Resonator element and resonator device

Abstract

The invention provides a resonator element and a resonator device having excellent G sensitivity characteristics and aging characteristics. The resonator element is composed of an SC cut quartz substrate having a surface perpendicular to the Y ''axis, and when the length from the outer edge of the excitation electrode side of the first portion of the slit to the other end of the SC 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 formulae (1) to (5).

Description

Technical Field

[0001] The present invention relates to a vibration plate and a vibration device. Background Art

[0002] For example, Patent Document 1 discloses a piezoelectric substrate, wherein the support portion includes: two beam portions extending from the other end portion along the free end via a vibration substrate; a first connecting portion connecting the other end portion of the vibration substrate to the two beam portions; and a second connecting portion connecting the terminal portions of the two beam portions extending beyond the free end, wherein a fixing portion is provided at the second connecting portion. That is, by forming a U-shaped slit through the outer periphery of the vibration substrate, the residual stress transmitted to the vibration substrate when the fixing portion is bonded to the package substrate via a bonding component is reduced.

[0003] Prior art literature

[0004] Patent Document 1: Japanese Patent Application Publication No. 2012-169890

[0005] However, the piezoelectric substrate described in Patent Document 1 reduces the influence of the support stress by providing a U-shaped gap between the support portion and the vibration substrate, but has a problem that the G sensitivity characteristics are not considered at all. Summary of the invention

[0006] The vibrating piece is composed of an SC-cut quartz substrate having a plane perpendicular to the Y" axis of the orthogonal coordinate system (X’, Y”, Z’), and the orthogonal coordinate system (X’, Y”, Z’) is obtained as follows: rotating a specified angle around the Z axis of the orthogonal coordinate system (X, Y, Z), and then rotating a specified angle around the X’ axis of the new orthogonal coordinate system (X’, Y’, Z) obtained by this rotation. The vibrating piece includes: a support portion provided at one end in the first direction in a plan view; an excitation portion arranged along the first direction with the support portion and having an excitation electrode disposed on the plane; and a slit having an opening on the plane. The slit includes: 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; and 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 on the excitation electrode side of the first portion of the slit to the other end of the SC-cut quartz substrate in the first direction is set as Lx, the length of the second portion is set as L1, and the length of the third portion is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (1) to (5).

[0007] 0.0 < L1 / Lx < 0.05, and, -3×L1 / Lx + 0.35 ≤ L2 / Lx ≤ 1.1×L1 / Lx + 0.805… (1)

[0008] 0.05 ≤ L1 / Lx < 0.27, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.5×L1 / Lx + 0.835…(2)

[0009] 0.27 ≤ L1 / Lx < 0.77, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.97… (3)

[0010] 0.77 ≤ L1 / Lx < 0.87, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ -1.0×L1 / Lx + 1.47…(4)

[0011] 0.87 ≤ L1 / Lx ≤ 0.97, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.6… (5)

[0012] The vibration piece is composed of an SC-cut quartz substrate, which has a surface perpendicular to the Y" axis of an orthogonal coordinate system (X', Y", Z'), and the orthogonal coordinate system (X', Y", Z') is obtained as follows: rotate a specified angle around the Z axis of the orthogonal coordinate system (X, Y, Z), and rotate a specified angle around the X' axis of a new orthogonal coordinate system (X', Y', Z) obtained by the rotation, the vibration piece includes: a support portion, which is arranged at one end in the first direction when viewed from above; an excitation portion, which is arranged along the first direction with the support portion and an excitation electrode is arranged on the surface; and a gap, which has an opening on the surface, the gap includes: a first part, which is arranged between the support portion and the excitation electrode, and is arranged along a first direction intersecting the first direction. The invention relates to a slotted quartz substrate having a first portion and a second portion, wherein the first portion includes a first portion and a second portion, wherein the first portion includes a first portion and a second portion, wherein the first portion and the second portion are connected to one end of the first portion in the second direction, and are arranged on an outer edge side of the excitation electrode in the second direction, and extend along the first direction; a second portion, which is connected to one end of the first portion in the second direction, and is arranged on an outer edge side of the excitation electrode in the second direction, and extend along the first direction; and a third portion, which is connected to the other end of the first portion in the second direction, and is arranged on the other outer edge side of the excitation electrode in the second direction, and extend along the first direction, and when the length from the outer edge of the first portion of the gap on the excitation electrode side to the other end of the SC-cut quartz substrate in the first direction is set to Lx, the length of the second portion is set to L1, and the length of the third portion is set to L2, L1 / Lx and L2 / Lx satisfy any one of the following equations (6) to (15).

[0013] 0.38≤L1 / Lx<0.43, and -2.6×L1 / Lx+1.588≤L2 / Lx≤5.2×L1 / Lx-1.376…(6)

[0014] 0.43≤L1 / Lx<0.49, and -0.625×L1 / Lx+0.739≤L2 / Lx≤1.167×L1 / Lx+0.358…(7)

[0015] 0.49≤L1 / Lx<0.51, and -0.625×L1 / Lx+0.739≤L2 / Lx≤2×L1 / Lx-0.05… (8)

[0016] 0.51≤L1 / Lx<0.6, and -0.444×L1 / Lx+0.647≤L2 / Lx≤0.97… (9)

[0017] 0.6≤L1 / Lx<0.68, and 0.231×L1 / Lx+0.242≤L2 / Lx≤0.97… (10)

[0018] 0.68≤L1 / Lx<0.7, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-5.5×L1 / Lx+4.5…(11)

[0019] 0.68≤L1 / Lx<0.7, and 5.5×L1 / Lx-2.98≤L2 / Lx≤0.97… (12)

[0020] 0.7≤L1 / Lx<0.73, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-1.1×L1 / Lx+1.42…(13)

[0021] 0.7≤L1 / Lx<0.73, and 3.333×L1 / Lx-1.463≤L2 / Lx≤0.97… (14)

[0022] 0.73≤L1 / Lx≤0.8, and 0.929×L1 / Lx-0.268≤L2 / Lx≤-1.1×L1 / Lx+1.42…(15)

[0023] A resonator device includes: a resonator element formed of the SC-cut quartz substrate described above; and a substrate to which the support portion of the resonator element is attached.

[0024] The vibrating piece is composed of an AT-cut quartz substrate having a surface perpendicular to the Y' axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating the X axis of the orthogonal coordinate system (X, Y, Z) by a predetermined angle, and the vibrating piece includes: a support portion, which is provided at one end in a first direction when viewed from above; an excitation portion, which is arranged along the first direction with the support portion and has an excitation electrode arranged on the surface; and a gap, which has an opening on the surface, the gap including: a first portion, which is provided between the support portion and the excitation electrode and extends along a second direction intersecting the first direction; a second portion, which is provided at one end in the second direction with the first portion end is connected, is arranged on an outer edge side of the excitation electrode in the second direction, and extends along the first direction; and a third part is connected to the other end of the first part in the second direction, is arranged on the other outer edge side of the excitation electrode in the second direction, and extends along the first direction, when the length from the outer edge of the excitation electrode side of the first part of the gap to the other end of the AT-cut quartz substrate in the first direction is set to Lx, the length of the second part is set to L1, and the length of the third part is set to L2, L1 / Lx and L2 / Lx satisfy any one of the following equations (16) to (25).

[0025] 0.0 < L1 / Lx < 0.2, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ 0.95… (16)

[0026] 0.2 ≤ L1 / Lx < 0.27, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ -2.0×L1 / Lx + 1.35…(17)

[0027] 0.27 ≤ L1 / Lx < 0.36, and, 0.0 < L2 / Lx ≤ 1.56×L1 / Lx + 0.39… (18)

[0028] 0.36 ≤ L1 / Lx < 0.54, and, 0.0 < L2 / Lx ≤ 0.95… (19)

[0029] 0.54 ≤ L1 / Lx < 0.61, and, 0.0 < L2 / Lx ≤ -1.0×L1 / Lx + 1.49… (20)

[0030] 0.61 ≤ L1 / Lx < 0.7, and, 0.0 < L2 / Lx ≤ 0.78×L1 / Lx + 0.41… (21)

[0031] 0.7 ≤ L1 / Lx < 0.88, and, 0.0 < L2 / Lx ≤ 0.95… (22)

[0032] 0.88 ≤ L1 / Lx ≤ 0.95, and, 0.0 < L2 / Lx ≤ -0.57×L1 / Lx + 0.77… (23)

[0033] 0.88 ≤ L1 / Lx ≤ 0.95, and, 0.86×L1 / Lx - 0.48 ≤ L2 / Lx ≤ -0.71×L1 / Lx + 1.24…(24)

[0034] 0.88 ≤ L1 / Lx ≤ 0.95, and, 1.29×L1 / Lx - 0.52 ≤ L2 / Lx ≤ 0.95… (25)

[0035] The vibrating piece is composed of an AT-cut quartz substrate, and the AT-cut quartz substrate has a plane perpendicular to the Y'-axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating a specified angle around the X-axis of the orthogonal coordinate system (X, Y, Z). The vibrating piece includes: a support portion provided at one end in the first direction along the X-axis; an excitation portion arranged in the first direction with the support portion and having an excitation electrode disposed on the plane; and a slit having an opening on the plane. The slit includes: 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; and 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 on the excitation electrode side of the first portion of the slit to the other end in the first direction of the AT-cut quartz substrate is set as Lx, the length of the second portion is set as L1, and the length of the third portion is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (26) to (33).

[0036] 0.0 < L1 / Lx < 0.34, and, 0.0 < L2 / Lx ≤ 1.294×L1 / Lx + 0.34… (26)

[0037] 0.34 ≤ L1 / Lx < 0.55, and, 0.857×L1 / Lx - 0.29 ≤ L2 / Lx ≤ 0.78… (27)

[0038] 0.55 ≤ L1 / Lx < 0.61, and, 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.78… (28)

[0039] 0.61 ≤ L1 / Lx < 0.80, and, 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.895×L1 / Lx + 0.23…(29)

[0040] 0.80 ≤ L1 / Lx < 0.83, and, 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.95… (30)

[0041] 0.83 ≤ L1 / Lx < 0.89, and, 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ -1.167×L1 / Lx + 1.51…(31)

[0042] 0.83 ≤ L1 / Lx < 0.89, and, 1.167 × L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95… (32)

[0043] 0.89 ≤ L1 / Lx ≤ 0.95, and, 1.167 × L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95… (33)

[0044] The vibrating piece is composed of an AT-cut quartz substrate, and the AT-cut quartz substrate has a plane perpendicular to the Y'-axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating a specified angle around the X-axis of the orthogonal coordinate system (X, Y, Z). The vibrating piece includes: a support portion provided at one end in the first direction along the X-axis; an excitation portion arranged in the first direction with the support portion and having excitation electrodes arranged on the plane; and a slit having an opening on the plane. The slit includes: a first portion provided between the support portion and the excitation electrodes 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, arranged 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, arranged 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 in the first direction of the AT-cut quartz substrate is set as Lx, the length of the second portion is set as L1, and the length of the third portion is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (34) to (41).

[0045] 0.0 < L1 / Lx < 0.12, and, 0.0 < L2 / Lx ≤ 1.043 × L1 / Lx + 0.10… (34)

[0046] 0.12 ≤ L1 / Lx < 0.23, and, 1.061 × L1 / Lx - 0.13 ≤ L2 / Lx ≤ 1.043 × L1 / Lx + 0.10…(35)

[0047] 0.23 ≤ L1 / Lx < 0.41, and, 1.061 × L1 / Lx - 0.13 ≤ L2 / Lx ≤ 1.556 × L1 / Lx - 0.02…(36)

[0048] 0.41 ≤ L1 / Lx < 0.45, and, 1.061 × L1 / Lx - 0.13 ≤ L2 / Lx ≤ 0.62… (37)

[0049] 0.45≤L1 / Lx<0.54, and 0.556×L1 / Lx+0.10≤L2 / Lx≤0.62… (38)

[0050] 0.54≤L1 / Lx<0.61, and 0.40≤L2 / Lx≤0.62… (39)

[0051] 0.61≤L1 / Lx<0.68, and 0.40≤L2 / Lx≤0.571×L1 / Lx+0.27… (40)

[0052] 0.68≤L1 / Lx≤0.75, and 0.571×L1 / Lx+0.01≤L2 / Lx≤0.571×L1 / Lx+0.27…(41)

[0053] A resonator device includes: a resonator element formed of the AT-cut quartz substrate described above; and a substrate to which the support portion of the resonator element is attached. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a plan view showing a schematic structure of the vibration device according to the first embodiment.

[0055] Figure 2 yes Figure 1 Cross-sectional view at line A1-A1.

[0056] Figure 3 It is a plan view showing a schematic structure of a vibrating element included in the vibrating device according to the first embodiment.

[0057] Figure 4 1 is a plan view illustrating the in-plane rotation angle Ψ of the vibrator element.

[0058] Figure 5 : is a graph showing the G sensitivity with respect to the in-plane rotation angle Ψ of the vibrator element.

[0059] Figure 6 2 is a diagram showing the frequency variation with respect to the in-plane rotation angle Ψ of the vibrator element.

[0060] Figure 7 Graphs showing G sensitivities with respect to L1 / Lx and L2 / Lx of the vibrator element.

[0061] Figure 8 It is a plan view showing a schematic structure of a vibration device according to a second embodiment.

[0062] Fig. 9 It is a plan view showing a schematic structure of a vibration device according to a third embodiment.

[0063] Fig.10It is a plan view showing a schematic structure of a vibrator element included in the vibrator device according to the third embodiment.

[0064] Fig.11 1 is a plan view illustrating the in-plane rotation angle Ψ of the vibrator element.

[0065] Fig.12 : is a graph showing the G sensitivity with respect to the in-plane rotation angle Ψ of the vibrator element.

[0066] Fig.13 2 is a diagram showing the frequency variation with respect to the in-plane rotation angle Ψ of the vibrator element.

[0067] Fig.14 Graphs showing G sensitivities with respect to L1 / Lx and L2 / Lx of the vibrator element.

[0068] Fig.15 Graphs showing G sensitivities with respect to L1 / Lx and L2 / Lx of the vibrator element.

[0069] Fig.16 It is a plan view showing a schematic structure of a vibration device according to a sixth embodiment.

[0070] Fig.17 yes Fig.16 Cross-sectional view at line A2-A2.

[0071] Description of symbols

[0072] 1, 1a, 1b, 1c: vibration device; 3, 3a, 3b, 3c: vibration piece; 10: substrate; 11, 12: electrode pad; 13: 3rd surface; 14: 4th surface; 15: external terminal; 20: cover; 21: recess; 22: storage space; 25: bonding component; 30: quartz substrate; 31: surface; 31a: 1st surface; 31b: 2nd surface; 32: excitation part; 33: support part; 34: gap; 35: 1st part; 36: 2nd part; 37: 3rd part; 38: excitation electrode; 39: lead electrode; 40: side electrode: 41: 1st connecting electrode; 42: 2nd connecting electrode; 43, 44: conductive bonding component; 45: bonding wire; A, B, C, D, E: area; L1, L2, Lx: length; Ψ: in-plane rotation angle. DETAILED DESCRIPTION

[0073] 1. First Implementation Method

[0074] First, regarding the vibration device 1 of the first embodiment, a vibration device in which the vibration piece 3 is accommodated in the substrate 10 and the cover 20 is taken as an example. Figure 1 to Figure 7 In addition, Figure 1 In order to facilitate the description of the internal structure of the vibration device 1, the state in which the cover body 20 is removed is shown.

[0075] In addition, for the sake of convenience, in the following drawings of the vibration devices 1, 1a, 1b, and 1c, the X-axis, Y-axis, and Z-axis are illustrated as three axes perpendicular to each other. In addition, the direction along the X-axis is referred to as the "X direction", the direction along the Y-axis is referred to as the "Y direction", and the direction along the Z-axis is referred to as the "Z direction". In addition, the end side of the arrow in each axis direction is also referred to as the "positive side", and the base end side is referred to as the "negative side".

[0076] Moreover, for the sake of convenience, Figure 3 and Figure 4 In the figure, the X' axis, the Y" axis and the Z' axis are illustrated as three crystal axes perpendicular to each other which are equivalent to the crystal axes of quartz. In addition, the direction along the X' axis is called the "X' direction", the direction along the Y" axis is called the "Y" direction, and the direction along the Z' axis is called the "Z' direction". In addition, the end side of the arrow in each axis direction is also called the "positive side", and the base end side is called the "negative side". In addition, in the present embodiment, the first direction is the X' direction, and the second direction is the Z' direction. In addition, except for the later vibration device 1b, the X-axis of each figure of the vibration devices 1, 1a, and 1c is consistent with the X' axis of the crystal axis, the Y-axis is consistent with the Z' axis of the crystal axis, and the Z-axis is consistent with the Y" axis of the crystal axis.

[0077] like Figure 1 and Figure 2 As shown, the vibration device 1 includes a substrate 10 , a cover 20 and a vibration piece 3 .

[0078] The substrate 10 has a third surface 13 and a fourth surface 14 in a front-back relationship, and the third surface 13 is opposite to the vibration piece 3. Two electrode pads 11 and 12 for bonding the vibration piece 3 are arranged along the Y direction on the third surface 13, and a plurality of external terminals 15 for supplying power and outputting frequencies are provided on the fourth surface 14. In addition, the electrode pads 11 and 12 are electrically connected to the external terminals 15 through wiring and through electrodes not shown. In addition, as a constituent material of the substrate 10, silicon is preferred, but glass, ceramics, etc. may also be used.

[0079] The cover 20 is provided with a recess 21 opened toward the substrate 10, and the end surface of the cover 20 surrounding the opening of the recess 21 is bonded to the third surface 13 of the substrate 10 via a bonding component 25, and together with the substrate 10, a storage space 22 for storing the vibration piece 3 is formed. In addition, the cover 20 and the substrate 10 may be bonded directly without using the bonding component 25. In addition, the storage space 22 is in a reduced pressure state, preferably a state closer to a vacuum. As a result, the viscous resistance is reduced, and the oscillation characteristics of the vibration piece 3 are improved. In addition, as a constituent material of the cover 20, silicon is preferred, but glass, ceramics, etc. may also be used.

[0080] like Figure 3As shown, the vibrating element 3 includes a quartz substrate 30 , an excitation electrode 38 , a first connection electrode 41 , and a second connection electrode 42 .

[0081] The quartz substrate 30 is an SC-cut quartz substrate. The SC-cut quartz substrate has crystal axes X, Y, and Z that 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 an orthogonal coordinate system (X', Y", Z'), and the orthogonal coordinate system (X', Y", Z') is obtained as follows: the Z axis of the orthogonal coordinate system (X, Y, Z) is rotated to the left by a specified angle, for example, about 22°, and the X' axis of the new orthogonal coordinate system (X', Y', Z) obtained by the rotation is rotated to the left by a specified angle, for example, about 34°.

[0082] The quartz substrate 30 is rectangular in shape when viewed from above, 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 surface 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.

[0083] The quartz substrate 30 includes a support portion 33 provided at one end in the X′ direction, i.e., the first direction, in a plan view; an excitation portion 32 arranged along the first direction with the support portion 33 and having an excitation electrode 38 disposed on a surface 31 ; and a slit 34 having an opening on the surface 31 .

[0084] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b in a front-back relationship, and the second surface 31b is opposite to the third surface 13 of the substrate 10. The second surface 31b, which is one surface 31 of the quartz substrate 30, is provided with an excitation electrode 38, a first connection electrode 41, and a second connection electrode 42. The excitation electrode 38 is arranged on the excitation portion 32, and the first connection electrode 41 and the second connection electrode 42 are arranged on the support portion 33. The first connection electrode 41 and the second connection electrode 42 are arranged along one side, i.e., the 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.

[0085] The excitation electrode 38 provided on the second surface 31b is electrically connected to the first connection electrode 41 via the lead electrode 39. The excitation electrode 38 provided on the first surface 31a is electrically connected to the second connection electrode 42 provided on the second surface 31b via the lead electrode 39 and the side electrode 40 provided on the side surface on the negative side in the X' direction of the quartz substrate 30. In addition, 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 when viewed from above.

[0086] A gap 34 is provided between the support portion 33 and the excitation electrode 38, and the gap 34 penetrates from the second surface 31b as one surface 31 to the first surface 31a as the other surface 31 located on the back side of the one surface 31. The gap 34 includes a first portion 35 extending along the second direction, which is the Z' direction intersecting the first direction; a second portion 36 connected to one end of the first portion 35 in the second direction, arranged 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, arranged on the other outer edge side of the excitation electrode 38 in the second direction, and extending along the first direction. Since the gap 34 is provided between the support portion 33 and the excitation electrode 38, it is possible to suppress the stress caused by deformation or temperature change caused by bonding the vibration piece 3 to the substrate 10 from being transmitted to the excitation portion 32.

[0087] like Figure 1 and Figure 2 As shown, the support portion 33 of the vibrating piece 3 is bonded to the substrate 10 via the conductive bonding members 43 and 44. Specifically, the conductive bonding member 43 bonds and electrically connects the first connection electrode 41 disposed 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 disposed on the support portion 33 to the electrode pad 12. In addition, the constituent materials of the conductive bonding members 43 and 44 are metal bumps, solder, conductive adhesives, etc.

[0088] Next, refer to Figure 4 , Figure 5 as well as Figure 6 , illustrating the relationship between the G sensitivity and the frequency variation relative to the in-plane rotation angle Ψ of the vibrating piece 3. Figure 5 and Figure 6 In the vibration piece 3 used in the simulation, the gap 34 is not provided in order to make the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ clearer.

[0089] like Figure 4 As shown, the in-plane rotation angle Ψ of the vibrator element 3 refers to an angle formed by an imaginary line 50 passing through the center of the support portion 33 and the center of the excitation electrode 38 and the X′ axis in a plan view.

[0090] Figure 5 The results of simulating the G sensitivity in each direction with respect to the in-plane rotation angle Ψ of the vibrating plate 3 are shown, and the in-plane rotation angle Ψ obtained by rotating counterclockwise about the Y" axis is set to positive and the in-plane rotation angle Ψ obtained by rotating clockwise about the Y" axis is set to negative. Figure 1The G sensitivity of the vibration device 1 in the X direction, Y direction, and Z direction. In addition, Γ is a value obtained by taking the square root of the sum of the squares of the G sensitivity in the X direction, Y direction, and Z direction. The in-plane rotation angle Ψ at which Γ is less than 1 ppb / G is greater than 30° and less than 65°, or greater than -150° and less than -125°.

[0091] Figure 6 It is the result obtained by simulating the frequency variation based on thermal stress with respect to the in-plane rotation angle Ψ of the vibration piece 3. In addition, the frequency variation on the vertical axis is represented by the maximum value of the absolute value of the frequency variation. In addition, the frequency variation is a numerical value that becomes an index for predicting the aging characteristics. When the frequency variation is positive, the aging characteristics become an increasing characteristic, and when the frequency variation is negative, the aging characteristics become a decreasing characteristic. According to Figure 6 The in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is greater than -180° and less than -170°, or greater than -20° and less than 5°, or greater than 165° and less than 180°.

[0092] according to Figure 5 and Figure 6 It is clear that the frequency variation in the range of the in-plane rotation angle Ψ where the G sensitivity in the X direction, Y direction, and Z direction is less than ±1ppb / G, respectively, is large, and the frequency variation in the range of the in-plane rotation angle Ψ where the G sensitivity is less than ±0.1 is large. There is no range of the in-plane rotation angle Ψ that minimizes the G sensitivity and the frequency variation.

[0093] Therefore, in order to reduce both the G sensitivity and the frequency variation, the in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is set to 0° and 180°, and the Figure 7 The relationship between the G sensitivity and the length of the second portion 36 and the length of the third portion 37 of the slit 34 will be described.

[0094] Figure 7 Shown as Figure 3When 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 portion in the first direction of the quartz substrate 30 is set as Lx, the length of the second portion 36 is set as L1, and the length of the third portion 37 is set as L2, the simulation results of the G sensitivity with respect to L1 / Lx and L2 / Lx, where 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. Further, Γ in region A is 0.0 ppb / G or more and less than 0.2 ppb / G, Γ in region B is 0.2 ppb / G or more and less than 0.6 ppb / G, Γ in region C is 0.6 ppb / G or more and less than 1.0 ppb / G, Γ in region D is 1.0 ppb / G or more and less than 1.4 ppb / G, and Γ in region E is 1.4 ppb / G or more and less than 1.8 ppb / G.

[0095] According to Figure 7 , the ranges in which the G sensitivities in the X direction, Y direction, and Z direction can be made less than ±1 ppb / G respectively are the cases where L1 / Lx and L2 / Lx satisfy any one of the following formulas (1) to (5).

[0096] 0.0 < L1 / Lx < 0.05, and, -3×L1 / Lx + 0.35 ≤ L2 / Lx ≤ 1.1×L1 / Lx + 0.805…(1)

[0097] 0.05 ≤ L1 / Lx < 0.27, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.5×L1 / Lx + 0.835…(2)

[0098] 0.27 ≤ L1 / Lx < 0.77, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.97…(3)

[0099] 0.77 ≤ L1 / Lx < 0.87, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ -1.0×L1 / Lx + 1.47…(4)

[0100] 0.87 ≤ L1 / Lx ≤ 0.97, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.6…(5)

[0101] As described above, since the vibration device 1 of this embodiment includes a vibration piece 3, the in-plane rotation angle Ψ of the vibration piece 3 with a smaller frequency variation is 0°, and the ratio of the length L1 of the second part 36 of the gap 34 and the length L2 of the third part 37 to the length Lx of the excitation part 32, namely L1 / Lx and L2 / Lx, satisfies any one of equations (1) to (5), the aging characteristics are excellent, and G sensitivity characteristics of less than ±1ppb / G in the X direction, Y direction, and Z direction can be obtained.

[0102] 2. Second Implementation Method

[0103] Next, refer to Figure 8 A vibration device 1a according to a second embodiment will be described. Figure 8 In order to facilitate the description of the internal structure of the vibration device 1a, the state in which the cover body 20 is removed is shown.

[0104] The vibration device 1a of this embodiment is the same as the vibration device 1 of the first embodiment except that the equations satisfied by L1 / Lx and L2 / Lx of the vibration plate 3a are different from those of the vibration device 1 of the first embodiment. In addition, the description will be centered on the differences from the above-mentioned first embodiment, and the description of the same matters will be omitted.

[0105] like Figure 8 As shown, the vibration device 1 a includes a substrate 10 , a cover 20 , and a vibration piece 3 a .

[0106] The relationship between the in-plane rotation angle Ψ of the vibrating piece 3a of this embodiment, which is less than ±0.1 and the G sensitivity with respect to the length L1 of the second portion 36 of the gap 34 and the length L2 of the third portion 37, is as follows: Figure 7 Therefore, according to Figure 7 The range in which the G sensitivity in the X direction, the Y direction, and the Z direction can be less than ±0.6 ppb / G is when L1 / Lx and L2 / Lx satisfy any one of the following equations (6) to (15).

[0107] 0.38≤L1 / Lx<0.43, and -2.6×L1 / Lx+1.588≤L2 / Lx≤5.2×L1 / Lx-1.376…(6)

[0108] 0.43≤L1 / Lx<0.49, and -0.625×L1 / Lx+0.739≤L2 / Lx≤1.167×L1 / Lx+0.358…(7)

[0109] 0.49≤L1 / Lx<0.51, and -0.625×L1 / Lx+0.739≤L2 / Lx≤2×L1 / Lx-0.05…(8)

[0110] 0.51≤L1 / Lx<0.6, and -0.444×L1 / Lx+0.647≤L2 / Lx≤0.97…(9)

[0111] 0.6≤L1 / Lx<0.68, and 0.231×L1 / Lx+0.242≤L2 / Lx≤0.97…(10)

[0112] 0.68≤L1 / Lx<0.7, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-5.5×L1 / Lx+4.5…(11)

[0113] 0.68≤L1 / Lx<0.7, and 5.5×L1 / Lx-2.98≤L2 / Lx≤0.97…(12)

[0114] 0.7≤L1 / Lx<0.73, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-1.1×L1 / Lx+1.42…(13)

[0115] 0.7≤L1 / Lx<0.73, and 3.333×L1 / Lx-1.463≤L2 / Lx≤0.97…(14)

[0116] 0.73≤L1 / Lx≤0.8, and 0.929×L1 / Lx-0.268≤L2 / Lx≤-1.1×L1 / Lx+1.42…(15)

[0117] As described above, the vibration device 1a of this embodiment includes a vibration piece 3a, the in-plane rotation angle Ψ of which the frequency variation is relatively small is 0°, L1 / Lx and L2 / Lx satisfy any one of equations (6) to (15), and therefore, the aging characteristics are excellent, and G sensitivity characteristics of less than ±0.6ppb / G in the X direction, Y direction, and Z direction can be obtained.

[0118] 3. Third Implementation Method

[0119] Next, refer to Figures 9 to 14 A vibration device 1b according to a third embodiment will be described. Fig. 9 In order to facilitate the description of the internal structure of the vibration device 1b, the state in which the cover body 20 is removed is shown.

[0120] In addition, for the sake of convenience, Fig.10 and Fig.11In the figure, the X-axis, Y'-axis, and Z'-axis are illustrated as three crystal axes perpendicular to each other that correspond to the crystal axes of quartz. In addition, the direction along the X-axis is referred to as the "X direction", the direction along the Y'-axis is referred to as the "Y' direction", and the direction along the Z'-axis is referred to as the "Z' direction". In addition, the end side of the arrow in each axis direction is also referred to as the "positive side", and the base end side is referred to as the "negative side". In addition, in the present embodiment, the first direction is the X direction, and the second direction is the Z' direction. In addition, Fig. 9 The X-axis of the crystal is consistent with the X-axis of the crystal axis, the Y-axis is consistent with the Z'axis of the crystal axis, and the Z-axis is consistent with the Y'axis of the crystal axis.

[0121] The resonator device 1b of this embodiment is the same as the resonator device 1 of the first embodiment except that the quartz substrate 30b of the resonator element 3b is different. The description will be mainly focused on the differences from the first embodiment, and the description of the same matters will be omitted.

[0122] like Fig. 9 As shown, the vibration device 1b includes a substrate 10, a cover 20 and a vibration piece 3b.

[0123] like Fig.10 As shown, the vibrating element 3 b includes a quartz substrate 30 b , an excitation electrode 38 , a first connection electrode 41 , and a second connection electrode 42 .

[0124] The quartz substrate 30b is an AT-cut quartz substrate. The AT-cut quartz substrate has crystal axes X, Y, and Z that 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 a new orthogonal coordinate system (X, Y', Z') obtained by rotating the X axis of the orthogonal coordinate system (X, Y, Z) to the left by a predetermined angle, for example, about 35°15'.

[0125] The quartz substrate 30b 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 surface 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.

[0126] Next, refer to Fig.11 , Fig.12 as well as Fig.13 The relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ of the vibrating piece 3b will be described. Fig.12 and Fig.13 In the vibration piece 3 b used in the simulation, the gap 34 is not provided in order to make the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ clearer.

[0127] like Fig.11As shown, the in-plane rotation angle Ψ of the vibrator element 3 b refers to an angle formed by an imaginary line 50 passing through the center of the support portion 33 and the center of the excitation electrode 38 and the X-axis in a plan view.

[0128] Fig.12 The results of simulating the G sensitivity in each direction with respect to the in-plane rotation angle Ψ of the vibration piece 3b are shown, and the in-plane rotation angle Ψ obtained by rotating counterclockwise about the Y' axis is set as positive and the in-plane rotation angle Ψ obtained by rotating clockwise about the Y' axis is set as negative. Fig. 9 The G sensitivity of the vibration device 1b in the X direction, Y direction, and Z direction. In addition, Γ is a value obtained by taking the square root of the sum of the squares of the G sensitivity in the X direction, Y direction, and Z direction. The in-plane rotation angle Ψ at which Γ is less than 1 ppb / G is greater than -180° and less than -140°, or greater than -20° and less than 30°, or greater than 160° and less than 180°.

[0129] Fig.13 It is the result of simulating the frequency variation due to thermal stress with respect to the in-plane rotation angle Ψ of the vibrating piece 3b. The frequency variation on the vertical axis is represented based on the maximum absolute value of the frequency variation. Fig.13 The in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is greater than -110° and less than -70°, or greater than 55° and less than 65°, or greater than 115° and less than 130°.

[0130] according to Fig.12 and Fig.13 It is clear that the frequency variation in the range of the in-plane rotation angle Ψ where the G sensitivity in the X direction, Y direction, and Z direction is less than ±1ppb / G, respectively, is large, and the frequency variation in the range of the in-plane rotation angle Ψ where the G sensitivity is less than ±0.1 is large. There is no range of the in-plane rotation angle Ψ that minimizes the G sensitivity and the frequency variation.

[0131] Therefore, in order to reduce both the G sensitivity and the frequency variation, the in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is set to -90°, and the Fig.14 The relationship between the G sensitivity and the length of the second portion 36 and the length of the third portion 37 of the slit 34 will be described.

[0132] Fig.14 Shown as Fig.10When the length from the outer edge on the excitation electrode 38 side of the first part 35 of the slit 34 to the other end in the first direction of the quartz substrate 30 is set as Lx, the length of the second part 36 is set as L1, and the length of the third part 37 is set as L2, the simulation results of the G sensitivity with respect to L1 / Lx and L2 / Lx are shown. 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, Γ in region B is 0.2 ppb / G or more and less than 0.6 ppb / G, Γ in region C is 0.6 ppb / G or more and less than 1.0 ppb / G, and Γ in region D is 1.0 ppb / G or more and less than 1.4 ppb / G.

[0133] According to Fig.14 , the range in which the G sensitivities in the X direction, Y direction, and Z direction can be made less than ±1 ppb / G respectively is the case where L1 / Lx and L2 / Lx satisfy any one of the following formulas (16) to (25).

[0134] 0.0 < L1 / Lx < 0.2, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ 0.95…(16)

[0135] 0.2 ≤ L1 / Lx < 0.27, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ -2.0×L1 / Lx + 1.35…(17)

[0136] 0.27 ≤ L1 / Lx < 0.36, and, 0.0 < L2 / Lx ≤ 1.56×L1 / Lx + 0.39…(18)

[0137] 0.36 ≤ L1 / Lx < 0.54, and, 0.0 < L2 / Lx ≤ 0.95…(19)

[0138] 0.54 ≤ L1 / Lx < 0.61, and, 0.0 < L2 / Lx ≤ -1.0×L1 / Lx + 1.49…(20)

[0139] 0.61 ≤ L1 / Lx < 0.7, and, 0.0 < L2 / Lx ≤ 0.78×L1 / Lx + 0.41…(21)

[0140] 0.7 ≤ L1 / Lx < 0.88, and, 0.0 < L2 / Lx ≤ 0.95…(22)

[0141] 0.88 ≤ L1 / Lx ≤ 0.95, and, 0.0 < L2 / Lx ≤ -0.57×L1 / Lx + 0.77…(23)

[0142] 0.88≤L1 / Lx≤0.95, and 0.86×L1 / Lx-0.48≤L2 / Lx≤-0.71×L1 / Lx+1.24…(24)

[0143] 0.88≤L1 / Lx≤0.95, and 1.29×L1 / Lx-0.52≤L2 / Lx≤0.95…(25)

[0144] As described above, since the vibration device 1b of this embodiment includes a vibration piece 3b, the in-plane rotation angle Ψ of the vibration piece 3b with a smaller frequency variation is -90°, and the ratios of the length L1 of the second part 36 of the gap 34 and the length L2 of the third part 37 to the length Lx of the excitation part 32, namely L1 / Lx and L2 / Lx, satisfy any one of equations (16) to (25), the aging characteristics are excellent, and G sensitivity characteristics of less than ±1ppb / G in the X direction, Y direction, and Z direction can be obtained.

[0145] 4. Fourth Implementation Method

[0146] Next, the vibration device of the fourth embodiment is described. The vibration device of this embodiment is the same as the vibration device 1b of the third embodiment except that the equations satisfied by L1 / Lx and L2 / Lx of the vibration plate 3b are different from those of the vibration device 1b of the third embodiment. Therefore, the vibration device used in the description of the third embodiment is used. Fig.10 as well as Fig.11 ,besides Fig.15 , the description will focus on the differences from the third embodiment, and the description of the same matters will be omitted.

[0147] The in-plane rotation angle Ψ of the vibrating piece of this embodiment is 0° or 180°. Fig.11 As shown, the in-plane rotation angle Ψ of the vibrator element refers to the angle formed by 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.

[0148] Next, refer to Fig.15 The relationship between the G sensitivity and the length of the second portion 36 and the length of the third portion 37 of the slit 34 will be described.

[0149] Fig.15 Shown as Fig.10When the length from the outer edge on the excitation electrode 38 side of the first part 35 of the slit 34 to the other end in the first direction of the quartz substrate 30 is set as Lx, the length of the second part 36 is set as L1, and the length of the third part 37 is set as L2, the simulation results of the G sensitivity with respect to L1 / Lx and L2 / Lx, where 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, Γ in region A is 0.0 ppb / G or more and less than 0.3 ppb / G, Γ in region B is 0.3 ppb / G or more and less than 0.6 ppb / G, Γ in region C is 0.6 ppb / G or more and less than 0.9 ppb / G, and Γ in region D is 0.9 ppb / G or more and less than 1.2 ppb / G.

[0150] According to Fig.15 , 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 ±0.6 ppb / G respectively are the cases where L1 / Lx and L2 / Lx satisfy any one of the following formulas (26) to (33).

[0151] 0.0 < L1 / Lx < 0.34, and, 0.0 < L2 / Lx ≤ 1.294 × L1 / Lx + 0.34…(26)

[0152] 0.34 ≤ L1 / Lx < 0.55, and, 0.857 × L1 / Lx - 0.29 ≤ L2 / Lx ≤ 0.78…(27)

[0153] 0.55 ≤ L1 / Lx < 0.61, and, 0.471 × L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.78…(28)

[0154] 0.61 ≤ L1 / Lx < 0.80, and, 0.471 × L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.895 × L1 / Lx + 0.23…(29)

[0155] 0.80 ≤ L1 / Lx < 0.83, and, 0.471 × L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.95…(30)

[0156] 0.83 ≤ L1 / Lx < 0.89, and, 0.471 × L1 / Lx - 0.08 ≤ L2 / Lx ≤ -1.167 × L1 / Lx + 1.51…(31)

[0157] 0.83 ≤ L1 / Lx < 0.89, and, 1.167 × L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95…(32)

[0158] 0.89 ≤ L1 / Lx ≤ 0.95, and, 1.167 × L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95…(33)

[0159] As described above, since the vibrating device of the present embodiment includes the vibrating piece 3, the in-plane rotation angle Ψ of the vibrating piece 3 is 0° or 180°, and the ratios 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, namely L1 / Lx and L2 / Lx, satisfy any one of the formulas (26) to (33). Therefore, the influence of the support stress can be reduced, and the G-sensitivity characteristics with G-sensitivities in the X, Y, and Z directions less than ±0.6 ppb / G can be obtained.

[0160] 5. Fifth Embodiment

[0161] Next, the vibrating device of the fifth embodiment will be described. The vibrating device of the present embodiment is the same as the vibrating device 1b of the third embodiment, except that the formulas satisfied by L1 / Lx and L2 / Lx of the vibrating piece 3b are different. Therefore, the Fig.10 and Fig.11 used in the description of the third embodiment Fig.15 will be used, and the description will be centered on the differences from the third embodiment, and the description of the same matters will be omitted.

[0162] The in-plane rotation angle Ψ of the vibrating piece of the present embodiment is 0° or 180°. In addition, as Fig.11 shown, the in-plane rotation angle Ψ of the vibrating piece means the angle formed by the imaginary line 50 passing through the center of the support portion 33 and the center of the excitation electrode 38 and the X-axis when viewed from above.

[0163] For the vibrating piece of the present embodiment, the relationship between the G-sensitivity with respect to Fig.10 the length L1 of the second portion 36 and the length L2 of the third portion 37 of the slit 34 shown Fig.15 is the same as Fig.15 . Therefore, according to

[0164] the range of L1 / Lx and L2 / Lx that can make the G-sensitivities in the X, Y, and Z directions less than ±0.3 ppb / G is the case where L1 / Lx and L2 / Lx satisfy any one of the following formulas (34) to (41).

[0165] 0.12≤L1 / Lx<0.23, and 1.061×L1 / Lx-0.13≤L2 / Lx≤1.043×L1 / Lx+0.10…(35)

[0166] 0.23≤L1 / Lx<0.41, and 1.061×L1 / Lx-0.13≤L2 / Lx≤1.556×L1 / Lx-0.02…(36)

[0167] 0.41≤L1 / Lx<0.45, and 1.061×L1 / Lx-0.13≤L2 / Lx≤0.62…(37)

[0168] 0.45≤L1 / Lx<0.54, and 0.556×L1 / Lx+0.10≤L2 / Lx≤0.62…(38)

[0169] 0.54≤L1 / Lx<0.61, and 0.40≤L2 / Lx≤0.62…(39)

[0170] 0.61≤L1 / Lx<0.68, and 0.40≤L2 / Lx≤0.571×L1 / Lx+0.27…(40)

[0171] 0.68≤L1 / Lx≤0.75, and 0.571×L1 / Lx+0.01≤L2 / Lx≤0.571×L1 / Lx+0.27…(41)

[0172] As described above, the vibration device of this embodiment includes a vibration plate, the in-plane rotation angle Ψ of the vibration plate is 0° or 180°, and L1 / Lx and L2 / Lx satisfy any one of equations (34) to (41). Therefore, it is possible to reduce the influence of the supporting stress and obtain a G sensitivity characteristic in which the G sensitivity in the X direction, the Y direction, and the Z direction is less than ±0.3ppb / G, respectively.

[0173] 6. Sixth Implementation Method

[0174] Next, refer to Fig.16 and Fig.17 A vibration device 1c according to a sixth embodiment will be described. Fig.16 In order to facilitate the description of the internal structure of the vibration device 1c, the figure shows a state where the cover body 20 is removed.

[0175] The resonator device 1c of this embodiment is the same as the resonator device 1 of the first embodiment except that the structure of the substrate 10c and the structure of the resonator plate 3c are different from the resonator device 1 of the first embodiment. In addition, the description will focus on the differences from the above-mentioned first embodiment, and the description of the same matters will be omitted.

[0176] like Fig.16 and Fig.17 As shown, the vibration device 1c includes a substrate 10c, a cover 20 and a vibration piece 3c.

[0177] The substrate 10c has two electrode pads 11c and 12c arranged side by side along the X direction, which is the longitudinal direction, on the third surface 13. A plurality of external terminals 15 for supplying power and outputting frequency are provided on the fourth surface 14.

[0178] The vibrating element 3 c includes a quartz substrate 30 , an excitation electrode 38 , a first connection electrode 41 c , and a second connection electrode 42 c .

[0179] The quartz substrate 30 includes a support portion 33, an excitation portion 32, and a slit 34 provided between the support portion 33 and the excitation electrode 38. The lengths L1 and L2 of the slit 34 satisfy any one of the above-mentioned equations (1) to (5).

[0180] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b in a front-back relationship, and a second connection electrode 42c is provided on the first surface 31a of one surface 31 as a support portion 33, and a first connection electrode 41c is provided on the second surface 31b of the other surface 31 as a support portion 33. The first connection electrode 41c and the second connection electrode 42c have a portion overlapping at the center of the short side direction of the quartz substrate 30 when viewed from above.

[0181] The excitation portion 32 of the quartz substrate 30 is provided with an excitation electrode 38, 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.

[0182] The first connection electrode 41c is arranged at a position overlapping with the electrode pad 11c provided on the substrate 10c and is bonded and electrically connected to the electrode pad 11c via a conductive bonding member 43c. The second connection electrode 42c is electrically connected to the electrode pad 12c provided on the substrate 10c via a bonding wire 45.

[0183] By adopting such a structure, the vibration piece 3c can be supported at one point, the influence of the support stress can be further reduced, and the same effect as the first embodiment can be obtained. The structure of this embodiment can also be applied to the vibration devices of the second to fifth embodiments, and the same effect as these embodiments can be obtained.

Claims

1. A vibrating piece is composed of an SC-cut quartz substrate, and the SC-cut quartz substrate has a plane perpendicular to the Y" axis of an orthogonal coordinate system (X’, Y”, Z’). The orthogonal coordinate system (X’, Y”, Z’) is obtained as follows: rotate a specified angle around the Z axis of the orthogonal coordinate system (X, Y, Z), and then rotate a specified angle around the X’ axis of the new orthogonal coordinate system (X’, Y’, Z) obtained by this rotation. The vibrating piece includes: A support portion provided at one end in the first direction in a top view. An excitation portion arranged along the first direction with the support portion, and an excitation electrode is arranged on the plane. And A slit having an opening on the plane, The slit includes: 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, arranged on one outer edge side of the excitation electrode 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, arranged 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 on the excitation electrode side of the first portion of the slit to the other end in the first direction of the SC-cut quartz substrate is set as Lx, the length of the second portion is set as L1, and the length of the third portion is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (1) to (5): 0.0 < L1 / Lx < 0.05, and, -3×L1 / Lx + 0.35 ≤ L2 / Lx ≤ 1.1×L1 / Lx + 0.805…(1) 0.05 ≤ L1 / Lx < 0.27, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.5×L1 / Lx + 0.835… (2) 0.27 ≤ L1 / Lx < 0.77, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.97…(3) 0.77 ≤ L1 / Lx < 0.87, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ -1.0×L1 / Lx + 1.47…(4) 0.87 ≤ L1 / Lx ≤ 0.97, and, -0.207×L1 / Lx + 0.21 ≤ L2 / Lx ≤ 0.6…(5).

2. The vibrating piece according to claim 1, wherein The slit penetrates from one plane to another plane on the back side of one plane.

3. The vibrating piece according to claim 1, wherein The support portion includes a first connection electrode and a second connection electrode arranged on one plane of the vibrating piece, The first connection electrode and the second connection electrode are arranged side by side along one side of the vibrating piece.

4. The vibrating piece according to claim 1, wherein The support portion includes: A second connection electrode arranged on one plane of the vibrating piece; and a first connecting electrode disposed on the other surface on the back side of one of the surfaces, The first connection electrode and the second connection electrode have overlapping portions in a plan view.

5. A vibrating plate, comprising an SC-cut quartz substrate, the SC-cut quartz substrate having a surface perpendicular to the Y" axis of an orthogonal coordinate system (X', Y", Z'), the orthogonal coordinate system (X', Y", Z') being obtained by rotating the orthogonal coordinate system (X, Y, Z) by a predetermined angle about the Z axis and rotating the orthogonal coordinate system (X', Y', Z) by a predetermined angle about the X' axis of the new orthogonal coordinate system (X', Y', Z) obtained by the rotation, The vibrating plate comprises: A support portion provided at one end portion in the first direction when viewed from above; an excitation portion arranged along the first direction with the support portion and having an excitation electrode disposed on the surface; and a slot having an opening in said face, The gap comprises: 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, arranged on one outer edge side of the excitation electrode 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, arranged 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 SC-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 equations (6) to (15): 0.38≤L1 / Lx<0.43, and -2.6×L1 / Lx+1.588≤L2 / Lx≤5.2×L1 / Lx-1.376… (6) 0.43≤L1 / Lx<0.49, and -0.625×L1 / Lx+0.739≤L2 / Lx≤1.167×L1 / Lx+0.358…(7) 0.49≤L1 / Lx<0.51, and -0.625×L1 / Lx+0.739≤L2 / Lx≤2×L1 / Lx-0.05… (8) 0.51≤L1 / Lx<0.6, and -0.444×L1 / Lx+0.647≤L2 / Lx≤0.97… (9) 0.6≤L1 / Lx<0.68, and 0.231×L1 / Lx+0.242≤L2 / Lx≤0.97… (10) 0.68≤L1 / Lx<0.7, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-5.5×L1 / Lx+4.5… (11) 0.68≤L1 / Lx<0.7, and 5.5×L1 / Lx-2.98≤L2 / Lx≤0.97… (12) 0.7≤L1 / Lx<0.73, and 0.231×L1 / Lx+0.242≤L2 / Lx≤-1.1×L1 / Lx+1.42… (13) 0.7≤L1 / Lx<0.73, and 3.333×L1 / Lx-1.463≤L2 / Lx≤0.97… (14) 0.73≤L1 / Lx≤0.8, and 0.929×L1 / Lx-0.268≤L2 / Lx≤-1.1×L1 / Lx+1.42…(15).

6. The vibrating piece according to claim 5, wherein: The slit passes through from one of the surfaces to the other surface located on the back side of the one surface.

7. The vibrating piece according to claim 5, wherein: The support portion includes a first connection electrode and a second connection electrode disposed on one of the surfaces of the vibrating piece. The first connection electrode and the second connection electrode are arranged side by side along one side of the vibrating element.

8. The vibrating piece according to claim 5, wherein: The support portion comprises: a second connection electrode disposed on one of the surfaces of the vibrating piece; and a first connecting electrode disposed on the other surface on the back side of one of the surfaces, The first connection electrode and the second connection electrode have overlapping portions in a plan view.

9. A vibration device comprising: A vibrating piece comprising an SC-cut quartz substrate according to any one of claims 1 to 8; and A substrate on which the support portion of the vibrating piece is mounted.

10. A vibrating piece, comprising an AT-cut quartz substrate having a surface perpendicular to the Y'-axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating the orthogonal coordinate system (X, Y, Z) around the X-axis by a predetermined angle, The vibrating plate comprises: A support portion provided at one end portion in the first direction when viewed from above; an excitation portion arranged along the first direction with the support portion and having an excitation electrode disposed on the surface; and a slot having an opening in said face, The gap comprises: 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, arranged on one outer edge side of the excitation electrode 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, arranged 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 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 equations (16) to (25): 0.0 < L1 / Lx < 0.2, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ 0.95… (16) 0.2 ≤ L1 / Lx < 0.27, and, -0.92×L1 / Lx + 0.26 ≤ L2 / Lx ≤ -2.0×L1 / Lx + 1.35… (17) 0.27 ≤ L1 / Lx < 0.36, and, 0.0 < L2 / Lx ≤ 1.56×L1 / Lx + 0.39… (18) 0.36 ≤ L1 / Lx < 0.54, and, 0.0 < L2 / Lx ≤ 0.95… (19) 0.54 ≤ L1 / Lx < 0.61, and, 0.0 < L2 / Lx ≤ -1.0×L1 / Lx + 1.49… (20) 0.61 ≤ L1 / Lx < 0.7, and, 0.0 < L2 / Lx ≤ 0.78×L1 / Lx + 0.41… (21) 0.7 ≤ L1 / Lx < 0.88, and, 0.0 < L2 / Lx ≤ 0.95… (22) 0.88 ≤ L1 / Lx ≤ 0.95, and, 0.0 < L2 / Lx ≤ -0.57×L1 / Lx + 0.77… (23) 0.88 ≤ L1 / Lx ≤ 0.95, and, 0.86×L1 / Lx - 0.48 ≤ L2 / Lx ≤ -0.71×L1 / Lx + 1.24… (24) 0.88 ≤ L1 / Lx ≤ 0.95, and, 1.29×L1 / Lx - 0.52 ≤ L2 / Lx ≤ 0.95… (25).

11. The diaphragm according to claim 10, wherein the slit penetrates from one surface to the other surface on the back side of one surface.

12. The diaphragm according to claim 10, wherein the support portion includes a first connection electrode and a second connection electrode disposed on one surface of the diaphragm, the first connection electrode and the second connection electrode are arranged along one side of the diaphragm.

13. The diaphragm according to claim 10, wherein the support portion includes: a second connection electrode disposed on one surface of the diaphragm; and a first connection electrode disposed on the other surface on the back side of one surface, the first connection electrode and the second connection electrode have an overlapping portion in a top view.

14. A diaphragm made of an AT-cut quartz substrate having a surface perpendicular to the Y' axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating a specified angle around the X axis of an orthogonal coordinate system (X, Y, Z), the diaphragm includes: a support portion provided at one end in a first direction along the X axis; an excitation portion arranged with the support portion in the first direction and having an excitation electrode disposed on the surface; and a slit having an opening on the surface, the slit includes: a first portion provided between the support portion and the excitation electrode and extending along a second direction intersecting the first direction A second part, which is connected to one end of the first part in the second direction, is disposed on one outer edge side of the excitation electrode in the second direction, and extends along the first direction; and A third part, which is connected to the other end of the first part in the second direction, is disposed on the other outer edge side of the excitation electrode in the second direction, and extends along the first direction, When the length from the outer edge on the excitation electrode side of the first part of the slit to the other end portion of the AT-cut quartz substrate in the first direction is set as Lx, the length of the second part is set as L1, and the length of the third part is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (26) to (33): 0.0 < L1 / Lx < 0.34, and 0.0 < L2 / Lx ≤ 1.294×L1 / Lx + 0.34… (26) 0.34 ≤ L1 / Lx < 0.55, and 0.857×L1 / Lx - 0.29 ≤ L2 / Lx ≤ 0.78… (27) 0.55 ≤ L1 / Lx < 0.61, and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.78… (28) 0.61 ≤ L1 / Lx < 0.80, and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.895×L1 / Lx + 0.23… (29) 0.80 ≤ L1 / Lx < 0.83, and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ 0.95… (30) 0.83 ≤ L1 / Lx < 0.89, and 0.471×L1 / Lx - 0.08 ≤ L2 / Lx ≤ -1.167×L1 / Lx + 1.51… (31) 0.83 ≤ L1 / Lx < 0.89, and 1.167×L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95… (32) 0.89 ≤ L1 / Lx ≤ 0.95, and 1.167×L1 / Lx - 0.35 ≤ L2 / Lx ≤ 0.95… (33).

15. The diaphragm according to claim 14, wherein The slit penetrates from one surface to the other surface on the back side of one surface.

16. The diaphragm according to claim 14, wherein The support portion includes a first connection electrode and a second connection electrode disposed on one surface of the diaphragm, The first connection electrode and the second connection electrode are arranged side by side along one side of the diaphragm.

17. The diaphragm according to claim 14, wherein The support portion includes: A second connection electrode disposed on one surface of the diaphragm; and A first connection electrode disposed on the other surface on the back side of one surface, The first connection electrode and the second connection electrode have an overlapping portion when viewed from above.

18. A vibrating piece is composed of an AT-cut quartz substrate, and the AT-cut quartz substrate has a plane perpendicular to the Y'-axis of a new orthogonal coordinate system (X, Y', Z') obtained by rotating a specified angle around the X-axis of an orthogonal coordinate system (X, Y, Z). The vibrating piece includes: A support portion provided at one end in the first direction along the X-axis; An excitation portion arranged in the first direction with the support portion, and an excitation electrode is disposed on the plane; and A slit having an opening on the plane, The slit includes: A first portion provided between the support portion and the excitation electrode and extending in a second direction intersecting with 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 in the first direction; and 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 in 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 in the first direction of the AT-cut quartz substrate is set as Lx, the length of the second portion is set as L1, and the length of the third portion is set as L2, L1 / Lx and L2 / Lx satisfy any one of the following formulas (34) to (41): 0.0 < L1 / Lx < 0.12, and, 0.0 < L2 / Lx ≤ 1.043×L1 / Lx + 0.10… (34) 0.12 ≤ L1 / Lx < 0.23, and, 1.061×L1 / Lx - 0.13 ≤ L2 / Lx ≤ 1.043×L1 / Lx + 0.10… (35) 0.23 ≤ L1 / Lx < 0.41, and, 1.061×L1 / Lx - 0.13 ≤ L2 / Lx ≤ 1.556×L1 / Lx - 0.02… (36) 0.41 ≤ L1 / Lx < 0.45, and, 1.061×L1 / Lx - 0.13 ≤ L2 / Lx ≤ 0.62… (37) 0.45 ≤ L1 / Lx < 0.54, and, 0.556×L1 / Lx + 0.10 ≤ L2 / Lx ≤ 0.62… (38) 0.54 ≤ L1 / Lx < 0.61, and, 0.40 ≤ L2 / Lx ≤ 0.62… (39) 0.61 ≤ L1 / Lx < 0.68, and, 0.40 ≤ L2 / Lx ≤ 0.571×L1 / Lx + 0.27… (40) 0.68 ≤ L1 / Lx ≤ 0.75, and, 0.571×L1 / Lx + 0.01 ≤ L2 / Lx ≤ 0.571×L1 / Lx + 0.27…(41).

19. The vibrating piece according to claim 18, wherein The slit penetrates from one plane to another plane on the back side of one plane.

20. The vibrating piece according to claim 18, wherein The support portion includes a first connection electrode and a second connection electrode disposed on one of the surfaces of the vibrating element, and the first connection electrode and the second connection electrode are arranged side by side along one side of the vibrating element.

21. The vibrating piece according to claim 18, wherein The support portion comprises: a second connection electrode disposed on one of the surfaces of the vibrating piece; and a first connecting electrode disposed on the other surface on the back side of one of the surfaces, The first connection electrode and the second connection electrode have overlapping portions in a plan view.

22. A vibration device comprising: A vibrating piece comprising an AT-cut quartz substrate according to any one of claims 10 to 21; and A substrate on which the support portion of the vibrating piece is mounted.

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