Piezoelectric vibration element

Abstract

A piezoelectric vibration element (10) is provided with: a piezoelectric sheet (11) having a first main surface (11A) and a second main surface (11B) facing the first main surface (11A); a first excitation electrode (14a) provided on the first main surface (11A); and a second excitation electrode (14b) provided on the second main surface (11B), the area of the second excitation electrode (14b) being larger than the area of the first excitation electrode (14a) in a plan view in the facing direction in which the first main surface (11A) and the second main surface (11B) face each other, and a part of the second excitation electrode (14b) overlapping the entire first excitation electrode (14a), and the area of the second excitation electrode (14b) being larger than the area of the first excitation electrode (14a) in a plan view in the facing direction in which the first main surface (11A) and the second main surface (11B) face each other. The thickness (Te2) of the second excitation electrode (14b) in the facing direction is larger than the thickness (Te) of the first excitation electrode (14a) in the facing direction.

Description

Technical Field

[0001] The present invention relates to a piezoelectric vibration element. Background Art

[0002] Piezoelectric vibration elements are used in various electronic devices such as mobile communication terminals, communication base stations, and home appliances for timekeeping devices, sensors, or oscillators. The piezoelectric vibration element includes a piezoelectric sheet having a pair of main surfaces and a pair of excitation electrodes provided on the pair of main surfaces of the piezoelectric sheet.

[0003] For example, patent document 1 discloses a vibration element, including: a substrate, which vibrates through thickness shear vibration and includes a first main surface and a second main surface in a front-back relationship; a first excitation electrode, which is arranged on the first main surface; and a second excitation electrode, which is arranged on the second main surface and is larger than the first excitation electrode when viewed from above, and the first excitation electrode is configured to be housed within the outer edge of the second excitation electrode when viewed from above.

[0004] Patent Document 1: Japanese Patent Application Publication No. 2014-154994

[0005] However, as electronic devices become more sophisticated, piezoelectric vibration elements having a high electromechanical coupling coefficient are required. Summary of the invention

[0006] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a piezoelectric vibration element capable of improving the electromechanical coupling coefficient.

[0007] A piezoelectric vibration element involved in one embodiment of the present invention comprises: a piezoelectric sheet having a first principal surface and a second principal surface opposite to the first principal surface; a first excitation electrode arranged on the first principal surface; and a second excitation electrode arranged on the second principal surface, wherein, when viewed from above in an opposing direction in which the first principal surface and the second principal surface are opposite to each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a portion of the second excitation electrode overlaps the entire first excitation electrode, and a thickness of the second excitation electrode along the opposing direction is larger than a thickness of the first excitation electrode along the opposing direction.

[0008] A piezoelectric vibration element according to another embodiment of the present invention comprises: a piezoelectric sheet having a first principal surface and a second principal surface opposite to the first principal surface; a first excitation electrode arranged on the first principal surface; a second excitation electrode arranged on the second principal surface; and an insulating film stacked on the second excitation electrode, wherein, when viewed from above in an opposing direction in which the first principal surface and the second principal surface are opposite to each other, an area of ​​a stack formed by the second excitation electrode and the insulating film is larger than an area of ​​the first excitation electrode, and a portion of the stack overlaps with the entire first excitation electrode, and a sum of a thickness of the second excitation electrode and a thickness of the insulating film along the opposing direction is larger than a thickness of the first excitation electrode along the opposing direction.

[0009] Effects of the Invention

[0010] According to the present invention, it is possible to provide a piezoelectric vibration element capable of improving the electromechanical coupling coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is an exploded perspective view of the crystal oscillator according to the first embodiment.

[0012] Figure 2 It is a top view of the vibration part concerning the first embodiment.

[0013] Figure 3 It is a cross-sectional view of the vibration portion according to the first embodiment.

[0014] Figure 4 It is a graph showing the simulation results based on the first embodiment.

[0015] Figure 5 This is a cross-sectional view when the first excitation electrode is positionally misaligned.

[0016] Figure 6 It is a graph showing the simulation results based on the first embodiment.

[0017] Figure 7 It is a graph showing the simulation results based on the first embodiment.

[0018] Figure 8 It is a graph showing the simulation results based on the first embodiment.

[0019] Fig. 9 It is a graph showing the simulation results based on the first embodiment.

[0020] Fig.10 It is a graph showing the simulation results based on the first embodiment.

[0021] Fig.11 It is a graph showing the simulation results based on the first embodiment.

[0022] Fig.12 It is a graph showing the simulation results based on the first embodiment.

[0023] Fig.13 It is a graph showing the simulation results based on the first embodiment.

[0024] Fig.14 It is a graph showing the simulation results based on the first embodiment.

[0025] Fig.15 It is a graph showing the simulation results based on the first embodiment.

[0026] Fig.16 It is a graph showing the simulation results based on the first embodiment.

[0027] Fig.17 It is a graph showing the simulation results based on the first embodiment.

[0028] Fig.18 It is a plan view of a vibration portion according to the second embodiment.

[0029] Fig.19 It is a cross-sectional view of a vibration portion according to the second embodiment.

[0030] Fig. 20 This is a graph showing simulation results based on the second embodiment.

[0031] Fig.21 This is a graph showing simulation results based on the second embodiment.

[0032] Fig. 22 This is a graph showing simulation results based on the second embodiment.

[0033] Fig.23 This is a graph showing simulation results based on the second embodiment.

[0034] Fig.24 This is a graph showing simulation results based on the second embodiment.

[0035] Fig.25 It is a graph showing the simulation results based on the first embodiment.

[0036] Fig.26 It is a perspective view showing the structure of a vibration unit according to the third embodiment.

[0037] Fig. 27 It is a diagram showing the vibration distribution of the vibration part according to the third embodiment.

[0038] Fig.28 This is a graph showing simulation results based on the third embodiment.

[0039] Fig.29 This is a graph showing simulation results based on the third embodiment.

[0040] Fig.30 It is a perspective view showing the structure of a vibration unit according to a fourth embodiment.

[0041] Fig.31 It is a diagram showing the vibration distribution of the vibration part according to the fourth embodiment.

[0042] Fig.32 It is a cross-sectional view of a vibration portion according to a fifth embodiment.

[0043] Fig.33 It is a cross-sectional view of a vibration portion according to a sixth embodiment.

[0044] Fig.34 It is a cross-sectional view of a vibration portion according to a seventh embodiment.

[0045] Fig.35 It is a cross-sectional view of a vibration portion according to the eighth embodiment. DETAILED DESCRIPTION

[0046] The following is an explanation of the embodiments of the present invention. In the following drawings, the same or similar components are represented by the same or similar reference numerals. The drawings are illustrative, and the size and shape of each part are schematic, and the technical scope of the present invention should not be interpreted as being limited to the embodiments.

[0047] In each of the drawings, for convenience, an orthogonal coordinate system consisting of an X-axis, a Y'axis, and a Z'axis is marked to make the relationship between the drawings clear and to help understand the positional relationship of the components. The X-axis, the Y'axis, and the Z'axis correspond to each other in each of the drawings. The X-axis, the Y'axis, and the Z'axis correspond to the crystal axes (Crystallographic Axes) of the crystal sheet 11 described later. The X-axis is equivalent to the electrical axis (polar axis) of the crystal, the Y-axis is equivalent to the mechanical axis of the crystal, and the Z-axis is equivalent to the optical axis of the crystal. The Y'axis and the Z'axis are the axes after the Y-axis and the Z-axis are rotated counterclockwise about the X-axis by θ degrees when viewed from the positive direction of the X-axis.

[0048] In the following description, the direction parallel to the X-axis is referred to as the "X-axis direction", the direction parallel to the Y'-axis is referred to as the "Y'-axis direction", and the direction parallel to the Z'-axis is referred to as the "Z'-axis direction". In addition, the tip direction of the arrows of the X-axis, Y'-axis, and Z'-axis is referred to as "positive" or "+(positive)", and the direction opposite to the arrow is referred to as "negative" or "-(negative)". In addition, for convenience, the +Y'-axis direction is described as the upward direction and the -Y'-axis direction is described as the downward direction, but the upper and lower directions of the crystal resonator element 10 and the crystal resonator 1 are not limited. In addition, the plane defined by the X-axis and the Z'-axis is referred to as the Z'X plane, and the same applies to the planes defined by other axes.

[0049] <First embodiment>

[0050] First, refer to Figures 1 to 3 , the structure of the crystal oscillator according to the first embodiment is described. Figure 1 It is an exploded perspective view of the crystal oscillator according to the first embodiment. Figure 2 It is a top view of the vibration part concerning the first embodiment. Figure 3is a cross-sectional view of the vibration portion according to the first embodiment. Figure 3 yes Figure 2 FIG. 1 is a cross-sectional view of the vibrating portion taken along line III-III.

[0051] The crystal oscillator 1 includes a crystal oscillator element 10, a lower cover 20, an upper cover 30, a lower joint 40, and an upper joint 50. The lower cover 20, the crystal oscillator element 10, and the upper cover 30 are arranged in this order along the Y' axis with intervals. Hereinafter, the Y' axis in which the lower cover 20, the crystal oscillator element 10, and the upper cover 30 are stacked is referred to as the "thickness direction". The Y' axis is equivalent to an example of an "opposing direction".

[0052] The crystal oscillator 1 is used as a component of, for example, a temperature compensated crystal oscillator (TCXO: Temperature Compensated Crystal Oscillator), a voltage controlled crystal oscillator (VCXO: Voltage Controlled Crystal Oscillator), or an oven controlled crystal oscillator (OCXO: Oven Controlled Crystal Oscillator).

[0053] The crystal vibrating element 10 is an electromechanical energy conversion element that converts electrical energy and mechanical energy into each other through the piezoelectric effect. Figure 1 As shown, the crystal resonator element 10 includes a vibrating portion 110 , a holding portion 120 , and a supporting arm 130 .

[0054] The vibration part 110 is excited at a predetermined frequency based on the applied AC voltage. The vibration part 110 is maintained to be able to vibrate in the vibration space provided between the lower cover 20 and the upper cover 30. The main vibration of the vibration part 110 is the thickness shear vibration mode. Figure 2 As shown, the shape of the vibration part 110 when looking down at the XZ' plane (hereinafter simply referred to as "top view") (hereinafter referred to as "top view shape") is a rectangle having a pair of short sides 111, 112 and a pair of long sides 113, 114. The pair of short sides 111, 112 extend along the Z' axis and face each other in the X axis. The pair of long sides 113, 114 extend along the X axis and face each other outward in the Z' axis.

[0055] In addition, the main vibration of the vibration part is not limited to the thickness shear vibration mode, for example, it can also be a thickness longitudinal vibration mode, an extension vibration mode, a length vibration mode or a bending vibration mode. In addition, the top view shape of the vibration part is not limited to a rectangle, for example, it can also be a square, a polygon, a circle, an ellipse or a combination of these shapes.

[0056] The holding portion 120 is a portion for holding the vibration portion 110. The holding portion 120 forms a vibration space of the vibration portion 110 together with the lower cover 20, the upper cover 30, the lower joint portion 40, and the upper joint portion 50. In a plan view, the holding portion 120 is provided in a frame shape, and surrounds the vibration portion 110 at a distance from the vibration portion 110. The holding portion 120 includes frame portions 121A, 121B, 121C, and 121D.

[0057] The frame portions 121A, 121B, 121C, and 121D are each a part of a substantially rectangular frame body surrounding the vibration portion 110. Figure 1 as well as Figure 2 As shown, the frame portion 121A is provided to be spaced apart from the short side 111 of the vibration portion 110 in the X-axis direction and to extend parallel to the short side 111 in the Z'-axis direction. The frame portion 121B is provided to be spaced apart from the short side 112 of the vibration portion 110 in the X-axis direction and to extend parallel to the short side 112 in the Z'-axis direction. The frame portion 121C is provided to be spaced apart from the long side 113 of the vibration portion 110 in the Z'-axis direction and to extend parallel to the long side 113 in the X-axis direction. The frame portion 121D is provided to be spaced apart from the long side 114 of the vibration portion 110 in the Z'-axis direction and to extend parallel to the long side 114 in the X-axis direction.

[0058] The two ends of the frame portion 121C are connected to one end of the frame portion 121A and one end of the frame portion 121B. The two ends of the frame portion 121D are connected to the other end of the frame portion 121A and the other end of the frame portion 121B. The frame portion 121A and the frame portion 121B are opposite to each other in the X-axis direction via the vibration portion 110. The frame portion 121C and the frame portion 121D are opposite to each other in the Z'-axis direction via the vibration portion 110.

[0059] In addition, the holding portion may be provided at least in part of the vibrating portion, and is not limited to a frame-like shape. The holding portion may be provided in a rail shape having two parallel frames, for example.

[0060] The support arm 130 supports the vibration part 110 so that the holding part 120 holds the vibration part 110. The support arm 130 connects the vibration part 110 and the holding part 120. Figure 1 as well as Figure 2 As shown, the support arm 130 connects the end portion of the vibrating portion 110 on the short side 112 side and the frame portion 121B of the holding portion 120. The support arm 130 extends along the X-axis.

[0061] The lower cover 20 is disposed opposite to the vibrating portion 110, the holding portion 120 and the supporting arm 130 of the crystal vibrating element 10 in the Y′-axis direction with a gap therebetween. The lower cover 20 is provided in a flat plate shape. Figure 1As shown, in a top view, the lower cover 20 has a pair of long sides extending along the X-axis direction and facing each other in the Z'-axis direction and a pair of short sides extending along the Z'-axis direction and facing each other in the Z-axis direction. In addition, the pair of long sides and the pair of short sides of the lower cover 20 are connected by sides inclined relative to the pair of long sides and the pair of short sides. In other words, cutouts are formed at the four corners of the lower cover 20 in a top view.

[0062] The upper cover 30 is disposed opposite to the lower cover 20 and is spaced apart from the vibration part 110, the holding part 120 and the support arm 130 of the crystal vibration element 10 in the Y'-axis direction. The upper cover 30 is provided in a flat plate shape. Figure 1 As shown, in a plan view, the upper cover 30 has a pair of long sides extending along the X-axis and facing each other in the Z'-axis direction, and a pair of short sides extending along the Z'-axis and facing each other in the Z-axis direction. The upper cover 30 is rectangular in a plan view.

[0063] The lower bonding portion 40 and the upper bonding portion 50 are provided in a frame shape along the holding portion 120 of the crystal vibrating element 10. The lower bonding portion 40 bonds the holding portion 120 of the crystal vibrating element 10 to the end of the lower cover 20. The upper bonding portion 50 bonds the holding portion 120 of the crystal vibrating element 10 to the end of the upper cover 30. The lower bonding portion 40 and the upper bonding portion 50 are provided by an organic adhesive including, for example, epoxy, vinyl, acrylic, polyurethane or silicone resin.

[0064] The material of the lower joint and the upper joint is not limited to an organic adhesive, and may be provided by an inorganic adhesive such as a silicon-based adhesive including water glass or a calcium-based adhesive including cement. The material of the lower joint and the upper joint may also be a low-melting-point glass (e.g., lead borate-based, tin phosphate-based, etc.). The material of the lower joint and the upper joint may also be gold (Au), tin (Sn), copper (Cu), titanium (Ti), aluminum (Al), germanium (Ge), silicon (Si), or a eutectic alloy including at least one of these materials.

[0065] Next, the detailed structures of the crystal resonator element 10 , the lower cover 20 , and the upper cover 30 will be described.

[0066] The crystal resonator element 10 includes a crystal piece 11 , a first excitation electrode 14 a , a second excitation electrode 14 b , a first extraction electrode 15 a , a second extraction electrode 15 b , a first connection electrode 16 a , and a second connection electrode 16 b .

[0067] The crystal piece 11 is a type of piezoelectric piece composed of a piezoelectric body that vibrates when a voltage is applied. The crystal piece 11 is continuously provided over the vibration part 110, the holding part 120, and the support arm 130. In the XZ' plane direction, the crystal piece 11 extends over substantially the entire area of ​​each of the vibration part 110, the holding part 120, and the support arm 130. The crystal piece 11 is a thin sheet of crystal crystal with the XZ' plane as the main surface.

[0068] The crystal plate 11 is, for example, an AT-cut crystal plate. That is, the counterclockwise rotation angle θ of the Z' axis and the Y' axis from the Z axis and the Y axis when viewed from the positive direction of the X axis is 35 degrees 15 minutes ± 1 minute 30 seconds. The crystal resonator element 10 using the AT-cut crystal plate 11 has high frequency stability over a wide temperature range.

[0069] In addition, the cutting angle of the crystal piece is not limited to the above. The rotation angle of the Y' axis and the Z' axis in the AT-cut crystal piece 11 can also be tilted from 35 degrees and 15 minutes to a range of more than -5 degrees or less than +15 degrees. In addition, the cutting angle of the crystal piece can also be applied to different cutting methods other than AT cutting, such as BT cutting, GT cutting, SC cutting, etc.

[0070] The top view shape of the crystal piece 11 in the vibration part 110 is a rectangle having a long side along the X-axis and a short side along the Z′-axis. Figure 3 As shown, in the vibration portion 110, the crystal piece 11 has an upper surface 11A provided on the upper cover 30 side and a lower surface 11B provided on the lower cover 20 side. The upper surface 11A and the lower surface 11B are an example of a pair of principal surfaces facing each other in the Y′ axis direction of the crystal piece 11.

[0071] In addition, the top view shape of the vibration part of the crystal piece is not limited to the above. For example, the top view shape of the vibration part of the crystal piece may also be a rectangle having long sides extending along the Z' axis and short sides extending along the X axis, or a rectangle having short sides extending along the Z' axis and long sides extending along the X axis. The top view shape of the vibration part of the crystal piece may also be a polygon, a circle, an ellipse, or a combination thereof. In addition, the vibration part of the crystal piece is not limited to a flat plate. The vibration part of the crystal piece may also be a table-type structure or an inverted table-type structure having a concave and convex structure on at least one of the upper surface and the lower surface. The vibration part of the crystal piece may also be a convex structure in which the thickness change continuously changes, or it may be an inclined structure in which the thickness change discontinuously changes.

[0072] The first excitation electrode 14a and the second excitation electrode 14b apply an AC voltage to the crystal piece 11 of the vibration part 110 to excite the vibration part 110. Figure 3As shown, the first excitation electrode 14a is provided on the upper surface 11A of the crystal piece 11 in the vibration part 110, and the second excitation electrode 14b is provided on the lower surface 11b of the crystal piece 11 in the vibration part 110. The first excitation electrode 14a and the second excitation electrode 14b are opposite to each other in the Y' axis direction with the crystal piece 11 interposed therebetween.

[0073] like Figure 2 As shown, in a plan view, the area of ​​the second excitation electrode 14b is larger than the area of ​​the first excitation electrode 14a, and a portion of the second excitation electrode 14b overlaps the entire first excitation electrode 14a. The first excitation electrode 14a and the second excitation electrode 14b are provided in the central portion of the vibration portion 110, and the center of the first excitation electrode 14a overlaps the center of the second excitation electrode 14b.

[0074] In addition, the positions of the first excitation electrode and the second excitation electrode are not limited to the central part of the vibration part. When viewed from above, the first excitation electrode and the second excitation electrode may be arranged outward from the central part of the vibration part. In addition, the positions of the centers of the first excitation electrode and the second excitation electrode are not limited to the positions where they overlap each other. When viewed from above, the center of the first excitation electrode may be away from the center of the second excitation electrode.

[0075] The top view shape of the first excitation electrode 14a is a rectangle having short sides extending in the Z' axis direction and long sides extending in the X axis direction. The top view shape of the second excitation electrode 14b is the same as the top view shape of the first excitation electrode 14a. In other words, the first excitation electrode 14a and the second excitation electrode 14b have short sides parallel to the short sides of the vibration part 110, and have long sides parallel to the long sides of the vibration part 110. In addition, the first excitation electrode 14a and the second excitation electrode 14b have thickness in the Y' axis direction, and the thickness of the second excitation electrode 14b is greater than the thickness of the first excitation electrode 14a.

[0076] In addition, the top view shape of the first excitation electrode and the second excitation electrode is not limited to the above. The top view shape of the first excitation electrode and the second excitation electrode may also be a rectangle having a short side extending along the X-axis direction. The top view shape of the first excitation electrode and the second excitation electrode may also be a square, a polygon, a circle, an ellipse, or a combination thereof. In addition, the top view shape of the first excitation electrode is not limited to being the same as the top view shape of the second excitation electrode, and the top view shapes of the first excitation electrode and the second excitation electrode may be different from each other.

[0077] The first extraction electrode 15a electrically connects the first excitation electrode 14a and the first connection electrode 16a. Figure 1As shown, the first extraction electrode 15a drawn out from the first excitation electrode 14a extends over the upper surface of the vibrating portion 110, the supporting arm 130, and the frame portion 121B of the holding portion 120, and the side surface of the holding portion 120, and is electrically connected to the first connection electrode 16a provided on the lower surface of the holding portion 120. The second extraction electrode 15b drawn out from the second excitation electrode 14b extends over the lower surface, side surface, and upper surface of the vibrating portion 110, the supporting arm 130, the upper surface of the frame portions 121B and 121D of the holding portion 120, and the side surface of the holding portion 120, and is electrically connected to the second connection electrode 16b provided on the lower surface of the holding portion 120.

[0078] The first connection electrode 16a electrically connects the first excitation electrode 14a to an external terminal, and the second connection electrode 16b electrically connects the second excitation electrode 14b to an external terminal. Figure 1 As shown, the first connection electrode 16a is provided on the lower surface (surface on the lower cover 20 side) of the crystal piece 11 at the corner of the holding part 120 where the frame part 121B and the frame part 121C are connected. The second connection electrode 16b is provided on the lower surface of the crystal piece 11 at the corner of the holding part 120 where the frame part 121A and the frame part 121D are connected.

[0079] The first excitation electrode 14a, the first extraction electrode 15a and the first connection electrode 16a are integrally arranged. The second excitation electrode 14b, the second extraction electrode 15b and the second connection electrode 16b are the same. The electrodes of these crystal vibration elements 10 are, for example, a single-layer structure composed of an aluminum layer. The electrodes of the crystal vibration element 10 can also be a multilayer structure in which a base layer and a surface layer are stacked in sequence. For example, the base layer is a chromium (Cr) layer with good adhesion to the crystal plate 11, and the surface layer is a gold (Au) layer with good chemical stability. The electrodes of the crystal vibration element 10 can also include silver (Ag), copper (Cu), titanium (Ti), molybdenum (Mo) or aluminum-copper alloy (AlCu).

[0080] The lower cover 20 has a crystal plate 21, power terminals ST1, ST2, and dummy terminals DT1, DT2. The crystal plate 21 is a flat substrate that overlaps with the substantially entire crystal vibration element 10 when viewed from above. The crystal plate 21 is formed by crystal crystallization with the same cutting angle as the crystal plate 11 of the crystal vibration element 10. As a result, thermal stress caused by the difference in thermal expansion coefficient and the difference in the direction of thermal expansion between the crystal vibration element 10 and the lower cover 20 can be reduced. As a result, the frequency fluctuation of the crystal vibration element 10 can be suppressed. The crystal plate 21 has an upper surface 21A disposed on the side of the crystal vibration element 10 and a lower surface 21B disposed on the side opposite to the upper surface 21A. When viewed from above, the crystal plate 21 has a long side extending in the X-axis direction and a short side extending in the Z'-axis direction. In addition, when viewed from above, the side surface connecting the upper surface 21A and the lower surface 21B of the crystal plate 21 overlaps with the outer side surface of the holding portion 120 in the crystal vibration element 10. A notch is formed at the corner where the short side and the long side of the crystal piece 21 are connected. The area of ​​the crystal piece 21 when viewed from above is smaller than the area of ​​the crystal piece 31 described later when viewed from above by an amount corresponding to the notch. The shape of the side surface formed by the notch at the corner of the crystal piece 21 is, for example, a plane. Among them, the shape of the side surface formed by the notch at the corner of the crystal piece 21 is not limited to this, and may also be a curved surface as a part of a cylinder or a prism.

[0081] The power terminals ST1, ST2 and the dummy terminals DT1, DT2 are provided on the lower surface 21B of the crystal piece 21. The power terminals ST1, ST2 and the dummy terminals DT1, DT2 are equivalent to an example of the external terminals of the crystal oscillator 1. The power terminals ST1, ST2 are used to provide a driving signal (driving voltage) to the crystal oscillator 1. The power terminal ST1 is electrically connected to the first connection electrode 16a via the side electrodes provided at the notch provided at the corner of the crystal piece 21 and the outer side surface of the lower joint 40. The power terminal ST2 is electrically connected to the second connection electrode 16b via the side electrodes provided at the notch provided at the corner of the crystal piece 21 and the outer side surface of the lower joint 40. The dummy terminals DT1, DT2 are used to achieve a balance of electrical characteristics such as electrostatic capacitance and a balance of mechanical strength between the power terminals ST1, ST2. The dummy terminals DT1, DT2 are so-called floating electrodes that are not electrically connected to the crystal oscillator element 10.

[0082] Furthermore, at least one of the dummy terminals DT1 and DT2 may be a ground electrode for electrically grounding a portion of the crystal oscillator 1 .

[0083] The upper cover 30 has a crystal plate 31. The crystal plate 31 is a flat plate-shaped substrate that overlaps with the substantially entire crystal vibration element 10 when viewed from above. The crystal plate 31 is formed by crystal crystallization with the same cutting angle as the crystal plate 11 of the crystal vibration element 10. As a result, thermal stress caused by the difference in thermal expansion coefficient and the difference in the direction of thermal expansion between the crystal vibration element 10 and the upper cover 30 can be reduced. As a result, the frequency fluctuation of the crystal vibration element 10 can be suppressed. The crystal plate 31 has a lower surface 31B disposed on the side of the crystal vibration element 10 and an upper surface 31A disposed on the side opposite to the lower surface 31B. When viewed from above, the crystal plate 31 is a rectangle having a long side extending along the X-axis and a short side extending along the Z'-axis. In addition, when viewed from above, the side surface connecting the upper surface 31A and the lower surface 31B of the crystal plate 31 overlaps with the outer side surface of the holding portion 120 in the crystal vibration element 10.

[0084] In addition, the cutting angle of the crystal plate of the lower cover and the upper cover is not particularly limited, and may be different from the cutting angle of the crystal plate of the crystal vibrating element. In addition, the lower cover and the upper cover may also have a glass substrate, a silicon substrate, a ceramic substrate, or a metal substrate instead of the crystal plate.

[0085] Next, refer to Figure 2 as well as Figure 3 , the detailed structure of the vibration unit 110 is described.

[0086] The first excitation electrode 14a has outer edge portions 71, 72, 73, and 74. The outer edge portion 71 is an edge portion of one side extending along the Z' axis on the negative side of the X axis in a plan view among the four edge portions of the first excitation electrode 14a. The outer edge portion 72 is an edge portion of one side extending along the Z' axis on the positive side of the X axis, the outer edge portion 73 is an edge portion of one side extending along the X axis on the positive side of the Z' axis, and the outer edge portion 74 is an edge portion of one side extending along the X axis on the negative side of the Z' axis. In other words, with respect to the center portion of the first excitation electrode 14a in a plan view, the outer edge portion 71 is located on the frame portion 121A side, the outer edge portion 72 is located on the frame portion 121B side, the outer edge portion 73 is located on the frame portion 121C side, and the outer edge portion 74 is located on the frame portion 121D side.

[0087] The second excitation electrode 14b has outer edge portions 81, 82, 83, and 84. The outer edge portion 81 is an edge portion of one side extending along the Z' axis on the negative side of the X axis in a plan view among the edge portions of the four sides of the second excitation electrode 14b. The outer edge portion 82 is an edge portion of one side extending along the Z' axis on the positive side of the X axis, the outer edge portion 83 is an edge portion of one side extending along the X axis on the positive side of the Z' axis, and the outer edge portion 84 is an edge portion of one side extending along the X axis on the negative side of the Z' axis. In other words, with respect to the center portion of the second excitation electrode 14b in a plan view, the outer edge portion 81 is located on the frame portion 121A side, the outer edge portion 82 is located on the frame portion 121B side, the outer edge portion 83 is located on the frame portion 121C side, and the outer edge portion 84 is located on the frame portion 121D side.

[0088] like Figure 2 As shown, in a plan view, the outer edges 71, 72, 73, and 74 of the first excitation electrode 14a are all located inside the outer edges 81, 82, 83, and 84 of the second excitation electrode 14b. The outer edge 81 is adjacent to the outer edge 71 of the outer edges 71, 72, 73, and 74, the outer edge 82 is adjacent to the outer edge 72 of the outer edges 71, 72, 73, and 74, the outer edge 83 is adjacent to the outer edge 73 of the outer edges 71, 72, 73, and 74, and the outer edge 84 is adjacent to the outer edge 74 of the outer edges 71, 72, 73, and 74. In a plan view, the outer edges 71 and 81 are arranged in parallel, the outer edges 72 and 82 are arranged in parallel, the outer edges 73 and 83 are arranged in parallel, and the outer edges 74 and 84 are arranged in parallel.

[0089] like Figure 2 As shown, in a plan view, the dimension of the vibration part 110 along the X-axis direction is set to length Lq, and the dimension of the vibration part 110 along the Z'-axis direction is set to length Wq. The dimension of the first excitation electrode 14a along the X-axis direction is set to length Le, and the dimension of the first excitation electrode 14a along the Z'-axis direction is set to length We. The dimension of the second excitation electrode 14b along the X-axis direction is set to length Le2, and the dimension of the second excitation electrode 14b along the Z'-axis direction is set to length We2.

[0090] The length Lq is determined, for example, as the distance along the X-axis direction between the short side 111 and the short side 112 at a specified position. The specified position is, for example, on a straight line passing through the center of the vibration part 110 and extending along the X-axis direction when viewed from above. The length Lq can also be determined as the average value or maximum value of the distance along the X-axis direction between the short side 111 and the short side 112. The length Wq is determined, for example, as the distance along the Z'-axis direction between the long side 113 and the long side 114 at a specified position. The specified position is, for example, on a straight line passing through the center of the vibration part 110 and extending along the Z'-axis direction when viewed from above. The length Wq can also be determined as the average value or maximum value of the distance along the Z'-axis direction between the long side 113 and the long side 114.

[0091] Similarly, the length Le is determined as the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 72 at a predetermined position (for example, on a straight line passing through the center of the first excitation electrode 14a and extending along the X-axis direction, or the average value or the maximum value of the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 72. The length We is determined as the distance along the Z'-axis direction between the outer edge portion 73 and the outer edge portion 74 at a predetermined position (for example, on a straight line passing through the center of the first excitation electrode 14a and extending along the Z'-axis direction, or the average value or the maximum value of the distance along the Z'-axis direction between the outer edge portion 73 and the outer edge portion 74. The length Le2 is determined as the distance along the X-axis direction between the outer edge portion 81 and the outer edge portion 82 at a predetermined position (for example, on a straight line passing through the center of the second excitation electrode 14b and extending along the X-axis direction, or the average value or the maximum value of the distance along the X-axis direction between the outer edge portion 81 and the outer edge portion 82. The length We2 is determined as the distance along the Z' axis between the outer edge portions 83 and 84 at a predetermined position (for example, on a straight line passing through the center of the second excitation electrode 14b and extending along the Z' axis), or the average or maximum value of the distances along the Z' axis between the outer edge portions 83 and 84.

[0092] In addition, in the case of comparing the length Le and the length Le2, the length Le and the length Le2 are determined by the same determination method. That is, if the length Le is determined as the distance between the outer edge portion 71 and the outer edge portion 72 at a specified position along the X-axis direction, the length Le2 is determined as the distance between the outer edge portion 81 and the outer edge portion 82 at a specified position along the X-axis direction. If the length Le is determined as the average value of the distance between the outer edge portion 71 and the outer edge portion 72 along the X-axis direction, the length Le2 is determined as the average value of the distance between the outer edge portion 81 and the outer edge portion 82 along the X-axis direction. If the length Le is determined as the maximum value of the distance between the outer edge portion 71 and the outer edge portion 72 along the X-axis direction, the length Le2 is determined as the maximum value of the distance between the outer edge portion 81 and the outer edge portion 82 along the X-axis direction. In the case of comparing other lengths and thicknesses, the determination method is also unified in the same manner.

[0093] The top view shape of the vibration part 110 is a rectangle with the X-axis direction as the long side direction, so the length Lq is greater than the length Wq (Wq<Lq). The top view shapes of the first excitation electrode 14a and the second excitation electrode 14b are also the same rectangle, so the length Le is greater than the length We (We<Le), and the length Le2 is greater than the length We2 (We2<Le2). The outer edges 81, 82, 83, and 84 of the second excitation electrode 14b are all located inside the short sides 111, 112 and the long sides 113, 114 of the vibration part 110, so the length Lq is greater than the length Le2 (Le2<Lq), and the length Wq is greater than the length We2 (We2<Wq). The outer edges 71, 72, 73, and 74 of the first excitation electrode 14a are all located inside the outer edges 81, 82, 83, and 84 of the second excitation electrode 14b, so the length Le2 is greater than the length Le (Le<Le2), and the length We2 is greater than the length We (We<We2). In short, the relationship of Le<Le2<Lq and We<We2<Wq holds.

[0094] like Figure 2 As shown, in the distance between the outer edge portions of the first excitation electrode 14a and the second excitation electrode 14b in a plan view, the distance between the outer edge portions 71 and 81 along the X-axis direction is set to length dLe1, the distance between the outer edge portions 72 and 82 along the X-axis direction is set to length dLe2, the distance between the outer edge portions 73 and 83 along the Z'-axis direction is set to length dWe1, and the distance between the outer edge portions 74 and 84 along the Z'-axis direction is set to length dWe2. The sum of the length dLe1 and the length dLe2 is set to dLe (dLe=dLe1+dLe2), and the sum of the length dWe1 and the length dWe2 is set to dWe (dWe=dWe1+dWe2).

[0095] The length dLe1 is determined, for example, as the distance between the outer edge portion 71 and the outer edge portion 81 at a predetermined position along the X-axis direction. The predetermined position is, for example, on a straight line extending along the X-axis direction through the center of the first excitation electrode 14a or the second excitation electrode 14b when viewed from above. The length dLe1 may also be determined as the average value or maximum value of the distance between the outer edge portion 71 and the outer edge portion 81 along the X-axis direction. The length dWe1 is determined, for example, as the distance between the outer edge portion 73 and the outer edge portion 83 at a predetermined position along the Z'-axis direction. The predetermined position is, for example, on a straight line extending along the Z'-axis direction through the center of the first excitation electrode 14a or the second excitation electrode 14b when viewed from above. The length dWe1 may also be determined as the average value or maximum value of the distance between the outer edge portion 73 and the outer edge portion 83 along the Z'-axis direction.

[0096] Similarly, the length dLe2 is determined as the distance along the X-axis direction between the outer edge portion 72 and the outer edge portion 82 at a predetermined position (for example, on a straight line passing through the center of the first excitation electrode 14a or the second excitation electrode 14b and extending along the X-axis direction), or the average value or maximum value of the distance along the X-axis direction between the outer edge portion 72 and the outer edge portion 82. The length dWe2 is determined as the distance along the Z'-axis direction between the outer edge portion 74 and the outer edge portion 84 at a predetermined position (for example, on a straight line passing through the center of the first excitation electrode 14a or the second excitation electrode 14b and extending along the Z'-axis direction), or the average value or maximum value of the distance along the Z'-axis direction between the outer edge portion 74 and the outer edge portion 84.

[0097] The length dLe is determined as the difference between the length Le and the length Le2. In other words, the length Le2 and Le are calculated using the formula dLe=Le2-Le, but it can also be calculated based on the lengths dLe1 and dLe2 using the formula dLe=dLe1+dLe2. The length dWe is determined as the difference between the length We and the length We2. In other words, the length We2 and We are calculated using the formula dWe=We2-We, but it can also be calculated based on the lengths dWe1 and dWe2 using the formula dWe=dWe1+dWe2.

[0098] Since the centers of the first excitation electrode 14a and the second excitation electrode 14b overlap, the length dLe1 is equal to the length dLe2, which is half the difference between the length Le2 and the length Le. In other words, the relationship 0<dLe1=dLe2=dLe / 2=(Le2-Le) / 2 is satisfied. Similarly, the length dWe1 is equal to the length dWe2, which is half the difference between the length We2 and the length We. In other words, the relationship 0<dWe1=dWe2=dWe / 2=(We2-We) / 2 is satisfied.

[0099] In addition, the size relationship between the length dLe1 and the length dLe2 is not limited to the above, and may also satisfy the relationship of 0<dLe1<dLe2 or 0<dLe2<dLe1. The size relationship between the length dWe1 and the length dWe2 is also not limited to the above, and may also satisfy the relationship of 0<dWe1<dWe2 or 0<dWe2<dWe1. In addition, if at least one of the lengths dLe1, dLe2, dWe1, and dWe2 is greater than 0, the others may also be 0. For example, the relationship of 0=dLe1=dLe2, 0<dWe1, and 0<dWe2 may also be satisfied, or the relationship of 0<dLe1, 0<dLe2, and 0=dWe1=dWe2 may also be satisfied. In addition, for example, the relationship of 0=dL2, 0<dLe1, 0<dWe1, and 0<dWe2 may also be satisfied. Among them, it is preferred that all the lengths dLe1, dLe2, dWe1, and dWe2 are greater than 0. In other words, it is preferable that the relationship of 0<dLe1, 0<dLe2, 0<dWe1, 0<dWe2 holds.

[0100] like Figure 3 As shown, the thickness of the crystal piece 11 in the vibration portion 110 is denoted as Tq, the thickness of the first excitation electrode 14 a is denoted as Te, and the thickness of the second excitation electrode 14 b is denoted as Te2.

[0101] The thickness Tq is determined, for example, as the distance between the upper surface 11A and the lower surface 11B along the Y' axis at a predetermined position. The predetermined position is, for example, on a straight line that passes through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed and extends along the Y' axis. The thickness Tq may also be determined as the average value or maximum value of the distance between the upper surface 11A and the lower surface 11B along the Y' axis in the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed.

[0102] Similarly, the thickness Te is determined as the average value or maximum value of the distance along the Y' axis between the upper surface and the lower surface of the first excitation electrode 14a at a predetermined position (for example, on a straight line extending along the Y' axis through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed to each other) or the distance along the Y' axis between the upper surface and the lower surface of the first excitation electrode 14a in the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed to each other. The thickness Te2 is determined as the distance along the Y' axis between the upper surface and the lower surface of the second excitation electrode 14b at a predetermined position (for example, on a straight line extending along the Y' axis through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed to each other) or the distance along the Y' axis between the upper surface and the lower surface of the second excitation electrode 14b in the region where the first excitation electrode 14a and the second excitation electrode 14b are opposed to each other.

[0103] The thickness Tq is greater than the thickness Te2, and the thickness Te2 is greater than the thickness Te. In other words, the relationship Te<Te2<Tq holds. In addition, the thickness of the crystal plate 11 is greater than the sum of the thicknesses of the first excitation electrode 14a and the second excitation electrode 14b, so the relationship Te+Te2<Tq holds.

[0104] Next, refer to Figures 4 to 17 , the simulation results based on the first embodiment are described.

[0105] Figure 4 is a graph showing simulation results based on the first embodiment. Figure 4 In the graph, the horizontal axis represents dLe or dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0106] exist Figure 4 When the horizontal axis of the graph is greater than 0, that is, Le2>Le or We2>We, the simulation conditions are as follows.

[0107] Tq=1.0μm

[0108] Te=0.05μm

[0109] Te2=0.12μm

[0110] Lq=Wq=120μm

[0111] Le=55μm,

[0112] We=50μm,

[0113] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0114] dWe=We2-We=2×dWe1=2×dWe2:variable

[0115] exist Figure 4 When the horizontal axis of the graph is below 0, that is, when Le2≤Le or We2≤We, the simulation conditions are as follows.

[0116] Tq=1.0μm

[0117] Te=0.05μm

[0118] Te2=0.12μm

[0119] Lq=Wq=120μm

[0120] Le2=55μm

[0121] We2=50μm

[0122] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0123] dWe=We2-We=2×dWe1=2×dWe2:variable

[0124] Figure 4 The plots in the graph of show the simulation results when dLe=dWe and both dLe and dWe are set as variables, the simulation results when dLe=0 (constant) and dWe is set as a variable, and the simulation results when dLe is set as a variable and dWe=0 (constant). Figure 4 The values ​​of dLe and dWe on the horizontal axis of the graph show the values ​​of the variables in each case. In other words, the values ​​of dLe and dWe on the horizontal axis show the values ​​of both dLe and dWe when dLe=dWe is a variable, the value of dWe when dLe is a constant and dWe is a variable, and the value of dLe when dLe is a variable and dWe is a constant. Hereinafter, the values ​​of the variables shown on the horizontal axis of the graph are expressed as "〔dLe, dWe〕".

[0125] In any of the cases where dLe=dWe is a variable, dLe is a variable and dWe=0 (constant), and dLe=0 (constant) and dWe is a variable, when 0<〔dLe, dWe〕, that is, when the area of ​​the thicker second excitation electrode 14b of the first excitation electrode 14a and the second excitation electrode 14b is larger than the area of ​​the thinner first excitation electrode 14a, the electromechanical coupling coefficient k increases. In the range of 0μm to 10μm, the larger the〔dLe, dWe〕, the higher the electromechanical coupling coefficient k. In the region of 10μm<〔dLe, dWe〕<25μm, the electromechanical coupling coefficient k is approximately constant even if〔dLe, dWe〕 changes. In addition, in the region of -25μm≤〔dLe, dWe〕≤0, the electromechanical coupling coefficient k when dLe=dWe is a variable, the electromechanical coupling coefficient k when dLe is a variable, and the electromechanical coupling coefficient k when dWe is a variable are approximately the same.

[0126] As shown in the plots when dLe is a variable and dWe=0 (constant), and when dLe=0 (constant) and dWe is a variable, even when one of dLe and dWe is set to 0 and the other is greater than 0, the electromechanical coupling coefficient k(%) is improved compared to the case where one of dLe and dWe is set to 0 and the other is less than 0. In addition, as shown in the plot when dLe=dWe is a variable, the electromechanical coupling coefficient k(%) when both dLe and dWe are greater than 0 is further improved compared to the electromechanical coupling coefficient k(%) when one of dLe and dWe is set to 0 and the other is greater than 0.

[0127] Figure 5 This is a cross-sectional view when the first excitation electrode is positionally misaligned. Figure 6 It is a graph showing the simulation results based on the first embodiment.

[0128] Figure 6 The diagram shows Figure 5 As shown in FIG. 1 , the electromechanical coupling coefficient k changes when the center of the first excitation electrode 14 a is displaced by Δ μm in the X-axis direction and the Z′-axis direction from the center of the second excitation electrode 14 b in a plan view. Figure 6 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). Figure 6 The size of the "position offset" in the chart is equivalent to Figure 5 The values ​​of dLe and dWe on the horizontal axis of the graph are expressed as "[dLe, dWe]".

[0129] exist Figure 5 The simulation conditions are as follows.

[0130] Tq=1.0μm

[0131] Te=0.05μm

[0132] Te2=0.12μm

[0133] Lq=Wq=120μm

[0134] Le=55μm

[0135] We=50μm

[0136] dLe=Le2-Le:variable

[0137] dWe=We2-We:variable

[0138] dLe=dWe

[0139] dLe1=dLe / 2-Δ

[0140] dLe2=dLe / 2+Δ

[0141] dWe1=dWe / 2-Δ

[0142] dWe2=dWe / 2+Δ

[0143] When dLe1=dLe / 2-Δ<0 and dWe1=dWe / 2-Δ<0, that is, when the relationship of dLe / 2<Δ and dWe / 2<Δ holds, the first excitation electrode 14a protrudes outward from the second excitation electrode 14b in a plan view. When the relationship of Δ≤dLe / 2 and Δ≤dWe / 2 holds, even if 0μm<Δ, the first excitation electrode 14a does not protrude from the second excitation electrode 14b in a plan view, and the entire first excitation electrode 14a overlaps a portion of the second excitation electrode 14b.

[0144] Figure 6 The plots in the graph represent the simulation results for Δ=0μm, 1μm, and 5μm, respectively. In the case of Δ=0μm, in the region where dLe and dWe are greater than 10μm and less than 25μm (10μm≤〔dLe, dWe〕≤25), the electromechanical coupling coefficient k is approximately constant regardless of dLe or dWe. In the case of Δ=0μm, in the region where dLe and dWe are less than 10μm and greater than 0μm (0μm≤〔dLe, dWe〕<10μm), the smaller dLe and dWe are, the lower the electromechanical coupling coefficient k is. In the case of Δ=1μm, a trend approximately the same as that of Δ=0μm is shown.

[0145] In the case of Δ=5μm, in the region where dLe and dWe are less than 10μm and equal to or greater than 0 (0μm≤〔dLe, dWe〕<10μm), the electromechanical coupling coefficient k is lower than that in the case of Δ=0μm. At this time, since Δ=5μm and 0μm≤〔dLe, dWe〕<10μm, the relationship of dLe / 2<Δ and dWe / 2<Δ holds, and the first excitation electrode 14a protrudes outward from the second excitation electrode 14b in a plan view. That is, in the case where the first excitation electrode 14a protrudes outward from the second excitation electrode 14b in a plan view, the electromechanical coupling coefficient k is lower than that in the case of Δ=0μm. On the other hand, even in the case of Δ=5μm, in the region where dLe and dWe are equal to or greater than 10μm and equal to or less than 25μm (10μm≤〔dLe, dWe〕≤25), a tendency substantially similar to that in the case of Δ=0μm is shown. At this time, since Δ=5 μm and 10 μm≤〔dLe, dWe〕≤25, the relationship of Δ≤dLe / 2 and Δ≤dWe / 2<Δ holds, and the entire first excitation electrode 14 a overlaps a portion of the second excitation electrode 14 b .

[0146] In other words, even if the center of the first excitation electrode 14a is positionally offset relative to the center of the second excitation electrode 14b, the effect of improving the electromechanical coupling coefficient k can be maintained as long as the entire first excitation electrode 14a overlaps with the second excitation electrode 14b. However, when the first excitation electrode 14a protrudes to the outside of the second excitation electrode 14b, the effect of improving the electromechanical coupling coefficient k is lost. Therefore, in order to maintain the effect of improving the electromechanical coupling coefficient k even if the center of the first excitation electrode 14a is slightly positionally offset relative to the center of the second excitation electrode 14b, it is preferable that dLe and dWe are large. Specifically, the allowable range of the positional offset of the first excitation electrode 14a relative to the second excitation electrode 14b is less than 1 / 2 of dLe and dWe. For example, when the maximum positional offset of the first excitation electrode 14a relative to the second excitation electrode 14b is assumed to be 5 μm, dLe and dWe are preferably 10 μm or more. When the maximum positional offset of the first excitation electrode 14a relative to the second excitation electrode 14b is assumed to be 2.5 μm, dLe and dWe are preferably 5 μm or more.

[0147] Figure 7 It is a graph showing the simulation results based on the first embodiment. Figure 8 is a graph showing simulation results based on the first embodiment. Figure 7 In the graph, the horizontal axis represents Te2 (μm), and the vertical axis represents the frequency change dF (ppm) based on the frequency when Te2 = 0.05 μm. Figure 8 In the graph, the horizontal axis represents Te2 (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0148] exist Figure 7 as well as Figure 8 The simulation conditions when 0 μm<dLe=dWe are as follows.

[0149] Tq=1.0μm

[0150] Te=0.05μm

[0151] Te2: Variable

[0152] Lq=Wq=120μm

[0153] Le=55μm

[0154] We=50μm

[0155] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0156] dWe=We2-We=2×dWe1=2×dWe2:variable

[0157] exist Figure 7 as well as Figure 8 The simulation conditions when dLe=dWe≤0μm are as follows.

[0158] Tq=1.0μm

[0159] Te=0.05μm

[0160] Te2: Variable

[0161] Lq=Wq=120μm

[0162] Le2=55μm

[0163] We2=50μm

[0164] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0165] dWe=We2-We=2×dWe1=2×dWe2:variable

[0166] like Figure 7 As shown, regardless of the values ​​of dLe and dWe, the larger Te2 is, the smaller dF is. In other words, the area of ​​the first excitation electrode 14a and the second excitation electrode 14b has little effect on the frequency.

[0167] like Figure 8 As shown in FIG. 1 , when dLe=dWe=0μm, within the range of 0μm<Te2<0.10μm (0<Te2 / Te<2), the smaller the Te2(μm), the lower the electromechanical coupling coefficient k(%). Within the range of 0.10μm≤Te2≤0.20μm (2≤Te2 / Te≤4), the larger the Te2(μm), the lower the electromechanical coupling coefficient k(%).

[0168] like Figure 8 As shown in the figure, when dLe<0μm and dWe<0μm, within the range of 0.05μm<Te2≤0.20μm (1<Te2 / Te≤4), the larger the Te2(μm), the lower the electromechanical coupling coefficient k(%). Within the range of 0.12μm<Te2≤0.20μm (2.4<Te2 / Te≤4), the electromechanical coupling coefficient k(%) when dLe<0μm and dWe<0μm is lower than the electromechanical coupling coefficient k(%) when dLe=dWe=0μm.

[0169] like Figure 8As shown, when 0μm<dLe and 0μm<dWe, in the range of 0.05μm<Te2≤0.15μm (1≤Te2 / Te≤3), the larger the Te2(μm), the higher the electromechanical coupling coefficient k(%). In the range of 0.15μm<Te2≤0.20μm (3≤Te2 / Te≤4), the larger the Te2(μm), the lower the electromechanical coupling coefficient k(%). In other words, when Te2 is about 0.15μm (Te2 / Te=3), the electromechanical coupling coefficient k(%) is the largest. In addition, in the range of 0.10μm≤Te2≤0.20μm (2≤Te2 / Te≤4), the change in the electromechanical coupling coefficient k relative to the change in Te2 is small, and the electromechanical coupling coefficient k is approximately constant. In the range of 0.05 μm≤Te2≤0.20 μm (1≤Te2 / Te≤4), the electromechanical coupling coefficient k(%) when 0 μm<dLe and 0 μm<dWe is higher than the electromechanical coupling coefficient k(%) when dLe=dWe=0 μm.

[0170] Therefore, when the area of ​​the thicker second excitation electrode 14b of the first excitation electrode 14a and the second excitation electrode 14b is larger than the area of ​​the thinner first excitation electrode 14a, the electromechanical coupling coefficient k(%) increases. In addition, within the range of 0.10μm≤Te2≤0.20μm (2≤Te2 / Te≤4) where the electromechanical coupling coefficient k(%) is stable, even if Te2(μm) is changed to adjust the frequency, the change of the electromechanical coupling coefficient k(%) can be suppressed.

[0171] Fig. 9 is a graph showing simulation results based on the first embodiment. Fig. 9 In the graph, the horizontal axis represents the ratio Te2 / Tq of the thickness Te2 of the second excitation electrode 14 b to the thickness Tq of the crystal piece 11 , and the vertical axis represents the electromechanical coupling coefficient k (%).

[0172] exist Fig. 9 The simulation conditions are as follows.

[0173] Tq=1.0μm

[0174] Te: 0.05

[0175] Te2: Variable

[0176] Lq=Wq=120μm

[0177] Le=55μm

[0178] We=50μm

[0179] dLe=Le2-Le=2×dLe1=2×dLe2=25μm

[0180] dWe=We2-We=2×dWe1=2×dWe2=25μm

[0181] ρ=2,699(kg / m 3 )

[0182] ρ(kg / m 3 ) is the average density of the first excitation electrode 14a and the second excitation electrode 14b. When the density of the first excitation electrode 14a is ρ1, the density of the second excitation electrode 14b is ρ2, the volume of the portion of the first excitation electrode 14a facing the second excitation electrode 14b is V1, and the volume of the portion of the second excitation electrode 14b facing the first excitation electrode 14a is V2, the following formula is used for calculation.

[0183] ρ=(ρ1×V1+ρ2×V2) / (V1+V2)

[0184] If the first excitation electrode 14a and the second excitation electrode 14b are made of the same material, the density of the material is ρ. In this simulation, since the first excitation electrode 14a and the second excitation electrode 14b are made of aluminum, ρ is set to the density of aluminum, 2.699 (kg / m3).

[0185] In the range of 0.05≤Te2 / Tq≤0.20, the electromechanical coupling coefficient k(%) is maximum near Te2 / Tq = 0.13. Here, Te2 / Tq with the maximum electromechanical coupling coefficient k(%) is defined as "optimal Te2 / Tq".

[0186] Fig.10 is a graph showing simulation results based on the first embodiment. Fig.10 In the graph, Te and ρ are plotted as variables. Fig. 9 The optimum Te2 / Tq is shown. Fig.10 In the graph, the horizontal axis represents ρ(kg / m 3 ), the vertical axis represents the optimal Te2 / Tq.

[0187] As the ratio Te / Tq of the thickness Te of the first excitation electrode 14a to the thickness Tq of the crystal piece 11 increases, the optimum Te2 / Tq increases. In addition, when Te / Tq is kept constant, as ρ(kg / m 3 ) increases, the optimal Te2 / Tq decreases. Fig.10 By fitting the graph shown, the conditional expression for maximizing the electromechanical coupling coefficient k (%) was obtained as follows.

[0188] Te2 / Tq=0.00001×ρ+b±0.01

[0189] When Te / Tq=0.02, b=0.16369. When Te / Tq=0.05, b=0.17572. When Te / Tq=0.10, b=0.19861. When Te / Tq=0.15, b=0.21293.

[0190] Fig.11 is a graph showing simulation results based on the first embodiment. Fig.11 In the graph, Te / Tq is plotted as a variable. Fig.10 b. Fig.11 In the graph of , the horizontal axis represents Te / Tq and the vertical axis represents b.

[0191] In the range of 0.02≤Te / Tq≤0.15, the larger the Te / Tq, the larger b. Fig.11 The relationship between b and Te / Tq was obtained as follows by fitting the graph shown.

[0192] b=0.39Te / Tq+0.16

[0193] By passing Fig.11 Substitute the obtained formula into Fig.10 The obtained equation is used as follows to determine the conditional equation for maximizing the electromechanical coupling coefficient k (%).

[0194] Te2 / Tq=0.00001×ρ+0.39Te / Tq+0.16±0.01

[0195] Fig.12 is a graph showing simulation results based on the first embodiment. Fig.12 In the graph, the horizontal axis represents Te2 (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0196] exist Fig.12 The simulation conditions when 0 μm<dLe=dWe are as follows.

[0197] Tq=1.0μm

[0198] Te=0.05μm

[0199] Te2: Variable

[0200] Lq=Wq=120μm

[0201] Le=55μm

[0202] We=50μm

[0203] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0204] dWe=We2-We=2×dWe1=2×dWe2:variable

[0205] exist Fig.12 The simulation conditions when dLe=dWe≤0μm are as follows.

[0206] Tq=1.0μm

[0207] Te=0.05μm

[0208] Te2: Variable

[0209] Lq=Wq=120μm

[0210] Le2=55μm

[0211] We2=50μm

[0212] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0213] dWe=We2-We=2×dWe1=2×dWe2:variable

[0214] When one of dLe and dWe is set to 0 and the other is greater than 0, the electromechanical coupling coefficient k (%) is maximum when Te2 is greater than 0.10 μm and less than 0.15 μm (2 ≤ Te2 / Te ≤ 3) within the range of 0.05 μm ≤ Te2 ≤ 0.20 μm (1 ≤ Te2 / Te ≤ 4). In addition, within the range of 0.10 μm ≤ Te2 ≤ 0.20 μm (2 ≤ Te2 / Te ≤ 4), the change in the electromechanical coupling coefficient k relative to the change in Te2 is small, and the electromechanical coupling coefficient k (%) is approximately constant. In other words, the change in the electromechanical coupling coefficient k (%) relative to Te2 shows the same trend as the case where both dLe and dWe are greater than 0, even when one of dLe and dWe is 0 and the other is greater than 0. However, if Te2 is the same within the range of 0.05μm≤Te2≤0.20μm (1≤Te2 / Te≤4), the electromechanical coupling coefficient k(%) when both dLe and dWe are greater than 0 is higher than the electromechanical coupling coefficient k(%) when one of dLe and dWe is 0 and the other is greater than 0.

[0215] Fig.13 is a graph showing simulation results based on the first embodiment. Fig.13 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The values ​​of the horizontal axis dLe and dWe in the graph are expressed as "[dLe, dWe]".

[0216] exist Fig.13When the horizontal axis of the graph is greater than 0, that is, Le<Le2 and We<We2, the simulation conditions are as follows.

[0217] Tq=1.5μm

[0218] Te=0.08μm

[0219] Te2=0.20μm

[0220] Lq=Wq=120μm

[0221] Le=70μm,

[0222] We=70μm,

[0223] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0224] dWe=We2-We=2×dWe1=2×dWe2:variable

[0225] dLe=dWe

[0226] exist Fig.13 When the horizontal axis of the graph is below 0, that is, Le2≤Le and We2≤We, the simulation conditions are as follows.

[0227] Tq=1.5μm

[0228] Te=0.08μm

[0229] Te2=0.20μm

[0230] Lq=Wq=120μm

[0231] Le2=70μm

[0232] We2=70μm

[0233] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0234] dWe=We2-We=2×dWe1=2×dWe2:variable

[0235] dLe=dWe

[0236] Fig.13 The drawing representation in Figure 4In other words, if one of the pair of excitation electrodes is thicker than the other excitation electrode, and the area of ​​the thicker excitation electrode is larger than the area of ​​the thinner excitation electrode, then even if the sizes of the pair of excitation electrodes and the crystal piece are different, the change of the electromechanical coupling coefficient k (%) relative to the change of dLe and dWe shows the same trend.

[0237] Fig.14 is a graph showing simulation results based on the first embodiment. Fig.14 In the graph, the horizontal axis represents Te2 (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0238] exist Fig.14 The simulation conditions when 0 μm<dLe=dWe are as follows.

[0239] Tq=1.5μm

[0240] Te=0.08μm

[0241] Te2: Variable

[0242] Lq=Wq=120μm

[0243] Le=70μm

[0244] We=70μm

[0245] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0246] dWe=We2-We=2×dWe1=2×dWe2:variable

[0247] exist Fig.14 The simulation conditions when dLe=dWe≤0μm are as follows.

[0248] Tq=1.5μm

[0249] Te=0.08μm

[0250] Te2: Variable

[0251] Lq=Wq=120μm

[0252] Le2=70μm

[0253] We2=70μm

[0254] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0255] dWe=We2-We=2×dWe1=2×dWe2:variable

[0256] Fig.14 The plot of dLe=dWe=15μm in Figure 8 In other words, if one of the pair of excitation electrodes is thicker than the other excitation electrode, and the area of ​​the thicker excitation electrode is larger than the area of ​​the thinner excitation electrode, then even if the sizes of the pair of excitation electrodes and the crystal piece are different, the change in the electromechanical coupling coefficient k (%) relative to the change in Te2 shows the same trend.

[0257] Fig.15 is a graph showing simulation results based on the first embodiment. Fig.15 In FIG. 1 , the horizontal axis represents dLe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0258] exist Fig.15 In the simulation, two configuration examples are performed in which the shape and area of ​​the overlapping portion of the first excitation electrode and the second excitation electrode are the same and the shapes of the first excitation electrode and the second excitation electrode are different.

[0259] In the first configuration example, the top view shape of the first excitation electrode 14a and the second excitation electrode 14b is a square of equal area. Each side of the first excitation electrode 14a extends in the X-axis direction and the Z'-axis direction. The second excitation electrode 14b is arranged at a 45-degree tilt relative to the first excitation electrode 14a in a centrally overlapped state, and the diagonal extends in the X-axis direction and the Z'-axis direction. The shape of the mutually opposing portions of the first excitation electrode 14a and the second excitation electrode 14b is a regular octagon. The length of the first excitation electrode 14a along the X-axis direction is Le, and the length of the second excitation electrode 14b along the X-axis direction is Le2.

[0260] In the second configuration example, the first excitation electrode 14a and the second excitation electrode 14b are regular octagons in plan view, with their centers overlapping. The length between the opposing sides of the first excitation electrode 14a is Le, and the length between the opposing sides of the second excitation electrode 14b is Le2.

[0261] exist Fig.15 The simulation conditions are as follows.

[0262] Tq=1.5μm

[0263] Te=0.08μm

[0264] Te2: 0.20 μm

[0265] Lq=Wq=120μm

[0266] Le=70μm

[0267] dLe=Le2-Le:variable

[0268] based on Fig.15 The second example of the drawing in FIG. Figure 4 In other words, if the area of ​​the thicker excitation electrode of the first excitation electrode 14a and the second excitation electrode 14b is larger than the area of ​​the thinner excitation electrode, and a part of the thicker excitation electrode overlaps the entire thinner excitation electrode, the electromechanical coupling coefficient k (%) is improved regardless of the top view shapes of the first excitation electrode 14a and the second excitation electrode 14b.

[0269] In the first configuration example, for example, on the diagonal line extending along the X-axis direction of the second excitation electrode 14b, dLe=Le2-Le=Le×2^(1 / 2)-Le≒28.99>0. However, the electromechanical coupling coefficient k(%) in the first configuration example is about the same as the electromechanical coupling coefficient k(%) in the second configuration example in the range of 0μm<dLe<5μm, and is smaller than the electromechanical coupling coefficient k(%) in the second configuration example under the same dLe. In other words, the facing area of ​​the pair of excitation electrodes in the first configuration example is the same as the facing area of ​​the pair of excitation electrodes in the second configuration example, and dLe>0 is partially satisfied in the first configuration example, but the electromechanical coupling coefficient k(%) in the first configuration example is not improved as much as the electromechanical coupling coefficient k(%) in the second configuration example under the same dLe. In other words, what is important for improving the electromechanical coupling coefficient k(%) is not the size relationship between the lengths of the first excitation electrode 14a and the second excitation electrode 14b, but the size relationship between the areas.

[0270] Fig.16 is a graph showing simulation results based on the first embodiment. Fig.16 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the standardized electromechanical coupling coefficient k (%). The values ​​of dLe and dWe on the horizontal axis of the graph are expressed as "[dLe, dWe]".

[0271] exist Fig.16 The simulation conditions when Tq=0.5 μm are as follows.

[0272] Tq=0.5μm

[0273] Te=0.05μm

[0274] Te2=0.12μm

[0275] Lq=Wq=120μm

[0276] Le=30μm

[0277] We=30μm

[0278] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0279] dWe=We2-We=2×dWe1=2×dWe2:variable

[0280] dLe=dWe

[0281] exist Fig.16 The simulation conditions when Tq=1.0 μm are as follows.

[0282] Tq=1.0μm

[0283] Te=0.05μm

[0284] Te2=0.12μm

[0285] Lq=Wq=120μm

[0286] Le=55μm

[0287] We=50μm

[0288] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0289] dWe=We2-We=2×dWe1=2×dWe2:variable

[0290] dLe=dWe

[0291] exist Fig.16 The simulation conditions when Tq=1.5 μm are as follows.

[0292] Tq=1.5μm

[0293] Te=0.05μm

[0294] Te2=0.12μm

[0295] Lq=Wq=120μm

[0296] Le=70μm

[0297] We=70μmdLe=Le2-Le=2×dLe1=2×dLe2:variable dWe=We2-We=2×dWe1=2×dWe2:variable dLe=dWe

[0298] exist Fig.16 The simulation conditions when Tq=2.0 μm are as follows.

[0299] Tq=2.0μm

[0300] Te=0.05μm

[0301] Te2=0.12μm

[0302] Lq=Wq=120μm

[0303] Le=55μm

[0304] We=50μmdLe=Le2-Le=2×dLe1=2×dLe2:variable dWe=We2-We=2×dWe1=2×dWe2:variable dLe=dWe

[0305] exist Fig.16 The simulation conditions when Tq=3.0 μm are as follows.

[0306] Tq=3.0μm

[0307] Te=0.05μm

[0308] Te2=0.12μm

[0309] Lq=Wq=120μm

[0310] Le=55μm

[0311] We=50μm

[0312] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0313] dWe=We2-We=2×dWe1=2×dWe2:variable

[0314] dLe=dWe

[0315] like Fig.16 As shown, the larger Tq is, the larger dLe and dWe are required to improve the electromechanical coupling coefficient k(%). Hereinafter, the minimum dLe and dWe required to maximize the electromechanical coupling coefficient k(%) are referred to as "minimum [dLe, dWe]".

[0316] Fig.17 It is a graph showing the simulation results based on the first embodiment. Fig.17 The chart is based on Fig.16 The relationship between Tq and the minimum 〔dLe, dWe〕 is obtained from the graph. Fig.17 In the graph, the horizontal axis represents Tq (μm) and the vertical axis represents the minimum [dLe, dWe] (μm).

[0317] As Tq increases, the minimum 〔dLe, dWe〕 increases. Fig.17By fitting the graph shown in FIG. 1 , the conditional expression for maximizing the electromechanical coupling coefficient k (%) is obtained as follows: The right side of the following expression [dLe, dWe] corresponds to an example of the distance De between the adjacent sides of the first excitation electrode and the second excitation electrode in a certain direction.

[0318] 5.22×Tq-0.45≤〔dLe,dWe〕

[0319] As described above, according to this embodiment, the area of ​​the second excitation electrode 14b is larger than that of the first excitation electrode 14a, a portion of the second excitation electrode 14b overlaps the entire first excitation electrode 14a, and the thickness Te2 of the second excitation electrode 14b is larger than the thickness Te of the first excitation electrode 14a.

[0320] Thereby, the electromechanical coupling coefficient k (%) can be improved.

[0321] In the present embodiment, the first excitation electrode 14 a is a side that is trimmed for frequency adjustment in a manufacturing process, for example.

[0322] Thus, by this trimming process, the thickness Te can be made smaller than the thickness Te2. Therefore, since Te<Te2 can be achieved even without providing the first excitation electrode 14a and the second excitation electrode 14b with different thicknesses during film formation, the manufacturing process can be simplified.

[0323] In addition, in the present embodiment, the second excitation electrode 14 b may be a side subjected to trimming processing for frequency adjustment.

[0324] Thus, since the area of ​​the second excitation electrode 14b is larger than the area of ​​the first excitation electrode 14a, the frequency adjustment efficiency by the trimming process can be improved compared to the case where the first excitation electrode 14a is trimmed. In addition, when the thickness Te2 is sufficiently larger than the thickness Te, for example, in the range of 2×Te≤Te2≤4×Te, the change in the electromechanical coupling coefficient k(%) is small relative to the change in the thickness Te2, so even if the thickness Te2 changes by the trimming process, the reduction in the electromechanical coupling coefficient k(%) can be suppressed.

[0325] In addition, in the present embodiment, all of the outer edge portions 71 to 74 of the first excitation electrode 14 a are located inside the outer edge portions 81 to 84 of the second excitation electrode 14 b.

[0326] Thus, the electromechanical coupling coefficient k(%) can be further improved compared to a configuration in which a part of the outer edge portions 71 to 74 of the first excitation electrode 14a overlaps a part of the outer edge portions 81 to 84 of the second excitation electrode 14b. In addition, the change in the electromechanical coupling coefficient k(%) can be made small with respect to the change in the thickness Te2 of the second excitation electrode 14b, so that when the second excitation electrode 14b is trimmed for frequency adjustment, the reduction in the electromechanical coupling coefficient k(%) can be suppressed. In addition, even if the first excitation electrode 14a is displaced relative to the second excitation electrode 14b, the state in which the entire first excitation electrode 14a overlaps with the second excitation electrode 14b is maintained, so that the reduction in the electromechanical coupling coefficient k(%) can be suppressed.

[0327] In addition, in the present embodiment, the relationship of Te2 / Tq=0.00001×ρ+0.39×Te / Tq+0.16±0.01 holds.

[0328] Therefore, when the thicknesses Tq, Te, and Te2 satisfy the conditions of the above formula, the electromechanical coupling coefficient k (%) is maximized.

[0329] In the present embodiment, at least one of the relationships of 5.22×Tq-0.45≤dLe and 5.22×Tq-0.45≤dWe holds true, and preferably both relationships hold true.

[0330] This can suppress a decrease in the electromechanical coupling coefficient k (%) caused by the relationship among Tq, dLe, and dWe. In other words, the electromechanical coupling coefficient k (%) can be sufficiently increased.

[0331] Other embodiments are described below. In addition, the same or similar reference numerals are used for the same or similar structures as those shown in the first embodiment, and their description is appropriately omitted. In addition, the same effects of the same structures are not mentioned in sequence.

[0332] <Second embodiment>

[0333] Next, refer to Fig.18 as well as Fig.19 The configuration of the crystal resonator element 200 according to the second embodiment will be described.

[0334] The area of ​​the first excitation electrode 214a is greater than the area of ​​the second excitation electrode 214b, the length Le of the first excitation electrode 214a is greater than the length Le2 of the second excitation electrode 214b, the length We of the first excitation electrode 214a is greater than the length We2 of the second excitation electrode 214b, and the thickness Te of the first excitation electrode 214a is greater than the thickness Te2 of the second excitation electrode 214b.

[0335] The crystal resonator element 200 further includes an insulating film 241 stacked on the second excitation electrode 214b. The material of the insulating film 241 is, for example, silicon oxide such as SiO2. The material of the insulating film 241 is not limited thereto, and may be any of inorganic insulators such as silicon nitride, silicon oxynitride, and aluminum oxide, and organic insulators such as polyvinyl phenol, polyvinyl alcohol, ether polymer, polyimide, and acrylic resin.

[0336] like Fig.18 As shown, the insulating film 241 extends over substantially the entire region of the vibration part 210. The area of ​​the insulating film 241 is larger than the area of ​​the first excitation electrode 214a and the area of ​​the second excitation electrode 214b, and is substantially equal to the area of ​​the vibration part 210. Therefore, when the length of the insulating film 241 along the X-axis direction is Le3 and the length of the insulating film 241 along the Z'-axis direction is We3 in a plan view, the relationship of Le2<Le<Le3=Lq and We2<We<We3=Wq holds. In a plan view, the center of the insulating film 241 overlaps with the center of the first excitation electrode 214a and the center of the second excitation electrode 214b. Therefore, the outer edge of the second excitation electrode 214b is entirely provided on the inner side than the outer edge of the first excitation electrode 214a, and the outer edge of the insulating film 241 is entirely provided on the outer side than the outer edge of the first excitation electrode 214a.

[0337] like Fig.19 As shown, the insulating film 241 is stacked on the surface of the second excitation electrode 214 b opposite to the crystal piece 11 . When the thickness of the insulating film 241 is Te3, the relationship of Te2<Te<Te3 and the relationship of Te<Te2+Te3 hold.

[0338] The thickness Te3 is determined, for example, as the distance along the Y' axis between the upper surface and the lower surface of the insulating film 241 at a predetermined position (for example, on a straight line extending along the Y' axis through the center of the region where the first excitation electrode 214a, the second excitation electrode 214b, and the insulating film 241 overlap). The thickness Te3 may also be determined as the average value, maximum value, or minimum value of the distance along the Y' axis between the upper surface and the lower surface of the insulating film 241 in the region where the first excitation electrode 214a, the second excitation electrode 214b, and the insulating film 241 overlap.

[0339] In addition, the position and size relationship of the insulating film 241, the first excitation electrode 214a, and the second excitation electrode 214b are not limited to the above-mentioned configuration if all of the following conditions are satisfied. The first condition is that the insulating film 241 is stacked on the excitation electrode with a smaller area in a pair of excitation electrodes when viewed from above. The second condition is that the sum of the thickness of the excitation electrode with a smaller area in a pair of excitation electrodes when viewed from above and the thickness of the insulating film 241 is greater than the thickness of the excitation electrode with a larger area in a pair of excitation electrodes when viewed from above. The third condition is that the area of ​​the stack 240 composed of the excitation electrode with a smaller area in a pair of excitation electrodes when viewed from above and the insulating film 241 is greater than the area of ​​the excitation electrode with a larger area in a pair of excitation electrodes when viewed from above. Here, the "area of ​​the stack 240" includes not only the area of ​​the portion where the excitation electrode with a smaller area in a pair of excitation electrodes when viewed from above and the insulating film 241 overlap and extend on both sides, but also includes the area of ​​the portion where only one side extends. The fourth condition is that, when viewed from above, a portion of the stack 240 overlaps the entire excitation electrode with a larger area in a pair of excitation electrodes when viewed from above.

[0340] For example, Fig.18 The configuration example shown may be modified so that the relationship of Le2<Le<Le3<Lq holds. Similarly, the configuration example may be modified so that the relationship of We2<We<We3<Wq holds.

[0341] In addition, for example, Fig.18 The illustrated configuration example may be modified so that the center of the insulating film 241 in a plan view is located on the positive X-axis side, the negative X-axis side, the positive Z′ axis side, or the negative Z′ axis side relative to the center of at least one of the first excitation electrode 214a and the second excitation electrode 214b in a plan view.

[0342] In addition, for example, Fig.19 The structure example shown can also be transformed into the relationship of Te2<Te3≤Te<Te2+Te3, or the relationship of Te3≤Te2≤Te<Te2+Te3. Similarly, it can be transformed into the relationship of Te≤Te2<Te3<Te2+Te3, or the relationship of Te≤Te3≤Te2<Te2+Te3, or the relationship of Te≤Te3≤Te2<Te2+Te3.

[0343] In addition, for example, Fig.19The illustrated configuration example may be modified so that the insulating film 241 is provided between the crystal piece 11 and the second excitation electrode 214b. The crystal resonator element 200 may further include an insulating film stacked on the first excitation electrode 214a. In other words, the first insulating film may be stacked on the excitation electrode with a smaller area when viewed from above in a pair of excitation electrodes, and the second insulating film may be stacked on the excitation electrode with a larger area when viewed from above in a pair of excitation electrodes. In addition, from the viewpoint of suppressing the reduction of the electromechanical coupling coefficient k, it is preferred that the sum of the thickness of the excitation electrode with a smaller area and the thickness of the first insulating film is greater than the sum of the thickness of the excitation electrode with a larger area and the thickness of the second insulating film.

[0344] Next, refer to Figure 20 to Figure 24 , simulation results based on the second embodiment are described.

[0345] Fig. 20 is a graph showing simulation results based on the second embodiment. Fig. 20 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The values ​​of dLe and dWe on the horizontal axis of the graph are expressed as "[dLe, dWe]". Fig. 20 The "SiO2" in FIG. 2 refers to the insulating film 241. The same applies to other drawings.

[0346] exist Fig. 20 In the case of Te2<Te, when [dLe, dWe] is greater than 0, that is, when Le2<Le and We<We, the simulation conditions are as follows.

[0347] Tq=1.0μm

[0348] Te: variable

[0349] Te2: Variable

[0350] Te3=0.12μm

[0351] Lq=Wq=120μm

[0352] Le=55μm,

[0353] We=50μm,

[0354] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0355] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0356] dLe=dWe

[0357] exist Fig. 20In the case of Te2<Te, when [dLe, dWe] is less than 0, that is, Le≤Le2 and We≤We2, the simulation conditions are as follows.

[0358] Tq=1.0μm

[0359] Te: variable

[0360] Te2: Variable

[0361] Te3=0.12μm

[0362] Lq=Wq=120μm

[0363] Le2=55μm

[0364] We2=50μm

[0365] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0366] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0367] dLe=dWe

[0368] exist Fig. 20 The simulation conditions for Te<Te2 are the same as those for Te2<Te, except that dLe=Le2-Le and dWe=We2-We. Fig. 20 In the case where it is recorded as "SiO2 is present", Le3=Lq, We3=Wq.

[0369] In any [dLe, dWe] within the range of -25 μm ≤ [dLe, dWe] ≤ 25 μm, the electromechanical coupling coefficient k (%) when Te < Te2 and the insulating film 241 is provided is higher than the electromechanical coupling coefficient k (%) when the insulating film 241 is not provided. In any [dLe, dWe] within the range of -25 μm ≤ [dLe, dWe] ≤ 25 μm, the electromechanical coupling coefficient k (%) when Te2 < Te and the insulating film 241 is provided is higher than the electromechanical coupling coefficient k (%) when Te < Te2 and the insulating film 241 is provided. In other words, the electromechanical coupling coefficient k (%) when the insulating film 241 is stacked on the thinner excitation electrode of the pair of excitation electrodes is higher than the electromechanical coupling coefficient k (%) when the insulating film 241 is stacked on the thicker excitation electrode of the pair of excitation electrodes.

[0370] In the case of Te2<Te, the electromechanical coupling coefficient k(%) in the range of 0<〔dLe, dWe〕is higher than the electromechanical coupling coefficient k(%) in the range of〔dLe, dWe〕≤0. In other words, in the case of Te2<Te, the electromechanical coupling coefficient k(%) is higher when Le2<Le and We2<We. In addition, in the case of Te<Te2, the electromechanical coupling coefficient k(%) in the range of 0<〔dLe, dWe〕is also higher than the electromechanical coupling coefficient k(%) in the range of〔dLe, dWe〕≤0. In other words, in the case of Te<Te2, the electromechanical coupling coefficient k(%) is higher when Le<Le2 and We<We2. In summary, in any case where the thickness of the excitation electrode on one side of a pair of excitation electrodes with a stacked insulating film is smaller or larger than the thickness of the excitation electrode on the other side of a pair of excitation electrodes without a stacked insulating film, the electromechanical coupling coefficient k(%) when the area of ​​the thicker excitation electrode in a pair of excitation electrodes is larger than the area of ​​the thinner excitation electrode is higher than the electromechanical coupling coefficient k(%) when the area of ​​the thicker excitation electrode in a pair of excitation electrodes is smaller than the area of ​​the thinner excitation electrode.

[0371] Fig.21 is a graph showing simulation results based on the second embodiment. Fig.21 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The values ​​of dLe and dWe on the horizontal axis of the graph are expressed as "[dLe, dWe]".

[0372] exist Fig.21 When [dLe, dWe] is greater than 0, that is, Le2<Le and We2<We, the simulation conditions are as follows.

[0373] Tq=1.0μm

[0374] Te=0.10μm

[0375] Te2=0.05μm

[0376] Te3=0.12μm

[0377] Lq=Wq=120μm

[0378] Le=55μm,

[0379] We=50μm,

[0380] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0381] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0382] dLe=dWe

[0383] Le3: Variables

[0384] We3: Variables

[0385] exist Fig.21 When [dLe, dWe] is less than 0, that is, Le≤Le2 and We≤We2, the simulation conditions are as follows.

[0386] Tq=1.0μm

[0387] Te=0.10μm

[0388] Te2=0.05μm

[0389] Te3=0.12μm

[0390] Lq=Wq=120μm

[0391] Le2=55μm

[0392] We2=50μm

[0393] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0394] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0395] dLe=dWe

[0396] Le3: Variables

[0397] We3: Variables

[0398] Fig.21 The simulation results are plotted for the case where the insulating film 241 is provided on the entire lower surface of the vibration part 210, the case where the insulating film 241 is provided only on the lower surface of the second excitation electrode 214b, and the case where the insulating film 241 is not provided. The case where the insulating film 241 is provided on the entire lower surface of the vibration part 210 means that the relationship of Le3=Lq and We3=Wq holds. The case where the insulating film 241 is provided only on the lower surface of the second excitation electrode 214b means that the relationship of Le3=Le2 and We3=We2 holds. The case where the insulating film 241 is not provided means that the relationship of Le3=We3=0 holds.

[0399] In any [dLe, dWe] within the range of −25 μm ≤ [dLe, dWe] ≤ 25 μm, the electromechanical coupling coefficient k (%) when the insulating film 241 is provided on the entire lower surface of the vibration portion 210 is improved compared to the electromechanical coupling coefficient k (%) when the insulating film 241 is not provided. However, in any [dLe, dWe] within the range of −25 μm ≤ [dLe, dWe] ≤ 25 μm, the electromechanical coupling coefficient k (%) when the insulating film 241 is provided only on the lower surface of the second excitation electrode 214 b is reduced compared to the electromechanical coupling coefficient k (%) when the insulating film 241 is not provided.

[0400] Based on the above, it is shown that when the insulating film 241 is provided only in the region overlapping with the smaller excitation electrode of the pair of excitation electrodes in a plan view, the effect of improving the electromechanical coupling coefficient k (%) cannot be obtained. In addition, it is shown that when the outer edge of the second excitation electrode 214b is entirely provided on the inner side than the outer edge of the first excitation electrode 214a in a plan view, and the outer edge of the insulating film 241 is entirely provided on the outer side than the outer edge of the first excitation electrode 214a, the effect of improving the electromechanical coupling coefficient k (%) can be obtained.

[0401] Fig. 22 is a graph showing simulation results based on the second embodiment. Fig. 22 In the graph, the horizontal axis represents Te3 (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0402] exist Fig. 22 The simulation conditions are as follows.

[0403] Tq=1.0μm

[0404] Te: variable

[0405] Te2: Variable

[0406] Te3: Variables

[0407] Lq=Wq=120μm

[0408] Le2=55μm

[0409] We2=50μm

[0410] Le3=Lq

[0411] We3=Wq

[0412] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0413] dWe=We2-We=2×dWe1=2×dWe2:variable

[0414] dLe=dWe

[0415] like Fig. 22 As shown in FIG. 1 , in the range of 0.06 μm ≤ Te3 ≤ 0.20 μm, the electromechanical coupling coefficient k (%) in the case of Te = 0.05 μm, Te2 = 0.10 μm, dLe = dWe = 25 μm is improved compared with the electromechanical coupling coefficient k (%) in the case of Te = 0.05 μm, Te2 = 0.05 μm, dLe = dWe = 0 μm. The electromechanical coupling coefficient k (%) in the case of Te = 0.10 μm, Te2 = 0.05 μm, dLe = dWe = -25 μm is further improved than the electromechanical coupling coefficient k (%) in the case of Te = 0.05 μm, Te2 = 0.10 μm, dLe = dWe = 25 μm. In other words, when the entire thinner excitation electrode of a pair of excitation electrodes overlaps a portion of the thicker excitation electrode in a plan view, the electromechanical coupling coefficient k (%) is improved regardless of which excitation electrode side the insulating film is provided on. However, when the insulating film is provided on one side of the thinner excitation electrode, the electromechanical coupling coefficient k (%) is improved compared to the case where the insulating film is provided on one side of the thicker excitation electrode.

[0416] In addition, when Te = 0.10 μm, Te2 = 0.05 μm, dLe = dWe = -25 μm, the change in the electromechanical coupling coefficient k (%) relative to the change in Te3 is small. In other words, when the thinner excitation electrode of a pair of excitation electrodes overlaps with a part of the thicker excitation electrode in a plan view, and when an insulating film is provided on one side of the thinner excitation electrode, the electromechanical coupling coefficient k (%) is stable relative to the film thickness of the insulating film. In other words, even if the insulating film is trimmed for adjusting the frequency during the manufacturing process, the reduction in the electromechanical coupling coefficient k (%) can be suppressed.

[0417] Fig.23 is a graph showing simulation results based on the second embodiment. Fig.23 In the graph, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The values ​​of dLe and dWe on the horizontal axis of the graph are expressed as "[dLe, dWe]".

[0418] exist Fig.23 In the case of Te2<Te, when [dLe, dWe] is greater than 0, that is, when Le2>Le and We2>We, the simulation conditions are as follows.

[0419] Tq=1.5μm

[0420] Te: variable

[0421] Te2: Variable

[0422] Te3=0.20μm

[0423] Lq=Wq=120μm

[0424] Le=70μm,

[0425] We=70μm,

[0426] Le3=Lq

[0427] We3=Wq

[0428] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0429] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0430] dLe=dWe

[0431] exist Fig.23 In the case of Te2<Te, when [dLe, dWe] is less than 0, that is, when Le2≤Le and We2≤We, the simulation conditions are as follows.

[0432] Tq=1.5μm

[0433] Te: variable

[0434] Te2: Variable

[0435] Te3=0.20μm

[0436] Lq=Wq=120μm

[0437] Le2=70μm

[0438] We2=70μm

[0439] Le3=Lq

[0440] We3=Wq

[0441] dLe=Le-Le2=2×dLe1=2×dLe2:variable

[0442] dWe=We-We2=2×dWe1=2×dWe2:Variable

[0443] dLe=dWe

[0444] exist Fig.23 , the simulation conditions in the case of Te<Te2 are the same as those in the case of Te2<Te except that dLe=Le2-Le and dWe=We2-We.

[0445] Fig.23 The drawing in Fig. 20 In other words, if the size relationship between a pair of excitation electrodes and the insulating film is the same, the change in the electromechanical coupling coefficient k (%) relative to the change in [dLe, dWe] shows the same trend even if the sizes of the pair of excitation electrodes and the insulating film are different.

[0446] Fig.24 is a graph showing simulation results based on the second embodiment. Fig.24 In the graph, the horizontal axis represents Te3 (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0447] exist Fig.24 The simulation conditions are as follows.

[0448] Tq=1.5μm

[0449] Te: variable

[0450] Te2=0.08μm

[0451] Te3: Variables

[0452] Lq=Wq=120μm

[0453] Le2=70μm

[0454] We2=70μm

[0455] Le3=Lq

[0456] We3=Wq

[0457] dLe=Le2-Le=2×dLe1=2×dLe2:variable

[0458] dWe=We2-We=2×dWe1=2×dWe2:variable

[0459] dLe=dWe

[0460] Fig.24 The plot of Te = 0.16 μm, Te2 = 0.08 μm, dLe = dWe = -20 μm shows the same as Fig. 22 In other words, if the size relationship between a pair of excitation electrodes and an insulating film is the same, then even if the sizes of a pair of excitation electrodes and an insulating film are different, the change in the electromechanical coupling coefficient k (%) relative to the change in Te3 shows the same trend.

[0461] As described above, according to the present embodiment, in a plan view, the area of ​​the stacked body 240 composed of the second excitation electrode 214b and the insulating film 241 is larger than the first excitation electrode 214a, and a portion of the stacked body 240 overlaps the entire first excitation electrode 214a. The sum of the thickness Te2 of the second excitation electrode 214b and the thickness Te3 of the insulating film 241 is larger than the thickness Te of the first excitation electrode 214a.

[0462] Thereby, the electromechanical coupling coefficient k (%) can be improved.

[0463] In addition, in the present embodiment, the insulating film 241 is stacked on the surface of the second excitation electrode 214 b on the side opposite to the crystal piece 11 .

[0464] This can reduce the distance between the first excitation electrode 214a and the second excitation electrode 214b compared to a configuration in which the insulating film 241 is present between the first excitation electrode 214a and the second excitation electrode 214b. This can reduce the thickness of the portion vibrating by the piezoelectric effect, thereby increasing the frequency of the crystal resonator element 200.

[0465] In this embodiment, the outer edge of the second excitation electrode 214 b is entirely provided inside the outer edge of the first excitation electrode 214 a , and the outer edge of the insulating film 241 is entirely provided outside the outer edge of the first excitation electrode 214 a .

[0466] Thus, the change in the electromechanical coupling coefficient k(%) can be made smaller with respect to the change in the thickness Te3 of the insulating film 241 , so that when the insulating film 241 is trimmed for frequency adjustment, a decrease in the electromechanical coupling coefficient k(%) can be suppressed.

[0467] In addition, in this embodiment, the thickness Te2 of the second excitation electrode 214 b is smaller than the thickness Te of the first excitation electrode 214 a .

[0468] Thereby, the electromechanical coupling coefficient k (%) can be further improved.

[0469] In addition, in the present embodiment, the relationship (Te2+Te3) / Tq=0.00001×ρ'+0.39×Te / Tq+0.16±0.01 holds. ρ' is the average density of the first excitation electrode 214a, the second excitation electrode 214b, and the insulating film 241. When the density of the first excitation electrode 214a is ρ1, the density of the second excitation electrode 214b is ρ2, the density of the insulating film 241 is ρ3, the volume of the portion of the first excitation electrode 214a facing the second excitation electrode 214b and the insulating film 241 is V1, the volume of the portion of the second excitation electrode 214b facing the first excitation electrode 214a and the insulating film 241 is V2, and the volume of the portion of the insulating film 241 facing the first excitation electrode 214a and the second excitation electrode 214b is V3, the following formula is used for calculation.

[0470] ρ'=(ρ1×V1+ρ2×V2+ρ3×V3) / (V1+V2+V3)

[0471] Therefore, when the thicknesses Tq, Te, Te2, and Te3 satisfy the conditions of the above formula, the electromechanical coupling coefficient k (%) is maximized, similarly to the first embodiment.

[0472] In addition, in the present embodiment, the material of the first excitation electrode 214 a and the second excitation electrode 214 b is aluminum, and the material of the insulating film 241 is silicon oxide.

[0473] Thus, the density of aluminum and the density of silicon oxide are close in value, so the calculation of the average density ρ' can be simplified. In addition, the adhesion between the crystal piece 11 and the insulating film 241 is good, and the adhesion between the crystal piece 11 and the second excitation electrode 214b can be roughly the same as the adhesion between the second excitation electrode 214b and the insulating film 241. Therefore, the peeling of the insulating film 241 from the crystal piece 11 or the second excitation electrode 214b and the peeling of the second excitation electrode 214b from the crystal piece 11 can be suppressed.

[0474] <Third Embodiment>

[0475] Next, refer to Figure 25 to Figure 29 , the structure of the crystal resonator element 300 according to the third embodiment will be described.

[0476] Fig.25 : is a graph showing the simulation results based on the first embodiment. Specifically, it shows the simulation results of the electromechanical coupling coefficient k (%) calculated by taking into account the influence of the second extraction electrode 15b. Fig.25In the graph, the horizontal axis represents the lead electrode wiring width Wwire (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The lead electrode wiring width refers to the dimension of the first lead electrode 15a extending in the X-axis direction in the Z′-axis direction.

[0477] exist Fig.25 The simulation conditions are as follows: The first extraction electrode 15 a is extracted from the center portion in the Z′-axis direction of the outer edge portion of the first excitation electrode 14 a on the positive side in the X-axis direction.

[0478] Tq=1.0μm

[0479] Te=0.05μm

[0480] Te2=0.05μm

[0481] Lq=Wq=120μm

[0482] Le=55μm

[0483] We=50μm

[0484] Le2=70μm

[0485] We2=60μm

[0486] dLe=Le2-Le=2×dLe1=2×dLe2=15μm

[0487] dWe=We2-We=2×dWe1=2×dWe2=10μm

[0488] Wwire: Variable

[0489] When Wwire=0μm, that is, in the case of simulation in which the first extraction electrode 15a is not provided and only the first excitation electrode 14a and the second excitation electrode 14b are used for excitation, the area where the first excitation electrode 14a and the second excitation electrode 14b overlap is excited. However, when 0μm<Wwire is set, the area where the second excitation electrode 14b overlaps with the first extraction electrode 15a is also excited. Therefore, Fig.25 As shown in FIG. 1 , the electromechanical coupling coefficient k(%) when 0 μm<Wwire is lower than the electromechanical coupling coefficient k(%) when Wwire=0 μm. In addition, when 0 μm<Wwire, the Q value is also lowered.

[0490] like Fig.25As shown in FIG. 1 , as Wwire increases from 0 μm, the electromechanical coupling coefficient k(%) decreases, and is extremely small near Wwire = 10 μm. As Wwire increases from 10 μm, the electromechanical coupling coefficient k(%) increases, and is extremely large near Wwire = 40 μm. It is believed that the electromechanical coupling coefficient k(%) increases as Wwire increases within the range of 10 μm < Wwire < 40 μm because the widened first extraction electrode 15a is like a part of the first excitation electrode 14a.

[0491] From the viewpoint of suppressing vibration leakage, etc., it is preferred that Wwire is smaller, but if Wwire is smaller, Fig.25 As shown in FIG. 1 , the electromechanical coupling coefficient k (%) decreases. Therefore, in order to suppress the decrease in the electromechanical coupling coefficient k (%) and the Q value, it is necessary to reduce Wwire and suppress the influence of the first extraction electrode 15a on the second excitation electrode 14b. The third embodiment and the fourth embodiment are one form of the invention completed in view of such a situation.

[0492] Fig.26 It is a perspective view of a vibration unit according to a third embodiment. Fig. 27 : is a diagram showing the vibration distribution of the vibration part involved in the third embodiment. The amplitude is represented by light and dark, and the bright part is the area with large amplitude, and the dark part is the area with small amplitude. Fig. 27 In the figure, the second excitation electrode 314b is omitted.

[0493] like Fig.26 As shown in FIG. 1 , the third embodiment is different from the first embodiment in that a notch 314N is formed in the region of the second excitation electrode 314b that is opposed to the first extraction electrode 315a, and the other aspects are the same as the first embodiment. Since the first extraction electrode 315a extends from the outer edge of the first excitation electrode 314a on the positive direction of the X axis in the positive direction of the X axis, the notch 314N is provided at the outer edge of the second excitation electrode 314b on the positive direction of the X axis. The notch 314N is a rectangular concave portion when viewed from above. The distance between the outer edge of the second excitation electrode 314b in the notch 314N and the first excitation electrode 314a along the X-axis direction is Ln, and the distance between the outer edge of the second excitation electrode 314b in the notch 314N and the first extraction electrode 315a along the Z'-axis direction is Wn.

[0494] like Fig. 27As shown, in the third embodiment, the vibration area is limited to the area overlapping with the first excitation electrode 314a, and the vibration of the area overlapping with the first extraction electrode 315a is suppressed. For example, if the simulation is performed in the configuration in which the first extraction electrode 315a and the cutout portion 314N are omitted from the third embodiment, k=6.86% and Q=8.720, but if the simulation is performed in the configuration in which the first extraction electrode 315a with Wwire=10μm is added to the configuration, k=6.77% and Q=8.540. However, if the simulation is performed in the configuration according to the third embodiment in which the cutout portion 314N is further formed, k=6.82% and Q=8.730. In other words, by forming the cutout portion 314N, the influence of the first extraction electrode 315a on the second excitation electrode 314b is suppressed, and the reduction of the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0495] As described above, according to the present embodiment, the notch portion 314N is formed in the region of the second excitation electrode 314 b that faces the first extraction electrode 315 a .

[0496] As a result, the influence of the first extraction electrode 315 a on the second excitation electrode 314 b is suppressed, and the reduction in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0497] In addition, the third embodiment is a configuration in which a cutout portion is formed in the region opposite to the lead-out electrode of the larger excitation electrode in the pair of excitation electrodes in the first embodiment, but a cutout portion may be formed in the region opposite to the lead-out electrode of the insulating film in the second embodiment. In such a configuration, the same effect as that of the third embodiment can be obtained. However, since the insulating film is lighter than the material of the excitation electrode, the vibration containment in the region opposite to the first excitation electrode and the second excitation electrode in the second embodiment is good. Therefore, the reduction in the electromechanical coupling coefficient k (%) and the Q value caused by the influence of the lead-out electrode in the second embodiment is not as great as the reduction in the electromechanical coupling coefficient k (%) and the Q value caused by the influence of the lead-out electrode in the first embodiment. Therefore, there is a case where even if a cutout portion is formed in the insulating film of the second embodiment, the effect to the same extent as when the cutout portion is formed in the first embodiment cannot be obtained.

[0498] Next, refer to Fig.28 as well as Fig.29 , Fig.28 as well as Fig.29 is a graph showing simulation results based on the third embodiment. Fig.28 as well as Fig.29 In the graph, the horizontal axis represents Wn (μm) and the vertical axis represents the electromechanical coupling coefficient k (%).

[0499] exist Fig.28 as well as Fig.29 The simulation conditions are as follows. Fig.28 The simulation results when Wwire = 10 μm are shown. Fig.29 The simulation results when Wwire=20 μm are shown.

[0500] Tq=1.0μm

[0501] Te=0.05μm

[0502] Te2=0.05μm

[0503] Lq=Wq=120μm

[0504] Le=55μm

[0505] We=50μm

[0506] Le2=70μm

[0507] We2=60μm

[0508] dLe=Le2-Le=2×dLe1=2×dLe2=15μm

[0509] dWe=We2-We=2×dWe1=2×dWe2=10μm

[0510] Ln: variable

[0511] Wn: variable

[0512] like Fig.28 as well as Fig.29 As shown in FIG. 1 , Ln and Wn are preferably 2 μm or more and 6 μm or less. This can suppress a decrease in the electromechanical coupling coefficient k (%) regardless of the size of Wwire.

[0513] <Fourth embodiment>

[0514] Next, refer to Fig.30 as well as Fig.31 , the structure of the crystal resonator element 400 according to the fourth embodiment will be described. Fig.30 It is a perspective view of a vibration unit according to a fourth embodiment. Fig.31 : is a diagram showing the vibration distribution of the vibration part involved in the fourth embodiment. The amplitude is represented by light and dark, and the bright part is the area with large amplitude, and the dark part is the area with small amplitude. Fig.31 In the figure, the second excitation electrode 414b is omitted.

[0515] like Fig.30As shown, the fourth embodiment is different from the first embodiment in that the center of the second excitation electrode 414b is located on the negative side of the X-axis relative to the center of the first excitation electrode 414a in a plan view, and is the same as the first embodiment except for the above-mentioned point. The first extraction electrode 315a extends from the outer edge of the first excitation electrode 314a on the positive side of the X-axis in the positive direction of the X-axis, so the center of the second excitation electrode 414b is located in a direction away from the first extraction electrode 415a relative to the center of the first excitation electrode 414a. In other words, in a plan view, the center of the excitation electrode with a larger area in a pair of excitation electrodes is offset relative to the center of the excitation electrode with a smaller area in a pair of excitation electrodes in a direction away from the extraction electrode electrically connected to the excitation electrode with a smaller area.

[0516] The interval along the X-axis direction between the outer edge portion 471 of the first excitation electrode 414a on the negative side of the X-axis and the outer edge portion 481 of the second excitation electrode 414b on the negative side of the X-axis is set to G1. The interval along the X-axis direction between the outer edge portion 472 of the first excitation electrode 414a on the positive side of the X-axis and the outer edge portion 481 of the second excitation electrode 414b on the positive side of the X-axis is set to G2. In the crystal resonator element 400, the relationship of 0≤G2<G1 holds.

[0517] like Fig.31 As shown, in the fourth embodiment, the vibration region is limited to the region overlapping with the first excitation electrode 414a, and the vibration of the region overlapping with the first extraction electrode 415a is suppressed. For example, if the simulation is performed in the configuration in which the first extraction electrode 415a is omitted from the fourth embodiment and G1=G2, k=6.86% and Q=8,720, but if the simulation is performed in the configuration in which the first extraction electrode 415a with Wwire=10μm is added to the configuration, k=6.77% and Q=8,540. However, if the simulation is performed in the configuration of the fourth embodiment further modified to G1=0μm, k=6.84% and Q=8,770. In other words, by 0μm≤G1<G2, the influence of the first extraction electrode 415a on the second excitation electrode 414b is suppressed, and the reduction of the electromechanical coupling coefficient k(%) and the Q value is suppressed.

[0518] As described above, according to this embodiment, the center of the second excitation electrode 414 b is offset from the center of the first excitation electrode 414 a in a direction away from the first extraction electrode 415 a , and the relationship 0≤G2<G1 holds.

[0519] As a result, the influence of the first extraction electrode 415 a on the second excitation electrode 414 b is suppressed, and the reduction in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0520] <Fifth embodiment>

[0521] Next, refer to Fig.32 The structure of the crystal resonator element 500 according to the fifth embodiment will be described. Fig.32 It is a cross-sectional view of a vibration portion according to a fifth embodiment.

[0522] The fifth embodiment is different from the first embodiment in that it further includes a mass addition film 542, and is the same as the first embodiment except for the above-mentioned points. The mass addition film 542 is provided on the surface of the first excitation electrode 14a on the opposite side to the crystal piece 11. When viewed from above, the mass addition film 542 is provided along the outer edge of the first excitation electrode 14a, outside the central part of the first excitation electrode 14a. In addition, when viewed from above, the mass addition film 542 is provided in a region overlapping with the outer edge of the first excitation electrode 14a, or in a region inside the outer edge of the first excitation electrode 14a. The material of the mass addition film 542 is an electrical conductor, for example, the same as the material of the first excitation electrode 14a.

[0523] In addition, the position and material of the mass-added film 542 are not limited to the above. The mass-added film 542 may be provided between the first excitation electrode 14a and the crystal piece 11, on the surface of the second excitation electrode 14b on the side opposite to the crystal piece 11, and between the second excitation electrode 14b and the crystal piece 11. The material of the mass-added film 542 may also be a metal different from that of the first excitation electrode 14a.

[0524] The mass addition film 542 reduces the sound velocity due to the mass addition effect. Therefore, the sound velocity of the area where the mass addition film 542 is provided is lower than the sound velocity of the area where the mass addition film 542 is not provided. In other words, when viewed from above, the area where the first excitation electrode 14a and the second excitation electrode 14b are opposite to each other has a high sound velocity area 517 provided in the center and a low sound velocity area 518 provided outside the high sound velocity area 517. The low sound velocity area 518 is provided, for example, in a frame shape that is continuous in the circumferential direction, but may also be provided in a frame shape that is discontinuous in the circumferential direction. For example, the low sound velocity area 518 may also be provided in a strip shape extending from the outer edge portion 71 to the outer edge portion 72, or in a strip shape extending from the outer edge portion 73 to the outer edge portion 74.

[0525] This makes it possible to suppress the electromechanical coupling coefficient k(%) of the stray mode and improve the electromechanical coupling coefficient k(%) of the main mode.

[0526] In the present embodiment, when the mass adding film 542 is regarded as a part of the first excitation electrode 14 a , the thickness Te is the average thickness of the stacked body including the mass adding film 542 and the first excitation electrode 14 a .

[0527] <Sixth embodiment>

[0528] Next, refer to Fig.33 , the structure of the crystal resonator element 600 according to the sixth embodiment is described. Fig.33 It is a cross-sectional view of a vibration portion according to a sixth embodiment.

[0529] The sixth embodiment is different from the first embodiment in that a plurality of holes H are formed in the center portion of the first excitation electrode 614 a in a plan view, but is the same as the first embodiment except for the above-mentioned points.

[0530] The hole H penetrates the first excitation electrode 614a in the Y'-axis direction. The multiple holes H increase the sound velocity due to the mass reduction effect. Therefore, the sound velocity of the region where the multiple holes H are formed is greater than the sound velocity of the region where the multiple holes H are not formed. In other words, when viewed from above, the region where the first excitation electrode 14a and the second excitation electrode 14b face each other has a high sound velocity region 617 provided in the center and a low sound velocity region 618 provided outside the high sound velocity region 617.

[0531] This makes it possible to suppress the electromechanical coupling coefficient k(%) of the stray mode and improve the electromechanical coupling coefficient k(%) of the main mode.

[0532] In this embodiment, the area of ​​the first excitation electrode 614a in a plan view is the area of ​​the region surrounded by the outer edge of the first excitation electrode 614a, and the interior of the plurality of holes H is also calculated as a part of the area of ​​the first excitation electrode 614a. When the thickness of the first excitation electrode 614a in the low-pitched region 618 is set to Te1 and the opening ratio of the plurality of holes H is set to Har, the thickness Te is calculated by the following formula.

[0533] Te=Te1×(1-Har)

[0534] In order to make the inside of the hole H in the high-sonic velocity region 617 function as a part of the first excitation electrode 614a, it is preferable that when the inner diameter of the hole H is set to Hr, the relationship of 0<Hr / Tq≤2.0 holds. In this case, since the reduction rate of the electrostatic capacitance caused by the hole H is suppressed to 1% or less, the inside of the hole H can also fully function as an excitation electrode. In addition, it is more preferable that the relationship of 0<Hr / Tq≤1.5 holds, and it is more preferable that the relationship of 0<Hr / Tq≤1.0 holds. If 0<Hr / Tq≤1.5, the reduction rate of the electrostatic capacitance can be suppressed to 0.5% or less, and if 0<Hr / Tq≤1.0, the reduction rate of the electrostatic capacitance can be suppressed to 0.1% or less. In addition, in order to form the hole H with sufficient processing accuracy, it is preferable that 0.1≤Hr / Tq, and it is more preferable that 0.5≤Hr / Tq.

[0535] In addition, the hole H may be formed in the second excitation electrode, or may be formed in both the first excitation electrode and the second excitation electrode.

[0536] <Seventh embodiment>

[0537] Next, refer to Fig.34 , the structure of the crystal resonator element 700 involved in the seventh embodiment is described. Fig.34 It is a cross-sectional view of a vibration portion according to a seventh embodiment.

[0538] The seventh embodiment is different from the second embodiment in that it further includes a mass adding film 542, and is the same as the second embodiment except for the above-mentioned points. In other words, in a plan view, the region where the first excitation electrode 214a and the second excitation electrode 214b face each other has a high-sonic velocity region 717 provided in the center and a low-sonic velocity region 718 provided outside the high-sonic velocity region 717. The mass adding film 542 is provided from the region overlapping with the outer edge of the second excitation electrode 214b to the inner side thereof. Therefore, in a plan view, the low-sonic velocity region 718 is located inside the outer edge of the first excitation electrode 214a.

[0539] This makes it possible to suppress the electromechanical coupling coefficient k(%) of the stray mode and improve the electromechanical coupling coefficient k(%) of the main mode.

[0540] <Eighth Embodiment>

[0541] Next, refer to Fig.35 , the structure of the crystal resonator element 800 involved in the eighth embodiment is described. Fig.35 It is a cross-sectional view of a vibration portion according to the eighth embodiment.

[0542] The eighth embodiment is different from the second embodiment in that a plurality of holes H are formed in the center portion of the first excitation electrode 814 a in a plan view, but is the same as the second embodiment except for the above-mentioned points.

[0543] This makes it possible to suppress the electromechanical coupling coefficient k(%) of the stray mode and improve the electromechanical coupling coefficient k(%) of the main mode.

[0544] The following will provide additional notes on a part or all of the embodiments of the present invention. However, the present invention is not limited to the following additional notes.

[0545] <1>

[0546] A piezoelectric vibration element, comprising:

[0547] A piezoelectric sheet having a first main surface and a second main surface opposite to the first main surface;

[0548] A first excitation electrode is disposed on the first main surface; and

[0549] A second excitation electrode is disposed on the second main surface;

[0550] When viewed from above in the direction in which the first main surface and the second main surface are opposed to each other, the area of ​​the second excitation electrode is larger than that of the first excitation electrode, and a part of the second excitation electrode overlaps the entirety of the first excitation electrode.

[0551] The thickness of the second excitation electrode along the opposing direction is greater than the thickness of the first excitation electrode along the opposing direction.

[0552] <2>

[0553] The piezoelectric vibration element according to <1>,

[0554] In a plan view in the opposing direction, all outer edge portions of the first excitation electrodes are located inside the outer edge portions of the second excitation electrodes.

[0555] <3>

[0556] The piezoelectric vibration element according to <1> or <2>, wherein:

[0557] The thickness of the first excitation electrode along the opposing direction is Te (μm), the thickness of the second excitation electrode along the opposing direction is Te2 (μm), and the thickness of the piezoelectric sheet along the opposing direction is Tq (μm).

[0558] The average density of the first excitation electrode and the second excitation electrode is ρ (kg / m 3 ), the following relationship holds:

[0559] Te2 / Tq=0.00001×ρ+0.39×Te / Tq+0.16±0.01.

[0560] <4>

[0561] A piezoelectric vibration element, comprising:

[0562] A piezoelectric sheet having a first main surface and a second main surface opposite to the first main surface;

[0563] A first excitation electrode is disposed on the first main surface;

[0564] A second excitation electrode is disposed on the second main surface; and

[0565] an insulating film stacked on the second excitation electrode,

[0566] When viewed from above in the direction in which the first main surface and the second main surface are opposed to each other, the area of ​​the stacked body composed of the second excitation electrode and the insulating film is larger than the area of ​​the first excitation electrode, and a part of the stacked body overlaps the entirety of the first excitation electrode.

[0567] The sum of the thickness of the second excitation electrode along the opposing direction and the thickness of the insulating film is greater than the thickness of the first excitation electrode along the opposing direction.

[0568] <5>

[0569] The piezoelectric vibration element according to <4>,

[0570] The insulating film is stacked on a surface of the second excitation electrode on the opposite side to the piezoelectric sheet.

[0571] <6>

[0572] The piezoelectric vibration element according to <4> or <5>, wherein:

[0573] When looking down from the opposite direction,

[0574] The outer edge of the second excitation electrode is entirely provided on the inner side than the outer edge of the first excitation electrode.

[0575] The outer edge portion of the insulating film is entirely provided outside the outer edge portion of the first excitation electrode.

[0576] <7>

[0577] The piezoelectric vibration element according to any one of <4> to <6>,

[0578] The thickness of the second excitation electrode along the opposing direction is smaller than the thickness of the first excitation electrode along the opposing direction.

[0579] <8>

[0580] The piezoelectric vibration element according to any one of <4> to <7>,

[0581] When the thickness of the first excitation electrode along the opposing direction is Te (μm), the thickness of the second excitation electrode along the opposing direction is Te2 (μm), the thickness of the insulating film along the opposing direction is Te3 (μm), and the thickness of the piezoelectric sheet along the opposing direction is Tq (μm),

[0582] The average density of the first excitation electrode, the second excitation electrode, and the insulating film is ρ' (kg / m 3 ), the following relationship holds:

[0583] (Te2+Te3) / Tq=0.00001×ρ'+0.39×Te / Tq+0.16±0.01.

[0584] <9>

[0585] The piezoelectric vibration element according to <8>,

[0586] The first excitation electrode and the second excitation electrode are made of aluminum.

[0587] The material of the insulating film is silicon oxide.

[0588] <10>

[0589] The piezoelectric vibration element according to any one of <1> to <9>, further comprising:

[0590] a first extraction electrode, disposed on the first main surface and electrically connected to the first excitation electrode; and

[0591] The second extraction electrode is disposed on the second main surface and is electrically connected to the second excitation electrode.

[0592] A notch is formed in a region of the first excitation electrode and the second excitation electrode having a larger area when viewed from above in the opposing direction and electrically connected to the first extraction electrode and the second extraction electrode having a smaller area when viewed from above in the opposing direction.

[0593] <11>

[0594] The piezoelectric vibration element according to any one of <1> to <10>, further comprising:

[0595] a first extraction electrode, disposed on the first main surface and electrically connected to the first excitation electrode; and

[0596] The second extraction electrode is disposed on the second main surface and is electrically connected to the second excitation electrode.

[0597] The center of the excitation electrode with a larger area when viewed from above in the opposing direction between the first excitation electrode and the second excitation electrode is offset relative to the center of the excitation electrode with a smaller area when viewed from above in the opposing direction toward a direction separating from the lead-out electrode electrically connected to the excitation electrode with a smaller area between the first lead-out electrode and the second lead-out electrode.

[0598] <12>

[0599] The piezoelectric vibration element according to any one of <1> to <11>,

[0600] In a plan view in the opposing direction, the region where the first excitation electrode and the second excitation electrode face each other has a high-speed sound region provided in the center and a low-speed sound region provided outside the high-speed sound region.

[0601] <13>

[0602] The piezoelectric vibration element according to any one of <1> to <12>, wherein

[0603] When viewed from above in the opposing direction, the first excitation electrode and the second excitation electrode are arranged in a rectangular shape with their centers overlapping each other, and have mutually parallel sides extending in a first direction and mutually parallel sides extending in a second direction intersecting the first direction.

[0604] When viewed from above in the opposing direction, the distance between the adjacent sides of the first excitation electrode and the second excitation electrode in a certain direction is denoted as De (μm).

[0605] When the thickness of the piezoelectric sheet along the opposing direction is Tq (μm), the following relationship holds:

[0606] 5.22×Tq-0.45≤De.

[0607] <14>

[0608] The piezoelectric vibration element according to any one of <1> to <13>,

[0609] The main vibration mode is thickness shear vibration.

[0610] <15>

[0611] The piezoelectric vibration element according to any one of <1> to <14>,

[0612] Piezoelectric plates are crystalline plates.

[0613] <16>

[0614] The piezoelectric vibration element according to <15>,

[0615] The cutting angle of the crystal piece is AT cut, BT cut or ST cut.

[0616] In addition, in this specification, a crystal resonator element (quartz crystal resonator) having a crystal piece (quartz crystal element) as a piezoelectric piece (piezoelectric element) is described as an example, but the piezoelectric resonator element (piezoelectric resonator) is not limited to this. As a piezoelectric piece suitable for the piezoelectric resonator involved in this embodiment, for example, piezoelectric ceramics such as lead zirconate titanate (PZT) and aluminum nitride, and piezoelectric single crystals such as lithium niobate and lithium tantalate can be cited, but it is not limited to these and can be appropriately selected.

[0617] The embodiments of the present invention are not particularly limited and can be appropriately applied to any device that performs electromechanical energy conversion by piezoelectric effect, such as a timer, a sound generator, an oscillator, and a load sensor.

[0618] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibration element capable of improving the electromechanical coupling coefficient.

[0619] In addition, the above-described embodiments are for easy understanding of the content of the present invention, and are not intended to be interpreted as limiting the content of the present invention. The present invention can be changed / improved without departing from its purport, and the present invention also includes its equivalents. That is, as long as the solution obtained by appropriately implementing the design changes for the embodiments and / or variations by those skilled in the art has the features of the present invention, it is included in the scope of the present invention. For example, the various elements and their configurations, materials, conditions, shapes, sizes, etc. possessed by the embodiments and / or variations are not limited to the illustrated contents and can be appropriately changed. In addition, the embodiments and variations are illustrative, and of course, the replacement or combination of the parts of the components shown in different embodiments and / or variations can be performed, as long as these include the features of the present invention, they are included in the scope of the present invention.

[0620] Description of Reference Numerals

[0621] 1…crystal oscillator; 10…crystal oscillator element; 11…crystal plate; 11A…upper surface; 11B…lower surface; 14a…first excitation electrode; 14b…second excitation electrode; 15a…first lead-out electrode; 15b…second lead-out electrode; 16a…first connecting electrode; 16b…second connecting electrode; Lq…length of the crystal plate along the X-axis direction; Wq…length of the crystal plate along the Z'-axis direction; Tq…thickness of the crystal plate; Le…length of the first excitation electrode along the X-axis direction; We…length of the first excitation electrode along the Z'-axis direction; Te…thickness of the first excitation electrode; Le2…length of the second excitation electrode along the X-axis direction; We2…length of the second excitation electrode along the Z'-axis direction; Te2…thickness of the second excitation electrode.

Claims

1. A piezoelectric vibration element, comprising: A piezoelectric sheet having a first main surface and a second main surface opposite to the first main surface; A first excitation electrode is disposed on the first main surface; and The second excitation electrode is provided on the second main surface. When viewed from above in the direction in which the first main surface and the second main surface are opposite to each other, the area of ​​the second excitation electrode is larger than that of the first excitation electrode, and a part of the second excitation electrode overlaps the entirety of the first excitation electrode. A thickness of the second excitation electrode along the opposing direction is greater than a thickness of the first excitation electrode along the opposing direction.

2. The piezoelectric vibration element according to claim 1, wherein When viewed in plan in the opposing direction, all outer edge portions of the first excitation electrodes are located inside of outer edge portions of the second excitation electrodes.

3. The piezoelectric vibration element according to claim 1 or 2, wherein: When the thickness of the first excitation electrode along the opposing direction is Te (μm), the thickness of the second excitation electrode along the opposing direction is Te2 (μm), and the thickness of the piezoelectric sheet along the opposing direction is Tq (μm), The average density of the first excitation electrode and the second excitation electrode is ρ (kg / m 3 ), the following relationship holds: Te2 / Tq=0.00001×ρ+0.39×Te / Tq+0.16±0.

01.

4. A piezoelectric vibration element, comprising: A piezoelectric sheet having a first main surface and a second main surface opposite to the first main surface; A first excitation electrode is disposed on the first main surface; A second excitation electrode is disposed on the second main surface; and an insulating film stacked on the second excitation electrode, When viewed from above in the direction in which the first main surface and the second main surface are opposite to each other, the area of ​​the stacked body composed of the second excitation electrode and the insulating film is larger than the area of ​​the first excitation electrode, and a part of the stacked body overlaps the entirety of the first excitation electrode. A sum of a thickness of the second excitation electrode along the opposing direction and a thickness of the insulating film is greater than a thickness of the first excitation electrode along the opposing direction.

5. The piezoelectric vibration element according to claim 4, wherein: The insulating film is stacked on a surface of the second excitation electrode on the opposite side to the piezoelectric sheet.

6. The piezoelectric vibration element according to claim 4 or 5, wherein: When looking down in the above-mentioned opposite direction, The outer edge of the second excitation electrode is entirely provided on the inner side than the outer edge of the first excitation electrode. The outer edge portion of the insulating film is entirely provided outside the outer edge portion of the first excitation electrode.

7. The piezoelectric vibration element according to any one of claims 4 to 6, wherein: A thickness of the second excitation electrode along the opposing direction is smaller than a thickness of the first excitation electrode along the opposing direction.

8. The piezoelectric vibration element according to any one of claims 4 to 7, wherein: When the thickness of the first excitation electrode along the opposing direction is Te (μm), the thickness of the second excitation electrode along the opposing direction is Te2 (μm), the thickness of the insulating film along the opposing direction is Te3 (μm), and the thickness of the piezoelectric sheet along the opposing direction is Tq (μm), The average density of the first excitation electrode, the second excitation electrode, and the insulating film is ρ' (kg / m 3 ), the following relationship holds: (Te2+Te3) / Tq=0.00001×ρ'+0.39×Te / Tq+0.16±0.

01.

9. The piezoelectric vibration element according to claim 8, wherein: The first excitation electrode and the second excitation electrode are made of aluminum. The insulating film is made of silicon oxide.

10. The piezoelectric vibration element according to any one of claims 1 to 9, wherein Also available: a first extraction electrode disposed on the first main surface and electrically connected to the first excitation electrode; and a second extraction electrode disposed on the second main surface and electrically connected to the second excitation electrode; A notch is formed in a region opposing an excitation electrode of the first excitation electrode and the second excitation electrode having a larger area when viewed from above in the opposing direction and electrically connected to an excitation electrode of the first lead-out electrode and the second lead-out electrode having a smaller area when viewed from above in the opposing direction.

11. The piezoelectric vibration element according to any one of claims 1 to 10, wherein Also available: a first extraction electrode disposed on the first main surface and electrically connected to the first excitation electrode; and a second extraction electrode disposed on the second main surface and electrically connected to the second excitation electrode; The center of the excitation electrode with a larger area when viewed from above in the opposing direction among the first excitation electrode and the second excitation electrode is offset relative to the center of the excitation electrode with a smaller area when viewed from above in the opposing direction in a direction away from the lead-out electrode electrically connected to the excitation electrode with the smaller area among the first lead-out electrode and the second lead-out electrode.

12. The piezoelectric vibration element according to any one of claims 1 to 11, wherein When viewed in plan in the opposing direction, the region where the first excitation electrode and the second excitation electrode face each other includes a high-speed sound region provided in the center and a low-speed sound region provided outside the high-speed sound region.

13. The piezoelectric vibration element according to any one of claims 1 to 12, wherein: The first excitation electrode and the second excitation electrode are provided in a rectangular shape with their centers overlapping each other when viewed in a plan view in the opposing direction. The first excitation electrode and the second excitation electrode have mutually parallel sides extending in a first direction and mutually parallel sides extending in a second direction intersecting the first direction. When viewed in plan in the opposing direction, let De (μm) be a distance between adjacent sides of the first excitation electrode and the second excitation electrode in a certain direction. When the thickness of the piezoelectric sheet along the opposing direction is Tq (μm), the following relationship holds: 5.22×Tq-0.45≤De.

14. The piezoelectric vibration element according to any one of claims 1 to 13, wherein The main vibration mode is thickness shear vibration.

15. The piezoelectric vibration element according to any one of claims 1 to 14, wherein The above-mentioned piezoelectric plate is a quartz crystal plate.

16. The piezoelectric vibration element according to claim 15, wherein: The cutting angle of the above-mentioned crystal piece is AT-cut, BT-cut or ST-cut.

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