# Patent

## Title
Resonator element, resonator, resonator device, oscillator, electronic apparatus, and moving object

## Abstract

A resonator element includes a first region which includes a first portion and a second portion having a thickness thinner than the first portion. In a plan view, the second portion includes an outer frame in two edges present in opposite regions to regions facing the first portion, and a contour of the outer frame is bent more gently than a contour of an edge of the first portion. When R is a length of the outer frame along the X axis, λ is a wavelength of flexural vibration of the quartz crystal substrate, and R/(λ/2)=k, a relation of “0.1<k<1.4” is satisfied.

## Background
BACKGROUND
1. Technical Field
The present invention relates to a resonator element, a resonator, a resonator device, an oscillator, an electronic apparatus, and a moving object.
2. Related Art
In the related art, there are known resonator elements using quartz crystal. Such resonator elements are widely used as reference frequency sources, oscillation sources, or the like of various electronic apparatuses since frequency-temperature characteristics are excellent. In particular, since the frequency-temperature characteristics of resonator elements using quartz crystal substrates cut at cut angles called AT-cut show cubic curves, the resonator elements are widely used in mobile communication apparatuses such as mobile phones.
For example, JP-A-2012-114496 and JP-A-2012-114495 disclose AT-cut quartz crystal resonator elements which have multistage mesa structures and in which vibration sections which are mesa sections include first portions and second portions having thicknesses thinner than the first portions and integrated in the circumferences of the first portions in a plan view. Here, when Z is the size of an AT-cut substrate in a Z′ axis, Mz is the size of the vibration section in the Z′ axis, and t is the thickness of the first portion of the vibration section and relations of “8≦Z/t≦11” and “0.6≦Mz/Z≦0.8” are satisfied, it is possible to reduce the value of equivalent series resistance, so-called crystal impedance (CI).
JP-A-2009-65270 discloses an AT-cut quartz crystal resonator element which has a one-stage mesa structure and in which the corners of a mesa section are chamfered to suppress contour vibration and flexural vibration which are unnecessary vibration.
JP-A-2014-90290 discloses an AT-cut quartz crystal resonator element which has a multistage mesa structure and in which the corners of a mesa section are chamfered to further suppress combination of a thickness shear vibration mode and an unnecessary vibration mode.
In the foregoing resonator element, it is preferable to reduce equivalent series resistance, that is, so-called crystal impedance (CI) value.
SUMMARY
An advantage of some aspects of the invention is that it provides a resonator element capable of reducing equivalent series resistance. Further, an advantage of some aspects of the invention is that it provides a resonator, a resonator device, an oscillator, an electronic apparatus, and a moving object including the resonator element.
The invention can be implemented as the following forms or application examples.
APPLICATION EXAMPLE 1
A resonator element according to this application example includes a quartz crystal substrate in which an X axis of an orthogonal coordinate system having the X axis serving as an electric axis, the Y axis serving as a mechanical axis, and the Z axis serving as an optical axis, which are crystallographic axes of quartz crystal, is set as a rotation axis, an axis inclined from the Z axis so that a +Z side is rotated in a −Y direction of the Y axis is set as a Z′ axis, an axis inclined from the Y axis so that a +Y side is rotated in a +Z direction of the Z axis is set as a Y′ axis, a plane including the X and Z′ axes is set as a main plane, and the direction oriented along the Y′ axis is set as a thickness direction. The quartz crystal substrate includes a first region which includes a first portion and a second portion having a thickness thinner than the first portion and in which thickness shear vibration is generated, and a second region which has a thickness thinner than the first region. In a plan view, the second portion includes an outer frame in two edges present in opposite regions to regions facing the first portion, and a contour of the outer frame is bent more gently than a contour of an edge of the first portion. When R is a length of the outer frame along the X axis, λ is a wavelength of flexural vibration of the quartz crystal substrate, and R/(λ/2)=k, a relation of “0.1<k<1.4” is satisfied.
In the resonator element, it is possible to reduce equivalent series resistance.
APPLICATION EXAMPLE 2
In the resonator element according to the application example, a relation of 0.3≦k≦1.1 may be satisfied.
In the resonator element, it is possible to further reduce equivalent series resistance.
APPLICATION EXAMPLE 3
In the resonator element according to the application example, a relation of 0.5≦k≦1.05 may be satisfied.
In the resonator element, it is possible to further reduce equivalent series resistance.
APPLICATION EXAMPLE 4
In the resonator element according to the application example, in the plan view, the contour of the outer frame may be one of a curved line, a straight line, and a line formed by connecting a plurality of straight lines.
In the resonator element, it is possible to reduce equivalent series resistance.
APPLICATION EXAMPLE 5
In the resonator element according to the application example, in the plan view, the contour of the edge of the first portion may be two straight lines meeting at right angles.
In the resonator element, it is possible to reduce equivalent series resistance.
APPLICATION EXAMPLE 6
In the resonator element according to the application example, the first region may include a projection portion projecting from the second region in a +Y′ direction of the Y′ axis. A side surface of the projection portion intersecting the Z′ axis may be an inclined surface or a vertical surface to a surface including the X axis and the Z′ axis. When Sz is a length of the side surface along the Z′ axis and Mz is a length of the first region along the Z′ axis in the plan view, a relation of “0≦Sz/Mz≦0.05” may be satisfied.
In the resonator element, it is possible to reduce equivalent series resistance.
APPLICATION EXAMPLE 7
The resonator element according to the application example may further include excitation electrodes that are formed in the first and second regions.
In the resonator element, it is possible to excite the quartz crystal substrate by the excitation electrode.
APPLICATION EXAMPLE 8
A resonator according to this application example includes: the resonator element according to the application example; and a package in which the resonator element is accommodated.
Since the resonator includes the resonator element according to the application example, it is possible to reduce the equivalent series resistance.
APPLICATION EXAMPLE 9
A resonator device according to this application example includes: the resonator element according to the application example; and an electronic element.
Since the resonator device includes the resonator element according to the application example, it is possible to reduce the equivalent series resistance.
APPLICATION EXAMPLE 10
In the resonator device according to the application example, the electronic element may be a thermosensitive element.
Since the resonator device includes the resonator element according to the application example, it is possible to reduce the equivalent series resistance.
APPLICATION EXAMPLE 11
An oscillator according to this application example includes: the resonator element according to the application example; and an oscillation circuit that is electrically connected to the resonator element.
Since the oscillator includes the resonator element according to the application example, it is possible to reduce power consumption.
APPLICATION EXAMPLE 12
An electronic apparatus according to this application example includes the resonator element according to the application example.
Since the electronic apparatus includes the resonator element according to the application example, it is possible to reduce power consumption.
APPLICATION EXAMPLE 13
A moving object according to this application example includes the resonator element according to the application example.
Since the moving object includes the resonator element according to the application example, it is possible to reduce power consumption.



BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements.
FIG. 1 is a perspective view schematically illustrating a resonator element according to an embodiment.
FIG. 2 is a plan view schematically illustrating the resonator element according to the embodiment.
FIG. 3 is a sectional view schematically illustrating the resonator element according to the embodiment.
FIG. 4 is a sectional view schematically illustrating the resonator element according to the embodiment.
FIG. 5 is a perspective view schematically illustrating an AT-cut quartz crystal substrate.
FIG. 6 is a sectional view schematically illustrating the resonator element according to the embodiment.
FIGS. 7A and 7B are plan views schematically illustrating the resonator element according to the embodiment.
FIG. 8 is a sectional view schematically illustrating the resonator element according to the embodiment.
FIG. 9 is a plan view schematically illustrating the resonator element according to a modification example of the embodiment.
FIG. 10 is a table illustrating a CI value of the resonator element according to an experimental example.
FIG. 11 is a graph illustrating the CI value of the resonator element according to the experimental example.
FIG. 12 is a graph illustrating the CI value of the resonator element according to the experimental example.
FIG. 13 is a plan view schematically illustrating a resonator according to the embodiment.
FIG. 14 is a sectional view schematically illustrating the resonator according to the embodiment.
FIG. 15 is a sectional view schematically illustrating a resonator device according to the embodiment.
FIG. 16 is a sectional view schematically illustrating a resonator device according to a first modification example of the embodiment.
FIG. 17 is a sectional view schematically illustrating a resonator device according to a second modification example of the embodiment.
FIG. 18 is a sectional view schematically illustrating an oscillator according to the embodiment.
FIG. 19 is a sectional view schematically illustrating an oscillator according to a modification example of the embodiment.
FIG. 20 is a plan view schematically illustrating an electronic apparatus according to the embodiment.
FIG. 21 is a perspective view schematically illustrating an electronic apparatus according to the embodiment.
FIG. 22 is a perspective view schematically illustrating an electronic apparatus according to the embodiment.
FIG. 23 is a perspective view schematically illustrating an electronic apparatus according to the embodiment.
FIG. 24 is a plan view schematically illustrating a moving object according to the embodiment.



DESCRIPTION OF EXEMPLARY EMBODIMENTS
Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings. The embodiments to be described below do not inappropriately limit content of the invention described in the appended claims. All of the configurations to be described below may not be said to be indispensable configuration prerequisites.
1. Resonator Element
First, a resonator element according to an embodiment will be described with reference to the drawings. FIG. 1 is a perspective view schematically illustrating a resonator element 100 according to the embodiment. FIG. 2 is a plan view schematically illustrating the resonator element 100 according to the embodiment. FIG. 3 is a sectional view taken along the line III-III of FIG. 2 schematically illustrating the resonator element 100 according to the embodiment. FIG. 4 is a sectional view taken along the line IV-IV of FIG. 2 schematically illustrating the resonator element 100 according to the embodiment.
As illustrated in FIGS. 1 to 4, the resonator element 100 includes a quartz crystal substrate 10 and excitation electrodes 20a and 20b. 
The quartz crystal substrate 10 is configured as an AT-cut quartz crystal substrate. Here, FIG. 5 is a perspective view schematically illustrating an AT-cut quartz crystal substrate 101.
A piezoelectric material such as quartz crystal is generally a trigonal system and has quartz crystal axes (X, Y, and Z), as illustrated in FIG. 5. The X axis is an electric axis, the Y axis is a mechanical axis, and the Z axis is an optical axis. The quartz crystal substrate 101 is a flat substrate which is a so-called rotational Y-cut quartz crystal substrate cut out from a piezoelectric material (for example, a synthetic crystal) along a flat plane rotated from the XZ plane (which is a plane including the X and Z axes) by an angle θ around the X axis. The Y and Z axes are also rotated by θ around the X axis to form Y′ and Z′ axes, respectively. The quartz crystal substrate 101 is a substrate that has a plane including the X and Z′ axes as a main plane and has a thickness in the direction oriented along the Y′ axis. Here, when θ=35°15′ is set, the quartz crystal substrate 101 is an AT-cut quartz crystal substrate. Accordingly, in the AT-cut quartz crystal substrate 101, an XZ′ plane (which is a plane including the X and Z′ axes) perpendicular to the Y′ axis is a main plane (a main plane of a vibration section) and thickness shear vibration can be realized as main vibration. The quartz crystal substrate 10 can be obtained by processing the AT-cut quartz crystal substrate 101.
As illustrated in FIG. 5, the quartz crystal substrate 10 is configured as an AT-cut quartz crystal substrate in which the X axis of the orthogonal coordinate system having the X axis serving as an electric axis, the Y axis serving as a mechanical axis, and the Z axis serving as an optical axis, which are crystallographic axes of quartz crystal, is set as a rotation axis, an axis inclined from the Z axis so that the +Z side is rotated in the −Y direction of the Y axis is set as a Z′ axis, an axis inclined from the Y axis so that the +Y side is rotated in the +Z direction of the Z axis is set as a Y′ axis, a plane including the X and Z′ axes is set as a main plane, and the direction oriented along the Y′ axis is set as a thickness direction. In FIGS. 1 to 4 and FIGS. 6 to 9 to be described below, the X, Y′, and Z′ axes orthogonal to each other are illustrated.
For example, as illustrated in FIG. 2, the quartz crystal substrate 10 has a rectangular shape in which a direction (Y′ axis direction) oriented along the Y′ axis is set as a thickness direction, a direction (X axis direction) oriented in the X axis is set as a long side in a plan view from the Y′ axis direction (hereinafter simply referred to as the “plan view”), and a direction (Z′ axis direction) oriented along the Z′ axis is set as a short side. The quartz crystal substrate 10 includes a peripheral section (second region) 12 and a vibration section (first region) 14.
As illustrated in FIG. 2, the peripheral section 12 is formed in the periphery of the vibration section 14. The peripheral section 12 is formed along the outer frame of the vibration section 14. The peripheral section 12 has a thickness thinner than the vibration section 14 (the thickness is thinner than that of the vibration section 14).
As illustrated in FIG. 2, in the plan view, the vibration section 14 is surrounded by the peripheral section 12 and has a thickness thicker than the peripheral section 12. The vibration section 14 has a side oriented along the X axis and a side oriented along the Z′ axis. The vibration section 14 includes a first portion 15 and a second portion 16.
The first portion 15 of the vibration section 14 has a thickness thicker than the second portion 16. In an example illustrated in FIGS. 3 and 4, the first portion 15 is a portion that has a thickness t1. The first portion 15 has a quadrangular shape in the plan view.
The second portion 16 of the vibration section 14 has a thickness thinner than the first portion 15 (the thickness is thinner than that of the first portion 15). In the illustrated example, the second portion 16 is a portion that has a thickness t2. The second portion 16 is formed in the +X direction of the X axis (+X axis direction) and the −X direction of the X axis (−X axis direction) of the first portion 15. That is, the first portion 15 is interposed between the second portion 16 in the X axis direction. As described above, the vibration section 14 includes two types of portions 15 and 16 having different thicknesses. Thus, the resonator element 100 can be said to have a two-stage mesa structure.
The vibration section 14 can vibrate so that thickness shear vibration is main vibration. Since the vibration section 14 has the two-stage mesa structure, the resonator element 100 can have an energy trapped effect. The “thickness shear vibration” refers to vibration in which a displacement direction of a quartz crystal substrate is parallel to a main plane of the quartz crystal substrate (in the illustrated example, the displacement direction of the quartz crystal substrate is the X axis direction) and a wave propagation direction is the thickness direction of the quartz crystal substrate.
As illustrated in FIGS. 3 and 4, the vibration section 14 includes a first projection portion 17 projecting from the peripheral section 12 in the +Y′ direction of the Y′ axis (+Y′ axis direction) and a second projection portion 18 projecting from the peripheral section 12 in the −Y′ direction of the Y′ axis (−Y′ axis direction). For example, the projection portions 17 and 18 have the same shape. The projection portions 17 and 18 have the same size.
On a side surface 17a of the first projection portion 17 in the +X axis direction and a side surface 17b of the first projection portion 17 in the −X axis direction and on a side surface 18a of the second projection portion 18 in the +X axis direction and a side surface 18b of the second projection portion 18 in the −X axis direction, as illustrated in FIG. 4, for example, two step differences are formed due to a difference between the thickness of the first portion 15 and the thickness of the second portion 16 or a difference between the thickness of the second portion 16 and the thickness of the peripheral section 12.
A side surface 17c of the first projection portion 17 in the +Z′ direction of the Z′ axis (the +Z′ axis direction) is, for example, a vertical surface to a plane including the X axis and the Z′ axis, as illustrated in FIG. 3. Aside surface 17d of the first projection portion 17 in the −Z′ axis direction of the Z′ axis (the −Z′ axis direction) is, for example, a surface inclined with respect to the plane including the X axis and the Z′ axis.
A side surface 18c of the second projection portion 18 in the +Z′ axis direction is, for example, a surface inclined with respect to the plane including the X axis and the Z′ axis, as illustrated in FIG. 3. A side surface 18d of the second projection portion 18 in the −Z′ axis direction is a plane vertical to the plane including the X axis and the Z′ axis.
The side surface 17d of the first projection portion 17 and the side surface 18c of the second projection portion 18 are formed as inclined surfaces with respect to the plane including the X axis and the Z′ axis, for example, when an m surface of quartz crystal is exposed by performing an etching process on the AT-cut quartz crystal substrate using a solution containing a hydrofluoric acid as an etchant. Although not illustrated, other side surfaces of the quartz crystal substrate 10 in the −Z′ direction other than the side surfaces 17d and 18c may also be formed as inclined surfaces with respect to the plane including the X axis and the Z′ axis by exposing the m surface of the quartz crystal.
As illustrated in FIG. 6, the side surfaces 17d and 18c may be vertical surfaces to the plane including the X axis and the Z′ axis. For example, by processing the AT-cut quartz crystal substrate by a laser or etching AT-cut quartz crystal substrate by dry etching, the side surfaces 17d and 18c can be formed as vertical surfaces to the plane including the X axis and the Z′ axis. For convenience, FIG. 1 illustrates the side surfaces 17d and 18c which are the vertical surfaces to the plane including the X axis and the Z′ axis.
In the resonator element 100, as illustrated in FIG. 2, when Sz is the length of the side surfaces 17d and 18c along the Z′ axis and Mz is the length of the vibration section 14 along the Z′ axis in the plan view, for example, formula (1) below is satisfied. Here, Mz is the size of a flat portion (specifically, the plane including the X axis and the Z′ axis) of the vibration section 14 in the Z′ axis direction.

0≦Sz/Mz≦0.05  (1)

When Sz/Mz=0, as illustrated in FIG. 6, the side surfaces 17d and 18c are vertical to the plane including the X axis and the Z′ axis.
The first excitation electrode 20a and the second excitation electrode 20b are formed to overlap each other in the plan view of the vibration section 14. In the illustrated example, the excitation electrodes 20a and 20b are also formed in the peripheral section 12. For example, the shapes of the excitation electrodes 20a and 20b in the plan view (the shapes when viewed in the Y′ axis direction) are rectangular. The vibration section 14 is formed inside the outer frames of the excitation electrodes 20a and 20b in the plan view. That is, the areas of the excitation electrodes 20a and 20b are greater than the area of the vibration section 14 in the plan view. The excitation electrodes 20a and 20b are electrodes that apply a voltage to the vibration section 14.
The first excitation electrode 20a is connected to the first electrode pad 24a via a first extraction electrode 22a. The second excitation electrode 20b is connected to the second electrode pad 24b via a second extraction electrode 22b. For example, the electrode pads 24a and 24b are electrically connected to an IC chip (not illustrated) that drives the resonator element 100. The electrode pads 24a and 24b are formed on the side of the peripheral section 12 in the +X axis direction. The excitation electrodes 20a and 20b, the extraction electrodes 22a and 22b, and the electrode pads 24a and 24b are formed, for example, by stacking chromium and gold in this order from the side of the quartz crystal substrate 10.
The quartz crystal substrate 10 includes protrusions 30a, 30b, 30c, and 30d. As illustrated in FIGS. 1 and 2, the protrusions 30a and 30b are formed on both sides of a middle region on a free end side of the peripheral section 12. Here, the resonator element 100 is fixed to another member (for example, a package) in the electrode pads 24a and 24b. Accordingly, in the resonator element 100, the side of the electrode pads 24a and 24b of the peripheral section 12 (the side in the +X axis direction in the illustrated example) is a mounting side (fixing end side) and the opposite side (the side in the −X axis direction in the illustrated example) is the free end side. In the example illustrated in FIG. 2, the protrusions 30a and 30b are disposed on both sides of the middle region of the peripheral section 12 (for example, both sides of an imaginary straight line α parallel to the X axis passing through the center of the quartz crystal substrate 10 in the plan view) on the side of the peripheral section 12 in the −X axis direction. The protrusions 30a and 30b are formed on the surface of the peripheral section 12 in the +Y′ axis direction.
The protrusions 30c and 30d are formed on the surface of the peripheral section 12 in the −Y′ axis direction, as illustrated in FIG. 4. In the plan view, the protrusion 30c is formed to overlap the protrusion 30a and the protrusion 30d is formed to overlap the protrusion 30b. 
For example, the shapes of the protrusions 30a, 30b, 30c, and 30d are rectangular parallelepipeds. For example, the thicknesses of the protrusions 30a, 30b, 30c, and 30d are the same as the thicknesses of the projection portions 17 and 18. In the resonator element 100, for example, the protrusions 30a, 30b, 30c, 30d come into contact with the package (the package accommodating the resonator element 100), and thus it is possible to prevent the vibration section 14 or the excitation electrodes 20a and 20b from colliding against the package and damaging. As a result, for example, the resonator element 100 can have high reliability. The protrusions 30a, 30b, 30c, and 30d may not be formed.
Here, in the resonator element 100, as illustrated in FIG. 4, the projections 17 and 18 are each configured to include a first step difference portion 2 of a first stage of the vibration section 14 and a second step difference portion 4 of a second stage of the vibration section 14. The first step difference portion 2 and the second step difference portion 4 are connected to each other. In the plan view, the area of the first step difference portion 2 is greater than the area of the second step difference portion 4. The second step difference portion 4 of the first projection portion 17 is located to be closer to the side in the +Y′ axis direction than the first step difference portion 2 of the first projection portion 17. The second step difference portion 4 of the second projection portion 18 is located to be closer to the side in the −Y′ axis direction than the first step difference portion 2 of the second projection portion 18. In the plan view, the first step difference portion 2 of the first projection portion 17 may substantially overlap the first step difference portion of the second projection portion 18. The second step difference portion 4 of the first projection portion 17 may substantially overlap the second step difference portion 4 of the second projection portion 18.
In the plan view, edges 2a of the first step difference portion 2 are chamfered portions. In other words, the first step difference portion 2 has a shape of which corners of a rectangle are cut out. The edges 2a are, for example, portions that connect the sides oriented along the X axis and the sides oriented along the Z′ axis in the plan view. In the illustrated example, four edges 2a are chamfered portions. However, the number of chamfered portions is not particularly limited as long as any one of the four edges 2a is the chamfered portion. As illustrated in FIG. 2, the contour of the edge 2a which is the chamfered portion is a curved line in the plan view. The contour of the edge 2a which is the chamfered portion may be an arc or may be an ellipse in the plan view. As illustrated in FIG. 7A, the contour of the edge 2a which is the chamfered portion may be a straight line in the plan view. As illustrated in FIG. 7B, the contour of the edge 2a may be a line formed by connecting a plurality of straight lines.
The contour of the edge 2a of the first step difference portion 2 which is the chamfered portion is gentler than the contour of an edge (an edge of the first portion 15) 4a of the second step difference portion 4 in the plan view. Here, the fact that “the contour of the edge 2a which is the chamfered portion is gentler than the contour of the edge 4a” means that a curvature of the contour of the edge 2a is less than a curvature of the edge 4a when the contours of the edges 2a and 4a are curved lines. When the contour of the edge 4a is two straight lines meeting at right angles, the contour of the edge 2a is a line that has a straight line connected to a side along the X axis and aside along the Z′ axis at a greater angle than a curved line or right angles. In the illustrated example, the contour of the edge 4a of the second step difference portion 4 is two straight lines meeting at right angles in the plan view. That is, the shape of the second step difference portion 4 in the plan view is a quadrangle (a square or a rectangle) of which all the angles of four corners are the same. In the plan view, the edge 4a of the second step difference portion 4 is not chamfered.
The edges 2a of the first step difference portion 2 which are the chamfered portions are the outer frame of the second portion 16. As illustrated in FIG. 2, the second portion 16 includes a pair of first sides 16a along the Z′ axis in the plan view. In the illustrated example, one of the one pair of first sides 16a is a boundary line with the peripheral section 12 of the second portion 16 and the other thereof is a boundary line with the first portion 15 of the second portion 16.
The one pair of first sides 16a of the second portion 16 overlap an imagined quadrangle (imaginary quadrangle) A in the plan view. When all the angles of four corners are the same, the imaginary quadrangle A includes one pair of second sides A1 oriented along the X axis and one pair of third sides A2 oriented along the Z′ axis. In the illustrated example, the imaginary quadrangle A is rectangular. The one pair of first sides 16a of the second portion 16 overlap the one pair of third sides A2. In the plan view, the second portion 16 includes an outer frame 2a which does not overlap at least two edges arranged along the Z′ axis among four corners of the imaginary quadrangle A. In the illustrated example, the outer frame 2a is located inside the imaginary quadrangle A when the second sides A1 and the third sides A2 of the imaginary quadrangle A overlap each other.
In the resonator element 100, as illustrated in FIG. 2, when R is the length of the edge (the outer frame of the second portion 16) 2a which is the chamfered portion along the X axis, λ is a wavelength of the flexural vibration of the quartz crystal substrate 10, and R/(λ/2)=k, a relation of formula (2) below is satisfied.

0.1<k<1.4  (2)

The “wavelength of the flexural vibration generated in the quartz crystal substrate 10” is a wavelength of flexural vibration which is spurious (unnecessary vibration) generated in the quartz crystal substrate 10. For example, the wavelength λ of the flexural vibration can be obtained by a mathematical formula such as “λ/2=(1.332/f)−0.0024” where a resonance frequency of the resonator element 100 is f.
In the example illustrated in FIG. 2, when Mx is the length of the vibration section 14 along the X axis (the length of the first step difference portion 2 along the X axis) and M2x is the length of the first portion 15 of the vibration section 14 along the X axis (the length of the second step difference portion 4 along the X axis), a length R can be expressed as “R=(Mx−M2x)/2”. The length of the edge 2a, which is the chamfered portion, along the X axis and the length thereof along the Z′ axis may be different from, but are the same as each other in the illustrated example.
When formula (2) is satisfied, it is possible to reduce the flexural vibration of the quartz crystal substrate 10 which is an unnecessary mode, and thus it is possible to reduce the equivalent series resistance (which will be described below in detail in “Experimental Example”).
For example, when the quartz crystal substrate is processed by wet etching, as illustrated in FIG. 8, the side surfaces 17a and 17b of the projection portion 17 are configured by a surface parallel to the XZ′ plane and a surface inclined with respect to the XZ′ plane by etching anisotropy. In this case, the length Mx is a distance between the center of the surface of the side surface 17a inclined with respect to the XZ′ plane and the center of the surface of the side surface 17b inclined with respect to the XZ′ plane. This is not limited to the length Mx, but the same applies for the length (for example, R or Mz) of each portion of the quartz crystal substrate 10 included in the resonator element according to the invention.
Further, in the resonator element 100, it is preferable to satisfy formulae (3) and (4) below.

0.3≦k≦1.1  (3)

0.5≦k≦1.05  (4)

When formulae (3) and (4) are satisfied, it is possible to reduce the equivalent series resistance (which will be described below in detail in “Experimental Example”).
In a method of manufacturing the resonator element 100, for example, the quartz crystal substrate 10 is formed by photolithography and etching. The etching may be dry etching or wet etching. The protrusions 30a, 30b, 30c, and 30d may be formed simultaneously with the vibration section 14. The excitation electrodes 20a and 20b, the extraction electrodes 22a and 22b, and the electrode pads 24a and 24b (hereinafter also referred to as “the excitation electrodes 20a and 20b and the like”) are formed, for example, by forming conductor layers (not illustrated) by a sputtering method or a vacuum evaporation method and patterning the conductor layers by photolithography and etching.
The resonator element 100 has, for example, the following characteristics.
In the resonator element 100, formula (2) is satisfied. More preferably, formulae (3) and (4) are satisfied. Therefore, in the resonator element 100, it is possible to reduce the flexural vibration of the quartz crystal substrate 10 which is an unnecessary mode, and thus it is possible to reduce the equivalent series resistance (which will be described below in detail in “Experimental Example”).
In the resonator element 100, the quartz crystal substrate 10 includes the protrusions 30a, 30b, 30c, and 30d. Therefore, for example, before the vibration section 14 or the excitation electrodes 20a and 20b collide against the package (the package accommodating the resonator element 100), the protrusions 30a, 30b, 30c, and 30d collide against the package. Therefore, it is possible to prevent the vibration section 14 or the excitation electrodes 20a and 20b from damaging. As a result, the resonator element 100 can have high reliability.
The example has been described above in which the areas of the excitation electrodes 20a and 20b are greater than the area of the vibration section 14 in the plan view. However, in the resonator element according to the invention, the areas of the excitation electrodes 20a and 20b may be less than the area of the vibration section 14 in the plan view. In this case, the excitation electrodes 20a and 20b are formed inside the outer frame of the vibration section 14 in the plan view.
Although the two-stage mesa structure in which the vibration section 14 has the two types of portions 15 and 16 having different thicknesses has been described above, as long as the number of stages of the mesa structure of the resonator element according to the invention is 2 or more, the number is not limited. That is, the resonator element according to the embodiment includes the vibration section in which a step difference of two or more stages is formed. For example, the resonator element according to the invention may have a three-stage mesa structure in which the vibration section includes three types of portions having different thicknesses.
The example has been described above in which a step difference is not formed by a difference between the thickness of the first portion 15 and the thickness of the second portion 16 in the side surfaces 17c and 17d of the first projection portion 17 and the side surfaces 18c and 18d of the second projection portions 18. However, in the resonator element according to the invention, a step difference (a step difference between the thickness of the first portion 15 and the thickness of the second portion 16) may be formed in the side surfaces 17c, 17d, 18c, and 18d. 
The example has been described above in which the resonator element includes the first projection portion 17 projecting from the peripheral section 12 in the +Y′ axis direction and the second projection portion 18 projecting from the peripheral section 12 in the −Y′ axis direction. However, the resonator element according to the invention may include only one of the projection portions.
The example in which the quartz crystal substrate 10 is the AT-cut quartz crystal substrate has been described above. However, in the resonator element according to the invention, the quartz crystal substrate is not limited to the AT-cut quartz crystal substrate, but may be a piezoelectric substrate in which thickness shear vibration is generated, such as an SC-cut quartz crystal substrate or a BT-cut quartz crystal substrate.
2. Modification Examples Of Resonator Element
Next, a resonator element according to a modification example of the invention will be described with reference to the drawings. FIG. 9 is a plan view schematically illustrating a resonator element 200 according to the modification example of the embodiment. Hereinafter, in the resonator element 200 according to the modification example of the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the resonator element 100 according to the embodiment and the detailed description thereof will be omitted.
In the above-described resonator element 100, as illustrated in FIG. 2, the quartz crystal substrate 10 has a rectangular shape in the plan view. Accordingly, in the resonator element 200, as illustrated in FIG. 9, edges (corners) of the quartz crystal substrate 10 in the −X axis direction are chamfered. In other words, the resonator element has a shape in which the rectangular corners are cut out. For example, edges of the quartz crystal substrate 10 in the +X axis direction may also be chamfered.
In the resonator element 200, the edges of the quartz crystal substrate 10 are chamfered. Therefore, when the quartz crystal substrate 10 is formed by etching, it is possible to reduce generation of burr (for example, etching residue). Further, when the resonator element 200 is mounted on a package, it is possible to reduce a possibility of the corners of the quartz crystal substrate 10 coming into contact with the package and damaging.
3. Experimental Example
Hereinafter, the invention will be described more specifically according to an experimental example. The invention is not limited to the following experimental example.
In the experimental example, the same resonator element as the above-described resonator element 200 was manufactured. The length X of the quartz crystal substrate 10 along the X axis was set to 1.06 mm, the length Z of the quartz crystal substrate 10 along the Z′ axis was set to 0.65 mm, a length Ex of the excitation electrodes 20a and 20b along the X axis was set to 0.7 mm, a length Ez of the excitation electrodes 20a and 20b along the Z′ axis was set to 0.5 mm, the length Mx of the vibration section 14 along the X axis was set to 0.6 mm, the length M2x of the first portion 15 of the vibration section 14 along the Z′ axis was set to 0.5 mm, the length Mz of the vibration section 14 along the Z′ axis was set to 0.4 mm, and the resonance frequency was set to 24 MHz. Further, resonator elements A, B, C, D, E, F and G were manufactured by changing the length R, and then a CI vale was measured. The dimensions were measured by a dimension measurement device and the CI value was measured using a network analyzer.
FIG. 10 is a table illustrating R, k(=R/(λ/2)), and the CI values of the resonator elements A, B, C, D, E, and F. FIG. 11 is a graph illustrating a relation between R and the CI value. FIG. 12 is a graph illustrating a relation between k and the CI value. Further, λ is a wavelength of flexural vibration which is spurious (unnecessary vibration) generated in the quartz crystal substrate. When f is a resonant frequency of the resonator element, a formula of “λ/2=(1.332/f)−0.0024(μm)” was calculated.
As illustrated in FIG. 12, by satisfying the relations of “0.1<k<1.4”, it can be understood that the CI value can be suppressed to a value less than 80Ω. By satisfying a relation of “0.3≦k≦1.1”, it can be understood that the CI value can be suppressed to a value less than 70Ω. By satisfying a relation of “0.5≦k≦1.05”, it can be understood that the CI value can be further reduced.
4. Resonator
Next, a resonator according to the embodiment will be described with reference to the drawings. FIG. 13 is a plan view schematically illustrating a resonator 700 according to the embodiment. FIG. 14 is a sectional view taken along the line XIV-XIV of FIG. 13 schematically illustrating the resonator 700 according to the embodiment. For convenience, a seal ring 713 and a lid 714 are not illustrated in FIG. 13.
The resonator 700 includes a resonator element according to the invention. Hereinafter, the resonator 700 including the resonator element 100 as the resonator element according to the invention will be described. As illustrated in FIGS. 13 and 14, the resonator 700 includes the resonator element 100 and a package 710.
The package 710 includes a box-shaped base 712 that has a concave portion 711 of which the top surface is opened and a plate-shaped lid 714 that is joined to the base 712 to close the opening of the concave portion 711. The package 710 has an accommodation space formed so that the concave portion 711 is closed with the lid 714, and thus the resonator element 100 is accommodated to be installed in the accommodation space so that the resonator element 100 is airtight. That is, the resonator element 100 is accommodated in the package 710.
For example, the accommodation space (the concave portion 711) in which the resonator element 100 is accommodated may be in a depressurized state (preferably, a vacuum state) or an inert gas such as nitrogen, helium, or argon may be enclosed. Accordingly, the vibration characteristics of the resonator element 100 are improved.
As the material of the base 712, for example, any of various ceramics such as aluminum oxide can be used. As the material of the lid 714, for example, a material with a close linear expansion coefficient to the material of the base 712 can be used. Specifically, when the material of the base 712 is a ceramic, the material of the lid 714 is an alloy such as Kovar.
The bonding of the base 712 and the lid 714 is performed by forming the seal ring 713 on the base 712, mounting the lid 714 on the seal ring 713, and welding the seal ring 713 to the base 712 using, for example, a resistance welder. The bonding of the base 712 and the lid 714 are not particularly limited, but may be performed using an adhesive or may be performed by seam welding.
A pillow portion 720 is formed on the bottom surface of the concave portion 711 of the package 710. For example, the pillow portion 720 is formed to come into contact with the protrusions 30c and 30d of the resonator element 100. For example, the material of the pillow portion 720 is the same as the material of the base 712. The pillow portion 720 may be integrated with the base 712. For example, even when an impact is applied to the resonator 700 from the outside, the pillow portion 720 and the protrusions 30c and 30d come into contact with each other, and thus it is possible to prevent the vibration section 14 of the resonator element 100 from colliding against the concave portion 711 of the package 710 and damaging. Further, for example, before the vibration section 14 collides against the lid 714, the protrusions 30c and 30d collide against the lid 714. Therefore, it is possible to prevent the vibration section 14 from damaging.
A first connection terminal 730 and a second connection terminal 732 are formed on the bottom surface of the concave portion 711 of the package 710. The first connection terminal 730 is formed to face the first electrode pad 24a of the resonator element 100. The second connection terminal 732 is formed to face the second electrode pad 24b of the resonator element 100. The connection terminals 730 and 732 are electrically connected to the electrode pads 24a and 24b via a conductive fixing member 734, respectively.
A first external terminal 740 and a second external terminal 742 are formed on the bottom surface (the bottom surface of the base 712) of the package 710. For example, the first external terminal 740 is formed at a position overlapping the first connection terminal 730 in the plan view. For example, the second external terminal 742 is formed at a position overlapping the second connection terminal 732 in the plan view. The first external terminal 740 is electrically connected to the first connection terminal 730 through a via (not illustrated). The second external terminal 742 is electrically connected to the second connection terminal 732 through a via (not illustrated).
As the connection terminals 730 and 732 and the external terminals 740 and 742, for example, metal coating films formed by stacking coating films of Ni (nickel), Au (gold), Ag (silver), Cu (copper), or the like on metalized layers (underlying layers) of Cr (chromium), W (tungsten), or the like are used. As the conductive fixing member 734, for example, a solder, a silver paste, a conductive adhesive (an adhesive in which conductive fillers such as metal particles are dispersed in a resin material), or the like is used.
Since the resonator 700 includes the resonator element 100, it is possible to reduce the equivalent series resistance.
5. Resonator Device
Next, a resonator device according to the embodiment will be described with reference to the drawings. FIG. 15 is a sectional view schematically illustrating a resonator device 800 according to the embodiment.
Hereinafter, in the resonator device 800 according to the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the above-described resonator 700 according to the embodiment and the detailed description thereof will be omitted.
The resonator device 800 includes the resonator element according to the invention. Hereinafter, a resonator device 800 including the resonator element 100 as the resonator element according to the invention will be described. The resonator device 800 includes the resonator element 100, the package 710, and a thermosensitive element (electronic element) 810, as illustrated in FIG. 15.
The package 710 includes an accommodation portion 812 that accommodates the thermosensitive element 810. For example, the accommodation portion 812 can be formed by forming a frame-shaped member 814 on the bottom surface of the base 712.
The thermosensitive element 810 is, for example, a thermistor in which a physical quantity, for example, electric resistance, is changed according to a change in temperature. The electric resistance of the thermistor can be detected by an external circuit to measure detection temperature of the thermistor.
Another electric component may be accommodated in the accommodation space (the concave portion 711) of the package 710. As the electric component, an IC chip or the like controlling driving of the resonator element 100 can be exemplified.
Since the resonator device 800 includes the resonator element 100, it is possible to reduce the equivalent series resistance.
6. Modification Examples Of Resonator Device
6.1. First Modification Example
Next, a resonator device according to a first modification example of the embodiment will be described with reference to the drawing. FIG. 16 is a sectional view schematically illustrating a resonator device 900 according to the first modification example of the embodiment.
Hereinafter, in the resonator device 900 according to the first modification example of the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the above-described resonator device 800 according to the embodiment and the detailed description thereof will be omitted.
In the above-described resonator device 800, as illustrated in FIG. 15, the accommodation portion 812 that accommodates a thermosensitive element 810 is formed by forming a frame-shaped member 814 on the bottom surface of the base 712.
On the other hand, in the resonator device 900, as illustrated in FIG. 16, the thermosensitive element 810 is accommodated in a concave portion 912 by forming the concave portion 912 on the bottom surface (the bottom surface of the base 712) of the package 710. In the illustrated example, a third connection terminal 930 is formed on the bottom surface of the concave portion 912 and the thermosensitive element 810 is formed under a third connection terminal 930 via a metal bump or the like. In the illustrated example, the third connection terminal 930 is connected to a wiring 932 formed in the base 712. The third connection terminal 930 is electrically connected to the first external terminal 740 and the first connection terminal 730 by the wiring 932. For example, the material of the third connection terminal 930 is the same as the material of the connection terminal 730 or 732. The material of the wiring 932 is not particularly limited as long as the material is conductive.
Since the resonator device 900 includes the resonator element 100, it is possible to reduce the equivalent series resistance.
6.2. Second Modification Example
Next, a resonator device according to a modification example of the embodiment will be described with reference to the drawing. FIG. 17 is a sectional view schematically illustrating a resonator device 1000 according to a second modification example of the embodiment.
Hereinafter, in the resonator device 1000 according to the second modification example of the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the above-described resonator devices 800 and 900 according to the embodiment and the detailed description thereof will be omitted.
In the resonator device 800, as illustrated in FIG. 15, the accommodation portion 812 that accommodates the thermosensitive element 810 is formed for the thermosensitive element 810 by forming the frame-shaped member 814 on the bottom surface side of the base 712.
On the other hand, in the resonator device 1000, as illustrated in FIG. 17, the concave portion 912 is formed on the bottom surface (upper surface of the base 712) of the concave portion 711 and the thermosensitive element 810 is accommodated in the concave portion 912. The thermosensitive element 810 is formed on the third connection terminal 930.
Since the resonator device 1000 includes the resonator element 100, it is possible to reduce the equivalent series resistance.
7. Oscillator
Next, an oscillator according to the embodiment will be described with reference to the drawing. FIG. 18 is a sectional view schematically illustrating an oscillator 1100 according to the embodiment.
Hereinafter, in the oscillator 1100 according to the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the above-described resonator 700 according to the embodiment and the detailed description thereof will be omitted.
The oscillator 1100 includes the resonator element according to the invention. Hereinafter, the oscillator 1100 including the resonator element 100 as the resonator element according to the invention will be described. As illustrated in FIG. 18, the oscillator 1100 includes the resonator element 100, the package 710, and an IC chip (chip component) 1110.
In the oscillator 1100, the concave portion 711 includes a first concave portion 711a formed on the top surface of the base 712, a second concave portion 711b formed in the middle of the bottom surface of the first concave portion 711a, and a third concave portion 711c formed in the middle of the bottom surface of the second concave portion 711b. 
The first connection terminal 730 and the second connection terminal 732 are formed on the bottom surface of the first concave portion 71a. The IC chip 1110 is formed on the bottom surface of the third concave portion 711c. The IC chip 1110 includes a driving circuit (oscillation circuit) that controls driving of the resonator element 100. When the resonator element 100 is driven by the IC chip 1110, vibration of a predetermined frequency can be extracted. The IC chip 1110 overlaps the resonator element 100 in the plan view. As illustrated in FIG. 18, the bottom surface of the first concave portion 711a may also function as the pillow portion 720 coming into contact with the protrusions 30c and 30d of the resonator element 100.
A plurality of internal terminals 1120 electrically connected to the IC chip 1110 via wires 1112 are formed on the bottom surface of the second concave portion 711b. For example, of the plurality of internal terminals 1120, one internal terminal 1120 is electrically connected to the first connection terminal 730 via a wiring (not illustrated). Of the plurality of internal terminals 1120, the other internal terminals 1120 are electrically connected to the second connection terminal 732 via wirings (not illustrated). Accordingly, the IC chip 1110 is electrically connected to the resonator element 100. The internal terminal 1120 may be electrically connected to the external terminal 740 through a via (not illustrated) formed in the base 712.
Since the oscillator 1100 includes the resonator element 100 capable of reducing the equivalent series resistance, it is possible to reduce power consumption.
8. Modification Example Of Oscillator
Next, an oscillator according to a modification example of the embodiment will be described with reference to the drawing. FIG. 19 is a sectional view schematically illustrating an oscillator 1200 according to a modification example of the embodiment.
Hereinafter, in the oscillator 1200 according to the modification example of the embodiment, the same reference numerals are given to elements having the same functions as the constituent elements of the above-described oscillator 1100 according to the embodiment and the detailed description thereof will be omitted.
In the above-described oscillator 1100, as illustrated in FIG. 18, the IC chip 1110 overlaps the resonator element 100 in the plan view.
On the other hand, in the oscillator 1200, as illustrated in FIG. 19, the IC chip 1110 does not overlap the resonator element 100 in the plan view. The IC chip 1110 is formed on the side of the resonator element 100.
In the oscillator 1200, the package 710 is configured to include a plate-shaped base 712 and a convex-shaped lid 714. The lid 714 is sealed hermetically by melting a metalized layer 1210 formed in the circumference of the base 712. At this time, a sealing step is performed in a vacuum state so that the inside of the oscillator can be vacuumized. As a sealing mechanism, a mechanism melting and welding the lid 714 using a laser beam or the like may be used.
In the illustrated example, the first connection terminal 730 is electrically connected to the first external terminal 740 through a via 1220 formed in the base 712. The internal terminal 1120 is electrically connected to the first external terminal 740 through the via 1220 formed in the base 712. The internal terminal 1120 is electrically connected to the first connection terminal 730 via a wiring (not illustrated). The IC chip 1110 is formed on the internal terminal 1120 via a metal bump or the like.
Since the oscillator 1200 includes the resonator element 100 capable of reducing the equivalent series resistance, it is possible to reduce power consumption.
9. Electronic Apparatus
Next, electronic apparatuses according to the embodiment will be described with reference to the drawings. An electronic apparatus according to the embodiment includes the resonator element according to the invention. Hereinafter, electronic apparatuses including the resonator element 100 as the resonator element according to the invention will be described.
FIG. 20 is a plan view schematically illustrating a smartphone 1300 as the electronic apparatus according to the embodiment. As illustrated in FIG. 20, the smartphone 1300 includes the oscillator 1100 including the resonator element 100.
In the smartphone 1300, the oscillator 1100 is used as, for example, a timing device such as a reference clock oscillation source or the like. The smartphone 1300 can further include a display unit (a liquid crystal display, an organic EL display, or the like) 1310, an operation unit 1320, a sound output unit 1330 (microphone or the like). The smartphone 1300 may include a touch detection mechanism on the display unit 1310 so that the display unit 1310 also serves as an operation unit.
An electronic apparatus typified by the smartphone 1300 preferably includes an oscillation circuit that drives the resonator element 100 and a temperature compensation circuit that corrects a frequency variation occurring with a change in the temperature of the resonator element 100.
Accordingly, the electronic apparatus typified by the smartphone 1300 includes the oscillation circuit that drives the resonator element 100 and the temperature compensation circuit that corrects a frequency variation occurring with a change in the temperature of the resonator element 100, and thus temperature-compensates a resonant frequency oscillated by the oscillation circuit. Therefore, it is possible to provide the electronic apparatus with excellent temperature characteristics.
FIG. 21 is a perspective view schematically illustrating a mobile (or notebook-type) personal computer 1400 as the electronic apparatus according to the embodiment. As illustrated in FIG. 21, the personal computer 1400 is configured to include a body unit 1404 including a keyboard 1402 and a display unit 1406 including a display unit 1405. The display unit 1406 is supported to be rotated via a hinge structure unit with respect to the body unit 1404. In the personal computer 1400, the resonator element 100 functioning as a filter, a resonator, a reference clock, or the like is built.
FIG. 22 is a perspective view schematically illustrating a mobile phone (also including a PHS) 1500 as the electronic apparatus according to the embodiment. The mobile phone 1500 includes a plurality of operation buttons 1502, a earpiece 1504, and a mouthpiece 1506. A display unit 1508 is disposed between the operation buttons 1502 and the earpiece 1504. In the mobile phone 1500, the resonator element 100 functioning as a filter, a resonator, or the like is built.
FIG. 23 is a perspective view schematically illustrating a digital still camera 1600 as the electronic apparatus according to the embodiment. In FIG. 23, connection with an external apparatus is also simply illustrated. Here, a normal camera exposes a silver-salt photo film by a light image of a subject, but the digital still camera 1600 performs photoelectric conversion on a light image of a subject using an image sensor such as a charge coupled device (CCD) and generates an imaging signal (image signal).
A display unit 1603 is formed on the rear surface of a case (body) 1602 of the digital still camera 1600 to perform display based on the imaging signal generated by the CCD. The display unit 1603 functions a finder that displays a subject as an electronic image. A light-receiving unit 1604 including an optical lens (imaging optical system) or a CCD is formed on the front surface (the front surface side of the drawing) of the case 1602.
When a photographer confirms a subject image displayed on the display unit and presses a shutter button 1606, an imaging signal of the CCD at that time is transmitted and stored in a memory 1608. In the digital still camera 1600, a video signal output terminal 1612 and a data communication input/output terminal 1614 are formed on a side surface of the case 1602. As illustrated, a television monitor 1630 is connected to the video signal output terminal 1612 and a personal computer 1640 is connected to the data communication input/output terminal 1614, as necessary. The imaging signal stored in the memory 1608 is configured to be output to the television monitor 1630 or the personal computer 1640 through a predetermined operation. In the digital still camera 1600, the resonator element 100 functioning as a filter, a resonator, or the like is built.
Since the electronic apparatuses 1300, 1400, 1500, and 1600 include the resonator element 100 capable of reducing the equivalent series resistance, it is possible to reduce power consumption.
The electronic apparatus including the resonator element according to the invention is not limited to the foregoing examples, but may be applied to, for example, an ink jet ejection apparatus (for example, an ink jet printer), a laptop personal computer, a television, a video camera, a video tape recorder, a car navigation apparatus, a pager, an electronic organizer (also including a communication function unit), an electronic dictionary, a calculator, an electronic game apparatus, a word processor, a workstation, a television phone, a security television monitor, electronic binoculars, a POS terminal, medical apparatuses (for example, an electronic thermometer, a blood pressure meter, a blood-sugar meter, an electrocardiographic apparatus, an ultrasonic diagnostic apparatus, and an electronic endoscope), a fish finder, various measurement apparatuses, meters (for example, meters for vehicles, airplanes, and ships), and a flight simulator.
10. Moving Object
Next, a moving object according to the embodiment will be described with reference to the drawing. FIG. 24 is a perspective view schematically illustrating an automobile as a moving object 1700 according to the embodiment.
The moving object according to the embodiment includes the resonator element according to the invention. Hereinafter, a moving object including the resonator element 100 as the resonator element according to the invention will be described.
The moving object 1700 according to the embodiment is configured to further include a controller 1720 that performs various kinds of control on an engine system, a brake system, a keyless entry system, and the like, a controller 1730, a controller 1740, a battery 1750, and a backup battery 1760. In the moving object 1700 according to the embodiment, some of the constituent elements (each unit) illustrated in FIG. 24 may be omitted or changed or other constituent elements may be added.
As the moving object 1700, various moving objects can be considered. For example, an automobile (also including an electric automobile), an airplane such as a jet plane or a helicopter, a ship, a rocket, and an artificial satellite can be exemplified.
Since the moving object 1700 includes the resonator element 100 capable of reducing the equivalent series resistance, it is possible to reduce power consumption.
The above-described embodiments and modification examples are merely examples and the invention is not limited thereto. For example, the embodiments and the modification examples can also be appropriately combined.
The invention includes substantially the same configurations (for example, configurations in which the functions, the methods, and the results are the same or configurations in which the goals and the advantages are the same) as the configurations described in the embodiments. The invention includes configurations in which unessential portions of the configurations described in the embodiments are substituted. The invention includes configurations in which the same operation and advantages as the configurations described in the embodiments or configurations in which the same goals can be achieved. The invention includes configurations in which known technologies are added to the configurations described in the embodiments.
The entire disclosure of Japanese Patent Application No. 2015-015369, filed Jan. 29, 2015 is expressly incorporated by reference herein.

## Claims

1. A resonator element comprising:
a quartz crystal substrate in which an X axis of an orthogonal coordinate system having the X axis serving as an electric axis, a Y axis serving as a mechanical axis, and a Z axis serving as an optical axis, which are crystallographic axes of quartz crystal, is set as a rotation axis, an axis inclined from the Z axis so that a +Z side is rotated in a −Y direction of the Y axis is set as a Z′ axis, an axis inclined from the Y axis so that a +Y side is rotated in a +Z direction of the Z axis is set as a Y′ axis, a plane including the X and Z′ axes is set as a main plane, and the direction oriented along the Y′ axis is set as a thickness direction,
wherein the quartz crystal substrate includes
a first region which includes a first portion and a second portion having a thickness thinner than the first portion and in which thickness shear vibration is generated, and
a second region which has a thickness thinner than the first region,

wherein in a plan view, the second portion includes an outer frame in two edges present in opposite regions to regions facing the first portion, and a contour of the outer frame is bent more gently than a contour of an edge of the first portion, and
wherein when R is a length of the outer frame along the X axis, λ is a wavelength of flexural vibration of the quartz crystal substrate, and R/(λ/2)=k, a relation of “0.1<k<1.4” is satisfied.

2. The resonator element according to claim 1,
wherein a relation of 0.3≦k≦1.1 is satisfied.

3. The resonator element according to claim 1,
wherein a relation of 0.5≦k≦1.05 is satisfied.

4. The resonator element according to claim 1,
wherein in the plan view, the contour of the outer frame is one of a curved line, a straight line, and a line formed by connecting a plurality of straight lines.

5. The resonator element according to claim 2,
wherein in the plan view, the contour of the outer frame is one of a curved line, a straight line, and a line formed by connecting a plurality of straight lines.

6. The resonator element according to claim 3,
wherein in the plan view, the contour of the outer frame is one of a curved line, a straight line, and a line formed by connecting a plurality of straight lines.

7. The resonator element according to claim 1,
wherein in the plan view, the contour of the edge of the first portion is two straight lines meeting at right angles.

8. The resonator element according to claim 1,
wherein the first region includes a projection portion projecting from the second region in a +Y′ direction of the Y′ axis,
wherein a side surface of the projection portion intersecting the Z′ axis is an inclined surface or a vertical surface to a surface including the X axis and the Z′ axis, and
wherein when Sz is a length of the side surface along the Z′ axis and Mz is a length of the first region along the Z′ axis in the plan view, a relation of “0≦Sz/Mz≦0.05 is satisfied.

9. The resonator element according to claim 4,
wherein the first region includes a projection portion projecting from the second region in a +Y′ direction of the Y′ axis,
wherein a side surface of the projection portion intersecting the Z′ axis is an inclined surface or a vertical surface to a surface including the X axis and the Z′ axis, and
wherein when Sz is a length of the side surface along the Z′ axis and Mz is a length of the first region along the Z′ axis in the plan view, a relation of “0≦Sz/Mz≦0.05” is satisfied.

10. The resonator element according to claim 1, further comprising:
excitation electrodes that are formed in the first and second regions.

11. The resonator element according to claim 4, further comprising:
excitation electrodes that are formed in the first and second regions.

12. A resonator comprising:
the resonator element according to claim 1; and
a package in which the resonator element is accommodated.

13. A resonator comprising:
the resonator element according to claim 4; and
a package in which the resonator element is accommodated.

14. A resonator device comprising:
the resonator element according to claim 1; and
an electronic element.

15. A resonator device comprising:
the resonator element according to claim 10; and
an electronic element.

16. The resonator device according to claim 14,
wherein the electronic element is a thermosensitive element.

17. An oscillator comprising:
the resonator element according to claim 1; and
an oscillation circuit that is electrically connected to the resonator element.

18. An oscillator comprising:
the resonator element according to claim 10; and
an oscillation circuit that is electrically connected to the resonator element.

19. An electronic apparatus comprising:
the resonator element according to claim 1.

20. A moving object comprising:
the resonator element according to claim 1.