the second direction and disposed on one outer edge side of the excitation electrodes in the second direction and extending along the first direction, and a third portion connected to the other end of the first portion in the second direction and disposed on the other outer edge side of the excitation electrodes in the second direction and extending along the first direction. When the length from the outer edge on the excitation electrode side of the first portion of the slit to the other end of the AT-cut quartz substrate in the first direction is Lx, the length of the second portion is L1, and the length of the third portion is L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (1) to (8). 0.0 < L1 / Lx < 0.34 and 0.0 < L2 / Lx ≤ 1.294×L1 / Lx + 0.34 ··· (1) 0.34 ≤ L1 / Lx < 0.55 and 0.857×L1 / Lx - 0.29 ≤ L2 / Lx ≤ 0.78 ··· (2) 0.55 ≤ L1 / Lx < 0.61 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.78 ··· (3) 0.61 ≤ L1 / Lx < 0.80 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.895×L1 / Lx + 0.23 ··· (4) 0.80 ≤ L1 / Lx < 0.83 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.95 ··· (5) 0.83 ≤ L1 / Lx < 0.89 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ -1.167×L1 / Lx + 1.51 ··· (6) 0.83 ≤ L1 / Lx < 0.89 and 1.167×L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95 ··· (7) 0.89 ≦ L1 / Lx ≦ 0.95 and 1.167 × L1 / Lx - 0.35 ≦ L2 / Lx ≦ 0.95 ···(8)

[0006] The vibrating piece is made of an AT-cut crystal substrate having a plane orthogonal to the Y' axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating by a predetermined angle around the X axis of the orthogonal coordinate system (X, Y, Z). It includes a support portion provided at one end in the first direction along the X axis, an excitation portion arranged side by side with the support portion along the first direction and having excitation electrodes disposed on the plane, and a slit having an opening on the plane. The slit is provided between the support portion and the excitation electrodes, and includes a first portion extending along a second direction intersecting the first direction, a second portion connected to one end of the first portion in the second direction and disposed on one outer edge side of the excitation electrodes in the second direction and extending along the first direction, and a third portion connected to the other end of the first portion in the second direction and disposed on the other outer edge side of the excitation electrodes in the second direction and extending along the first direction. When the length from the outer edge on the excitation electrode side of the first portion of the slit to the other end of the AT-cut crystal substrate in the first direction is Lx, the length of the second portion is L1, and the length of the third portion is L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (9) to (16). 0.0 < L1 / Lx < 0.12 and 0.0 < L2 / Lx ≦ 1.043 × L1 / Lx + 0.10 ···(9) 0.12 ≦ L1 / Lx < 0.23 and 1.061 × L1 / Lx - 0.13 ≦ L2 / Lx ≦ 1.043 × L1 / Lx + 0.10 ···(10) 0.23 ≦ L1 / Lx < 0.41 and 1.061 × L1 / Lx - 0.13 ≦ L2 / Lx ≦ 1.556 × L1 / Lx - 0.02 ···(11) 0.41 ≦ L1 / Lx < 0.45 and 1.061 × L1 / Lx - 0.13 ≦ L2 / Lx ≦ 0.62 ···(12) 0.45 ≦ L1 / Lx < 0.54 and 0.556 × L1 / Lx + 0.10 ≦ L2 / Lx ≦ 0.62 ···(13) 0.54≦L1 / Lx<0.61 and 0.40≦L2 / Lx≦0.62 (14) 0.61≦L1 / Lx<0.68 and 0.40≦L2 / Lx≦0.571×L1 / Lx+0.27 (15) 0.68≦L1 / Lx≦0.75 and 0.571×L1 / Lx+0.01≦L2 / Lx≦0.571×L1 / Lx+0.27 (16)

[0007] The vibrating device includes a vibrating element made of the above-described AT-cut quartz crystal substrate, and a substrate to which the support portion of the vibrating element is attached. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a plan view showing a schematic structure of a vibration device according to a first embodiment. [Figure 2] Cross-sectional view taken along line A1-A1 in Figure 1. [Figure 3] FIG. 2 is a plan view showing a schematic structure of a vibrating element included in the vibrating device according to the first embodiment. [Figure 4] FIG. 4 is a plan view illustrating an in-plane rotation angle Ψ of the vibrating element. [Figure 5] FIG. 10 is a graph showing the G sensitivity of the vibrating element with respect to L1 / Lx and L2 / Lx. [Figure 6] FIG. 10 is a plan view showing a schematic structure of a vibration device according to a second embodiment. [Figure 7] FIG. 10 is a plan view showing a schematic structure of a resonation device according to a third embodiment. [Figure 8] Cross-sectional view taken along line A2-A2 in Figure 7. DETAILED DESCRIPTION OF THE INVENTION

[0009] 1. First embodiment First, a resonator device 1 according to a first embodiment will be described with reference to Fig. 1 to Fig. 5, taking as an example a resonator in which a resonator element 3 is housed in a substrate 10 and a lid body 20. Note that Fig. 1 illustrates a state in which the lid body 20 is removed for the convenience of explaining the internal configuration of the resonator device 1.

[0010] For ease of explanation, the following drawings of the vibration devices 1, 1a, and 1c show three mutually perpendicular axes: an X axis, a Y axis, and a Z axis. The direction along the X axis is referred to as the "X direction," the direction along the Y axis as the "Y direction," and the direction along the Z axis as the "Z direction." The tip end of the arrow in each axial direction is referred to as the "plus side," and the base end as the "minus side."

[0011] Furthermore, for ease of explanation, FIGS. 3 and 4 illustrate three mutually orthogonal crystal axes corresponding to the crystal axes of quartz: the X-axis, the Y'-axis, and the Z'-axis. The direction along the X-axis is referred to as the "X-direction," the direction along the Y'-axis as the "Y'-direction," and the direction along the Z'-axis as the "Z'-direction." The tip end of each axial arrow is also referred to as the "plus side," and the base end as the "minus side." In this embodiment, the first direction is the X-direction, and the second direction is the Z'-direction. In the following drawings of the resonation devices 1, 1a, and 1c, the X-axis coincides with the X-axis of the crystal, the Y-axis coincides with the Z'-axis of the crystal, and the Z-axis coincides with the Y'-axis of the crystal.

[0012] As shown in FIGS. 1 and 2, the resonator device 1 includes a substrate 10, a lid 20, and a resonator element 3.

[0013] The substrate 10 has a third surface 13 and a fourth surface 14, which are opposite surfaces, and the third surface 13 faces the vibrating element 3. Two electrode pads 11 and 12 that join the vibrating element 3 are arranged side by side along the Y direction on the third surface 13, and a plurality of external terminals 15 used for supplying power and outputting frequencies are provided on the fourth surface 14. The electrode pads 11 and 12 and the external terminals 15 are electrically connected by wiring or through electrodes (not shown). Silicon is a suitable material for the substrate 10, but glass, ceramic, etc. may also be used.

[0014] The lid 20 has a recess 21 that opens toward the substrate 10. An end face of the lid 20 surrounding the opening of the recess 21 is joined to the third surface 13 of the substrate 10 via a joining member 25, thereby forming a housing space 22 that houses the vibrating element 3 together with the substrate 10. The lid 20 and the substrate 10 may be joined directly without using the joining member 25. The inside of the housing space 22 is in a reduced pressure state, preferably a state closer to a vacuum. This reduces viscous resistance and improves the oscillation characteristics of the vibrating element 3. The inside of the housing space 22 may be at atmospheric pressure, for example, in an N2 purged state. Silicon is a suitable material for the lid 20, but glass, ceramic, etc. may also be used.

[0015] As shown in FIG. 3, the vibrating element 3 includes a quartz crystal substrate 30, an excitation electrode 38, a first connection electrode 41, and a second connection electrode 42. The quartz crystal substrate 30 is an AT-cut quartz crystal substrate. An AT-cut quartz crystal substrate has three crystal axes, X, Y, and Z, which are perpendicular to each other; the X axis is called the electrical axis, the Y axis is called the mechanical axis, and the Z axis is called the optical axis. It has a surface 31 that is perpendicular to the Y' axis of the new Cartesian coordinate system (X,Y',Z') obtained by rotating it counterclockwise by a predetermined angle, for example, about 35°15', around the X axis of the Cartesian coordinate system (X,Y,Z).

[0016] The quartz crystal substrate 30 is rectangular in plan view, with the X direction as the long side direction, the Z' direction as the short side direction, and the Y' direction as the thickness direction. The plane 31 including the X axis and the Z' axis perpendicular to the Y' axis is the main surface, and thickness-shear vibration is excited on the main surface as the main vibration.

[0017] The in-plane rotation angle Ψ of the quartz crystal substrate 30 is 0° or 180°. The in-plane rotation angle Ψ of the quartz crystal substrate 30 is the angle between the X-axis and an imaginary line 50 passing through the center of the support portion 33 and the center of the excitation electrode 38 in a plan view, as shown in FIG.

[0018] In a plan view, the quartz crystal substrate 30 includes a support portion 33 provided at one end in a first direction, which is the X direction, an excitation portion 32 aligned with the support portion 33 along the first direction and having an excitation electrode 38 arranged on a surface 31, and a slit 34 having an opening on the surface 31.

[0019] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b, which are opposite surfaces, with the second surface 31b facing the third surface 13 of the substrate 10. An excitation electrode 38, two first connection electrodes 41, and a second connection electrode 42 are provided on the second surface 31b, which is one surface 31 of the quartz substrate 30. The excitation electrode 38 is provided on the excitation portion 32, and the first connection electrode 41 and the second connection electrode 42 are provided on the support portion 33. The first connection electrode 41 and the second connection electrode 42 are arranged side by side along one short side of the quartz substrate 30. The excitation electrode 38 is provided on the first surface 31a, which is the other surface 31 of the quartz substrate 30.

[0020] The excitation electrode 38 provided on the second surface 31b is electrically connected to a first connection electrode 41 via a lead electrode 39. The excitation electrode 38 provided on the first surface 31a is electrically connected to a second connection electrode 42 provided on the second surface 31b via the lead electrode 39 and a side surface electrode 40 provided on the side surface on the negative side in the X direction of the quartz crystal substrate 30. The excitation electrode 38 provided on the first surface 31a and the excitation electrode 38 provided on the second surface 31b are arranged to overlap in a plan view.

[0021] A slit 34 penetrating from the second surface 31b of one surface 31 to the first surface 31a of the other surface 31, which is the back side of the one surface 31, is provided between the support portion 33 and the excitation electrode 38. The slit 34 includes a first portion 35 extending along a second direction, which is the Z' direction intersecting with the first direction, a second portion 36 connected to one end of the first portion 35 in the second direction, disposed on one outer edge side of the excitation electrode 38 in the second direction, and extending along the first direction, and a third portion 37 connected to the other end of the first portion 35 in the second direction, disposed on the other outer edge side of the excitation electrode 38 in the second direction, and extending along the first direction. Because the slit 34 is provided between the support portion 33 and the excitation electrode 38, it is possible to suppress transmission of distortion generated by bonding the vibrating element 3 to the substrate 10 and stress associated with temperature changes to the excitation portion 32.

[0022] 1 and 2, the support portion 33 of the resonator element 3 and the substrate 10 are joined via conductive bonding members 43 and 44. Specifically, the conductive bonding member 43 bonds and electrically connects the first connection electrode 41 arranged on the support portion 33 to the electrode pad 11, and the conductive bonding member 44 bonds and electrically connects the second connection electrode 42 arranged on the support portion 33 to the electrode pad 12. The conductive bonding members 43 and 44 are made of materials such as metal bumps, solder, and conductive adhesive.

[0023] Next, the relationship between the G sensitivity and the lengths of the second portion 36 and the third portion 37 of the slit 34 when the in-plane rotation angle Ψ of the quartz substrate 30 is set to 0° or 180° will be described with reference to FIG.

[0024] As shown in FIG. 3, FIG. 5 shows the result of simulating the G sensitivity with respect to L1 / Lx and L2 / Lx when the length from the outer edge on the excitation electrode 38 side of the first portion 35 of the slit 34 to the other end of the crystal substrate 30 in the first direction is Lx, the length of the second portion 36 is L1, and the length of the third portion 37 is L2. The G sensitivity is Γ obtained by taking the square root of the sum of the squares of the G sensitivities in the X direction, Y direction, and Z direction. In addition, in region A, Γ is 0.0 ppb / G or more and less than 0.3 ppb / G; in region B, Γ is 0.3 ppb / G or more and less than 0.6 ppb / G; in region C, Γ is 0.6 ppb / G or more and less than 0.9 ppb / G; in region D, Γ is 0.9 ppb / G or more and less than 1.2 ppb / G.

[0025] From FIG. 5, the ranges of L1 / Lx and L2 / Lx for which the G sensitivities in the X direction, Y direction, and Z direction can be less than ±0.6 ppb / G respectively are the cases where L1 / Lx and L2 / Lx satisfy any of the following formulas (1) to (8). 0.0 < L1 / Lx < 0.34 and 0.0 < L2 / Lx ≤ 1.294×L1 / Lx + 0.34 ··· (1) 0.34 ≤ L1 / Lx < 0.55 and 0.857×L1 / Lx - 0.29 ≤ L2 / Lx ≤ 0.78 ··· (2) 0.55 ≤ L1 / Lx < 0.61 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.78 ··· (3) 0.61 ≤ L1 / Lx < 0.80 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.895×L1 / Lx + 0.23 ··· (4) 0.80 ≤ L1 / Lx < 0.83 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.95 ··· (5) 0.83 ≤ L1 / Lx < 0.89 and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ -1.167×L1 / Lx + 1.51 ··· (6) 0.83 ≤ L1 / Lx < 0.89 and 1.167×L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95 ··· (7) 0.89 ≤ L1 / Lx ≤ 0.95 and 1.167×L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95 ··· (8)

[0026] As described above, since the vibration device 1 of the present embodiment includes the vibrating piece 3 in which the in-plane rotation angle Ψ is 0° or 180°, and the ratios L1 / Lx and L2 / Lx of the length L1 of the second portion 36 and the length L2 of the third portion 37 of the slit 34 to the length Lx of the excitation portion 32 satisfy any one of the formulas (1) to (8), the influence of the support stress can be reduced, and G sensitivity characteristics in which the G sensitivities in the X direction, Y direction, and Z direction are each less than ±0.6 ppb / G can be obtained.

[0027] 2. Second Embodiment Next, the vibration device 1a according to the second embodiment will be described with reference to FIG. 6. In FIG. 6, for convenience of explaining the internal configuration of the vibration device 1a, a state in which the lid body 20 is removed is illustrated.

[0028] The vibration device 1a of the present embodiment is the same as the vibration device 1 of the first embodiment except that the formulas satisfying L1 / Lx and L2 / Lx of the vibrating piece 3a are different. Hereinafter, the description will focus on the differences from the above-described first embodiment, and the description of the same matters will be omitted.

[0029] As shown in FIG. 6, the vibration device 1a includes a substrate 10, a lid body 20, and a vibrating piece 3a.

[0030] The vibrating piece 3a of the present embodiment has an in-plane rotation angle Ψ of 0° or 180°, and the relationship between the lengths L1 and L2 of the second portion 36 and the third portion 37 of the slit 34 and the G sensitivity is the same as that in FIG. 5. Therefore, from FIG. 5, the ranges of L1 / Lx and L2 / Lx that can make the G sensitivities in the X direction, Y direction, and Z direction less than ±0.3 ppb / G are the cases where L1 / Lx and L2 / Lx satisfy any one of the following formulas (9) to (16). 0.0 < L1 / Lx < 0.12 and 0.0 < L2 / Lx ≦ 1.043 × L1 / Lx + 0.10 ··· (9) 0.12 ≦ L1 / Lx < 0.23 and 1.061 × L1 / Lx - 0.13 ≦ L2 / Lx ≦ 1.043 × L1 / Lx + 0.10 ··· (10) 0.23≦L1 / Lx<0.41 and 1.061×L1 / Lx-0.13≦L2 / Lx≦1.556×L1 / Lx-0.02 (11) 0.41≦L1 / Lx<0.45 and 1.061×L1 / Lx-0.13≦L2 / Lx≦0.62 (12) 0.45≦L1 / Lx<0.54 and 0.556×L1 / Lx+0.10≦L2 / Lx≦0.62 (13) 0.54≦L1 / Lx<0.61 and 0.40≦L2 / Lx≦0.62 (14) 0.61≦L1 / Lx<0.68 and 0.40≦L2 / Lx≦0.571×L1 / Lx+0.27 (15) 0.68≦L1 / Lx≦0.75 and 0.571×L1 / Lx+0.01≦L2 / Lx≦0.571×L1 / Lx+0.27 (16)

[0031] As described above, the vibration device 1a of this embodiment has a vibration element 3a in which the in-plane rotation angle Ψ is 0° or 180° and L1 / Lx and L2 / Lx satisfy any one of equations (9) to (16). This reduces the influence of the support stress and achieves G sensitivity characteristics in which the G sensitivity in the X direction, Y direction, and Z direction is less than ±0.3 ppb / G, respectively.

[0032] 3. Third embodiment Next, a resonation device 1c according to a third embodiment will be described with reference to Fig. 7 and Fig. 8. In Fig. 7, for the sake of convenience in describing the internal configuration of the resonation device 1c, the cover 20 is removed.

[0033] The resonator device 1c of this embodiment is similar to the resonator device 1 of the first embodiment except that the structure of the substrate 10c and the structure of the resonator element 3c are different from those of the resonator device 1 of the first embodiment. Note that the following description will focus on the differences from the first embodiment described above, and a description of similar points will be omitted.

[0034] As shown in FIGS. 7 and 8, the resonation device 1c includes a substrate 10c, a lid 20, and a resonator element 3c.

[0035] The substrate 10c has two electrode pads 11c and 12c arranged side by side along the longitudinal direction, i.e., the X direction, on a third surface 13. A plurality of external terminals 15 used for supplying power and outputting frequencies are provided on a fourth surface 14.

[0036] The vibrating element 3c has a quartz crystal substrate 30, an excitation electrode 38, a first connection electrode 41c, and a second connection electrode 42c.

[0037] The quartz crystal substrate 30 includes a support portion 33, an excitation portion 32, and a slit 34 provided between the support portion 33 and an excitation electrode 38. The lengths L1 and L2 of the slit 34 satisfy any one of the above-mentioned formulas (1) to (8) or any one of the above-mentioned formulas (9) to (16).

[0038] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b, which are opposite surfaces, and a first connection electrode 41c is provided on the second surface 31b, which is one surface 31 of the support portion 33, and a second connection electrode 42c is provided on the first surface 31a, which is the other surface 31 of the support portion 33. The first connection electrode 41c and the second connection electrode 42c overlap in a central portion in the short side direction of the quartz substrate 30 in a plan view.

[0039] An excitation electrode 38 is provided on the excitation portion 32 of the quartz crystal substrate 30, and the excitation electrode 38 provided on the first surface 31a of the excitation portion 32 is electrically connected to the second connection electrode 42c via the lead electrode 39. The excitation electrode 38 provided on the second surface 31b of the excitation portion 32 is electrically connected to the first connection electrode 41c via the lead electrode 39.

[0040] The first connection electrode 41c is disposed at a position overlapping with an electrode pad 11c provided on the substrate 10c, and is joined and electrically connected to the electrode pad 11c via a conductive bonding member 43c. The second connection electrode 42c is electrically connected to an electrode pad 12c provided on the substrate 10c via a bonding wire 45.

[0041] With this configuration, the vibrating element 3c is supported at one point, the influence of the support stress can be further reduced, and the same effect as in the first embodiment can be obtained. [Explanation of symbols]

[0042] 1, 1a, 1c... vibrating device, 3, 3a, 3c... vibrating piece, 10... substrate, 11, 12... electrode pad, 13... third surface, 14... fourth surface, 15... external terminal, 20... lid, 21... recess, 22... accommodation space, 25... bonding member, 30... quartz substrate, 31... surface, 31a... first surface, 31b... second surface, 32... excitation portion, 33... support portion, 34... slit, 35... first portion, 36... second portion, 37... third portion, 38... excitation electrode, 39... lead electrode, 40... side electrode, 41... first connection electrode, 42... second connection electrode, 43, 44... conductive bonding member, 45... bonding wire, 50... virtual line, A, B, C, D... area, L1, L2, Lx... length, Ψ... in-plane rotation angle.

Claims

1. an AT-cut quartz crystal substrate that has been rotated by a predetermined angle around the X-axis of a Cartesian coordinate system (X, Y, Z) and has a surface that is orthogonal to the Y'-axis of a new Cartesian coordinate system (X, Y', Z') obtained by this rotation; a support portion provided at one end in a first direction along the X axis; an excitation portion aligned with the support portion along the first direction and having excitation electrodes disposed on the surface; a slit having an opening on the surface, The slit is a first portion provided between the support portion and the excitation electrode and extending along a second direction intersecting the first direction; a second portion connected to one end of the first portion in the second direction, disposed on one outer edge side of the excitation electrode in the second direction, and extending along the first direction; a third portion connected to the other end of the first portion in the second direction, disposed on the other outer edge side of the excitation electrode in the second direction, and extending along the first direction, When the length from the outer edge of the first portion of the slit on the excitation electrode side to the other end of the AT-cut quartz crystal substrate in the first direction is Lx, the length of the second portion is L1, and the length of the third portion is L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (1) to (8): vibrating piece. 0.0<L1 / Lx<0.34 and 0.0<L2 / Lx≦1.294×L1 / Lx+0.34 (1) 0.34≦L1 / Lx<0.55 and 0.857×L1 / Lx−0.29≦L2 / Lx≦0.78 (2) 0.55≦L1 / Lx<0.61 and 0.471×L1 / Lx−0.08≦L2 / Lx≦0.78 (3) 0.61≦L1 / Lx<0.80 and 0.471×L1 / Lx−0.08≦L2 / Lx≦0.895×L1 / Lx+0.23 (4) 0.80≦L1 / Lx<0.83 and 0.471×L1 / Lx−0.08≦L2 / Lx≦0.95 (5) 0.83≦L1 / Lx<0.89 and 0.471×L1 / Lx−0.08≦L2 / Lx≦−1.167×L1 / Lx+1.51 (6) 0.83≦L1 / Lx<0.89 and 1.167×L1 / Lx−0.35≦L2 / Lx≦0.95 (7) 0.89≦L1 / Lx≦0.95 and 1.167×L1 / Lx−0.35≦L2 / Lx≦0.95 (8)

2. an AT-cut quartz crystal substrate that has been rotated by a predetermined angle around the X-axis of a Cartesian coordinate system (X, Y, Z) and has a surface that is orthogonal to the Y'-axis of a new Cartesian coordinate system (X, Y', Z') obtained by this rotation; a support portion provided at one end in a first direction along the X axis; an excitation portion aligned with the support portion along the first direction and having excitation electrodes disposed on the surface; a slit having an opening on the surface, The slit is a first portion provided between the support portion and the excitation electrode and extending along a second direction intersecting the first direction; a second portion connected to one end of the first portion in the second direction, disposed on one outer edge side of the excitation electrode in the second direction, and extending along the first direction; a third portion connected to the other end of the first portion in the second direction, disposed on the other outer edge side of the excitation electrode in the second direction, and extending along the first direction, When the length from the outer edge of the first portion of the slit on the excitation electrode side to the other end of the AT-cut quartz crystal substrate in the first direction is Lx, the length of the second portion is L1, and the length of the third portion is L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (9) to (16): vibrating piece. 0.0<L1 / Lx<0.12 and 0.0<L2 / Lx≦1.043×L1 / Lx+0.10 (9) 0.12≦L1 / Lx<0.23 and 1.061×L1 / Lx−0.13≦L2 / Lx≦1.043×L1 / Lx+0.10 (10) 0.23≦L1 / Lx<0.41 and 1.061×L1 / Lx−0.13≦L2 / Lx≦1.556×L1 / Lx−0.02 (11) 0.41≦L1 / Lx<0.45 and 1.061×L1 / Lx−0.13≦L2 / Lx≦0.62 (12) 0.45≦L1 / Lx<0.54 and 0.556×L1 / Lx+0.10≦L2 / Lx≦0.62 (13) 0.54≦L1 / Lx<0.61 and 0.40≦L2 / Lx≦0.62 (14) 0.61≦L1 / Lx<0.68 and 0.40≦L2 / Lx≦0.571×L1 / Lx+0.27 (15) 0.68≦L1 / Lx≦0.75 and 0.571×L1 / Lx+0.01≦L2 / Lx≦0.571×L1 / Lx+0.27 (16)

3. The slit penetrates from one of the surfaces to the other surface that is the back side of the one surface. The vibrator element according to claim 1 or 2.

4. the support portion includes a first connection electrode and a second connection electrode arranged on one of the surfaces of the vibrating element, the first connection electrode and the second connection electrode are arranged side by side along one side of the vibrating element; The vibrator element according to claim 1 or 2.

5. The support portion is a first connection electrode disposed on one of the surfaces of the vibrating element, and a second connection electrode disposed on the other surface that is a back side of the one of the surfaces, the first connection electrode and the second connection electrode have an overlapping portion in a plan view; The vibrator element according to claim 1 or 2.

6. A vibrating piece made of the AT-cut quartz crystal substrate according to claim 1 or 2; a substrate on which the support portion of the vibrating element is attached; Equipped with Vibration device.

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