Vibration piece and vibration device

Abstract

To provide a vibration piece and a vibration device with excellent G sensitivity and aging characteristics.SOLUTION: A vibration piece 3 consists of an SC-cut quartz substrate having a surface perpendicular to the Y'' axis, and when the length from the outer edge of a first portion 35 of a slit 34 on the excitation electrode 38 side to the other end of the SC-cut quartz substrate 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, L1 / Lx and L2 / Lx satisfy any of the equations (1) to (5).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 tips 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 the package substrate via a bonding member. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2012-169890 A Summary of the Invention [Problem to be solved by the invention]

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

[0005] The vibrating piece is made of an SC-cut crystal substrate having a plane orthogonal to the Y'' axis of a rectangular coordinate system (X', Y'', Z') obtained by rotating a predetermined angle around the X axis of a rectangular coordinate system (X, Y, Z) and then rotating a predetermined angle around the Z' axis of the new rectangular coordinate system (X, Y', Z') obtained by this rotation. In plan view, it includes a support portion provided at one end in the first direction, 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 is provided between the support portion and the excitation electrode, 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 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 and 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 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 (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)

[0006] The vibrating piece is made of an SC-cut quartz crystal substrate having a surface orthogonal to the Y''-axis of a Cartesian coordinate system (X',Y'',Z') that is rotated by a predetermined angle around the X-axis of a Cartesian coordinate system (X,Y,Z) and rotated by a predetermined angle around the Z'-axis of a new Cartesian coordinate system (X,Y',Z') obtained by this rotation, and includes a support portion provided at one end in a first direction in a plan view, an excitation portion that is aligned with the support portion along the first direction and has an excitation electrode arranged on the surface, and a slit having an opening on the surface, the slit being provided between the support portion and the excitation electrode and including a first portion extending along a second direction intersecting the first direction, and a second portion extending along the first portion. a second portion connected to one end of the slit 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, where Lx is the length from the outer edge of the first portion on the excitation electrode side to the other end of the SC-cut quartz crystal substrate in the first direction, L1 is the length of the second portion, and L2 is the length of the third portion, L1 / Lx and L2 / Lx satisfy any of the following formulas (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)

[0007] 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 a predetermined angle around the X-axis of an orthogonal coordinate system (X, Y, Z). In plan view, it includes a support portion provided at one end in the first direction, an excitation portion arranged along the first direction and parallel to the support portion with 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 (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)

[0008] The vibrating device includes a vibrating piece made of the above-described SC-cut quartz crystal substrate, and a substrate to which the support portion of the vibrating piece is attached.

[0009] The vibrating device includes a vibrating piece made of the above-described AT-cut quartz crystal substrate, and a substrate to which the support portion of the vibrating piece is attached. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a plan view showing a schematic structure of a vibration device according to a first embodiment. [Diagram 2] Cross-sectional view taken along line A1-A1 in Figure 1. [Diagram 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 a vibrating element. [Diagram 5] FIG. 13 is a graph showing G sensitivity versus the in-plane rotation angle Ψ of the vibrating element. [Figure 6] FIG. 4 is a graph showing the amount of frequency variation with respect to the in-plane rotation angle Ψ of the vibrating element. [Figure 7] 1 is a graph showing the G sensitivity of a vibrating element relative to L1 / Lx and L2 / Lx. [Figure 8] FIG. 11 is a plan view showing a schematic structure of a vibration device according to a second embodiment. [Figure 9] FIG. 11 is a plan view showing a schematic structure of a vibration device according to a third embodiment. [Figure 10] FIG. 11 is a plan view showing a schematic structure of a vibrating element included in a vibrating device according to a third embodiment. [Figure 11] FIG. 4 is a plan view illustrating an in-plane rotation angle Ψ of a vibrating element. [Figure 12] FIG. 13 is a graph showing G sensitivity versus the in-plane rotation angle Ψ of the vibrating element. [Figure 13] FIG. 4 is a graph showing the amount of frequency variation with respect to the in-plane rotation angle Ψ of the vibrating element. [Figure 14] 1 is a graph showing the G sensitivity of a vibrating element relative to L1 / Lx and L2 / Lx. [Figure 15] FIG. 13 is a plan view showing a schematic structure of a vibration device according to a fourth embodiment. [Figure 16] 16 is a cross-sectional view taken along line A2-A2 in FIG. 15. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] 1. First embodiment First, a resonator 1 according to a first embodiment will be described with reference to Fig. 1 to Fig. 7, 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 sake of convenience in describing the internal configuration of the resonator device 1.

[0012] For ease of explanation, the following drawings of the vibration devices 1, 1a, 1b, and 1c show three mutually orthogonal axes, an X axis, a Y axis, and a Z axis. 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". The tip side of the arrow in each axial direction is called the "plus side", and the base side is called the "minus side".

[0013] Furthermore, for convenience of explanation, in FIG. 3 and FIG. 4, the X' axis, the Y'' axis, and the Z' axis are illustrated as three mutually orthogonal crystal axes corresponding to the crystal axes of quartz. 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". The tip side of the arrow in each axial direction is also called the "plus side", and the base side is also called the "minus side". In this embodiment, the first direction is the X' direction, and the second direction is the Z' direction. In addition, the X axis of each of the following vibration devices 1, 1a, and 1c except for the vibration device 1b coincides with the X' axis of the crystal axis, the Y axis coincides with the Z' axis of the crystal axis, and the Z axis coincides with the Y'' axis of the crystal axis.

[0014] As shown in FIGS. 1 and 2, the vibration device 1 includes a substrate 10, a cover 20, and a vibration element 3.

[0015] 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 bar 3. On the third surface 13, two electrode pads 11 and 12 that join the vibrating bar 3 are arranged side by side along the Y direction, and on the fourth surface 14, a plurality of external terminals 15 used for supplying power and outputting frequencies are provided. The electrode pads 11 and 12 and the external terminals 15 are electrically connected by wiring or through electrodes (not shown). Silicon is preferable as a constituent material of the substrate 10, but glass, ceramics, etc. may also be used.

[0016] The cover 20 is provided with a recess 21 that opens to the substrate 10 side, and an end face surrounding the opening of the recess 21 of the cover 20 is joined to the third surface 13 of the substrate 10 via a joining member 25, forming a storage space 22 that houses the vibrating element 3 together with the substrate 10. The cover 20 and the substrate 10 may be directly joined together without using the joining member 25. The inside of the storage 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. Silicon is a suitable material for the cover 20, but glass, ceramics, etc. may also be used.

[0017] As shown in FIG. 3, the vibrating element 3 has 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 SC-cut quartz crystal substrate. The SC-cut quartz crystal substrate has crystal axes X, Y, and Z that are perpendicular to each other, where 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. The substrate has a surface 31 that is perpendicular to the Y''-axis of a Cartesian coordinate system (X',Y'',Z') that is rotated left by a predetermined angle, for example, about 34° around the X-axis of a Cartesian coordinate system (X,Y,Z), and rotated left by a predetermined angle, for example, about 22° around the Z'-axis of a new Cartesian coordinate system (X,Y',Z') obtained by this rotation.

[0018] The quartz crystal substrate 30 is rectangular in plan view, with the X' direction being the long side direction, the Z' direction being the short side direction, and the Y'' direction being the thickness direction. A 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.

[0019] 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.

[0020] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b which are opposite to each other, and the second surface 31b faces 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, and the excitation electrode 38 is disposed on the excitation portion 32, and the first connection electrode 41 and the second connection electrode 42 are disposed on the support portion 33. The first connection electrode 41 and the second connection electrode 42 are disposed side by side along a short side which is one 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.

[0021] 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 electrode 40 provided on a 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 each other in a plan view.

[0022] A slit 34 penetrating from the second surface 31b of the 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. Since the slit 34 is provided between the support portion 33 and the excitation electrode 38, it is possible to suppress the transmission of distortion generated by bonding the vibrating element 3 to the substrate 10 and stress associated with temperature change to the excitation portion 32.

[0023] 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 a material such as a metal bump, solder, or conductive adhesive.

[0024] Next, the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ of the vibrating bar 3 will be described with reference to Fig. 4, Fig. 5, and Fig. 6. Note that the vibrating bar 3 used in the simulations of Fig. 5 and Fig. 6 does not have the slits 34 in order to clarify the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ.

[0025] The in-plane rotation angle Ψ of the vibrator element 3 is, as shown in FIG. 4, 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.

[0026] FIG. 5 shows the results of simulating the G sensitivity in each direction relative to the in-plane rotation angle Ψ of the vibrating element 3, and shows the G sensitivity in the X, Y, and Z directions of the vibrating device 1 in FIG. 1 when the in-plane rotation angle Ψ rotated left around the Y'' axis with respect to the X' axis as a reference is positive, and the in-plane rotation angle Ψ rotated right around the Y'' axis is negative. Γ is the square root of the sum of the squares of the G sensitivity in the X, Y, and Z directions. The in-plane rotation angle Ψ at which Γ is less than 1 ppb / G is 30° or more and 65° or less, or -150° or more and -125° or less.

[0027] FIG. 6 shows the results of simulating the frequency variation caused by thermal stress with respect to the in-plane rotation angle Ψ of the vibrating bar 3. The frequency variation on the vertical axis is shown based on the maximum absolute value of the frequency variation. The frequency variation is a numerical value that serves as an index for predicting aging characteristics; when the frequency variation is positive, the aging characteristics are upward-sloping, and when the frequency variation is negative, the aging characteristics are downward-sloping. From FIG. 6, the in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is -180° or more and -170° or less, or -20° or more and 5° or less, or 165° or more and 180° or less.

[0028] As can be seen from FIGS. 5 and 6, the range of the in-plane rotation angle Ψ that can make the G sensitivities in the X, Y, and Z directions less than ±1 ppb / G respectively is such that the frequency fluctuation amount is large, the range of the in-plane rotation angle Ψ where the frequency fluctuation amount is less than ±0.1 is such that the G sensitivity is large, and it has become clear that there is no range of the in-plane rotation angle Ψ that minimizes both the G sensitivity and the frequency fluctuation amount.

[0029] Therefore, in order to simultaneously reduce the G sensitivity and the frequency fluctuation amount, the in-plane rotation angle Ψ where the frequency fluctuation amount is less than ±0.1 is set to 0°, and the relationship between the lengths of the second part 36 and the third part 37 of the slit 34 and the G sensitivity will be described with reference to FIG. 7.

[0030] As shown in FIG. 3, FIG. 7 shows the results 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 part 35 of the slit 34 to the other end in the first direction of the crystal substrate 30 is Lx, the length of the second part 36 is L1, and the length of the third part 37 is L2. The G sensitivity is Γ which is the square root of the sum of the squares of the G sensitivities in the X, Y, and Z directions. Incidentally, in region A, Γ is 0.0 ppb / G or more and less than 0.2 ppb / G, in region B, Γ is 0.2 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 1.0 ppb / G, in region D, Γ is 1.0 ppb / G or more and less than 1.4 ppb / G, and in region E, Γ is 1.4 ppb / G or more and less than 1.8 ppb / G.

[0031] As can be seen from FIG. 7, the range of the in-plane rotation angle Ψ that can make the G sensitivities in the X, Y, and Z directions less than ±1 ppb / G respectively is the case where 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)

[0032] As described above, the vibration device 1 of this embodiment has a vibration piece 3 in which the in-plane rotation angle Ψ, which has a small frequency fluctuation, is 0°, and the ratios L1 / Lx and L2 / Lx of the length L1 of the second part 36 and the length L2 of the third part 37 of the slit 34 to the length Lx of the excitation section 32 satisfy any one of formulas (1) to (5). Therefore, the device has excellent aging characteristics and can obtain G sensitivity characteristics in which the G sensitivity in the X direction, Y direction, and Z direction is each less than ±1 ppb / G.

[0033] 2. Second embodiment Next, a vibration device 1a according to a second embodiment will be described with reference to Fig. 8. In Fig. 8, for the sake of convenience in describing the internal configuration of the vibration device 1a, a state in which the lid 20 is removed is illustrated.

[0034] The resonator device 1a of this embodiment is similar to the resonator device 1 of the first embodiment, except that the equations satisfying L1 / Lx and L2 / Lx of the resonator element 3a 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, and descriptions of similar matters will be omitted.

[0035] As shown in FIG. 8, the vibration device 1a includes a substrate 10, a cover 20, and a vibration element 3a.

[0036] In the vibrator element 3a of this embodiment, the in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is set to 0°, and the relationship between the length L1 of the second portion 36 of the slit 34 and the length L2 of the third portion 37 and the G sensitivity is the same as that in Fig. 7. Therefore, according to Fig. 7, the range of the in-plane rotation angle Ψ at which the G sensitivity in the X direction, Y direction, and Z direction can each be less than ±0.6 ppb / G is when L1 / Lx and L2 / Lx satisfy any of the following formulas (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)

[0037] As described above, the vibration device 1a of this embodiment is provided with a vibration piece 3a in which the in-plane rotation angle Ψ, which has a small frequency fluctuation, is 0°, and L1 / Lx and L2 / Lx satisfy any one of equations (6) to (15). As a result, the device has excellent aging characteristics and can obtain G sensitivity characteristics in which the G sensitivity in the X direction, Y direction, and Z direction is each less than ±0.6 ppb / G.

[0038] 3. Third embodiment Next, a vibration device 1b according to a third embodiment will be described with reference to Fig. 9 to Fig. 14. In Fig. 9, for the sake of convenience in describing the internal configuration of the vibration device 1b, the cover 20 is removed.

[0039] For convenience of explanation, in Figs. 10 and 11, the X-axis, Y'-axis, and Z'-axis are illustrated as three mutually orthogonal crystal axes corresponding to the crystal axes of quartz. 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". The tip side of the arrow in each axial direction is also called the "plus side", and the base side is also called the "minus side". In this embodiment, the first direction is the X-direction, and the second direction is the Z'-direction. In Fig. 9, the X-axis coincides with the X-axis of the crystal axis, the Y-axis coincides with the Z'-axis of the crystal axis, and the Z-axis coincides with the Y'-axis of the crystal axis.

[0040] The resonator device 1b of this embodiment is similar to the resonator device 1 of the first embodiment, except that the quartz substrate 30b of the resonator element 3b is different. Note that the following description will focus on the differences from the first embodiment, and descriptions of the similar points will be omitted.

[0041] As shown in FIG. 9, the resonator device 1b includes a substrate 10, a cover 20, and a resonator element 3b.

[0042] As shown in FIG. 10, the vibrating element 3b includes a quartz crystal substrate 30b, an excitation electrode , a first connection electrode 41, and a second connection electrode . The quartz crystal substrate 30b is an AT-cut quartz crystal substrate. The AT-cut quartz crystal substrate has crystal axes X, Y, and Z that are perpendicular to each other, where 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 orthogonal coordinate system (X,Y',Z') obtained by rotating a predetermined angle, for example, about 35°15' counterclockwise around the X-axis of the orthogonal coordinate system (X,Y',Z').

[0043] The quartz crystal substrate 30b is rectangular in plan view, with the long side direction being the X direction, the short side direction being the Z' direction, and the thickness direction being the Y' direction. A 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.

[0044] Next, the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ of the vibrating bar 3b will be described with reference to Fig. 11, Fig. 12, and Fig. 13. Note that the vibrating bar 3b used in the simulations of Fig. 12 and Fig. 13 does not have the slits 34 in order to clarify the relationship between the G sensitivity and the frequency variation with respect to the in-plane rotation angle Ψ.

[0045] The in-plane rotation angle Ψ of the vibrating element 3b is, as shown in FIG. 11, an angle between 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.

[0046] 12 shows the results of simulating the G sensitivity in each direction with respect to the in-plane rotation angle Ψ of the vibrating element 3b, and shows the G sensitivity in the X, Y, and Z directions of the vibrating device 1b in FIG. 9 when the in-plane rotation angle Ψ rotated left around the Y' axis with respect to the X axis as a reference is positive, and the in-plane rotation angle Ψ rotated right around the Y' axis is negative. Γ is a value obtained by taking the square root of the sum of the squares of the G sensitivity in the X, Y, and Z directions. The in-plane rotation angle Ψ at which Γ is less than 1 ppb / G is -180° or more and -140° or less, or -20° or more and 30° or less, or 160° or more and 180° or less.

[0047] Fig. 13 shows the results of simulating the frequency variation caused by thermal stress with respect to the in-plane rotation angle Ψ of the vibrating bar 3b. The frequency variation on the vertical axis is shown based on the maximum absolute value of the frequency variation. Fig. 13 shows that the in-plane rotation angle Ψ at which the frequency variation is less than ±0.1 is -110° to -70°, or 55° to 65°, or 115° to 130°.

[0048] 12 and 13, it is clear that the range of the in-plane rotation angle Ψ in which the G sensitivity in the X direction, Y direction, and Z direction can be made less than ±1 ppb / G has a large frequency variation, and the range of the in-plane rotation angle Ψ in which the frequency variation is less than ±0.1 has a large G sensitivity, and there is no range of the in-plane rotation angle Ψ in which the G sensitivity and frequency variation are minimum.

[0049] Therefore, in order to simultaneously reduce 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 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 with reference to FIG. 14.

[0050] 14 shows the results of simulating the G sensitivity for L1 / Lx and L2 / Lx when the length from the outer edge of the first portion 35 of the slit 34 on the excitation electrode 38 side to the other end of the quartz 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, as shown in FIG. 10, and the G sensitivity is Γ, which is the square root of the sum of the squares of the G sensitivity in the X direction, Y direction, and Z direction. In addition, in region B, Γ is 0.2 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 1.0 ppb / G, and in region D, Γ is 1.0 ppb / G or more and less than 1.4 ppb / G.

[0051] From FIG. 14, the range of the in-plane rotation angle Ψ in which the G sensitivity in the X direction, Y direction, and Z direction can be made less than ±1 ppb / G is when L1 / Lx and L2 / Lx satisfy any of the following formulas (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)

[0052] As described above, the vibration device 1b of the present embodiment has an in-plane rotation angle Ψ with a small frequency variation amount of -90°, and L1 / Lx and L2 / Lx, which are 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, satisfy any one of the formulas (16) to (25). Therefore, the vibration piece 3b has excellent aging characteristics, and G sensitivity characteristics with G sensitivities in the X direction, Y direction, and Z direction of less than ±1 ppb / G can be obtained.

[0053] 4. Fourth Embodiment Next, a vibration device 1c according to a fourth embodiment will be described with reference to Fig. 15 and Fig. 16. In Fig. 15, for the sake of convenience in describing the internal configuration of the vibration device 1c, a state in which the lid 20 is removed is illustrated.

[0054] 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, and descriptions of similar matters will be omitted.

[0055] As shown in FIGS. 15 and 16, the resonator device 1c includes a substrate 10c, a cover 20, and a resonator element 3c.

[0056] The substrate 10c has two electrode pads 11c and 12c arranged side by side along the longitudinal direction, that is, 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.

[0057] 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.

[0058] 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 (5).

[0059] The surface 31 of the quartz substrate 30 has a first surface 31a and a second surface 31b which are opposite surfaces, and a second connection electrode 42c is provided on the first surface 31a which is one surface 31 of the support portion 33, and a first connection electrode 41c is provided on the second surface 31b which is the other surface 31 of the support portion 33. The first connection electrode 41c and the second connection electrode 42c have an overlapping portion in the center of the short side direction of the quartz substrate 30 in a plan view.

[0060] 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.

[0061] 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.

[0062] With this configuration, the vibrating arm 3c is supported at one point, and the influence of the supporting stress can be further reduced, thereby obtaining the same effect as in the first embodiment. [Explanation of symbols]

[0063] 1, 1a, 1b, 1c...vibration device, 3, 3a, 3b, 3c...vibration 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, A, B, C, D, E...area, L1, L2, Lx...length, Ψ...in-plane rotation angle.

Claims

1. A crystal substrate made of an SC cut having a plane perpendicular to the Y'' axis of a Cartesian coordinate system (X', Y'', Z'), In a plan view, a support portion is provided at one end in the first direction, The support portion and the excitation portion are aligned along the first direction, and an excitation electrode is arranged on the surface thereof. The aforementioned surface includes a slit having an opening, The aforementioned slit is A first portion is provided between the support portion and the excitation electrode, and extends along a second direction intersecting the first direction, A second portion is connected to one end of the first portion in the second direction, positioned on one outer edge side of the excitation electrode in the second direction, and extending along the first direction, A third portion is connected to the other end of the first portion in the second direction, positioned on the other outer edge side of the excitation electrode in the second direction, and extending along the first direction, When Lx is 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, L1 is the length of the second portion, and L2 is the length of the third portion, L1 / Lx and L2 / Lx satisfy any of the following equations (1) to (5): vibrating piece. 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. A SC-cut quartz substrate having a plane perpendicular to the Y'' axis of a Cartesian coordinate system (X', Y'', Z'), In a plan view, a support portion is provided at one end in the first direction, The support portion and the excitation portion are aligned along the first direction, and an excitation electrode is arranged on the surface thereof. The aforementioned surface includes a slit having an opening, The aforementioned slit is A first portion is provided between the support portion and the excitation electrode, and extends along a second direction intersecting the first direction, A second portion is connected to one end of the first portion in the second direction, positioned on one outer edge side of the excitation electrode in the second direction, and extending along the first direction, A third portion is connected to the other end of the first portion in the second direction, positioned on the other outer edge side of the excitation electrode in the second direction, and extending along the first direction, When Lx is 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, L1 is the length of the second portion, and L2 is the length of the third portion, L1 / Lx and L2 / Lx satisfy any of the following equations (6) to (15): vibrating piece. 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)

3. Made of an AT-cut quartz substrate having a plane perpendicular to the Y' axis of a Cartesian coordinate system (X, Y', Z'), In a plan view, a support portion is provided at one end in the first direction, The support portion and the excitation portion are aligned along the first direction, and an excitation electrode is arranged on the surface thereof. The aforementioned surface includes a slit having an opening, The aforementioned slit is A first portion is provided between the support portion and the excitation electrode, and extends along a second direction intersecting the first direction, A second portion is connected to one end of the first portion in the second direction, positioned on one outer edge side of the excitation electrode in the second direction, and extending along the first direction, A third portion is connected to the other end of the first portion in the second direction, positioned on the other outer edge side of the excitation electrode in the second direction, and extending along the first direction, When Lx is 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, L1 is the length of the second portion, and L2 is the length of the third portion, L1 / Lx and L2 / Lx satisfy any of the following equations (16) to (25): vibrating piece. 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)

4. The slit penetrates from one surface to the other surface, which is the back side of the first surface. The vibrating piece according to any one of claims 1 to 3.

5. The support portion includes a first connecting electrode and a second connecting electrode arranged on one of the surfaces of the vibrating piece. The first connecting electrode and the second connecting electrode are arranged side by side along one side of the vibrating piece. The vibrating piece according to any one of claims 1 to 3.

6. The aforementioned support portion is The vibrating piece includes a second connecting electrode disposed on one of the surfaces of the vibrating piece, and a first connecting electrode disposed on the other surface, which is the back side of the first surface. The first connecting electrode and the second connecting electrode have an overlapping portion in a plan view. The vibrating piece according to any one of claims 1 to 3.

7. A vibrating piece made of an SC-cut quartz substrate according to claim 1 or claim 2, A substrate to which the support portion of the vibrating piece is attached, It is equipped with Vibration device.

8. A vibrating piece made of an AT-cut quartz substrate as described in claim 3, A substrate to which the support portion of the vibrating piece is attached, It is equipped with Vibration device.

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