JP2017200014A - Vibration piece substrate, manufacturing method for vibration piece, vibrator, oscillator, electronic apparatus, and movable body - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a vibration piece substrate capable of achieving improvement in yield of a vibration piece, and a manufacturing method for the vibration piece, a vibrator, an oscillator, an electronic apparatus and a movable body.SOLUTION: A vibration piece substrate has: a vibration piece 4; and a support section 2 connected to the vibration piece via a coupling section. The vibration piece has: a base section 41; and vibration arms 42 and 43 extending in a first direction from the base section. When n is defined as a natural number of 2 or more, and j is defined as a natural number of 1 or more and of n or less, the vibration piece is subjected to vibration having n pieces of natural vibration modes having resonance frequencies different from one another. The n pieces of natural vibration modes include a natural vibration mode of main vibration, and, in a relation among resonance frequencies fcorresponding to individual ones of the n pieces of natural vibration modes and an arbitrary integer k, standardize frequency differences by the arbitrary integer, and have a predetermined relationship among a resonance frequency of the main vibration and the frequency differences.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a resonator element substrate, a method for manufacturing a resonator element, a vibrator, an oscillator, an electronic device, and a moving body.

  Conventionally, as shown in Patent Document 1, a plurality of vibrating pieces are formed on a quartz wafer, and the resonance frequency or CI of the main vibration of each vibrating piece on the quartz wafer (that is, in a state of being connected to the quartz wafer). Measuring the value is done. Then, by removing the resonator element whose measurement result does not satisfy the predetermined condition, the yield of the resonator element is improved.

JP 2008-177723 A

  However, conventionally, since the coupling between the main vibration of the resonator element and the vibration mode of the crystal wafer is not taken into consideration, the resonance frequency and CI value of the main vibration of the resonator element on the crystal wafer and the crystal wafer can be removed from the crystal wafer. In some cases, the resonance frequency or CI value of the main vibration of the resonator element in the above state may be greatly different. Therefore, even if the predetermined condition is satisfied on the quartz wafer, a vibrating piece that does not satisfy the predetermined condition may be generated after being broken from the quartz wafer. Therefore, the yield of the resonator element cannot be increased.

  An object of the present invention is to provide a resonator element substrate, a method of manufacturing a resonator element, a resonator, an oscillator, an electronic device, and a moving body that can improve the yield of the resonator element.

  SUMMARY An advantage of some aspects of the invention is to solve at least a part of the problems described above, and the invention can be implemented as the following application examples.

としたとき、

の関係を満たし、
前記任意の整数ｋ_ｊは、

および、

の関係を満足することを特徴とする。
これにより、水晶ウエハ上で振動片の主振動の共振周波数やＣＩ値を測定する際に内部共振が発生し難くなり、水晶ウエハ上での振動片の主振動の共振周波数やＣＩ値と、水晶ウエハから折り取った状態での振動片の主振動の共振周波数やＣＩ値と、のズレを小さくすることができる。そのため、振動片の歩留まりの向上を図ることができる。 The vibration piece substrate of this application example includes at least one vibration piece,
A connecting part;
A support portion connected to the vibrating piece via the connecting portion;
Have
The vibrating piece is
The base,
A vibrating arm extending in a first direction from the base;
Have
n is a natural number of 2 or more,
When j is 1 or more and the natural number is n or less,
The vibrating piece vibrates having the n natural vibration modes having different resonance frequencies,
The n natural vibration modes include a natural vibration mode of a main vibration,
In the relationship between the resonance frequency f _j corresponding to each of the n natural vibration modes and an arbitrary integer k _j ,
Let the resonance frequency of the main vibration be f ₁ and the standardized frequency difference Δf be

When

Satisfy the relationship
The arbitrary integer k _j is

and,

It is characterized by satisfying the relationship.
This makes it difficult for internal resonance to occur when measuring the resonance frequency and CI value of the main vibration of the resonator element on the crystal wafer, and the resonance frequency and CI value of the main vibration of the resonator element on the crystal wafer and the crystal Deviations from the resonance frequency and CI value of the main vibration of the resonator element in the state of being broken from the wafer can be reduced. For this reason, the yield of the resonator element can be improved.

の関係を満足することが好ましい。
これにより、低次の非線形性が顕著に現れる振動片においても主振動と他の固有振動モードとの内部共振に起因した主振動の振動エネルギーの漏洩（以下、「振動漏れ」とも言う）を低減することができる。 In the vibration piece substrate of this application example,

It is preferable to satisfy this relationship.
As a result, leakage of vibration energy of the main vibration (hereinafter also referred to as “vibration leakage”) due to internal resonance between the main vibration and other natural vibration modes is reduced even in a resonator element in which low-order nonlinearity appears remarkably. can do.

In the resonator element substrate of this application example, the resonator element is
A pair of vibrating arms arranged in a second direction intersecting the first direction and extending from the base in the first direction;
A second direction anti-phase mode in which the pair of vibrating arms bend and vibrate in the opposite direction to the second direction;
A second direction in-phase mode in which the pair of vibrating arms flexurally vibrate in the second direction in phase;
A third direction anti-phase mode in which the pair of vibrating arms bend and vibrate in a reverse phase in a third direction along the thickness direction of the base,
A third direction in-phase mode in which the pair of vibrating arms bend and vibrate in phase in the third direction;
A torsional anti-phase mode in which the pair of vibrating arms is twisted in an anti-phase around an axis extending in the first direction;
A torsional in-phase mode in which the pair of vibrating arms are twisted in-phase around an axis extending in the first direction;
At least two of the third direction substrate mode in which the resonator element substrate deforms along the third direction and the substrate contour mode in which the contour of the resonator element substrate deforms in a direction intersecting the third direction. It is preferable to include a higher-order mode of the eigenmode.
As a result, vibrations in parts other than the vibrating arms are reduced, and the vibrator has a small vibration leakage.

In the resonator element substrate of this application example, it is preferable that the higher-order modes of the third direction substrate mode and the substrate contour mode are modes of the second order or more and the tenth order or less.
Since the higher order mode has a larger influence on the main vibration as the order is smaller, the effect of the present invention is further increased.

In the resonator element substrate of this application example, it is preferable that the main vibration is in the second direction antiphase mode.
As a result, a high Q value can be realized, and a resonator element having a small CI value can be obtained.

の関係を満足することが好ましい。
ただし、

ρ［ｋｇ／ｍ^３］は、前記振動腕の質量密度
Ｃｐ［Ｊ／（ｋｇ・Ｋ）］は、前記振動腕の熱容量
ｋ［Ｗ／（ｍ・Ｋ）］は、前記振動腕の前記主振動の振動方向に沿った熱伝導率
これにより、Ｑ値の劣化を低減することができる。 In the resonator element substrate of this application example, the vibrating arm has a groove portion that opens to a main surface,
When the length of the vibrating arm in the first direction is L [m],
At least a part of the groove is provided between the base end of the vibrating arm and a position spaced from the base end to the tip side by L / 3,
When the length of the vibration direction of the main vibration of the vibrating arm is W [m],

It is preferable to satisfy this relationship.
However,

ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm k [W / (m · K)] is the main density of the vibrating arm Thermal conductivity along the vibration direction of the vibration. Thereby, deterioration of the Q value can be reduced.

の関係を満足することが好ましい。
ただし、

ρ［ｋｇ／ｍ^３］は、前記振動腕の質量密度
Ｃｐ［Ｊ／（ｋｇ・Ｋ）］は、前記振動腕の熱容量
ｋ［Ｗ／（ｍ・Ｋ）］は、前記振動腕の前記主振動の振動方向に沿った熱伝導率
これにより、Ｑ値の劣化を低減することができる。 In the resonator element substrate of this application example, when the length of the vibration direction of the main vibration of the vibrating arm is W [m],

It is preferable to satisfy this relationship.
However,

ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm k [W / (m · K)] is the main density of the vibrating arm Thermal conductivity along the vibration direction of the vibration. Thereby, deterioration of the Q value can be reduced.

In the resonator element substrate of this application example, it is preferable that the resonator element has one virtual vibration symmetry plane that is a symmetry plane with respect to the main vibration.
As a result, vibration leakage is reduced, and a decrease in Q value is reduced.

In the resonator element substrate of this application example, it is preferable that the resonator element has at least two virtual vibration symmetry planes that are symmetry planes with respect to the main vibration.
As a result, vibration leakage is reduced, and a decrease in Q value is reduced.

In the resonator element substrate of this application example, it is preferable that the connecting portion overlaps the virtual vibration symmetry plane.
Thereby, the vibration of the vibrating arm is difficult to leak to the support portion.

In the resonator element substrate of this application example, it is preferable that the connecting portion is separated from the virtual vibration symmetry plane.
Thereby, since the vibration of the vibrating arm is likely to leak to the support portion, the effect of the present invention is further increased.

の関係を満足することが好ましい。
ただし、

Ａ＝７．３６９０×１０^−２
Ｂ＝１．２５４４×１０^−５
Ｃ＝１．１以上、１．３以下
ρ［ｋｇ／ｍ^３］は、前記振動腕の質量密度
Ｃｐ［Ｊ／（ｋｇ・Ｋ）］は、前記振動腕の熱容量
ｃ［Ｎ／ｍ^２］は、前記振動腕の延在方向に関する弾性定数
α［１／Ｋ］は、前記振動腕の延びる方向に関する熱膨張係数
Θ［Ｋ］は、環境温度
ｋ［Ｗ／（ｍ・Ｋ）］は、前記振動腕の前記主振動の振動方向に沿った熱伝導率
πは、円周率
これにより、小型で、Ｑ値の高い振動片となる。 In the vibration piece substrate of this application example,
When the Q value of the resonator element is Q,

It is preferable to satisfy this relationship.
However,

A = 7.3690 × 10 ⁻²
B = 1.2544 × 10 ⁻⁵
C = 1.1 or more and 1.3 or less ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm c [N / m ² ] Is the elastic constant α [1 / K] in the extending direction of the vibrating arm, the thermal expansion coefficient Θ [K] in the extending direction of the vibrating arm is the environmental temperature k [W / (m · K)], The thermal conductivity π along the vibration direction of the main vibration of the vibrating arm is the circumferential ratio. Thus, the vibration piece is small and has a high Q value.

The manufacturing method of the resonator element according to the application example includes a step of preparing the resonator element substrate according to the application example,
Cutting the connecting portion to separate the vibrating piece from the support portion.
Thereby, a resonator element with little deviation from desired vibration characteristics (resonance frequency and CI value) can be obtained.

The vibrator according to the application example includes the resonator element separated from the resonator element substrate according to the application example,
And a package for housing the vibration piece.
Thereby, a highly reliable vibrator is obtained.

The oscillator of this application example, the resonator element separated from the resonator element substrate of the application example,
And an oscillation circuit.
Thereby, a highly reliable oscillator can be obtained.

An electronic apparatus according to this application example includes the resonator element separated from the resonator element substrate according to the application example.
As a result, a highly reliable electronic device can be obtained.

The moving body of this application example includes the vibration piece separated from the vibration piece substrate of the application example.
Thereby, a mobile body with high reliability is obtained.

FIG. 3 is a plan view showing the resonator element substrate according to the first embodiment of the invention. FIG. 2 is a top view of a resonator element included in the resonator element substrate illustrated in FIG. 1. FIG. 3 is a transmission diagram when the resonator element shown in FIG. 2 is viewed from the upper surface side. FIG. 3 is a cross-sectional view of the resonator element shown in FIG. 2. It is sectional drawing of the vibrating arm explaining the heat conduction at the time of bending vibration. It is a graph showing the relationship between the Q value and _f 1 / f0. It is a top view which shows the natural vibration mode of a vibration piece board | substrate. It is a top view which shows the natural vibration mode of a vibration piece board | substrate. It is a graph which shows the relationship between (DELTA) f and Q value. It is a graph which shows the relationship between (DELTA) f and temperature. It is a graph which shows the relationship between CI increase rate and temperature. It is a graph which shows the relationship between CI and temperature. It is a graph which shows the relationship between the length of a vibrating arm, and the width | variety of a vibrating arm. 6 is a plan view of a resonator element substrate according to a second embodiment of the invention. FIG. 6 is a plan view of a resonator element substrate according to a third embodiment of the invention. FIG. 6 is a plan view of a resonator element substrate according to a fourth embodiment of the invention. FIG. It is a figure explaining the action | operation of the vibration piece which the vibration piece board | substrate shown in FIG. It is a figure explaining the action | operation of the vibration piece which the vibration piece board | substrate shown in FIG. FIG. 10 is a plan view of a resonator element substrate according to a fifth embodiment of the invention. FIG. 20 is a plan view illustrating a modification of the resonator element substrate illustrated in FIG. 19. FIG. 10 is a plan view of a resonator element substrate according to a sixth embodiment of the invention. It is a figure explaining the action | operation of the vibration piece which the vibration piece board | substrate shown in FIG. 21 has. It is a figure explaining the action | operation of the vibration piece which the vibration piece board | substrate shown in FIG. 21 has. It is a top view showing a vibrator concerning a 7th embodiment of the present invention. FIG. 25 is a cross-sectional view of the vibrator shown in FIG. 24. It is a flowchart which shows the manufacturing method of a vibration piece. It is sectional drawing which shows the oscillator concerning 8th Embodiment of this invention. 1 is a perspective view illustrating a configuration of a mobile (or notebook) personal computer to which an electronic apparatus of the present invention is applied. It is a perspective view which shows the structure of the mobile telephone (a smart phone, PHS etc. are included) to which the electronic device of this invention is applied. It is a perspective view which shows the structure of the digital still camera to which the electronic device of this invention is applied. It is a perspective view which shows the motor vehicle to which the mobile body of this invention is applied.

  Hereinafter, the resonator element substrate, the method for manufacturing the resonator element, the vibrator, the oscillator, the electronic apparatus, and the moving body of the present invention will be described in detail based on preferred embodiments shown in the drawings.

<First Embodiment>
First, the resonator element substrate according to the first embodiment of the invention will be described.

FIG. 1 is a plan view showing a resonator element substrate according to the first embodiment of the present invention. FIG. 2 is a top view of the resonator element included in the resonator element substrate illustrated in FIG. 1. 3 is a transmission diagram when the resonator element shown in FIG. 2 is viewed from the upper surface side. 4 is a cross-sectional view of the resonator element shown in FIG. FIG. 5 is a cross-sectional view of a vibrating arm for explaining heat conduction during bending vibration. FIG. 6 is a graph showing the relationship between the Q value and f ₁ / f 0. 7 and 8 are plan views showing natural vibration modes of the resonator element substrate. FIG. 9 is a graph showing the relationship between Δf and the Q value. FIG. 10 is a graph showing the relationship between Δf and temperature. FIG. 11 is a graph showing the relationship between the CI increase rate and temperature. FIG. 12 is a graph showing the relationship between CI and temperature. FIG. 13 is a graph showing the relationship between the length of the vibrating arm and the width of the vibrating arm.

  In each figure, the X axis, the Y axis, and the Z axis are appropriately illustrated as three axes orthogonal to each other, and the X axis (electrical axis) in which the X axis, the Y axis, and the Z axis are crystal axes of the crystal. , Y axis (mechanical axis) and Z axis (optical axis). In the following description, the direction parallel to the X axis (second direction) is the “X axis direction”, the direction parallel to the Y axis (first direction) is the “Y axis direction”, and the direction parallel to the Z axis ( The third direction) is referred to as the “Z-axis direction”, and the tip side of the X-axis, Y-axis, and Z-axis arrows shown in each figure is “+ (plus)”, and the base end side is “− ( It is also called “minus”. The −Z-axis direction side is also referred to as “upper”, and the + Z-axis direction side is also referred to as “lower”. In the following description, the plan view when viewed from the Z-axis direction is also simply referred to as “plan view”.

  A vibrating reed substrate 1 shown in FIG. 1 is obtained by patterning a quartz crystal wafer 10 as a base material by using a photolithography technique and an etching technique (particularly, a wet etching technique), and at least one (a plurality in this embodiment). And the support part 2 connected to the vibration piece 4 via the folding part 3. In such a resonator element substrate 1, the resonator element 4 can be separated into pieces by folding the resonator element 4 in the folding unit 3. As shown in FIG. 2, a groove portion 31 is provided in the breaker portion 3 to make a part thereof weak so that the breaker portion 3 can be easily broken.

  In this embodiment, a Z-cut quartz wafer whose Z axis coincides with the thickness direction is used as the quartz wafer 10, but the cut angle of the quartz wafer 10 is not particularly limited. For example, from the viewpoint of reducing the frequency temperature change near normal temperature, the Z axis may be slightly inclined (for example, less than about ± 15 °) with respect to the thickness direction of the crystal wafer 10, You may use the crystal wafer of the cut | disconnection corresponding to a Y-axis. Further, the number of the vibrating pieces 4 formed on the quartz wafer 10 differs depending on the size of the vibrating piece 4 or the quartz wafer 10 and may be at least one. Moreover, the shape of the support part 2 or the folding part 3 will not be specifically limited if the function can be fulfill | performed.

  Next, the vibration piece 4 will be described. As shown in FIGS. 2 and 3, the resonator element 4 includes a vibrating body 40 configured as a part of the quartz wafer 10 and an electrode disposed on the surface of the vibrating body 40. The vibrating body 40 includes a base 41, a pair of vibrating arms 42 and 43 extending from the base 41 in the −Y axis direction, and a base 41, extending in the −Y axis direction, and a pair of vibrating arms 42 and 43. And a support arm 44 located between the two.

  The base 41 extends along the XY plane and has a plate shape with the Z-axis direction as the thickness direction. The base portion 41 is connected to the support portion 2 via the folding portion 3. The vibrating arms 42 and 43 extend in the −Y axis direction from the base portion 41 so as to be aligned in the X axis direction and parallel to each other. In addition, the vibrating arms 42 and 43 are arranged on the distal end side of the arm portions 421 and 431 whose width (length in the X-axis direction) is substantially constant, and the arm portions 421 and 431, and more than the arm portions 421 and 431. Wide portions 429 and 439 having a wide width. However, the configuration of the vibrating arms 42 and 43 is not particularly limited. For example, the wide portions 429 and 439 may be omitted.

  As shown in FIG. 4, the arm portion 421 includes a bottomed groove portion 422 that opens to the upper surface (the main surface on the −Z axis side) and a bottomed groove portion that opens to the lower surface (the main surface on the + Z axis side). 423. Similarly, the arm portion 431 includes a bottomed groove portion 432 that opens to the upper surface and a bottomed groove portion 433 that opens to the lower surface. As described above, by providing the groove portions 422 and 423 on the vibrating arm 42 and the groove portions 432 and 433 on the vibrating arm 43, as will be described later, the movement path of heat generated by bending vibration becomes longer, and in the adiabatic region. The thermoelastic loss can be reduced, and the Q value of the resonator element 4 can be improved. When the wet etching technique is used, the grooves 422 and 423 do not have a rectangular shape as shown in FIG. 4, but have a complicated shape due to the crystal anisotropy, but the description thereof is omitted here. To do.

  The support arm 44 extends in the −Y-axis direction from the base 41 and is positioned between the vibrating arms 42 and 43. After the vibration piece 4 is broken off from the vibration piece substrate 1, the vibration piece 4 is fixed to an object (for example, a base 91 of a seventh embodiment described later) via the support arm 44. Note that the support arm 44 may be omitted, and in this case, the vibrating piece 4 may be fixed to the above-described object via the base 41.

  The electrodes include a first drive electrode 481 and a first drive terminal 482, and a second drive electrode 491 and a second drive terminal 492. As shown in FIG. 4, the first drive electrode 481 is disposed on the upper and lower surfaces of the vibrating arm 42 (the inner surfaces of the groove portions 422 and 423) and the both sides of the vibrating arm 43, and the second drive electrode 491 is the vibrating arm 42. 42 and the upper and lower surfaces of the vibrating arm 43 (inner surfaces of the grooves 432 and 433). As shown in FIG. 3, the first drive terminal 482 is disposed on the support arm 44 and is electrically connected to the first drive electrode 481. Similarly, the second drive terminal 492 is disposed on the support arm 44 and is electrically connected to the second drive electrode 491.

  In such a resonator element 4, when a drive signal (for example, an alternating voltage having a frequency substantially equal to the resonance frequency of the main vibration) is applied between the first drive electrode 481 and the second drive electrode 491, in FIG. 2 and FIG. 3. As shown by the arrow A, the vibrating arms 42 and 43 bend and vibrate in the opposite phase in the X-axis direction (so as to repeatedly approach and separate from each other). This vibration mode is also referred to as “X-axis reversed phase mode (second direction reversed phase mode)”, and is a vibration mode (natural vibration mode) that is the main vibration of the resonator element 4. Thus, by setting the X-axis reverse phase mode as the main vibration, a high Q value can be realized, and the vibration piece 4 having a small CI value is obtained. The “main vibration” refers to a natural vibration mode in which the resonator element 4 is electrically driven directly.

  As shown in FIG. 4, the resonator element 4 has one virtual vibration symmetry plane F <b> 1 (YZ plane) that is a symmetry plane with respect to the X-axis reverse phase mode that is the main vibration of the pair of vibration arms 42 and 43. Have. Therefore, the vibrations of the vibrating arms 42 and 43 are canceled, and the vibration energy is difficult to leak to the base 41. Therefore, it is possible to reduce a decrease in the Q value. In practice, the resonator element 4 vibrates in a state in which the Z-axis anti-phase mode and the torsion anti-phase mode that are unnecessary vibrations are coupled to the X-axis anti-phase mode that is the main vibration. The plane of symmetry F1 is a plane of symmetry when only the main vibration is taken into account while eliminating these unnecessary vibrations. These unnecessary vibrations will be described later. Moreover, the vibration piece 4 does not need to have a completely symmetrical shape with respect to the virtual vibration symmetry plane F1, and may have an asymmetric shape within a range in which the effect of the present invention can be obtained. Specifically, even if there is a fine asymmetry generated due to the anisotropy of the crystal when the crystal is wet-etched, an asymmetry of the electrode wiring, etc., the main surface of the resonator element 4 is viewed in plan view. The outer shape may be substantially symmetric with respect to the virtual vibration symmetry plane F1.

The resonance frequency f ₁ in the X-axis reversed phase mode that is the main vibration is not particularly limited, but is preferably 1 × 10 ³ [Hz] or more and 1 × 10 ⁶ [Hz] or less, and 31.768 [kHz] ], More preferably 33.768 [kHz] or less, that is, within a range of 32.768 ± 1.0 [kHz]. By setting f ₁ to such a frequency, a highly convenient resonator element 4 can be obtained.

  As shown in FIG. 3, the first and second drive electrodes 481, 491 are drawn out to the support part 2 through the folding part 3, and the measurement terminal 21 arranged on the support part 2. , 22 are electrically connected. When measuring the resonance frequency and CI value of the main vibration of the resonator element 4 on the resonator element substrate 1, the measurement terminals 21 and 22 are used. In this way, since the above measurement can be performed in non-contact with the resonator element 4, it is possible to reduce that the resonator element 4 is unintentionally broken off.

  The configuration of the resonator element substrate 1 has been briefly described above. Next, the above-described “thermoelastic loss” will be briefly described by taking the vibrating arm 42 as an example. As described above, when the vibrating arm 42 bends and vibrates in the X-axis direction, if one side surface of the arm portion 421 contracts, the other side surface expands. Conversely, if one side surface expands, the other side surface contracts. . When the vibrating arm 42 does not generate the Gough-Joule effect (energy elasticity is dominant with respect to entropy elasticity), as shown in FIG. Since it descends, a temperature difference occurs between both side surfaces, that is, inside the arm portion 421. Loss of vibration energy occurs due to heat transfer (see the arrow in FIG. 5) resulting from such a temperature difference, and thereby the Q value of the resonator element 4 decreases. Such a decrease in the Q value is also referred to as a thermoelastic effect, and energy loss due to the thermoelastic effect is referred to as “thermoelastic loss”.

In a vibrating piece that vibrates in the bending vibration mode, such as the vibrating piece 4, when the resonance frequency f ₁ (mechanical bending vibration frequency) of the main vibration of the vibrating arm 42 matches the thermal relaxation frequency f0, the minimum Q value ( Q0). The thermal relaxation frequency f0 can be obtained by f0 = 1 / (2πτ) (where π is the circumference ratio, and e is the Napier number, τ is the temperature difference of the thermal conductivity. Is the relaxation time required for e ⁻¹ times).

  As described above, in the vibrating arm 42, the groove portions 422 and 423 are disposed so as to be positioned between both side surfaces. For this reason, a heat transfer path is formed so as to bypass the groove portions 422 and 423 in order to balance the temperature difference between the two side surfaces generated during flexural vibration of the vibrating arm 42 by heat conduction. It becomes longer than the straight line distance (shortest distance). Therefore, the relaxation time τ becomes longer than in the case where the vibrating arms 42 are not provided with the groove portions 422 and 423, and the thermal relaxation frequency f0 of the vibrating arm 42 having the groove portions 422 and 423 becomes smaller than the groove portions 422 and 423. It becomes lower than the thermal relaxation frequency f0 of the vibrating arm 42 which does not have.

FIG. 6 is a graph showing the f ₁ / f 0 dependence of the Q value of the vibration piece in the bending vibration mode. A region where f ₁ / f 0 <1 is also referred to as an “isothermal region”. In this isothermal region, the Q value increases as f ₁ / f 0 decreases. This is because, as the resonance frequency f ₁ of the main vibration (mechanical frequency of the vibrating arm) becomes lower (the vibration of the vibrating arm becomes slower), the above-described temperature difference in the vibrating arm becomes difficult to occur. Therefore, in the limit when f ₁ / f 0 is brought as close as possible to 0 (zero), the operation becomes an isothermal quasi-static operation, and the thermoelastic loss approaches 0 (zero) as much as possible. On the other hand, the region of f ₁ / f 0> 1 is also referred to as “adiabatic region”. In this adiabatic region, the Q value increases as f ₁ / f 0 increases. This, as the resonance frequency f ₁ of the main vibration is high, switches become faster temperature rise and temperature effects of each side, is because there is no time for heat conduction, as described above (heat transfer) occurs. Therefore, in the limit when f ₁ / f 0 is increased as much as possible, the operation becomes adiabatic and the thermoelastic loss approaches 0 (zero) as much as possible. The resonator element 4 of the present embodiment is in such a heat insulating region.

In FIG. 6, a curved line K <b> 1 indicated by a chain line indicates a case where a groove is formed on the vibrating arm like the vibrating piece 4, and a curved line K <b> 2 indicated by a solid line indicates that the groove is formed on the vibrating arm. The case where it is not formed is shown. Although the shapes of the curves K1 and K2 are hardly changed, the curve K1 is shifted in the frequency decreasing direction with respect to the curve K2 as the thermal relaxation frequency f0 is decreased as described above. Therefore, in the adiabatic region, the Q value of the vibrating piece in which the groove portion is formed in the vibrating arm is higher than the Q value of the vibrating piece in which the groove portion is not formed in the vibrating arm. Therefore, as described above, the resonator element 4 of the present embodiment can realize a high Q value. As is clear from FIG. 6, the point where the Q value of the resonator element corresponding to the curve K1 in the isothermal region is equal to the Q value of the resonator element corresponding to the curve K2, that is, the curve K1 and the curve K2 intersect. In a region where f ₁ / f 0 is smaller than the point to be formed, if a groove is formed in the vibrating arm, the thermoelastic loss increases and the Q value deteriorates.

  Here, as shown in FIGS. 2 and 3, when the length of the vibrating arm 42 (the length in the Y-axis direction) is L [m], the base end (the vibrating arm 42, the base 41, At least a part of the groove portions 422 and 423 is provided in a region Sy between the base end portion and a position separated by L / 3 from the base end to the distal end side of the vibrating arm 42. At the time of vibration, the base end portion of the vibrating arm 42 is deformed more greatly than the distal end portion, so that the temperature difference in the vibrating arm 42 is increased. Therefore, by disposing the groove portions 422 and 423 on the base end side of the vibrating arm 42, the effect of disposing the groove portions 422 and 423 (that is, the effect of reducing the thermoelastic loss in the adiabatic region) can be achieved. Can be increased.

  As shown in FIG. 4, the total depth T ′ of the grooves 422 and 423 is not particularly limited, but when the thickness of the vibrating arm 42 is T, the relationship of 0.8T ≦ T ′ <T is satisfied. It is preferable to satisfy. Satisfying such a relationship can further enhance the effect of disposing the groove portions 422 and 423 (that is, the effect of reducing the thermoelastic loss in the adiabatic region). Here, when the groove portions 422 and 423 are formed by wet etching, a crystal plane of quartz appears, and the cross-sectional shape of the groove portions 422 and 423 does not become a rectangle as shown in FIG. 4, but in this case, the groove portions 422 and 423 The deepest part is defined as the “depth”. The same applies to the grooves 432 and 433 of the vibrating arm 43.

  Further, when the width (length in the X-axis direction (vibration direction of the main vibration)) of the arm portion 421 of the vibrating arm 42 (the same applies to the vibrating arm 43) is W [m], the following formula (1A) ) Is preferably satisfied, the following formula (1B) is more preferably satisfied, the following formula (1C) is more preferably satisfied, and the following formula (1D) is more preferably satisfied.

W ₀ is an imaginary width (length in the direction of bending vibration) when the cross-sectional shape of the vibrating arm 42 is rectangular, the mass density of the vibrating arm 42 is ρ [kg / m ³ ], and vibration is performed. The heat capacity of the arm 42 is Cp [J / (kg · K)], the thermal conductivity along the vibration direction of the main vibration of the vibrating arm 42 is k [W / (m · K)], and the circumference is π. When the resonance frequency of the main vibration (X-axis reversed phase mode) is f ₁ [Hz], it is expressed by the following equation (2).

  By satisfying the expressions (1A) to (1D) as described above, the main vibration becomes vibration in the adiabatic region, and by forming the groove portions 422 and 423 in the vibrating arms 42 and 43, the vibrating arms 42 and 43 are formed. The deterioration of the Q value due to the thermoelastic loss generated by the bending vibration of is reduced.

  The thermoelastic loss has been described above. Next, the relationship between the X-axis reverse phase mode that is the main vibration of the resonator element 4 and other unnecessary vibration modes will be described.

First, the unnecessary vibration mode will be described. In addition to the main vibration (X-axis reverse phase mode) described above, the resonator element 4 is unstable with respect to temperature and is not designed to reduce vibration leakage, or is difficult to reduce. It has an unnecessary vibration mode that is a natural vibration mode. When the resonance frequency of the undesired oscillation mode has a relationship described below the resonance frequency f ₁ of the main vibration, unwanted vibration mode is the main vibration and internal resonance, the energy of the primary vibration to the outside through the unnecessary vibration mode It will leak. For this reason, the vibration characteristics are deteriorated, for example, the Q value of the main vibration is deteriorated, the CI value of the main vibration is increased, and the resonance frequency of the main vibration is not stabilized.

  Such an unnecessary vibration mode is not particularly limited as long as it is a natural vibration mode other than the main vibration, but for example, an X-axis common mode (second direction common mode), a Z-axis reverse phase mode (third direction reverse phase), for example. Mode), Z-axis common mode (third direction common mode), torsional anti-phase mode, torsional common mode, Z-axis substrate mode (third direction substrate mode) and substrate contour mode. Preferably it includes a mode. These unnecessary vibration modes have a low resonance frequency among many unnecessary vibration modes, and tend to be easily coupled to the main vibration. Therefore, by having these modes as unnecessary vibrations, the effects of the present invention described below become more remarkable. In addition, these unnecessary vibration modes reduce the vibrations of the parts other than the vibrating arms 22 and 23, so that the vibration piece 2 with small vibration leakage is obtained. In addition, when the main vibration is not the X-axis reverse phase mode, the X-axis reverse phase mode may be included in such an unnecessary vibration mode.

  Moreover, it is preferable that the higher-order mode includes at least one of secondary modes of the X-axis reverse phase mode, the X-axis common-mode, the Z-axis reverse-phase mode, and the Z-axis common-mode. Moreover, it is also preferable that the higher-order mode includes at least one of a second-order or higher-order mode of the Z-axis substrate mode and the substrate contour mode. Since the higher order mode tends to be coupled to the main vibration as the order is smaller, the effect of the present invention described below becomes more remarkable by having the above higher order mode as unnecessary vibration.

  As shown in FIG. 7, the X-axis common mode is a natural vibration mode in which the vibrating arms 42 and 43 flexurally vibrate in the X-axis direction (in the same direction as each other). The Z-axis reverse phase mode is a natural vibration mode in which the vibrating arms 42 and 43 bend and vibrate in the reverse phase in the Z-axis direction. The Z-axis common mode is a natural vibration mode in which the vibrating arms 42 and 43 flexurally vibrate in the Z-axis direction. Further, in the torsional anti-phase mode, the vibrating arms 42 and 43 have their axes (virtual center line along the Y-axis direction passing through the center of the cross section along the X-axis direction and the Z-axis direction of the vibrating arms 42 and 43). The natural vibration mode is twisted in the opposite phase. The torsional in-phase mode is a natural vibration mode in which the vibrating arms 42 and 43 are twisted in phase around the axis.

  As shown in FIG. 8, the Z-axis substrate mode is a natural vibration mode in which the resonator element substrate 1 is entirely deformed along the Z-axis direction. The substrate contour mode is a natural vibration mode in which the contour of the resonator element substrate 1 is deformed in the direction intersecting the Z-axis direction, that is, in the XY plane. 7 and 8, “×” in “•” and “×” in “◯” indicates the displacement direction of the vibrating arm (“•” in “◯” indicates the front side of the page). , “×” in “O” indicates that the repetition is repeated depending on the presence or absence of a solid line and a broken line, or parentheses.

  Next, the relationship between the resonance frequency of the main vibration (X-axis reversed phase mode) and the resonance frequency of the unnecessary vibration mode will be described.

When n is a natural number of 2 or more and j is a natural number of 1 or more and less than or equal to n, the resonator element 4 has n natural vibration modes having different resonance frequencies, that is, an X axis that is a main vibration. It vibrates with a negative phase mode and at least one unnecessary vibration mode, and the resonance frequency corresponding to each of the n natural vibration modes is f _j , and an arbitrary integer is k _j (however, two of k _j ) The above is not 0 (≠ 0) and k ₁ ≠ 0). In the relationship between f _j and k _j , the resonance frequency of the main vibration of the resonator element 4 among the n natural vibration modes is f. _{When 1} (that is, j = 1) and the normalized frequency difference Δf is represented by the following expression (3), the following expression (4) is satisfied.

Further, the integer k _j and the natural number n satisfy the following expressions (5) and (6).

  By satisfying the above formula (4), it is possible to reduce the unnecessary vibration mode from internal resonance with the main vibration and the leakage of the energy of the main vibration through the unnecessary vibration mode. Therefore, the vibration piece 4 can be provided with less vibration leakage and exhibiting excellent vibration characteristics. Further, the resonance frequency and CI value of the main vibration of the vibration piece 4 measured on the vibration piece substrate 1 and the resonance frequency and CI of the main vibration of the vibration piece 4 measured in a state of being broken from the vibration piece substrate 1. The deviation from the value can be reduced, and the yield of the resonator element 4 can be improved. Hereinafter, this reason will be described.

First, conditions for causing internal resonance will be described. In order to generate internal resonance, it is necessary that the resonator element 4 has a plurality of natural vibration modes, that is, an X-axis antiphase mode that is a main vibration and at least one unnecessary vibration mode (Condition A1). ). Furthermore, it is necessary to satisfy the following formula (7) (condition A2). Here, the expression “≈” in the following equation (7) means that there is an allowable amount that causes some internal resonance even if the left side of the following equation (7) is not strictly zero. Yes. Note that when the resonance frequency of each natural vibration mode is f _n , the relationship of at least f _i > 0 is satisfied. N is a natural number of 2 or more. However, _{k 1,} k 2 in the formula _{(7), ..., k i} , ..., k n is an integer of at least two of these are not 0 (≠ 0). I is a natural number of 1 or more and n or less.

In this case, although not necessary as a condition for internal resonance, in order to actually excite the main vibration, the frequency Ω (> 0) of the electric signal for exciting the main vibration is substantially equal to the resonance frequency f _{1 of the} main vibration. It is necessary to be equal. That is, it is necessary to satisfy the relationship of Ω≈f ₁ (Condition A3). Here, “substantially equal” is because, for example, there is a slight difference between the resonance frequency electrically excited by the oscillation circuit and the resonance frequency mechanically excited of the main vibration. They are identified as “equal” rather than “equal”. In the present invention, since it is assumed that only the main vibration is directly electrically excited, strictly speaking, the resonance frequency f ₁ of the main vibration is an electrically excited series resonance frequency, Since this is approximated by a resonance frequency that is mechanically excited in an electrically shorted state, these are identified and if the capacitance ratio γ is 300 or more, the electrically opened state Since the difference between the mechanically excited resonance frequency and the resonance frequency mechanically excited in an electrically shorted state is small, both are also regarded as the same. That is, if the capacity ratio γ of the main vibration is 300 or more, the resonance frequency f ₁ of the main vibration is the electrically excited series resonance frequency, or the resonance frequency mechanically excited in the electrically shorted state. The resonance frequency f ₁ of the main vibration is mechanically excited in a state of being electrically opened, and if the capacity ratio γ of the main vibration is less than 300, the resonance frequency f ₁ of the main vibration is electrically excited The resonance frequency is either a series resonance frequency or a resonance frequency mechanically excited in an electrically shorted state.

  In the present invention, it is assumed that only the main vibration is directly electrically excited. Strictly speaking, the resonance frequency of the unnecessary vibration mode is mechanically excited in an electrically open state. If the capacity ratio γ of the unnecessary vibration mode is 300 or more, the series resonance frequency is electrically excited as in the case of the main vibration. It is equated with the resonant frequency excited automatically.

  This is because the difference is sufficiently small even when compared with the above-described formula (4) and formula (14) described later. Note that the resonance frequency of the main vibration mode and the unnecessary vibration mode can be measured on the vibrating reed substrate 1 by heterodyne interferometry or the like. At this time, if the vibration displacement in each vibration mode is not excessive, the inventors have confirmed that the error is sufficiently small from the measurement in the reduced pressure state even if the measurement is performed in the atmospheric state. ing.

  Internal resonance occurs when all of the conditions A1, A2, and A3 described above are satisfied. Therefore, in order to reduce internal resonance, it is only necessary to satisfy at least one of the conditions A1, A2, and A3. The resonator element substrate 1 is configured not to satisfy the condition A2. That is, the resonator element substrate 1 satisfies the following expression (8) instead of the above expression (7).

Next, the allowable amount contained in the expression “≈” in the above formula (7) is defined. Assuming that the virtual resonance frequency near the main vibration is f ₁ ′, f ₁ ′ can be defined by the following equation (9).

The virtual resonance frequency f ₁ ′ is calculated from the resonance frequency of the natural vibration other than the main vibration, and the strongest internal resonance occurs when it is equal to the resonance frequency f ₁ of the main vibration. When the difference between the virtual resonance frequency f ₁ ′ near the main vibration and the resonance frequency f ₁ of the main vibration is normalized by the resonance frequency f ₁ of the main vibration is Δf, Δf is the allowable amount described above. And can be expressed by the following formula (10).

  Substituting equation (9) into equation (10) yields equation (11) below.

And if the said Formula (11) is rearranged, the said Formula (3) will be obtained. Therefore, it can be seen that satisfying the above expression (3) results in the resonator element substrate 1 with reduced internal resonance. Here, as described above, _{k 1,} k 2 in the formula _{(7), ..., k i} , ..., k n is an integer of at least two of these are non-zero. Then, the resonant frequency f _m of the non-zero k (a k _m) and coefficients, unnecessary vibration mode of the direction displacing the Z-axis direction perpendicular to the X axis is a vibration direction of the main vibration, i.e., Z-axis phase It is preferable that the resonance frequency is substantially equal to the resonance frequency of the mode or the Z-axis antiphase mode. In other words, the resonator element 4 of the resonator element substrate 1 preferably has the Z-axis in-phase mode or the Z-axis opposite-phase mode as an unnecessary vibration mode. In addition, these higher-order modes are preferably included, but it is particularly preferable to include the lowest-order mode or the second-order mode. Such an unnecessary vibration mode is a vibration that is easily coupled to the X-axis reversed phase mode, which is the main vibration, among other unnecessary vibration modes. Therefore, the effect by satisfying the expression (3) is further increased.

The resonance frequency f _m is a Z-axis substrate that is a unique unnecessary vibration mode of the resonator element substrate 1, that is, an unnecessary mode that cannot be generated in the resonator element 4 that is separated from the resonator element substrate 1. Preferably it is approximately equal to the mode or substrate contour mode. In other words, the resonator element substrate 1 preferably has the Z-axis substrate mode or the substrate contour mode as the unnecessary vibration mode. Moreover, it is preferable that these higher order modes are included, but it is particularly preferable that higher order modes of the second order or higher and the tenth order are included. As described above, such an unnecessary vibration mode is a vibration mode that does not occur in the singulated vibration piece 4, and therefore, by having such an unnecessary vibration mode, the expression (3) is satisfied. The effect is greater. That is, the resonance frequency and CI value of the main vibration of the vibration piece 4 measured on the vibration piece substrate 1 and the resonance frequency and CI value of the main vibration of the vibration piece 4 measured in a state of being broken from the vibration piece substrate 1. , And the yield of the resonator element 4 can be improved. In this case, as a matter of course, the resonance frequency fm of the specific unnecessary vibration mode of the resonator element substrate 1 and the resonance frequency f ₁ of the main vibration are not matched with each other in the prior art. It is not included in the present invention.

  In particular, in the present embodiment, the folded portion 3 is disposed apart from the virtual vibration symmetry plane F1 of the main vibration of the pair of vibrating arms 42 and 43 in plan view. Therefore, the vibration balance when the main vibration of the resonator element 4 is excited is poor, and the vibration energy of the vibrating arms 42 and 43 is likely to leak to the support portion 2 via the folding portion 3. As a result, the resonator element substrate 1 can be easily combined with the Z-axis substrate mode and the substrate contour mode as described above. Therefore, the effect by satisfy | filling Formula (3) becomes larger. That is, the resonance frequency and CI value of the main vibration of the vibration piece 4 measured on the vibration piece substrate 1 and the resonance frequency and CI value of the main vibration of the vibration piece 4 measured in a state of being broken from the vibration piece substrate 1. , And the yield of the resonator element 4 can be improved.

Also, resonator element substrate 1 preferably has an unnecessary vibration mode having a resonant frequency f _j of less than 10 times the resonance frequency f ₁ of the main vibration, unnecessary with 3 times the resonance frequency f _j vibration More preferably, it has a mode. Such an unnecessary vibration mode having a frequency may be strongly coupled with the main vibration. Therefore, the effect by satisfying the expression (3) is further increased.

The resonator element substrate 1 preferably satisfies the above formula (4) for all unnecessary modes having a resonance frequency that is three times or less of the resonance frequency f ₁ of the main vibration, and the resonance frequency that is 10 times or less. It is more preferable that the above expression (4) is satisfied with respect to all unnecessary modes having. By satisfying such a relationship, it is possible to further reduce the possibility of internal resonance with an unnecessary mode that is easily coupled to the main vibration.

Moreover, it is preferable to have an unnecessary vibration mode having a resonance frequency lower than the resonance frequency f ₁ of the main vibration mode. That is, it is preferable to have an unnecessary vibration mode having a resonant frequency f ₂ to satisfy the relationship of f _{2 <f 1} with respect to the resonance frequency f ₁ of the main vibration modes. _It is more preferable to have an unnecessary vibration mode having a resonant frequency _{f 2} to satisfy the relation of _{f 1/10 ≦ f 2 <} f 1, satisfy the relationship of _{f 1/3 ≦ f 2 <} f 1 it is further preferred to have an unnecessary vibration mode having a resonant frequency f ₂ to. This is among other unnecessary vibration mode, a low frequency than the primary vibration mode, unwanted vibration mode having a resonant frequency close to the resonance frequency f ₁ of the main vibration modes is liable to primary vibration and internal resonance.

  As described above, the resonator element substrate 1 further satisfies the above formula (5). In equation (5), the internal resonance order is limited. The internal resonance order is related to the nonlinear order, and the smaller the nonlinear order, the greater the influence of the internal resonance even if the nonlinearity is small. Therefore, satisfying Expression (5) and Expression (4) can effectively reduce the possibility of occurrence of internal resonance, particularly under conditions where the influence of internal resonance is large.

  The resonator element substrate 1 is not particularly limited as long as the expression (5) is satisfied, but it is more preferable that the expression (12) is satisfied, and it is more preferable that the expression (13) is satisfied. Thereby, even in the vibrating piece substrate 1 in which low-order nonlinearity appears remarkably, coupling between the main vibration and the unnecessary vibration mode hardly occurs, and vibration leakage of the main vibration through the unnecessary vibration mode can be reduced.

  Further, n is preferably 3 or less, and more preferably 2. This is because as the value of n is smaller, internal resonance tends to occur and the effect of the present invention is greater.

  In addition, as described above, the resonator element substrate 1 satisfies the formula (4). If | Δf | is too close to 0, an unnecessary vibration mode is likely to be generated due to internal resonance with the main vibration. Therefore, the occurrence of the unnecessary vibration mode can be reduced by satisfying Expression (4). This will be briefly described below. In the following, for convenience of explanation, the case where the unnecessary vibration mode is the X-axis common mode will be described as a representative. However, it is confirmed that the same relationship is satisfied even in the unnecessary vibration mode other than the X-axis common mode. Has been.

FIG. 9 is a graph showing the relationship between | Δf | and the Q value. FIG. 9 shows Δf in the case where the resonance frequency f ₁ of the X-axis opposite phase mode which is the main vibration mode and the resonance frequency f ₂ of the X-axis common mode which is the unnecessary vibration mode are close to each other by 1: 1, that is, Δf = ( Although it is an actual measurement value in the case of f ₂ −f ₁ ) / f ₁ , it has been confirmed that a similar effect is obtained even in a coupling other than 1: 1. In FIG. 9, an index obtained by normalizing the Q value with the maximum value is shown on the vertical axis (that is, the maximum value of the index is 1). Further, in FIG. 9, the vibrating piece 4 having a size in which the length L of the vibrating arms 42 and 43 is 930 μm, the width W of the vibrating arms 42 and 43 is 60 μm, the total length of the vibrating piece 4 is 1160 μm, and the entire width is 520 μm It is a measured value.

  As can be seen from FIG. 9, if Expression (4) is satisfied, 60% or more of the maximum value of the normalized index can be exhibited, and the unnecessary vibration mode can be sufficiently reduced. The resonator element substrate 1 is not particularly limited as long as the expression (4) is satisfied, but preferably satisfies the following expression (14A), more preferably satisfies the following expression (14B), and It is more preferable that the formula (15C) is satisfied. Thereby, it is possible to further effectively reduce the occurrence of the unnecessary vibration mode due to internal resonance with the main vibration, and it is possible to further reduce the possibility that vibration leakage increases.

  If Expression (4) and the following Expressions (14A) to (14C) are satisfied at room temperature, energy leakage of main vibration at room temperature can be reduced. Further, in the operating temperature range including other than normal temperature, for example, generally in the range of −40 ° C. to 85 ° C., and in the case of in-vehicle use, in all of the range of −40 ° C. to 150 ° C., the formula (4) and the following formula (14A) If (14C) is satisfied, the energy leakage of the main vibration can be reduced within the temperature range.

Next, some specific examples will be given for the case where the number (n) of natural vibration modes is 2, 3, and 4. In the following, it is assumed that the relationship of the following formula (15) is satisfied. Further, the resonance frequency of the main vibration and f _1, the frequency of the undesired oscillation mode and f _2.

[Specific Example 1: m = 3, n = 2]
In this case, the following formula (16) can be derived from the above formula (9).

For example, when k ₁ = 1 and k ₂ = −2, f ₁ ′ = 2f ₂ , and the following equation (17) can be derived from the equation (10), and k ₁ = 2 and k ₂ = in the case of _{-1, f 1 '= f 2/} 2 , and the can be derived the following equation from equation (10) to (18).

In the present invention, since it is necessary to satisfy the formula (5) (or the formula (13) and the formula (15)), when n = 2, if 3 ≦ | k ₁ | + | k ₂ | Don't be. That is, the conditions of k ₁ = 1 and k ₂ = −1 are not included in the present invention. Under such conditions, f ₁ ′ = f ₂ is derived from the above equation (16), and Δf = (f ₂ −f ₁ ) / f ₁ is derived from the above equation (10), so that | Δf | ≈0. In the end, f ₂ ≈f ₁ . It expresses the main oscillation mode and the resonance frequency f ₁ and the resonance frequency f ₂ of the unnecessary vibration mode has been known to bind in close proximity coupling. The present invention discloses a coupling state that cannot be known at all from the coupling that occurs when the resonance frequency of the main vibration mode and the resonance frequency of the unnecessary vibration mode that are conventionally known are close to each other.

  In the present invention, the electrical signal for exciting the main vibration is based on the assumption that only a sine wave signal having a frequency Ω equal to the resonance frequency of the main vibration or an electric signal in a state close thereto is input. For example, when a rectangular wave is input as an electrical signal, a sine wave having a frequency component of an odd multiple of Ω (3Ω, 5Ω,...) Is input in addition to a sine wave of frequency Ω. When one of the frequencies of odd multiples of Ω (particularly 3Ω having a small number has a large influence due to its large amplitude) and one of the unnecessary vibration modes is close to each other, the unnecessary vibration mode is This is not included in the present invention. When the duty ratio is other than 50%, a sine wave having an even multiple (2Ω, 4Ω,...) Of the Ω is input, but this is not included in the present invention.

[Specific example 2: m = 3, n = 3]
In this case, the following formula (19) can be derived from the above formula (9).

For example, when k ₁ = −1 and k ₂ = k ₃ = 1, f ₁ ′ = f ₂ + f ₃ , and the following equation (20) can be derived from equation (10), and k ₁ = K ₃ = −1, k ₂ = 1, f ₁ ′ = f ₂ −f ₃ , and the following formula (21) can be derived from the formula (10).

[Specific Example 3: m = 4, n = 2]
For example, when k ₁ = −1 and k ₂ = 3, f ₁ ′ = 3f ₂ , and the following formula (22) can be derived from the formula (10), and k ₁ −3, k ₂ = 1 in the case _{of, f 1 '= f 2/} 3 , and the can be derived the following equation from equation (10) to (23).

[Specific Example 4: m = 4, n = 3]
For example, when k ₁ = −2 and k ₂ = k ₃ = 1, f ₁ ′ = (f ₂ + f ₃ ) / 2, and the following equation (24) can be derived from equation (10), When k ₁ = −2, k ₂ = 1, and k ₃ = −1, f ₁ ′ = (f ₂ −f ₃ ) / 2, and the following equation (25) can be derived from equation (10). When k ₁ = −1, k ₂ = 2 and k ₃ = 1, f ₁ ′ = 2f ₂ + f ₃ , and the following formula (26) can be derived from the formula (10), and k ₁ When = 1, k ₂ = 2 and k ₃ = −1, f ₁ ′ = 2f ₂ −f ₃ , and the following equation (27) can be derived from the equation (10).

[Specific Example 4: m = 4, n = 4]
In this case, the following formula (28) can be derived from the above formula (9).

For example, when k ₁ = −1 and k ₂ = k ₃ = k ₄ = 1, f ₁ ′ = f ₂ + f ₃ + f ₄ , and the following formula (29) is derived from the formula (10). When k ₁ = k ₃ = −1 and k ₂ = k ₄ = 1, f ₁ ′ = f ₂ −f ₃ + f ₄ , and the following formula (30) is derived from the formula (10). When k ₁ = k ₄ = −1 and k ₂ = k ₃ = 1, f ₁ ′ = f ₂ + f ₃ −f ₄ , and the following equation (31) is derived from equation (10). When k ₁ = k ₃ = k ₄ = −1 and k ₂ = 1, f ₁ ′ = f ₂ −f ₃ −f ₄ , and the following equation (32) is derived from equation (10). be able to.

Next, some specific examples will be given for the case where the natural vibration mode is specified.
[Specific Example 1]
For example, the resonator element 4 arranged on the resonator element substrate 1 has a main vibration (resonance frequency f ₁ = 32.768 kHz) in the X-axis anti-phase mode, and a Z-axis common mode (resonance frequency f ₂ ) as an unnecessary vibration mode. = 20.49 kHz), it is necessary to satisfy k ₁ f ₁ + k ₂ f ₂ = 0 as a condition for causing the strongest internal resonance. However, there is no combination of {k ₁ , k ₂ } that satisfies the above formula within the range of m ≦ 10 (see formula (5)). Therefore, in this case, if m = 3, which is the condition that | Δf | is the smallest, is satisfied as an example, | Δf | = 25.06% from the above equation (17). Thus, it can be seen that it is difficult to couple the unnecessary vibration mode to the main vibration.

[Specific Example 2]
For example, the resonator element 4 arranged on the resonator element substrate 1 has the main vibration (resonance frequency f ₁ = 32.768 kHz) in the X-axis anti-phase mode, and the Z-axis anti-phase mode (resonance frequency f) as the unnecessary vibration mode. ₂ = 82.05 kHz), it is necessary to satisfy k ₁ f ₁ + k ₂ f ₂ = 0 as a condition for causing the strongest internal resonance. However, there is no combination of {k ₁ , k ₂ } that satisfies the above formula within the range of m ≦ 10 (see formula (5)). Accordingly, in this case, if m = 3, which is the condition that | Δf | is the smallest, satisfies the above equation (8), | Δf | = 25.20% from the above equation (18). Thus, it can be seen that it is difficult to couple the unnecessary vibration mode to the main vibration.

  In the above, a specific example was given and demonstrated. The size of the vibrating piece 4 is not particularly limited, but the length L of the vibrating arms 42 and 43 preferably satisfies the relationship of 0.1 mm ≦ L ≦ 0.9 mm, and 0.2 mm ≦ L ≦ It is more preferable to satisfy the relationship of 0.7 mm, and it is further preferable to satisfy the relationship of 0.3 mm ≦ L ≦ 0.5 mm. The thickness T of the vibrating arms 42 and 43 preferably satisfies the relationship of 50 μm ≦ T ≦ 150 μm, more preferably satisfies the relationship of 80 μm ≦ T ≦ 140 μm, and the relationship of 120 μm ≦ T ≦ 130 μm. It is further preferable to satisfy. The width W of the arm portions 421 and 431 of the vibrating arms 42 and 43 is preferably 12.8 μm ≦ W ≦ 50 μm, more preferably 15 μm ≦ W ≦ 45 μm, and 20 μm ≦ W ≦ 30 μm. More preferably. The width W ′ of the main surface remaining on both sides of the groove portions 422, 423 (432, 433) of the arm portion 421 (431) preferably satisfies the relationship of 1 μm ≦ W ′ ≦ 6 μm, and 1 μm ≦ W ′. It is more preferable to satisfy the relationship of ≦ 4.5 μm, and it is further preferable to satisfy the relationship of 1 μm ≦ W ′ ≦ 3 μm. Further, the length L ′ of the wide portion 429 (439) of the arm portion 421 (431) preferably satisfies the relationship of 0.1 ≦ L ′ / L ≦ 0.5, and 0.1 ≦ L ′ / It is more preferable to satisfy the relationship of L ≦ 0.35, and it is further preferable to satisfy the relationship of 0.1 ≦ L ′ / L ≦ 0.25. The width W ″ and the length L ′ of the wide portion 429 (439) preferably satisfy the relationship L ′ <W ″.

  By setting the size of the vibrating piece 4 as described above, a relatively small vibrating piece 4 is obtained. Therefore, when the vibrating body 40 is obtained by patterning the quartz wafer by wet etching, the shape symmetry is lost and nonlinearity is increased mainly due to the etching anisotropy of the quartz substrate. The vibration and the unnecessary vibration are likely to cause internal resonance, so that the energy of the main vibration leaks to the outside through the unnecessary vibration that is not designed (or difficult to reduce). In particular, since the width W ′ is set to be relatively narrow, the wide portions 429 and 439 are provided, and the relationship of L ′ <W ″ is satisfied, Asymmetry of the shape is likely to occur, and the above-described problem becomes more prominent.Therefore, in the resonator element substrate 1 including the resonator element 4 having a size in which such unnecessary vibration is likely to occur, the above-described configuration is obtained. The effect mentioned above can be exhibited more notably.

  Further, when only a pair of vibrating arms extending in the same direction is included as a vibrating arm, such as a tuning fork type vibrating element, the symmetry of the shape with respect to the direction opposite to the extending direction described above cannot be taken with respect to the base. The present invention works more effectively. In addition, since the crystal plane is complicatedly formed in quartz, the present invention works more effectively when the vibration element is formed by wet etching using quartz as a base material.

Next, effects (effects not described above) obtained by satisfying the above-described expression (4) will be described. FIG. 10 is a graph showing the relationship between Δf and environmental temperature regarding the normal sample S1 and the two abnormal samples S2 and S3. Δf here corresponds to the above equation (18), and the resonance frequency of the X-axis antiphase mode, which is the main vibration mode, is f ₁ (= 32.768 kHz), and is considered to be in internal resonance with the main vibration. the resonant frequency of the Z-axis common mode is unnecessary oscillation mode and f _2. That is, Δf here can be said to be a value indicating how much f ₂ is deviated from 65.536 kHz (a frequency twice that of f ₁ ).

  On the other hand, FIG. 11 is a graph showing the relationship between the CI increase rate for the normal sample S1 and the two abnormal samples S2 and S3 and the environmental temperature, and FIG. 12 shows the CI for the normal sample S1 and the two abnormal samples S2 and S3. It is a graph which shows the relationship of environmental temperature. FIG. 11 and FIG. 12 are graphs showing how much the CI increase rate (CI value) changes from the reference value (0) with respect to the CI value at −50 °.

  As shown in FIGS. 11 and 12, the CI increase rate (CI value) increases moderately in the normal sample S1, whereas the CI increase rate abnormally increases around 35 ° C. in the abnormal sample S2. In the abnormal sample S3, the CI increase rate is abnormally increased around 110 ° C. For the abnormal samples S2 and S3, the temperature at which the CI increase rate is abnormally increased substantially matches the temperature at which Δf shown in FIG. 10 is 0%. Therefore, it is understood that such an abnormal increase in the CI increase rate (CI value) can be reduced by satisfying the relationship of the above formula (4) (that is, by excluding the vicinity of Δf = 0%). . Note that if the resonator element substrate 1 satisfies the formula (4) in any temperature range of the operating temperature range (−40 ° C. to 85 ° C., −40 ° C. to 150 ° C., etc.) of the resonator element 4, By using the temperature range, it is possible to reduce the possibility of the abnormal increase in the CI value described above. Preferably, if Expression (4) is satisfied at all temperatures in the operating temperature range, the possibility that the above-described abnormal increase in the CI value occurs in the entire operating temperature range can be reduced.

  Further, in the resonator element substrate 1, when the Q value of the resonator element 4 is Q, the relationship of the following equation (33) is satisfied, and f0max in the equation (33) satisfies the relationship of the following equation (34). In the equation (34), Wemin satisfies the relationship of the following equation (35). By satisfying these relationships, the resonator element 4 is small and has a sufficiently high Q value.

However, in the formulas (33), (34), and (35), A = 7.3690 × 10 ⁻² , B = 1.2544 × 10 ⁻⁵ , C = 1.1 to 1.3, f0max [Hz ], The equivalent arm width We of the vibrating arms 42 and 43 when the cross-sectional shape of the vibrating arms 42 and 43 (arm portions 421 and 431) is replaced with a rectangle so that the thermoelastic loss is equal is a minimum value Wemin described later. The resonance frequency (thermal relaxation frequency) at which the thermoelastic loss is sometimes maximum, L [m] is the length in the extending direction of the vibrating arms 42 and 43, and ρ [kg / m ³ ] is the mass of the vibrating arms 42 and 43. Density, Cp [J / (kg · K)] is the heat capacity of the vibrating arms 42, 43, c [N / m ² ] is an elastic constant in the extending direction of the vibrating arms 42, 43, and α [1 / K] is vibration. The thermal expansion coefficient in the extending direction of the arms 42 and 43, Θ [K] is the environmental temperature, and k [W / (m · K)] is The thermal conductivity along the vibration direction of the main vibration of Doude 42, 43, [pi is circle ratio.

Hereinafter, the derivation method of Formula (33) is demonstrated. First, Table 1 below shows the relationship between the length L of the vibrating arms 42 and 43, which is considered effective for downsizing, and the minimum value Qmin of the Q value obtained at that length. Satisfying such a relationship means that the resonator element substrate 1 having the resonator element 4 having a small size and a higher Q value can be obtained. Therefore, for example, the power consumption of the oscillation circuit using the resonator element 4 can be reduced, and the emission of CO ₂ generated at the time of manufacture can be reduced by downsizing. 1

Substituting f ₁ = 32.768 kHz, Qmin into Q _TED (Q value considering only thermoelastic loss) into the following formulas (36) and (37), and calculating the width W satisfying the relationship of f ₁ > f0 Thus, the minimum value Wemin for the length L is calculated. The calculation result of the minimum value Wemin is shown in Table 3 below. The numerical values in the formulas (36) and (37) are as shown in Table 2 below. As described above, f0 is the thermal relaxation frequency, and f ₁ > f0 (f ₁ / f0> 1) means that the resonator element 4 is in the adiabatic region.

The minimum value Wemin with respect to the length L is as shown in the graph of FIG. 13, and its approximate expression is Wemin = 7.3690 × 10 ⁻² L + 1.2544 × 10 ⁻⁵ . Further, the above equation (35) is obtained by multiplying the right side of this equation by a coefficient C (where C is 1.1 to 1.3). From this equation (35), the minimum value Wemin of the width W of the vibrating arms 42 and 43 with respect to the length L of the vibrating arms 42 and 43 can be calculated. Furthermore, f0 can be calculated by substituting the obtained minimum value Wemin into the equation (37). Note that f0 is a resonance frequency at which the thermoelastic loss is maximized when the width W of the vibrating arms 42 and 43 is the minimum value Wemin (= f0max). As described above, in the present embodiment, since it is limited to the adiabatic region (f ₁ > f0), Qmin (Q _TED ) that is the lower limit value of the Q value can be determined by f0. That is, Qmin can be calculated by substituting f0 into equation (36). Then, if the relationship of Q ≧ Qmin is satisfied, a sufficiently high Q value can be obtained, so that Expression (33) is derived.

Second Embodiment
Next, a resonator element substrate according to a second embodiment of the invention will be described.

  FIG. 14 is a plan view of the resonator element substrate according to the second embodiment of the invention. In FIG. 14, the electrodes are not shown for convenience of explanation.

  Hereinafter, the resonator element substrate of the second embodiment will be described with a focus on the differences from the first embodiment described above, and description of similar matters will be omitted.

  The resonator element substrate according to the second embodiment of the present invention is the same as that of the first embodiment described above except that the structure of the resonator element is different. In addition, the same code | symbol is attached | subjected to the structure similar to embodiment mentioned above.

  As shown in FIG. 14, in the resonator element substrate 1 of the present embodiment, the folded portion 3 is disposed so as to overlap the virtual vibration symmetry plane F1 in plan view. In the present embodiment, the folding part 3 is arranged so as to connect the tip of the support arm 44 of the vibrating piece 4 and the support part 2. However, as the arrangement of the folding part 3, a virtual vibration symmetry plane F <b> 1 is provided. If it overlaps with, it will not specifically limit, For example, you may arrange | position so that the base 41 and the support part 2 may be connected. Thus, by arranging the folding part 3 so as to overlap the virtual vibration symmetry plane F1, the vibration energy of the vibrating arms 42 and 43 is difficult to leak to the support part 2 via the folding part 3, and adjacent to each other. It is difficult to internally resonate with the resonator element 4 and the Z-axis substrate mode and the substrate contour mode which the resonator element substrate 1 has. Therefore, the resonance frequency and CI value of the main vibration of the vibration piece 4 measured on the vibration piece substrate 1 and the resonance frequency and CI value of the main vibration of the vibration piece 4 measured in a state of being broken from the vibration piece substrate 1. , And the yield of the resonator element 4 can be improved.

  According to the second embodiment as described above, the same effect as that of the first embodiment described above can be exhibited.

<Third Embodiment>
Next, a resonator element substrate according to a third embodiment of the invention is described.

  FIG. 15 is a plan view of a resonator element substrate according to the third embodiment of the invention. In FIG. 15, illustration of electrodes is omitted for convenience of explanation.

  Hereinafter, the resonator element substrate of the third embodiment will be described focusing on the differences from the first embodiment described above, and description of similar matters will be omitted.

  The resonator element substrate according to the third embodiment of the present invention is the same as that of the first embodiment described above except that the structure of the resonator element is different. In addition, the same code | symbol is attached | subjected to the structure similar to embodiment mentioned above.

  As shown in FIG. 15, in the resonator element 4 according to the present embodiment, no groove is formed in the vibrating arms 42 and 43, and the upper and lower surfaces of the vibrating arms 42 and 43 are each formed as a flat surface. That is, the resonator element 4 of the present embodiment has a configuration in which the grooves (422, 423, 432, 433) are omitted from the configuration of the first embodiment described above.

  In addition, the vibration piece 4 of the first embodiment described above is in the adiabatic region and satisfies the formula (1), whereas the vibration piece 4 of the present embodiment is in the isothermal region, The following formula (38A) is satisfied. By satisfying the following formula (38A), an isothermal region is obtained, and the small vibrating piece 4 having reduced Q value deterioration can be obtained. Furthermore, in order to make this effect more prominent, it is preferable to satisfy the following formula (38B), more preferably to satisfy the following formula (38C), and to satisfy the following formula (38D). Is more preferable.

  According to the third embodiment as described above, the same effects as those of the first embodiment described above can be exhibited.

<Fourth embodiment>
Next, a resonator element substrate according to a fourth embodiment of the invention is described.

  FIG. 16 is a plan view of a resonator element substrate according to the fourth embodiment of the invention. FIGS. 17 and 18 are diagrams for explaining the operation of the resonator element included in the resonator element substrate illustrated in FIG. 16. In FIG. 15, illustration of electrodes is omitted for convenience of explanation.

  Hereinafter, the resonator element substrate according to the fourth embodiment will be described with a focus on differences from the first embodiment described above, and description of similar matters will be omitted.

  The resonator element substrate according to the fourth embodiment of the present invention is the same as that of the first embodiment described above except that the structure of the resonator element is different. In addition, the same code | symbol is attached | subjected to the structure similar to embodiment mentioned above.

  The vibrating piece 6 of the present embodiment shown in FIG. 16 is an angular velocity detection element that can detect the angular velocity. The vibrating piece 6 includes a vibrating body 60 configured as a part of the quartz wafer 10 and an electrode (not shown) provided on the vibrating body 60.

  The vibrating body 60 includes a base 61, detection arms 621 and 622 as vibrating arms extending from the base 61 to both sides in the Y-axis direction, and connecting arms 631 extending from the base 61 to both sides in the X-axis direction. 632, driving arms 641 and 642 as vibrating arms extending from the connecting arm 631 to both sides in the Y-axis direction, and driving arms 643 and 644 as vibrating arms extending from the connecting arm 632 to both sides in the Y-axis direction, , Support portions 651 and 652, and beam portions 661, 662, 663, and 664 connecting the support portions 651 and 652 and the base portion 61. The vibrating piece 6 is connected to the support portion 2 via the folding portion 3 at the support portions 651 and 652.

  Further, drive signal electrodes and drive ground electrodes (not shown) are arranged on the drive arms 641 to 644, and when a drive signal is applied between these electrodes, the drive arms 641 to 644 are moved in the direction (X (X) shown in FIG. Axial bending). This vibration is called a drive vibration mode, and this mode becomes the main vibration of the resonator element 6. On the other hand, the detection arms 621 and 622 are provided with detection signal electrodes and detection ground electrodes. As shown in FIG. 18, when an angular velocity ωz around the Z axis is applied while the drive arms 641 to 644 are vibrated in the drive vibration mode, Coriolis force acts on the drive arms 641 to 644 and the arrow C indicates. Directional vibration is excited, and the detection arms 621 and 622 bend and vibrate in the direction indicated by the arrow D so as to respond to the vibration. The charges generated in the detection arms 621 and 622 by such vibration are taken out as a detection signal from between the detection signal electrode and the detection ground electrode, and the angular velocity ωz is obtained based on the detection signal.

  Such a vibrating piece 6 has at least two virtual vibration symmetry planes that are symmetry planes with respect to the main vibrations of the drive arms 641 to 644. Specifically, the resonator element 6 has a first virtual vibration symmetry plane F2 (YZ plane) and a second virtual vibration symmetry plane F3 (XZ plane). Therefore, the vibrations of the drive arms 641, 642, 643, 644 are canceled, and vibration energy is difficult to leak. In practice, the resonator element 6 may vibrate in a state where the X-axis reverse phase mode that is the main vibration is combined with the Z-axis reverse phase mode that is unnecessary vibration, the torsional reverse phase mode, and the like. The first and second virtual vibration symmetry planes F2 and F3 are target surfaces when only the main vibration is considered, not these unnecessary vibrations. In the main vibration, the base 61 provided including the region where the first and second virtual vibration symmetry planes F2 and F3 intersect is connected to the resonator element substrate 1 via the beam portions 661 to 664 and the like. The configuration is such that the internal resonance with the Z-axis substrate mode and the substrate contour mode of the adjacent resonator element 6 (not shown) and the resonator element substrate 1 has increased.

  According to the fourth embodiment as described above, the same effects as those of the first embodiment described above can be exhibited.

<Fifth Embodiment>
Next, a resonator element substrate according to a fifth embodiment of the invention is described.

  FIG. 19 is a plan view of a resonator element substrate according to the fifth embodiment of the invention. 20 is a plan view showing a modification of the resonator element substrate shown in FIG.

  Hereinafter, the resonator element substrate of the fifth embodiment will be described focusing on the differences from the first embodiment described above, and description of similar matters will be omitted.

  The resonator element substrate according to the fifth embodiment of the present invention is the same as that of the first embodiment described above except that the structure of the resonator element is different. In addition, the same code | symbol is attached | subjected to the structure similar to embodiment mentioned above.

  As shown in FIG. 19, the resonator element 7 of the present embodiment includes a vibrating body 70 configured as a part of the crystal wafer 10 and an electrode (not shown) arranged on the surface of the vibrating body 70. ing.

  The vibrating body 70 includes a base portion 71, a pair of vibrating arms 72 and 73 extending from the base portion 71 in the −Y axis direction, and a support portion 74 connected to an end portion of the base portion 71 on the + Y axis side, have. Such a vibrating piece 7 also vibrates with the X-axis reverse phase mode as the main vibration, as in the first embodiment described above.

  Further, the support part 74 is a pair of support arms 741 and 742 that are arranged so as to sandwich the vibrating arms 72 and 73 therebetween in a plan view, and a connecting part 743 that connects the support arms 741 and 742 and the base 71. ,have. The vibrating piece 7 is connected to the support portion 2 via the breaker portion 3 at the connecting portion 743. After such a vibrating piece 7 is broken off from the vibrating piece substrate 1, it is fixed to an object (for example, a base 91 of a seventh embodiment described later) via support arms 741 and 742.

  According to the fifth embodiment as described above, the same effect as that of the first embodiment described above can be exhibited. As a modification of the resonator element 7, the lengths of the support arms 741 and 742 may be varied as shown in FIG.

<Sixth Embodiment>
Next, a resonator element substrate according to a sixth embodiment of the invention is described.

  FIG. 21 is a plan view of the resonator element substrate according to the sixth embodiment of the invention. 22 and FIG. 23 are diagrams illustrating the operation of the resonator element included in the resonator element substrate illustrated in FIG. 21. In FIG. 21, for convenience of explanation, illustration of electrodes is omitted.

  Hereinafter, the resonator element substrate of the sixth embodiment will be described focusing on the differences from the first embodiment described above, and the description of the same matters will be omitted.

  The resonator element substrate according to the sixth embodiment of the present invention is the same as that of the first embodiment described above except that the structure of the resonator element is different. In addition, the same code | symbol is attached | subjected to the structure similar to embodiment mentioned above.

  The vibrating piece 8 of the present embodiment shown in FIG. 21 is an angular velocity detection element that can detect the angular velocity. The vibrating piece 8 includes a vibrating body 80 configured as a part of the crystal wafer 10 and an electrode (not shown) provided on the vibrating body 80.

  The vibrating body 80 includes a base portion 81, drive arms 82 and 83 as a pair of vibrating arms extending from the base portion 81 in the + Y axis direction, and a pair of vibrating arms extending from the base portion 81 in the −Y axis direction. Detection arms 84 and 85, and a pair of support arms 86 and 87 extending from the base portion 81 to both sides in the X-axis direction and bent in the middle and extending in the −Y-axis direction. The vibrating piece 8 is connected to the support portion 2 via the folding portion 3 at the support arms 86 and 87. After such a vibrating piece 8 is broken off from the vibrating piece substrate 1, it is fixed to an object (for example, a base 91 of a seventh embodiment described later) via support arms 86 and 87.

  Further, drive signal electrodes and drive ground electrodes (not shown) are arranged on the drive arms 82 and 83, and when a drive signal is applied between these electrodes, the drive arms 82 and 83 become X as shown by an arrow E in FIG. Bends and vibrates in the shaft reverse phase mode. On the other hand, detection signal electrodes and detection ground electrodes are arranged on the detection arms 84 and 85. As shown in FIG. 23, when an angular velocity ωy about the Y axis is applied in a state where the driving arms 82 and 83 are vibrated in the X-axis reverse phase mode, Coriolis force acts on the driving arms 82 and 83 and the arrow F The detection arms 84 and 85 bend and vibrate in the direction indicated by the arrow G so as to respond to this vibration. The charges generated in the detection arms 84 and 85 by such vibration are taken out as a detection signal from between the detection signal electrode and the detection ground electrode, and the angular velocity ωy is obtained based on the detection signal.

  According to the sixth embodiment as described above, the same effect as that of the first embodiment described above can be exhibited.

<Seventh embodiment>
Next, a resonator according to a seventh embodiment of the invention will be described.

  FIG. 24 is a top view showing the vibrator according to the seventh embodiment of the invention. 25 is a cross-sectional view of the vibrator shown in FIG. FIG. 26 is a flowchart illustrating a method for manufacturing the resonator element.

  A vibrator 100 illustrated in FIG. 24 includes the vibration piece 4 separated from the vibration piece substrate 1 of the first embodiment described above and a package 9 that accommodates the vibration piece 4. The package 9 has a box-shaped base 91 having a recess 911 that opens on the upper surface, and a plate-shaped lid 92 that closes the opening of the recess 911 and is joined to the base 91. The package 9 has an airtight housing space S formed by closing the opening of the recess 911 with the lid 92, and the vibrating piece 4 is housed in the housing space S. Note that the inside of the accommodation space S is preferably in a reduced pressure (preferably vacuum) state. Thereby, viscous resistance can be reduced and the vibration characteristic of the vibration piece 4 improves.

  Further, as shown in FIG. 25, two internal terminals 95 are disposed on the bottom surface of the recess 911 of the base 91, and two external terminals 96 are disposed on the bottom surface of the base 91. Corresponding internal terminals 95 and external terminals 96 are electrically connected via internal wirings (not shown) disposed on the base 91, respectively. In addition, a conductive adhesive 97 is provided on the internal terminal 95, and the resonator element 4 is fixed to the base 91 via the conductive adhesive 97 and is electrically connected to the internal terminal 95. Has been.

  According to such a vibrator 100, since the resonator element 4 having a small deviation from desired vibration characteristics (resonance frequency and CI value) is used, high reliability can be obtained.

  Next, a method for manufacturing the resonator element 4 used in such a vibrator 100 will be described. As shown in FIG. 26, the method for manufacturing the resonator element 4 includes a preparation step for preparing the resonator element substrate 1, a measurement step for measuring the vibration characteristics of the resonator element 4, and the breaker 3 by cutting the breaker 3. Separating from the support part 2.

  In the preparation step, first, the crystal wafer 10 is prepared, and the crystal wafer 10 is patterned using a photolithography technique and an etching technique, so that the support portion 2, the folding portion 3, and the vibrating body 40 are integrally formed. Next, a metal film is formed on the surface of the quartz wafer 10 by vapor deposition, sputtering, or the like, and this metal film is patterned using a photolithography technique and an etching technique to form an electrode. As a result, the resonator element substrate 1 that holds the resonator element 4 is obtained.

  In the measurement process, the resonance frequency and CI value of the resonator element 4 are measured. Then, if there is a vibrating piece 4 whose values deviate from a desired condition, the vibrating piece 4 is removed (or the arrangement location is stored so as not to be separated in a separation step described later). In this step, the resonance frequency and the CI value are adjusted by increasing / decreasing the mass of the vibrating arms 42 and 43 with respect to the vibrating piece 4 that is out of the desired condition, and these values are within the desired condition. You may make it fit in.

  In the separation step, for example, the breaker 3 is folded by pressing the vibrating piece 4 against the support 2 in the Z-axis direction, whereby the vibrating piece 4 is separated from the support 2 and separated into pieces. . Thus, the resonator element 4 is obtained.

  According to such a manufacturing method, it is relatively easy to obtain the resonator element 4 with little deviation from desired vibration characteristics (resonance frequency and CI value).

<Eighth Embodiment>
Next, an oscillator according to an eighth embodiment of the invention will be described.

FIG. 27 is a sectional view showing an oscillator according to the eighth embodiment of the invention.
An oscillator 200 illustrated in FIG. 27 includes a resonator element 4 separated from the resonator element substrate 1, an IC 210 electrically connected to the resonator element 4, and a package 9 that accommodates the resonator element 4 and the IC 210. ing. That is, the oscillator 200 has a configuration in which an IC 210 is added to the vibrator 100 described above. The IC 210 is fixed to the bottom surface of the recess 911 of the base 91 and is electrically connected to the internal terminal 95 and the external terminal 96. Further, the IC 210 includes an oscillation circuit 211, and a signal having a predetermined frequency can be extracted by driving the resonator element 4 with a drive signal from the IC 210.

  According to such an oscillator 200, since the resonator element 4 having a small deviation from desired vibration characteristics (resonance frequency and CI value) is used, high reliability can be obtained.

[Electronics]
Next, the electronic apparatus of the present invention will be described.

  FIG. 28 is a perspective view showing the configuration of a mobile (or notebook) personal computer to which the electronic apparatus of the present invention is applied. In this figure, a personal computer 1100 includes a main body 1104 provided with a keyboard 1102 and a display unit 1106 provided with a display 1108. The display unit 1106 is connected to the main body 1104 via a hinge structure. It is rotatably supported. Such a personal computer 1100 incorporates a resonator element 4 used as a part of an oscillator, for example.

  FIG. 29 is a perspective view illustrating a configuration of a mobile phone (including a smartphone, a PHS, and the like) to which the electronic device of the invention is applied. In this figure, a cellular phone 1200 includes an antenna (not shown), a plurality of operation buttons 1202, an earpiece 1204, and a mouthpiece 1206, and a display unit 1208 is provided between the operation buttons 1202 and the earpiece 1204. Has been placed. Such a cellular phone 1200 incorporates the resonator element 4 used as a part of an oscillator, for example.

  FIG. 30 is a perspective view showing a configuration of a digital still camera to which the electronic apparatus of the present invention is applied. In this figure, a display unit 1310 is provided on the back of a case (body) 1302 in the digital still camera 1300, and a display is performed based on an image pickup signal by a CCD. Functions as a viewfinder that displays images. A light receiving unit 1304 including an optical lens (imaging optical system), a CCD, and the like is provided on the front side (the back side in the drawing) of the case 1302. When the photographer confirms the subject image displayed on the display unit 1310 and presses the shutter button 1306, the CCD image pickup signal at that time is transferred and stored in the memory 1308. Such a digital still camera 1300 incorporates the resonator element 4 used as a part of an oscillator, for example.

  Since such an electronic device has the resonator element 4 with little deviation from desired vibration characteristics (resonance frequency and CI value), it has high accuracy and low power consumption, and the yield of the resonator element 4 is high. Due to its high price, it has a low price.

  In addition to the personal computer of FIG. 28, the mobile phone of FIG. 29, and the digital still camera of FIG. 30, the electronic device of the present invention includes, for example, a smartphone, a tablet terminal, a watch (including a smart watch), an inkjet discharge Wearable terminals such as devices (for example, inkjet printers), laptop personal computers, televisions, HMDs (head-mounted displays), video cameras, video tape recorders, car navigation devices, pagers, electronic notebooks (including those with communication functions), electronic Dictionary, calculator, electronic game device, word processor, workstation, video phone, crime prevention TV monitor, electronic binoculars, POS terminal, medical device (eg electronic thermometer, blood pressure monitor, blood glucose meter, electrocardiogram measuring device, ultrasound diagnostic device, electronic Endoscope), a fish finder, various measurement devices, gauges (e.g., gages for vehicles, aircraft, and ships), can be applied to a flight simulator or the like.

[Moving object]
Next, the moving body of the present invention will be described.

  FIG. 31 is a perspective view showing an automobile to which the moving body of the present invention is applied. In this figure, an automobile 1500 has a vibrating piece 4 used as a part of an oscillator, for example. The vibration piece 4 includes keyless entry, immobilizer, car navigation system, car air conditioner, anti-lock brake system (ABS), airbag, tire pressure monitoring system (TPMS), engine control, hybrid car, The present invention can be widely applied to electronic control units (ECUs) such as battery monitors for electric vehicles, vehicle body posture control systems, and the like.

  Since such a moving body has the resonator element 4 with little deviation from desired vibration characteristics (resonance frequency and CI value), it has characteristics of high accuracy, low power consumption, and low price.

  As described above, the resonator element substrate, the method for manufacturing the resonator element, the vibrator, the oscillator, the electronic device, and the moving body of the present invention have been described based on the illustrated embodiments, but the present invention is not limited to this. The configuration of each unit can be replaced with any configuration having the same function. In addition, any other component may be added to the present invention. Moreover, you may combine each embodiment mentioned above suitably.

  In the above-described embodiment, the vibration piece whose main vibration is the X-axis reverse phase mode has been described. However, the main vibration of the vibration piece is not limited to the X-axis reverse phase mode, for example, the Z-axis reverse phase mode. It may be. When the main vibration is in the Z-axis anti-phase mode, the thickness direction of the vibrating arm is the bending vibration direction, and thus the size can be easily reduced by reducing the thickness of the vibrating arm.

In the above-described embodiment, the resonator element substrate (vibrating body) is made of crystal. However, the constituent material of the resonator element substrate is not limited to crystal, and for example, aluminum nitride (AlN), niobic acid, and the like. Lithium (LiNbO ₃ ), lithium tantalate (LiTaO ₃ ), lead zirconate titanate (PZT), lithium tetraborate (Li ₂ B ₄ O ₇ ), langasite (La ₃ Ga ₅ SiO ₁₄ ), potassium niobate (KNbO ₃ ), gallium phosphate (GaPO ₄ ), gallium arsenide (GaAs), aluminum nitride (AlN), zinc oxide (ZnO, Zn ₂ O ₃ ), barium titanate (BaTiO ₃ ), lead titanate (PbPO ₃₎ ), potassium sodium niobate _{((K, Na) NbO 3} ), bismuth ferrite (BiFeO _3), sodium niobate (NaNbO _3), bismuth titanate _{(Bi 4 Ti 3 O 12)} , bismuth sodium titanate _{(Na 0.5 Bi 0.5} TiO ₃₎ oxide substrate or the like, aluminum nitride on a glass substrate or a tantalum pentoxide A laminated piezoelectric substrate formed by laminating piezoelectric materials such as (Ta ₂ O ₅ ), piezoelectric ceramics, or the like can be used.

  In the above-described embodiment, the resonator element is configured by disposing an electrode on a resonator substrate made of quartz. However, the resonator element is not limited to this, for example, a silicon substrate (silicon single crystal (Si ), A piezoelectric element (piezo element) is placed on a substrate made of a non-piezoelectric material such as polycrystalline silicon (polysilicon) or amorphous silicon (amorphous silicon), and this piezoelectric element is expanded and contracted to vibrate. In addition to the above, a vibration piece such as an electrostatic drive type using electrostatic force or a Lorentz drive type using magnetic force may be used.

  DESCRIPTION OF SYMBOLS 1 ... Vibrating piece board | substrate, 10 ... Quartz wafer, 2 ... Support part, 21 ... Terminal, 22 ... Terminal, 3 ... Folding part, 31 ... Groove part, 4 ... Vibrating piece, 40 ... Vibrating body, 41 ... Base part, 42 ... Vibration arm, 421 ... arm part, 422, 423 ... groove part, 429 ... wide part, 43 ... vibrating arm, 431 ... arm part, 432,433 ... groove part, 439 ... wide part, 44 ... support arm, 481 ... first drive Electrode, 482 ... first drive terminal, 491 ... second drive electrode, 492 ... second drive terminal, 6 ... vibrating piece, 60 ... vibrating body, 61 ... base, 621,622 ... detection arm, 631, 632 ... connection arm , 641, 642, 643, 644... Driving arm, 651, 652... Support section, 661, 662, 663, 664... Beam section, 7. , 74 ... support part, 741, 742 ... support arm, 743 ... connection , 8 ... Vibrating piece, 80 ... Vibrating body, 81 ... Base, 82, 83 ... Driving arm, 84, 85 ... Detection arm, 86, 87 ... Support arm, 9 ... Package, 91 ... Base, 911 ... Recess, 92 ... Lid, 95 ... internal terminal, 96 ... external terminal, 97 ... conductive adhesive, 100 ... vibrator, 200 ... oscillator, 210 ... IC, 211 ... oscillation circuit, 1100 ... personal computer, 1102 ... keyboard, 1104 ... main body DESCRIPTION OF SYMBOLS 1106 ... Display unit, 1108 ... Display part, 1200 ... Mobile phone, 1202 ... Operation button, 1204 ... Earpiece, 1206 ... Mouthpiece, 1208 ... Display part, 1300 ... Digital still camera, 1302 ... Case, 1304 ... Light reception Unit 1306 ... Shutter button 1308 ... Memory 1310 ... Display unit 1500 ... Car, A, B, C, D E, F, G ... arrows, F1 ... virtual vibration symmetry plane, F2 ... first virtual vibration symmetry plane, F3 ... second virtual vibration symmetry plane, S ... accommodation space, Sy ... area, ωy ... angular velocity, ωz ... angular velocity, K1, K2 ... curve, L, L '... length, T ... thickness, W, W', W "... width

Claims (17)

At least one vibrating piece;
A connecting portion;
A support portion connected to the vibrating piece via the connecting portion;
Have
The vibrating piece is
The base,
A vibrating arm extending in a first direction from the base;
Have
n is a natural number of 2 or more,
When j is 1 or more and the natural number is n or less,
The vibrating piece vibrates having the n natural vibration modes having different resonance frequencies,
The n natural vibration modes include a natural vibration mode of a main vibration,
In the relationship between the resonance frequency f _j corresponding to each of the n natural vibration modes and an arbitrary integer k _j ,
The resonant frequency of the main vibration and f _1, the normalized frequency difference Δf

When

Satisfy the relationship
The arbitrary integer k _j is

and,

A vibrating piece substrate characterized by satisfying the relationship: In claim 1,

A vibrating piece substrate characterized by satisfying the relationship: In claim 1 or 2,
The vibrating piece is
A pair of vibrating arms arranged in a second direction intersecting the first direction and extending from the base in the first direction;
A second direction anti-phase mode in which the pair of vibrating arms bend and vibrate in the opposite direction to the second direction;
A second direction in-phase mode in which the pair of vibrating arms flexurally vibrate in the second direction in phase;
A third direction anti-phase mode in which the pair of vibrating arms bend and vibrate in a reverse phase in a third direction along the thickness direction of the base,
A third direction in-phase mode in which the pair of vibrating arms bend and vibrate in phase in the third direction;
A torsional anti-phase mode in which the pair of vibrating arms is twisted in an anti-phase around an axis extending in the first direction;
A torsional in-phase mode in which the pair of vibrating arms are twisted in-phase around an axis extending in the first direction;
At least two of the third direction substrate mode in which the resonator element substrate deforms along the third direction and the substrate contour mode in which the contour of the resonator element substrate deforms in a direction intersecting the third direction. A vibrating piece substrate comprising a higher-order mode of an eigenmode. In claim 3,
The high-order mode of the third direction substrate mode and the substrate contour mode is a second-order or higher-order or lower-order mode, wherein the resonator element substrate is characterized in that: In claim 3 or 4,
The vibration piece substrate according to claim 1, wherein the main vibration is the second direction anti-phase mode. In claim 5,
The resonating arm has a groove that opens in a main surface,
When the length of the vibrating arm in the first direction is L [m],
At least a part of the groove is provided between the base end of the vibrating arm and a position spaced from the base end to the tip side by L / 3,
When the length of the vibration direction of the main vibration of the vibrating arm is W [m],

A vibrating piece substrate characterized by satisfying the relationship:
However,

ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm k [W / (m · K)] is the main density of the vibrating arm Thermal conductivity along the vibration direction of vibration In claim 5,
When the length of the vibration direction of the main vibration of the vibrating arm is W [m],

A vibrating piece substrate characterized by satisfying the relationship:
However,

ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm k [W / (m · K)] is the main density of the vibrating arm Thermal conductivity along the vibration direction of vibration In any one of Claims 5 thru | or 7,
The vibration piece substrate has one virtual vibration symmetry plane which is a symmetry plane with respect to the main vibration. In any one of Claims 5 thru | or 7,
The vibration piece substrate has at least two virtual vibration symmetry planes that are symmetrical with respect to the main vibration. In any one of Claims 5 thru | or 9,
The connecting piece overlaps with the virtual vibration symmetry plane. In any one of Claims 5 thru | or 9,
The connecting part is spaced apart from the virtual vibration symmetry plane. In any one of Claims 1 thru | or 11,
When the Q value of the resonator element is Q,

A vibrating piece substrate characterized by satisfying the relationship:
However,

A = 7.3690 × 10 ⁻²
B = 1.2544 × 10 ⁻⁵
C = 1.1 or more and 1.3 or less ρ [kg / m ³ ] is the mass density of the vibrating arm Cp [J / (kg · K)] is the heat capacity of the vibrating arm c [N / m ² ] Is the elastic constant α [1 / K] in the extending direction of the vibrating arm, the thermal expansion coefficient Θ [K] in the extending direction of the vibrating arm is the environmental temperature k [W / (m · K)], The thermal conductivity π along the vibration direction of the main vibration of the vibrating arm π is the circumference ratio A step of preparing the resonator element substrate according to any one of claims 1 to 12,
Cutting the connecting portion to separate the vibrating piece from the support portion. The vibration piece separated from the vibration piece substrate according to any one of claims 1 to 12,
And a package for housing the resonator element. The vibration piece separated from the vibration piece substrate according to any one of claims 1 to 12,
And an oscillator circuit.   An electronic apparatus comprising the resonator element separated from the resonator element substrate according to claim 1.   A moving body comprising the resonator element separated from the resonator element substrate according to any one of claims 1 to 12.

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