Piezoelectric vibration element

Abstract

To provide a piezoelectric vibration element capable of improving vibration characteristics.SOLUTION: The quartz crystal resonator 1 includes the quartz crystal blank 11, which has the upper-surface 11A portion and the lower-surface 11B portion that face each other, the first electrodes, which include the first excitation-electrode 14a portions provided on the first main surface and the first extraction-electrode 15a portions connected to the first outer peripheral portions of the first excitation electrodes, and the second excitation-electrode 14b portions provided on the second main surface. In a plan view, a high-acoustic-velocity region located at a central portion in a region where the first excitation electrode and the second excitation electrode overlap each other and a low-acoustic-velocity region located at a peripheral portion in the region where the first excitation electrode and the second excitation electrode overlap each other and having an acoustic velocity lower than that of the high-acoustic-velocity region are provided, a first outer periphery of the first excitation electrode is provided on an inner side of a second outer periphery of the second excitation electrode, an acoustic velocity in a region where the first extraction electrode and the second excitation electrode overlap each other is lower than the acoustic velocity in the high-acoustic-velocity region and equal to or higher than the acoustic velocity in the low-acoustic-velocity region.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a piezoelectric vibration element. [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. A piezoelectric vibration element includes a piezoelectric plate having a pair of main surfaces and a pair of excitation electrodes provided on the pair of main surfaces of the piezoelectric plate.

[0003] For example, Patent Document 1 discloses a vibration element that includes a substrate that vibrates by thickness-shear vibration, a first excitation electrode that is provided on one main surface of the substrate and has a rectangular shape with the four corners cut out, and a second excitation electrode that is provided on the other main surface of the substrate, and in which the ratio (S2 / S1) of the area S1 of the rectangle to the area S2 of the first excitation electrode is 87.7%≦(S2 / S1)<95.0%. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-158149 Summary of the Invention [Problem to be solved by the invention]

[0005] The vibration element described in Patent Document 1 can reduce the excitation intensity of spurious inharmonic modes, but as electronic devices become more sophisticated, further improvements in vibration characteristics are required for piezoelectric vibration elements.

[0006] The present invention has been made in view of the above circumstances, and has an object to provide a piezoelectric vibration element that can improve vibration characteristics. [Means for solving the problem]

[0007] A piezoelectric vibration element according to one aspect of the present invention is a piezoelectric vibration element including a piezoelectric piece having a first principal surface and a second principal surface facing each other, a first electrode including a first excitation electrode provided on the first principal surface and a first extraction electrode connected to the first excitation electrode, and a second excitation electrode provided on the second principal surface, wherein, in a plan view, a high acoustic velocity region is provided in the center of an area where the first excitation electrode and the second excitation electrode overlap, and a low acoustic velocity region is provided in the periphery of the area where the first excitation electrode and the second excitation electrode overlap, and has a lower acoustic velocity than the high acoustic velocity region. a first outer periphery of the first excitation electrode is located more inward than a second outer periphery of the second excitation electrode; the sound velocity in the region where the first extraction electrode and the second excitation electrode overlap is lower than the sound velocity in the high sound velocity region and equal to or higher than the sound velocity in the low sound velocity region; at least one opening is provided in at least one of the first electrode and the second excitation electrode in the region where the first electrode and the second excitation electrode overlap; and the at least one opening is located substantially within a distance from the boundary between the first excitation electrode and the first extraction electrode that is four times the thickness of the piezoelectric piece or less.

[0008] A piezoelectric vibration element according to another aspect of the present invention is a piezoelectric vibration element including a piezoelectric piece having a first principal surface and a second principal surface facing each other, a first electrode including a first excitation electrode provided on the first principal surface and a first extraction electrode connected to the first excitation electrode, and a second excitation electrode provided on the second principal surface, wherein, in a plan view, a high acoustic velocity region is provided in a central portion within a region where the first excitation electrode and the second excitation electrode overlap, and a low acoustic velocity region is provided in a peripheral portion within the region where the first excitation electrode and the second excitation electrode overlap, and the high acoustic velocity region has an acoustic velocity slower than that of the high acoustic velocity region, and a first outer periphery of the first excitation electrode is The first excitation electrode is provided inside the second outer periphery of the second excitation electrode, and the sound velocity in the region where the first extraction electrode and the second excitation electrode overlap is lower than the sound velocity in the high sound velocity region and equal to or higher than the sound velocity in the low sound velocity region, and at least one first opening is provided in at least one of the first excitation electrode and the second excitation electrode in the region of the low sound velocity region that is on the first extraction electrode side relative to the high sound velocity region, and at least one second opening is provided in at least one of the first excitation electrode and the second excitation electrode in the region of the low sound velocity region that is on the opposite side of the high sound velocity region from the first extraction electrode. [Effects of the Invention]

[0009] According to the present invention, it is possible to provide a piezoelectric vibration element that can improve vibration characteristics. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is an exploded perspective view of a quartz crystal resonator according to a first embodiment. [Figure 2] 1 is a cross-sectional view of a quartz crystal resonator according to a first embodiment. [Figure 3] FIG. 1 is a plan view of a quartz crystal vibrating element according to a first embodiment. [Figure 4] 1 is a cross-sectional view of a quartz crystal vibrating element according to a first embodiment. [Figure 5] 3A and 3B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the first embodiment. [Figure 6] 3A and 3B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the first embodiment. [Figure 7] 3A and 3B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the first embodiment. [Figure 8] FIG. 10 is a plan view of a quartz crystal vibrating element according to a comparative example. [Figure 9] FIG. 10 is a diagram showing the vibration distribution of a quartz crystal vibration element according to a comparative example. [Figure 10] FIG. 10 is a diagram showing the vibration distribution of a quartz crystal vibration element according to a comparative example. [Figure 11] FIG. 10 is a diagram showing the vibration distribution of a quartz crystal vibration element according to a comparative example. [Figure 12] 4 is a graph showing a simulation result based on the first embodiment. [Figure 13] 4 is a graph showing a simulation result based on the first embodiment. [Figure 14] FIG. 10 is a plan view of a quartz crystal vibrating element according to a second embodiment. [Figure 15] 10 is a graph showing a simulation result based on the second embodiment. [Figure 16]10 is a graph showing a simulation result based on the second embodiment. [Figure 17] 10 is a graph showing a simulation result based on the second embodiment. [Figure 18] 10 is a graph showing a simulation result based on the second embodiment. [Figure 19] 10 is a graph showing a simulation result based on the second embodiment. [Figure 20] FIG. 10 is a plan view of a quartz crystal vibrating element according to a third embodiment. [Figure 21] 10A and 10B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the third embodiment. [Figure 22] 10A and 10B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the third embodiment. [Figure 23] 10A and 10B are diagrams illustrating vibration distribution of the quartz crystal vibration element according to the third embodiment. [Figure 24] FIG. 10 is a plan view of a quartz crystal vibrating element according to a fourth embodiment. [Figure 25] 10A and 10B are diagrams illustrating vibration distributions of the quartz crystal vibration element according to the fourth embodiment. [Figure 26] 10A and 10B are diagrams illustrating vibration distributions of the quartz crystal vibration element according to the fourth embodiment. [Figure 27] 10A and 10B are diagrams illustrating vibration distributions of the quartz crystal vibration element according to the fourth embodiment. [Figure 28] FIG. 10 is a plan view of a quartz crystal vibrating element according to a fifth embodiment. [Figure 29] 13 is a graph showing a simulation result based on the fifth embodiment. [Figure 30] FIG. 10 is a plan view of a quartz crystal vibrating element according to a sixth embodiment. [Figure 31] 13 is a graph showing a simulation result based on the sixth embodiment. [Figure 32] 13 is a graph showing a simulation result based on the sixth embodiment. [Figure 33] FIG. 11 is a plan view of a quartz crystal vibrating element according to a seventh embodiment. [Figure 34] FIG. 13 is an enlarged plan view of a connection portion in the seventh embodiment. [Figure 35] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the seventh embodiment. [Figure 36] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the seventh embodiment. [Figure 37] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the seventh embodiment. [Figure 38] 13 is a graph showing a simulation result based on the seventh embodiment. [Figure 39] 13 is a graph showing a simulation result based on the seventh embodiment. [Figure 40] FIG. 13 is a plan view of the quartz crystal vibrating element according to the eighth embodiment. [Figure 41] 13 is a graph showing a simulation result based on the eighth embodiment. [Figure 42] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the eighth embodiment. [Figure 43] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the eighth embodiment. [Figure 44] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the eighth embodiment. [Figure 45] FIG. 13 is a plan view of a quartz crystal vibrating element according to a ninth embodiment. [Figure 46] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the ninth embodiment. [Figure 47] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the ninth embodiment. [Figure 48] FIG. 13 is a diagram showing a vibration distribution of the quartz crystal vibration element according to the ninth embodiment. [Figure 49] FIG. 22 is a plan view of the quartz crystal vibrating element according to the tenth embodiment. [Figure 50] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the tenth embodiment. [Figure 51] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the tenth embodiment. [Figure 52] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the tenth embodiment. [Figure 53]FIG. 22 is a plan view of the quartz crystal vibrating element according to the eleventh embodiment. [Figure 54] 23 is a graph showing a simulation result based on the eleventh embodiment. [Figure 55] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eleventh embodiment. [Figure 56] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eleventh embodiment. [Figure 57] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eleventh embodiment. [Figure 58] FIG. 22 is a plan view of the quartz crystal vibrating element according to the twelfth embodiment. [Figure 59] FIG. 23 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twelfth embodiment. [Figure 60] FIG. 23 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twelfth embodiment. [Figure 61] FIG. 23 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twelfth embodiment. [Figure 62] FIG. 22 is a plan view of the quartz crystal vibrating element according to the thirteenth embodiment. [Figure 63] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the thirteenth embodiment. [Figure 64] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the thirteenth embodiment. [Figure 65] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the thirteenth embodiment. [Figure 66] FIG. 22 is a plan view of the quartz crystal vibrating element according to the fourteenth embodiment. [Figure 67] FIG. 22 is a plan view of the quartz crystal vibrating element according to the fifteenth embodiment. [Figure 68] 20 is a graph showing simulation results based on the fourteenth and fifteenth embodiments. [Figure 69] 23 is a graph showing a simulation result based on the fifteenth embodiment. [Figure 70] 23 is a graph showing a simulation result based on the fourteenth embodiment. [Figure 71]23 is a graph showing a simulation result based on the fourteenth embodiment. [Figure 72] FIG. 22 is a plan view of the quartz crystal vibrating element according to the sixteenth embodiment. [Figure 73] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the sixteenth embodiment. [Figure 74] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the sixteenth embodiment. [Figure 75] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the sixteenth embodiment. [Figure 76] FIG. 22 is a plan view of the quartz crystal vibrating element according to the seventeenth embodiment. [Figure 77] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the seventeenth embodiment. [Figure 78] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the seventeenth embodiment. [Figure 79] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the seventeenth embodiment. [Figure 80] FIG. 22 is a plan view of the quartz crystal vibrating element according to the eighteenth embodiment. [Figure 81] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eighteenth embodiment. [Figure 82] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eighteenth embodiment. [Figure 83] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the eighteenth embodiment. [Figure 84] FIG. 22 is a plan view of the quartz crystal vibrating element according to the nineteenth embodiment. [Figure 85] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the nineteenth embodiment. [Figure 86] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the nineteenth embodiment. [Figure 87] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the nineteenth embodiment. [Figure 88] FIG. 20 is a plan view of a quartz crystal vibrating element according to a twentieth embodiment. [Figure 89] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twentieth embodiment. [Figure 90] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twentieth embodiment. [Figure 91] FIG. 20 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twentieth embodiment. [Figure 92] FIG. 21 is a plan view of a quartz crystal vibrating element according to a twenty-first embodiment. [Figure 93] FIG. 21 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twenty-first embodiment. [Figure 94] FIG. 21 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twenty-first embodiment. [Figure 95] FIG. 21 is a diagram showing the vibration distribution of the quartz crystal vibration element according to the twenty-first embodiment. [Figure 96] FIG. 22 is a plan view of a quartz crystal vibrating element according to a twenty-second embodiment. [Figure 97] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibrating element according to the twenty-second embodiment. [Figure 98] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibrating element according to the twenty-second embodiment. [Figure 99] FIG. 22 is a diagram showing the vibration distribution of the quartz crystal vibrating element according to the twenty-second embodiment. DETAILED DESCRIPTION OF THE INVENTION

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

[0012] For the sake of clarity, each drawing may be accompanied by a Cartesian coordinate system consisting of an X-axis, a Y'-axis, and a Z'-axis to clarify the relationship between the drawings and to aid in understanding the positional relationship of each component. The X-axis, Y'-axis, and Z'-axis correspond to each other in each drawing. The X-axis, Y'-axis, and 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 Z'-axis are axes obtained by rotating the Y-axis and Z-axis counterclockwise around the X-axis by θ degrees when viewed from the positive direction of the X-axis.

[0013] In the following description, the direction parallel to the X-axis is referred to as the "X-axis direction," the direction parallel to the Y'-axis as the "Y'-axis direction," and the direction parallel to the Z'-axis as the "Z'-axis direction." The directions of the arrows on the X-axis, Y'-axis, and Z'-axis are referred to as "positive" or "+ (plus)," and the directions opposite the arrows are referred to as "negative" or "- (minus)." For convenience, the +Y'-axis direction will be described as the upward direction, and the -Y'-axis direction will be described as the downward direction, but the up-down orientation of the quartz crystal vibrating element 10 and the quartz crystal unit 1 is not limited to this. The plane defined by the X-axis and Z'-axis will be referred to as the Z'X plane, and the same applies to planes defined by the other axes.

[0014] First Embodiment First, the configuration of a quartz crystal resonator according to a first embodiment will be described with reference to Figures 1 and 2. Figure 1 is an exploded perspective view of the quartz crystal resonator according to the first embodiment. Figure 2 is a cross-sectional view of the quartz crystal resonator according to the first embodiment.

[0015] The quartz crystal resonator 1 includes a quartz crystal resonator element 10, a base member 30, a lid member 40, and a bonding portion 50. Hereinafter, the Y′-axis direction will be referred to as the “thickness direction” of the quartz crystal resonator element 10.

[0016] The crystal resonator 1 is used as a component of, for example, a temperature compensated crystal oscillator (TCXO), a voltage controlled crystal oscillator (VCXO), or an oven controlled crystal oscillator (OCXO).

[0017] The quartz crystal vibrating element 10 is an electromechanical energy conversion element that converts electrical energy into mechanical energy and vice versa using the piezoelectric effect. The main mode frequency of the quartz crystal vibrating element 10 is, for example, between 0.8 GHz and 2.0 GHz, for example, about 0.95 GHz. The inharmonic mode frequency of the quartz crystal vibrating element 10 is, for example, within a range of about 1% of the main mode frequency.

[0018] The quartz crystal vibrating element 10 is excited at a predetermined frequency based on the applied alternating voltage. The quartz crystal vibrating element 10 is held so as to be able to vibrate in a vibration space provided between a base member 30 and a cover member 40. The main vibration of the quartz crystal vibrating element 10 is a thickness shear vibration mode.

[0019] The main vibration of the quartz crystal vibration element is not limited to the thickness shear vibration mode, but may be, for example, a thickness extensional vibration mode, a divergence vibration mode, a length vibration mode, or a bending vibration mode.

[0020] As shown in FIG. 1, the quartz crystal element 10 includes a thin quartz crystal element 11, a first excitation electrode 14a and a second excitation electrode 14b that form a pair of excitation electrodes, a first extraction electrode 15a and a second extraction electrode 15b that form a pair of extraction electrodes, and a first connection electrode 16a and a second connection electrode 16b that form a pair of connection electrodes.

[0021] Crystal blank 11 has upper surface 11A and lower surface 11B that face each other. Upper surface 11A is located on the side facing top wall portion 41 of lid member 40. Lower surface 11B is located on the side facing base member 30. Upper surface 11A and lower surface 11B correspond to a pair of main surfaces of crystal blank 11. Upper surface 11A corresponds to an example of a first main surface, and lower surface 11B corresponds to an example of a second main surface.

[0022] The quartz crystal 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 direction parallel to the Y' axis is the thickness. As an example, when the top surface 11A is viewed in a plan view in the thickness direction (hereinafter simply referred to as "plan view"), the shape of the quartz crystal blank 11 (hereinafter referred to as "planar shape") is rectangular with a pair of short sides extending in the Z'-axis direction and a pair of long sides extending in the X-axis direction. As an example, the shape of the quartz crystal blank 11 is a flat plate with a uniform thickness.

[0023] The planar shape of the crystal blank is not limited to the above. For example, the planar shape of the crystal blank may be rectangular with long sides extending in the Z'-axis direction and short sides extending in the X-axis direction, or square with sides extending in the Z'-axis direction and sides extending in the X-axis direction. The planar shape of the crystal blank may also be rectangular with sides extending in directions intersecting the Z-axis direction and the Z'-axis direction. The planar shape of the crystal blank may also be polygonal, circular, elliptical, or a combination thereof. Furthermore, the crystal blank is not limited to a flat shape. The crystal blank may have a mesa structure or an inverted mesa structure with irregularities on at least one of the top and bottom surfaces. The crystal blank may have 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.

[0024] The AT-cut crystal piece 11 is cut out with the XZ' plane as the main surface, with the Y'-axis and Z'-axis being the axes obtained 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 toward the Z-axis, out of the X-axis, Y-axis, and Z-axis, which are the crystal axes of synthetic quartz crystal.

[0025] The quartz crystal vibrating element 10 using the AT-cut quartz crystal blank 11 has high frequency stability over a wide temperature range. The AT-cut quartz crystal vibrating element also 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 primary vibration mode.

[0026] The cut angle of the quartz crystal blank is not limited to the above. The rotation angle of the Y'-axis and Z'-axis in the AT-cut quartz crystal blank 11 may be inclined within a range of -5 degrees or more or +15 degrees or less from 35 degrees 15 minutes. The cut angle of the quartz crystal blank may also be a cut other than the AT cut, such as a BT cut, a GT cut, or an SC cut. The primary vibration mode of the quartz crystal vibrating element is not limited to thickness-shear vibration mode, and may be, for example, thickness-extensional vibration, lateral vibration, longitudinal vibration, or flexural vibration.

[0027] The first excitation electrode 14a and the second excitation electrode 14b apply an AC voltage to the crystal blank 11 to excite the crystal blank 11. The first excitation electrode 14a and the second excitation electrode 14b are provided in the center of the crystal blank 11 in a plan view. The first excitation electrode 14a is provided on the upper surface 11A, and the second excitation electrode 14b is provided on the lower surface 11B. The first excitation electrode 14a and the second excitation electrode 14b face each other in the Y'-axis direction, sandwiching the crystal blank 11 therebetween.

[0028] The first excitation electrode 14a has a rectangular planar shape with short sides extending in the Z'-axis direction and long sides extending in the X-axis direction. The first excitation electrode 14a also has a thickness in the Y'-axis direction. The second excitation electrode 14b has a similar shape.

[0029] The planar shapes of the first excitation electrode and the second excitation electrode are not limited to those described above. The planar shapes of the first excitation electrode and the second excitation electrode may be rectangular having short sides extending in the X-axis direction, or may be square having sides extending in the X-axis direction and sides extending in the Z'-axis direction. The planar shapes of the first excitation electrode and the second excitation electrode may be rectangular having sides extending in directions intersecting the Z-axis direction and the Z'-axis direction. The planar shapes of the first excitation electrode and the second excitation electrode may be polygonal, circular, elliptical, or a combination thereof.

[0030] The first extraction electrode 15a electrically connects the first excitation electrode 14a and the first connection electrode 16a, and the second extraction electrode 15b electrically connects the second excitation electrode 14b and the second connection electrode 16b. The first extraction electrode 15a is provided across the top surface 11A and the bottom surface 11B of the crystal blank 11, and the second extraction electrode 15b is provided on the bottom surface 11B of the crystal blank 11.

[0031] The first connection electrode 16a and the second connection electrode 16b electrically connect the quartz crystal vibrating element 10 to the base member 30. The first connection electrode 16a and the second connection electrode 16b are provided on the bottom surface 11B of the quartz crystal blank 11.

[0032] The first excitation electrode 14a, the first extraction electrode 15a, and the first connection electrode 16a are integrally formed. The same is true for the second excitation electrode 14b, the second extraction electrode 15b, and the second connection electrode 16b. A group of electrodes consisting of the first excitation electrode 14a, the first extraction electrode 15a, and the first connection electrode 16a is referred to as the first electrodes, and a group of electrodes consisting of the second excitation electrode 14b, the second extraction electrode 15b, and the second connection electrode 16b is referred to as the second electrodes.

[0033] The first electrode and the second electrode have a multilayer structure, for example, in which a base layer and a surface layer are laminated in this order. For example, the base layer is a chromium (Cr) layer that has good adhesion to the crystal blank 11, and the surface layer is a gold (Au) layer that has good chemical stability. The first electrode and the second electrode may contain titanium (Ti), aluminum (Al), molybdenum (Mo), or an aluminum-copper alloy (AlCu) mainly composed of aluminum (Al). The first electrode and the second electrode may have a single-layer structure.

[0034] The base member 30 holds the quartz crystal vibrating element 10 in an excitable manner. The base member 30 includes a substrate 31, connection electrodes 33a and 33b, lead electrodes 34a and 34b, external electrodes 35a, 35b, 35c, and 35d, and conductive holding members 36a and 36b.

[0035] The base 31 is a plate-shaped insulator having an upper surface 31A and a lower surface 31B that face each other in the thickness direction. The upper surface 31A and the lower surface 31B correspond to a pair of main surfaces of the base 31. The upper surface 31A is located on the side facing the quartz crystal resonator element 10 and the lid member 40, and corresponds to the mounting surface on which the quartz crystal resonator element 10 is mounted. From the viewpoint of suppressing thermal stress acting from the base 31 on the quartz crystal resonator element 10 due to thermal history such as reflow, the base 31 is preferably made of a heat-resistant material. From the same viewpoint, the base 31 may be made of a material with a thermal expansion coefficient similar to that of the quartz crystal blank 11. The base 31 is made of, for example, a ceramic substrate, a glass substrate, or a quartz crystal substrate.

[0036] The corners of the base 31 have cutout side surfaces formed in a cylindrical curved surface shape (also called a castellation shape). However, the shape of the corners of the base 31 is not limited to this. The corners of the base may have cutout side surfaces formed in a prismatic shape, or may be substantially right-angled corners without any cutouts.

[0037] The connection electrodes 33a and 33b are electrically connected to the quartz crystal vibrating element 10. The connection electrode 33a is electrically connected to the connection electrode 16a of the quartz crystal vibrating element 10, and the connection electrode 33b is connected to the connection electrode 16b of the quartz crystal vibrating element 10.

[0038] The lead electrode 34a electrically connects the connection electrode 33a and the external electrode 35a, and the lead electrode 34b electrically connects the connection electrode 33b and the external electrode 35b. The lead electrodes 34a and 34b are provided on the upper surface 31A of the base 31.

[0039] The external electrodes 35a and 35b are external terminals for electrically connecting the quartz crystal vibrating element 10 to an external substrate (not shown). The external electrode 35a electrically connects the first excitation electrode 14a of the quartz crystal vibrating element 10 to the external substrate, and the external electrode 35b electrically connects the second excitation electrode 14b of the quartz crystal vibrating element 10 to the external substrate. One of the external electrodes 35c and 35d is a ground electrode that grounds the lid member 40, and the other is a dummy electrode that is not electrically connected to the quartz crystal vibrating element 10 or the lid member 40. The external electrodes 35a, 35b, 35c, and 35d are each continuously provided from the cutout side surfaces provided at four corners of the base 31 to the bottom surface 31B. In the example shown in FIG. 1, the external electrodes 35a and 35b are located at diagonal corners on the top surface 31A of the base 31, and the external electrodes 35c and 35d are located at another diagonal corner on the top surface 31A of the base 31.

[0040] The functions and positions of the external electrodes 35a, 35b, 35c, and 35d are not limited to those described above. Both external electrodes 35c and 35d may be ground electrodes, or both may be dummy electrodes. The external electrodes 35c and 35d may be omitted. The external electrode 35c may be electrically connected to one of the external electrodes 35a and 35b, and the external electrode 35d may be electrically connected to the other of the external electrodes 35a and 35b. In a plan view, the external electrodes 35a and 35b may be located on the same short side or the same long side of the upper surface 31A of the base 31.

[0041] The conductive holding members 36a and 36b electrically connect the base member 30 and the quartz vibrating element 10 and mechanically hold the quartz vibrating element 10. The conductive holding member 36a electrically connects the first connection electrode 16a of the quartz vibrating element 10 to the connection electrode 33a of the base member 30. The conductive holding member 36b electrically connects the second connection electrode 16b of the quartz vibrating element 10 to the connection electrode 33b of the base member 30. The conductive holding members 36a and 36b are a cured product of a conductive adhesive containing a thermosetting resin, a photocurable resin, or the like. The main component of the conductive holding members 36a and 36b is, for example, a silicone resin. The conductive holding members 36a and 36b contain conductive particles, such as metal particles containing silver (Ag).

[0042] The main component of the conductive holding members 36a, 36b is not limited to silicone resin, but may be, for example, epoxy resin or acrylic resin. Furthermore, the conductive particles contained in the conductive holding members 36a, 36b are not limited to silver particles, but may be formed from other metals, conductive ceramics, conductive organic materials, etc. The conductive holding members 36a, 36b may also contain a conductive polymer.

[0043] The lid member 40 forms an internal space 39 between itself and the base member 30, in which the quartz vibrating element 10 is housed. The lid member 40 has a top wall 41, a side wall 42 extending from the outer periphery of the top wall 41 toward the base member 30, and a flange 43 extending outward from the tip of the side wall 42. The top wall 41 faces the base member 30 in the Y′-axis direction, sandwiching the quartz vibrating element 10 therebetween. The side wall 42 surrounds the quartz vibrating element 10 in the XZ′-plane direction, with a gap therebetween. The flange 43 has a frame shape in a plan view and is located closest to the base member 30 on the lid member 40. The lid member 40 is preferably made of a conductive material, more preferably a highly airtight metal material. By using a conductive material for the lid member 40, an electromagnetic shielding function that reduces the amount of electromagnetic waves entering and leaving the internal space 39 can be imparted to the lid member 40. In order to suppress the occurrence of thermal stress, it is desirable that the material of the lid member 40 has a thermal expansion coefficient close to that of the base member 30, such as an Fe-Ni-Co alloy, whose thermal expansion coefficient at room temperature matches that of glass or ceramic over a wide temperature range. The lid member 40 is electrically connected to at least one of the external electrodes 35c, 35d by a grounding member (not shown).

[0044] The joint 50 joins the base member 30 and the lid member 40 and seals the internal space 39. The joint 50 is provided in a frame shape around the entire periphery of the flange portion 43 of the base member 30 and is sandwiched between the lower surface of the flange portion 43 of the lid member 40 and the upper surface 31A of the base member 30. The joint 50 is made of an insulating material. The joint 50 is formed using an organic adhesive containing, for example, an epoxy-based, vinyl-based, acrylic-based, urethane-based, or silicone-based resin. The material of the joint 50 is not limited to organic adhesives, and may be inorganic adhesives such as silicon-based adhesives containing water glass or calcium-based adhesives containing cement. The material of the joint 50 may also be low-melting-point glass (e.g., lead borate-based or tin phosphate-based).

[0045] Next, the configuration of the quartz vibrating element 10 according to the first embodiment will be described with reference to FIGS. 3 and 4. FIG. 3 is a plan view of the quartz vibrating element according to the first embodiment. FIG. 4 is a cross-sectional view of the quartz vibrating element according to the first embodiment. FIG. 4 is a cross-sectional view of the quartz vibrating element shown in FIG. 3, taken along line IV-IV. In FIG. 3, line IV-IV extends from the negative X-axis side of the quartz vibrating element 10 across the second low acoustic velocity region 18B and the high acoustic velocity region 17 in the X-axis direction, bends in the first low acoustic velocity region 18A, extends in the X-axis direction, bends again, and crosses the opening h1 and the first extraction electrode 15a in the X-axis direction to the positive X-axis side of the quartz vibrating element 10. Note that, for simplicity of explanation, the first connection electrode 16a and the second connection electrode 16b are not shown in FIGS. 3 and 4.

[0046] The quartz crystal vibrating element 10 has an excitation region 19, a high acoustic velocity region 17, and a low acoustic velocity region 18. The excitation region 19 is a region where the first excitation electrode 14a and the second excitation electrode 14b overlap, and is a region where a voltage is applied to the quartz crystal blank 11 to cause excitation. The high acoustic velocity region 17 is a region of the excitation region 19 where the acoustic velocity is higher than the average acoustic velocity throughout the excitation region 19. The low acoustic velocity region 18 is a region of the excitation region 19 where the acoustic velocity is lower than the average acoustic velocity throughout the excitation region 19. The acoustic velocity in the low acoustic velocity region 18 is lower than the acoustic velocity in the high acoustic velocity region 17. The acoustic velocity in the region where the first extraction electrode 15a and the second excitation electrode 14b overlap is lower than the acoustic velocity in the high acoustic velocity region 17 and equal to or higher than the acoustic velocity in the low acoustic velocity region 18.

[0047] 3, the planar shape of the excitation region 19 is a rectangle having a pair of sides extending along the X-axis direction and a pair of sides extending along the Z'-axis direction. The planar shape of the excitation region 19 is determined by the planar shapes of the first excitation electrode 14a, the second excitation electrode 14b, and the positional relationship between the first excitation electrode 14a and the second excitation electrode 14b.

[0048] 3, in a plan view, the high acoustic velocity region 17 is located in the center of the excitation region 19. The planar shape of the high acoustic velocity region 17 is a rectangle having a pair of sides extending along the X-axis direction and a pair of sides extending along the Z'-axis direction.

[0049] The planar shape of the high sound velocity region is not limited to the above. The planar shape of the high sound velocity region may be rectangular having sides extending in directions intersecting the Z-axis direction and the Z'-axis direction. The planar shape of the high sound velocity region may be rectangular or square. The planar shape of the high sound velocity region may be polygonal, circular, elliptical, or a combination thereof.

[0050] Furthermore, in a planar view, the high acoustic velocity region may be provided from the end of the excitation region on the positive side of the Z' axis to the end on the negative side of the Z' axis, or from the end of the excitation region on the positive side of the X axis to the end on the negative side of the X axis.

[0051] 3, in a plan view, the low acoustic velocity region 18 is located in the peripheral portion of the excitation region 19. The low acoustic velocity region 18 is provided in the shape of a rectangular frame surrounding the high acoustic velocity region 17. The low acoustic velocity region 18 has a first low acoustic velocity region 18A, a second low acoustic velocity region 18B, a third low acoustic velocity region 18C, and a fourth low acoustic velocity region 18D.

[0052] The first low acoustic velocity region 18A is adjacent to the high acoustic velocity region 17 on the positive side of the X-axis and extends along the Z'-axis direction. The second low acoustic velocity region 18B is adjacent to the high acoustic velocity region 17 on the negative side of the X-axis and extends along the Z'-axis direction. The third low acoustic velocity region 18C is adjacent to the high acoustic velocity region 17 on the positive side of the Z'-axis and extends along the X-axis direction. The fourth low acoustic velocity region 18D is adjacent to the high acoustic velocity region 17 on the negative side of the Z'-axis and extends along the X-axis direction. The end of the first low acoustic velocity region 18A on the positive side of the Z'-axis connects to the end of the third low acoustic velocity region 18C on the positive side of the X-axis, and the end of the first low acoustic velocity region 18A on the negative side of the Z'-axis connects to the end of the fourth low acoustic velocity region 18D on the positive side of the X-axis. The end of the second low sound speed region 18B on the positive side of the Z' axis is connected to the end of the third low sound speed region 18C on the negative side of the X axis, and the end of the second low sound speed region 18B on the negative side of the Z' axis is connected to the end of the fourth low sound speed region 18D on the negative side of the X axis.

[0053] In plan view, the end of first low sound speed region 18A on the positive Z'-axis direction overlaps with the end of third low sound speed region 18C on the positive X-axis direction, and the end of first low sound speed region 18A on the negative Z'-axis direction overlaps with the end of fourth low sound speed region 18D on the positive X-axis direction. The end of second low sound speed region 18B on the positive Z'-axis direction overlaps with the end of third low sound speed region 18C on the negative X-axis direction, and the end of second low sound speed region 18B on the negative Z'-axis direction overlaps with the end of fourth low sound speed region 18D on the negative X-axis direction.

[0054] The planar shape of the low acoustic velocity region is determined by the planar shapes of the excitation region and the high acoustic velocity region, and is not limited to the above. The planar shape of the low acoustic velocity region may be a polygon, a circle, an ellipse, or a frame shape that is a combination of these. The third low acoustic velocity region and the fourth low acoustic velocity region may be omitted. That is, the high acoustic velocity region, the first low acoustic velocity region, and the second low acoustic velocity region may be provided in strip shapes extending parallel to each other along the Z'-axis direction. The first low acoustic velocity region and the second low acoustic velocity region may be omitted, and the high acoustic velocity region, the third low acoustic velocity region, and the fourth low acoustic velocity region may be provided in strip shapes extending parallel to each other along the X-axis direction. The end of the first low acoustic velocity region on the positive side of the Z'-axis may be spaced apart from the third low acoustic velocity region, and the end of the first low acoustic velocity region on the negative side of the Z'-axis may be spaced apart from the fourth low acoustic velocity region. The end of the second low sound speed region on the positive side of the Z' axis may be spaced apart from the third low sound speed region, and the end of the second low sound speed region on the negative side of the Z' axis may be spaced apart from the fourth low sound speed region.

[0055] As shown in FIG. 3 , in a plan view, crystal blank 11 has outer peripheral portions 91, 92, 93, and 94. Outer peripheral portion 91 is the outer peripheral portion of one of the four outer peripheral portions of crystal blank 11 in a plan view, extending along the Z'-axis direction on the positive X-axis side. Outer peripheral portion 92 is the outer peripheral portion of one of the four outer peripheral portions of crystal blank 11 in a plan view, extending along the Z'-axis direction on the negative X-axis side. Outer peripheral portion 93 is the outer peripheral portion of one of the four outer peripheral portions of crystal blank 11 in a plan view, extending along the X-axis direction on the positive Z'-axis side. Outer peripheral portion 94 is the outer peripheral portion of one of the four outer peripheral portions of crystal blank 11 in a plan view, extending along the X-axis direction on the negative Z'-axis side.

[0056] As shown in FIG. 3 , the first excitation electrode 14a has outer peripheral portions 71, 72, 73, and 74 in a plan view. The outer peripheral portion 71 is the outer peripheral portion of one of the four outer peripheral portions of the first excitation electrode 14a in a plan view, which extends along the Z′-axis direction on the positive X-axis side. The outer peripheral portion 72 is the outer peripheral portion of one of the four outer peripheral portions of the first excitation electrode 14a in a plan view, which extends along the Z′-axis direction on the negative X-axis side. The outer peripheral portion 73 is the outer peripheral portion of one of the four outer peripheral portions of the first excitation electrode 14a in a plan view, which extends along the X-axis direction on the positive Z′-axis side. The outer peripheral portion 74 is the outer peripheral portion of one of the four outer peripheral portions of the first excitation electrode 14a in a plan view, which extends along the X-axis direction on the negative Z′-axis side. The outer peripheral portions 71, 72, 73, and 74 correspond to an example of a first outer peripheral portion.

[0057] As shown in FIG. 3 , the second excitation electrode 14b has outer peripheral portions 81, 82, 83, and 84 in a plan view. The outer peripheral portion 81 is the outer peripheral portion of one of the four outer peripheral portions of the second excitation electrode 14b in a plan view, which extends along the Z′-axis direction on the positive X-axis side. The outer peripheral portion 82 is the outer peripheral portion of one of the four outer peripheral portions of the second excitation electrode 14b in a plan view, which extends along the Z′-axis direction on the negative X-axis side. The outer peripheral portion 83 is the outer peripheral portion of one of the four outer peripheral portions of the second excitation electrode 14b in a plan view, which extends along the X-axis direction on the positive Z′-axis side. The outer peripheral portion 84 is the outer peripheral portion of one of the four outer peripheral portions of the second excitation electrode 14b in a plan view, which extends along the X-axis direction on the negative Z′-axis side. The outer peripheral portions 81, 82, 83, and 84 correspond to an example of a first outer peripheral portion.

[0058] In a plan view, the second excitation electrode 14b is smaller than the crystal blank 11, and outer peripheral portions 81, 82, 83, and 84 of the second excitation electrode 14b are located more inward than outer peripheral portions 91, 92, 93, and 94 of the crystal blank 11. The first excitation electrode 14a is smaller than the second excitation electrode 14b, and outer peripheral portions 71, 72, 73, and 74 of the first excitation electrode 14a are located more inward than outer peripheral portions 81, 82, 83, and 84 of the second excitation electrode 14b. In a plan view, the outer peripheral portions 71, 81, and 91 are arranged parallel to each other, the outer peripheral portions 72, 82, and 92 are arranged parallel to each other, the outer peripheral portions 73, 83, and 93 are arranged parallel to each other, and the outer peripheral portions 74, 84, and 94 are arranged parallel to each other.

[0059] 3, in a plan view, the dimension of crystal blank 11 along the X-axis direction is length Lq, and the dimension of crystal blank 11 along the Z'-axis direction is length Wq. The dimension of first excitation electrode 14a along the X-axis direction is length Le, and the dimension of first excitation electrode 14a along the Z'-axis direction is length We. The dimension of second excitation electrode 14b along the X-axis direction is length Le2, and the dimension of second excitation electrode 14b along the Z'-axis direction is length We2.

[0060] The length Lq is the distance along the X-axis direction between the outer peripheral portion 91 and the outer peripheral portion 92 at a predetermined position, and is specified, for example, as the distance between the outer peripheral portion 91 and the outer peripheral portion 92 in the X-axis direction. The predetermined position is, for example, on a line that passes through the center of the crystal blank 11 in a planar view and extends in the X-axis direction. The length Lq may be specified as the average or maximum value of the distance between the outer peripheral portion 91 and the outer peripheral portion 92 in the X-axis direction. The length Wq is the distance along the Z'-axis direction between the outer peripheral portion 93 and the outer peripheral portion 94 at a predetermined position, and is specified, for example, as the distance between the outer peripheral portion 93 and the outer peripheral portion 94 in the Z'-axis direction. The predetermined position is, for example, on a line that passes through the center of the crystal blank 11 in a planar view and extends in the Z'-axis direction. The length Wq may be specified as the average or maximum value of the distance between the outer peripheral portion 93 and the outer peripheral portion 94 in the Z'-axis direction.

[0061] Similarly, the length Le is the distance along the X-axis direction between the outer circumferential portion 71 and the outer circumferential portion 72 at a predetermined position (for example, on a line passing through the center of the first excitation electrode 14a and extending in the X-axis direction), and is specified as, for example, the distance between the outer circumferential portion 71 and the outer circumferential portion 72 in the X-axis direction. The length Le may be specified as the average value or maximum value of the distance between the outer circumferential portion 71 and the outer circumferential portion 72 in the X-axis direction. The length We is the distance along the Z'-axis direction between the outer circumferential portion 73 and the outer circumferential portion 74 at a predetermined position (for example, on a line passing through the center of the first excitation electrode 14a and extending in the Z'-axis direction), and is specified as, for example, the distance between the outer circumferential portion 73 and the outer circumferential portion 74 in the Z'-axis direction. The length We may be specified as the average value or maximum value of the distance between the outer circumferential portion 73 and the outer circumferential portion 74 in the Z'-axis direction. The length Le2 is the distance along the X-axis direction between the outer circumferential portion 81 and the outer circumferential portion 82 at a predetermined position (for example, on a line passing through the center of the second excitation electrode 14b and extending in the X-axis direction), and is specified as, for example, the distance between the outer circumferential portion 81 and the outer circumferential portion 82 in the X-axis direction. The length Le2 may be specified as the average value or maximum value of the distance between the outer circumferential portion 81 and the outer circumferential portion 82 in the X-axis direction. The length We2 is the distance along the Z'-axis direction between the outer circumferential portion 83 and the outer circumferential portion 84 at a predetermined position (for example, on a line passing through the center of the second excitation electrode 14b and extending in the Z'-axis direction), and is specified as, for example, the distance between the outer circumferential portion 83 and the outer circumferential portion 84 in the Z'-axis direction. The length We2 may be specified as the average value or maximum value of the distance between the outer circumferential portion 83 and the outer circumferential portion 84 in the Z'-axis direction.

[0062] Since the planar shape of the crystal piece 11 is rectangular with the longitudinal direction along the X-axis direction, the length Lq is larger than the length Wq (Wq < Lq). Since the planar shapes of the first excitation electrode 14a and the second excitation electrode 14b are also similar rectangular shapes, the length Le is larger than the length We (We < Le), and the length Le2 is larger than the length We2 (We2 < Le2). Since all of the outer peripheral portions 81, 82, 83, 84 of the second excitation electrode 14b are located inside the outer peripheral portions 91, 92, 93, 94 of the crystal piece 11, the length Lq is larger than the length Le2 (Le2 < Lq), and the length Wq is larger than the length We2 (We2 < Wq). Since all of the outer peripheral portions 71, 72, 73, 74 of the first excitation electrode 14a are located inside the outer peripheral portions 81, 82, 83, 84 of the second excitation electrode 14b, the length Le2 is larger than the length Le (Le < Le2), and the length We2 is larger than the length We (We < We2). In summary, the relationships of Le < Le2 < Lq and We < We2 < Wq hold.

[0063] As shown in FIG. 4, let the thickness of the crystal piece 11 be Tq, the thickness of the first excitation electrode 14a be Te, and the thickness of the second excitation electrode 14b be Te2.

[0064] The thickness Tq is the distance along the Y'-axis direction between the upper surface 11A and the lower surface 11B at a predetermined position, and is specified, for example, as the distance in the Y'-axis direction between the upper surface 11A and the lower surface 11B. The predetermined position is, for example, on a straight line passing through the center of the excitation region 19 and extending in the Y'-axis direction. The thickness Tq may be specified as the average value or the maximum value of the distance in the Y'-axis direction between the upper surface 11A and the lower surface​​​Similarly, the thickness Te is the distance along the Y'-axis direction between the upper surface and the lower surface of the first excitation electrode 14a at a predetermined position (for example, on a straight line passing through the center of the excitation region 19 and extending in the Y'-axis direction), and is specified as, for example, the distance in the Y'-axis direction between the upper surface and the lower surface of the first excitation electrode 14a. The thickness Te may be specified as the average value or the maximum value of the distance in the Y'-axis direction between the upper surface and the lower surface of the first excitation electrode 14a in the excitation region 19. The thickness Te2 is the distance along the Y'-axis direction between the upper surface and the lower surface of the second excitation electrode 14b at a predetermined position (for example, on a straight line passing through the center of the excitation region 19 and extending in the Y'-axis direction), and is specified as, for example, the distance in the Y'-axis direction between the upper surface and the lower surface of the second excitation electrode 14b. The thickness Te2 may be specified as the average value or the maximum value of the distance in the Y'-axis direction between the upper surface and the lower surface of the second excitation electrode 14b in the excitation region 19.

[0066] The thickness Tq and the thickness Te2 are substantially constant across the high sound velocity region 17 and the low sound velocity region 18. The thickness Te is substantially constant across the high sound velocity region 17 and the low sound velocity region 18 except for the portion where a plurality of hole portions H and opening portions h1 described later are formed.

[0067] The thickness Tq is larger than the thickness Te and the thickness Te2, and the thickness Te is equal to the thickness Te2 (Te = Te2 < Tq). Also, the thickness Tq is larger than the sum of the thickness Te and the thickness Te2 (Te + Te2 < Tq). However, the magnitude relationship between the thickness Te and the thickness Te2 is not limited to the above, and the relationship Te < Te2 may hold, or the relationship Te2 < Te may hold.

[0068] Note that the thickness of the first lead-out electrode 15a is equal to the thickness Te of the first excitation electrode 14a. That is, the first electrode has a uniform thickness Te. Also, the thickness of the second lead-out electrode 15b is equal to the thickness Te2 of the second excitation electrode 14b. That is, the second electrode has a uniform thickness Te2.

[0069] As shown in FIGS. 3 and 4, a plurality of holes H are provided in the first excitation electrode 14a in the high supersonic region 17. Therefore, the average mass of the crystal vibration element 10 in the high supersonic region 17 is smaller than the average mass of the crystal vibration element 10 in the low supersonic region 18. Due to the effect of the reduced average mass, the speed of sound in the high supersonic region 17 is higher than the speed of sound in the low supersonic region 18. By having the high supersonic region 17 and the low supersonic region 18 in the excitation region 19, the electromechanical coupling coefficient k (%) of the spurious mode can be suppressed and the electromechanical coupling coefficient k (%) of the main mode can be improved.

[0070] As shown in FIG. 4, the hole H is a through hole that penetrates the first excitation electrode 14a in the Y' axis direction. However, the hole is not limited to a through hole, and the hole may be a bottomed groove shape that opens in the Y' axis direction. Further, the hole may be provided in the second excitation electrode or may be provided in both the first excitation electrode and the second excitation electrode.

[0071] As shown in FIG. 3, the planar shape of the hole H is a square shape having a pair of sides extending along the Z' axis direction and a pair of sides extending along the X axis direction. Therefore, when the dimension of the hole H in the X axis direction is Hx and the dimension in the Z' axis direction is Hz, Hx = Hz.

[0072] Note that the planar shape of the hole is not limited to a square shape having sides extending along the X axis direction and the Z' axis direction. For example, the planar shape of the hole may be a rectangular shape where Hx < Hz or Hz < Hx, or may be a rectangular shape having sides extending along a direction intersecting the X axis direction and the Z' axis direction. The planar shape of the hole may be a polygonal shape, a circular shape, an elliptical shape, or a combination thereof.

[0073] As shown in FIG. 3, the plurality of holes H are arranged in a matrix along the X-axis direction and the Z'-axis direction. Let PHz be the arrangement period of the plurality of holes H in the Z'-axis direction, that is, the distance between the ends on the negative Z'-axis side of two adjacent holes H in the Z'-axis direction. Let PHx be the arrangement period of the holes H in the X-axis direction, that is, the distance between the ends on the negative X-axis side of two adjacent holes H in the X-axis direction. The plurality of holes H are arranged at equal intervals in each of the Z'-axis direction and the X-axis direction. That is, PHz = PHx.

[0074] Note that the arrangement period of the plurality of holes H is not limited to the above, and PHz < PHx or PHx < PHz may be satisfied. Also, the arrangement of the plurality of holes H is not limited to the above. The plurality of holes H may be arranged along a direction intersecting the Z'-axis direction and the X-axis direction. The plurality of holes H may be arranged in a staggered pattern or irregularly.

[0075] When the hole H is a through hole, in order to make the inside of the hole H in the high supersonic region 17 function as a part of the first excitation electrode 14a, when the thickness of the crystal piece 11 is Tq and the inner diameter of the hole H is Hr, it is desirable that the relationship 0 < Hr / Tq ≦ 2.0 holds. At this time, since the reduction rate of the capacitance due to the hole H can be suppressed to 1% or less, the inside of the hole H can also function sufficiently as an excitation electrode. Further, it is more desirable that the relationship 0 < Hr / Tq ≦ 1.5 holds, and it is more desirable that the relationship 0 < Hr / Tq ≦ 1.0 holds. If 0 < Hr / Tq ≦ 1.5, the reduction rate of the capacitance can be suppressed to 0.5% or less, and if 0 < Hr / Tq ≦ 1.0, the reduction rate of the capacitance can be suppressed to 0.1% or less. Note that in order to form the hole H with sufficient processing accuracy, it is desirable that 0.1 ≦ Hr / Tq, and it is more desirable that 0.5 ≦ Hr / Tq.

[0076] Note that the inner diameter Hr of the hole H is the length of one side when the shape of the hole H is square (Hr = Hx = Hz), and is the length of one side when the shape of the hole H is converted to a square while keeping the area constant when the shape of the hole H is other than square.

[0077] 3, the first extraction electrode 15a is connected to a corner formed by the outer periphery 71 and the outer periphery 73 of the first excitation electrode 14a. Moreover, the first extraction electrode 15a is connected only to the outer periphery 71 of the outer peripheries 71, 72, 73, and 74 of the first excitation electrode 14a. Therefore, a boundary B between the first excitation electrode 14a and the first extraction electrode 15a is located on an extension of the outer periphery 71. The connection portion between the first excitation electrode 14a and the first extraction electrode 15a overlaps with the second excitation electrode 14b.

[0078] The connection position of the first extraction electrode to the first excitation electrode is not limited to the above. For example, the first extraction electrode may be connected to both the outer peripheral portion 71 and the outer peripheral portion 73 at the corners of the first excitation electrode. The first extraction electrode may be connected to the center of the outer peripheral portion 71 of the first excitation electrode in the Z'-axis direction.

[0079] 3, the second extraction electrode 15b is connected to a corner formed by the outer periphery 81 and the outer periphery 84 of the second excitation electrode 14b. Moreover, the second extraction electrode 15b is connected only to the outer periphery 81 of the outer peripheries 81, 82, 83, and 84 of the second excitation electrode 14b.

[0080] The connection position of the second extraction electrode to the second excitation electrode is not limited to the above. For example, the second extraction electrode may be connected to both the outer peripheral portion 81 and the outer peripheral portion 84 at the corners of the second excitation electrode. The second extraction electrode may be connected to the center of the outer peripheral portion 81 of the second excitation electrode in the Z'-axis direction. However, from the viewpoint of suppressing the occurrence of spurious vibrations between the first extraction electrode and the second extraction electrode, it is desirable that the first extraction electrode does not overlap the second extraction electrode in a plan view, and it is even more desirable that they are as far apart as possible.

[0081] As shown in FIG. 3, an opening h1 is provided in the first electrode in a region overlapping the connection portion between the first excitation electrode 14a and the first extraction electrode 15a. That is, the multiple holes H and the opening h1 are provided in the first electrode on the same side of the quartz-crystal vibrating element 10. The opening h1 overlaps the second electrode. The opening h1 is provided on the first extraction electrode 15a side of the boundary B between the first excitation electrode 14a and the first extraction electrode 15a. The opening h1 is provided within a distance from the boundary B that is four times or less the thickness Tq of the quartz-crystal blank 11. The opening h1 is a through-hole that penetrates the first excitation electrode 14a in the Y′-axis direction. The opening h1 is provided in the shape of a slit with its longitudinal axis extending in a direction parallel to the boundary B. The planar shape of the opening h1 is rectangular with a pair of long sides extending along the Z′-axis direction and a pair of short sides extending along the X-axis direction. The opening h1 is formed in the shape of a notch that opens to the negative Z'-axis direction side of the first extracted electrode 15a.

[0082] The position of the opening is not particularly limited as long as it is in a region overlapping the connection between the first excitation electrode 14a and the first extraction electrode 15a and is substantially within a distance of four times the thickness Tq of the crystal blank 11 from the boundary B between the first excitation electrode 14a and the first extraction electrode 15a. For example, the opening may be provided on the first excitation electrode 14a side of the boundary B, or may be provided in both the first extraction electrode 15a and the first excitation electrode 14a across the boundary B. When the opening is provided in the first extraction electrode 15a, the opening may be a notch-shaped opening that opens toward the positive Z'-axis direction of the first extraction electrode 15a. The opening may be provided in the first electrode in the shape of an island surrounded by the first electrode. The opening may be provided in the second electrode, or in both the first electrode and the second electrode. The longitudinal direction of the slit-shaped opening is, for example, parallel to the boundary B, but may also be a direction that intersects with the boundary B as long as it is along the boundary B. Here, the direction along boundary B refers to a direction in which the absolute value of the angle formed with boundary B is 45° or less, and may be, for example, a direction in which the absolute value of the angle formed with boundary B is 30° or less, or may be a direction in which the absolute value of the angle formed with boundary B is 20° or less. When the longitudinal direction of the slit-shaped opening is a direction along boundary B, the angle formed by the longitudinal direction of the slit-shaped opening with boundary B is, for example, not less than −45° and not more than 45°.

[0083] The phrase "the openings are located substantially within a distance of four times the thickness Tq of the crystal blank 11 from the boundary B between the first excitation electrode 14a and the first extraction electrode 15a" means that 90% or more of the openings are located within a distance of four times the thickness Tq of the crystal blank 11 from the boundary B between the first excitation electrode 14a and the first extraction electrode 15a. It is preferable that the openings are located substantially within a distance of 3.5 times the thickness Tq of the crystal blank 11 from the boundary B, and more preferably within a distance of three times the thickness Tq of the crystal blank 11 from the boundary B. It is also preferable that all of the openings are located within a distance of four times the thickness Tq of the crystal blank 11 from the boundary B, and more preferably within a distance of 3.5 times the thickness Tq of the crystal blank 11 from the boundary B, and even more preferably within a distance of three times the thickness Tq of the crystal blank 11 from the boundary B.

[0084] The number of openings is not limited to one. For example, if the openings are slit-shaped with a longitudinal direction extending in a direction along the boundary B, multiple slit-shaped openings may be arranged side by side in a direction intersecting the boundary B. The openings may also be a row of openings, with multiple openings lined up in a direction along the boundary B. Furthermore, multiple openings may be lined up in a direction intersecting the boundary B as long as the direction is along the boundary B. In this case, the angle between the direction in which the row of openings is lined up and the boundary B is, for example, between -45° and 45°.

[0085] The longitudinal direction of the slit-shaped openings and the direction in which the row-like openings are arranged may be a direction perpendicular to the boundary B (hereinafter referred to as "the direction perpendicular to the boundary B"). Here, the direction perpendicular to the boundary B is a direction in which the absolute value of the angle formed with the boundary B is greater than 45° and less than 135°, and may be, for example, a direction in which the absolute value of the angle formed with the boundary B is greater than 60° and less than 120°, or a direction in which the absolute value of the angle formed with the boundary B is greater than 70° and less than 110°.

[0086] 3, the dimension of the opening h1 along the X-axis direction is defined as length Lh1, and the dimension of the opening h1 along the Z'-axis direction is defined as length Wh1. The dimension of the portion of the first extraction electrode 15a narrowed by the opening h1 (hereinafter referred to as the "narrow path portion") along the X-axis direction is defined as length Ls, and the dimension of the narrow path portion along the Z'-axis direction is defined as length Ws.

[0087] The length Lh1 is the distance along the X-axis direction between the long sides of the opening h1 at a predetermined position, and is specified, for example, as the distance in the X-axis direction between the long sides of the opening h1. The predetermined position is, for example, on a line that passes through the center of the opening h1 in a plan view and extends in the X-axis direction. The length Lh1 may be specified as the average or maximum value of the distance in the X-axis direction between the long sides of the opening h1. The length Wh1 is the distance along the Z'-axis direction between the short sides of the opening h1 at a predetermined position, and is specified, for example, as the distance in the Z'-axis direction between the short sides of the opening h1. The predetermined position is, for example, on a line that passes through the center of the opening h1 in a plan view and extends in the Z'-axis direction. The length Wh1 may be specified as the average or maximum value of the distance in the Z'-axis direction between the short sides of the opening h1.

[0088] The length Ls is determined in the same manner as the length Lh1. The length Ws is the distance along the Z'-axis direction between the end of the bottleneck portion on the positive side of the Z'-axis and the end of the bottleneck portion on the negative side of the Z'-axis at a predetermined position, and is determined, for example, as the distance in the Z'-axis direction between the end of the bottleneck portion on the positive side of the Z'-axis and the end of the bottleneck portion on the negative side of the Z'-axis. The predetermined position is, for example, on a line that passes through the center of the bottleneck portion in a plan view and extends in the Z'-axis direction. The length Ws may be determined as the average or minimum value of the distance in the Z'-axis direction between the end of the bottleneck portion on the positive side of the Z'-axis and the end of the bottleneck portion on the negative side of the Z'-axis. The length Ws may be calculated by subtracting the length Wh1 from the length Wc. In addition, when the opening is provided in the center of the first extraction electrode 15a in the Z'-axis direction and bottleneck sections are formed on both the positive Z'-axis side and the negative Z'-axis side of the opening, the length Ws is determined as the sum of the dimension in the Z'-axis direction of the bottleneck section on the positive Z'-axis side and the dimension in the Z'-axis direction of the bottleneck section on the negative Z'-axis side.

[0089] The length Wc is the distance along the Z'-axis direction between the end on the positive Z'-axis side and the end on the negative Z'-axis side of the first extraction electrode 15a at a predetermined position, and is specified, for example, as the distance in the Z'-axis direction between the end on the positive Z'-axis side and the end on the negative Z'-axis side of the first extraction electrode 15a. The predetermined position is, for example, a straight line that is equidistant from the second excitation electrode 14b and the first connection electrode 16a in the X-axis direction and extends in the Z'-axis direction when viewed in plan view. The length Wc may be specified as the average value or the maximum value of the distance in the Z'-axis direction between the end on the positive Z'-axis side and the end on the negative Z'-axis side of the first extraction electrode 15a. The length Wc corresponds to the length of the first extraction electrode 15a in the direction parallel to the boundary B.

[0090] The length Wh1 is greater than the length Lh1 (Lh1 < Wh1). The length Lh1 is equal to the length Ls (Lh1 = Ls). Desirably, the length Wh1 is equal to or greater than the length Ws (Ws ≦ Wh1). Desirably, the length Wh1 is 50% or more and 90% or less of the length Wc (Wc × 0.50 ≦ Wh1 ≦ Wc × 0.90). When a plurality of openings are provided along the boundary B, it is desirable that the sum of the lengths of the plurality of openings in the direction along the boundary B is 50% or more and 90% or less of the length Wc.

[0091] <000049�>It is desirable that the relationship 2 < Lh1 / Tq ≦ Wh1 / Tq holds, it is more desirable that the relationship 2.5 ≦ Lh1 / Tq ≦ Wh1 / Tq holds, it is even more desirable that the relationship 3 ≦ Lh1 / Tq ≦ Wh1 / Tq holds, it is even more desirable that the relationship 3.5 ≦ Lh1 / Tq ≦ Wh1 / Tq holds, and it is even more desirable that the relationship 4 ≦ Lh1 / Tq ≦ Wh1 / Tq holds.

[0092] Next, the simulation results based on the first embodiment will be described while referring to FIGS. 5 to 13. <00,00498> 5 to 7 are diagrams illustrating vibration distributions of the quartz crystal vibrating element according to the first embodiment. FIG. 5 illustrates the vibration distribution of the S0 mode, which is the main mode, as a result of a simulation based on the first embodiment. FIG. 6 illustrates the vibration distribution of the spurious A0 mode, in which vibrations of opposite phases are aligned in the Z'-axis direction (hereinafter referred to as the "A0Z mode"), as a result of a simulation based on the first embodiment. FIG. 7 illustrates the vibration distribution of the spurious A0 mode, in which vibrations of opposite phases are aligned in the X-axis direction (hereinafter referred to as the "A0X mode"), as a result of a simulation based on the first embodiment. In FIGS. 5 to 7, the first excitation electrode 14a and the first extraction electrode 15a are illustrated, while the second excitation electrode 14b and the second extraction electrode 15b are omitted.

[0094] The simulation conditions for the vibration distribution based on the first embodiment are as follows: Note that under these simulation conditions, the center of the first excitation electrode 14a and the center of the second excitation electrode 14b overlap in plan view. Tq=1.52μm Te = Te2 = 0.08 μm Lq=160μm Wq=120μm Le=100μm We=80μm Le2=120μm We2=100μm Wc=20μm Hx=Hz=1.5μm PHx=PHz=3μm Number of Hs = 8 x 8 Ls=5μm Ws=5μm

[0095] As shown in FIG. 5, the electromechanical coupling coefficient k of the S0 mode (hereinafter referred to as "k_S0") in the first embodiment is 7.37%, and the frequency Fr of the S0 mode (hereinafter referred to as "Fr_S0") is 985.14 MHz. As shown in FIG. 6, the electromechanical coupling coefficient k of the A0Z mode (hereinafter referred to as "k_A0Z") in the first embodiment is 0.04%, and the frequency Fr of the A0Z mode (hereinafter referred to as "Fr_A0Z") is 985.64 MHz. As shown in FIG. 7, the electromechanical coupling coefficient k of the A0X mode (hereinafter referred to as "k_A0X") in the first embodiment is 0.00%, and the frequency Fr of the A0X mode (hereinafter referred to as "Fr_A0X") is 985.67 MHz.

[0096] FIG. 8 is a plan view of a quartz crystal vibrating element according to a comparative example. FIGS. 9 to 11 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the comparative example. FIG. 9 shows the vibration distribution of the S0 mode as a simulation result based on the comparative example. FIG. 10 shows the vibration distribution of the A0Z mode as a simulation result based on the comparative example. FIG. 11 shows the vibration distribution of the A0X mode. In FIGS. 9 to 11, the first excitation electrode 14a and the first extraction electrode 15a are shown, and the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0097] 8, the quartz crystal vibrating element 100 according to the comparative example is similar to the quartz crystal vibrating element 10 according to the first embodiment except that the opening h1 is omitted. The simulation conditions based on the comparative example are the same as those based on the first embodiment except that Ls = 0 and Ws = Wc.

[0098] As shown in Fig. 9, k_S0 in the comparative example is 7.39%, and Fr_S0 is 985.13 MHz. As shown in Fig. 10, k_A0Z in the comparative example is 0.37%, and Fr_S0 is 985.61 MHz. As shown in Fig. 11, k_A0X in the comparative example is 0.12%, and Fr_S0 is 985.67 MHz.

[0099] Comparing Figure 9 and Figure 5, k_S0 is 7.39% when the opening h1 is not provided, and k_S0 is 7.37% when the opening h1 is provided, so the presence or absence of the opening h1 has little effect on k_S0. Comparing Figure 10 and Figure 6, providing the opening h1 reduces k_A0Z from 0.37% to 0.04%. Comparing Figure 11 and Figure 7, providing the opening h1 reduces k_A0X from 0.12% to 0.00%.

[0100] 10 and 11, in the comparative example, the vibration is distributed as if leaking from the excitation region to the first extracted electrode. As a result, the vibration intensity on the first extracted electrode side in the excitation region is stronger than the vibration intensity on the opposite side of the first extracted electrode, resulting in an imbalance in the vibration distribution. In contrast, in the first embodiment, as shown in FIGS. 6 to 8, there is no leakage of vibration to the first extracted electrode, and the balance of the vibration distribution within the excitation region is improved.

[0101] In the comparative example, the vibrations appear to leak from the excitation region to the first extraction electrode. This is thought to be due to the coupling of the vibrations excited between the first extraction electrode and the second excitation electrode with the vibrations excited between the first excitation electrode and the second excitation electrode. In particular, the antisymmetric A0 mode is not excited because positive and negative charges cancel each other out under ideal conditions. However, when the vibration distribution is unbalanced, as in the comparative example, the lack of cancellation is accentuated. In the first embodiment, the opening h1 suppresses the coupling of the A0 mode in the excitation region with the vibrations excited by the first extraction electrode. This improves the balance of the A0 mode vibration distribution in the excitation region, bringing the A0 mode vibration distribution closer to the ideal state. Therefore, the positive and negative charges in the A0 mode cancel each other out, suppressing the increase in k_A0Z and k_A0X caused by the first extraction electrode.

[0102] 12 and 13 are graphs showing the results of a simulation based on the first embodiment. In the graph shown in Fig. 12, the horizontal axis represents the length Ls [μm] of the narrow path portion along the X-axis direction, and the vertical axis represents the electromechanical coupling coefficient k [%]. In the graph shown in Fig. 13, the horizontal axis represents the length Ws [μm] of the narrow path portion along the Z'-axis direction, and the vertical axis represents the electromechanical coupling coefficient k [%]. The simulation conditions at this time are the same as the simulation conditions for the vibration distribution based on the first embodiment, except that Ls and Ws are variables.

[0103] The graph plots not only k_A0X and k_A0Z, but also k_A0ZX. k_A0ZX is the electromechanical coupling coefficient k of the spurious A0 mode in which vibrations of opposite phases are aligned in the Z'-axis direction and the Z-axis direction. Since k_A0ZX is small over the entire range of the horizontal axis of the graphs shown in FIGS. 12 and 13, a description of k_A0ZX will be omitted.

[0104] As shown in FIG. 12, when the length Ls is 3 μm or more, i.e., when Tq×2≦Ls, both k_A0X and k_A0Z become sufficiently small. From the viewpoint of suppressing an increase in the wiring resistance of the narrow path and suppressing a decrease in the Q value due to an increase in the resonance resistance, it is desirable that the relationship Ls≦Ws / Rs holds. Rs is the sheet resistance of the first extraction electrode. From the above, it is desirable that the relationship Tq×2≦Ls≦Ws / Rs holds. It is even more desirable that the relationship Tq×3≦Ls≦Ws / Rs holds.

[0105] As shown in Figure 13, the smaller the length Ws, the smaller both k_A0X and k_A0Z become. When the length Ws is 16 μm or less, i.e., when Ws / We≦0.20, k_A0X becomes sufficiently small. When the length Ws is 12 μm or less, i.e., when Ws / We≦0.15, both k_A0X and k_A0Z become sufficiently small. From the perspective of suppressing an increase in wiring resistance in the narrow path section, it is desirable that the relationship 0.05≦Ws / We be satisfied. From the above, it is desirable that the relationship 0.05≦Ws / We≦0.20 be satisfied, and it is even more desirable that the relationship 0.05≦Ws / We≦0.15 be satisfied. It is even more desirable that the relationship 0.075≦Ws / We be satisfied, and it is even more desirable that the relationship 0.10≦Ws / We be satisfied.

[0106] As described above, according to this embodiment, the quartz crystal vibrating element 10 includes the quartz crystal blank 11, a first electrode including the first excitation electrode 14a and the first extraction electrode 15a provided on the first main surface 11A of the quartz crystal blank 11, and a second electrode including the second excitation electrode 14b and the second extraction electrode 15b provided on the second main surface 11B of the quartz crystal blank 11. In a plan view, the quartz crystal vibrating element 10 includes a high acoustic velocity region 17 located in the center of the excitation region 19 where the first excitation electrode 14a and the second excitation electrode 14b overlap, and a low acoustic velocity region 18 located in the periphery of the excitation region 19. The first excitation electrode 14a in the high acoustic velocity region 17 has a plurality of holes H for increasing the acoustic velocity. The outer peripheries 71-74 of the first excitation electrode 14a are located inside the outer peripheries 81-84 of the second excitation electrode 14b, and the connection between the first excitation electrode 14a and the first extraction electrode 15a overlaps with the second excitation electrode 14b. An opening h1 is provided at the connection between the first excitation electrode 14a and the first extraction electrode 15a, and the opening h1 is located substantially within a distance range of four times the thickness Tq of the crystal blank 11 from the boundary B between the first excitation electrode 14a and the first extraction electrode 15a.

[0107] According to this, the coupling between the vibration excited between the first extraction electrode 15a and the second excitation electrode 14b and the vibration excited in the excitation region 19 is suppressed, and the deterioration of the balance of the vibration distribution in the excitation region 19 caused by the first extraction electrode 15a is suppressed. As a result, k_S0 increases and k_A0Z and k_A0X decrease. Therefore, the vibration characteristics can be improved.

[0108] As one aspect of this embodiment, the length Wh1 of the opening h1 in the Z'-axis direction along the boundary B is 50% or more and 90% or less of the length Wc of the first extraction electrode 15a in the Z'-axis direction along the boundary B (0.50 ≤ Wh1 / Wc ≤ 0.90).

[0109] According to this, by setting 0.50 ≤ Wh1 / Wc, the coupling between the vibration excited between the first extraction electrode 15a and the second excitation electrode 14b and the vibration excited in the excitation region 19 can be effectively suppressed. By setting Wh1 / Wc ≤ 0.90, the decrease in the Q value due to the increase in the resonance resistance caused by the increase in the wiring resistance can be suppressed.

[0110] As one aspect of this embodiment, for the thickness Tq of the crystal piece 11, the length Wh1 of the opening h1 in the Z'-axis direction along the boundary B, and the length Lh1 of the opening h1 in the X-axis direction intersecting the boundary B, the relationship 2 < Lh1 / Tq ≤ Wh1 / Tq holds.

[0111] According to this, the electric field generated in the region overlapping the opening h1 can be sufficiently suppressed. Therefore, the coupling between the vibration excited between the first extraction electrode 15a and the second excitation electrode 14b and the vibration excited in the excitation region 19 can be effectively suppressed by the opening h1.

[0112] As one aspect of this embodiment, the length Lh1 of the opening h1 in the X-axis direction intersecting the boundary B is 3 times or more the thickness Tq of the crystal piece 11 (3 ≤ Lh1 / Tq).

[0113] This makes it possible to more effectively suppress coupling between the vibration excited between the first extraction electrode 15a and the second excitation electrode 14b and the vibration excited in the excitation region 19 by the opening h1.

[0114] In one aspect of this embodiment, the difference Ws between the length Wc of the first extraction electrode 15a in the Z'-axis direction along the boundary B and the length Wh1 of the opening h1 is defined as Ws, and the relationship 0.05≦Ws / We≦0.15 holds true for the length We of the first excitation electrode 14a in the Z'-axis direction along the boundary B.

[0115] According to this, by setting Ws / We to 0.05≦Ws / We, it is possible to suppress a decrease in the Q value caused by an increase in resonance resistance due to an increase in wiring resistance. By setting Ws / We≦0.15, it is possible to effectively suppress coupling between the vibration excited between the first extraction electrode 15a and the second excitation electrode 14b and the vibration excited in the excitation region 19.

[0116] In one aspect of this embodiment, the relationship Ls≦Ws / Rs holds for the difference Ws between the length Wc of the first extraction electrode 15a in the Z'-axis direction along the boundary B and the length Wh1 of the opening h1, the length Lh1 of the opening h1 in the X-axis direction intersecting the boundary B, and the sheet resistance Rs of the first extraction electrode 15a.

[0117] This makes it possible to suppress a decrease in the Q value caused by an increase in resonance resistance due to an increase in wiring resistance.

[0118] Other embodiments will be described below. Note that the same or similar components as those in the first embodiment will be denoted by the same or similar reference numerals, and their description will be omitted as appropriate. Furthermore, similar effects and advantages resulting from similar components will not be mentioned one after another.

[0119] Second Embodiment Next, the configuration of the quartz crystal vibrating element 102 according to the second embodiment will be described with reference to Fig. 14. Fig. 14 is a plan view of the quartz crystal vibrating element according to the second embodiment.

[0120] The opening h1 is spaced apart from the boundary B. The dimension in the X-axis direction from the boundary B to the end of the opening h1 on the negative X-axis side is defined as length Lx. The length Lx is the distance from the boundary B to the opening h1 in a direction intersecting the boundary B, for example, the distance in a direction perpendicular to the boundary B. The length Lx is the distance along the X-axis direction between the boundary B and the end of the opening h1 on the negative X-axis side at a predetermined position, and is specified, for example, as the distance in the X-axis direction between the boundary B and the end of the opening h1 on the negative X-axis side. The predetermined position is, for example, on a line that passes through the center of the opening h1 in a planar view and extends in the X-axis direction. The length Lx may be specified as the average or minimum value of the distance in the X-axis direction between the boundary B and the end of the opening h1 on the negative X-axis side.

[0121] 15 to 19, the simulation results based on the second embodiment will be described. In the graphs shown in Fig. 15 to 18, the horizontal axis represents the length Lx [µm] from the boundary B to the opening h1, and the vertical axis represents the electromechanical coupling coefficient k [%]. In the graph shown in Fig. 19, the horizontal axis represents the length Ls [µm] of the narrow path portion along the X-axis direction, and the vertical axis represents the length Lx [µm] from the boundary B to the opening h1. The simulation conditions based on the second embodiment are the same as the simulation conditions for vibration distribution based on the first embodiment, except that Ls and Lx are variables.

[0122] FIG. 15 is a graph showing the relationship between the length Lx and the electromechanical coupling coefficient k when Ls=2 μm. When the relationship -5.0 μm≦Lx≦1.0 μm holds, k_A0Z becomes sufficiently small. When the relationship -3.0 μm≦Lx≦5.0 μm holds, k_A0X becomes sufficiently small. Therefore, when the relationship -3.0 μm≦Lx≦1.0 μm holds, both k_A0X and k_A0Z become sufficiently small. When Lx=-1.0 μm, both k_A0X and k_A0Z are minimum.

[0123] FIG. 16 is a graph showing the relationship between the length Lx and the electromechanical coupling coefficient k when Ls=3 μm. When the relationship -4.0 μm≦Lx≦1.0 μm holds, k_A0Z becomes sufficiently small. When the relationship -2.0 μm≦Lx≦5.0 μm holds, k_A0X becomes sufficiently small. Therefore, when the relationship -2.0 μm≦Lx≦1.0 μm holds, both k_A0X and k_A0Z become sufficiently small. When Lx=0 μm, both k_A0X and k_A0Z are minimum.

[0124] FIG. 17 is a graph showing the relationship between the length Lx and the electromechanical coupling coefficient k when Ls=4 μm. When the relationship -3.5 μm≦Lx≦1.5 μm holds, k_A0Z becomes sufficiently small. When the relationship -2.0 μm≦Lx≦5.0 μm holds, k_A0X becomes sufficiently small. Therefore, when the relationship -2.0 μm≦Lx≦1.5 μm holds, both k_A0X and k_A0Z become sufficiently small. When Lx=0 μm, both k_A0X and k_A0Z become minimum.

[0125] FIG. 17 is a graph showing the relationship between the length Lx and the electromechanical coupling coefficient k when Ls=5 μm. When the relationship -4.0 μm≦Lx≦2.5 μm holds, k_A0Z becomes sufficiently small. When the relationship -1.0 μm≦Lx≦5.0 μm holds, k_A0X becomes sufficiently small. Therefore, when the relationship -1.0 μm≦Lx≦2.5 μm holds, both k_A0X and k_A0Z become sufficiently small. When Lx=0 μm, both k_A0X and k_A0Z are minimum.

[0126] 18 is a graph plotting the upper limit, lower limit, and central value of Lx when both k_A0X and k_A0Z are sufficiently small. By fitting these plots, the conditional expression for making both k_A0X and k_A0Z sufficiently small can be found as follows: Lx=0.48×Ls-1.88±1.70

[0127] <Third embodiment> Next, the configuration of the quartz crystal vibrating element 103 according to the third embodiment will be described with reference to Fig. 20. Fig. 20 is a plan view of the quartz crystal vibrating element according to the third embodiment.

[0128] The quartz crystal vibrating element 103 has two openings h11 and h12. The openings h11 and h12 each have a rectangular slit shape in plan view. The opening h11 is provided along the boundary B. The opening h12 is provided on the positive X-axis side of the opening h11. The longitudinal direction of the opening h11 and the longitudinal direction of the opening h12 extend parallel to each other. The length Ls of the opening h11 along the X-axis direction is the same as the length Ls of the opening h12 along the X-axis direction. The opening h11 is a notch that opens on the negative Z'-axis side of the first extraction electrode 15a. The opening h12 is a notch that opens on the positive Z'-axis side of the first extraction electrode 15a. A portion of each of the openings h11 and h12 is aligned in the X-axis direction.

[0129] 21 to 23 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the third embodiment. FIG. 21 shows the vibration distribution of the S0 mode, which is the main mode, as a result of a simulation based on the third embodiment. FIG. 22 shows the vibration distribution of the A0Z mode as a result of a simulation based on the third embodiment. FIG. 23 shows the vibration distribution of the A0X mode as a result of a simulation based on the third embodiment. In FIGS. 21 to 23, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0130] As shown in Fig. 21, k_S0 in one example of the third embodiment is 7.29%, and Fr_S0 is 985.20 MHz. As shown in Fig. 22, k_A0Z in one example of the third embodiment is 0.18%, and Fr_A0Z is 985.73 MHz. As shown in Fig. 23, k_A0X in one example of the third embodiment is 0.15%, and Fr_A0X is 985.72 MHz.

[0131] Compared to the quartz crystal vibrating element 100 according to the comparative example having no openings, k_S0 increases, k_A0Z decreases, and k_A0X remains almost unchanged in the example of the third embodiment. Therefore, in the quartz crystal vibrating element 103 according to the third embodiment, the electromechanical coupling coefficient k is improved, although not as much as in the quartz crystal vibrating element 10 according to the first embodiment.

[0132] <Fourth embodiment> Next, the configuration of the quartz crystal vibrating element 104 according to the fourth embodiment will be described with reference to Fig. 24. Fig. 24 is a plan view of the quartz crystal vibrating element according to the fourth embodiment.

[0133] The quartz crystal vibrating element 104 has two openings h11 and h12. The openings h11 and h12 have the same rectangular slit-like planar shape and the same dimensions. The opening h11 is provided along the boundary B. The opening h12 is provided on the positive X-axis side of the opening h11. The longitudinal direction of the opening h11 and the longitudinal direction of the opening h12 extend parallel to each other. Both openings h11 and h12 are notch-shaped and open to the negative Z'-axis side of the first extraction electrode 15a.

[0134] 25 to 27 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the fourth embodiment. FIG. 25 shows the vibration distribution of the S0 mode, which is the main mode, as a result of a simulation based on the fourth embodiment. FIG. 26 shows the vibration distribution of the A0Z mode as a result of a simulation based on the fourth embodiment. FIG. 27 shows the vibration distribution of the A0X mode as a result of a simulation based on the fourth embodiment. In FIGS. 25 to 27, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0135] As shown in Fig. 25, k_S0 in one example of the fourth embodiment is 7.29%, and Fr_S0 is 985.21 MHz. As shown in Fig. 26, k_A0Z in one example of the fourth embodiment is 0.03%, and Fr_A0Z is 985.75 MHz. As shown in Fig. 27, k_A0X in one example of the fourth embodiment is 0.06%, and Fr_A0X is 985.72 MHz.

[0136] Compared to the quartz crystal vibrating element 100 according to the comparative example having no openings, k_S0 increases and k_A0Z and k_A0X decrease in the example of the fourth embodiment. Therefore, the electromechanical coupling coefficient k is improved in the quartz crystal vibrating element 104 according to the fourth embodiment compared to the quartz crystal vibrating element 103 according to the third embodiment. When two openings are provided, the electromechanical coupling coefficient k can be improved more effectively by providing the two openings on the same side, either the positive or negative Z'-axis side, rather than by providing the two openings alternately on both the positive and negative Z'-axis sides.

[0137] Fifth Embodiment Next, the configuration of the quartz crystal vibrating element 105 according to the fifth embodiment will be described with reference to Fig. 28. Fig. 28 is a plan view of the quartz crystal vibrating element according to the fifth embodiment.

[0138] The quartz crystal vibrating element 105 has a plurality of openings h11. Each of the openings h11 has the same planar shape, a rectangular slit shape, and the same dimensions. Each of the openings h11 is a notch that opens on the negative Z'-axis side of the first extraction electrode 15a. The openings h11 have their longitudinal direction in the Z'-axis direction along the boundary B, and are aligned in the X-axis direction that intersects with the boundary B.

[0139] The simulation results based on the fifth embodiment will be described with reference to Fig. 29. Fig. 29 is a graph showing the simulation results based on the fifth embodiment. In the graph shown in Fig. 29, the horizontal axis represents the total value Ls_total of the lengths Ls of the multiple openings h11, and the vertical axis represents the electromechanical coupling coefficient k (k_A0Z) [%] of the A0Z mode. The simulation conditions based on the fifth embodiment are the same as the simulation conditions based on the first embodiment, except that Ws = 8 µm and that Ls and the number of openings h11 are variables.

[0140] When Ls=0.5 μm to 2.0 μm, the electromechanical coupling coefficient k decreases as the total length Ls increases within the range of 0 μm to 5.0 μm. From the perspective of reducing k_A0Z, it is desirable that Ls_total be 1.5 μm≦Ls_total, more desirably 3.0 μm≦Ls_total, and even more desirably 4.5 μm≦Ls_total. In other words, it is desirable that the total length Ls, Ls_total, be equal to or greater than the thickness Tq of the crystal blank 11, more desirably at least twice Tq, and even more desirably at least three times Tq. If the total length Ls, Ls_total, is equal to or greater than twice the thickness Tq of the crystal blank 11, k_A0Z will be sufficiently small. When Ls=1.5 μm or 2.0 μm, k_A0Z shows the same trend when there are multiple openings h11 and when there is a single opening h11. However, when Ls = 0.5 μm or 1.0 μm, k_A0Z when there are multiple openings h11 is larger than k_A0Z when there is one opening h11. In other words, when there are multiple openings h11, the suppression effect of the A0 mode decreases when Ls < 1.5 μm. Therefore, when there are multiple openings h11, it is desirable that the relationship 1.5 μm ≦ Ls holds.

[0141] Sixth Embodiment Next, the configuration of the quartz crystal vibrating element 106 according to the sixth embodiment will be described with reference to Fig. 30. Fig. 30 is a plan view of the quartz crystal vibrating element according to the sixth embodiment.

[0142] The lengths along the Z'-axis direction of the first excitation electrode 14a and the second excitation electrode 14b of the quartz crystal vibrating element 106 according to the sixth embodiment are smaller than the lengths along the Z'-axis direction of the first excitation electrode 14a and the second excitation electrode 14b of the quartz crystal vibrating element 101 according to the first embodiment. In other words, the aspect ratio of the first excitation electrode 14a and the second excitation electrode 14b of the quartz crystal vibrating element 106 according to the sixth embodiment is larger than the aspect ratio of the first excitation electrode 14a and the second excitation electrode 14b of the quartz crystal vibrating element 101 according to the first embodiment.

[0143] Simulation results based on the sixth embodiment will be described with reference to Fig. 31 and Fig. 32. Fig. 31 and Fig. 32 are graphs showing simulation results based on the sixth embodiment. In the graph shown in Fig. 31, the horizontal axis represents the length Ls [μm] of the narrow path portion along the X-axis direction, and the vertical axis represents the electromechanical coupling coefficient k [%]. In the graph shown in Fig. 32, the horizontal axis represents the length Ws [μm] of the narrow path portion along the Z'-axis direction, and the vertical axis represents the electromechanical coupling coefficient k [%].

[0144] The simulation conditions for the graph shown in Fig. 31 are the same as the simulation conditions for the vibration distribution based on the first embodiment, except that We = 60 μm, Ws = 6 μm, and Ls is a variable. The simulation conditions for the graph shown in Fig. 32 are the same as the simulation conditions for the vibration distribution based on the first embodiment, except that We = 60 μm and Ws is a variable.

[0145] As shown in Fig. 31, when the length Ls is 3 µm or more, i.e., when Tq × 2 ≦ Ls, both k_A0X and k_A0Z become sufficiently small. As shown in Fig. 32, when the length Ws is 9 µm or less, i.e., when Ws / We ≦ 0.15, both k_A0X and k_A0Z become sufficiently small. That is, even if the length We of the first excitation electrode 14a and the aspect ratio of the first excitation electrode 14a are different as in the first and sixth embodiments, the conditions for the lengths Ls and Ws that result in a good electromechanical coupling coefficient k are the same.

[0146] Seventh Embodiment Next, the configuration of a quartz crystal vibrating element 107 according to the seventh embodiment will be described with reference to Fig. 33 and Fig. 34. Fig. 33 is a plan view of the quartz crystal vibrating element according to the seventh embodiment. Fig. 34 is an enlarged plan view of a connection portion in the seventh embodiment.

[0147] A row of openings h2 is provided on the first extraction electrode 15a side of the boundary B between the first excitation electrode 14a and the first extraction electrode 15a. The openings h2 are arranged at equal intervals from the end of the first extraction electrode 15a on the positive side of the Z' axis to the end on the negative side of the Z' axis. The planar shape of the openings h2 is rectangular, having a pair of sides extending along the Z' axis direction and a pair of sides extending along the X axis direction. One side of the openings h2 overlaps the boundary B.

[0148] The dimension of the opening h2 along the X-axis direction is defined as length Lh2. Length Lh2 is the length of the openings h2 along the direction in which the openings h2 are arranged, and is specified, for example, as the length of the openings h2 in a direction parallel to the direction in which the openings h2 are arranged. Length Wh2 is the dimension of the opening h2 along the Z'-axis direction. Length Wh2 is the length of the openings h2 along a direction intersecting the direction in which the openings h2 are arranged, and is specified, for example, as the length of the openings h2 in a direction perpendicular to the direction in which the openings h2 are arranged. The arrangement period of the openings h2 in the Z'-axis direction, i.e., the distance between the ends of two adjacent openings h2 in the Z'-axis direction on the negative side of the Z'-axis, is defined as Wp. The arrangement period Wp is the arrangement period of the openings h2 along the direction in which the openings h2 are arranged, and is specified, for example, as the arrangement period of the openings h2 in the direction in which the openings h2 are arranged.

[0149] Next, with reference to FIGS. 35 to 39, the results of a simulation based on the seventh embodiment will be described.

[0150] 35 to 37 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the seventh embodiment. FIG. 35 shows the vibration distribution of the S0 mode as a result of a simulation based on the seventh embodiment. FIG. 36 shows the vibration distribution of the A0Z mode as a result of a simulation based on the seventh embodiment. FIG. 37 shows the vibration distribution of the A0X mode as a result of a simulation based on the seventh embodiment. In FIGS. 35 to 37, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0151] As shown in Fig. 35, k_S0 in one example of the seventh embodiment is 7.37%, and Fr_S0 is 985.13 MHz. As shown in Fig. 36, k_A0Z in one example of the seventh embodiment is 0.03%, and Fr_A0Z is 985.62 MHz. As shown in Fig. 37, k_A0X in one example of the seventh embodiment is 0.01%, and Fr_A0X is 985.66 MHz.

[0152] 38 and 39 are graphs showing simulation results based on the seventh embodiment. In the graph shown in Fig. 38, the horizontal axis represents the length Lh2 [μm] of the openings h2 along the X-axis direction, and the vertical axis represents k_A0Z [%]. In the graph shown in Fig. 39, the horizontal axis represents the ratio Wh2 / Wp of the length Lh2 of the openings h2 along the Z'-axis direction to the array pitch Wp of the openings h2 (hereinafter referred to as the opening ratio), and the vertical axis represents k_A0Z [%].

[0153] The simulation conditions for the graph shown in Fig. 38 are the same as those for the vibration distribution based on the first embodiment, except that openings h2 are provided instead of openings h1, Wp = 3 μm, and Lh2 and Wh2 are variables. The simulation conditions for the graph shown in Fig. 39 are the same as those for the vibration distribution based on the first embodiment, except that openings h2 are provided instead of openings h1, the number of openings h2 and Wp are variables, and Lh2 = Wh2 = 1.5 μm.

[0154] As shown in FIG. 38, k_A0Z decreases as the length Lh2 decreases. When the length Lh2 is 3 μm or greater, i.e., when Tq×2≦Lh2, k_A0Z becomes sufficiently small. As shown in FIG. 39, k_A0Z decreases as the aperture ratio Wh2 / Wp increases. When the aperture ratio Wh2 / Wp is 50% or greater but 90% or less (0.50≦Wh2 / Wp≦0.90), k_A0Z becomes sufficiently small. Specifically, when 0.50≦Wh2 / Wp≦0.90, k_A0Z<0.10. To further reduce k_A0Z, it is more desirable that Wh2 / Wp be 0.60≦Wh2 / Wp. Note that, from the viewpoint of suppressing an increase in wiring resistance, it is more desirable that Wh2 / Wp≦0.90, and even more desirable that Wh2 / Wp≦0.80.

[0155] Eighth Embodiment Next, the configuration of the quartz crystal vibrating element 108 according to the eighth embodiment will be described with reference to Fig. 40. Fig. 40 is a plan view of the quartz crystal vibrating element according to the eighth embodiment.

[0156] In the quartz-crystal vibrating element 108, the row of openings h2 is provided on the first excitation electrode 14a side of the boundary B. In the X-axis direction, the dimension from the boundary B to the end of the openings h2 on the negative X-axis direction side is defined as a distance Lx.

[0157] Next, with reference to FIGS. 41 to 44, a simulation result based on the eighth embodiment will be described.

[0158] Fig. 41 is a graph showing the results of a simulation based on the eighth embodiment. In the graph shown in Fig. 41, the horizontal axis represents the distance Lx [μm] from the boundary B to the end of opening h2 on the negative X-axis side, and the vertical axis represents the electromechanical coupling coefficient k [%]. The simulation conditions for the graph shown in Fig. 41 are the same as the simulation conditions for the vibration distribution based on the first embodiment, except that opening h2 is provided instead of opening h1, Lh2 = Wh2 = 2 μm, and Lx is a variable.

[0159] The smaller Lx is, the larger the electromechanical coupling coefficient of the A0 mode is. That is, the closer the opening h2 is to the high acoustic velocity region 17, the smaller the effect of the opening h2 in suppressing the A0 mode is. When the opening h2 is provided on the first excitation electrode 14a side, it is desirable that −5 μm≦Lx≦0 μm be satisfied in order to sufficiently suppress the A0 mode.

[0160] Next, with reference to FIGS. 42 to 44, a simulation result based on the eighth embodiment will be described.

[0161] 42 to 44 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the eighth embodiment. FIG. 42 shows the vibration distribution of the S0 mode as a result of a simulation based on the eighth embodiment. FIG. 43 shows the vibration distribution of the A0Z mode as a result of a simulation based on the eighth embodiment. FIG. 44 shows the vibration distribution of the A0X mode as a result of a simulation based on the eighth embodiment. In FIGS. 42 to 44, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0162] As shown in Fig. 42, k_S0 in one example of the eighth embodiment is 7.36%, and Fr_S0 is 985.63 MHz. As shown in Fig. 43, k_A0Z in one example of the eighth embodiment is 0.02%, and Fr_A0Z is 985.63 MHz. As shown in Fig. 44, k_A0X in one example of the eighth embodiment is 0.01%, and Fr_A0X is 985.67 MHz.

[0163] The k_S0 in the example of the eighth embodiment is substantially the same as the k_S0 in the comparative example. The k_A0Z and Fr_A0X in the example of the eighth embodiment are smaller than the k_A0Z and Fr_A0X in the comparative example.

[0164] Ninth Embodiment Next, the configuration of the quartz crystal vibrating element 109 according to the ninth embodiment will be described with reference to Fig. 45. Fig. 45 is a plan view of the quartz crystal vibrating element according to the ninth embodiment.

[0165] In the quartz-crystal vibrating element 109, in addition to the row of openings h21 provided on the first excitation electrode 14a side of the boundary B, row of openings h22, h23, and h24 are further provided. The openings h21 in the quartz-crystal vibrating element 109 according to the ninth embodiment have the same configuration as the openings h2 provided in the quartz-crystal vibrating element 108 according to the eighth embodiment. The row of openings h21 is provided at a corner of the first excitation electrode 14a on the positive X-axis and positive Z'-axis sides. The row of openings h22 is provided at a corner of the first excitation electrode 14a on the negative X-axis and negative Z'-axis sides. The row of openings h23 is provided at a corner of the first excitation electrode 14a on the positive X-axis and negative Z'-axis sides. The row of openings h24 is provided at a corner of the first excitation electrode 14a on the negative X-axis and positive Z'-axis sides. The openings h22, h23, and h34 are aligned in a row in the Z'-axis direction. The openings h21 and h23 are located substantially within a distance from the outer periphery 71 that is four times the thickness Tq of the crystal blank 11. The openings h22 and h24 are located substantially within a distance from the outer periphery 72 that is four times the thickness Tq of the crystal blank 11.

[0166] The opening h21 is provided in a region of the low acoustic velocity region 18 that is closer to the first extraction electrode 15a than the high acoustic velocity region 17. The opening h22 is provided in a region of the low acoustic velocity region 18 that is on the opposite side of the high acoustic velocity region 17 from the first extraction electrode 15a. The openings h23 and h24 are provided diagonally opposite each other in the low acoustic velocity region 18, with the high acoustic velocity region 17 in between. The opening h21 corresponds to an example of a first opening, the opening h22 corresponds to an example of a second opening, the opening h23 corresponds to an example of a third opening, and the opening h24 corresponds to an example of a fourth opening.

[0167] The openings h21 and h22 are provided at positions that are point-symmetric with respect to the center of the first excitation electrode 14a. The openings h21 and h22 are provided in shapes that are point-symmetric with respect to the center of the first excitation electrode 14a. The openings h23 and h24 are provided at positions that are point-symmetric with respect to the center of the first excitation electrode 14a. The openings h23 and h24 are provided in shapes that are point-symmetric with respect to the center of the first excitation electrode 14a.

[0168] The row-shaped openings h21, h22, h23, and h24 are all provided in the first excitation electrode 14a, but are not limited to this. At least one of the row-shaped openings h21, h22, h23, and h24 may be provided in the second excitation electrode 14b.

[0169] Next, with reference to FIGS. 46 to 48, simulation results based on the ninth embodiment will be described. FIGS. 46 to 48 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the ninth embodiment. FIG. 46 shows the vibration distribution of the S0 mode as a simulation result based on the ninth embodiment. FIG. 47 shows the vibration distribution of the A0Z mode as a simulation result based on the ninth embodiment. FIG. 48 shows the vibration distribution of the A0X mode as a simulation result based on the ninth embodiment. In FIGS. 46 to 48, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0170] As shown in Fig. 46, k_S0 in one example of the ninth embodiment is 7.37%, and Fr_S0 is 985.14 MHz. As shown in Fig. 47, k_A0Z in one example of the ninth embodiment is 0.07%, and Fr_A0Z is 985.64 MHz. As shown in Fig. 48, k_A0X in one example of the ninth embodiment is 0.06%, and Fr_A0X is 985.68 MHz.

[0171] The k_S0 in the example of the ninth embodiment is substantially the same as the k_S0 in the comparative example. The k_A0Z and k_A0X in the example of the ninth embodiment are smaller than the k_A0Z and k_A0X in the comparative example.

[0172] Tenth Embodiment Next, the configuration of the quartz crystal vibrating element 110 according to the tenth embodiment will be described with reference to Fig. 49. Fig. 49 is a plan view of the quartz crystal vibrating element according to the tenth embodiment.

[0173] The multiple openings h21, h22, h23, and h24 are arranged in a matrix in the X-axis direction and the Z'-axis direction. The opening h21 is provided in a region of the low acoustic velocity region 18 that is closer to the first extraction electrode 15a than the high acoustic velocity region 17. The opening h22 is provided in a region of the low acoustic velocity region 18 that is on the opposite side of the high acoustic velocity region 17 from the first extraction electrode 15a. The openings h23 and h24 are provided diagonally opposite each other in the low acoustic velocity region 18, with the high acoustic velocity region 17 in between.

[0174] The number of openings h21 arranged in the Z'-axis direction increases toward the positive X-axis direction. The number of openings h21 arranged in the X-axis direction increases toward the positive Z'-axis direction. The openings h21 are provided in a region surrounded by the end of the first excitation electrode 14a on the positive X-axis direction side, the end of the first excitation electrode 14a on the positive Z'-axis direction side, and an arc centered on the high acoustic velocity region 17.

[0175] The number of openings h22 arranged in the Z'-axis direction increases toward the negative X-axis direction. The number of openings h22 arranged in the X-axis direction increases toward the negative Z'-axis direction. The openings h22 are provided in a region surrounded by the end of the first excitation electrode 14a on the negative X-axis direction side, the end of the first excitation electrode 14a on the negative Z'-axis direction side, and an arc centered on the high acoustic velocity region 17.

[0176] The number of openings h23 arranged in the Z'-axis direction increases toward the positive X-axis direction. The number of openings h23 arranged in the X-axis direction increases toward the negative Z'-axis direction. The openings h23 are provided in a region surrounded by the end of the first excitation electrode 14a on the positive X-axis direction side, the end of the first excitation electrode 14a on the negative Z'-axis direction side, and an arc centered on the high acoustic velocity region 17.

[0177] The number of openings h24 arranged in the Z'-axis direction increases toward the negative X-axis direction. The number of openings h24 arranged in the X-axis direction increases toward the positive Z'-axis direction. The openings h24 are provided in a region surrounded by the end of the first excitation electrode 14a on the negative X-axis direction side, the end of the first excitation electrode 14a on the positive Z'-axis direction side, and an arc centered on the high acoustic velocity region 17.

[0178] Next, with reference to FIGS. 50 to 52, simulation results based on the tenth embodiment will be described. FIGS. 50 to 52 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the tenth embodiment. FIG. 50 shows the vibration distribution of the S0 mode as a simulation result based on the tenth embodiment. FIG. 51 shows the vibration distribution of the A0Z mode as a simulation result based on the tenth embodiment. FIG. 52 shows the vibration distribution of the A0X mode as a simulation result based on the tenth embodiment. In FIGS. 50 to 52, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0179] As shown in Figure 50, k_S0 in one example of the tenth embodiment is 7.25%, and Fr_S0 is 985.20 MHz. As shown in Figure 51, k_A0Z in one example of the tenth embodiment is 0.07%, and Fr_A0Z is 985.71 MHz. As shown in Figure 52, k_A0X in one example of the tenth embodiment is 0.01%, and Fr_A0X is 985.75 MHz.

[0180] The k_S0 in the example of the tenth embodiment is substantially the same as the k_S0 in the comparative example. The k_A0Z and k_A0X in the example of the tenth embodiment are smaller than the k_A0Z and k_A0X in the comparative example.

[0181] Eleventh Embodiment Next, the configuration of the quartz crystal vibrating element 111 according to the eleventh embodiment will be described with reference to Fig. 53. Fig. 53 is a plan view of the quartz crystal vibrating element according to the eleventh embodiment.

[0182] In the quartz-crystal vibrating element 111, the matrix-shaped openings h21 are provided in a region surrounded by an end of the first excitation electrode 14a on the positive X-axis side, an end on the positive Z'-axis side, and an arc centered on the high acoustic velocity region 17. The dimension in the X-axis direction from the boundary B to the end on the negative X-axis side of the opening among the multiple openings h21 that is provided farthest from the boundary B is defined as a distance Lx.

[0183] Next, with reference to FIGS. 54 to 57, the results of a simulation based on the eleventh embodiment will be described.

[0184] Fig. 54 is a graph showing the results of a simulation based on the eleventh embodiment. In the graph shown in Fig. 54, the horizontal axis represents the distance Lx [μm] from boundary B to the end of the farthest opening on the negative X-axis side, and the vertical axis represents the electromechanical coupling coefficient k [%]. The simulation conditions for the graph shown in Fig. 54 are the same as those for the vibration distribution simulation based on the first embodiment, except that opening h21 is provided instead of opening h1, Lh2 = Wh2 = 2 μm, and Lx is a variable.

[0185] The smaller Lx is, the larger the electromechanical coupling coefficient of the A0 mode is. That is, the closer the opening h21 is to the high acoustic velocity region 17, the smaller the effect of the opening h2 in suppressing the A0 mode is. In order to suppress the A0 mode more than in the comparative example, it is desirable that -5 μm≦Lx≦0 μm.

[0186] 55 to 57 are diagrams showing vibration distributions of a quartz crystal vibrating element according to a comparative example of the eleventh embodiment. FIG. 55 shows the vibration distribution of the S0 mode as a simulation result based on the comparative example of the eleventh embodiment. FIG. 56 shows the vibration distribution of the A0Z mode as a simulation result based on the comparative example of the eleventh embodiment. FIG. 57 shows the vibration distribution of the A0X mode as a simulation result based on the comparative example of the eleventh embodiment. In FIGS. 55 to 57, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0187] As shown in Fig. 55, k_S0 in the comparative example for the 11th embodiment is 7.23%, and Fr_S0 is 985.24 MHz. As shown in Fig. 56, k_A0Z in the comparative example for the 11th embodiment is 0.41%, and Fr_A0Z is 985.41 MHz. As shown in Fig. 57, k_A0X in the comparative example for the 11th embodiment is 0.16%, and Fr_A0X is 985.73 MHz.

[0188] In the comparative example for the eleventh embodiment, k_S0 is smaller than k_S0 when no apertures are provided. In the comparative example for the eleventh embodiment, k_A0Z and k_A0X are larger than k_A0Z and k_A0X when no apertures are provided. The reason why the A0 mode is less suppressed in the comparative example for the eleventh embodiment than when no apertures are provided is because, in the comparative example for the eleventh embodiment, a maximum of six apertures h21 are arranged in the X-axis direction, and Lx is << -5 μm. When the length Wh2 of the apertures h21 along the X-axis direction is 2 μm and the distance Wp between the ends of two adjacent apertures h2 on the negative X-axis direction side is 3 μm, Lx is -18 μm in the comparative example for the eleventh embodiment, which is significantly outside the range of -5 μm ≦ Lx ≦ 0 μm. As described in FIG. 54, if the relationship -5 μm ≦ Lx ≦ 0 μm holds, the A0 mode can also be suppressed in this embodiment more than when no apertures are provided.

[0189] <Twelfth embodiment> Next, the configuration of the quartz crystal vibrating element 112 according to the twelfth embodiment will be described with reference to Fig. 58. Fig. 58 is a plan view of the quartz crystal vibrating element according to the twelfth embodiment.

[0190] The multiple openings h21, h22, h23, and h24 are arranged in an arc shape with the high acoustic velocity region 17 as the center. The multiple openings h21 are provided at corners on the positive X-axis and positive Z'-axis sides of the first excitation electrode 14a. The multiple openings h22 are provided at corners on the negative X-axis and negative Z'-axis sides of the first excitation electrode 14a. The multiple openings h23 are provided at corners on the positive X-axis and negative Z'-axis sides of the first excitation electrode 14a. The multiple openings h24 are provided at corners on the negative X-axis and positive Z'-axis sides of the first excitation electrode 14a.

[0191] The opening h21 is provided in a region of the low acoustic velocity region 18 that is closer to the first extraction electrode 15a than the high acoustic velocity region 17. The opening h22 is provided in a region of the low acoustic velocity region 18 that is on the opposite side of the high acoustic velocity region 17 from the first extraction electrode 15a. The opening h23 and the opening h24 are provided diagonally opposite each other in the low acoustic velocity region 18, with the high acoustic velocity region 17 in between.

[0192] Next, with reference to FIGS. 59 to 61, simulation results based on the twelfth embodiment will be described. FIGS. 59 to 61 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the twelfth embodiment. FIG. 59 shows the vibration distribution of the S0 mode as a simulation result based on the twelfth embodiment. FIG. 60 shows the vibration distribution of the A0Z mode as a simulation result based on the twelfth embodiment. FIG. 61 shows the vibration distribution of the A0X mode as a simulation result based on the twelfth embodiment. In FIGS. 59 to 61, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0193] As shown in Figure 59, k_S0 in one example of the twelfth embodiment is 7.17%, and Fr_S0 is 985.33 MHz. As shown in Figure 60, k_A0Z in one example of the twelfth embodiment is 0.02%, and Fr_A0Z is 985.91 MHz. As shown in Figure 61, k_A0X in one example of the twelfth embodiment is 0.07%, and Fr_A0X is 985.88 MHz.

[0194] In one example of the twelfth embodiment, k_S0 is slightly smaller than k_S0 in the comparative example. In one example of the twelfth embodiment, k_A0Z and k_A0X are smaller than k_A0Z and k_A0X in the comparative example. The reason why k_S0 is small is that, as shown in FIG. 59, the vibration distribution does not spread over the entire surface of the first excitation electrode 14a, and only the area surrounded by the multiple openings h21, h22, h23, and h24 vibrates strongly. On the other hand, the reason why k_A0Z and k_A0X are small and the A0 mode is suppressed is that, in the area surrounded by the multiple openings h21, h22, h23, and h24, vibrations of opposite phases are distributed symmetrically on either side of the high acoustic velocity region 17, and the vibrations of opposite phases are canceled out by each other.

[0195] <Thirteenth embodiment> Next, the configuration of the quartz crystal vibrating element 113 according to the thirteenth embodiment will be described with reference to Fig. 62. Fig. 62 is a plan view of the quartz crystal vibrating element according to the thirteenth embodiment.

[0196] The quartz crystal vibrating element 113 according to the thirteenth embodiment differs from the quartz crystal vibrating element 112 according to the twelfth embodiment in that the openings h22, h23, and h24 are omitted.

[0197] Next, with reference to FIGS. 63 to 65, simulation results based on the thirteenth embodiment will be described. FIGS. 63 to 65 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the thirteenth embodiment. FIG. 63 shows the vibration distribution of the S0 mode as a simulation result based on the thirteenth embodiment. FIG. 64 shows the vibration distribution of the A0Z mode as a simulation result based on the thirteenth embodiment. FIG. 65 shows the vibration distribution of the A0X mode as a simulation result based on the thirteenth embodiment. In FIGS. 63 to 65, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0198] As shown in Figure 63, k_S0 in one example of the thirteenth embodiment is 7.32%, and Fr_S0 is 985.16 MHz. As shown in Figure 64, k_A0Z in one example of the thirteenth embodiment is 0.16%, and Fr_A0Z is 985.65 MHz. As shown in Figure 65, k_A0X in one example of the thirteenth embodiment is 0.45%, and Fr_A0X is 985.71 MHz.

[0199] k_S0 in one example of the thirteenth embodiment is approximately the same as k_S0 in the comparative example. k_A0Z in one example of the thirteenth embodiment is smaller than k_A0Z in the comparative example. k_A0X in one example of the thirteenth embodiment is larger than k_A0X in the comparative example. k_A0Z is small because, as shown in FIG. 64, the positions of the multiple openings h21 are far from the position of the vibration peak of the A0Z mode and do not have much effect on the balance of the anti-phase vibrations. k_A0X is large because, as shown in FIG. 65, the positions of the multiple openings h21 are close to the position of the vibration peak of the A0Z mode and the multiple openings h21 disrupt the balance of the anti-phase vibrations.

[0200] <Fourteenth embodiment> Next, the configuration of the quartz crystal vibrating element 114 according to the fourteenth embodiment will be described with reference to Fig. 66. Fig. 66 is a plan view of the quartz crystal vibrating element according to the fourteenth embodiment.

[0201] The multiple openings h21, h22, h23, and h24 are aligned in a line in a direction intersecting the Z'-axis direction. The line-shaped openings h21 are spaced further away from the end of the first excitation electrode 14a on the positive X-axis direction side as they move toward the positive Z'-axis direction. The line-shaped openings h21 are spaced further away from the end of the first excitation electrode 14a on the negative X-axis direction side as they move toward the negative Z'-axis direction. The line-shaped openings h23 are spaced further away from the end of the first excitation electrode 14a on the positive X-axis direction side as they move toward the negative Z'-axis direction. The line-shaped openings h24 are spaced further away from the end of the first excitation electrode 14a on the negative X-axis direction side as they move toward the positive Z'-axis direction. The angle formed by the line-shaped openings h21, h22, h23, and h24 and the Z'-axis direction is, for example, 30°.

[0202] <Fifteenth embodiment> Next, the configuration of the quartz crystal vibrating element 115 according to the fifteenth embodiment will be described with reference to Fig. 67. Fig. 67 is a plan view of the quartz crystal vibrating element according to the fifteenth embodiment.

[0203] Each of the openings h21, h22, h23, and h24 is a slit-shaped opening that extends in a straight line, and has a longitudinal direction intersecting the Z'-axis direction. The slit-shaped opening h21 becomes increasingly distant from the end of the first excitation electrode 14a on the positive X-axis direction side as it moves toward the positive Z'-axis direction. The slit-shaped opening h21 becomes increasingly distant from the end of the first excitation electrode 14a on the negative X-axis direction side as it moves toward the negative Z'-axis direction. The slit-shaped opening h23 becomes increasingly distant from the end of the first excitation electrode 14a on the positive X-axis direction side as it moves toward the negative Z'-axis direction. The slit-shaped opening h24 becomes increasingly distant from the end of the first excitation electrode 14a on the negative X-axis direction side as it moves toward the positive Z'-axis direction. The angle formed by the longitudinal direction of each of the slit-shaped openings h21, h22, h23, and h24 and the Z'-axis direction is, for example, 30°.

[0204] Next, the influence of length Ls in the fourteenth and fifteenth embodiments will be described with reference to Fig. 68. Fig. 68 is a graph showing simulation results based on the fourteenth and fifteenth embodiments. In Fig. 68, the horizontal axis represents length Ls or length Lh2, and the vertical axis represents k_A0Z. Length Ls is the dimension along the short side of the slit-shaped openings, and length Lh2 is the dimension along the direction intersecting the arrangement direction of the row-shaped openings.

[0205] The simulation conditions for the graph shown in Figure 68 are the same as the simulation conditions for the vibration distribution based on the first embodiment, except for the conditions related to the openings. The direction in which the row-shaped openings are arranged is inclined by 30° from the Z'-axis direction. The longitudinal direction of the slit-shaped openings is inclined by 30° from the Z'-axis direction. For the row-shaped openings, the arrangement period of the openings is Wp = 3 μm, the length in the direction in which the openings are arranged Wh2 = 2 μm, and the number of openings arranged in a row is 7. For the slit-shaped openings, the longitudinal length of the openings is Wh1 = 20 μm.

[0206] k_A0Z shows a similar tendency with respect to the length Ls of the slit-shaped openings and the length Lh2 of the row-shaped openings. In the fourteenth embodiment, k_A0Z decreases as the length Ls increases, and in the fifteenth embodiment, k_A0Z decreases as the length Lh2 increases. When the length Ls or the length Lh2 is 3 μm or more, i.e., when Tq×2≦Ls or Tq×2≦Lh2, k_A0Z becomes sufficiently small.

[0207] Next, with reference to FIG. 69, the influence of the angle of the opening in the fifteenth embodiment will be described. FIG. 69 is a graph showing simulation results based on the fifteenth embodiment. In FIG. 69, the horizontal axis represents length Ls, and the vertical axis represents k_A0Z. Length Ls is the dimension along the short side of the opening. k_A0Z is plotted against length Ls when the angle between the longitudinal direction of the opening and the Z'-axis direction is 0°, 20°, 40°, 60°, 80°, and 90°. This angle is the angle obtained by rotating the longitudinal direction of opening h21 clockwise, i.e., toward the negative X-axis direction, around the end of opening h21 on the negative Z'-axis side as the center of rotation. This angle is the angle obtained by rotating the longitudinal direction of opening h22 clockwise, i.e., toward the positive X-axis direction, around the end of opening h22 on the positive Z'-axis side as the center of rotation. This angle is the angle obtained by rotating the longitudinal direction of opening h23 counterclockwise, i.e., toward the negative X-axis direction, around the end of opening h23 on the positive Z'-axis side as the center of rotation. This angle is the angle obtained by rotating the longitudinal direction of opening h24 counterclockwise, i.e., toward the positive X-axis direction, around the end of opening h24 on the negative Z'-axis side as the center of rotation.

[0208] The simulation conditions for the graph shown in FIG. 69 are the same as those for the graph shown in FIG. 68, except that the angle formed by the longitudinal direction of the opening and the Z'-axis direction is used as a variable.

[0209] When the angle between the longitudinal direction of the opening and the Z'-axis direction is in the range of 0° to 90°, k_A0Z decreases as Ls increases, regardless of the angle. When the length Ls is 3 μm or more, that is, when Tq×2≦Ls, k_A0Z becomes sufficiently small. Even when the angle between the longitudinal direction of the opening and the Z'-axis direction is 90°, k_A0Z becomes small when Tq×2≦Ls. Therefore, even if the slit-shaped opening has its longitudinal direction intersecting the boundary B, it can sufficiently suppress the A0 mode.

[0210] Next, with reference to FIG. 70, the influence of the angle of the openings in the fourteenth embodiment will be described. FIG. 70 is a graph showing simulation results based on the fourteenth embodiment. In FIG. 70, the horizontal axis represents (Lh2 / Tq)×(Wh2 / Wp), and the vertical axis represents k_A0Z. k_A0Z is plotted when the angle between the direction in which the openings are arranged and the Z'-axis direction is set to 0°, 30°, 60°, and 90°. This angle is the angle obtained by rotating the direction in which the openings h21 are arranged clockwise, i.e., toward the negative X-axis direction, around the opening among the multiple openings h21 that is closest to the negative Z'-axis direction as the center of rotation. This angle is the angle obtained by rotating the direction in which the openings h22 are arranged clockwise, i.e., toward the positive X-axis direction, around the opening among the multiple openings h22 that is closest to the positive Z'-axis direction as the center of rotation. This angle is the angle obtained by rotating the arrangement of the multiple openings h23 counterclockwise, i.e., toward the negative X-axis direction, around the opening of the multiple openings h23 that is furthest in the positive Z'-axis direction as the center of rotation. This angle is the angle obtained by rotating the arrangement of the multiple openings h24 counterclockwise, i.e., toward the positive X-axis direction, around the opening of the multiple openings h24 that is furthest in the negative Z'-axis direction as the center of rotation.

[0211] The simulation conditions for the graph shown in Figure 70 are the same as those for the graph shown in Figure 68, except that the lengths Wh2 and Lh2 are variables and the angle between the direction in which the openings are arranged and the Z'-axis direction is a variable.

[0212] When the angle between the direction in which the openings are arranged and the Z'-axis direction is between 0° and 90°, k_A0Z decreases as (Lh2 / Tq) × (Wh2 / Wp) increases, regardless of the angle. When 0.6≦(Lh2 / Tq) × (Wh2 / Wp), k_A0Z becomes sufficiently small. Even when the angle between the direction in which the openings are arranged and the Z'-axis direction is 90°, k_A0Z becomes small when 0.6≦(Lh2 / Tq) × (Wh2 / Wp). Therefore, even if the row of openings is arranged in a direction that intersects with boundary B, the A0 mode can be sufficiently suppressed as long as the relationship 0.6≦(Lh2 / Tq) × (Wh2 / Wp) holds.

[0213] Next, the influence of the angle of the openings in the fourteenth embodiment will be described with reference to Fig. 71. Fig. 71 is a graph showing the results of a simulation based on the fourteenth embodiment. In Fig. 71, the horizontal axis represents (Lh2 / Tq) x (Wh2 / Wp), and the vertical axis represents k_S0. k_S0 is plotted when the angle between the direction in which the openings are arranged and the Z'-axis direction is set to 0°, 30°, 60°, and 90°.

[0214] The simulation conditions for the graph shown in FIG. 71 are the same as those for the graph shown in FIG.

[0215] When the angle between the direction in which the openings are arranged and the Z'-axis direction is in the range of 0° to 90°, k_S0 increases as (Lh2 / Tq)×(Wh2 / Wp) decreases, regardless of the angle. When (Lh2 / Tq)×(Wh2 / Wp)≦2.3, k_S0 in the fourteenth embodiment is larger than k_S0 in the comparative example. Even when the angle between the direction in which the openings are arranged and the Z'-axis direction is 90°, k_S0 increases when (Lh2 / Tq)×(Wh2 / Wp)≦2.3. Therefore, even if the row of openings is arranged in a direction intersecting with boundary B, the A0 mode can be sufficiently suppressed as long as the relationship (Lh2 / Tq)×(Wh2 / Wp)≦2.3 holds.

[0216] <Sixteenth embodiment> Next, the configuration of the quartz crystal vibrating element 116 according to the sixteenth embodiment will be described with reference to Fig. 72. Fig. 72 is a plan view of the quartz crystal vibrating element according to the sixteenth embodiment.

[0217] The area of ​​the high acoustic velocity region 17 in the quartz crystal vibrating element 116 is larger than the area of ​​the high acoustic velocity region 17 in the quartz crystal vibrating element 10. The quartz crystal vibrating element 116 has 16×12 holes H formed therein.

[0218] Next, with reference to FIGS. 73 to 75, simulation results based on the sixteenth embodiment will be described. FIGS. 73 to 75 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the sixteenth embodiment. FIG. 73 shows the vibration distribution of the S0 mode as a simulation result based on the sixteenth embodiment. FIG. 74 shows the vibration distribution of the A0Z mode as a simulation result based on the sixteenth embodiment. FIG. 75 shows the vibration distribution of the A0X mode as a simulation result based on the sixteenth embodiment. In FIGS. 73 to 75, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0219] As shown in Figure 73, k_S0 in one example of the sixteenth embodiment is 7.25%, and Fr_S0 is 986.39 MHz. As shown in Figure 74, k_A0Z in one example of the sixteenth embodiment is 0.75%, and Fr_A0Z is 986.65 MHz. As shown in Figure 75, k_A0X in one example of the sixteenth embodiment is 0.07%, and Fr_A0X is 986.88 MHz.

[0220] Although not shown, in a comparative example in which the opening h1 is omitted from the 16th embodiment, k_S0 is 7.09%, Fr_S0 is 986.348 MHz, k_A0Z is 1.75%, Fr_A0Z is 986.616 MHz, k_A0X is 0.63%, and Fr_A0X is 986.844 MHz.

[0221] k_S0 in one example of the sixteenth embodiment is larger than k_S0 in the comparative example. k_A0Z in one example of the sixteenth embodiment is smaller than k_A0Z in the comparative example. k_A0X in one example of the sixteenth embodiment is smaller than k_A0X in the comparative example. From the simulation results of the first embodiment and the sixteenth embodiment, even if the area ratio between the high sound velocity region 17 and the low sound velocity region 18 changes, providing the opening h1 suppresses the A0 mode and improves the vibration characteristics of the S0 mode.

[0222] <Seventeenth embodiment> Next, the configuration of the quartz crystal vibrating element 117 according to the seventeenth embodiment will be described with reference to Fig. 76. Fig. 76 is a plan view of the quartz crystal vibrating element according to the seventeenth embodiment.

[0223] An opening h1' is provided in the second excitation electrode 14b in a region overlapping with the connection portion between the first excitation electrode 14a and the first extraction electrode 15a. The planar shape, position, and dimensions of the opening h1' are similar to those of the opening h1 in the first embodiment. The opening h1' is provided in the second electrode on the opposite side to the first electrode in which the multiple holes H are provided.

[0224] Next, with reference to FIGS. 77 to 79, simulation results based on the seventeenth embodiment will be described. FIGS. 77 to 79 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the seventeenth embodiment. FIG. 77 shows the vibration distribution of the S0 mode as a simulation result based on the seventeenth embodiment. FIG. 78 shows the vibration distribution of the A0Z mode as a simulation result based on the seventeenth embodiment. FIG. 79 shows the vibration distribution of the A0X mode as a simulation result based on the seventeenth embodiment. In FIGS. 77 to 79, the first excitation electrode 14a and the first extraction electrode 15a are shown, and the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0225] As shown in Figure 77, k_S0 in one example of the seventeenth embodiment is 7.37%, and Fr_S0 is 985.14 MHz. As shown in Figure 78, k_A0Z in one example of the seventeenth embodiment is 0.03%, and Fr_A0Z is 985.63 MHz. As shown in Figure 79, k_A0X in one example of the seventeenth embodiment is 0.03%, and Fr_A0X is 985.67 MHz.

[0226] k_S0 in an example of the seventeenth embodiment is substantially the same as k_S0 in an example of the first embodiment. k_A0Z in an example of the seventeenth embodiment is substantially the same as k_A0Z in an example of the first embodiment. k_A0X in an example of the seventeenth embodiment is substantially the same as k_A0X in an example of the first embodiment. In other words, whether the opening is provided in the first electrode or the second electrode, the same effect can be obtained.

[0227] <Eighteenth embodiment> Next, the configuration of a quartz crystal vibrating element 118 according to the eighteenth embodiment will be described with reference to Fig. 80. Fig. 80 is a plan view of the quartz crystal vibrating element according to the eighteenth embodiment.

[0228] In a region overlapping with the connection portion between the first excitation electrode 14a and the first extraction electrode 15a, an opening h1 is provided in the first excitation electrode 14a, and an opening h1' is provided in the second excitation electrode 14b. The planar shape, position, and dimensions of the opening h1 are substantially the same as those of the opening h1'.

[0229] Next, with reference to FIGS. 81 to 83, simulation results based on the 18th embodiment will be described. FIGS. 81 to 83 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the 18th embodiment. FIG. 81 shows the vibration distribution of the S0 mode as a simulation result based on the 18th embodiment. FIG. 82 shows the vibration distribution of the A0Z mode as a simulation result based on the 18th embodiment. FIG. 83 shows the vibration distribution of the A0X mode as a simulation result based on the 18th embodiment. In FIGS. 81 to 83, the first excitation electrode 14a and the first extraction electrode 15a are shown, but the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0230] As shown in Figure 81, k_S0 in one example of the eighteenth embodiment is 7.36%, and Fr_S0 is 985.14 MHz. As shown in Figure 82, k_A0Z in one example of the eighteenth embodiment is 0.14%, and Fr_A0Z is 985.64 MHz. As shown in Figure 83, k_A0X in one example of the eighteenth embodiment is 0.35%, and Fr_A0X is 985.68 MHz.

[0231] k_S0 in an example of the 18th embodiment is substantially the same as k_S0 in an example of the first embodiment. k_A0Z in an example of the 18th embodiment is substantially the same as k_A0Z in an example of the first embodiment. k_A0X in an example of the 18th embodiment is substantially the same as k_A0X in an example of the first embodiment. In other words, even if openings are provided in both the first electrode and the second electrode, the same effect as when openings are provided in one of the first electrode and the second electrode can be obtained.

[0232] <Nineteenth embodiment> Next, the configuration of the quartz crystal vibrating element 119 according to the nineteenth embodiment will be described with reference to Fig. 84. Fig. 84 is a plan view of the quartz crystal vibrating element according to the nineteenth embodiment.

[0233] In the high acoustic velocity region 17, the second excitation electrode 14b has a plurality of holes H. That is, the second excitation electrode 14b, which has a larger area than the first excitation electrode 14a or the second excitation electrode 14b, has a plurality of holes H. The opening h1 is provided in the first electrode on the opposite side to the second electrode in which the plurality of holes H are provided.

[0234] Next, with reference to FIGS. 85 to 87, simulation results based on the 19th embodiment will be described. FIGS. 85 to 87 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the 19th embodiment. FIG. 85 shows the vibration distribution of the S0 mode as a simulation result based on the 19th embodiment. FIG. 86 shows the vibration distribution of the A0Z mode as a simulation result based on the 19th embodiment. FIG. 87 shows the vibration distribution of the A0X mode as a simulation result based on the 19th embodiment. In FIGS. 85 to 87, the second excitation electrode 14b is shown, and the first excitation electrode 14a, the first extraction electrode 15a, and the second extraction electrode 15b are not shown.

[0235] As shown in Figure 85, k_S0 in one example of the 19th embodiment is 7.37%, and Fr_S0 is 985.14 MHz. As shown in Figure 86, k_A0Z in one example of the 19th embodiment is 0.10%, and Fr_A0Z is 985.64 MHz. As shown in Figure 87, k_A0X in one example of the 19th embodiment is 0.01%, and Fr_A0X is 985.67 MHz.

[0236] k_S0 in one example of the 19th embodiment is approximately the same as k_S0 in the comparative example. k_A0Z in one example of the 19th embodiment is smaller than k_A0Z in the comparative example. k_A0X in one example of the 19th embodiment is smaller than k_A0X in the comparative example. In this way, when a plurality of holes H are provided in the second excitation electrode 14b, which has a larger area, of the first excitation electrode 14a and the second excitation electrode 14b, and an opening h1 is provided in the first electrode opposite to the second electrode in which the plurality of holes H are provided, the A0 mode is suppressed and the vibration characteristics of the S0 mode are improved.

[0237] <Twentieth Embodiment> Next, the configuration of the quartz crystal vibrating element 120 according to the twentieth embodiment will be described with reference to Fig. 88. Fig. 88 is a plan view of the quartz crystal vibrating element according to the twentieth embodiment.

[0238] In the high acoustic velocity region 17, the second excitation electrode 14b has a plurality of holes H. That is, the second excitation electrode 14b, which has a larger area than the first excitation electrode 14a or the second excitation electrode 14b, has a plurality of holes H. The opening h1' is provided in the first electrode on the same side as the second electrode on which the plurality of holes H are provided.

[0239] Next, with reference to FIGS. 89 to 91, simulation results based on the twentieth embodiment will be described. FIGS. 89 to 91 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the twentieth embodiment. FIG. 89 shows the vibration distribution of the S0 mode as a simulation result based on the twentieth embodiment. FIG. 90 shows the vibration distribution of the A0Z mode as a simulation result based on the twentieth embodiment. FIG. 91 shows the vibration distribution of the A0X mode as a simulation result based on the twentieth embodiment. In FIGS. 89 to 91, the second excitation electrode 14b is shown, and the first excitation electrode 14a, the first extraction electrode 15a, and the second extraction electrode 15b are not shown.

[0240] As shown in Figure 89, k_S0 in one example of the twentieth embodiment is 7.37%, and Fr_S0 is 985.14 MHz. As shown in Figure 90, k_A0Z in one example of the twentieth embodiment is 0.12%, and Fr_A0Z is 985.64 MHz. As shown in Figure 91, k_A0X in one example of the twentieth embodiment is 0.00%, and Fr_A0X is 985.67 MHz.

[0241] k_S0 in one example of the 20th embodiment is substantially the same as k_S0 in one example of the 19th embodiment. k_A0Z in one example of the 20th embodiment is substantially the same as k_A0Z in one example of the 19th embodiment. k_A0X in one example of the 20th embodiment is substantially the same as k_A0X in one example of the 19th embodiment. In other words, whether the opening is provided in the first electrode or the second electrode, the same effect can be obtained.

[0242] <Twenty-first embodiment> Next, the configuration of the quartz crystal vibrating element 121 according to the 21st embodiment will be described with reference to Fig. 92. Fig. 92 is a plan view of the quartz crystal vibrating element according to the 21st embodiment.

[0243] A plurality of holes H are provided in the second excitation electrode 14b, which has the larger area of ​​the first excitation electrode 14a and the second excitation electrode 14b. In a region overlapping with the connection portion between the first excitation electrode 14a and the first extraction electrode 15a, an opening h1 is provided in the first excitation electrode 14a, and an opening h1' is provided in the second excitation electrode 14b. The planar shape, position, and dimensions of the opening h1 are approximately the same as the planar shape, position, and dimensions of the opening h1'.

[0244] Next, with reference to FIGS. 93 to 95, simulation results based on the 21st embodiment will be described. FIGS. 93 to 95 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the 21st embodiment. FIG. 93 shows the vibration distribution of the S0 mode as a simulation result based on the 21st embodiment. FIG. 94 shows the vibration distribution of the A0Z mode as a simulation result based on the 21st embodiment. FIG. 95 shows the vibration distribution of the A0X mode as a simulation result based on the 21st embodiment. In FIGS. 93 to 95, the second excitation electrode 14b is shown, and the first excitation electrode 14a, the first extraction electrode 15a, and the second extraction electrode 15b are not shown.

[0245] As shown in Figure 93, k_S0 in one example of the 21st embodiment is 7.36%, and Fr_S0 is 985.14 MHz. As shown in Figure 94, k_A0Z in one example of the 21st embodiment is 0.06%, and Fr_A0Z is 985.64 MHz. As shown in Figure 95, k_A0X in one example of the 21st embodiment is 0.04%, and Fr_A0X is 985.68 MHz.

[0246] k_S0 in one example of the 21st embodiment is substantially the same as k_S0 in one example of the 19th and 20th embodiments. k_A0Z in one example of the 21st embodiment is substantially the same as k_A0Z in one example of the 19th and 20th embodiments. k_A0X in one example of the 21st embodiment is substantially the same as k_A0X in one example of the 19th and 20th embodiments. In other words, even if openings are provided in both the first electrode and the second electrode, the same effect as when openings are provided in either the first electrode or the second electrode can be obtained.

[0247] <Twenty-second embodiment> Next, the configuration of a quartz crystal vibrating element 122 according to the 22nd embodiment will be described with reference to Fig. 96. Fig. 96 is a plan view of the quartz crystal vibrating element according to the 22nd embodiment.

[0248] The first extraction electrode 15a is connected to the center in the Z'-axis direction of the end of the first excitation electrode 14a on the positive X-axis direction side. An opening h11 is provided on the first excitation electrode 14a side of the boundary B, and an opening h12 is provided on the opposite side of the opening h11 with the high acoustic velocity region 17 in between. The openings h11 and h12 are slit-shaped openings with their longitudinal directions extending in the direction along the boundary B.

[0249] Next, with reference to FIGS. 97 to 99, simulation results based on the 22nd embodiment will be described. FIGS. 97 to 99 are diagrams showing vibration distributions of the quartz crystal vibrating element according to the 22nd embodiment. FIG. 97 shows the vibration distribution of the S0 mode as a simulation result based on the 22nd embodiment. FIG. 98 shows the vibration distribution of the A0Z mode as a simulation result based on the 22nd embodiment. FIG. 99 shows the vibration distribution of the A0X mode as a simulation result based on the 22nd embodiment. In FIGS. 97 to 99, the first excitation electrode 14a and the first extraction electrode 15a are shown, and the second excitation electrode 14b and the second extraction electrode 15b are not shown.

[0250] As shown in Figure 97, k_S0 in one example of the 22nd embodiment is 7.33%, and Fr_S0 is 985.21 MHz. As shown in Figure 98, k_A0Z in one example of the 22nd embodiment is 0.03%, and Fr_A0Z is 985.64 MHz. As shown in Figure 99, k_A0X in one example of the 22nd embodiment is 0.10%, and Fr_A0X is 985.81 MHz.

[0251] Although not shown, in a comparative example in which the openings h11 and h12 are omitted from the 22nd embodiment, k_S0 is 7.34%, Fr_S0 is 985.08 MHz, k_A0Z is 0.03%, Fr_A0Z is 985.63 MHz, k_A0X is 1.05%, and Fr_A0X is 985.58 MHz.

[0252] k_S0 in one example of the 22nd embodiment is approximately the same as k_S0 in the comparative example. k_A0Z in one example of the 22nd embodiment is approximately the same as k_A0Z in the comparative example. k_A0X in one example of the 22nd embodiment is smaller than k_A0X in the comparative example. In this way, even if the first extraction electrode 15a is connected to the center of the end portion of the first excitation electrode 14a rather than to the corner portion, by providing an opening h11 in the region overlapping with the connection portion between the first excitation electrode 14a and the first extraction electrode 15a, it is possible to suppress the A0 mode and improve the vibration characteristics of the S0 mode.

[0253] Some or all of the embodiments of the present invention will be described below, but the present invention is not limited to the following descriptions.

[0254] <1> a piezoelectric element having a first principal surface and a second principal surface facing each other; a first electrode including a first excitation electrode provided on the first main surface and a first extraction electrode connected to the first excitation electrode; a second excitation electrode provided on the second principal surface; A piezoelectric vibration element comprising: In plan view, a high sound velocity region located in the center of the region where the first excitation electrode and the second excitation electrode overlap, and a low sound velocity region located in the periphery of the region where the first excitation electrode and the second excitation electrode overlap, the low sound velocity region having a sound velocity lower than that of the high sound velocity region; a first outer circumferential portion of the first excitation electrode is provided inside a second outer circumferential portion of the second excitation electrode; the sound velocity in the region where the first extraction electrode and the second excitation electrode overlap is lower than the sound velocity in the high sound velocity region and is equal to or higher than the sound velocity in the low sound velocity region; At least one opening is provided in at least one of the first electrode and the second excitation electrode in a region where the first electrode and the second excitation electrode overlap each other; At least one opening is provided substantially within a range of a distance from a boundary between the first excitation electrode and the first extraction electrode that is four times or less the thickness of the piezoelectric piece. Piezoelectric vibration element.

[0255] <2> In the high sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with a plurality of holes. <1> The piezoelectric vibration element according to claim 1.

[0256] <3> In a plan view, the first excitation electrode has a rectangular shape, the first extraction electrode is connected to a corner of the first excitation electrode; <1> or <2> The piezoelectric vibration element according to claim 1.

[0257] <4> the first extraction electrode is connected to only one side of the first excitation electrode; <3> The piezoelectric vibration element according to claim 1.

[0258] <5> The at least one opening has at least one of a slit-shaped opening having a length extending in a direction along the boundary and a row-shaped opening aligned in a direction along the boundary. <1> from <4> 10. The piezoelectric vibration element according to claim 9, wherein

[0259] <6> the at least one opening has at least one of a slit-shaped opening having a longitudinal direction extending in a direction parallel to the boundary and a row-shaped opening arranged in a direction parallel to the boundary; The sum of the lengths of the at least one opening in a direction parallel to the boundary is the length of the first extraction electrode in a direction parallel to the boundary is 50% or more and 90% or less. <1> from <5> 10. The piezoelectric vibration element according to claim 9, wherein

[0260] <7> the at least one opening has a row of openings aligned in a direction parallel to the boundary; In the direction in which the row of openings is arranged, when the length of one opening is Wh2 and the period at which the openings are arranged is Wp, 0.50≦Wh2 / Wp≦0.90 The relationship between <1> from <6> 10. The piezoelectric vibration element according to claim 9, wherein

[0261] <8> The thickness of the piezoelectric strip is Tq, In a plan view, when the length of one of the at least one opening in a direction along the boundary is Wh, and the length of one of the at least one opening in a direction perpendicular to the length Wh along the boundary is Lh, 2 <Lh / Tq The relationship between <1> from <7> 10. The piezoelectric vibration element according to claim 9, wherein

[0262] <9> The at least one opening has a plurality of openings aligned in a direction intersecting the boundary. <1> from <8> 10. The piezoelectric vibration element according to claim 9, wherein

[0263] <10> The total length of the at least one opening in a direction perpendicular to the boundary is at least twice the thickness of the piezoelectric strip. <1> from <9> 10. The piezoelectric vibration element according to claim 9, wherein

[0264] <11> At least one opening is a slit-shaped opening having a longitudinal direction. <1> from <10> 10. The piezoelectric vibration element according to claim 9, wherein

[0265] <12> The at least one opening has a plurality of slit-shaped openings each having a longitudinal direction; The longitudinal directions of the plurality of slit-shaped openings extend parallel to one another. <1> from <10> 10. The piezoelectric vibration element according to claim 9, wherein

[0266] <13> When the difference between the length of the first extraction electrode in the direction parallel to the boundary and the length of at least one opening is Ws, and the length of the first excitation electrode in the direction parallel to the boundary is We, Ws / We≦0.15 The relationship between <1> from <12> 10. The piezoelectric vibration element according to claim 9, wherein

[0267] <14> At least one opening is formed in the first extraction electrode; When the difference between the length of the first extraction electrode in a direction parallel to the boundary and the length of the at least one opening is defined as Ws, the length of the at least one opening in a direction perpendicular to the boundary is defined as Ls, and the sheet resistance of a portion of the first extraction electrode aligned with the at least one opening in a direction parallel to the boundary is defined as Rs, Ls≦Ws / Rs The relationship between <1> from <13> 10. The piezoelectric vibration element according to claim 9, wherein

[0268] <15> When the distance between the boundary and the at least one opening in a direction perpendicular to the boundary is Lx, and the difference between the length of the first extraction electrode in a direction parallel to the boundary and the length of the at least one opening is Ws, Lx=0.48×Ls-1.88±1.70 The relationship between <1> from <14> 10. The piezoelectric vibration element according to claim 9, wherein

[0269] <16> the at least one opening has a plurality of openings aligned in a line; When the arrangement period of the plurality of openings is Wp, the length of each of the plurality of openings in the direction in which the plurality of openings are arranged is Wh2, the length of each of the plurality of openings in the direction perpendicular to the direction in which the plurality of openings are arranged is Lh2, and the thickness of the piezoelectric piece is Tq, 0.6≦(Lh2 / Tq)×(Wh2 / Wp)≦2.3 The relationship between <1> from <15> 10. The piezoelectric vibration element according to claim 9, wherein

[0270] <17> At least one opening and a plurality of holes are formed in the electrode on the same side of the piezoelectric piece. <2> The piezoelectric vibration element according to claim 1.

[0271] <18> a piezoelectric element having a first principal surface and a second principal surface facing each other; a first electrode including a first excitation electrode provided on the first main surface and a first extraction electrode connected to the first excitation electrode; a second excitation electrode provided on the second principal surface; A piezoelectric vibration element comprising: In plan view, a high sound velocity region located in the center of the region where the first excitation electrode and the second excitation electrode overlap, and a low sound velocity region located in the periphery of the region where the first excitation electrode and the second excitation electrode overlap, the low sound velocity region having a sound velocity lower than that of the high sound velocity region; a first outer circumferential portion of the first excitation electrode is provided inside a second outer circumferential portion of the second excitation electrode; the sound velocity in the region where the first extraction electrode and the second excitation electrode overlap is lower than the sound velocity in the high sound velocity region and is equal to or higher than the sound velocity in the low sound velocity region; at least one first opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region that is closer to the first extraction electrode than the high acoustic velocity region; At least one second opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region opposite to the first extraction electrode across the high acoustic velocity region. Piezoelectric vibration element.

[0272] <19> In the high sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with a plurality of holes. <18> The piezoelectric vibration element according to claim 1.

[0273] <20> the at least one first opening and the at least one second opening are substantially provided within a range of a distance from a first outer periphery of the first excitation electrode to four times or less the thickness of the piezoelectric piece; <18> or <19> The piezoelectric vibration element according to claim 1.

[0274] <21> In plan view, The first excitation electrode has a rectangular shape, the first excitation electrode has a first corner portion and a second corner portion diagonally positioned to each other, the first extraction electrode is connected to a first corner portion of the first excitation electrode, the at least one first opening is provided in a region overlapping with the first corner portion, At least one second opening is provided in a region overlapping with the second corner portion. <18> from <20> 10. The piezoelectric vibration element according to claim 9, wherein

[0275] <22> the first excitation electrode further has a third corner portion and a fourth corner portion diagonally positioned to each other, at least one third opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region that overlaps with the third corner portion, In a region overlapping with the fourth corner portion in the low sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with at least one fourth opening. The piezoelectric vibration element according to <21>.

[0276] <23> In a plan view, at least one first opening and at least one second opening are provided at positions that are point-symmetrical with respect to the center of the first excitation electrode. The piezoelectric vibration element according to any one of <18> to <22>.

[0277] <24> In a plan view, at least one first opening and at least one second opening are provided in a shape that is point-symmetrical with respect to the center of the first excitation electrode. The piezoelectric vibration element according to any one of <18> to <23>.

[0278] <25> At least one first opening and at least one second opening are provided on the same excitation electrode among the first excitation electrode and the second excitation electrode. The piezoelectric vibration element according to any one of <18> to <24>.

[0279] <26> In the high sound velocity region, a plurality of holes are provided in at least one of the first excitation electrode and the second excitation electrode. The plurality of holes are holes that penetrate the excitation electrode in the thickness direction. Let the thickness of the piezoelectric sheet be Tq. In a plan view, when the shape of the plurality of holes is a square shape, let the length of one side be Hr, and when the shape of the plurality of holes is other than a square shape, let the length of one side when converted into a square shape while keeping the area constant be Hr. The relationship of 0 < Hr / Tq ≦ 2.0 holds. The piezoelectric vibration element according to any one of <1> to <25>.

[0280] In this specification, a quartz crystal resonator having a quartz crystal element as a piezoelectric element has been described as an example, but the piezoelectric resonator is not limited to this. Examples of piezoelectric elements suitable for use in the piezoelectric vibrator according to this 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 the present invention is not limited to these and can be selected as appropriate.

[0281] The embodiments according to the present invention are not particularly limited and can be appropriately applied to any device that performs electromechanical energy conversion by the piezoelectric effect, such as a timing device, a sound generator, an oscillator, or a load sensor.

[0282] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibration element that can improve vibration characteristics.

[0283] The above-described embodiments are intended to facilitate understanding of the present invention and are not intended to limit the scope of the present invention. The present invention may be modified or improved without departing from its spirit, and equivalents are also encompassed within the scope of the present invention. In other words, designs resulting from appropriate design modifications made by a person skilled in the art to the embodiments and / or modifications are also encompassed within the scope of the present invention as long as they incorporate the characteristics of the present invention. For example, the elements of the embodiments and / or modifications, as well as their arrangement, materials, conditions, shape, size, etc., are not limited to those illustrated and may be modified as appropriate. Furthermore, the embodiments and modifications are merely examples, and it goes without saying that partial substitution or combination of the configurations shown in different embodiments and / or modifications is possible. These are also encompassed within the scope of the present invention as long as they incorporate the characteristics of the present invention. [Explanation of symbols]

[0284] 1...Crystal resonator 10...Crystal oscillator element 30...Base member 40...Cover member 50…Joint part 11...Crystal piece 11A…Top surface 11B…Bottom surface 14a...first excitation electrode 14b…Second excitation electrode 15a...1st extraction electrode 15b...Second extraction electrode 16a...first connection electrode 16b...Second connection electrode 17…High sound velocity region 18…Low sound velocity region 19...Excitation region 71, 72, 73, 74...Outer periphery 81, 82, 83, 84...Outer periphery B…boundary h1...opening H…Hole

Claims

1. a piezoelectric element having a first main surface and a second main surface facing each other; a first electrode including a first excitation electrode provided on the first main surface and a first extraction electrode connected to the first excitation electrode; a second excitation electrode provided on the second main surface; A piezoelectric vibration element comprising: In plan view, a high acoustic velocity region located in a central portion of an area where the first excitation electrode and the second excitation electrode overlap, and a low acoustic velocity region located in a peripheral portion of an area where the first excitation electrode and the second excitation electrode overlap, and having an acoustic velocity lower than that of the high acoustic velocity region, a first outer periphery of the first excitation electrode is provided inside a second outer periphery of the second excitation electrode, a sound velocity in a region where the first extraction electrode and the second excitation electrode overlap is lower than a sound velocity in the high sound velocity region and is equal to or higher than a sound velocity in the low sound velocity region, at least one of the first electrode and the second excitation electrode is provided with at least one opening in a region where the first electrode and the second excitation electrode overlap; the at least one opening is provided substantially within a range of a distance from a boundary between the first excitation electrode and the first extraction electrode that is four times or less the thickness of the piezoelectric piece; Piezoelectric vibration element.

2. In the high sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with a plurality of holes. The piezoelectric vibration element according to claim 1 .

3. In a plan view, the first excitation electrode has a rectangular shape, the first extraction electrode is connected to a corner portion of the first excitation electrode; The piezoelectric vibration element according to claim 1 or 2.

4. the first extraction electrode is connected to only one side of the first excitation electrode; The piezoelectric vibration element according to claim 3 .

5. the at least one opening has at least one of a slit-shaped opening having a longitudinal direction extending in a direction along the boundary and a row-shaped opening arranged in a direction along the boundary. The piezoelectric vibration element according to claim 1 .

6. the at least one opening has at least one of a slit-shaped opening having a longitudinal direction extending in a direction parallel to the boundary and a row-shaped opening arranged in a direction parallel to the boundary, The sum of the lengths of the at least one opening in a direction parallel to the boundary is the length of the first extraction electrode in a direction parallel to the boundary is 50% or more and 90% or less of the length of the first extraction electrode in a direction parallel to the boundary. The piezoelectric vibration element according to claim 1 .

7. the at least one opening has a row of openings aligned in a direction parallel to the boundary, In the direction in which the row of openings is arranged, when the length of one opening is Wh2 and the period at which the openings are arranged is Wp, 0.50≦Wh2 / Wp≦0.90 The relationship between The piezoelectric vibration element according to claim 1 .

8. The thickness of the piezoelectric piece is Tq, In a plan view, when a length of one of the at least one openings in a direction along the boundary is defined as Wh, and a length of one of the at least one openings in a direction perpendicular to the length Wh along the boundary is defined as Lh, 2<Lh / Tq The relationship between The piezoelectric vibration element according to claim 1 .

9. The at least one opening has a plurality of openings aligned in a direction intersecting the boundary. The piezoelectric vibration element according to claim 1 .

10. a total length of the at least one opening in a direction perpendicular to the boundary is equal to or greater than twice the thickness of the piezoelectric piece; The piezoelectric vibration element according to claim 1 .

11. The at least one opening is a slit-shaped opening having a longitudinal direction. The piezoelectric vibration element according to claim 1 .

12. the at least one opening has a plurality of slit-shaped openings each having a longitudinal direction; The longitudinal directions of the plurality of slit-shaped openings extend parallel to one another. The piezoelectric vibration element according to claim 1 .

13. When a difference between the length of the first extraction electrode in a direction parallel to the boundary and the length of the at least one opening is defined as Ws and a length of the first excitation electrode in a direction parallel to the boundary is defined as We, Ws / We≦0.15 The relationship between The piezoelectric vibration element according to claim 1 .

14. the at least one opening is formed in the first extraction electrode; When a difference between the length of the first extraction electrode in a direction parallel to the boundary and the length of the at least one opening is defined as Ws, a length of the at least one opening in a direction perpendicular to the boundary is defined as Ls, and a sheet resistance of a portion of the first extraction electrode aligned with the at least one opening in the direction parallel to the boundary is defined as Rs, Ls≦Ws / Rs The relationship between The piezoelectric vibration element according to claim 1 .

15. When a distance between the boundary and the at least one opening in a direction perpendicular to the boundary is defined as Lx, and a difference between a length of the first extraction electrode and a length of the at least one opening in a direction parallel to the boundary is defined as Ws, Lx=0.48×Ls-1.88±1.70 The relationship between The piezoelectric vibration element according to claim 1 .

16. the at least one opening comprises a plurality of openings arranged in a line; When the arrangement period of the plurality of openings is Wp, the length of each of the plurality of openings in the direction in which the plurality of openings are arranged is Wh2, the length of each of the plurality of openings in the direction perpendicular to the direction in which the plurality of openings are arranged is Lh2, and the thickness of the piezoelectric piece is Tq, 0.6≦(Lh2 / Tq)×(Wh2 / Wp)≦2.3 The relationship between The piezoelectric vibration element according to any one of claims 1 to 15.

17. the at least one opening and the plurality of holes are formed in the electrodes on the same side with respect to the piezoelectric piece; The piezoelectric vibration element according to claim 2 .

18. a piezoelectric element having a first main surface and a second main surface facing each other; a first electrode including a first excitation electrode provided on the first main surface and a first extraction electrode connected to the first excitation electrode; a second excitation electrode provided on the second main surface; A piezoelectric vibration element comprising: In plan view, a high acoustic velocity region located in a central portion of an area where the first excitation electrode and the second excitation electrode overlap, and a low acoustic velocity region located in a peripheral portion of an area where the first excitation electrode and the second excitation electrode overlap, and having an acoustic velocity lower than that of the high acoustic velocity region, a first outer periphery of the first excitation electrode is provided inside a second outer periphery of the second excitation electrode, a sound velocity in a region where the first extraction electrode and the second excitation electrode overlap is lower than a sound velocity in the high sound velocity region and is equal to or higher than a sound velocity in the low sound velocity region, at least one first opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region that is closer to the first extraction electrode than the high acoustic velocity region; At least one second opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region opposite to the first extraction electrode across the high acoustic velocity region. Piezoelectric vibration element.

19. In the high sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with a plurality of holes. The piezoelectric vibration element according to claim 18.

20. the at least one first opening and the at least one second opening are substantially provided within a range of a distance from the first outer periphery of the first excitation electrode that is four times or less the thickness of the piezoelectric piece; 20. The piezoelectric vibration element according to claim 18 or 19.

21. In plan view, The first excitation electrode has a rectangular shape, the first excitation electrode has a first corner portion and a second corner portion diagonally positioned to each other, the first extraction electrode is connected to the first corner portion of the first excitation electrode, the at least one first opening is provided in a region overlapping with the first corner portion, The at least one second opening is provided in a region overlapping with the second corner portion. The piezoelectric vibration element according to any one of claims 18 to 20.

22. the first excitation electrode further has a third corner portion and a fourth corner portion diagonally positioned to each other, at least one third opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region that overlaps with the third corner portion, At least one fourth opening is provided in at least one of the first excitation electrode and the second excitation electrode in a region of the low acoustic velocity region that overlaps with the fourth corner portion. The piezoelectric vibration element according to claim 21.

23. In a plan view, the at least one first opening and the at least one second opening are provided at positions that are point-symmetric with respect to a center of the first excitation electrode. The piezoelectric vibration element according to any one of claims 18 to 22.

24. In a plan view, the at least one first opening and the at least one second opening are provided in a shape that is point-symmetric with respect to a center of the first excitation electrode. The piezoelectric vibration element according to any one of claims 18 to 23.

25. the at least one first opening and the at least one second opening are provided in the same excitation electrode of the first excitation electrode and the second excitation electrode; The piezoelectric vibration element according to any one of claims 18 to 24.

26. In the high sound velocity region, at least one of the first excitation electrode and the second excitation electrode is provided with a plurality of holes, the plurality of holes are holes penetrating the first excitation electrode or the second excitation electrode in a thickness direction, The thickness of the piezoelectric piece is Tq, In a plan view, when the shape of the plurality of holes is a square, the length of one side thereof is defined as Hr. When the shape of the plurality of holes is other than a square, the length of one side thereof when converted into a square shape while keeping the area constant is defined as Hr. The relationship 0<Hr / Tq≦2.0 holds true. The piezoelectric vibration element according to claim 1 .

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