Piezoelectric vibrator

Abstract

The piezoelectric vibrator (10) includes a piezoelectric element (11) having a first main surface (11A) and a second main surface (11B) facing the first main surface (11A), a first exciting electrode (14a) provided on the first main surface (11A), and a second exciting electrode (14b) provided on the second main surface (11B). 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 area of the second exciting electrode (14b) is larger than the area of the first exciting electrode (14a), and a part of the second exciting electrode (14b) overlaps all of the first exciting electrode (14a). The thickness (Te2) of the second exciting electrode (14b) along the facing direction is larger than the thickness (Te) of the first exciting electrode (14a) along the facing direction.

Description

Technical Field

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

Background Art

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

[0003] For example, Patent Document 1 discloses a vibration element that vibrates in thickness-shear vibration and includes a substrate including a first main surface and a second main surface that are related to the front and back, a first excitation electrode provided on the first main surface, and a second excitation electrode provided on the second main surface and larger than the first excitation electrode in plan view, and the first excitation electrode is arranged so as to be within the outer edge of the second excitation electrode in plan view.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] By the way, with the improvement of the performance of electronic devices, piezoelectric vibration elements having a high electromechanical coupling coefficient are required.

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

Means for Solving the Problems

[0007] A piezoelectric vibration element according to one aspect of the present invention includes a piezoelectric piece having a first main surface and a second main surface facing the first main surface, a first excitation electrode provided on the first main surface, and a second excitation electrode provided on the second main surface. In a plan view in the facing direction in which the first main surface and the second main surface face each other, the area of the second excitation electrode is larger than the area of the first excitation electrode, and a part of the second excitation electrode overlaps with all of the first excitation electrode. The thickness of the second excitation electrode along the facing direction is larger than the thickness of the first excitation electrode along the facing direction.

[0008] A piezoelectric vibration element according to another aspect of the present invention includes a piezoelectric piece having a first main surface and a second main surface facing the first main surface, a first excitation electrode provided on the first main surface, a second excitation electrode provided on the second main surface, and an insulating film laminated on the second excitation electrode. In a plan view in the facing direction in which the first main surface and the second main surface face each other, the area of the laminate 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 laminate overlaps with all of the first excitation electrode. The sum of the thickness of the second excitation electrode and the thickness of the insulating film along the facing direction is larger than the thickness of the first excitation electrode along the facing direction.

Advantages of the Invention

[0009] 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

[0010]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Figure 31

Figure 32

Figure 33

Figure 34

Figure 35

Embodiments for Carrying Out the Invention

[0011] Embodiments of the present invention will be described below. In the following description of the drawings, the same or similar components are denoted by the same or similar reference numerals. The drawings are illustrative, and the dimensions and shapes of each part are schematic, and the technical scope of the present invention should not be construed as being limited to the embodiments.

[0012] For each drawing, for the purpose of clarifying the mutual relationship between the drawings and assisting in understanding the positional relationship of each member, a rectangular coordinate system composed of an X-axis, a Y'-axis, and a Z'-axis may be attached for convenience. The X-axis, Y'-axis, and Z'-axis correspond to each other in each drawing. The X-axis, Y'-axis, and Z'-axis respectively correspond to the crystallographic axes of the crystal piece 11 described later. The X-axis corresponds to the electrical axis (polar axis) of the crystal, the Y-axis corresponds to the mechanical axis of the crystal, and the Z-axis corresponds to the optical axis of the crystal. The Y'-axis and Z'-axis are respectively the axes obtained by rotating the Y-axis and Z-axis counterclockwise by θ degrees around the X-axis when viewed from the positive direction of the X-axis direction.

[0013] 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". Also, the tip direction of the arrows of the X-axis, Y'-axis, and Z'-axis is referred to as "positive" or "+", and the direction opposite to the arrow is referred to as "negative" or "-". 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 up and down directions of the crystal oscillator 10 and the crystal resonator 1 are not limited. Also, the plane specified by the X-axis and Z'-axis is defined as the Z'X plane, and the same applies to the planes specified by other axes.

[0014] <First Embodiment>

[0015] First, with reference to FIGS. 1 to 3, the configuration of the crystal resonator according to the first embodiment will be described. FIG. 1 is an exploded perspective view of the crystal resonator according to the first embodiment. FIG. 2 is a plan view of the vibrating portion according to the first embodiment. FIG. 3 is a cross-sectional view of the vibrating portion according to the first embodiment. Note that FIG. 3 is a cross-sectional view taken along line III-III of the vibrating portion shown in FIG. 2.

[0016] The crystal oscillator 1 includes a crystal vibration element 10, a lower cover 20, an upper cover 30, a lower joint portion 40, and an upper joint portion 50. The lower cover 20, the crystal vibration element 10, and the upper cover 30 are arranged at intervals in the Y' - axis direction in this order. Hereinafter, the Y' - axis direction in which the lower cover 20, the crystal vibration element 10, and the upper cover 30 are stacked is referred to as the "thickness direction". The Y' - axis direction is an example of the "opposing direction".

[0017] The crystal oscillator 1 is used, for example, as a component of 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).

[0018] The crystal vibration element 10 is an electromechanical energy conversion element that mutually converts electrical energy and mechanical energy by the piezoelectric effect. As shown in FIG. 1, the crystal vibration element 10 has a vibration portion 110, a holding portion 120, and a support arm 130.

[0019] The vibration portion 110 is excited at a predetermined frequency based on the applied alternating voltage. The vibration portion 110 is held so as to be vibratable in a vibration space provided between the lower cover 20 and the upper cover 30. The main vibration of the vibration portion 110 is the thickness - shear vibration mode. As shown in FIG. 2, when the XZ' plane is viewed in plan view (hereinafter simply referred to as "plan view"), the shape of the vibration portion 110 (hereinafter referred to as "planar shape") is a rectangular shape 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 direction and face each other in the X - axis direction. The pair of long sides 113, 114 extend along the X - axis direction and face outward in the Z' - axis direction.

[0020] Note that the main vibration of the vibrating part is not limited to the thickness sliding vibration mode. For example, it may be a thickness longitudinal vibration mode, a spreading vibration mode, a length vibration mode, or a bending vibration mode. Further, the planar shape of the vibrating part is not limited to a rectangular shape. For example, it may be a square shape, a polygonal shape, a circular shape, an elliptical shape, or a combination thereof.

[0021] The holding part 120 is a part for holding the vibrating part 110. The holding part 120, together with the lower lid 20, the upper lid 30, the lower joint part 40, and the upper joint part 50, forms a vibration space for the vibrating part 110. When viewed in plan, the holding part 120 is provided in a frame shape so as to surround the vibrating part 110 with a space therebetween. The holding part 120 has frame parts 121A, 121B, 121C, and 121D.

[0022] The frame parts 121A, 121B, 121C, and 121D are each a part of a substantially rectangular frame surrounding the vibrating part 110. As shown in FIGS. 1 and 2, the frame part 121A is provided at a distance from the short side 111 of the vibrating part 110 in the X-axis direction and extends parallel to the short side 111 along the Z'-axis direction. The frame part 121B is provided at a distance from the short side 112 of the vibrating part 110 in the X-axis direction and extends parallel to the short side 112 along the Z'-axis direction. The frame part 121C is provided at a distance from the long side 113 of the vibrating part 110 in the Z'-axis direction and extends parallel to the long side 113 along the X-axis direction. The frame part 121D is provided at a distance from the long side 114 of the vibrating part 110 in the Z'-axis direction and extends parallel to the long side 114 along the X-axis direction.

[0023] Both ends of the frame part 121C are connected to one end of the frame part 121A and one end of the frame part 121B, respectively. Both ends of the frame part 121D are connected to the other end of the frame part 121A and the other end of the frame part 121B, respectively. The frame part 121A and the frame part 121B face each other in the X-axis direction with the vibrating part 110 interposed therebetween. The frame part 121C and the frame part 121D face each other in the Z'-axis direction with the vibrating part 110 interposed therebetween.

[0024] Note that the holding part only needs to be provided on at least a part of the periphery of the vibrating part, and is not limited to a frame shape. The holding part may be provided, for example, in a rail shape having two parallel frame parts.

[0025] The support arm 130 supports the vibrating part 110 and holds the vibrating part 110 in the holding part 120. The support arm 130 connects the vibrating part 110 and the holding part 120. As shown in FIGS. 1 and 2, the support arm 130 connects the end of the vibrating part 110 on the short side 112 side and the frame part 121B of the holding part 120. The support arm 130 extends in the X-axis direction.

[0026] The lower cover 20 faces the vibrating part 110, the holding part 120, and the support arm 130 of the crystal oscillator 10 with a space in the Y'-axis direction. The lower cover 20 is provided in a flat plate shape. As shown in FIG. 1, when viewed in plan, 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. Also, the pair of long sides and the pair of short sides of the lower cover 20 are connected by sides inclined with respect to the pair of long sides and the pair of short sides. That is, notches are formed at the four corners of the lower cover 20 in plan view.

[0027] The upper cover 30 faces the vibrating part 110, the holding part 120, and the support arm 130 of the crystal oscillator 10 with a space in the Y'-axis direction on the side opposite to the lower cover 20. The upper cover 30 is provided in a flat plate shape. As shown in FIG. 1, when viewed in plan, the upper cover 30 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. The planar shape of the upper cover 30 is rectangular.

[0028] The lower bonding portion 40 and the upper bonding portion 50 are provided in a frame shape along the holding portion 120 of the quartz vibrating element 10. The lower bonding portion 40 bonds the holding portion 120 of the quartz vibrating element 10 to an end of the lower lid 20. The upper bonding portion 50 bonds the holding portion 120 of the quartz vibrating element 10 to an end of the upper lid 30. The lower bonding portion 40 and the upper bonding portion 50 are provided by an organic adhesive containing, for example, an epoxy-based, vinyl-based, acrylic-based, urethane-based, or silicone-based resin.

[0029] The material of the lower and upper joints is not limited to organic adhesives, and may be inorganic adhesives such as silicon-based adhesives containing water glass, calcium-based adhesives containing cement, etc. The material of the lower and upper joints may be low-melting glass (e.g., lead borate-based or tin phosphate-based). The material of the lower and upper joints may be gold (Au), tin (Sn), copper (Cu), titanium (Ti), aluminum (Al), germanium (Ge), silicon (Si), or a eutectic alloy containing at least one of these.

[0030] Next, the detailed configurations of the crystal vibrating element 10, the lower cover 20, and the upper cover 30 will be described.

[0031] The quartz crystal vibrating element 10 includes a quartz crystal blank 11, a first excitation electrode 14a, a second excitation electrode 14b, a first extraction electrode 15a, a second extraction electrode 15b, a first connection electrode 16a, and a second connection electrode 16b.

[0032] The quartz crystal blank 11 is a type of piezoelectric blank made of a piezoelectric body that vibrates in response to an applied voltage. The quartz crystal blank 11 is provided continuously across the vibrating part 110, the holding part 120, and the support arm 130. In the XZ' plane direction, the quartz crystal blank 11 extends over almost the entire area of ​​each of the vibrating part 110, the holding part 120, and the support arm 130. The quartz crystal blank 11 is a thin flake of quartz crystal with the XZ' plane as its main surface.

[0033] The crystal piece 11 is, for example, an AT-cut crystal piece. That is, the rotation angle θ of the Z'-axis and Y'-axis counterclockwise from the Z-axis and Y-axis as viewed from the positive X-axis direction side is 35 degrees 15 minutes ± 1 minute 30 seconds. The crystal oscillator 10 using the AT-cut crystal piece 11 has high frequency stability in a wide temperature range.

[0034] Note that the cut angle of the crystal piece is not limited to the above. The rotation angles of the Y'-axis and Z'-axis in the AT-cut type crystal piece 11 may be inclined within the range of -5 degrees or more or +15 degrees or less from 35 degrees 15 minutes. Also, different cuts other than AT-cut, such as BT-cut, GT-cut, SC-cut, etc., may be applied to the cut angle of the crystal piece.

[0035] The planar shape of the crystal piece 11 in the vibrating portion 110 is a rectangular shape having a long side along the X-axis direction and a short side along the Z'-axis direction. As shown in FIG. 3, in the vibrating portion 110, the crystal piece 11 has an upper surface 11A provided on the upper lid 30 side and a lower surface 11B provided on the lower lid 20 side. The upper surface 11A and the lower surface 11B correspond to an example of a pair of main surfaces facing each other in the Y'-axis direction of the crystal piece 11.

[0036] Note that the planar shape of the vibrating portion of the crystal piece is not limited to the above. For example, the planar shape of the vibrating portion of the crystal piece may be a rectangular shape having a long side extending in the Z'-axis direction and a short side extending in the X-axis direction, or a rectangular shape having a short side extending in the Z'-axis direction and a long side extending in the X-axis direction. The planar shape of the vibrating portion of the crystal piece may be a polygonal shape, a circular shape, an elliptical shape, or a combination thereof. Also, the vibrating portion of the crystal piece is not limited to a flat plate shape. The vibrating portion of the crystal piece may be a mesa-type structure or an inverse mesa-type structure having unevenness on at least one of the upper surface and the lower surface. The vibrating portion of the crystal piece may be a convex structure in which the amount of change in thickness changes continuously, or a bevel structure in which the amount of change in thickness changes discontinuously.

[0037] The first excitation electrode 14a and the second excitation electrode 14b apply an alternating voltage to the crystal piece 11 of the vibrating part 110 to excite the vibrating part 110. As shown in FIG. 3, the first excitation electrode 14a is provided on the upper surface 11A of the crystal piece 11 in the vibrating part 110, and the second excitation electrode 14b is provided on the lower surface 11b of the crystal piece 11 in the vibrating part 110. The first excitation electrode 14a and the second excitation electrode 14b face each other in the Y' axis direction with the crystal piece 11 interposed therebetween.

[0038] As shown in FIG. 2, 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 part of the second excitation electrode 14b overlaps the whole of the first excitation electrode 14a. The first excitation electrode 14a and the second excitation electrode 14b are provided at the central part of the vibrating part 110, and the center of the first excitation electrode 14a overlaps the center of the second excitation electrode 14b.

[0039] Note that the positions of the first excitation electrode and the second excitation electrode are not limited to the central part of the vibrating part. In a plan view, the first excitation electrode and the second excitation electrode may be provided closer to the outside from the central part of the vibrating part. Also, the positions of the centers of the first excitation electrode and the second excitation electrode are not limited to positions overlapping each other. In a plan view, the center of the first excitation electrode may be separated from the center of the second excitation electrode.

[0040] The planar shape of the first excitation electrode 14a is a rectangular shape having a short side extending in the Z' axis direction and a long side extending in the X axis direction. The planar shape of the second excitation electrode 14b is the same as the planar shape of the first excitation electrode 14a. That is, the first excitation electrode 14a and the second excitation electrode 14b have a short side parallel to the short side of the vibrating part 110 and a short side parallel to the long side of the vibrating part 110. Also, the first excitation electrode 14a and the second excitation electrode 14b have a thickness in the Y' axis direction, and the thickness of the second excitation electrode 14b is larger than the thickness of the first excitation electrode 14a.

[0041] Note that the planar shapes of the first excitation electrode and the second excitation electrode are not limited to the above. The planar shapes of the first excitation electrode and the second excitation electrode may be rectangular shapes having short sides extending in the X-axis direction. The planar shapes of the first excitation electrode and the second excitation electrode may be square shapes, polygonal shapes, circular shapes, elliptical shapes, or combinations thereof. Further, the planar shape of the first excitation electrode is not limited to being the same as the planar shape of the second excitation electrode, and the planar shapes of the first excitation electrode and the second excitation electrode may be different from each other.

[0042] The first lead electrode 15a electrically connects the first excitation electrode 14a and the first connection electrode 16a. As shown in FIG. 1, the first lead electrode 15a drawn from the first excitation electrode 14a extends across the upper surface of the vibration part 110, the support arm 130, and the frame part 121B of the holding part 120, and the side surface of the holding part 120, and is electrically connected to the first connection electrode 16a provided on the lower surface of the holding part 120. The second lead electrode 15b drawn from the second excitation electrode 14b extends across the lower surface, side surface, and upper surface of the vibration part 110 and the support arm 130, the upper surfaces of the frame parts 121B and 121D of the holding part 120, and the side surface of the holding part 120, and is electrically connected to the second connection electrode 16b provided on the lower surface of the holding part 120.

[0043] 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. As shown in FIG. 1, the first connection electrode 16a is provided on the lower surface (the surface on the lower lid 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.

[0044] The first excitation electrode 14a, the first lead-out electrode 15a, and the first connection electrode 16a are integrally provided. The same applies to the second excitation electrode 14b, the second lead-out electrode 15b, and the second connection electrode 16b. The electrodes of these crystal vibration elements 10 are, for example, of a single-layer structure composed of an aluminum layer. The electrodes of the crystal vibration element 10 may also be of a multilayer structure provided by laminating a base layer and a surface layer in this order. For example, the base layer is a chromium (Cr) layer with good adhesion to the crystal piece 11, and the surface layer is a gold (Au) layer with good chemical stability. The electrodes of the crystal vibration element 10 may contain silver (Ag), copper (Cu), titanium (Ti), molybdenum (Mo), or an aluminum-copper alloy (AlCu).

[0045] The lower lid 20 has a crystal piece 21, power supply terminals ST1 and ST2, and dummy terminals DT1 and DT2. The crystal piece 21 is a flat substrate that overlaps substantially the entire crystal vibration element 10 in plan view. The crystal piece 21 is formed of a crystal crystal with the same cut angle as the crystal piece 11 of the crystal vibration element 10. According to this, it is possible to reduce the thermal stress caused by the difference in the coefficient of thermal expansion and the difference in the direction of thermal expansion and contraction between the crystal vibration element 10 and the lower lid 20. Thereby, it is possible to suppress the variation in the frequency of the crystal vibration element 10. The crystal piece 21 has an upper surface 21A provided on the side of the crystal vibration element 10 and a lower surface 21B provided on the side opposite to the upper surface 21A. When viewed in plan, the crystal piece 21 has a long side extending along the X-axis direction and a short side extending along the Z'-axis direction. Also, when viewed in plan, the side surface connecting the upper surface 21A and the lower surface 21B of the crystal piece 21 overlaps the outer 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 in plan view is smaller than the area of the crystal piece 31 to be described later by the amount of this notch. The shape of the side surface formed by the notch at the corner of the crystal piece 21 is, for example, planar. However, 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 be a curved surface shape that is a part of a cylinder or a prism.

[0046] The power supply terminals ST1, ST2 and the dummy terminals DT1, DT2 are provided on the lower surface 21B of the crystal piece 21. The power supply terminals ST1, ST2 and the dummy terminals DT1, DT2 correspond to an example of the external terminals of the crystal oscillator 1. The power supply terminals ST1, ST2 are for applying a drive signal (drive voltage) to the crystal oscillator 1. The power supply terminal ST1 is electrically connected to the first connection electrode 16a through the notch at the corner of the crystal piece 21 and the side electrode provided on the outer surface of the lower joint portion 40. The power supply terminal ST2 is electrically connected to the second connection electrode 16b through the notch at the corner of the crystal piece 21 and the side electrode provided on the outer surface of the lower joint portion 40. The dummy terminals DT1, DT2 are for taking a balance of electrical characteristics such as capacitance and a balance of mechanical strength between the power supply terminals ST1, ST2. The dummy terminals DT1, DT2 are so-called floating electrodes that are not electrically connected to the crystal vibration element 10.

[0047] Note that at least one of the dummy terminals DT1, DT2 may be a ground electrode that electrically grounds a part of the crystal oscillator 1.

[0048] The upper lid 30 has a crystal piece 31. The crystal piece 31 is a flat substrate that overlaps substantially the whole of the crystal vibration element 10 in plan view. The crystal piece 31 is formed of a crystal having the same cut angle as the crystal piece 11 of the crystal vibration element 10. According to this, the thermal stress caused by the difference in the coefficient of thermal expansion and the difference in the direction of thermal expansion and contraction between the crystal vibration element 10 and the upper lid 30 can be reduced. Thereby, the variation in the frequency of the crystal vibration element 10 can be suppressed. The crystal piece 31 has a lower surface 31B provided on the crystal vibration element 10 side and an upper surface 31A provided on the side opposite to the lower surface 31B. When viewed in plan, the crystal piece 31 has a rectangular shape having a long side extending along the X-axis direction and a short side extending along the Z'-axis direction. Further, when viewed in plan, the side surface connecting the upper surface 31A and the lower surface 31B of the crystal piece 31 overlaps the outer surface of the holding portion 120 in the crystal vibration element 10.

[0049] Note that the cut angles of the crystal pieces of the lower cover and the upper cover are not particularly limited and may be different from the cut angles of the crystal pieces of the crystal vibration element. Further, the lower cover and the upper cover may have a glass substrate, a silicon substrate, a ceramic substrate, a metal substrate, or the like instead of the crystal piece.

[0050] Next, with reference to FIGS. 2 and 3, the detailed configuration of the vibrating portion 110 will be described.

[0051] 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 X-axis side among the edges of the four sides of the first excitation electrode 14a in plan view. The outer edge portion 72 is an edge portion of one side extending along the Z'-axis on the positive X-axis side, the outer edge portion 73 is an edge portion of one side extending along the X-axis on the positive Z'-axis side, and the outer edge portion 74 is an edge portion of one side extending along the X-axis on the negative Z'-axis side. That is, with respect to the central portion of the first excitation electrode 14a in 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.

[0052] 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 X-axis side among the edges of the four sides of the second excitation electrode 14b in plan view. The outer edge portion 82 is an edge portion of one side extending along the Z'-axis on the positive X-axis side, the outer edge portion 83 is an edge portion of one side extending along the X-axis on the positive Z'-axis side, and the outer edge portion 84 is an edge portion of one side extending along the X-axis on the negative Z'-axis side. That is, with respect to the central portion of the second excitation electrode 14b in 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.

[0053] As shown in FIG. 2, in a plan view, all of the outer edge portions 71, 72, 73, 74 of the first excitation electrode 14a are located inside the outer edge portions 81, 82, 83, 84 of the second excitation electrode 14b. The outer edge portion 81 is adjacent to the outer edge portion 71 among the outer edge portions 71, 72, 73, 74, the outer edge portion 82 is adjacent to the outer edge portion 72 among the outer edge portions 71, 72, 73, 74, the outer edge portion 83 is adjacent to the outer edge portion 73 among the outer edge portions 71, 72, 73, 74, and the outer edge portion 84 is adjacent to the outer edge portion 74 among the outer edge portions 71, 72, 73, 74. In a plan view, the outer edge portion 71 and the outer edge portion 81 are provided in parallel, the outer edge portion 72 and the outer edge portion 82 are provided in parallel, the outer edge portion 73 and the outer edge portion 83 are provided in parallel, and the outer edge portion 74 and the outer edge portion 84 are provided in parallel.

[0054] As shown in FIG. 2, in a plan view, let the dimension along the X-axis direction of the vibrating portion 110 be the length Lq, and the dimension along the Z'-axis direction of the vibrating portion 110 be the length Wq. Let the dimension along the X-axis direction of the first excitation electrode 14a be the length Le, and the dimension along the Z'-axis direction of the first excitation electrode 14a be the length We. Let the dimension along the X-axis direction of the second excitation electrode 14b be the length Le2, and the dimension along the Z'-axis direction of the second excitation electrode 14b be the length We2.

[0055] The length Lq is specified, for example, as the distance along the X-axis direction between the short sides 111 and 112 at a predetermined position. The predetermined position is, for example, on a straight line passing through the center of the vibrating portion 110 in a plan view and extending along the X-axis direction. The length Lq may be specified as the average value or the maximum value of the distance along the X-axis direction between the short sides 111 and 112. The length Wq is specified, for example, as the distance along the Z'-axis direction between the long sides 113 and 114 at a predetermined position. The predetermined position is, for example, on a straight line passing through the center of the vibrating portion 110 in a plan view and extending along the Z'-axis direction. The length Wq may be specified as the average value or the maximum value of the distance along the Z'-axis direction between the long sides 113 and 114.

[0056] Similarly, the length Le is specified 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 extending along the X-axis direction passing through the center of the first excitation electrode 14a), or as 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 specified 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 extending along the Z'-axis direction passing through the center of the first excitation electrode 14a), or as 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 specified 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 extending along the X-axis direction passing through the center of the second excitation electrode 14b), or as 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 specified as the distance along the Z'-axis direction between the outer edge portion 83 and the outer edge portion 84 at a predetermined position (for example, on a straight line extending along the Z'-axis direction passing through the center of the second excitation electrode 14b), or as the average value or the maximum value of the distance along the Z'-axis direction between the outer edge portion 83 and the outer edge portion 84.

[0057] When comparing the length Le and the length Le2, etc., the length Le and the length Le2 are specified by the same specifying method. That is, if the length Le is specified as the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 72 at a predetermined position, then the length Le2 is specified as the distance along the X-axis direction between the outer edge portion 81 and the outer edge portion 82 at a predetermined position. If the length Le is specified as the average value of the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 72, then the length Le2 is specified as the average value of the distance along the X-axis direction between the outer edge portion 81 and the outer edge portion 82. If the length Le is specified as the maximum value of the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 72, then the length Le2 is specified as the maximum value of the distance along the X-axis direction between the outer edge portion 81 and the outer edge portion 82. The specifying method is unified in the same way when comparing other lengths and thicknesses, etc.

[0058] Since the planar shape of the vibrating portion 110 is rectangular with the longitudinal direction along the X-axis direction, the length Lq is greater than the length Wq (Wq < Lq). Since the planar shapes of the first exciting electrode 14a and the second exciting electrode 14b are also similar rectangles, the length Le is greater than the length We (We < Le), and the length Le2 is greater than the length We2 (We2 < Le2). Since all of the outer edge portions 81, 82, 83, 84 of the second exciting electrode 14b are located inside the short sides 111, 112 and the long sides 113, 114 of the vibrating portion 110, the length Lq is greater than the length Le2 (Le2 < Lq), and the length Wq is greater than the length We2 (We2 < Wq). Since all of the outer edge portions 71, 72, 73, 74 of the first exciting electrode 14a are located inside the outer edge portions 81, 82, 83, 84 of the second exciting electrode 14b, the length Le2 is greater than the length Le (Le < Le2), and the length We2 is greater than the length We (We < We2). In summary, the relationships of Le < Le2 < Lq and We < We2 < Wq hold.

[0059] As shown in FIG. 2, in a plan view, among the distances between the outer edge portions of the first exciting electrode 14a and the second exciting electrode 14b, the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 81 is defined as the length dLe1, the distance along the X-axis direction between the outer edge portion 72 and the outer edge portion 82 is defined as the length dLe2, the distance along the Z'-axis direction between the outer edge portion 73 and the outer edge portion 83 is defined as the length dWe1, and the distance along the Z'-axis direction between the outer edge portion 74 and the outer edge portion 84 is defined as the length dWe2. The sum of the length dLe1 and the length dLe2 is defined as dLe (dLe = dLe1 + dLe2), and the sum of the length dWe1 and the length dWe2 is defined as dWe (dWe = dWe1 + dWe2).

[0060] The length dLe1 is specified, for example, as the distance along the X-axis direction between the outer edge portion 71 and the outer edge portion 81 at a predetermined position. The predetermined position is, 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 in a plan view. The length dLe1 may be specified as 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 81. The length dWe1 is specified, for example, as the distance along the Z'-axis direction between the outer edge portion 73 and the outer edge portion 83 at a predetermined position. The predetermined position is, 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 in a plan view. The length dWe1 may be specified as 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 83.

[0061] Similarly, the length dLe2 is specified 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 as the average value or the 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 specified 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 as the average value or the maximum value of the distance along the Z'-axis direction between the outer edge portion 74 and the outer edge portion 84.

[0062] The length dLe is specified as the difference between the length Le and the length Le2. That is, it is calculated based on the lengths Le2 and Le using the formula dLe = Le2 - Le, but it may also be calculated based on the lengths dLe1 and dLe2 using the formula dLe = dLe1 + dLe2. The length dWe is specified as the difference between the length We and the length We2. That is, it is calculated based on the lengths We2 and We using the formula dWe = We2 - We, but it may also be calculated based on the lengths dWe1 and dWe2 using the formula dWe = dWe1 + dWe2.

[0063] Since the central positions of the first excitation electrode 14a and the second excitation electrode 14b overlap each other, the length dLe1 is equal to the length dLe2, and is half the magnitude of the difference between the length Le2 and the length Le. That is, the relationship 0 < dLe1 = dLe2 = dLe / 2 = (Le2 - Le) / 2 is satisfied. Similarly, the length dWe1 is equal to the length dWe2, and is half the magnitude of the difference between the length We2 and the length We. That is, the relationship 0 < dWe1 = dWe2 = dWe / 2 = (We2 - We) / 2 is satisfied.

[0064] Note that the magnitude relationship between the length dLe1 and the length dLe2 is not limited to the above, and the relationship 0 < dLe1 < dLe2 or 0 < dLe2 < dLe1 may be satisfied. The magnitude relationship between the length dWe1 and the length dWe2 is also not limited to the above, and the relationship 0 < dWe1 < dWe2 or 0 < dWe2 < dWe1 may be satisfied. Note that if at least one of the lengths dLe1, dLe2, dWe1, dWe2 is greater than 0, the others may be 0. For example, the relationship 0 = dLe1 = dLe2, 0 < dWe1, and 0 < dWe2 may be satisfied, or the relationship 0 < dLe1, 0 < dLe2, and 0 = dWe1 = dWe2 may be satisfied. Also, for example, the relationship 0 = dL2, 0 < dLe1, 0 < dWe1, and 0 < dWe2 may be satisfied. However, it is desirable that all of the lengths dLe1, dLe2, dWe1, dWe2 are greater than 0. That is, it is desirable that the relationship 0 < dLe1, 0 < dLe2, 0 < dWe1, 0 < dWe2 holds.

[0065] As shown in FIG. 3, let the thickness of the crystal piece 11 in the vibrating portion 110 be Tq, the thickness of the first excitation electrode 14a be Te, and the thickness of the second excitation electrode 14b be Te2.

[0066] The thickness Tq is specified, for example, as the distance along the Y'-axis direction between the upper surface 11A and the lower surface 11B at a predetermined position. The predetermined position is, for example, on a straight line passing through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b face each other and extending along the Y'-axis direction. The thickness Tq may be specified as the average value or the maximum value of the distance along the Y'-axis direction between the upper surface 11A and the lower surface 11B in the region where the first excitation electrode 14a and the second excitation electrode 14b face each other.

[0067] Similarly, the thickness Te is the distance along the Y'-axis direction between the upper surface and the lower surface of the first excitation electrode 14a at a predetermined position (for example, on a straight line passing through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b face each other and extending along the Y'-axis direction), or the average value or the maximum value of the distance along the Y'-axis direction 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 face each other. The thickness Te2 is the distance along the Y'-axis direction between the upper surface and the lower surface of the second excitation electrode 14b at a predetermined position (for example, on a straight line passing through the center of the region where the first excitation electrode 14a and the second excitation electrode 14b face each other and extending along the Y'-axis direction), or the average value or the maximum value of the distance along the Y'-axis direction 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 face each other.

[0068] The thickness Tq is larger than the thickness Te2, and the thickness Te2 is larger than the thickness Te. That is, the relationship Te < Te2 < Tq holds. Also, since the thickness of the crystal piece 11 is larger than the sum of the thicknesses of the first excitation electrode 14a and the second excitation electrode 14b, the relationship Te + Te2 < Tq holds.

[0069] Next, the simulation results based on the first embodiment will be described with reference to FIGS. 4 to 17.

[0070] FIG. 4 is a graph showing the simulation results based on the first embodiment. In the graph of FIG. 4, the horizontal axis indicates dLe or dWe (μm), and the vertical axis indicates the electromechanical coupling coefficient k (%).

[0071] In FIG. 4, when the horizontal axis of the graph is greater than 0, that is, when Le2 > Le or We2 > We, the simulation conditions are as follows. Tq = 1.0 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 55 μm, We = 50 μm, dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable

[0072] In FIG. 4, when the horizontal axis of the graph is 0 or less, that is, when Le2 ≤ Le or We2 ≤ We, the simulation conditions are as follows. Tq = 1.0 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le2 = 55 μm We2 = 50 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable

[0073] The plots in the graph of FIG. 4 respectively show the simulation results when both dLe and dWe are variables with dLe = dWe, the simulation results when dWe is a variable with dLe = 0 (constant), and the simulation results when dLe is a variable with dWe = 0 (constant). The values of dLe and dWe, which are the horizontal axes in the graph of FIG. 4, indicate the values of the variables in each case. That is, the values of the horizontal axes dLe and dWe indicate 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. In the following, the values of the variables shown on the horizontal axis of the graph are expressed as "[dLe, dWe]".

[0074] When dLe = dWe is a variable, when dLe is a variable and dWe = 0 (constant), and when dLe = 0 (constant) and dWe is a variable, in any of these cases, when 0 < 〔dLe, dWe〕, that is, when the area of the thicker second excitation electrode 14b among the first excitation electrode 14a and the second excitation electrode 14b becomes larger than the area of the thinner first excitation electrode 14a, the electromechanical coupling coefficient k improves. From 0 μm to 10 μm, the larger 〔dLe, dWe〕 becomes, the more the electromechanical coupling coefficient k improves. In the region of 10 μm < 〔dLe, dWe〕 < 25 μm, the electromechanical coupling coefficient k remains substantially constant even when 〔dLe, dWe〕 changes. Note that in the region of -25 μm ≦ 〔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 substantially the same.

[0075] As shown by the plots when dLe is a variable and dWe = 0 (constant), and the plots when dLe = 0 (constant) and dWe is a variable, even when one of dLe and dWe is 0 and the other is greater than 0, the electromechanical coupling coefficient k (%) is improved compared to the case when one of dLe and dWe is 0 and the other is 0 or less. Also, as shown by 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 0 and the other is greater than 0.

[0076] FIG. 5 is a cross-sectional view when displacement occurs in the first excitation electrode. FIG. 6 is a graph showing the simulation results based on the first embodiment.

[0077] As shown in Fig. 5, the graph in Fig. 6 shows the change in the electromechanical coupling coefficient k when the center of the first excitation electrode 14a is displaced by Δμm in the X-axis direction and the Z'-axis direction from the center of the second excitation electrode 14b in a plan view. In the graph of Fig. 6, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%). The magnitude of "displacement" in the graph of Fig. 6 corresponds to "Δ" shown in Fig. 5. The values of the horizontal axis dLe and dWe of the graph are expressed as "[dLe, dWe]".

[0078] In Fig. 5, the simulation conditions are as follows. Tq = 1.0μm Te = 0.05μm Te2 = 0.12μm Lq = Wq = 120μm Le = 55μm We = 50μm dLe = Le2 - Le: variable dWe = We2 - We: variable dLe = dWe dLe1 = dLe / 2 - Δ dLe2 = dLe / 2 + Δ dWe1 = dWe / 2 - Δ dWe2 = dWe / 2 + Δ

[0079] When dLe1 = dLe / 2 - Δ < 0 and dWe1 = dWe / 2 - Δ < 0, that is, when the relationship dLe / 2 < Δ and dWe / 2 < Δ holds, the first excitation electrode 14a protrudes outside the second excitation electrode 14b in a plan view. When the relationship 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 all of the first excitation electrode 14a overlaps a part of the second excitation electrode 14b.

[0080] The plots in the graph of FIG. 6 respectively show the simulation results for the cases of Δ = 0 μm, 1 μm, and 5 μm. In the case of Δ = 0 μm, in the region where dLe and dWe are 10 μm or more and 25 μm or less (10 μm ≤ [dLe, dWe] ≤ 25), the electromechanical coupling coefficient k is substantially constant regardless of dLe or dWe. In the case of Δ = 0 μm, in the region where dLe and dWe are less than 10 μm and 0 μm or more (0 μm ≤ [dLe, dWe] < 10 μm), the electromechanical coupling coefficient k decreases as dLe and dWe decrease. In the case of Δ = 1 μm, it shows substantially the same tendency as in the case of Δ = 0 μm.

[0081] In the case of Δ = 5 μm, in the region where dLe and dWe are less than 10 μm and 0 or more (0 μm ≤ [dLe, dWe] < 10 μm), the electromechanical coupling coefficient k is lower than in the case of Δ = 0 μm. At this time, since Δ = 5 μm and 0 μm ≤ [dLe, dWe] < 10 μm, the relationships dLe / 2 < Δ and dWe / 2 < Δ hold, and in plan view, the first excitation electrode 14a protrudes outside the second excitation electrode 14b. That is, when the first excitation electrode 14a protrudes outside the second excitation electrode 14b in plan view, the electromechanical coupling coefficient k is lower than in the case of Δ = 0 μm. On the other hand, even in the case of Δ = 5 μm, in the region where dLe and dWe are 10 μm or more and 25 μm or less (10 μm ≤ [dLe, dWe] ≤ 25), it shows substantially the same tendency as in the case of Δ = 0 μm. At this time, since Δ = 5 μm and 10 μm ≤ [dLe, dWe] ≤ 25, the relationships Δ ≤ dLe / 2 and Δ ≤ dWe / 2 < Δ hold, and all of the first excitation electrode 14a overlaps a part of the second excitation electrode 14b.

[0082] That is, even if the center of the first excitation electrode 14a is displaced with respect to the center of the second excitation electrode 14b, as long as the entire first excitation electrode 14a overlaps the second excitation electrode 14b, the effect of improving the electromechanical coupling coefficient k is maintained. However, when the first excitation electrode 14a protrudes outside the second excitation electrode 14b, the effect of improving the electromechanical coupling coefficient k is lost. Therefore, even if the center of the first excitation electrode 14a is slightly displaced with respect to the center of the second excitation electrode 14b, in order to maintain the effect of improving the electromechanical coupling coefficient k, it is desirable that dLe and dWe are large. Specifically, the allowable range of the displacement of the first excitation electrode 14a with respect to the second excitation electrode 14b is 1 / 2 or less of dLe and dWe. For example, when the maximum displacement of the first excitation electrode 14a with respect to the second excitation electrode 14b is assumed to be 5 μm, it is desirable that dLe and dWe are 10 μm or more. When the maximum displacement of the first excitation electrode 14a with respect to the second excitation electrode 14b is assumed to be 2.5 μm, it is desirable that dLe and dWe are 5 μm or more.

[0083] FIG. 7 is a graph showing the simulation results based on the first embodiment. FIG. 8 is a graph showing the simulation results based on the first embodiment. In the graph of FIG. 7, the horizontal axis represents Te2 (μm), and the vertical axis represents the frequency change dF (ppm) with reference to the frequency when Te2 = 0.05 μm. In the graph of FIG. 8, the horizontal axis represents Te2 (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0084] In FIGS. 7 and 8, the simulation conditions when 0 μm < dLe = dWe are as follows. Tq = 1.0 μm Te = 0.05 μm Te2: variable Lq = Wq = 120 μm Le = 55 μm We = 50 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: variable

[0085] In FIGS. 7 and 8, the simulation conditions when dLe = dWe ≤ 0 μm are as follows. Tq = 1.0 μm Te = 0.05 μm Te2: variable Lq = Wq = 120 μm Le2 = 55 μm We2 = 50 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: variable

[0086] As shown in FIG. 7, regardless of the values of dLe and dWe, the larger Te2 is, the smaller dF becomes. That is, the influence of the areas of the first excitation electrode 14a and the second excitation electrode 14b on the frequency is slight.

[0087] As shown in FIG. 8, when dLe = dWe = 0 μm, in the range of 0 μm < Te2 < 0.10 μm (0 < Te2 / Te < 2), the smaller Te2 (μm) is, the lower the electromechanical coupling coefficient k (%) is. In the range of 0.10 μm ≤ Te2 ≤ 0.20 μm (2 ≤ Te2 / Te ≤ 4), the larger Te2 (μm) is, the lower the electromechanical coupling coefficient k (%) is.

[0088] As shown in FIG. 8, when dLe < 0 μm and dWe < 0 μm, in the range of 0.05 μm < Te2 ≤ 0.20 μm (1 < Te2 / Te ≤ 4), the larger Te2 (μm) is, the lower the electromechanical coupling coefficient k (%) is. In the range of 0.12 μm < Te2 ≤ 0.20 μm (2.4 < Te2 / Te ≤ 4), when dLe < 0 μm and dWe < 0 μm, the electromechanical coupling coefficient k (%) is lower than that when dLe = dWe = 0 μm.

[0089] As shown in Fig. 8, when 0μm < dLe and 0μm < dWe, in the range of 0.05μm < Te2 ≦ 0.15μm (1 ≦ Te2 / Te ≦ 3), the electromechanical coupling coefficient k (%) improves as Te2 (μm) increases. In the range of 0.15μm < Te2 ≦ 0.20μm (3 ≦ Te2 / Te ≦ 4), the electromechanical coupling coefficient k (%) decreases as Te2 (μm) increases. That is, when Te2 is about 0.15μm (Te2 / Te = 3), the electromechanical coupling coefficient k (%) is maximized. Also, in the range of 0.10μm ≦ Te2 ≦ 0.20μm (2 ≦ Te2 / Te ≦ 4), the change in the electromechanical coupling coefficient k with respect to the change in Te2 is small, and the electromechanical coupling coefficient k is substantially constant. In the range of 0.05μm ≦ Te2 ≦ 0.20μm (1 ≦ Te2 / Te ≦ 4), when 0μm < dLe and 0μm < dWe, the electromechanical coupling coefficient k (%) is improved compared to the electromechanical coupling coefficient k (%) when dLe = dWe = 0μm.

[0090] Therefore, when the area of the thicker second excitation electrode 14b is larger than the area of the thinner first excitation electrode 14a among the first excitation electrode 14a and the second excitation electrode 14b, the electromechanical coupling coefficient k (%) improves. Also, in 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 varied to adjust the frequency, the variation of the electromechanical coupling coefficient k (%) can be suppressed.

[0091] Fig. 9 is a graph showing the simulation results based on the first embodiment. In the graph of Fig. 9, the horizontal axis indicates the ratio Te2 / Tq of the thickness Te2 of the second excitation electrode 14b to the thickness Tq of the crystal piece 11, and the vertical axis indicates the electromechanical coupling coefficient k (%).

[0092] In Fig. 9, the simulation conditions are as follows. Tq = 1.0μm Te: 0.05 Te2: variable Lq = Wq = 120μm Le = 55μm We = 50 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2 = 25 μm dWe = We2 - We = 2 × dWe1 = 2 × dWe2 = 25 μm ρ = 2,699 (kg / m 3 )

[0093] 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, it is calculated by the following formula. ρ = (ρ1 × V1 + ρ2 × V2) / (V1 + V2) If the materials of the first excitation electrode 14a and the second excitation electrode 14b are the same, the density of the material is ρ. Since the materials of the first excitation electrode 14a and the second excitation electrode 14b are aluminum in this simulation, ρ is the density of aluminum, which is 2,699 (kg / m 3 )

[0094] In the range of 0.05 ≤ Te2 / Tq ≤ 0.20, the electromechanical coupling coefficient k (%) becomes maximum near Te2 / Tq = 0.13. Here, Te2 / Tq at which the electromechanical coupling coefficient k (%) becomes maximum is defined as "optimal Te2 / Tq".

[0095] Figure 10 is a graph showing the simulation results based on the first embodiment. In the graph of Figure 10, the optimal Te2 / Tq shown in Figure 9 is plotted with Te and ρ as variables. In the graph of Figure 10, the horizontal axis represents ρ (kg / m 3 ) and the vertical axis represents the optimal Te2 / Tq.

[0096] 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 optimal Te2 / Tq increases. Also, when Te / Tq is constant, ρ (kg / m 3) As it increases, the optimal Te2 / Tq decreases. By fitting the graph shown in Fig. 10, the conditional expression for maximizing the electromechanical coupling coefficient k(%) is obtained as follows. Te2 / Tq = 0.00001×ρ + b ± 0.01

[0097] 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.

[0098] Fig. 11 is a graph showing the simulation results based on the first embodiment. In the graph of Fig. 11, b shown in Fig. 10 is plotted with Te / Tq as a variable. In the graph of Fig. 11, the horizontal axis represents Te / Tq and the vertical axis represents b.

[0099] In the range of 0.02 ≤ Te / Tq ≤ 0.15, the larger Te / Tq is, the larger b becomes. By fitting the graph shown in Fig. 11, the relational expression between b and Te / Tq is obtained as follows. b = 0.39Te / Tq + 0.16

[0100] By substituting the expression obtained in Fig. 11 into the expression obtained in Fig. 10, the conditional expression for maximizing the electromechanical coupling coefficient k(%) is obtained as follows. Te2 / Tq = 0.00001×ρ + 0.39Te / Tq + 0.16 ± 0.01

[0101] Fig. 12 is a graph showing the simulation results based on the first embodiment. In the graph of Fig. 12, the horizontal axis represents Te2 (μm) and the vertical axis represents the electromechanical coupling coefficient k(%).

[0102] In Fig. 12, the simulation conditions when 0 μm < dLe = dWe are as follows. Tq = 1.0 μm Te = 0.05 μm Te2: variable Lq = Wq = 120 μm Le = 55 μm We = 50 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: Variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: Variable

[0103] In Fig. 12, the simulation conditions when dLe = dWe ≤ 0 μm are as follows. Tq = 1.0 μm Te = 0.05 μm Te2: Variable Lq = Wq = 120 μm Le2 = 55 μm We2 = 50 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: Variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: Variable

[0104] When one of dLe and dWe is set to 0 and the other is made larger than 0, the electromechanical coupling coefficient k (%) reaches its maximum in the range of 0.05 μm ≤ Te2 ≤ 0.20 μm (1 ≤ Te2 / Te ≤ 4) when Te2 is in the range of 0.10 μm or more and 0.15 μm or less (2 ≤ Te2 / Te ≤ 3). Also, in the range of 0.10 μm ≤ Te2 ≤ 0.20 μm (2 ≤ Te2 / Te ≤ 4), the change in the electromechanical coupling coefficient k with respect to the change in Te2 is small, and the electromechanical coupling coefficient k (%) is substantially constant. That is, the change in the electromechanical coupling coefficient k (%) with respect to Te2 shows the same tendency even when one of dLe and dWe is 0 and the other is larger than 0 as when both dLe and dWe are larger than 0. However, if Te2 is the same in the range of 0.05 μm ≤ Te2 ≤ 0.20 μm (1 ≤ Te2 / Te ≤ 4), the electromechanical coupling coefficient k (%) when both dLe and dWe are larger than 0 is improved compared to the electromechanical coupling coefficient k (%) when one of dLe and dWe is 0 and the other is larger than 0.

[0105] Figure 13 is a graph showing the simulation results based on the first embodiment. In Figure 13, 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 of the graph are expressed as "[dLe, dWe]".

[0106] In Figure 13, when the horizontal axis of the graph is greater than 0, that is, when Le < Le2 and We < We2, the simulation conditions are as follows. Tq = 1.5μm Te = 0.08μm Te2 = 0.20μm Lq = Wq = 120μm Le = 70μm, We = 70μm, dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0107] In Figure 13, when the horizontal axis of the graph is 0 or less, that is, when Le2 ≤ Le and We2 ≤ We, the simulation conditions are as follows. Tq = 1.5μm Te = 0.08μm Te2 = 0.20μm Lq = Wq = 120μm Le2 = 70μm We2 = 70μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0108] The plots in Fig. 13 show the same tendency as the plots of dLe = dWe in Fig. 4. That is, if one of the pair of exciting electrodes is thicker than the other and the area of the thicker exciting electrode is larger than that of the thinner exciting electrode, even if the respective dimensions of the pair of exciting electrodes and the crystal piece are different, the change in the electromechanical coupling coefficient k(%) with respect to the change in dLe and dWe shows the same tendency.

[0109] Fig. 14 is a graph showing the simulation results based on the first embodiment. In the graph of Fig. 14, the horizontal axis represents Te2 (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0110] In Fig. 14, the simulation conditions when 0μm < dLe = dWe are as follows. Tq = 1.5μm Te = 0.08μm Te2: variable Lq = Wq = 120μm Le = 70μm We = 70μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: variable

[0111] In Fig. 14, the simulation conditions when dLe = dWe ≤ 0μm are as follows. Tq = 1.5μm Te = 0.08μm Te2: variable Lq = Wq = 120μm Le2 = 70μm We2 = 70μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2: variable dWe = We2 - We = 2 × dWe1 = 2 × dWe2: variable

[0112] The plot with dLe = dWe = 15 μm in FIG. 14 shows the same tendency as the plots with dLe = dWe = 5 μm, 15 μm, and 25 μm in FIG. 8. That is, if one of the pair of excitation electrodes is thicker than the other and the area of the thicker excitation electrode is larger than the area of the thinner excitation electrode, even if the respective dimensions of the pair of excitation electrodes and the crystal piece are different, the change in the electromechanical coupling coefficient k (%) with respect to the change in Te2 shows the same tendency.

[0113] FIG. 15 is a graph showing the simulation results based on the first embodiment. In FIG. 15, the horizontal axis represents dLe (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0114] In FIG. 15, simulations are performed for two configuration examples where 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.

[0115] In the first configuration example, the planar shapes of the first excitation electrode 14a and the second excitation electrode 14b are squares with equal areas. Each side of the first excitation electrode 14a extends along the X-axis direction and the Z'-axis direction. The second excitation electrode 14b is arranged at a 45-degree inclination with its center overlapping the first excitation electrode 14a, and its diagonal extends along the X-axis direction and the Z'-axis direction. The shape of the portion where the first excitation electrode 14a and the second excitation electrode 14b face each other is a regular octagon. Let the length of the first excitation electrode 14a along the X-axis direction be Le, and the length of the second excitation electrode 14b along the X-axis direction be Le2.

[0116] In the second configuration example, the planar shapes of the first excitation electrode 14a and the second excitation electrode 14b are regular octagons, and their centers overlap each other. Let the length between the opposite sides of the first excitation electrode 14a be Le, and the length between the opposite sides of the second excitation electrode 14b be Le2.

[0117] In FIG. 15, the simulation conditions are as follows. Tq = 1.5 μm Te = 0.08 μm Te2: 0.20 μm Lq = Wq = 120 μm Le = 70 μm dLe = Le2 - Le: variable

[0118] The plot based on the second configuration example in FIG. 15 shows a similar trend to the plot of dLe = dWe in FIG. 4. That is, if the area of the thicker excitation electrode among 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 whole of the thinner excitation electrode, the electromechanical coupling coefficient k (%) improves regardless of the planar shape of the first excitation electrode 14a and the second excitation electrode 14b.

[0119] Also, in the first configuration example, for example, on the diagonal line extending in 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 comparable to the electromechanical coupling coefficient k (%) in the second configuration example in the range of 0 μm < dLe < 5 μm, and is smaller than the electromechanical coupling coefficient k (%) in the second configuration example with the same dLe. That is, 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. Although dLe > 0 partially in the first configuration example, the electromechanical coupling coefficient k (%) in the first configuration example does not improve as much as the electromechanical coupling coefficient k (%) in the second configuration example with the same dLe. That is, it is not the magnitude relationship of the partial lengths of the first excitation electrode 14a and the second excitation electrode 14b, but the magnitude relationship of the areas that is important for the improvement of the electromechanical coupling coefficient k (%).

[0120] FIG. 16 is a graph showing the simulation results based on the first embodiment. In the graph of FIG. 16, the horizontal axis represents dLe and dWe (μm), and the vertical axis represents the normalized electromechanical coupling coefficient k (%). The values of the horizontal axis dLe, dWe of the graph are expressed as "[dLe, dWe]".

[0121] In Fig. 16, the simulation conditions for Tq = 0.5 μm are as follows. Tq = 0.5 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 30 μm We = 30 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0122] In Fig. 16, the simulation conditions for Tq = 1.0 μm are as follows. Tq = 1.0 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 55 μm We = 50 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0123] In Fig. 16, the simulation conditions for Tq = 1.5 μm are as follows. Tq = 1.5 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 70 μm We = 70 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0124] In Fig. 16, the simulation conditions for Tq = 2.0 μm are as follows. Tq = 2.0 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 55 μm We = 50 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: Variable dWe = We2 - We = 2×dWe1 = 2×dWe2: Variable dLe = dWe

[0125] In FIG. 16, the simulation conditions when Tq = 3.0 μm are as follows. Tq = 3.0 μm Te = 0.05 μm Te2 = 0.12 μm Lq = Wq = 120 μm Le = 55 μm We = 50 μm dLe = Le2 - Le = 2×dLe1 = 2×dLe2: Variable dWe = We2 - We = 2×dWe1 = 2×dWe2: Variable dLe = dWe

[0126] As shown in FIG. 16, as Tq increases, dLe and dWe required for improving the electromechanical coupling coefficient k(%) increase. Hereinafter, the minimum dLe and dWe required to maximize the electromechanical coupling coefficient k(%) are referred to as "minimum [dLe, dWe]".

[0127] FIG. 17 is a graph showing the simulation results based on the first embodiment. In the graph of FIG. 17, the relationship between Tq and minimum [dLe, dWe] obtained based on the graph of FIG. 16 is plotted. In the graph of FIG. 17, the horizontal axis represents Tq (μm), and the vertical axis represents minimum [dLe, dWe] (μm).

[0128] As Tq increases, the minimum of [dLe, dWe] is increasing. By fitting the graph shown in FIG. 17, the conditional expression for maximizing the electromechanical coupling coefficient k(%) is obtained as follows. Note that [dLe, dWe] on the right side of the following equation corresponds to an example of the distance De between adjacent sides in a certain direction of the first excitation electrode and the second excitation electrode. 5.22×Tq - 0.45 ≤ [dLe, dWe]

[0129] As described above, according to the present embodiment, the area of the second excitation electrode 14b is larger than the area of the first excitation electrode 14a, a part of the second excitation electrode 14b overlaps with all of the 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.

[0130] According to this, the electromechanical coupling coefficient k(%) can be improved.

[0131] Further, in the present embodiment, the first excitation electrode 14a is, for example, the side that is trimmed to adjust the frequency in the manufacturing process.

[0132] According to this, by the trimming process, the thickness Te can be made smaller than the thickness Te2. Therefore, even if the first excitation electrode 14a and the second excitation electrode 14b are not provided with different thicknesses during film formation, Te < Te2 can be achieved, so that the manufacturing process can be simplified.

[0133] Further, in the present embodiment, the second excitation electrode 14b may be the side that is trimmed to adjust the frequency.

[0134] According to this, 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 increased as compared with the case where the first excitation electrode 14a is trimmed. Further, when the thickness Te2 is sufficiently larger than the thickness Te, for example, in the range of 2×Te ≦ Te2 ≦ 4×Te, since the change in the electromechanical coupling coefficient k(%) with respect to the change in the thickness Te2 is small, even if the thickness Te2 fluctuates due to the trimming process, a decrease in the electromechanical coupling coefficient k(%) can be suppressed.

[0135] Further, in the present embodiment, all of the outer edge portions 71 to 74 of the first excitation electrode 14a are located inside the outer edge portions 81 to 84 of the second excitation electrode 14b.

[0136] According to this, the electromechanical coupling coefficient k(%) can be further improved as compared with 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. Further, since the change in the electromechanical coupling coefficient k(%) with respect to the change in the thickness Te2 of the second excitation electrode 14b can be made small, when the second excitation electrode 14b is trimmed to adjust the frequency, a decrease in the electromechanical coupling coefficient k(%) can be suppressed. Further, even if the first excitation electrode 14a is displaced with respect to the second excitation electrode 14b, since the entire first excitation electrode 14a is maintained in a state of overlapping the second excitation electrode 14b, a decrease in the electromechanical coupling coefficient k(%) can be suppressed.

[0137] Further, in the present embodiment, the relationship of Te2 / Tq = 0.00001×ρ + 0.39×Te / Tq + 0.16 ± 0.01 holds.

[0138] According to this, when the thicknesses Tq, Te, and Te2 satisfy the conditions of the above formula, the electromechanical coupling coefficient k(%) becomes maximum.

[0139] Further, 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, and preferably both relationships hold.

[0140] According to this, it is possible to suppress a decrease in the electromechanical coupling coefficient k (%) due to the relationship among Tq, dLe, and dWe. That is, the electromechanical coupling coefficient k (%) can be sufficiently improved.

[0141] Other embodiments will be described below. Note that the same or similar components as those shown in the first embodiment are denoted by the same or similar reference numerals, and the description thereof will be omitted as appropriate. Also, the same operational effects due to the same components will not be sequentially mentioned.

[0142] <Second Embodiment> Next, with reference to FIGS. 18 and 19, the configuration of the crystal oscillator 200 according to the second embodiment will be described.

[0143] The area of the first excitation electrode 214a is larger than the area of the second excitation electrode 214b, the length Le of the first excitation electrode 214a is larger than the length Le2 of the second excitation electrode 214b, and the length We of the first excitation electrode 214a is larger than the length We2 of the second excitation electrode 214b. The thickness Te of the first excitation electrode 214a is larger than the thickness Te2 of the second excitation electrode 214b.

[0144] The crystal oscillator 200 further includes an insulating film 241 laminated on the second excitation electrode 214b. The material of the insulating film 241 is, for example, silicon oxide such as SiO 2 However, the material of the insulating film 241 is not limited to this, and may be any of inorganic insulators such as silicon nitride, silicon oxynitride, and aluminum oxide, and organic insulators such as polyvinylphenol, polyvinyl alcohol, ether polymer, polyimide, and acrylic resin.

[0145] As shown in FIG. 18, the insulating film 241 extends over substantially the entire area of the vibrating portion 210. The area of the insulating film 241 is larger than the areas of the first excitation electrode 214a and the second excitation electrode 214b, and is substantially equal to the area of the vibrating portion 210. Therefore, in a plan view, 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, the relationships of Le2 < Le < Le3 = Lq and We2 < We < We3 = Wq hold. In a plan view, the center of the insulating film 241 overlaps with the centers of the first excitation electrode 214a and the second excitation electrode 214b. Therefore, all of the outer edge portions of the second excitation electrode 214b are provided inside the outer edge portion of the first excitation electrode 214a, and all of the outer edge portions of the insulating film 241 are provided outside the outer edge portion of the first excitation electrode 214a.

[0146] As shown in FIG. 19, the insulating film 241 is laminated, for example, on the surface of the crystal piece 11 of the second excitation electrode 214b on the side opposite to the first excitation electrode 214a. When the thickness of the insulating film 241 is Te3, the relationships of Te2 < Te < Te3 and Te < Te2 + Te3 hold.

[0147] The thickness Te3 is specified, for example, as the distance along the Y'-axis direction 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 direction passing 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 be specified as the average value, the maximum value, or the minimum value of the distance along the Y'-axis direction 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.

[0148] Note that the positions and size relationships of the insulating film 241, the first excitation electrode 214a, and the second excitation electrode 214b are not limited to the above configuration as long as all of the following conditions are satisfied. The first condition is that the insulating film 241 is laminated on the excitation electrode with the smaller area in plan view among the pair of excitation electrodes. The second condition is that the sum of the thickness of the excitation electrode with the smaller area in plan view among the pair of excitation electrodes and the thickness of the insulating film 241 is larger than the thickness of the excitation electrode with the larger area in plan view among the pair of excitation electrodes. The third condition is that the area of the laminate 240 composed of the excitation electrode with the smaller area in plan view among the pair of excitation electrodes and the insulating film 241 is larger than the area of the excitation electrode with the larger area in plan view among the pair of excitation electrodes. Here, the "area of the laminate 240" includes not only the area of the portion where both the excitation electrode with the smaller area in plan view among the pair of excitation electrodes and the insulating film 241 overlap and extend, but also the area of the portion where only one of them extends. The fourth condition is that in plan view, a part of the laminate 240 overlaps with all of the excitation electrode with the larger area in plan view among the pair of excitation electrodes.

[0149] For example, the configuration example shown in FIG. 18 may be modified so that the relationship Le2 < Le < Le3 < Lq holds. Similarly, it may be modified so that the relationship We2 < We < We3 < Wq holds.

[0150] Also, for example, the configuration example shown in FIG. 18 may be modified so that the center of the insulating film 241 in 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 with respect to the center of at least one of the first excitation electrode 214a and the second excitation electrode 214b in plan view.

[0151] Further, for example, the configuration example shown in FIG. 19 may be modified so that Te2 < Te3 ≤ Te < Te2 + Te3 holds, or may be modified so that the relationship Te3 ≤ Te2 ≤ Te < Te2 + Te3 holds. Similarly, it may be modified so that the relationship Te ≤ Te2 < Te3 < Te2 + Te3 holds, or may be modified so that the relationship Te ≤ Te3 ≤ Te2 < Te2 + Te3 holds, or may be modified so that the relationship Te < Te3 ≤ Te2 < Te2 + Te3 holds.

[0152] Further, for example, the configuration example shown in FIG. 19 may be modified such that the insulating film 241 is provided between the crystal piece 11 and the second excitation electrode 214b. The crystal oscillator 200 may further include an insulating film laminated on the first excitation electrode 214a. That is, the first insulating film may be laminated on the excitation electrode with the smaller area in plan view among the pair of excitation electrodes, and the second insulating film may be laminated on the excitation electrode with the larger area in plan view among the pair of excitation electrodes. From the viewpoint of suppressing a decrease in the electromechanical coupling coefficient k, it is desirable that the sum of the thickness of the excitation electrode with the smaller area and the thickness of the first insulating film is larger than the sum of the thickness of the excitation electrode with the larger area and the thickness of the second insulating film.

[0153] Next, with reference to FIGS. 20 to 24, the simulation results based on the second embodiment will be described.

[0154] FIG. 20 is a graph showing the simulation results based on the second embodiment. In the graph of FIG. 20, 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 of the graph are expressed as "[dLe, dWe]". "SiO2" in FIG. 20 means the insulating film 241. The same applies to other drawings.

[0155] In FIG. 20, when Te2 < Te and [dLe, dWe] is greater than 0, that is, when Le2 < Le and We < We, the simulation conditions are as follows. Tq = 1.0 μm Te: variable Te2: Variable Te3 = 0.12 μm Lq = Wq = 120 μm Le = 55 μm, We = 50 μm, dLe = Le - Le2 = 2×dLe1 = 2×dLe2: Variable dWe = We - We2 = 2×dWe1 = 2×dWe2: Variable dLe = dWe

[0156] In Fig. 20, when Te2 < Te and [dLe, dWe] is 0 or less, that is, when Le ≤ Le2 and We ≤ We2, the simulation conditions are as follows. Tq = 1.0 μm Te: Variable Te2: Variable Te3 = 0.12 μm Lq = Wq = 120 μm Le2 = 55 μm We2 = 50 μm dLe = Le - Le2 = 2×dLe1 = 2×dLe2: Variable dWe = We - We2 = 2×dWe1 = 2×dWe2: Variable dLe = dWe

[0157] In Fig. 20, 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. In Fig. 20, when "with SiO2" is described, Le3 = Lq and We3 = Wq.

[0158] 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 improved compared to 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 further improved compared to the electromechanical coupling coefficient k (%) when Te < Te2 and the insulating film 241 is provided. That is, the electromechanical coupling coefficient k (%) when the insulating film 241 is laminated on the thinner one of the pair of exciting electrodes is improved compared to the electromechanical coupling coefficient k (%) when the insulating film 241 is laminated on the thicker one of the pair of exciting electrodes.

[0159] When Te2 < Te, the electromechanical coupling coefficient k (%) in the range of 0 < [dLe, dWe] is improved compared to the electromechanical coupling coefficient k (%) in the range of [dLe, dWe] ≤ 0. That is, when Te2 < Te, the electromechanical coupling coefficient k (%) is improved when Le2 < Le and We2 < We. Also, when Te < Te2, the electromechanical coupling coefficient k (%) in the range of 0 < [dLe, dWe] is improved compared to the electromechanical coupling coefficient k (%) in the range of [dLe, dWe] ≤ 0. That is, when Te < Te2, the electromechanical coupling coefficient k (%) is improved when Le < Le2 and We < We2. In summary, in both cases where the thickness of the exciting electrode with the insulating film laminated thereon is smaller and larger than the thickness of the exciting electrode without the insulating film laminated thereon among the pair of exciting electrodes, the electromechanical coupling coefficient k (%) when the area of the thicker exciting electrode among the pair of exciting electrodes is larger than the area of the thinner exciting electrode is improved compared to the electromechanical coupling coefficient k (%) when the area of the thicker exciting electrode among the pair of exciting electrodes is smaller than the area of the thinner exciting electrode.

[0160] Figure 21 is a graph showing the simulation results based on the second embodiment. In the graph of Figure 21, 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 of the graph are expressed as "[dLe, dWe]".

[0161] In Figure 21, when [dLe, dWe] is greater than 0, that is, when Le2 < Le and We2 < We, the simulation conditions are as follows. Tq = 1.0μm Te = 0.10μm Te2 = 0.05μm Te3 = 0.12μm Lq = Wq = 120μm Le = 55μm, We = 50μm, dLe = Le - Le2 = 2×dLe1 = 2×dLe2: variable dWe = We - We2 = 2×dWe1 = 2×dWe2: variable dLe = dWe Le3: variable We3: variable

[0162] In Figure 21, when [dLe, dWe] is 0 or less, that is, when Le ≤ Le2 and We ≤ We2, the simulation conditions are as follows. Tq = 1.0μm Te = 0.10μm Te2 = 0.05μm Te3 = 0.12μm Lq = Wq = 120μm Le2 = 55μm We2 = 50μm dLe = Le - Le2 = 2×dLe1 = 2×dLe2: variable dWe = We - We2 = 2×dWe1 = 2×dWe2: variable dLe = dWe Le3: variable We3: variable

[0163] FIG. 21 plots the simulation results when an insulating film 241 is provided on the entire lower surface of the vibrating portion 210, when the insulating film 241 is provided only on the lower surface of the second exciting electrode 214b, and when no insulating film 241 is provided. Providing the insulating film 241 on the entire lower surface of the vibrating portion 210 means that the relationship Le3 = Lq and We3 = Wq holds. Providing the insulating film 241 only on the lower surface of the second exciting electrode 214b means that the relationship Le3 = Le2 and We3 = We2 holds. Not providing the insulating film 241 means that the relationship Le3 = We3 = 0 holds.

[0164] In any [dLe, dWe] in 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 vibrating portion 210 is improved compared to the electromechanical coupling coefficient k (%) when no insulating film 241 is provided. However, in any [dLe, dWe] in 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 exciting electrode 214b is lower than the electromechanical coupling coefficient k (%) when no insulating film 241 is provided.

[0165] From the above, it is shown that when the insulating film 241 is provided only in the region overlapping the smaller-area exciting electrode among the pair of exciting electrodes in plan view, the effect of improving the electromechanical coupling coefficient k (%) cannot be obtained. Also, in plan view, when all of the outer edge portions of the second exciting electrode 214b are provided inside the outer edge portions of the first exciting electrode 214a, and all of the outer edge portions of the insulating film 241 are provided outside the outer edge portions of the first exciting electrode 214a, it is shown that the effect of improving the electromechanical coupling coefficient k (%) can be obtained.

[0166] FIG. 22 is a graph showing the simulation results based on the second embodiment. In the graph of FIG. 22, the horizontal axis represents Te3 (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0167] In FIG. 22, the simulation conditions are as follows. Tq = 1.0 μm Te: variable Te2: variable Te3: variable Lq = Wq = 120 μm Le2 = 55 μm We2 = 50 μm Le3 = Lq We3 = Wq dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0168] As shown in FIG. 22, in the range of 0.06 μm ≤ Te3 ≤ 0.20 μm, the electromechanical coupling coefficient k (%) when Te = 0.05 μm, Te2 = 0.10 μm, and dLe = dWe = 25 μm is improved compared to the electromechanical coupling coefficient k (%) when Te = 0.05 μm, Te2 = 0.05 μm, and dLe = dWe = 0 μm. The electromechanical coupling coefficient k (%) when Te = 0.10 μm, Te2 = 0.05 μm, and dLe = dWe = -25 μm is further improved compared to the electromechanical coupling coefficient k (%) when Te = 0.05 μm, Te2 = 0.10 μm, and dLe = dWe = 25 μm. That is, in a plan view, when all of the thinner excitation electrode overlaps a part of the thicker excitation electrode among a pair of excitation electrodes, the electromechanical coupling coefficient k (%) improves regardless of whether the insulating film is provided on the side of either excitation electrode. However, when the insulating film is provided on the side of the thinner excitation electrode, the electromechanical coupling coefficient k (%) improves more than when the insulating film is provided on the side of the thicker excitation electrode.

[0169] Also, when Te = 0.10 μm, Te2 = 0.05 μm, and dLe = dWe = -25 μm, the change in the electromechanical coupling coefficient k (%) with respect to the change in Te3 is small. That is, in a plan view, all of the thinner excitation electrode overlaps a part of the thicker excitation electrode among the pair of excitation electrodes, and an insulating film is provided on the side of the thinner excitation electrode. In this case, the electromechanical coupling coefficient k (%) is stable with respect to the film thickness of the insulating film. That is, even if a trimming process for adjusting the frequency is performed on the insulating film in the manufacturing process, a decrease in the electromechanical coupling coefficient k (%) can be suppressed.

[0170] FIG. 23 is a graph showing simulation results based on the second embodiment. In the graph of FIG. 23, 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 of the graph are expressed as "[dLe, dWe]".

[0171] In FIG. 23, when Te2 < Te and [dLe, dWe] is greater than 0, that is, when Le2 > Le and We2 > We, the simulation conditions are as follows. Tq = 1.5 μm Te: variable Te2: variable Te3 = 0.20 μm Lq = Wq = 120 μm Le = 70 μm, We = 70 μm, Le3 = Lq We3 = Wq dLe = Le - Le2 = 2 × dLe1 = 2 × dLe2: variable dWe = We - We2 = 2 × dWe1 = 2 × dWe2: variable dLe = dWe

[0172] In FIG. 23, when Te2 < Te and [dLe, dWe] is 0 or less, that is, when Le2 ≤ Le and We2 ≤ We, the simulation conditions are as follows. Tq = 1.5 μm Te: variable Te2: variable Te3 = 0.20 μm Lq = Wq = 120 μm Le2 = 70 μm We2 = 70 μm Le3 = Lq We3 = Wq dLe = Le - Le2 = 2×dLe1 = 2×dLe2: variable dWe = We - We2 = 2×dWe1 = 2×dWe2: variable dLe = dWe

[0173] In FIG. 23, the simulation conditions when Te < Te2 are the same as the simulation conditions when Te2 < Te, except that dLe = Le2 - Le and dWe = We2 - We.

[0174] The plot in FIG. 23 shows a similar trend to the "with SiO2" plot in FIG. 20. That is, if the size relationship of each dimension of a pair of excitation electrodes and the insulating film is the same, even if the dimensions of each of the pair of excitation electrodes and the insulating film are different, the change in the electromechanical coupling coefficient k (%) with respect to the change in [dLe, dWe] shows a similar trend.

[0175] FIG. 24 is a graph showing the simulation results based on the second embodiment. In the graph of FIG. 24, the horizontal axis represents Te3 (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0176] In FIG. 24, the simulation conditions are as follows. Tq = 1.5 μm Te: variable Te2 = 0.08 μm Te3: variable Lq = Wq = 120 μm Le2 = 70 μm We2 = 70 μm Le3 = Lq We3 = Wq dLe = Le2 - Le = 2×dLe1 = 2×dLe2: variable dWe = We2 - We = 2×dWe1 = 2×dWe2: Variable dLe = dWe

[0177] The plot with Te = 0.16μm, Te2 = 0.08μm, and dLe = dWe = -20μm in FIG. 24 shows the same tendency as the plot with Te = 0.10μm, Te2 = 0.05μm, and dLe = dWe = -25μm in FIG. 22. That is, if the size relationship of each dimension of the pair of excitation electrodes and the insulating film is the same, even if the dimensions of the pair of excitation electrodes and the insulating film are different, the change in the electromechanical coupling coefficient k(%) with respect to the change in Te3 shows the same tendency.

[0178] As described above, according to the present embodiment, in a plan view, the area of the laminate 240 composed of the second excitation electrode 214b and the insulating film 241 is larger than that of the first excitation electrode 214a, and a part of the laminate 240 overlaps all of the 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.

[0179] According to this, the electromechanical coupling coefficient k(%) can be improved.

[0180] Also, in the present embodiment, the insulating film 241 is laminated on the surface of the second excitation electrode 214b opposite to the crystal piece 11.

[0181] According to this, compared with the configuration in which the insulating film 241 exists between the first excitation electrode 214a and the second excitation electrode 214b, the distance between the first excitation electrode 214a and the second excitation electrode 214b can be reduced. According to this, since the portion vibrating by the piezoelectric effect can be thinned, the crystal oscillator 200 can be made to have a higher frequency.

[0182] Also, in the present embodiment, all of the outer edge portions of the second excitation electrode 214b are provided inside the outer edge portion of the first excitation electrode 214a, and all of the outer edge portions of the insulating film 241 are provided outside the outer edge portion of the first excitation electrode 214a.

[0183] According to this, since the change in the electromechanical coupling coefficient k(%) can be made small with respect to the change in the thickness Te3 of the insulating film 241, when the insulating film 241 is subjected to a trimming process to adjust the frequency, a decrease in the electromechanical coupling coefficient k(%) can be suppressed.

[0184] Also, in the present embodiment, the thickness Te2 of the second excitation electrode 214b is smaller than the thickness Te of the first excitation electrode 214a.

[0185] According to this, the electromechanical coupling coefficient k(%) can be further improved.

[0186] Also, in the present embodiment, the relationship of (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, it is calculated by the following formula. ρ’=(ρ1×V1 + ρ2×V2 + ρ3×V3) / (V1 + V2 + V3)

[0187] According to this, when the thicknesses Tq, Te, Te2, Te3 satisfy the conditions of the above formula, the electromechanical coupling coefficient k(%) becomes maximum as in the first embodiment.

[0188] Also, in the present embodiment, the materials of the first excitation electrode 214a and the second excitation electrode 214b are aluminum, and the material of the insulating film 241 is silicon oxide.

[0189] According to this, since the density of aluminum and the density of silicon oxide are close values, the calculation of the average density ρ' can be simplified. Further, 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 exciting electrode 214b can be made substantially equal to the adhesion between the second exciting electrode 214b and the insulating film 241. For this reason, peeling of the insulating film 241 from the crystal piece 11 or the second exciting electrode 214b, and peeling of the second exciting electrode 214b from the crystal piece 11 can be suppressed.

[0190] <Third Embodiment> Next, with reference to FIGS. 25 to 29, the configuration of the crystal oscillator 300 according to the third embodiment will be described.

[0191] 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 in consideration of the influence of the second extraction electrode 15b. In the graph of FIG. 25, the horizontal axis is the wiring width Wwire (μm) of the extraction electrode, and the vertical axis shows the electromechanical coupling coefficient k (%). The wiring width of the extraction electrode is the dimension along the Z' axis in the first extraction electrode 15a extending in the X-axis direction.

[0192] In FIG. 25, the simulation conditions are as follows. It is assumed that the first extraction electrode 15a is drawn from the central portion in the Z' axis direction of the outer edge portion on the positive X-axis side of the first exciting electrode 14a. Tq = 1.0 μm Te = 0.05 μm Te2 = 0.05 μm Lq = Wq = 120 μm Le = 55 μm We = 50 μm Le2 = 70 μm We2 = 60 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2 = 15 μm dWe = We2 - We = 2 × dWe1 = 2 × dWe2 = 10 μm Wwire: variable

[0193] When Wwire = 0 μm, that is, when the simulation of excitation is performed only with the first excitation electrode 14a and the second excitation electrode 14b without providing the first lead-out electrode 15a, the region where the first excitation electrode 14a and the second excitation electrode 14b overlap is excited. However, when set to 0 μm < Wwire, the region where the second excitation electrode 14b and the first lead-out electrode 15a overlap is also excited. Therefore, as shown in FIG. 25, 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 also decreases.

[0194] As shown in FIG. 25, as Wwire increases from 0 μm, the electromechanical coupling coefficient k (%) decreases, and the electromechanical coupling coefficient k (%) becomes a minimum near Wwire = 10 μm. As Wwire increases from 10 μm, the electromechanical coupling coefficient k (%) improves, and the electromechanical coupling coefficient k (%) becomes a maximum near Wwire = 40 μm. The increase in the electromechanical coupling coefficient k (%) with the increase in Wwire in the range of 10 μm < Wwire < 40 μm is considered to be because the widened first lead-out electrode 15a behaves like a part of the first excitation electrode 14a.

[0195] From the viewpoint of suppressing vibration leakage, etc., it is desirable that Wwire be small. However, when Wwire is small, the electromechanical coupling coefficient k (%) decreases as shown in FIG. 25. Therefore, in order to suppress the decrease in the electromechanical coupling coefficient k (%) and the Q value, it is necessary to reduce Wwire and then suppress the influence of the first lead-out electrode 15a on the second excitation electrode 14b. The third embodiment and the fourth embodiment are one aspect of the invention made in view of such circumstances.

[0196] FIG. 26 is a perspective view of the vibrating part according to the third embodiment. FIG. 27 is a diagram showing the vibration distribution of the vibrating part according to the third embodiment. The magnitude of the amplitude is indicated by light and dark, the bright part is the region with a large amplitude, and the dark part is the region with a small amplitude. In addition, in FIG. 27, the illustration of the second excitation electrode 314b is omitted.

[0197] As shown in Fig. 26, 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 facing the first extraction electrode 315a, and is the same as the first embodiment in other respects. Since the first extraction electrode 315a extends in the positive X-axis direction from the outer edge portion on the positive X-axis direction side of the first excitation electrode 314a, the notch 314N is provided at the outer edge portion on the positive X-axis direction side of the second excitation electrode 314b. In plan view, the notch 314N is a rectangular recess. Let the distance along the X-axis direction between the outer edge of the second excitation electrode 314b and the first excitation electrode 314a in the notch 314N be Ln, and the distance along the Z'-axis direction between the outer edge of the second excitation electrode 314b and the first extraction electrode 315a in the notch 314N be Wn.

[0198] As shown in Fig. 27, in the third embodiment, the vibrating region is limited to the region overlapping the first excitation electrode 314a, and the vibration in the region overlapping the first extraction electrode 315a is suppressed. For example, when simulating in a configuration in which the first extraction electrode 315a and the notch 314N are omitted from the third embodiment, k = 6.86% and Q = 8,720 are obtained. However, when simulating in a configuration in which the first extraction electrode 315a with Wwire = 10 μm is added to that configuration, k = 6.77% and Q = 8,540 are obtained. However, when simulating in the configuration according to the third embodiment in which the notch 314N is further formed therein, k = 6.82% and Q = 8,730 are obtained. That is, by forming the notch 314N, the influence of the first extraction electrode 315a on the second excitation electrode 314b is suppressed, and the decrease in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0199] As described above, according to the present embodiment, the notch 314N is formed in the region of the second excitation electrode 314b facing the first extraction electrode 315a.

[0200] According to this, the influence of the first extraction electrode 315a on the second excitation electrode 314b is suppressed, and the decrease in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0201] Note that the third embodiment has a configuration in which a notch is formed in the region facing the lead electrode of the excitation electrode with the larger area among the pair of excitation electrodes in the first embodiment. However, a notch may be formed in the region facing the lead electrode of the insulating film in the second embodiment. Even in such a configuration, the same effects as those of the third embodiment can be obtained. However, since the insulating film is lighter than the material of the excitation electrode, the vibration confinement property in the region where the first excitation electrode and the second excitation electrode face each other in the second embodiment is good. For this reason, the decrease in the electromechanical coupling coefficient k (%) and the Q value due to the influence of the lead electrode in the second embodiment is not as large as the decrease in the electromechanical coupling coefficient k (%) and the Q value due to the influence of the lead electrode in the first embodiment. Therefore, even if a notch is formed in the insulating film of the second embodiment, the same effects as when a notch is formed in the first embodiment may not be obtained.

[0202] Next, while referring to FIGS. 28 and 29, FIGS. 28 and 29 are graphs showing simulation results based on the third embodiment. In the graphs of FIGS. 28 and 29, the horizontal axis represents Wn (μm), and the vertical axis represents the electromechanical coupling coefficient k (%).

[0203] In FIGS. 28 and 29, the simulation conditions are as follows. FIG. 28 shows the simulation result when Wwire = 10 μm, and FIG. 29 shows the simulation result when Wwire = 20 μm. Tq = 1.0 μm Te = 0.05 μm Te2 = 0.05 μm Lq = Wq = 120 μm Le = 55 μm We = 50 μm Le2 = 70 μm We2 = 60 μm dLe = Le2 - Le = 2 × dLe1 = 2 × dLe2 = 15 μm dWe = We2 - We = 2 × dWe1 = 2 × dWe2 = 10 μm Ln: Variable Wn: Variable

[0204] As shown in FIGS. 28 and 29, it is desirable that Ln and Wn be 2 μm or more and 6 μm or less. According to this, regardless of the size of Wwire, it is possible to suppress a decrease in the electromechanical coupling coefficient k (%).

[0205] <Fourth Embodiment> Next, with reference to FIGS. 30 and 31, the configuration of the crystal oscillator 400 according to the fourth embodiment will be described. FIG. 30 is a perspective view of the vibrating portion according to the fourth embodiment. FIG. 31 is a diagram showing the vibration distribution of the vibrating portion according to the fourth embodiment. The amplitude is indicated by light and dark, with the bright portion being the region of large amplitude and the dark portion being the region of small amplitude. In FIG. 31, the illustration of the second excitation electrode 414b is omitted.

[0206] As shown in FIG. 30, the fourth embodiment is different from the first embodiment in that, in a plan view, the center of the second excitation electrode 414b is located on the negative X-axis side with respect to the center of the first excitation electrode 414a, and is the same as the first embodiment except for the above point. Since the first lead electrode 315a extends in the positive X-axis direction from the outer edge portion on the positive X-axis side of the first excitation electrode 314a, the center of the second excitation electrode 414b is located in a direction away from the first lead electrode 415a with respect to the center of the first excitation electrode 414a. That is, in a plan view, the center of the excitation electrode with the larger area among the pair of excitation electrodes is shifted in a direction away from the lead electrode electrically connected to the excitation electrode with the smaller area among the pair of excitation electrodes with respect to the center of the excitation electrode with the smaller area.

[0207] Let the interval along the X-axis direction between the outer edge portion 471 on the negative X-axis side of the first excitation electrode 414a and the outer edge portion 481 on the negative X-axis side of the second excitation electrode 414b be G1. Let the interval along the X-axis direction between the outer edge portion 472 on the positive X-axis side of the first excitation electrode 414a and the outer edge portion 481 on the positive X-axis side of the second excitation electrode 414b be G2. In the crystal oscillator 400, the relationship 0 ≦ G2 < G1 holds.

[0208] As shown in FIG. 31, in the fourth embodiment, the vibrating region is limited to the region overlapping the first excitation electrode 414a, and the vibration in the region overlapping the first extraction electrode 415a is suppressed. For example, when simulating in a configuration where the first extraction electrode 415a is omitted from the fourth embodiment and G1 = G2, k = 6.86% and Q = 8,720. However, when simulating in a configuration where the first extraction electrode 415a with Wwire = 10 μm is added to that configuration, k = 6.77% and Q = 8,540. However, when simulating in a configuration according to the fourth embodiment further modified to G1 = 0 μm, k = 6.84% and Q = 8,770. That is, by setting 0 μm ≦ G1 < G2, the influence of the first extraction electrode 415a on the second excitation electrode 414b is suppressed, and the decrease in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0209] As described above, according to the present embodiment, the center of the second excitation electrode 414b is shifted in a direction away from the first extraction electrode 415a with respect to the center of the first excitation electrode 414a, and the relationship of 0 ≦ G2 < G1 holds.

[0210] According to this, the influence of the first extraction electrode 415a on the second excitation electrode 414b is suppressed, and the decrease in the electromechanical coupling coefficient k (%) and the Q value is suppressed.

[0211] <Fifth Embodiment> Next, with reference to FIG. 32, the configuration of the crystal oscillator 500 according to the fifth embodiment will be described. FIG. 32 is a cross-sectional view of the vibrating portion according to the fifth embodiment.

[0212] 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 in other respects. The mass addition film 542 is provided on the surface of the first excitation electrode 14a opposite to the crystal piece 11. When viewed in plan, the mass addition film 542 is provided along the outer edge of the first excitation electrode 14a outside the central portion of the first excitation electrode 14a. Also, when viewed in plan, the mass addition film 542 is provided in a region overlapping 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.

[0213] Note that the position and material of the mass addition film 542 are not limited as described above. The mass addition film 542 may be provided at any position between the first excitation electrode 14a and the crystal piece 11, on the surface of the second excitation electrode 14b opposite to the crystal piece 11, or between the second excitation electrode 14b and the crystal piece 11. The material of the mass addition film 542 may be a metal different from that of the first excitation electrode 14a.

[0214] The mass addition film 542 reduces the speed of sound due to the mass addition effect. Therefore, the speed of sound in the region where the mass addition film 542 is provided is lower than the speed of sound in the region where the mass addition film 542 is not provided. That is, when viewed in plan, the region where the first excitation electrode 14a and the second excitation electrode 14b face each other has a high-speed sound region 517 provided in the central portion and a low-speed sound region 518 provided outside the high-speed sound region 517. The low-speed sound region 518 is provided, for example, in a continuous frame shape in the circumferential direction, but may also be provided in a non-continuous frame shape in the circumferential direction. For example, the low-speed sound region 518 may be provided in a strip shape extending from the outer edge 71 to the outer edge 72 or in a strip shape extending from the outer edge 73 to the outer edge 74.

[0215] According to this, it is possible to suppress the electromechanical coupling coefficient k (%) of the spurious mode and improve the electromechanical coupling coefficient k (%) of the main mode.

[0216] In addition, in the present embodiment, when the mass addition film 542 is treated as a part of the first excitation electrode 14a, the thickness Te is the average thickness of the laminate composed of the mass addition film 542 and the first excitation electrode 14a.

[0217] <Sixth Embodiment> Next, with reference to FIG. 33, the configuration of the crystal oscillator 600 according to the sixth embodiment will be described. FIG. 33 is a cross-sectional view of the vibrating portion according to the sixth embodiment.

[0218] The sixth embodiment is different from the first embodiment in that a plurality of holes H are formed in the central portion of the first excitation electrode 614a in plan view, and is the same as the first embodiment in other respects.

[0219] The holes H penetrate the first excitation electrode 614a in the Y' axis direction. The plurality of holes H increase the speed of sound due to the mass reduction effect. For this reason, the speed of sound in the region where the plurality of holes H are formed is higher than the speed of sound in the region where the plurality of holes H are not formed. That is, when viewed in plan, the region where the first excitation electrode 14a and the second excitation electrode 14b face each other has a high-speed region 617 provided at the center and a low-speed region 618 provided outside the high-speed region 617.

[0220] According to this, the electromechanical coupling coefficient k (%) of the spurious mode can be suppressed, and the electromechanical coupling coefficient k (%) of the main mode can be improved.

[0221] In the present embodiment, the area of the first excitation electrode 614a in plan view is the area of the region surrounded by the outer edge portion of the first excitation electrode 614a, and the inside 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-speed region 618 is Te1 and the aperture ratio of the plurality of holes H is Har, the thickness Te is calculated by the following formula. Te = Te1 × (1 - Har)

[0222] In order for the inside of the hole H in the high supersonic region 617 to function as part of the first excitation electrode 614a, when the inner diameter of the hole H is Hr, it is desirable that the relationship 0 < Hr / Tq ≤ 2.0 holds. At this time, since the reduction rate of the capacitance due to the hole H can be suppressed to 1% or less, the inside of the hole H can also function sufficiently as an excitation electrode. Further, it is more desirable that the relationship 0 < Hr / Tq ≤ 1.5 holds, and it is even more desirable that the relationship 0 < Hr / Tq ≤ 1.0 holds. If 0 < Hr / Tq ≤ 1.5, the reduction rate of the capacitance can be suppressed to 0.5% or less, and if 0 < Hr / Tq ≤ 1.0, the reduction rate of the capacitance can be suppressed to 0.1% or less. In addition, in order to form the hole H with sufficient machining accuracy, it is desirable that 0.1 ≤ Hr / Tq, and it is more desirable that 0.5 ≤ Hr / Tq.

[0223] Note that 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.

[0224] <Seventh Embodiment> Next, while referring to FIG. 34, the configuration of the crystal oscillator 700 according to the seventh embodiment will be described. FIG. 34 is a cross-sectional view of the vibrating portion according to the seventh embodiment.

[0225] The seventh embodiment is different from the second embodiment in that it further includes a mass addition film 542, and is the same as the second embodiment in other respects. That is, when viewed in plan, the region where the first excitation electrode 214a and the second excitation electrode 214b face each other has a high supersonic region 717 provided in the central portion and a low supersonic region 718 provided outside the high supersonic region 717. The mass addition film 542 is provided from the region overlapping the outer edge portion of the second excitation electrode 214b to the inside thereof. Therefore, in plan view, the low supersonic region 718 is located inside the outer edge portion of the first excitation electrode 214a.

[0226] According to this, the electromechanical coupling coefficient k (%) of the spurious mode can be suppressed, and the electromechanical coupling coefficient k (%) of the main mode can be improved.

[0227] <Eighth Embodiment> Next, with reference to FIG. 35, the configuration of the crystal oscillator 800 according to the eighth embodiment will be described. FIG. 35 is a cross-sectional view of the vibrating portion according to the eighth embodiment.

[0228] The eighth embodiment is different from the second embodiment in that a plurality of holes H are formed in the central portion of the first excitation electrode 814a in plan view, and is the same as the second embodiment in other respects.

[0229] According to this, it is possible to suppress the electromechanical coupling coefficient k (%) of the spurious mode and improve the electromechanical coupling coefficient k (%) of the main mode.

[0230] A part or all of the embodiments of the present invention are appended below. Note that the present invention is not limited to the following appendices.

[0231] <1> A piezoelectric piece having a first main surface and a second main surface facing the first main surface, A first excitation electrode provided on the first main surface, A second excitation electrode provided on the second main surface and comprising In a plan view in the facing direction in which the first main surface and the second main surface face each other, the area of the second excitation electrode is larger than the area of the first excitation electrode, and a part of the second excitation electrode overlaps all of the first excitation electrode, The thickness of the second excitation electrode along the facing direction is larger than the thickness of the first excitation electrode along the facing direction, A piezoelectric oscillator.

[0232] <2> In a plan view in the facing direction, all of the outer edge portions of the first excitation electrode are located inside the outer edge portion of the second excitation electrode, The piezoelectric oscillator according to <1>.

[0233] <3> Let the thickness of the first excitation electrode along the opposing direction be Te (μm), the thickness of the second excitation electrode along the opposing direction be Te2 (μm), and the thickness of the piezoelectric element along the opposing direction be Tq (μm). When the average density of the first excitation electrode and the second excitation electrode is ρ (kg / m3), Te2 / Tq = 0.00001 × ρ + 0.39 × Te / Tq + 0.16 ± 0.01 The following relationship holds. The piezoelectric vibration element according to <1> or <2>.

[0234] <4> A piezoelectric element having a first main surface and a second main surface opposing the first main surface, A first excitation electrode provided on the first main surface, A second excitation electrode provided on the second main surface, An insulating film laminated on the second excitation electrode, Comprising, In a plan view in the opposing direction in which the first main surface and the second main surface face each other, the area of the laminate 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 laminate overlaps all of the first excitation electrode. The sum of the thickness of the second excitation electrode and the thickness of the insulating film along the opposing direction is larger than the thickness of the first excitation electrode along the opposing direction. Piezoelectric vibration element.

[0235] <5> The insulating film is laminated on the surface of the second excitation electrode opposite to the piezoelectric element. The piezoelectric vibration element according to <4>.

[0236] <6> In a plan view in the opposing direction, All of the outer edge portions of the second excitation electrode are provided inside the outer edge portion of the first excitation electrode. All of the outer edge portions of the insulating film are provided outside the outer edge portion of the first excitation electrode. The piezoelectric vibration element according to <4> or <5>.

[0237] <7> 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. The piezoelectric vibration element according to any one of <4> to <6>.

[0238] <8> Let the thickness of the first excitation electrode along the opposing direction be Te (μm), the thickness of the second excitation electrode along the opposing direction be Te2 (μm), the thickness of the insulating film along the opposing direction be Te3 (μm), and the thickness of the piezoelectric piece along the opposing direction be Tq (μm). When the average density of the first excitation electrode, the second excitation electrode, and the insulating film is ρ' (kg / m3), (Te2 + Te3) / Tq = 0.00001×ρ' + 0.39×Te / Tq + 0.16 ± 0.01 the following relationship holds. The piezoelectric vibration element according to any one of <4> to <7>.

[0239] <9> The materials of the first excitation electrode and the second excitation electrode are aluminum. The material of the insulating film is silicon oxide. The piezoelectric vibration element according to <8>.

[0240] <10> A first lead electrode provided on the first main surface and electrically connected to the first excitation electrode, and a second lead electrode provided on the second main surface and electrically connected to the second excitation electrode. The piezoelectric vibration element further includes: In the excitation electrode with the larger area in plan view in the opposing direction among the first excitation electrode and the second excitation electrode, a notch is formed in a region facing the lead electrode that is electrically connected to the excitation electrode with the smaller area in plan view in the opposing direction among the first lead electrode and the second lead electrode. The piezoelectric vibration element according to any one of <1> to <9>.

[0241] <11> A first lead electrode provided on the first main surface and electrically connected to the first excitation electrode, A second extraction electrode provided on the second main surface and electrically connected to the second excitation electrode, and further includes The center of the larger excitation electrode in terms of area in a plan view in the facing direction among the first excitation electrode and the second excitation electrode is shifted in a direction away from the extraction electrode electrically connected to the smaller excitation electrode in terms of area among the first extraction electrode and the second extraction electrode with respect to the center of the smaller excitation electrode in terms of area in a plan view in the facing direction. The piezoelectric vibration element according to any one of <1> to <10>.

[0242] <12> In a plan view in the facing direction, the region where the first excitation electrode and the second excitation electrode face each other has a high sound velocity region provided in the central portion and a low sound velocity region provided outside the high sound velocity region. The piezoelectric vibration element according to any one of <1> to <11>.

[0243] <13> In a plan view in the facing direction, the first excitation electrode and the second excitation electrode are provided in a rectangular shape with their centers overlapping, having sides parallel to each other extending in the first direction and sides parallel to each other extending in a second direction intersecting the first direction. In a plan view in the facing direction, when the distance between adjacent sides of the first excitation electrode and the second excitation electrode in a certain direction is De (μm), and the thickness of the piezoelectric sheet along the facing direction is Tq (μm), 5.22×Tq - 0.45 ≤ De is satisfied. The piezoelectric vibration element according to any one of <1> to <12>.

[0244] <14> The main vibration mode is thickness shear vibration. The piezoelectric vibration element according to any one of <1> to <13>.

[0245] <15> The piezoelectric sheet is a quartz sheet. The piezoelectric vibrator according to any one of <1> to <14>.

[0246] <16> The cut angle of the crystal piece is AT cut, BT cut or ST cut. The piezoelectric vibrator according to <15>.

[0247] In the present specification, a quartz crystal resonator having a quartz crystal piece as a piezoelectric element has been described as an example. However, the piezoelectric resonator is not limited to this. Examples of the piezoelectric piece suitably used for the piezoelectric vibrator according to the present embodiment include piezoelectric ceramics such as lead zirconate titanate (PZT) and aluminum nitride, and piezoelectric single crystals such as lithium niobate and lithium tantalate. However, the piezoelectric piece is not limited to these and can be appropriately selected.

[0248] The embodiment according to the present invention can be appropriately applied without particular limitation to devices that perform electromechanical energy conversion by the piezoelectric effect, such as timing devices, sound emitters, oscillators, load sensors, and the like.

[0249] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibrator capable of improving the electromechanical coupling coefficient.

[0250] Note that the embodiments described above are for facilitating the understanding of the present invention and are not for limiting the interpretation of the present invention. The present invention can be modified / improved without departing from its gist, and equivalents thereof are also included in the present invention. That is, those obtained by appropriately making design changes by those skilled in the art to the embodiments and / or variations are also included in the scope of the present invention as long as they have the features of the present invention. For example, each element included in the embodiments and / or variations and its arrangement, material, conditions, shape, size, etc. are not limited to those illustrated and can be changed as appropriate. Also, the embodiments and variations are illustrative, and it goes without saying that partial substitution or combination of the configurations shown in different embodiments and / or variations is possible, and these are also included in the scope of the present invention as long as they include the features of the present invention.

Description of Reference Numerals

[0251] 1…Crystal oscillator 10…Crystal vibration element 11…Crystal piece 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 connection electrode 16b…Second connection electrode Lq…Length along the X-axis direction of the crystal piece Wq…Length along the Z'-axis direction of the crystal piece Tq…Thickness of the crystal piece Le…Length along the X-axis direction of the first excitation electrode We…Length along the Z'-axis direction of the first excitation electrode Te…Thickness of the first excitation electrode Le2…Length along the X-axis direction of the second excitation electrode We2…Length along the Z'-axis direction of the second excitation electrode Te2…Thickness of the second excitation electrode

Claims

1. a piezoelectric piece having a first main surface and a second main surface opposite to the first main surface; A first excitation electrode provided on the first main surface; a second excitation electrode provided on the second main surface; Equipped with In a plan view in a direction in which the first principal surface and the second principal surface face each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a part of the second excitation electrode overlaps with the entirety of the first excitation electrode, a thickness of the second excitation electrode along the facing direction is greater than a thickness of the first excitation electrode along the facing direction, The thickness of the first excitation electrode along the facing direction is Te (μm), the thickness of the second excitation electrode along the facing direction is Te2 (μm), and the thickness of the piezoelectric piece along the facing direction is Tq (μm), When the average density of the first excitation electrode and the second excitation electrode is ρ (kg / m3), Te2 / Tq=-0.00001×ρ+0.39×Te / Tq+0.16±0.01 The relationship is established as follows: Piezoelectric vibration element.

2. A piezoelectric piece having a first principal surface and a second principal surface opposite the first principal surface; A first excitation electrode provided on the first main surface; a second excitation electrode provided on the second main surface; Equipped with In a plan view in a direction in which the first principal surface and the second principal surface face each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a part of the second excitation electrode overlaps with the entirety of the first excitation electrode, a thickness of the second excitation electrode along the facing direction is greater than a thickness of the first excitation electrode along the facing direction, a first extraction electrode provided on the first main surface and electrically connected to the first excitation electrode; a second extraction electrode provided on the second main surface and electrically connected to the second excitation electrode, a cutout portion is formed in a region of one of the first excitation electrode and the second excitation electrode, which has a larger area in a plan view in the opposing direction, facing an extraction electrode that is electrically connected to one of the first extraction electrode and the second extraction electrode, which has a smaller area in a plan view in the opposing direction; Piezoelectric vibration element.

3. A piezoelectric piece having a first principal surface and a second principal surface opposite the first principal surface; A first excitation electrode provided on the first main surface; a second excitation electrode provided on the second main surface; Equipped with In a plan view in a direction in which the first principal surface and the second principal surface face each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a part of the second excitation electrode overlaps with the entirety of the first excitation electrode, a thickness of the second excitation electrode along the facing direction is greater than a thickness of the first excitation electrode along the facing direction, a first extraction electrode provided on the first main surface and electrically connected to the first excitation electrode; a second extraction electrode provided on the second main surface and electrically connected to the second excitation electrode; Further equipped with Only the first excitation electrode and the first extraction electrode are provided on the first principal surface, Only the second excitation electrode and the second extraction electrode are provided on the second principal surface, a center of one of the first excitation electrode and the second excitation electrode, which has a larger area in a plan view in the opposing direction, is shifted in a direction away from the extraction electrode, which is electrically connected to the excitation electrode having a smaller area, of the first extraction electrode and the second extraction electrode, with respect to a center of the excitation electrode having a smaller area in a plan view in the opposing direction. Piezoelectric vibration element.

4. A piezoelectric piece having a first principal surface and a second principal surface opposite the first principal surface; A first excitation electrode provided on the first main surface; a second excitation electrode provided on the second main surface; Equipped with In a plan view in a direction in which the first principal surface and the second principal surface face each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a part of the second excitation electrode overlaps with the entirety of the first excitation electrode, a thickness of the second excitation electrode along the facing direction is greater than a thickness of the first excitation electrode along the facing direction, the first excitation electrode has a high sound velocity region and a low sound velocity region; In a plan view in the opposing direction, the high sound velocity region is provided in a central portion of a region where the first excitation electrode and the second excitation electrode oppose each other, and the low sound velocity region is provided outside the high sound velocity region. Piezoelectric vibration element.

5. A piezoelectric piece having a first principal surface and a second principal surface opposite the first principal surface; A first excitation electrode provided on the first main surface; a second excitation electrode provided on the second main surface; Equipped with In a plan view in a direction in which the first principal surface and the second principal surface face each other, an area of ​​the second excitation electrode is larger than an area of ​​the first excitation electrode, and a part of the second excitation electrode overlaps with the entirety of the first excitation electrode, a thickness of the second excitation electrode along the facing direction is greater than a thickness of the first excitation electrode along the facing direction, In a plan view in the opposing direction, the first excitation electrode and the second excitation electrode are They are arranged in a rectangular shape with their centers overlapping, The substrate has parallel sides extending in a first direction and parallel sides extending in a second direction intersecting the first direction, In a plan view in the opposing direction, a distance between adjacent sides in a direction in which the first excitation electrode and the second excitation electrode are located is defined as De (μm), When the thickness of the piezoelectric piece along the facing direction is Tq (μm), 5.22×Tq−0.45≦De The relationship is established as follows: Piezoelectric vibration element.

6. a piezoelectric piece having a first main surface and a second main surface opposite to the first main surface; A first excitation electrode provided on the first main surface; A second excitation electrode provided on the second main surface; an insulating film laminated on the second excitation electrode; Equipped with an area of ​​a laminate including the second excitation electrode and the insulating film is larger than an area of ​​the first excitation electrode in a plan view in a direction in which the first principal surface and the second principal surface face each other, and a part of the laminate overlaps with the entirety of the first excitation electrode; a sum of a thickness of the second excitation electrode and a thickness of the insulating film along the opposing direction is greater than a thickness of the first excitation electrode along the opposing direction; Piezoelectric vibration element.

7. In a plan view in the opposing direction, all of the outer edges of the first excitation electrode are located inside the outer edges of the second excitation electrode. The piezoelectric vibration element according to claim 1 .

8. The insulating film is laminated on a surface of the second excitation electrode opposite to the piezoelectric piece. The piezoelectric vibration element according to claim 6 .

9. In a plan view in the opposing direction, The entire outer edge of the second excitation electrode is provided inside the outer edge of the first excitation electrode, the entire outer edge of the insulating film is provided outside the outer edge of the first excitation electrode; The piezoelectric vibration element according to claim 6 or 8.

10. a thickness of the second excitation electrode along the facing direction is smaller than a thickness of the first excitation electrode along the facing direction; The piezoelectric vibration element according to claim 6 .

11. The first excitation electrode and the second excitation electrode are made of aluminum, The insulating film is made of silicon oxide. The piezoelectric vibration element according to claim 6 .

12. a first extraction electrode provided on the first main surface and electrically connected to the first excitation electrode; a second extraction electrode provided on the second main surface and electrically connected to the second excitation electrode; Further equipped with a center of one of the first excitation electrode and the second excitation electrode, which has a larger area in a plan view in the opposing direction, is shifted in a direction away from the extraction electrode, which is electrically connected to the excitation electrode having a smaller area, of the first extraction electrode and the second extraction electrode, with respect to a center of the excitation electrode having a smaller area in a plan view in the opposing direction.

7. The piezoelectric vibration element according to claim 1, 2, 5 or 6.

13. In a plan view in the opposing direction, a region where the first excitation electrode and the second excitation electrode oppose each other has a high sound velocity region provided in a central portion and a low sound velocity region provided outside the high sound velocity region.

7. The piezoelectric vibration element according to claim 1, 2, 5 or 6.

14. The main vibration mode is thickness-shear vibration. The piezoelectric vibration element according to claim 1 .

15. The piezoelectric piece is a quartz crystal piece. The piezoelectric vibration element according to claim 1 .

16. The cut angle of the quartz crystal piece is an AT cut, a BT cut, or an ST cut. The piezoelectric vibration element according to claim 15.

Images