Resonator element, resonator, resonator device, oscillator, electronic apparatus, and moving object
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.
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 .