Piezoelectric vibration element, piezoelectric vibrator and piezoelectric oscillator

Description

[Technical field]

[0001] The present invention relates to a piezoelectric vibration element, a piezoelectric vibrator, and a piezoelectric oscillator. [Background technology]

[0002] Piezoelectric vibration elements are used in various electronic devices such as mobile communication terminals, communication base stations, home appliances, etc. as timing devices, sensors, oscillators, etc. 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 quartz crystal unit having excitation electrodes facing both main surfaces of a quartz crystal piece, characterized in that a hole is provided in the central region of the excitation electrodes to reduce the mass and distance the vibration frequency of the overtone vibration from the fundamental vibration. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2010-81317 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, when the quartz crystal element is thinned to achieve higher frequencies, it is difficult to sufficiently separate the vibration frequency of the inharmonic mode from the fundamental vibration of the main mode in the quartz crystal resonator described in Patent Document 1, and for example, the frequency of the inharmonic mode may exist within a range of about ±1% from the frequency of the main mode. This causes a problem in that the influence of the inharmonic mode on the main mode cannot be sufficiently suppressed by simply separating the frequency of the overtone mode from the frequency of the main mode.

[0006] The present invention has been made in consideration of the above circumstances, and an object of the present invention is to provide a piezoelectric vibration element, a piezoelectric vibrator, and a piezoelectric oscillator that can improve the electromechanical coupling coefficient. [Means for solving the problem]

[0007] A piezoelectric vibration element according to one embodiment of the present invention comprises a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction and having a thickness in a third direction intersecting the first direction and the second direction, and an excitation electrode provided on the main surface, wherein when the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, a relationship of 45≦Le1 / Tq≦120 holds, and a first hole portion penetrating the excitation electrode along the third direction is formed in the center of the excitation electrode in the first direction. Effect of the Invention

[0008] According to the present invention, it is possible to provide a piezoelectric vibration element, a piezoelectric vibrator, and a piezoelectric oscillator that are capable of improving the electromechanical coupling coefficient. [Brief description of the drawings]

[0009] [Figure 1] 1 is a cross-sectional view of a crystal oscillator according to a first embodiment. [Diagram 2] 1 is a cross-sectional view of a quartz crystal resonator according to a first embodiment. [Diagram 3] FIG. 1 is a plan view of a quartz crystal vibration element according to a first embodiment. [Figure 4] FIG. 2 is a plan view of a first excitation electrode according to the first embodiment. [Diagram 5] 3 is a cross-sectional view of a vibration section according to the first embodiment. FIG. [Figure 6] FIG. 11 is a plan view of a first excitation electrode according to a second embodiment. [Figure 7] FIG. 11 is a plan view of a first excitation electrode according to a third embodiment. [Figure 8] FIG. 13 is a plan view of a first excitation electrode according to a fourth embodiment. [Figure 9] FIG. 13 is a plan view of a first excitation electrode according to a fifth embodiment. [Figure 10] FIG. 13 is a plan view of a first excitation electrode according to a sixth embodiment. [Figure 11] FIG. 13 is a plan view of a first excitation electrode according to the seventh embodiment. [Figure 12] FIG. 13 is a plan view of a first excitation electrode according to the eighth embodiment. [Figure 13] FIG. 13 is a plan view of a first excitation electrode according to the ninth embodiment. [Figure 14] FIG. 11 is a diagram showing a simulation result in the first embodiment. [Figure 15] 6 is a graph showing the influence of the shape and size of a first hole in a rectangular first excitation electrode. [Figure 16] 6 is a graph showing the influence of the shape and size of a first hole in a rectangular first excitation electrode. [Figure 17] 13 is a graph showing the influence of the area ratio of a first hole portion in a square first excitation electrode. [Figure 18] 13 is a graph showing the influence of the area ratio of a first hole portion in a square first excitation electrode. [Figure 19] 11 is a graph showing an optimum condition for the area ratio of a first hole portion in a square first excitation electrode. [Figure 20] 11 is a graph showing conditions for improving K in the S0 mode in a rectangular first excitation electrode. [Figure 21] 11 is a graph showing the condition under which K of the S0 mode becomes maximum in a rectangular first excitation electrode. [Figure 22] 11 is a graph showing the condition under which K of the S1Z mode is minimized in a rectangular first excitation electrode. [Figure 23] FIG. 13 is a diagram showing a simulation result in the second embodiment. [Figure 24] 11 is a graph showing the influence of the size of the first hole and the positions of the second and third holes. [Diagram 25] 6 is a graph showing the influence of the shape of the first excitation electrode and the positions of the second hole portion and the third hole portion. [Figure 26] 13 is a graph showing the relationship between the short side length and the hole interval. [Figure 27] 1 is a graph showing area conditions for improving K in the S0 mode. [Figure 28] 1 is a graph showing area conditions for improving K in the S0 mode. [Figure 29] 13 is a graph showing the influence of the dimensions of a notched first hole portion in a rectangular first excitation electrode. [Diagram 30] 13 is a graph showing the influence of the dimensions of a notched first hole portion in a rectangular first excitation electrode. [Diagram 31] 11 is a graph showing the condition under which K of the S0 mode becomes maximum in a rectangular first excitation electrode. [Diagram 32] 11 is a graph showing the influence of the area ratio of a hole in a square first excitation electrode. [Diagram 33] 11 is a graph showing the influence of the area ratio of a hole in a square first excitation electrode. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, an embodiment of the present invention will be described. In the following description of the drawings, the same or similar components are represented 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 interpreted as being limited to the embodiment.

[0011] In order to clarify the mutual relationships between the drawings and to aid in understanding the positional relationships of the various components, an orthogonal coordinate system consisting of an X-axis, a Y'-axis, and a Z'-axis may be conveniently attached to each drawing. The X-axis, the Y'-axis, and the Z'-axis correspond to each other in each drawing. The X-axis, the Y'-axis, and the Z'-axis each correspond to the crystallographic axes of the quartz blank 11, which will be described later. The X-axis corresponds to the electrical axis (polarity axis) of the quartz, the Y-axis corresponds to the mechanical axis of the quartz, and the Z-axis corresponds to the optical axis of the quartz. The Y'-axis and the Z'-axis are respectively axes obtained by rotating the Y-axis and Z-axis around the X-axis by 35 degrees 15 minutes ± 1 minute 30 seconds in the direction from the Y-axis to the Z-axis.

[0012] 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". The directions of the tips of the arrows of the X-axis, Y'-axis, and Z'-axis are referred to as "positive" or "+ (plus)", and the directions opposite to the arrows are referred to as "negative" or "- (minus)". 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-down directions of the crystal resonator element 10, the crystal resonator 1, and the crystal oscillator 100 are not limited to these directions. The plane specified by the X-axis and the Z'-axis is referred to as the Z'X plane, and the same applies to the planes specified by the other axes.

[0013] First Embodiment

[0014] First, a schematic configuration of a crystal oscillator according to an embodiment will be described with reference to Fig. 1. Fig. 1 is a cross-sectional view of the crystal oscillator according to the first embodiment.

[0015] In the following description, a crystal oscillator (XO: Crystal Oscillator) having a crystal resonator (Quartz Crystal Resonator Unit) is taken as an example of a piezoelectric oscillator. A crystal resonator unit having a crystal resonator element (Quartz Crystal Resonator) is taken as an example of a piezoelectric resonator unit. A crystal resonator element having a crystal piece is taken as an example of a piezoelectric resonator element. A crystal piece is a type of piezoelectric body (piezoelectric piece) that vibrates in response to an applied voltage. The piezoelectric oscillator is not limited to a crystal resonator, and may use other piezoelectric bodies such as ceramics. Similarly, the piezoelectric resonator is not limited to a crystal resonator, and may use other piezoelectric bodies such as ceramics. Similarly, the piezoelectric resonator element is not limited to a crystal resonator element, and may use other piezoelectric bodies such as ceramics.

[0016] As shown in FIG. 1, the crystal oscillator 100 includes a crystal unit 1, a mounting substrate 130, a cover 140, and an electronic component 156.

[0017] The crystal unit 1 and the electronic component 156 are housed in a space formed between the mounting substrate 130 and the lid 140. The space formed by the mounting substrate 130 and the lid 140 is, for example, hermetically sealed. This space may be hermetically sealed in a vacuum state, or may be hermetically sealed in a state filled with a gas such as an inert gas.

[0018] The mounting substrate 130 is a flat circuit board and is configured to include, for example, a glass epoxy plate and a wiring layer patterned on the glass epoxy plate.

[0019] The quartz crystal unit 1 is provided on one surface (the upper surface in FIG. 1) of the mounting substrate 130. More specifically, the quartz crystal unit 1 is electrically connected to the wiring layer of the mounting substrate 130 by a bonding wire 166. The quartz crystal unit 1 and the wiring layer of the mounting substrate 130 are also joined by solder 153. As a result, the quartz crystal unit 1 is sealed in the space formed between the mounting substrate 130 and the lid 140.

[0020] The lid 140 includes an opening with a bottom that is open on one side (the lower side in FIG. 1). In other words, the lid 140 includes a flat top wall, a side wall extending from the outer edge of the top wall toward the mounting substrate 130, and a flange extending outward from the tip of the side wall. The flange is bonded to one surface (the upper surface in FIG. 1) of the mounting substrate 130. In this way, the crystal unit 1 bonded to the mounting substrate 130 is housed inside the lid 140. The lid 140 is made of a metal material and is formed, for example, by drawing a metal plate.

[0021] The electronic component 156 is provided on one surface (the upper surface in FIG. 1) of the mounting board 130. More specifically, the wiring layer of the mounting board 130 and the electronic component 156 are joined by solder 153. In this way, the electronic component 156 is mounted on the mounting board 130.

[0022] The electronic component 156 is electrically connected to the crystal unit 1 through a wiring layer of the mounting substrate 130. The electronic component 156 includes, for example, a capacitor, an IC chip, and the like. The electronic component 156 is, for example, a part of an oscillation circuit that causes the crystal unit 1 to oscillate, or a part of a temperature compensation circuit that compensates for the temperature characteristics of the crystal unit 1. When the electronic component 156 includes a temperature compensation circuit, the crystal oscillator 100 is sometimes called a temperature compensated crystal oscillator (TCXO).

[0023] Next, a schematic configuration of a quartz crystal resonator according to an embodiment will be described with reference to Figs. 2 to 5. Fig. 2 is a cross-sectional view of a quartz crystal resonator according to the first embodiment. Fig. 3 is a plan view of a quartz crystal resonator element according to the first embodiment. Fig. 4 is a plan view of a first excitation electrode according to the first embodiment. Fig. 5 is a cross-sectional view of a vibration part according to the first embodiment. Fig. 2 shows a cross section parallel to the Y'Z' plane along line II-II shown in Fig. 3. Fig. 5 shows a cross section parallel to the Y'Z' plane along line VV shown in Fig. 3.

[0024] The Z'-axis direction corresponds to an example of a "first direction", the X-axis direction corresponds to an example of a "second direction", and the Y'-axis direction corresponds to an example of a "third direction". However, the first direction, second direction, and third direction are not limited to the above. For example, the X-axis direction may be the first direction, and the Z'-axis direction may be the second direction.

[0025] The quartz crystal resonator 1 includes a quartz crystal resonator element 10, an upper cover 20, a bonding portion 30, an insulating layer 40, and a supporting substrate 50. The insulating layer 40 and the supporting substrate 50 correspond to an example of a "first cover member," and the upper cover 20 corresponds to an example of a "second cover member."

[0026] The quartz crystal element 10 is an electromechanical energy conversion element that converts electrical energy and mechanical energy into each other by the piezoelectric effect. The frequency of the main mode of the quartz crystal element 10 is, for example, in the GHz band, for example, about 1.0 GHz to 2.0 GHz, for example, about 1.45 GHz. The frequency of the inharmonic mode of the quartz crystal element 10 exists, for example, within a range of about 1% of the main mode frequency. The quartz crystal element 10 includes a thin quartz crystal piece (Quartz Crystal Element) 11, a first excitation electrode 14a and a second excitation electrode 14b that constitute a pair of excitation electrodes, a first extraction electrode 15a and a second extraction electrode 15b that constitute a pair of extraction electrodes, a first connection electrode 16a and a second connection electrode 16b that constitute a pair of connection electrodes, and a via electrode 17.

[0027] The quartz crystal blank 11 has an upper surface 12a and a lower surface 12b that face each other. The upper surface 12a is located on the side that faces the upper cover 20. The lower surface 12b is located on the side that faces the support substrate 50. The upper surface 12a and the lower surface 12b correspond to a pair of main surfaces of the quartz crystal blank 11.

[0028] The quartz blank 11 is, for example, an AT-cut quartz crystal. An AT-cut quartz crystal is formed so that the XZ' plane is the main surface and the thickness is in the direction parallel to the Y' axis. As an example, when the top surface 12a is viewed in a plan view (hereinafter simply referred to as "plan view"), the shape of the quartz blank 11 (hereinafter referred to as the "planar shape") is rectangular with long sides extending in the Z'-axis direction and short sides extending in the X-axis direction. The quartz blank 11 also has a thickness in the Y'-axis direction. As an example, the quartz blank 11 is in the shape of a flat plate with a uniform thickness.

[0029] The planar shape of the crystal piece is not limited to the above, and may be a rectangle with a short side extending in the Z'-axis direction and a long side extending in the X-axis direction. The planar shape of the crystal piece may be a polygonal shape, a circular shape, an elliptical shape, or a combination of these. The crystal piece is not limited to a flat plate shape, and may be a so-called mesa structure in which the thickness of the portion overlapping the first excitation electrode 14a and the second excitation electrode 14b is greater than the surrounding thickness. The crystal piece may be a so-called inverted mesa structure in which the thickness of the portion overlapping the first excitation electrode 14a and the second excitation electrode 14b is smaller than the surrounding thickness. When the thickness of the crystal piece is changed partially, it 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.

[0030] The AT-cut quartz piece 11 is cut out with the XZ' plane as the principal surface, and the Y'-axis and Z'-axis are respectively determined by rotating the Y-axis and Z-axis around the X-axis by 35 degrees 15 minutes ± 1 minute 30 seconds from the Y-axis in the direction of the Z-axis out of the X-axis, Y-axis, and Z-axis, which are the crystal axes of synthetic quartz crystal.

[0031] The quartz crystal vibrating element 10 using the AT-cut quartz crystal blank 11 has high frequency stability over a wide temperature range. In addition, the AT-cut quartz crystal vibrating element has excellent aging characteristics and can be manufactured at low cost. Furthermore, the AT-cut quartz crystal vibrating element uses the thickness shear vibration mode as its main vibration.

[0032] The cut angle of the quartz crystal piece is not limited to the above. The rotation angle of the Y'-axis and Z'-axis of the AT-cut quartz crystal piece 11 may be tilted from 35°15′ in the range of −5° to +15°. The cut angle of the quartz crystal piece may be a cut other than the AT cut, such as a BT cut, a GT cut, or an SC cut.

[0033] Crystal piece 11 includes a vibrating portion 11A, an opening 11B, and a holding portion 11C.

[0034] As described above, the vibrating portion 11A of the crystal blank 11 vibrates at a predetermined resonance frequency with the thickness-shear vibration mode as the main vibration. The opening 11B of the crystal blank 11 is an opening formed to surround the vibrating portion 11A when the upper surface 12a is viewed in plan. The opening 11B penetrates the crystal blank 11 in the thickness direction parallel to the Z'-axis direction and communicates with a cavity 41 described later. The opening 11B is formed so that the vibrating portion 11A and the holding portion 11C are spaced apart, for example, by about 10 μm. The holding portion 11C of the crystal blank 11 holds the end of the vibrating portion 11A (the lower end in FIG. 2). The holding portion 11C is connected, for example, to the side of the vibrating portion 11A on the negative side of the X-axis.

[0035] The first excitation electrode 14a and the second excitation electrode 14b apply an alternating voltage to the vibration part 11A to excite the vibration part 11A. The first excitation electrode 14a and the second excitation electrode 14b are provided in the center of the vibration part 11A. The first excitation electrode 14a is provided on the upper surface 12a, and the second excitation electrode 14b is provided on the lower surface 12b. The first excitation electrode 14a and the second excitation electrode 14b face each other in the Y'-axis direction with the vibration part 11A in between.

[0036] The first excitation electrode 14a has a rectangular shape in plan view with long sides extending in the Z'-axis direction and short sides extending in the X-axis direction. The first excitation electrode 14a has a thickness in the Y'-axis direction. The second excitation electrode 14b has a similar shape.

[0037] 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 with long sides extending in the X-axis direction. The planar shapes of the first excitation electrode and the second excitation electrode may be square, polygonal, circular, elliptical, or a combination of these.

[0038] As shown in FIG. 4 and FIG. 5, a hole H1 is formed in the center of the first excitation electrode 14a in the plan view, penetrating the first excitation electrode 14a along the Y'-axis direction. The hole H1 corresponds to an example of a "first hole". In the plan view, the center of the hole H1 is located in the center of the first excitation electrode 14a in the Z'-axis direction, and is located in the center of the first excitation electrode 14a in the X-axis direction. In other words, the hole H1 is formed so that its geometric center coincides with the geometric center of the first excitation electrode 14a. The hole H1 is spaced apart from the ends along the long and short sides of the first excitation electrode 14a. The planar shape of the hole H1 is a rectangle having a short side extending in the Z'-axis direction and a long side extending in the X-axis direction. That is, the longitudinal direction of the hole H1 is perpendicular to the longitudinal direction of the first excitation electrode 14a.

[0039] Note that the hole may be spaced apart from the center of the first excitation electrode 14a in the X-axis direction, as long as it is located at the center of the first excitation electrode 14a in the Z'-axis direction.

[0040] The planar shape of the hole is not limited to the above. The planar shape of the hole may be a polygon, a circle, an ellipse, or a combination of these. The hole H1 may include a plurality of small holes, and the shape of the plurality of small holes is not particularly limited.

[0041] No hole is formed in the second excitation electrode 14b, and the hole H1 faces the second excitation electrode 14b in the Y'-axis direction. The crystal blank 11 is excited in a vibration region Rv where the first excitation electrode 14a and the second excitation electrode 14b overlap in the Y'-axis direction, and the crystal blank 11 is not excited in a non-vibration region Rnv where the hole H1 overlaps in the Y'-axis direction.

[0042] A hole may be formed in the center of the second excitation electrode, similar to the first excitation electrode. In this case, it is preferable that the planar shape and area of ​​the hole formed in the second excitation electrode are substantially the same as those of the hole formed in the first excitation electrode. It is also preferable that the end of the hole formed in the second excitation electrode and the end of the hole formed in the first excitation electrode overlap in the Y'-axis direction. This is to suppress the occurrence of spurious vibrations caused by disturbances in the direction and magnitude of the voltage applied to the crystal blank 11.

[0043] As shown in FIG. 4 and FIG. 5, the dimension of the crystal blank 11 along the Y'-axis direction is defined as the crystal thickness Tq. The dimension of the first excitation electrode 14a along the Z'-axis direction is defined as the first electrode length Le1, the dimension of the first excitation electrode 14a along the X-axis direction is defined as the second electrode length Le2, and the dimension of the first excitation electrode 14a along the Y'-axis direction is defined as the electrode thickness Te. The dimension of the hole H1 along the Z'-axis direction is defined as the first hole length Lh11, and the dimension of the hole H1 along the X-axis direction is defined as the second hole length Lh12. The distance of the geometric center of the hole H1 along the Z'-axis direction from the short side of the first excitation electrode 14a is defined as the first hole distance Ph1. The distance of the geometric center of the hole H1 along the X-axis direction from the long side of the first excitation electrode 14a is defined as the second hole distance Ph2.

[0044] The quartz crystal thickness Tq is, for example, in the range of 0.5 μm to 3 μm, for example, about 1 μm. The first electrode length Le1 is, for example, about 120 μm, the second electrode length Le2 is, for example, about 50 μm, and the electrode thickness is, for example, about 0.05 μm.

[0045] The relationship between the quartz crystal thickness Tq and the first electrode length Le1 is 45≦Le1 / Tq≦120. When the relationship 45≦Le1 / Tq is satisfied, the equivalent series resistance is small, making it easier to satisfy the oscillation conditions, and the equivalent series capacitance is large, making it less susceptible to the effects of parasitic capacitance. It is even more desirable that the relationship 60≦Le1 / Tq≦120 is satisfied. When the relationship Le1 / Tq≦120 is satisfied, it is possible to prevent the frequency of the inharmonic mode (hereinafter referred to as the "first direction inharmonic mode") whose vibration loops are aligned in the Z'-axis direction from becoming excessively close to the frequency of the main mode.

[0046] A relationship of 10 ≤ Le2 / Tq ≤ 45 holds between the crystal thickness Tq and the second electrode length Le2. When 10 ≤ Le2 / Tq holds, the equivalent series resistance becomes small, making it easier to satisfy the oscillation conditions, and the equivalent series capacitance becomes large, making it less susceptible to the influence of parasitic capacitance. When Le2 / Tq ≤ 45 holds, the frequency of the inharmonic mode (hereinafter referred to as the "second-direction inharmonic mode") where the vibration antinodes are arranged in the X-axis direction is sufficiently separated from the frequency of the main mode. Therefore, even without suppressing the second-direction inharmonic mode, the influence of the second-direction inharmonic mode on the main mode can be reduced.

[0047] The first hole length Lh11 is, for example, about 5 μm, and the second hole length Lh12 is, for example, about 15 μm. The first hole distance Ph1 is, for example, about half of the first electrode length Le1 ± 10%. That is, a relationship of 0.9×{(1 / 2)×Le1} ≤ Ph1 ≤ 1.1×{(1 / 2)×Le1} holds. The second hole distance Ph2 is, for example, about half of the second electrode length Le2 ± 10%. That is, a relationship of 0.9×{(1 / 2)×Le2} ≤ Ph2 ≤ 1.1×{(1 / 2)×Le2} holds.

[0048] However, the relationships among the first electrode length Le1, the second electrode length Le2, the first hole distance Ph1, and the second hole distance Ph2 are not limited to the above. For example, when a relationship of 45 ≤ Le1 / Tq ≤ 120 and 10 ≤ Le2 / Tq ≤ 45 holds, if a relationship of 0.9×{(1 / 2)×Le1} ≤ Ph1 ≤ 1.1×{(1 / 2)×Le1} holds, a relationship of 0.9×{(1 / 2)×Le2} ≤ Ph2 ≤ 1.1×{(1 / 2)×Le2} does not necessarily have to hold. That is, in such a case, a relationship of Ph2 < 0.9×{(1 / 2)×Le2} or 1.1×{(1 / 2)×Le2} < Ph2 may hold.

[0049] On the other hand, when the relationship of 10 ≦ Le1 / Tq ≦ 45 and 45 ≦ Le2 / Tq ≦ 120 holds, if the relationship of 0.9×{(1 / 2)×Le2} ≦ Ph2 ≦ 1.1×{(1 / 2)×Le2} holds, the relationship of Ph1 < 0.9×{(1 / 2)×Le1} or 1.1×{(1 / 2)×Le1} < Ph1 may hold.

[0050] When the relationships of 45 ≦ Le1 / Tq ≦ 120 and 45 ≦ Le2 / Tq ≦ 120 hold, at least one of the relationships of 0.9×{(1 / 2)×Le1} ≦ Ph1 ≦ 1.1×{(1 / 2)×Le1} and 0.9×{(1 / 2)×Le2} ≦ Ph2 ≦ 1.1×{(1 / 2)×Le2} may hold, and preferably both of these relationships hold.

[0051] The first lead electrode 15a electrically connects the first excitation electrode 14a and the first connection electrode 16a, and the second lead electrode 15b electrically connects the second excitation electrode 14b and the second connection electrode 16b. The first lead electrode 15a and the second lead electrode 15b are provided across the vibrating portion 11A to the holding portion 11C. The first lead electrode 15a is provided on the upper surface 12a of the crystal piece 11, and the second lead electrode 15b is provided on the lower surface 12b of the crystal piece 11. The first lead electrode 15a is electrically connected to the first excitation electrode 14a in the vibrating portion 11A and electrically connected to the first connection electrode 16a in the holding portion 11C. The second lead electrode 15b is electrically connected to the second excitation electrode 14b in the vibrating portion 11A and electrically connected to the second connection electrode 16b in the holding portion 11C.

[0052] The first connection electrode 16a and the second connection electrode 16b are terminals for electrically connecting to the external electrodes provided on the upper lid 20. The first connection electrode 16a and the second connection electrode 16b are provided in the holding portion 11C. Also, the first connection electrode 16a and the second connection electrode 16b are provided on the upper surface 12a of the crystal piece 11.

[0053] The materials of the first excitation electrode 14a, the second excitation electrode 14b, the first extraction electrode 15a, the second extraction electrode 15b, the first connection electrode 16a, and the second connection electrode 16b are, for example, aluminum (Al), molybdenum (Mo), gold (Au), or an aluminum-copper alloy (AlCu) mainly composed of aluminum. These electrodes may be single-layer films or multi-layer films. In the case of a multi-layer film, the first excitation electrode 14a and the second excitation electrode 14b may include, for example, an underlayer having good adhesion to quartz and a surface having good chemical stability. The underlayer is, for example, a chromium (Cr) layer or a titanium (Ti) layer, and the surface layer is, for example, a gold (Au) layer.

[0054] The via electrode 17 electrically connects the second extraction electrode 15b and the second connection electrode 16b. The via electrode 17 is provided penetrating from the upper surface 12a to the lower surface 12b of the crystal piece 11. The material of the via electrode 17 is, for example, aluminum (Al), and the thickness of the via electrode 17 is, for example, 1.0 μm. The material of the via electrode 17 may be, for example, copper (Cu) or an aluminum-copper alloy (AlCu) mainly composed of aluminum. The thickness of the via electrode 17 is, for example, in the range of 0.5 μm to 3.0 μm.

[0055] The top cover 20 is a flat, plate-like member. The dimensions of the top cover 20 in a plan view are the same or approximately the same as the dimensions of the quartz crystal vibrating element 10 (quartz crystal blank 11). The thickness of the top cover 20 is, for example, in the range of 100 μm to 200 μm.

[0056] The material of the upper cover 20 is, for example, quartz crystal, which makes it possible to reduce stress caused by the difference in thermal expansion coefficient between the bonding portion 30 and the quartz crystal vibrating element 10.

[0057] The upper cover 20 is not limited to a quartz plate, and may be, for example, a ceramic plate or a glass plate. When the upper cover is made of a heat-resistant ceramic plate, it is possible to suppress the occurrence of deformation and thermal stress of the quartz vibrating element 10 due to thermal history. When the upper cover is made of a transparent glass plate, it is possible to adjust the resonant frequency by externally irradiating the first excitation electrode 14a with a laser after sealing the quartz vibrating element 10.

[0058] Moreover, the top cover 20 may be conductive. By making the top cover 20 out of a conductive material, an electromagnetic shielding function that reduces the ingress and egress of electromagnetic waves into the internal space is imparted to the top cover 20. In this case, the top cover 20 is desirably made of 42 alloy, which is an alloy containing iron (Fe) and nickel (Ni), or Kovar, which is an Fe-Ni-Co alloy containing iron (Fe), nickel (Ni), and cobalt (Co). The Fe-Ni-Co alloy has a thermal expansion coefficient near room temperature that matches that of glass and ceramics over a wide temperature range, and therefore can suppress the occurrence of thermal stress.

[0059] The bonding portion 30 bonds the quartz crystal vibrating element 10 and the top cover 20. A space is formed by the bonded top cover 20 and the quartz crystal vibrating element 10. The space forms a part of the vibration space of the vibration portion 11A. The bonding portion 30 is provided around the entire circumference of each of the top cover 20 and the quartz crystal vibrating element 10. Specifically, the bonding portion 30 is provided between the lower surface of the top cover 20 and the upper surface 12a of the quartz crystal blank 11. In a plan view, the bonding portion 30 is provided in a frame shape. The width of the bonding portion 30, i.e., the difference between the outer circumference and the inner circumference, is, for example, about 20 μm.

[0060] The joint 30 is provided by, for example, a low melting point glass such as lead borate-based or tin phosphate-based. The joint 30 may be provided by, for example, an organic adhesive containing an epoxy-based, vinyl-based, acrylic-based, urethane-based, or silicone-based resin, a silicon-based adhesive containing water glass or the like, a calcium-based adhesive containing cement or the like, or a metal joint such as a gold-tin (Au-Sn) eutectic alloy. The crystal vibration element 10 and the upper cover 20 may be joined by seam welding.

[0061] The insulating layer 40 includes a cavity 41 formed in a portion corresponding to the vibration portion 11A of the quartz crystal vibrating element 10. The cavity 41 has a concave shape, and forms a space between the cavity 41 and the second excitation electrode 14b provided on the lower surface 12b of the quartz crystal piece 11.

[0062] The insulating layer 40 bonds the quartz crystal vibrating element 10 to the support substrate 50. More specifically, the insulating layer 40 is formed on the lower surface of the quartz crystal vibrating element 10 and bonds the upper surface of the support substrate 50 to the lower surface 12b of the quartz crystal piece 11.

[0063] The material of the insulating layer 40 is, for example, a silicon oxide film containing silicon dioxide (SiO2), etc. This makes it possible to reduce the stress caused by the difference in thermal expansion coefficient between the crystal vibration element 10 and the supporting substrate 50.

[0064] The thickness of the insulating layer 40 is desirably 0.5 μm or more, for example, in the range of 1 μm to 1.5 μm. In this case, the depth of the cavity 41 in the Y′-axis direction is, for example, in the range of 0.2 μm to 0.5 μm.

[0065] The material of the insulating layer 40 is not limited to silicon oxide film, but may be silicon nitride film, silicon oxynitride film, or various adhesives.

[0066] The support substrate 50 is configured to support the quartz crystal vibrating element 10 and the insulating layer 40. Specifically, the support substrate 50 supports the holder 11C of the quartz crystal blank 11 via the insulating layer 40.

[0067] The support substrate 50 is, for example, a flat plate-like substrate. The dimensions of the support substrate 50 in a plan view are the same or approximately the same as the dimensions of the quartz crystal vibrating element 10 (quartz crystal blank 11). The thickness of the support substrate 50 along the Y'-axis direction is, for example, in the range of 50 μm to 500 μm.

[0068] The material of the support substrate 50 is, for example, quartz crystal. This makes it possible to reduce stress caused by the difference in thermal expansion coefficient between the quartz crystal vibrating element 10 and the insulating layer 40.

[0069] The support substrate 50 is not limited to a quartz plate, and may be, for example, a ceramic plate, a silicon substrate, or a glass plate. When the support substrate 50 is made of a heat-resistant ceramic plate, deformation of the quartz crystal vibrating element 10 due to thermal history can be suppressed.

[0070] As described above, when the dimension of the first excitation electrode 14a in the first direction is Le1 and the thickness of the crystal blank 11 is Tq, and the relationship 45≦Le1 / Tq≦120 is satisfied, a through hole is formed in the center of the first excitation electrode 14a in the first direction. As a result, as will be described later, it is possible to reduce the electromechanical coupling coefficient of the inharmonic mode in which vibration loops are aligned in the first direction, and the electromechanical coupling coefficient of the main mode is increased.

[0071] Next, the configurations of the first excitation electrodes 214a-914a according to the second to ninth embodiments will be described with reference to Figs. 6-13. Figs. 6-13 are plan views of the first excitation electrodes 214a-914a according to the second to ninth embodiments. In the following embodiments, matters common to the first embodiment will be omitted, and only the differences will be described. In particular, similar actions and effects due to similar configurations will not be mentioned one by one.

[0072] <Second embodiment> The planar shape of the hole H2 formed in the first excitation electrode 214a shown in Fig. 6 is a rectangle having a long side extending in the Z'-axis direction and a short side extending in the X-axis direction. That is, the longitudinal direction of the hole H2 is parallel to the longitudinal direction of the first excitation electrode 214a.

[0073] <Third embodiment> The planar shape of the hole H3 formed in the first excitation electrode 314a shown in FIG. 7 is circular.

[0074] <Fourth embodiment> The planar shape of the hole H4 formed in the first excitation electrode 414a shown in FIG. 8 is a square having a side extending in the Z'-axis direction and a side extending in the X-axis direction.

[0075] <Fifth embodiment> The hole portion H5 formed in the first excitation electrode 514a shown in FIG. 9 includes a plurality of small holes H51. The planar shape of the plurality of small holes H51 is, for example, a circular shape with a radius of about 1 μm. The plurality of small holes H51 are arranged in a lattice pattern in the Z'-axis direction and the X-axis direction. The distance between the centers of adjacent small holes H51 is, for example, about 3 μm. The number of the plurality of small holes H51 is, for example, 21.

[0076] The planar shape, area and arrangement of the multiple small holes are not limited to the above. The planar shape of the multiple small holes may be, for example, a rectangular shape, a square shape, another polygonal shape, a circular shape, an elliptical shape, or a combination thereof. The multiple small holes may include different types of small holes having different planar shapes. The multiple small holes may include different types of small holes having different areas. The arrangement of the multiple small holes may be, for example, a staggered shape or a concentric circle shape.

[0077] Sixth embodiment 10 is a notched opening that opens in the X-axis direction at an end along the long side of the first excitation electrode 614a. The hole H6 includes a notched portion H61 formed at an end of the first excitation electrode 614a on the negative side in the X-axis direction and a notched portion H62 formed at an end of the first excitation electrode 614a on the positive side in the X-axis direction.

[0078] The notch H61 and the notch H62 are spaced apart from each other and arranged side by side in the X-axis direction. The geometric centers of the notches H61 and H62 are located on a center line that passes through the geometric center of the first excitation electrode 614a and extends in the X-axis direction. The planar shapes of the notches H61 and H62 are rectangular shapes having a short side extending in the Z'-axis direction and a long side extending in the X-axis direction. Let the dimension of the notch H61 along the Z'-axis direction be the hole length Wh11, the dimension of the notch H61 along the X-axis direction be the hole length Wh12, the dimension of the notch H62 along the Z'-axis direction be the hole length Wh21, and the dimension of the notch H62 along the X-axis direction be the hole length Wh22. Since the notches H61 and H62 are rectangular shapes with the X-axis direction as the longitudinal direction, the hole length Wh11 is smaller than the hole length Wh12 (Wh11 < Wh12), and the hole length Wh21 is smaller than the hole length Wh22 (Wh21 < Wh22). Also, since the notches H61 and H62 are spaced apart from each other, the sum of the hole length Wh12 and the hole length Wh22 is smaller than the second electrode length Le2 (Wh12 + Wh22 < Le2). As an example, the hole length Wh11 is substantially equal to the hole length Wh21 (Wh11 = Wh21), and the hole length Wh12 is substantially equal to the hole length Wh22 (Wh12 = Wh22). That is, the area of the notch H61 is substantially equal to the area of the notch H62.

[0079] Note that the positions, planar shapes, and areas of the two notches are not limited to the above. The geometric centers of the two notches may be spaced apart from the center line extending in the X-axis direction of the first excitation electrode. For example, the two notches may be arranged at intervals in the Z'-axis direction. At this time, the sum of the hole length Wh12 and the hole length Wh22 is equal to or greater than the second electrode length Le2 (Le2 ≦ Wh12 + Wh22). The planar shapes of the two notches may be, for example, rectangular shapes, square shapes, other polygonal shapes, circular shapes, elliptical shapes, or combinations thereof. The planar shapes of the two notches may be different from each other. Also, the areas of the two notches may be different from each other. For example, the relationship Wh11 < Wh21 or Wh11 > Wh21 may hold, and the relationship Wh12 < Wh22 or Wh12 > Wh22 may hold.

[0080] In addition, in addition to the two cutouts, an additional hole may be formed in the first excitation electrode. The additional hole is formed, for example, between the two cutouts and spaced apart from the two cutouts. The planar shape of the additional hole is not particularly limited, and may be, for example, a rectangular shape, a square shape, another polygonal shape, a circular shape, an elliptical shape, or a combination thereof. In addition, the area of ​​the additional hole is not particularly limited, and may be smaller or larger than the area of ​​the two cutouts, or may be equal to the area of ​​the two cutouts.

[0081] Seventh embodiment The first excitation electrode 714a shown in FIG. 11 has holes H71, H72, and H73. Among the holes H71, H72, and H73, the hole H71 is similar to the hole H1 in the first embodiment. The hole H72 corresponds to an example of the "second hole." The hole H73 corresponds to an example of the "third hole."

[0082] The hole H72 is formed in the center in the Z'-axis direction of a portion of the first excitation electrode 714a on the negative Z'-axis direction side with respect to the hole H71. The hole H72 is also formed in the center in the X-axis direction of the first excitation electrode 714a. The hole H72 is separated from the hole H71, the short side of the first excitation electrode 714a on the negative Z'-axis direction side, the long side of the first excitation electrode 714a on the negative X-axis direction side, and the long side of the first excitation electrode 714a on the positive X-axis direction side. The hole H72 is provided between the hole H71 and the short side of the first excitation electrode 714a on the negative Z'-axis direction side.

[0083] The hole H73 is formed in the center in the Z'-axis direction of a portion of the first excitation electrode 714a on the Z'-axis positive side relative to the hole H71. The hole H73 is also formed in the center in the X-axis direction of the first excitation electrode 714a. The hole H73 is spaced apart from the hole H71, the short side of the first excitation electrode 714a on the Z'-axis positive side, the long side of the first excitation electrode 714a on the X-axis negative side, and the long side of the first excitation electrode 714a on the X-axis positive side. The hole H73 is provided between the hole H71 and the short side of the first excitation electrode 714a on the Z'-axis positive side.

[0084] The planar shape of the holes H72 and H73 is a square having sides extending in the Z'-axis direction and sides extending in the X-axis direction. Each side of the holes H72 and H73 is approximately the same size as the short side of the hole H71. Therefore, the area of ​​each of the holes H72 and H73 is smaller than the area of ​​the hole H71.

[0085] In plan view, the geometric centers of the holes H71, H72, and H73 are located on a center line that passes through the geometric center of the first excitation electrode 714a and extends in the Z'-axis direction, and are aligned in the Z'-axis direction. That is, the distances of the geometric centers of the holes H71, H72, and H73 from the long side of the first excitation electrode 714a along the X-axis direction are all the second hole distance Ph2. The distance between the geometric center of the hole H71 and the geometric center of the hole H72 in the Z'-axis direction (hereinafter referred to as "hole interval Ph12") is approximately one-quarter of the first electrode length Le1 and approximately one-half of the first hole distance Ph1 (Ph12=(1 / 4)×Le1, Ph12=(1 / 2)×Ph1). The distance between the geometric center of hole H71 and the geometric center of hole H73 in the Z'-axis direction (hereinafter referred to as "hole interval Ph13") is also similar (Ph13 = (1 / 4) × Le1, Ph13 = (1 / 2) × Ph1). Therefore, hole interval Ph12 and hole interval Ph13 are approximately equal (Ph12 = Ph13).

[0086] The electrode area of ​​the first excitation electrode 714a is Se, the area of ​​the portion of the hole H72 in the first excitation electrode 714a on the negative side in the Z'-axis direction is Se1, the area of ​​the portion of the hole H72 in the first excitation electrode 714a on the positive side in the Z'-axis direction and on the negative side in the Z'-axis direction of the hole H71 is Se2, the area of ​​the portion of the hole H71 in the first excitation electrode 714a on the positive side in the Z'-axis direction and on the negative side in the Z'-axis direction of the hole H73 is Se3, and the area of ​​the portion of the hole H73 in the first excitation electrode 714a on the positive side in the Z'-axis direction is Se4. For example, the areas Se1 to Se4 are approximately equal to each other (Se1 ≒ Se2 ≒ Se3 ≒ Se4). That is, the hole H71 is formed at a position that divides the area of ​​the first excitation electrode 714a in half in the Z'-axis direction. The hole H72 is formed at a position that divides the area of ​​the portion of the first excitation electrode 714a on the negative side of the hole H71 in the Z'-axis direction into two equal parts in the Z'-axis direction. The hole H73 is formed at a position that divides the area of ​​the portion of the first excitation electrode 714a on the positive side of the hole H71 in the Z'-axis direction into two equal parts in the Z'-axis direction. In summary, the holes H71, H72, and H73 are formed at positions that divide the electrode area Se of the first excitation electrode 714a into four equal parts in the Z'-axis direction.

[0087] Incidentally, if the second hole portion is formed at the central portion in the Z'-axis direction of the portion on the negative Z'-axis direction side with respect to the first hole portion among the first excitation electrodes, its position, planar shape, and size are not limited to the above. Similarly, if the third hole portion is formed at the central portion in the Z'-axis direction of the portion on the positive Z'-axis direction side with respect to the first hole portion among the first excitation electrodes, its position, planar shape, and size are not limited to the above. For example, the geometric centers of the second hole portion and the third hole portion may be separated from the center line extending in the Z'-axis direction of the first excitation electrode. Further, the geometric centers of the second hole portion and the third hole portion may not be aligned in the Z'-axis direction with the geometric center of the first hole portion. The second hole portion may be formed at a position where the relationship Ph12 > (1 / 2) × Ph1 or Ph12 < (1 / 2) × Ph1 holds, and the third hole portion may be formed at a position where the relationship Ph13 > (1 / 2) × Ph1 or Ph13 < (1 / 2) × Ph1 holds. Also, the second hole portion may be formed at a position where the relationship Se1 > Se2 or Se1 < Se2 holds, and the third hole portion may be formed at a position where the relationship Se3 > Se4 or Se3 < Se4 holds.

[0088] The planar shapes of the second hole portion and the third hole portion may be a rectangular shape having a long side extending in the X-axis direction, a rectangular shape having a long side extending in the Z'-axis direction, other polygonal shapes, circular shape, elliptical shape, or a combination thereof. Also, the second hole portion and the third hole portion may include a plurality of small holes, and may include a notch-shaped opening that opens to the positive X-axis direction side or the negative X-axis direction side of the first excitation electrode. The area of each of the second hole portion and the third hole portion may be substantially equal to the area of the first hole portion, or may be larger than the area of the first hole portion. The area of the second hole portion and the area of the third hole portion may be different from each other.

[0089] <Eighth Embodiment> The first excitation electrode 814a shown in FIG. 12 is octagonal, and hole portions H81, H82, and H83 are formed in the first excitation electrode 814a. The shapes and sizes of the hole portions H81, H82, and H83 are the same as those of the hole portions H71 to H73 according to the seventh embodiment.

[0090] The planar shape of the first excitation electrode 814a is an octagonal shape obtained by cutting off a square from the first excitation electrode 714a according to the seventh embodiment to form a triangular shape. That is, the first excitation electrode 814a has sides extending in the Z'-axis direction, sides extending in the X-axis direction, and sides connecting these sides. The dimension of the side of the first excitation electrode 814a extending in the X-axis direction is defined as the short side length Le12, and the dimension of the side extending in the Z'-axis direction is defined as the long side length Le11. The short side length Le12 is smaller than the second electrode length Le2, and the long side length Le11 is smaller than the first electrode length Le1. For example, the short side length Le12 is smaller than the long side length Le11.

[0091] The hole H81 is formed such that its geometric center coincides with the geometric center of the first excitation electrode 814a, and the holes H82 and H83 are formed at positions where Se1 = Se2 = Se3 = Se4 = (1 / 4)×Se. The geometric centers of the holes H81, H82, and H83 are aligned in the Z'-axis direction. The distance between the geometric center of the hole H81 and the geometric center of the hole H82 in the Z'-axis direction (hereinafter referred to as "hole interval Ph12'") is smaller than the hole interval Ph12 according to the seventh embodiment (Ph12' < Ph12). The distance between the geometric center of the hole H81 and the geometric center of the hole H83 in the Z'-axis direction (hereinafter referred to as "hole interval Ph13'") is smaller than the hole interval Ph13 according to the seventh embodiment (Ph13' < Ph13). The hole interval Ph12' and the hole interval Ph13' are substantially equal (Ph12' = Ph13'). For example, the sum of the hole interval Ph12' and the hole interval Ph13' is larger than the long side length Le11 (Le11 < Ph12' + Ph13').

[0092] In addition, when the short side length on the positive Z'-axis direction side of the first excitation electrode is different from the short side length on the negative Z'-axis direction side, the hole interval Ph12' and the hole interval Ph13' are different from each other (Ph12' ≠ Ph13'). Also, the magnitude relationship among the hole interval Ph12', the hole interval Ph13', and the long side length Le11 is not limited to Le11 < Ph12' + Ph13'. The sum of the hole interval Ph12' and the hole interval Ph13' may be substantially equal to the long side length Le11 (Le11 = Ph12' + Ph13'), or may be smaller than the long side length Le11 (Ph12' + Ph13' < Le11).

[0093] <Ninth embodiment> The first excitation electrode 914a shown in FIG. 13 has a square planar shape, and the hole H9 formed in the first excitation electrode 914a has a circular planar shape.

[0094] The first electrode length Le1 and the second electrode length Le2 are approximately equal (Le1=Le2). The relationship between the crystal thickness Tq and the first electrode length Le1 is 45≦Le1 / Tq≦120. The relationship between the crystal thickness Tq and the second electrode length Le2 is 45≦Le2 / Tq≦120. The hole H9 is located at the center of the first excitation electrode 914a in the Z'-axis direction and at the center of the first excitation electrode 914a in the X-axis direction. That is, the first hole distance Ph1 is approximately equal to the second hole distance Ph2 (Ph1=Ph2).

[0095] Even when the planar shape of the first excitation electrode is square as in the present embodiment, the planar shape of the first hole is not particularly limited, as in the case where the planar shape of the first excitation electrode is rectangular. The planar shape of the first hole formed in the square-shaped first excitation electrode may be a rectangle having a long side extending in the X-axis direction, a rectangle having a long side extending in the Z'-axis direction, a square, another polygonal shape, a circle, an ellipse, or a combination of these. The first hole formed in the square-shaped first excitation electrode may include a plurality of small holes. In addition, the first hole formed in the square-shaped first excitation electrode may include a notch-shaped opening opening on the X-axis positive side or negative side of the first excitation electrode, or a notch-shaped opening opening on the Z'-axis positive side or negative side of the first excitation electrode.

[0096] The square-shaped first excitation electrode may have a second hole formed in the center in the Z'-axis direction of a portion on the Z'-axis negative side with respect to the first hole, and a third hole formed in the center in the Z'-axis direction of a portion on the Z'-axis positive side with respect to the first hole. The square-shaped first excitation electrode may have a fourth hole formed in the center in the X-axis direction of a portion on the X-axis negative side with respect to the first hole, and a fifth hole formed in the center in the X-axis direction of a portion on the X-axis positive side with respect to the first hole. For example, the positions and planar shapes of the fourth and fifth holes are the same as those of the second and third holes rotated 90 degrees around the Y'-axis. For example, the areas of the fourth and fifth holes are the same as those of the second and third holes. The square-shaped first excitation electrode may have all of the second, third, fourth and fifth holes formed.

[0097] <Example> Next, a first example will be described with reference to Fig. 14. Fig. 14 is a diagram showing a simulation result in the first example. The first example is a vibration simulation of a quartz crystal vibrating element including a first excitation electrode according to the first embodiment, and the comparative example is a vibration simulation of a quartz crystal vibrating element that is the same as the first example except that the first hole portion is not formed. (First embodiment) crystal piece Cut angle: AT cut Planar shape: square Top surface dimensions: 140μm x 140μm Thickness Tq: 1 μm Main mode S0: 1.45GHz 1st excitation electrode Material: Aluminum (Al) or Aluminum Copper Alloy (AlCu) First electrode length Le1: 120μm (Le1 / Tq=120) Second electrode length Le2: 50μm (Le2 / Tq=50) Electrode thickness Te: 0.05μm 1st hole 1st hole length Lh11: 5μm 2nd hole length Lh12: 15μm

[0098] The electromechanical coupling coefficient K of the main mode S0 is 6.87(%) in the comparative example, but is improved to 7.08 in the first example. Among the inharmonic modes in which a plurality of vibration loops are arranged in the Z'-axis direction, the electromechanical coupling coefficient K of the inharmonic mode S1Z, which has a frequency closest to the main mode S0, is 2.27(%) in the comparative example, but is reduced to 0.08 in the first example. Looking at the distribution of vibration of the inharmonic mode S1Z, the vibration range in the center is expanded in the first example, which causes the vibrations of opposite phases to cancel each other out, and therefore the K of the inharmonic mode S1Z is reduced. It is considered that the reduction in the K of the inharmonic mode S1Z reduces the influence of the inharmonic mode S1Z on the main mode S0, and the K of the main mode S0 is improved. Thus, in the first example based on the first embodiment, the electromechanical coupling coefficients K of the main mode S0 and the inharmonic mode S1Z are improved compared to the comparative example.

[0099] Next, the electromechanical coupling coefficient K when the shape and size of the first hole of the first embodiment are changed will be described with reference to Fig. 15 and Fig. 16. Fig. 15 is a graph showing the influence of the shape and size of the first hole in the rectangular first excitation electrode. Fig. 16 is a graph showing the influence of the shape and size of the first hole in the rectangular first excitation electrode. The horizontal axis of Fig. 15 and Fig. 16 shows the ratio Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode, the vertical axis of Fig. 15 shows the electromechanical coupling coefficient K (%) of the main mode S0, and the vertical axis of Fig. 16 shows the electromechanical coupling coefficient K (%) of the inharmonic mode S1Z.

[0100] 15 and 16 plot simulation results based on an example in which the shape of the first hole portion from the first example is changed to a rectangular shape based on the second embodiment, an example in which the shape of the first hole portion from the first example is changed to a circular shape based on the third embodiment, and an example in which the shape of the first hole portion from the first example is changed to a square shape based on the fourth embodiment.

[0101] 15 and 16, the contribution of the planar shape of the first hole to the electromechanical coupling coefficient K of the main mode S0 and the inharmonic mode S1Z is small. The electromechanical coupling coefficient K of the main mode S0 and the inharmonic mode S1Z is greatly influenced by the area ratio Har=Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode. Specifically, the electromechanical coupling coefficient K of the main mode S0 increases with an increase in Har=Sh / Se when Har=Sh / Se is from 0 to about 0.003, regardless of the planar shape of the first hole, and decreases with an increase in Har=Sh / Se when Har=Sh / Se is greater than about 0.003. The electromechanical coupling coefficient K of the inharmonic mode S1Z decreases as Har=Sh / Se increases when Har=Sh / Se is between 0 and approximately 0.008, regardless of the planar shape of the first hole portion, and increases as Har=Sh / Se increases when Har=Sh / Se is greater than approximately 0.008.

[0102] Next, with reference to Figs. 17 to 19, a simulation result regarding the electromechanical coupling coefficient when the area ratio Har=Sh / Se of the first hole to the electrode area Se of the first excitation electrode is changed in an example based on the ninth embodiment will be described. The example used in the simulation is similar to the first example except for the shape and size of the first excitation electrode and the first hole. Fig. 17 is a graph showing the influence of the area ratio of the first hole in the square-shaped first excitation electrode. Fig. 18 is a graph showing the influence of the area ratio of the first hole in the square-shaped first excitation electrode. Fig. 19 is a graph showing the optimum condition of the area ratio of the first hole in the square-shaped first excitation electrode. The horizontal axis of Figs. 17 and 18 indicates the area ratio Har=Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode, the vertical axis of Fig. 17 indicates the electromechanical coupling coefficient K(%) of the main mode S0, and the vertical axis of Fig. 18 indicates the electromechanical coupling coefficient K(%) of the inharmonic mode S1Z. The horizontal axis of Figure 19 shows the ratio Le1 / Tq = Le2 / Tq of the electrode lengths Le1, Le2 (Le1 = Le2) to the quartz crystal thickness Tq, and the vertical axis of Figure 19 shows the area ratio Har = Sh / Se of the hole area Sh of the first hole portion to the electrode area Se of the first excitation electrode.

[0103] Fig. 17 plots the simulation results of the electromechanical coupling coefficient K in the main mode S0 when the area ratio Har=Sh / Se is changed when the electrode lengths Le1, Le2 (Le1=Le2) are set to 40μm, 60μm, 80μm, 100μm, and 120μm. Fig. 18 plots the simulation results of the electromechanical coupling coefficient K in the inharmonic mode S1Z when the area ratio Har=Sh / Se is changed when the electrode lengths Le1, Le2 (Le1=Le2) are set to 40μm, 60μm, 80μm, 50μm, 100μm, and 120μm. The change in the area ratio Har=Sh / Se is achieved by changing the radius R of the first hole portion. As described with reference to FIGS. 15 and 16, the contribution of the planar shape of the first hole portion to the electromechanical coupling coefficient K is small, so by fixing the planar shape of the first hole portion and varying the area ratio Har=Sh / Se, it is possible to know the trend of change in the electromechanical coupling coefficient K.

[0104] As shown in FIG. 17, the electromechanical coupling coefficient K of the main mode S0 shows a convex-up graph within the range of 0 < Har < 0.30. The area ratio Har at which the electromechanical coupling coefficient K of the main mode S0 is maximized varies depending on the electrode lengths Le1 and Le2. As the electrode lengths Le1 and Le2 become smaller, the area ratio Har at which the electromechanical coupling coefficient K of the main mode S0 is maximized becomes larger. Also, as the electrode lengths Le1 and Le2 become smaller, the maximum value of the electromechanical coupling coefficient K of the main mode S0 becomes larger. The electromechanical coupling coefficient K of the main mode S0 is improved compared to the configuration without holes (Har = 0) in the range of 0 < Har ≦ 0.23. As shown in FIG. 18, the electromechanical coupling coefficient K of the inharmonic mode S1Z shows a convex-down graph within the range of 0 < Har < 0.20. The area ratio Har at which the electromechanical coupling coefficient K of the inharmonic mode S1Z is minimized varies depending on the electrode lengths Le1 and Le2. As the electrode lengths Le1 and Le2 become larger, the area ratio Har at which the electromechanical coupling coefficient K of the inharmonic mode S1Z is minimized becomes smaller. Also, as the electrode lengths Le1 and Le2 become larger, the minimum value of the electromechanical coupling coefficient K of the inharmonic mode S1Z becomes smaller. The electromechanical coupling coefficient K of the inharmonic mode S1Z is lower than the configuration without holes (Har = 0) in the range of 0 < Har ≦ 0.1. The electromechanical coupling coefficient K of the inharmonic mode S1Z further decreases in the range of 0.01 ≦ Har ≦ 0.05.

[0105] As shown in the approximate formula in FIG. 19, the electromechanical coupling coefficient K of the main mode S0 is maximized further within the range of 0 < Har ≦ 0.23, Har = 1.52×(Le2 / Tq) -0.82 ±0.01 when the relationship holds.

[0106] As shown in the approximate formula in FIG. 19, the electromechanical coupling coefficient K of the inharmonic mode S1Z is minimized further within the range of 0.01 ≦ Har ≦ 0.05, Har = 1.05×(Le2 / Tq) -0.92 ±0.01 This is when the following relationship holds true.

[0107] Next, referring to Figs. 20 to 22, a simulation result when changing the area ratio Har=Sh / Se of the hole area of ​​the first hole to the electrode area Se of the first excitation electrode in an example based on the third embodiment will be described. The example used in the simulation is the same as the first example except for the shape and dimensions of the first hole. Fig. 20 is a graph showing the condition under which K of the S0 mode is improved in a rectangular first excitation electrode. Fig. 21 is a graph showing the condition under which K of the S0 mode is maximized in a rectangular first excitation electrode. Fig. 22 is a graph showing the condition under which K of the S1Z mode is minimized in a rectangular first excitation electrode. The horizontal axis in Figs. 20 to 22 is the ratio Le2 / Le1 of the second electrode length Le2 to the first electrode length Le1 of the first excitation electrode. 20 to 22, the vertical axis represents the area ratio Har=Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode, normalized by Har where Le2 / Le1=1.

[0108] As shown in Fig. 20, the tendency of the conditions under which the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example without the first hole portion differs at Le2 / Le1=1.3. As shown in Fig. 21, the tendency of the conditions under which the electromechanical coupling coefficient K of the main mode S0 is maximized also differs at Le2 / Le1=1.3. As shown in Fig. 22, the tendency of the conditions under which the electromechanical coupling coefficient K of the inharmonic mode S1Z is minimized also differs at Le2 / Le1=1.3.

[0109] As shown in the approximation formula in FIG. 20, when 0.5≦Le2 / Le1≦1.3 and Le2 / Le1≠1.0, the condition under which the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example having no first hole portion is as follows: 0 <Har≦0.23×0.066×exp(2.53×Le2 / Le1)=0.015×exp(2.53×Le2 / Le1) The condition range of Har where the electromechanical coupling coefficient K of the main mode S0 in the rectangular first excitation electrode is improved is calculated by multiplying the conditional expression (1) related to Har(SQ) by the conditional expression (2) related to Har(N) (Har=Har(SQ)×Har(N)). The conditional expression (1) related to Har(SQ) is the condition where the electromechanical coupling coefficient K of the main mode S0 is improved in the square first excitation electrode (Le2 / Le1=1.0), which is the normalization condition. The conditional expression (2) related to Har(N) is the condition where the electromechanical coupling coefficient K of the main mode S0 normalized at Le2 / Le1=1.0 is improved in the rectangular first excitation electrode that satisfies the relationship 0.5≦Le2 / Le1≦1.3. The conditional expression (1) related to Har(SQ) is expressed by the following inequality, which has been described with reference to FIG. 17. 0 <Har(SQ)≦0.23 …(1) Condition (2) regarding Har(N) is expressed by the following approximation shown in FIG. Har(N)=0.066×exp(2.53×Le2 / Le1) …(2)

[0110] As shown in the approximation formula in FIG. 21, when 0.5≦Le2 / Le1≦1.3 and Le2 / Le1≠1.0, the condition in which the electromechanical coupling coefficient K of the main mode S0 becomes maximum within the above range is as follows: Har=0.04×exp(3.25×Le2 / Le1)×1.52×(Le2 / Tq) -0.82 ±0.01 =0.061×exp(3.25×Le2 / Le1)×(Le2 / Tq) -0.82 ±0.01 which is further satisfied. The conditional expression for maximizing the electromechanical coupling coefficient K of the main mode S0 in the rectangular first excitation electrode was calculated by the product of the conditional expression (3) for Har(SQ) and the conditional expression (4) for Har(N). The conditional expression (3) for Har(SQ) is the condition for maximizing the electromechanical coupling coefficient K of the main mode S0 in the square first excitation electrode (Le2 / Le1 = 1.0) under the normalization condition. The conditional expression (4) for Har(N) is the condition for maximizing the electromechanical coupling coefficient K of the main mode S0, which is normalized by Le2 / Le1 = 1.0, in the rectangular first excitation electrode satisfying the relationship 0.5 ≦ Le2 / Le1 ≦ 1.3. The conditional expression (3) for Har(SQ) is represented by the following approximate expression, which will be described with reference to FIG. 19. Har(SQ)=1.52×(Le2 / Tq) -0.82 ±0.01 …(3) The conditional expression (4) for Har(N) is represented by the approximate expression shown in FIG. 21. Har(N)=0.04×exp(3.25×Le2 / Le1) …(4)

[0111] As shown in the approximate expression in FIG. 20, when 1.3 < Le2 / Le1 ≦ 2.0, the condition for improving the electromechanical coupling coefficient K of the main mode S0 compared to the comparative example without the first hole portion is 0 < Har ≦ 0.23×3.06×exp(-1.07×Le2 / Le1)=0.704×exp(-1.07×Le2 / Le1) which is satisfied. The above conditional range was also calculated by the product of the conditional expression (1) for Har(SQ) and the conditional expression (5) for Har(N), similar to the conditional range when 0.5 ≦ Le2 / Le1 ≦ 1.3 and Le2 / Le1 ≠ 1.0. The conditional expression (5) for Har(N) is the condition for improving the electromechanical coupling coefficient K of the main mode S0, which is normalized by Le2 / Le1 = 1.0, in the rectangular first excitation electrode satisfying the relationship 1.3 < Le2 / Le1 ≦ 2.0. The conditional expression (5) for Har(N) is represented by the following approximate expression shown in FIG. 20. Har(N)=3.06×exp(-1.07×Le2 / Le1) …(5)

[0112] As shown in the approximate formula in FIG. 21, when 1.3 < Le2 / Le1 ≤ 2.0, the condition for the electromechanical coupling coefficient K of the main mode S0 to be maximized is further within the above range, Har = 3.17×exp(−0.96×Le2 / Le1)×1.52×(Le2 / Tq) -0.82 ±0.01 = 4.82×exp(−0.96×Le2 / Le1)×(Le2 / Tq) -0.82 ±0.01 is further satisfied. The above conditional expression is also calculated by the product of the conditional expression (3) for Har(SQ) and the conditional expression (6) for Har(N), similar to the conditional expression when 0.5 ≤ Le2 / Le1 ≤ 1.3 and Le2 / Le1 ≠ 1.0. The conditional expression (6) for Har(N) is the condition for the electromechanical coupling coefficient K of the main mode S0, normalized by Le2 / Le1 = 1.0, to be maximized in the rectangular first excitation electrode that satisfies the relationship 1.3 < Le2 / Le1 ≤ 2.0. The conditional expression (6) for Har(N) is represented by the following approximate formula shown in FIG. 21. Har(N) = 3.17×exp(−0.96×Le2 / Le1) …(6)

[0113] As shown in FIG. 16, when Le2 / Le1 ≠ 1.0, the electromechanical coupling coefficient K of the inharmonic mode S1Z is lower than that of the configuration without the first hole (Har = 0) in the range of 0 < Har ≤ 0.02.

[0114] As shown in the approximate formula in FIG. 22, when 0.5 ≤ Le2 / Le1 ≤ 1.3 and Le2 / Le1 ≠ 1.0, the condition for the electromechanical coupling coefficient K of the inharmonic mode S1Z to be minimized is Har = 0.65×exp(0.48×Le2 / Le1)×1.05×(Le2 / Tq) -0.92 ±0.01 = 0.68×exp(0.48×Le2 / Le1)×(Le2 / Tq) -0.92 ±0.01 should hold. The conditional expression for the minimum electromechanical coupling coefficient K of the inharmonic mode S1Z in the rectangular first excitation electrode is calculated by the product of the conditional expression (7) for Har(SQ) and the conditional expression (8) for Har(N). The conditional expression (7) for Har(SQ) is the condition for the minimum electromechanical coupling coefficient K of the inharmonic mode S1Z in the square first excitation electrode (Le2 / Le1 = 1.0) which is a normalization condition. The conditional expression (8) for Har(N) is the condition for the minimum electromechanical coupling coefficient K of the inharmonic mode S1Z normalized by Le2 / Le1 = 1.0 in the rectangular first excitation electrode satisfying the relation 0.5 ≦ Le2 / Le1 ≦ 1.3. The conditional expression (7) for Har(SQ) is represented by the following approximate expression as described with reference to Fig. 19. Har(SQ)=1.05×(Le2 / Tq) -0.92 ±0.01 …(7) The conditional expression (8) for Har(N) is represented by the following approximate expression shown in Fig. 22. Har(N)=0.65×exp(0.48×Le2 / Le1) …(8)

[0115] As shown in the approximate expression in Fig. 22, when 1.3 < Le2 / Le1 ≦ 2.0, the condition for the minimum electromechanical coupling coefficient K of the inharmonic mode S1Z is Har=0.42×exp(0.61×Le2 / Le1)×1.05×(Le2 / Tq) -0.92 ±0.01 =0.44×exp(0.61×Le2 / Le1)×(Le2 / Tq) -0.92 ±0.01 should hold. The above conditional expression is also calculated by the product of the conditional expression (7) for Har(SQ) and the conditional expression (9) for Har(N), similar to the conditional expression when 0.5 ≦ Le2 / Le1 ≦ 1.3 and Le2 / Le1 ≠ 1.0. The conditional expression (9) for Har(N) is the condition where the electromechanical coupling coefficient K of the inharmonic mode S1Z, normalized by Le2 / Le1 = 1.0, is minimized in the rectangular first excitation electrode satisfying the relationship of 1.3 < Le2 / Le1 ≦ 2.0. The conditional expression (9) for Har(N) is represented by the following approximate expression shown in FIG. 22. Har = 0.42 × exp(0.61 × Le2 / Le1) …(9)

[0116] Next, with reference to FIG. 23, the second embodiment will be described. FIG. 23 is a diagram showing the simulation results in the second embodiment. The second embodiment is a vibration simulation of a crystal oscillator provided with the first excitation electrode according to the seventh embodiment, and the comparative example is a vibration simulation of a crystal oscillator that is the same as the second embodiment except that the first hole portion, the second hole portion, and the third hole portion are not formed. The second embodiment has the same conditions as the first embodiment except for the second hole portion and the third hole portion. (Second Embodiment) Quartz wafer Cut angle: AT cut Planar shape: Square Top surface dimensions: 140 μm × 140 μm Thickness Tq: 1 μm Main mode S0: 1.45 GHz First excitation electrode Material: Aluminum (Al) or aluminum copper alloy (AlCu) First electrode length Le1: 120 μm (Le1 / Tq = 120) Second electrode length Le2: 50 μm (Le2 / Tq = 50) Electrode thickness Te: 0.05 μm First hole portion (hole portion H71) First hole length Lh11: 5 μm Second hole length Lh12: 15 μm Second hole portion (hole portion H72) and third hole portion (hole portion H73) Planar shape: Square Plane dimensions: 5μm×5μm Hole spacing Ph12: 30μm Hole spacing Ph13: 30μm

[0117] The electromechanical coupling coefficient K of the main mode S0 is 6.87(%) in the comparative example, but is improved to 7.38 in the second embodiment. Among the inharmonic modes in which a plurality of vibration antinodes are arranged in the Z'-axis direction, the electromechanical coupling coefficient K of the inharmonic mode S1Z, whose frequency is closest to the main mode S0, is 2.27(%) in the comparative example, but is reduced to 0.45 in the second embodiment. Among the inharmonic modes in which a plurality of vibration antinodes are arranged in the Z'-axis direction, the electromechanical coupling coefficient K of the inharmonic mode S2Z, whose frequency is next closest to the main mode S0 after the inharmonic mode S1Z, is 1.38(%) in the comparative example, but is reduced to 0.92 in the second embodiment. Among the inharmonic modes in which a plurality of vibration antinodes are arranged in the Z'-axis direction, the electromechanical coupling coefficient K of the inharmonic mode S3Z, whose frequency is next closest to the main mode S0 after the inharmonic mode S2Z, is 0.98(%) in the comparative example, but is reduced to 0.41 in the second embodiment. Thus, in the second example based on the seventh embodiment, the electromechanical coupling coefficients K of the main mode S0, the inharmonic mode S1Z, the inharmonic mode S2Z, and the inharmonic mode S1Z are improved compared to the comparative example.

[0118] Next, the influence of the positions of the holes H72 and H73 in the second embodiment will be described with reference to Fig. 24. Fig. 24 is a graph showing the influence of the size of the first hole and the positions of the second and third holes. The horizontal axis of Fig. 24 represents the hole intervals Ph12 and Ph13 (μm), and the vertical axis of Fig. 24 represents the electromechanical coupling coefficient K (%) of the main mode S0.

[0119] FIG. 24 is a graph plotting simulation results of the electromechanical coupling coefficient K of the main mode S0 corresponding to the hole spacing Ph12 and the hole spacing Ph13 when the first hole length Lh11 and the second hole length Lh12 of the hole H71 in the second embodiment are changed.

[0120] The electromechanical coupling coefficient K of the main mode S0 shows the same change with respect to the change in the hole pitch Ph12 and the hole pitch Ph13 even when the first hole length Lh11 and the second hole length Lh12 of the hole H71 are changed. The electromechanical coupling coefficient K of the main mode S0 is independent of the dimensions of the hole H71 and is maximized when Ph12 = Ph13 = 30 μm. In the range of 16 μm ≤ Ph12 = Ph13 < 30 μm, the electromechanical coupling coefficient K of the main mode S0 increases monotonically. In the range of 24 μm ≤ Ph12 = Ph13, the electromechanical coupling coefficient K of the main mode S0 is larger than the electromechanical coupling coefficient K = 6.87 (%) of the main mode S0 in the comparative example. In the range of 30 μm ≤ Ph12 = Ph13 ≤ 43 μm, the electromechanical coupling coefficient K of the main mode S0 decreases monotonically. When Ph12 = Ph13 ≤ 38, the electromechanical coupling coefficient K of the main mode S0 is larger than the electromechanical coupling coefficient K = 6.87 (%) of the main mode S0 in the comparative example. In the range of 34 μm < Ph12 = Ph13 ≤ 50 μm, the electromechanical coupling coefficient K of the main mode S0 increases monotonically. However, the change in the electromechanical coupling coefficient K of the main mode S0 in the range of 34 μm < Ph12 = Ph13 ≤ 50 μm is smaller than the change in the electromechanical coupling coefficient K of the main mode S0 in the range of 30 μm ≤ Ph12 = Ph13 ≤ 43 μm, and even when Ph12 = Ph13 = 50 μm, the electromechanical coupling coefficient K of the main mode S0 is smaller than the electromechanical coupling coefficient K = 6.87 (%) of the main mode S0 in the comparative example.

[0121] In summary, the condition for the electromechanical coupling coefficient K of the main mode S0 to be improved compared to the configuration without the holes H71, H72, and H73 is that 24 μm ≤ Ph12 = Ph13 ≤ 38 μm holds regardless of the dimensions and shape of the hole H71. Also, the condition for the electromechanical coupling coefficient K of the main mode S0 to be maximized is that Ph12 = Ph13 = 30 ± 1 μm holds. Since Le1 = 120 μm, this means that when the holes H71, H72, and H73 are formed at the positions that divide the first electrode length Le1 of the first excitation electrode into four equal parts in the Z'-axis direction, the electromechanical coupling coefficient K of the main mode S0 is maximized.

[0122] Next, the optimal positions of the holes H82, H83 in an example based on the eighth embodiment will be described with reference to Figs. 25 and 26. Fig. 25 is a graph showing the influence of the shape of the first excitation electrode and the positions of the second and third holes. Fig. 26 is a graph showing the relationship between the short side length and the hole interval. The horizontal axis of Fig. 25 shows the hole intervals Ph12, Ph13 (μm), and the vertical axis of Fig. 25 shows the electromechanical coupling coefficient K (%) of the main mode S0. The horizontal axis of Fig. 26 shows the short side length Le12 (μm), and the vertical axis of Fig. 26 shows the hole intervals Ph12, Ph13 (μm).

[0123] FIG. 25 is a graph plotting the simulation results of the electromechanical coupling coefficient K of the main mode S0 when the hole intervals Ph12, Ph13 (Ph12=Ph13) are changed when the short side length Le12 is set to 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, and 0 μm. The conditions other than the planar shape of the first excitation electrode and the hole intervals Ph12, Ph13 are the same as those in the second embodiment. When Le12=50 μm, the planar shape of the first excitation electrode is rectangular. When Le12=0 μm, the planar shape of the first excitation electrode is rhombic. When Le12=40 to 10 μm, the angle of the side of the first excitation electrode inclined to the Z'-axis direction with respect to the Z'-axis direction is constant.

[0124] When the short side length Le12 is set to 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, and 0 μm, the shape of the graph of the electromechanical coupling coefficient K of the main mode S0 is similar to that shown in FIG. 24. However, the graph of the electromechanical coupling coefficient K of the main mode S0 slides in the horizontal axis direction according to the magnitude of the short side length Le12. As the short side length Le12 becomes smaller, the hole interval Ph12, Ph13 (Ph12=Ph13) at which the electromechanical coupling coefficient K of the main mode S0 is maximized becomes smaller. The graph in FIG. 26 plots this result. The condition at which the electromechanical coupling coefficient K of the main mode S0 is maximized is approximately the same as the condition at which Se1=Se2=Se3=Se4. This means that when the holes H81, H82, and H83 are formed at positions that divide the electrode area Se of the first excitation electrode into four equal parts in the Z'-axis direction, the electromechanical coupling coefficient K of the main mode S0 becomes maximum.

[0125] Next, with reference to Figs. 27 and 28, conditions under which the electromechanical coupling coefficient K of the main mode S0 is improved and maximized in an example based on the eighth embodiment will be described. Fig. 27 is a graph showing area conditions under which K of the S0 mode is improved. Fig. 28 is a graph showing area conditions under which K of the S0 mode is improved. The horizontal axis of Figs. 27 and 28 indicates the hole intervals Ph12, Ph13 (μm). The vertical axis of Fig. 27 indicates the area ratio Se1 / Se of the area Se1 of the portion on the Z'-axis negative side of the second hole in the first excitation electrode to the electrode area Se of the first excitation electrode. The vertical axis of Fig. 28 indicates the area ratio Se1 / Se2 of the area Se1 of the portion on the Z'-axis negative side of the second hole in the first excitation electrode to the area Se2 of the portion on the Z'-axis positive side of the second hole in the first excitation electrode and on the Z'-axis negative side of the first hole. The vertical axis of Fig. 27 is also the area ratio Se4 / Se of the area Se4 of the portion of the third hole portion on the positive Z'-axis direction side in the first excitation electrode to the electrode area Se of the first excitation electrode. The vertical axis of Fig. 28 is also the area ratio Se4 / Se3 of the area Se4 of the portion of the third hole portion on the positive Z'-axis direction side in the first excitation electrode to the area Se3 of the portion of the first hole portion on the positive Z'-axis direction side in the first excitation electrode and on the negative Z'-axis direction side of the third hole portion.

[0126] The plots in the graphs shown in Fig. 27 and Fig. 28 are calculated based on the graph shown in Fig. 25. Specifically, when the short side length Le12 is set to 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, and 0 μm, the upper and lower limits of the hole intervals Ph12 and Ph13 at which the electromechanical coupling coefficient K of the main mode S0 is improved compared to a comparative example without the first hole, the second hole, and the third hole are read from Fig. 25. The area ratios Se1 / Se and Se4 / Se (Se1 / Se = Se4 / Se) at these hole intervals Ph12 and Ph13 are calculated and plotted on the graph in Fig. 27. In addition, the hole intervals Ph12 and Ph13 at which the electromechanical coupling coefficient K of the main mode S0 is maximized are read from Fig. 25, and the area ratios Se1 / Se and Se4 / Se at these hole intervals Ph12 and Ph13 are calculated and plotted on the graph in Fig. 27.

[0127] Similarly, the upper and lower limits of the hole intervals Ph12, Ph13 at which the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example are read from Fig. 25, and the area ratios Se1 / Se2, Se4 / Se3 (Se1 / Se2=Se4 / Se3) at these hole intervals Ph12, Ph13 are calculated and plotted on the graph in Fig. 28. Also, the hole intervals Ph12, Ph13 at which the electromechanical coupling coefficient K of the main mode S0 is maximized are read from Fig. 25, and the area ratios Se1 / Se2, Se4 / Se3 at these hole intervals Ph12, Ph13 are calculated and plotted on the graph in Fig. 28.

[0128] As shown in Fig. 27, the upper and lower limits of the area ratios Se1 / Se and Se4 / Se at which the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example are substantially constant, regardless of the short side length Le12. The area ratios Se1 / Se and Se4 / Se at which the electromechanical coupling coefficient K of the main mode S0 is maximized are substantially constant, regardless of the short side length Le12. When the relationship of 0.18≦Se1 / Se≦0.32 and 0.18≦Se4 / Se≦0.32 is satisfied, the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example. When the relationship of Se1 / Se=0.24±0.02 and Se4 / Se=0.24±0.02 is satisfied, the electromechanical coupling coefficient K of the main mode S0 is maximized.

[0129] As shown in Fig. 28, the upper and lower limits of the area ratios Se1 / Se2 and Se4 / Se3 at which the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example are substantially constant, regardless of the short side length Le12. The area ratios Se1 / Se2 and Se4 / Se3 at which the electromechanical coupling coefficient K of the main mode S0 is maximized are substantially constant, regardless of the short side length Le12. When the relationship of 0.58≦Se1 / Se2≦1.72 and 0.58≦Se4 / Se3≦1.72 is satisfied, the electromechanical coupling coefficient K of the main mode S0 is improved compared to the comparative example. When the relationship of Se1 / Se2=0.90±0.05 and Se4 / Se3=0.90±0.05 is satisfied, the electromechanical coupling coefficient K of the main mode S0 is maximized.

[0130] Next, the electromechanical coupling coefficient K in the third example based on the sixth embodiment will be described with reference to Figs. 29 to 31. Fig. 29 is a graph showing the influence of the dimensions of the notched first hole in the rectangular first excitation electrode. Fig. 30 is a graph showing the influence of the dimensions of the notched first hole in the rectangular first excitation electrode. Fig. 31 is a graph showing the condition under which K of the S0 mode is maximized in the rectangular first excitation electrode. The horizontal axis of Figs. 29 and 30 shows the area ratio Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode, the vertical axis of Fig. 29 shows the electromechanical coupling coefficient K (%) of the main mode S0, and the vertical axis of Fig. 30 shows the electromechanical coupling coefficient K (%) of the inharmonic mode S1Z. The horizontal axis of FIG. 31 indicates the ratio Wh11 / Tq of the hole length Wh11 to the quartz crystal thickness Tq, and the vertical axis of FIG. 31 indicates the area ratio Har=Sh / Se of the hole area Sh of the first hole to the electrode area Se of the first excitation electrode. (Third Example) crystal piece Cut angle: AT cut Planar shape: square Top surface dimensions: 140μm x 140μm Thickness Tq: 1 μm Main mode S0: 1.45GHz 1st excitation electrode Material: Aluminum (Al) or Aluminum Copper Alloy (AlCu) First electrode length Le1: 120μm (Le1 / Tq=120) Second electrode length Le2: 50μm (Le2 / Tq=50) Electrode thickness Te: 0.05μm 1st hole Hole length Wh12, Wh22: Parameter (Wh12 = Wh22) Hole length Wh11, Wh21: Parameter (Wh11=Wh21)

[0131] Fig. 29 plots the simulation results of the electromechanical coupling coefficient K of the main mode S0 when the hole lengths Wh11, Wh21 (Wh11 = Wh21) are 5 μm, 10 μm, 15 μm, and 20 μm and the area ratio Har = Sh / Se is changed. The change in the area ratio Har = Sh / Se is realized by changing the hole lengths Wh21, Wh22.

[0132] The electromechanical coupling coefficient K of the main mode S0 shows a convex-up graph within the range of 0 < Har < 0.08. The electromechanical coupling coefficient K of the main mode S0 is 6.87 when Har = 0, while it reaches a maximum of about 7.1 in all cases of Wh11 = Wh21 = 5 μm, 10 μm, 15 μm, and 20 μm. The smaller the hole lengths Wh11, Wh21 (Wh11 = Wh21), the smaller the area ratio Har = Sh / Se at which the electromechanical coupling coefficient K of the main mode S0 reaches its maximum. The graph in Fig. 31 plots this result. As shown in the approximate formula in Fig. 31, the condition for the electromechanical coupling coefficient K of the main mode S0 to reach its maximum is Har = -0.0024×(Wh11 / Tq) + 0.0695 ± 0.01 is satisfied.

[0133] Fig. 30 plots the simulation results of the electromechanical coupling coefficient K of the inharmonic mode S1Z when the hole lengths Wh11, Wh21 (Wh11 = Wh21) are 5 μm, 10 μm, 15 μm, and 20 μm and the area ratio Har = Sh / Se is changed. The change in the area ratio Har = Sh / Se is realized by changing the hole lengths Wh21, Wh22.

[0134] The electromechanical coupling coefficient K of the inharmonic mode S1Z shows a downwardly convex graph within the range of 0 < Har < 0.08. The electromechanical coupling coefficient K of the inharmonic mode S1Z is 2.27 when Har = 0, whereas it becomes 0.2 or less at minimum in any of the cases where Wh11 = Wh21 = 5μm, 10μm, 15μm, 20μm, and becomes 0.1 or less at minimum in the cases where Wh11 = Wh21 = 5μm, 10μm, 15μm. The smaller the hole lengths Wh11, Wh21 (Wh11 = Wh21), the smaller the area ratio Har = Sh / Se at which the electromechanical coupling coefficient K of the inharmonic mode S1Z becomes minimum.

[0135] Next, while referring to FIGS. 32 and 33, the simulation results of the electromechanical coupling coefficient K in the case where the crystal piece is BT cut in the example based on the ninth embodiment will be described. The example used in the simulation is the same as the first example except for the cut angle of the crystal piece, the electrode length of the first excitation electrode, and the shape and dimensions of the first hole. FIGS. 32 and 33 are graphs showing the influence of the area ratio of the holes in the square first excitation electrode. The horizontal axis in FIGS. 32 and 33 indicates the area ratio Har = Sh / Se of the hole area Sh of the first hole with respect to the electrode area Se of the first excitation electrode, the vertical axis in FIG. 32 indicates the electromechanical coupling coefficient K of the main mode S0, and the vertical axis in FIG. 33 indicates the electromechanical coupling coefficient K of the inharmonic mode S1Z.

[0136] In FIGS. 32 and 33, the simulation results of the electromechanical coupling coefficient K when the area ratio Har = Sh / Se is changed are plotted for the cases where the electrode lengths Le1, Le2 (Le1 = Le2) of the first excitation electrode are 40μm, 60μm, 80μm. The area ratio Har = Sh / Se is realized by changing the radius R of the first hole.

[0137] As shown in FIG. 32, the electromechanical coupling coefficient K of the main mode S0 mode shows a convex upward graph in the range of 0 < Har < 0.30. The electromechanical coupling coefficient K of the main mode S0 is about 4.10 when Har = 0, and becomes about 4.40 at maximum. The electromechanical coupling coefficient K of the main mode S0 is improved compared to the configuration without the first hole portion (Har = 0) in the range of 0 < Har ≤ 0.125.

[0138] As shown in FIG. 33, the electromechanical coupling coefficient K of the inharmonic mode S1Z shows a convex downward graph in the range of 0 < Har < 0.20. The electromechanical coupling coefficient K of the inharmonic mode S1Z is about 1.40 when Har = 0, while it is about 0.01 at minimum when Le1 = Le2 = 40 μm, about 0.10 at minimum when Le1 = Le2 = 60 μm, and about 0.12 at minimum when Le1 = Le2 = 80 μm. The electromechanical coupling coefficient K of the inharmonic mode S1Z is lower than the configuration without holes (Har = 0) in the range of 0 < Har ≤ 0.15. The electromechanical coupling coefficient K of the inharmonic mode S1Z further decreases in the range of 0.025 ≤ Har ≤ 0.075.

[0139] 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.

[0140] <1> A piezoelectric element having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction, An exciting electrode provided on the main surface and When the dimension of the exciting electrode along the first direction is Le1 and the dimension of the piezoelectric element along the third direction is Tq, 45 ≤ Le1 / Tq ≤ 120 a relationship holds, A first hole portion penetrating the exciting electrode along the third direction is formed in the central portion of the exciting electrode in the first direction, a piezoelectric vibration element.

[0141] <2> 60≦Le1 / Tq The relationship between <1> The piezoelectric vibration element described in

[0142] <3> The first hole portion is formed in a center portion of the excitation electrode in the second direction and is spaced apart from an end portion of the excitation electrode extending in the first direction. <1> or <2> The piezoelectric vibration element described in

[0143] <4> The first hole portion opens in the second direction at an end portion of the excitation electrode extending in the first direction. <1> or <2> The piezoelectric vibration element described in

[0144] <5> The first hole portion has a plurality of small holes. <1> from <4> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0145] <6> When the dimension of the excitation electrode in the second direction is Le2, 10≦Le2 / Tq≦45 The relationship is established as follows: <1> from <5> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0146] <7> When the dimension of the excitation electrode in the second direction is Le2, 45≦Le2 / Tq≦120 The relationship is established, The first hole is formed in the center of the excitation electrode in the second direction. <1> from <5> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0147] <8> The piezoelectric strip is a quartz crystal strip. <1> from <7> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0148] <9> The crystal piece is AT cut. The second direction is parallel to the X-axis of the crystal axis of the quartz crystal blank. <8> The piezoelectric vibration element described in

[0149] <10> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le1=Le2 and 0 <Har≦0.23 The relationship is established as follows: <9> The piezoelectric vibration element described in

[0150] <11> Har = 1.52 × (Le2 / Tq) -0.82 ±0.01 The relationship is established as follows: <10> The piezoelectric vibration element described in

[0151] <12> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le1=Le2 and 0 <Har≦0.05 The relationship is established as follows: <9> from <11> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0152] <13> Har = 1.05 × (Le2 / Tq) -0.92 ±0.01 The relationship is established as follows: <12> The piezoelectric vibration element described in

[0153] <14> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, 0.5≦Le2 / Le1≦1.3 and Le2 / Le1 ≠ 1.0 and 0 <Har≦0.015×exp(2.53×Le2 / Le1) The relationship is established as follows: <9> The piezoelectric vibration element described in

[0154] <15> Har=0.061×exp(3.25×Le2 / Le1)×(Le2 / Tq) -0.82 ±0.01 The relationship is established as follows: <14> The piezoelectric vibration element described in

[0155] <16> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, 1.3 <Le2 / Le1≦2.0 and Le2 / Le1 ≠ 1.0 and 0 <Har≦0.704×exp(-1.07×Le2 / Le1) The relationship is established as follows: <9> The piezoelectric vibration element described in

[0156] <17> Har=4.82×exp(-0.96×Le2 / Le1)×(Le2 / Tq) -0.82 ±0.01 The relationship is <16> The piezoelectric vibration element described in

[0157] <18> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2 / Le1 ≠ 1.0 and 0 <Har≦0.02 The relationship is established as follows: <9> The piezoelectric vibration element described in

[0158] <19> 0.5≦Le2 / Le1≦1.3 and Le2 / Le1 ≠ 1.0 and Har=0.68×exp(0.48×Le2 / Le1)×(Le2 / Tq) -0.92 ±0.01 The relationship is established as follows: <9> The piezoelectric vibration element described in

[0159] <20> 1.3 <Le2 / Le1≦2.0 and Har=0.44×exp(0.61×Le2 / Le1)×(Le2 / Tq) -0.92 ±0.01 The relationship is established as follows: <9> The piezoelectric vibration element described in

[0160] <21> The crystal piece is BT cut. The second direction is parallel to the X-axis of the crystal axis of the quartz crystal blank. <8> The piezoelectric vibration element described in

[0161] <22> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2=Le1 and 0 <Har≦0.125 The relationship is established as follows: <21> The piezoelectric vibration element described in

[0162] <23> When the dimension of the excitation electrode in the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2=Le1 and 0.025≦H ≦0.075 The relationship is established as follows: <21> or <22> The piezoelectric vibration element described in

[0163] <24> When the dimension of the excitation electrode in the second direction is Le2, Le2 / Le1 ≠ 1.0 The relationship is established, The first hole portion has a longitudinal direction along a direction perpendicular to a longitudinal direction of the excitation electrode. <1> from <9> and <14> from <21> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0164] <25> When the dimension of the excitation electrode in the second direction is Le2, Le2 / Le1 ≠ 1.0 The relationship is established, The first hole portion has a longitudinal direction parallel to the longitudinal direction of the excitation electrode. <1> from <9> and <14> from <21> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0165] <26> A second hole is further formed in a center portion in the first direction of a portion of the excitation electrode on the negative side in the first direction with respect to the first hole, A third hole portion is further formed in a center portion in the first direction of a portion of the excitation electrode on the positive side in the first direction with respect to the first hole portion. <1> from <25> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0166] <27> When the area of ​​the excitation electrode is Se, the area of ​​the portion of the second hole portion in the excitation electrode on the negative side in the first direction is Se1, and the area of ​​the portion of the third hole portion in the excitation electrode on the positive side in the first direction is Se4, 0.18≦Se1 / Se≦0.32 and 0.18≦Se4 / Se≦0.32 The relationship is established as follows: <26> The piezoelectric vibration element described in

[0167] <28> Se1 / Se=0.24±0.02 and Se4 / Se=0.24±0.02 The relationship is established as follows: <27> The piezoelectric vibration element described in

[0168] <29> When the area of ​​the portion of the second hole portion in the excitation electrode on the negative side in the first direction is Se1, the area of ​​the portion of the second hole portion in the excitation electrode on the positive side in the first direction of the second hole portion and on the negative side in the first direction of the first hole portion is Se2, the area of ​​the portion of the first hole portion in the excitation electrode on the positive side in the first direction of the first hole portion and on the negative side in the first direction of the third hole portion is Se3, and the area of ​​the portion of the third hole portion in the excitation electrode on the positive side in the first direction of the third hole portion is Se4, 0.58≦Se1 / Se2≦1.72 and 0.58≦Se4 / Se3≦1.72 The relationship is established as follows: <26> The piezoelectric vibration element described in

[0169] <30> Se1 / Se2=0.90±0.05 and Se4 / Se3=0.90±0.05 The relationship is established as follows: <29> The piezoelectric vibration element described in

[0170] <31> The second hole portion is formed at a position that divides an area of ​​a portion of the excitation electrode on a negative side in the first direction with respect to the first hole portion in half in the first direction, The third hole portion is formed at a position that divides an area of ​​a portion of the excitation electrode on a positive side in the first direction with respect to the first hole portion in half in the first direction. <26> The piezoelectric vibration element described in

[0171] <32> The area of ​​the second hole portion is smaller than the area of ​​the first hole portion. <26> from <31> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0172] <33> The thickness-shear vibration mode is the dominant vibration mode. <1> from <32> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0173] <34> The main component of the excitation electrode is aluminum. <1> from <33> 13. A piezoelectric vibration element according to any one of claims 1 to 12.

[0174] <35> <1> from <34> The piezoelectric vibration element according to any one of claims 1 to 5, A first cover member; a second cover member that is joined to the piezoelectric vibration element or the first cover member and forms a space between the second cover member and the first cover member to accommodate a vibration part of the piezoelectric vibration element; Equipped with Piezoelectric vibrator.

[0175] <36> <35> The piezoelectric vibrator according to claim 1, a mounting substrate on which the piezoelectric vibrator is mounted; a lid that is joined to the mounting substrate and forms a space between the mounting substrate and the lid to accommodate the piezoelectric vibrator; Equipped with Piezoelectric oscillator.

[0176] In addition, the embodiment according to the present invention is not limited to a quartz crystal resonator, and can be applied to other piezoelectric resonators (Piezoelectric Resonator Units). Examples of piezoelectric pieces suitable for use in the piezoelectric resonator 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, but are not limited thereto and can be appropriately selected.

[0177] The embodiments according to the present invention can be appropriately applied to any device that performs electromechanical energy conversion by utilizing the piezoelectric effect, such as a timing device, a sound generator, an oscillator, or a load sensor, without any particular limitation.

[0178] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibration element, a piezoelectric vibrator, and a piezoelectric oscillator that are capable of improving the electromechanical coupling coefficient.

[0179] The above-described embodiments are provided to facilitate understanding of the present invention, and are not intended to limit the present invention. The present invention may be modified / improved without departing from the spirit thereof, and equivalents are also included in the present invention. In other words, the embodiment and / or modification may be modified by a person skilled in the art as long as it has the characteristics of the present invention. For example, the elements and their arrangements, materials, conditions, shapes, sizes, etc. of the embodiment and / or modification are not limited to those shown as examples, and may be modified as appropriate. In addition, the embodiment and modification are illustrative, and it goes without saying that partial replacement or combination of the configurations shown in different embodiments and / or modifications is possible, and these are also included in the scope of the present invention as long as they include the characteristics of the present invention. [Explanation of symbols]

[0180] 100...Crystal oscillator 1...Crystal resonator 10...Crystal vibration element 11...Crystal piece 11A…Vibration part 11B…Opening 11C...Holding part 12a…Top surface 12b…Bottom surface 14a...first excitation electrode 14b…Second excitation electrode H1…hole Le1…1st electrode length Le2…2nd electrode length Lh11…1st hole manager Lh12…Second hole manager Te…electrode thickness Lq: Crystal thickness 214a~914a...first excitation electrode H2~H6,H71,H81,H9...hole H61, H62…Notch H72, H73, H82, H83…Hole

Claims

1. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; When the dimension of the excitation electrode along the second direction is Le2, 45≦Le2 / Tq≦120 The relationship is established, The first hole portion is formed in a central portion of the excitation electrode in the second direction. Piezoelectric vibration element.

2. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; the piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le1=Le2 and 0<Har≦0.23 The relationship is established, Hair = 1.52 × (L2 / Tq) －０．８２ ±0.01 The relationship is established as follows: Piezoelectric vibration element.

3. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; the piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le1=Le2 and 0<Har≦0.05 The relationship is established, Hair = 1.05 × (L2 / Tq) －０．９２ ±0.01 The relationship is established as follows: Piezoelectric vibration element.

4. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; the piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, 0.5≦Le2 / Le1≦1.3 and Le2 / Le1≠1.0 and 0<Har≦0.015×exp(2.53×Le2 / Le1) The relationship is established, Har=0061×exp(325×Ler / Leq)×(Lerer / To) －０．８２ ±0.01 The relationship is established as follows: Piezoelectric vibration element.

5. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; the piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, 1.3<Le2 / Le1≦2.0 and Le2 / Le1≠1.0 and 0<Har≦0.704×exp(-1.07×Le2 / Le1) The relationship is established as follows: Piezoelectric vibration element.

6. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; The piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2 / Le1≠1.0 and 0<Har≦0.02 The relationship is established as follows: Piezoelectric vibration element.

7. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; The piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, 0.5≦Le2 / Le1≦1.3 and Le2 / Le1≠1.0 and Har=0.68×exp(048×Ler / Leq)×(Lerer / To) －０．９２ ±0.01 The relationship is established as follows: Piezoelectric vibration element.

8. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; The piezoelectric piece is a quartz crystal piece, The quartz crystal piece is an AT cut. the second direction is a direction parallel to an X-axis of the crystal axis of the quartz crystal piece, 1.3<Le2 / Le1≦2.0 and Har=044×exp(061×Ler / Leq)×(Ler��To) －０．９２ ±0.01 The relationship is established as follows: Piezoelectric vibration element.

9. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; A second hole is further formed in a center portion in the first direction of a portion of the excitation electrode on a negative side in the first direction with respect to the first hole, a third hole portion is further formed in a center portion in the first direction of a portion of the excitation electrode on a positive side in the first direction with respect to the first hole portion, When the area of ​​the excitation electrode is Se, the area of ​​a portion of the second hole portion in the excitation electrode on the negative side in the first direction is Se1, and the area of ​​a portion of the third hole portion in the excitation electrode on the positive side in the first direction is Se4, 0.18≦Se1 / Se≦0.32 and 0.18≦Se4 / Se≦0.32 The relationship is established as follows: Piezoelectric vibration element.

10. a piezoelectric piece having a main surface extending in a first direction and a second direction intersecting the first direction, and having a thickness in a third direction intersecting the first direction and the second direction; An excitation electrode provided on the main surface; Equipped with When the dimension of the excitation electrode along the first direction is Le1 and the dimension of the piezoelectric piece along the third direction is Tq, 45≦Le1 / Tq≦120 The relationship is established, a first hole portion is formed in a center portion of the excitation electrode in the first direction, the first hole portion penetrating the excitation electrode along the third direction; A second hole is further formed in a center portion in the first direction of a portion of the excitation electrode on a negative side in the first direction with respect to the first hole, a third hole portion is further formed in a center portion in the first direction of a portion of the excitation electrode on a positive side in the first direction with respect to the first hole portion, When an area of ​​a portion of the second hole portion in the excitation electrode on the negative side in the first direction is Se1, an area of ​​a portion of the second hole portion in the excitation electrode on the positive side in the first direction and on the negative side in the first direction of the first hole portion is Se2, an area of ​​a portion of the first hole portion in the excitation electrode on the positive side in the first direction and on the negative side in the first direction of the third hole portion is Se3, and an area of ​​a portion of the third hole portion in the excitation electrode on the positive side in the first direction is Se4, 0.58≦Se1 / Se2≦1.72 and 0.58≦Se4 / Se3≦1.72 The relationship is established as follows: Piezoelectric vibration element.

11. 60≦Le1 / Tq The relationship between The piezoelectric vibration element according to claim 1 .

12. The first hole portion is formed in a central portion of the excitation electrode in the second direction and is spaced apart from an end portion of the excitation electrode extending in the first direction. The piezoelectric vibration element according to claim 1 .

13. The first hole portion opens in the second direction at an end portion of the excitation electrode extending in the first direction. The piezoelectric vibration element according to claim 1 .

14. The first hole portion has a plurality of small holes. The piezoelectric vibration element according to claim 1 .

15. When the dimension of the excitation electrode along the second direction is Le2, 10≦Le2 / Tq≦45 The relationship is established as follows: The piezoelectric vibration element according to claim 2 .

16. When the dimension of the excitation electrode along the second direction is Le2, Le2 / Le1≠1.0 The relationship is established, The first hole portion has a longitudinal direction along a direction perpendicular to a longitudinal direction of the excitation electrode.

11. The piezoelectric vibration element according to claim 1, or any one of claims 4 to 10.

17. When the dimension of the excitation electrode along the second direction is Le2, Le2 / Le1≠1.0 The relationship is established, The first hole portion has a longitudinal direction parallel to a longitudinal direction of the excitation electrode.

11. The piezoelectric vibration element according to claim 1, or any one of claims 4 to 10.

18. The thickness-shear vibration mode is the dominant vibration mode. The piezoelectric vibration element according to claim 1 .

19. The main component of the excitation electrode is aluminum. The piezoelectric vibration element according to claim 1 .

20. The piezoelectric vibration element according to claim 1 , A first cover member; a second cover member that is joined to the piezoelectric vibration element or the first cover member and that forms a space between the second cover member and the first cover member to accommodate a vibration portion of the piezoelectric vibration element; Equipped with Piezoelectric vibrator.

21. The piezoelectric vibrator according to claim 20; a mounting substrate on which the piezoelectric vibrator is mounted; a lid that is bonded to the mounting substrate and that forms a space between the mounting substrate and the lid to accommodate the piezoelectric vibrator; Equipped with Piezoelectric oscillator.

22. The piezoelectric piece is a quartz crystal piece, The quartz crystal piece is a BT cut, The second direction is a direction parallel to the X-axis of the crystal axis of the quartz crystal piece.

11. The piezoelectric vibration element according to claim 1, 9 or 10.

23. When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2 = Le1 and 0<Har≦0.125 The relationship is established as follows: The piezoelectric vibration element according to claim 22.

24. When the dimension of the excitation electrode along the second direction is Le2 and the ratio of the area of ​​the first hole portion to the area of ​​the excitation electrode is Har, Le2 = Le1 and 0.025≦Har≦0.075 The relationship is established as follows: The piezoelectric vibration element according to claim 22.

25. the second hole portion is formed at a position that divides an area of ​​a portion of the excitation electrode on a negative side in the first direction with respect to the first hole portion in half in the first direction, The third hole portion is formed at a position that divides an area of ​​a portion of the excitation electrode on a positive side in the first direction with respect to the first hole portion in half in the first direction. The piezoelectric vibration element according to claim 9 or 10.

26. The area of ​​the second hole portion is smaller than the area of ​​the first hole portion. The piezoelectric vibration element according to claim 9 or 10.

27. Har=4.82×exp(-0.96×Ler / Leq)×(Lerer / To) －０．８２ ±0.01 The relationship is established as follows: The piezoelectric vibration element according to claim 5 .

28. Se1 / Se=0.24±0.02 and Se4 / Se=0.24±0.02 The relationship is established as follows: The piezoelectric vibration element according to claim 9 .

29. Se1 / Se2=0.90±0.05 and Se4 / Se3=0.90±0.05 The relationship is established as follows: The piezoelectric vibration element according to claim 10.

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