Piezoelectric vibration element

Abstract

This piezoelectric vibration element comprises: a piezoelectric piece that has a first main surface and a second main surface; a first electrode that includes a first excitation electrode provided on the first main surface and a first lead-out electrode connected to a first outer peripheral portion of the first excitation electrode; and a second excitation electrode that is provided on the second main surface. When the piezoelectric vibration element is viewed in a plan view, a high acoustic velocity region and a low acoustic velocity region are provided, the high acoustic velocity region being positioned at a central portion of a region in which the first excitation electrode and the second excitation electrode overlap each other, the low acoustic velocity region being positioned at a peripheral portion of said region, and the first outer peripheral portion of the first excitation electrode is provided inward of a second outer peripheral portion of the second excitation electrode. The acoustic velocity in a region in which the first lead-out 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. In a region in which the first electrode and the second excitation electrode overlap each other, at least one of the first electrode or the second excitation electrode is provided with at least one opening portion, and the at least one opening portion is provided at a distance from the boundary between the first excitation electrode and the first lead-out electrode, said distance being four times the thickness of the piezoelectric piece or less.

Description

Piezoelectric vibration element

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

[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%.

[0004] JP 2014-158149 A

[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.

[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 not more than four times the thickness of the piezoelectric piece.

[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 low 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 speed in the region where the first extraction electrode and the second excitation electrode overlap is smaller than the sound speed in the high sound speed region and equal to or greater than the sound speed in the low sound speed 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 speed region that is on the first extraction electrode side relative to the high sound speed 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 speed region that is on the opposite side of the high sound speed region from the first extraction electrode.

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

[0010] FIG. 1 is an exploded perspective view of a quartz crystal vibrator according to a first embodiment. FIG. 2 is a cross-section of the quartz crystal vibrator according to the first embodiment. FIG. 3 is a plan view of the quartz crystal vibrating element according to the first embodiment. FIG. 4 is a cross-sectional view of the quartz crystal vibrating element according to the first embodiment. FIG. 5 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the first embodiment. FIG. 6 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the first embodiment. FIG. 7 is a plan view of a quartz crystal vibrating element according to a comparative example. FIG. 8 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the comparative example. FIG. 9 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the comparative example. FIG. 10 is a graph illustrating a simulation result based on the first embodiment. FIG. 11 is a graph illustrating a simulation result based on the first embodiment. FIG. 12 is a plan view of a quartz crystal vibrating element according to a second embodiment. FIG. 13 is a graph illustrating a simulation result based on the second embodiment. FIG. 14 is a graph illustrating a simulation result based on the second embodiment. FIG. 15 is a graph illustrating a simulation result based on the second embodiment. FIG. 16 is a plan view of a quartz crystal vibrating element according to a third embodiment. FIG. 17 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the third embodiment. FIG. 18 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the third embodiment. FIG. 19 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the third embodiment. FIG. 19 is a diagram illustrating a vibration distribution of the quartz crystal vibrating element according to the third embodiment. FIG. 19 is a plan view of a quartz crystal vibrating element according to a fourth embodiment. FIG. 10 is a diagram showing the vibration distribution of the quartz vibrating element according to the fourth embodiment. FIG. 11 is a diagram showing the vibration distribution of the quartz vibrating element according to the fourth embodiment. FIG. 12 is a diagram showing the vibration distribution of the quartz vibrating element according to the fourth embodiment. FIG. 13 is a plan view of the quartz vibrating element according to the fifth embodiment. FIG. 14 is a graph showing the simulation results based on the fifth embodiment. FIG. 15 is a plan view of the quartz vibrating element according to the sixth embodiment. FIG. 16 is a graph showing the simulation results based on the sixth embodiment. FIG. 17 is a graph showing the simulation results based on the sixth embodiment. FIG. 18 is a plan view of the quartz vibrating element according to the seventh embodiment. FIG. 19 is an enlarged plan view of a connection portion in the seventh embodiment. FIG. 11 is a diagram showing the vibration distribution of the quartz vibrating element according to the seventh embodiment. FIG. 12 is a diagram showing the vibration distribution of the quartz vibrating element according to the seventh embodiment.10 is a graph showing a simulation result based on the seventh embodiment. FIG. 10 is a graph showing a simulation result based on the seventh embodiment. FIG. 10 is a plan view of a quartz crystal vibrating element according to an eighth embodiment. FIG. 10 is a graph showing a simulation result based on the eighth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the eighth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the eighth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the eighth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the ninth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the ninth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the ninth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the tenth embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to the tenth embodiment. FIG. 10 is a graph showing a simulation result based on the eleventh embodiment. FIG. 10 is a graph showing a vibration distribution of the quartz crystal vibrating element according to ... FIG. 12 is a diagram showing the vibration distribution of the quartz vibrating element according to the 12th embodiment. FIG. 13 is a diagram showing the vibration distribution of the quartz vibrating element according to the 12th embodiment. FIG. 14 is a plan view of the quartz vibrating element according to the 13th embodiment. FIG. 15 is a diagram showing the vibration distribution of the quartz vibrating element according to the 13th embodiment. FIG. 16 is a diagram showing the vibration distribution of the quartz vibrating element according to the 13th embodiment. FIG. 17 is a diagram showing the vibration distribution of the quartz vibrating element according to the 13th embodiment. FIG. 18 is a plan view of the quartz vibrating element according to the 14th embodiment. FIG. 19 is a plan view of the quartz vibrating element according to the 15th embodiment. FIG. 19 is a graph showing simulation results based on the 14th and 15th embodiments. FIG. 20 is a graph showing simulation results based on the 15th embodiment. FIG. 21 is a graph showing simulation results based on the 14th embodiment. FIG. 22 is a plan view of the quartz vibrating element according to the 16th embodiment.16 is a diagram showing a vibration distribution of the quartz vibrating element according to the sixteenth embodiment. FIG. 17 is a diagram showing a vibration distribution of the quartz vibrating element according to the sixteenth embodiment. FIG. 18 is a diagram showing a vibration distribution of the quartz vibrating element according to the seventeenth embodiment. FIG. 19 is a diagram showing a vibration distribution of the quartz vibrating element according to the seventeenth embodiment. FIG. 20 is a diagram showing a vibration distribution of the quartz vibrating element according to the seventeenth embodiment. FIG. 21 is a diagram showing a vibration distribution of the quartz vibrating element according to the eighteenth embodiment. FIG. 22 is a diagram showing a vibration distribution of the quartz vibrating element according to the eighteenth embodiment. FIG. 23 is a diagram showing a vibration distribution of the quartz vibrating element according to the eighteenth embodiment. FIG. 24 is a diagram showing a vibration distribution of the quartz vibrating element according to the eighteenth embodiment. FIG. 25 is a diagram showing a vibration distribution of the quartz vibrating element according to the nineteenth embodiment. FIG. 26 is a diagram showing a vibration distribution of the quartz vibrating element according to the nineteenth embodiment. FIG. 27 is a diagram showing a vibration distribution of the quartz vibrating element according to the nineteenth embodiment. FIG. 28 is a diagram showing a vibration distribution of the quartz vibrating element according to the nineteenth embodiment. FIG. 29 is a diagram showing a vibration distribution of the quartz vibrating element according to the nineteenth embodiment. FIG. 21 is a diagram showing the vibration distribution of the quartz vibrating element according to the 21st embodiment. FIG. 22 is a diagram showing the vibration distribution of the quartz vibrating element according to the 21st embodiment. FIG. 23 is a diagram showing the vibration distribution of the quartz vibrating element according to the 21st embodiment. FIG. 24 is a plan view of the quartz vibrating element according to the 22nd embodiment. FIG. 25 is a diagram showing the vibration distribution of the quartz vibrating element according to the 22nd embodiment. FIG. 26 is a diagram showing the vibration distribution of the quartz vibrating element according to the 22nd embodiment.

[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 interrelationships between the drawings and to aid in understanding the positional relationships of the various components. 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 is referred to as the "Y'-axis direction," and the direction parallel to the Z'-axis is referred to as the "Z'-axis direction." The directions of the 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 vibrator 1 is not limited to this. The plane specified by the X-axis and Z'-axis will be referred to as the Z'X plane, and the same applies to planes specified 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 Fig. 1 and Fig. 2. Fig. 1 is an exploded perspective view of the quartz crystal resonator according to the first embodiment. Fig. 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 vibrable in a vibration space provided between a base member 30 and a lid 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 constitute a pair of excitation electrodes, a first extraction electrode 15a and a second extraction electrode 15b that constitute a pair of extraction electrodes, and a first connection electrode 16a and a second connection electrode 16b that constitute a pair of connection electrodes.

[0021] The crystal blank 11 has an upper surface 11A and a lower surface 11B that face each other. The upper surface 11A is located on the side facing the top wall portion 41 of the lid member 40. The lower surface 11B is located on the side facing the base member 30. The upper surface 11A and the lower surface 11B correspond to a pair of main surfaces of the crystal blank 11. The upper surface 11A corresponds to an example of a first main surface, and the 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 thickness is in the direction parallel to the Y' axis. 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 quartz 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 the thickness-shear vibration mode, and may be, for example, thickness-extensional vibration, diaphragm 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 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 along 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 to the first connection electrode 16a, and the second extraction electrode 15b electrically connects the second excitation electrode 14b to 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 lower 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 stacked 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 also 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 vibrating element 10 and the lid member 40, and corresponds to the mounting surface on which the quartz vibrating element 10 is mounted. From the viewpoint of suppressing thermal stress acting from the base 31 on the quartz vibrating 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 blank 11. The base 31 is made of, for example, a ceramic substrate, a glass substrate, or a quartz substrate.

[0036] The corner portions 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 corner portions of the base 31 is not limited to this. The corner portions of the base may have cutout side surfaces formed in a prismatic shape, or may be substantially right-angled corner portions without 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 to the external electrode 35a, and the lead electrode 34b electrically connects the connection electrode 33b to 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 side surfaces of the notches provided at the 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, 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, 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, 36b is, for example, a silicone resin. The conductive holding members 36a, 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-crystal 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-crystal vibrating element 10 therebetween. The side wall 42 surrounds the quartz-crystal vibrating element 10 at a distance in the XZ′-plane direction. 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, the material of the lid member 40 is preferably a material having 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 provided with an organic adhesive, 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 an inorganic adhesive, such as a silicon-based adhesive containing water glass or a calcium-based adhesive 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 according to the first embodiment, taken along line IV-IV of the quartz vibrating element shown in FIG. 3 . In FIG. 3 , line IV-IV extends from the negative X-axis side of the quartz vibrating element 10, crosses 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 omitted from 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 14 a, the second excitation electrode 14 b, and the positional relationship between the first excitation electrode 14 a and the second excitation electrode 14 b.

[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 extending 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 X-axis side 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 X-axis side 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 Z'-axis side 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 Z'-axis side and extends along the X-axis direction. The end of the first low acoustic velocity region 18A on the positive Z'-axis side is connected to the end of the third low acoustic velocity region 18C on the positive X-axis side, and the end of the first low acoustic velocity region 18A on the negative Z'-axis side is connected to the end of the fourth low acoustic velocity region 18D on the positive X-axis side. 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 a 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 arranged in a strip shape 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 arranged in a strip shape 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 velocity region on the positive side of the Z' axis may be spaced apart from the third low sound velocity region, and the end of the second low sound velocity region on the negative side of the Z' axis may be spaced apart from the fourth low sound velocity region.

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

[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 examples of first outer peripheral portions.

[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 provided 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 provided 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 provided in parallel, the outer peripheral portions 72, 82, and 92 are provided in parallel, the outer peripheral portions 73, 83, and 93 are provided in parallel, and the outer peripheral portions 74, 84, and 94 are provided in parallel.

[0059] 3, in a plan view, the dimension of the crystal blank 11 along the X-axis direction is defined as length Lq, and the dimension of the crystal blank 11 along the Z'-axis direction is defined as length Wq. The dimension of the first excitation electrode 14a along the X-axis direction is defined as length Le, and the dimension of the first excitation electrode 14a along the Z'-axis direction is defined as length We. The dimension of the second excitation electrode 14b along the X-axis direction is defined as length Le2, and the dimension of the second excitation electrode 14b along the Z'-axis direction is defined as 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 in the X-axis direction between the outer peripheral portion 91 and the outer peripheral portion 92. 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 in the X-axis direction between the outer peripheral portion 91 and the outer peripheral portion 92. 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 in the Z'-axis direction between the outer peripheral portion 93 and the outer peripheral portion 94. 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 in the Z'-axis direction between the outer peripheral portion 93 and the outer peripheral portion 94.

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

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

[0063] As shown in FIG. 4, the thickness of the crystal blank 11 is Tq, the thickness of the first excitation electrode 14a is Te, and the thickness of the second excitation electrode 14b is 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 line that passes through the center of the excitation region 19 and extends in the Y'-axis direction. The thickness Tq may be specified as the average or maximum value of the distance in the Y'-axis direction between the upper surface 11A and the lower surface 11B in the excitation region 19.

[0065] Similarly, the thickness Te is the distance along the Y'-axis direction between the upper and lower surfaces of the first excitation electrode 14a at a predetermined position (e.g., on a line passing through the center of the excitation region 19 and extending in the Y'-axis direction), and is specified, for example, as the distance between the upper and lower surfaces of the first excitation electrode 14a in the Y'-axis direction. The thickness Te may be specified as the average or maximum value of the distance between the upper and lower surfaces of the first excitation electrode 14a in the Y'-axis direction in the excitation region 19. The thickness Te2 is the distance along the Y'-axis direction between the upper and lower surfaces of the second excitation electrode 14b at a predetermined position (e.g., on a line passing through the center of the excitation region 19 and extending in the Y'-axis direction), and is specified, for example, as the distance between the upper and lower surfaces of the second excitation electrode 14b in the Y'-axis direction. The thickness Te2 may be specified as the average or maximum value of the distance between the upper and lower surfaces of the second excitation electrode 14b in the Y'-axis direction in the excitation region 19.

[0066] The thickness Tq and the thickness Te2 are substantially constant throughout the high sound velocity region 17 and the low sound velocity region 18. The thickness Te is substantially constant throughout the high sound velocity region 17 and the low sound velocity region 18, except for the portions where a plurality of holes H and an opening h1, which will be described later, are formed.

[0067] The thickness Tq is greater 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 greater 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 or the relationship Te2 < Te may also be true.

[0068] The thickness of the first extraction electrode 15a is equal to the thickness Te of the first excitation electrode 14a. That is, the first electrode has a uniform thickness Te. The thickness of the second extraction 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] 3 and 4 , the first excitation electrode 14a in the high acoustic velocity region 17 has a plurality of holes H. Therefore, the average mass of the quartz crystal vibrating element 10 in the high acoustic velocity region 17 is smaller than the average mass of the quartz crystal vibrating element 10 in the low acoustic velocity region 18. Due to the effect of the reduced average mass, the acoustic velocity in the high acoustic velocity region 17 is greater than the acoustic velocity in the low acoustic velocity region 18. By having the high acoustic velocity region 17 and the low acoustic velocity 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] 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 may be a groove-like hole with a bottom that opens in the Y'-axis direction. Furthermore, 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] 3, the planar shape of hole H is a square 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 hole H in the X-axis direction is Hx and the dimension in the Z'-axis direction is Hz, Hx = Hz.

[0072] 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 rectangle with Hx < Hz or Hz < Hx, or a rectangle with sides extending along a direction intersecting the X-axis direction and the Z'-axis direction. The planar shape of the hole may be a polygon, a circle, an ellipse, or a combination thereof.

[0073] As shown in Figure 3, the multiple holes H are arranged in a matrix along the X-axis direction and the Z'-axis direction. The arrangement period of the multiple holes H in the Z'-axis direction, i.e., the distance between the ends of two adjacent holes H in the Z'-axis direction on the negative side of the Z'-axis, is defined as PHz. The arrangement period of the holes H in the X-axis direction, i.e., the distance between the ends of two adjacent holes H in the X-axis direction on the negative side of the X-axis, is defined as PHx. The multiple holes H are arranged at equal intervals in both the Z'-axis direction and the X-axis direction. In other words, PHz = PHx.

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

[0075] When the hole H is a through hole, in order for the interior of the hole H in the high acoustic velocity region 17 to function as part of the first excitation electrode 14a, it is desirable that the relationship 0<Hr / Tq≦2.0 be satisfied, where Tq is the thickness of the crystal blank 11 and Hr is the inner diameter of the hole H. In this case, the capacitance reduction rate due to the hole H is kept to 1% or less, allowing the interior of the hole H to function sufficiently as an excitation electrode. It is even more desirable that the relationship 0<Hr / Tq≦1.5 be satisfied, and even more desirable that the relationship 0<Hr / Tq≦1.0 be satisfied. If 0<Hr / Tq≦1.5, the capacitance reduction rate can be kept to 0.5% or less, and if 0<Hr / Tq≦1.0, the capacitance reduction rate can be kept to 0.1% or less. To form the hole H with sufficient processing precision, it is desirable that the relationship 0.1≦Hr / Tq be satisfied, and even more desirable that the relationship 0.5≦Hr / Tq be satisfied.

[0076] 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 when the shape of the hole H is other than square, it is the length of one side when the hole H is converted into a square while keeping the area constant.

[0077] 3, the first extraction electrode 15a is connected to the 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, the 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 periphery 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 with 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. In other words, 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 less than four times 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 a slit shape 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 toward the negative Z'-axis direction of the first extraction electrode 15a.

[0082] The position of the opening is not particularly limited as long as it is in a region overlapping the connection portion 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 or less 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 opening 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 intersecting the boundary B as long as it is along the boundary B. Here, the direction along the boundary B refers to a direction in which the absolute value of the angle formed with the boundary B is 45° or less, and may be, for example, a direction in which the absolute value of the angle formed with the boundary B is 30° or less, or may be a direction in which the absolute value of the angle formed with the boundary B is 20° or less. When the longitudinal direction of the slit-shaped opening is a direction along the boundary B, the angle formed by the longitudinal direction of the slit-shaped opening with the boundary B is, for example, not less than −45° and not more than 45°.

[0083] "The openings are substantially located within a 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" means that 90% or more of the openings are located within a 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. It is preferable that the openings are substantially located within a range of 3.5 times the thickness Tq of the crystal blank 11 from the boundary B, and it is even more preferable that the openings are substantially located within a range 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 range of four times the thickness Tq of the crystal blank 11 from the boundary B, and it is even more preferable that all of the openings are located within a range of 3.5 times the thickness Tq of the crystal blank 11 from the boundary B, and it is even more preferable that all of the openings are located within a range 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, when the openings are slit-shaped with a longitudinal direction extending in a direction along the boundary B, a plurality of 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 a plurality of openings lined up in a direction along the boundary B. Furthermore, a plurality of openings may be arranged side by side in a direction intersecting the boundary B, as long as the direction is along the boundary B. In this case, the angle formed by the direction in which the row of openings is arranged 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-shaped 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 specified 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 specified, 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 specified 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 of the first extraction electrode 15a on the positive side of the Z'-axis and the end of the first extraction electrode 15a on the negative side of the Z'-axis at a predetermined position. For example, it is specified as the distance in the Z'-axis direction between the end of the first extraction electrode 15a on the positive side of the Z'-axis and the end of the first extraction electrode 15a on the negative side of the Z'-axis. For example, when viewed in a plan view, the predetermined position is equidistant from the second excitation electrode 14b and the first connection electrode 16a in the X-axis direction and on a straight line extending in the Z'-axis direction. The length Wc may be specified as the average or maximum value of the distance in the Z'-axis direction between the end of the first extraction electrode 15a on the positive side of the Z'-axis and the end of the first extraction electrode 15a on the negative side of the Z'-axis. The length Wc corresponds to the length of the first extraction electrode 15a in a 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). Preferably, the length Wh1 is equal to or greater than the length Ws (Ws≦Wh1). Preferably, the length Wh1 is 50% to 90% of the length Wc (Wc×0.50≦Wh1≦Wc×0.90). When multiple openings are provided along the boundary B, it is desirable that the total length of the multiple openings in the direction along the boundary B is 50% to 90% of the length Wc.

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

[0092] Next, simulation results based on the first embodiment will be described with reference to FIGS.

[0093] 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 when viewed in a plan view. Tq = 1.52 μm Te = Te2 = 0.08 μm Lq = 160 μm Wq = 120 μm Le = 100 μm We = 80 μm Le2 = 120 μm We2 = 100 μm Wc = 20 μm Hx = Hz = 1.5 μm PHx = PHz = 3 μm Number of H = 8 × 8 Ls = 5 μm Ws = 5 μm

[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 the simulation conditions 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] 9 and 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 FIG. 10 and FIG. 6, k_A0Z is reduced from 0.37% to 0.04% by providing the opening h1. Comparing FIG. 11 and FIG. 7, k_A0X is reduced from 0.12% to 0.00% by providing the opening h1.

[0100] 10 and 11 , in the comparative example, the vibrations are distributed in a manner that causes them to leak 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, as shown in FIGS. 6 to 8 , in the first embodiment, there is no leakage of vibrations 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 fact that the vibrations excited between the first extraction electrode and the second excitation electrode couple 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 emphasized. In the first embodiment, the opening h1 suppresses coupling between the A0 mode in the excitation region and 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 increases 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 passage 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 passage 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 Figure 12, when the length Ls is 3 µm or more, i.e., when Tq x 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 portion 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 x 2 ≤ Ls ≤ Ws / Rs holds. It is even more desirable that the relationship Tq x 3 ≤ Ls ≤ Ws / Rs holds.

[0105] As shown in FIG. 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 viewpoint of suppressing an increase in the wiring resistance of the bottleneck 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 a quartz crystal blank 11, a first electrode including a first excitation electrode 14a and a first extraction electrode 15a provided on a first main surface 11A of the quartz crystal blank 11, and a second electrode including a second excitation electrode 14b and a second extraction electrode 15b provided on a second main surface 11B of the quartz crystal blank 11. In a plan view, a high acoustic velocity region 17 is provided in the center of an excitation region 19 where the first excitation electrode 14a and the second excitation electrode 14b overlap, and a low acoustic velocity region 18 is provided in the periphery of the excitation region 19. The first excitation electrode 14a in the high acoustic velocity region 17 is provided with 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 portion between the first excitation electrode 14a and the first extraction electrode 15a overlaps with the second excitation electrode 14b. An opening h1 is located at the connection portion 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] This suppresses 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, thereby suppressing deterioration of the balance of the vibration distribution in the excitation region 19 caused by the first extraction electrode 15a. This increases k_S0 and reduces k_A0Z and k_A0X. Therefore, the vibration characteristics can be improved.

[0108] In 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 making Wh1 / Wc 0.50≦Wh1 / Wc, 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. By making Wh1 / Wc ≦0.90, 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.

[0110] In one aspect of this embodiment, the relationship 2<Lh1 / Tq≦Wh1 / Tq holds 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.

[0111] This can sufficiently suppress the electric field generated in the region overlapping with the opening h1, and therefore the opening h1 can 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.

[0112] In one aspect of this embodiment, the length Lh1 of the opening h1 in the X-axis direction intersecting the boundary B is three times or more the thickness Tq of the crystal blank 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 We of the length We of the first excitation electrode 14a in the Z'-axis direction along the boundary B satisfies 0.05≦Ws / We≦0.15.

[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 to 0.15≦Ws / We, it is possible to effectively suppress coupling between the vibration excited between the first extraction electrode 15 a and the second excitation electrode 14 b 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 components that are the same as or similar to those in the first embodiment are denoted by the same or similar reference numerals, and descriptions thereof will be omitted as appropriate. Furthermore, similar effects resulting from similar components will not be mentioned one after another.

[0119] Second Embodiment Next, the configuration of a quartz crystal vibrating element 102 according to a 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 a 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] Simulation results based on the second embodiment will be described with reference to Figures 15 to 19. In the graphs shown in Figures 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 Figure 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] 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 become minimum.

[0123] 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 become minimum.

[0124] 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] 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 become minimum.

[0126] 18 is a graph plotting the upper limit, lower limit, and center 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 a quartz crystal vibrating element 103 according to a 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 planar shapes of the openings h11 and h12 are both rectangular slits. 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 directions of the opening h11 and 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-shaped opening on the negative Z'-axis side of the first extraction electrode 15a. The opening h12 is a notch-shaped opening 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 is 7.29% and Fr_S0 is 985.20 MHz in one example of the third embodiment. As shown in Fig. 22, k_A0Z is 0.18% and Fr_A0Z is 985.73 MHz in one example of the third embodiment. As shown in Fig. 23, k_A0X is 0.15% and Fr_A0X is 985.72 MHz in one example of the third embodiment.

[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 a quartz crystal vibrating element 104 according to a 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 is 7.29% and Fr_S0 is 985.21 MHz in one example of the fourth embodiment. As shown in Fig. 26, k_A0Z is 0.03% and Fr_A0Z is 985.75 MHz in one example of the fourth embodiment. As shown in Fig. 27, k_A0X is 0.06% and Fr_A0X is 985.72 MHz in one example of the fourth embodiment.

[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 a quartz crystal vibrating element 105 according to a 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 has a notch shape that opens on the negative Z'-axis side of the first extraction electrode 15a. The openings h11 have their elongated 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] Simulation results based on the fifth embodiment will be described with reference to Fig. 29 . Fig. 29 is a graph showing 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 those 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 larger the total value of lengths Ls is in the range of 0 μm to 5.0 μm, the smaller the electromechanical coupling coefficient k. 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 value Ls_total of lengths Ls is 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 value Ls_total of lengths Ls 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 tendency when there are multiple openings h11 and when there is only one 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 be established.

[0141] Sixth Embodiment Next, the configuration of a quartz crystal vibrating element 106 according to a 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] 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 a 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, aligned in a direction along the boundary B. The multiple 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 openings 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 openings 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, a simulation result 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 is 7.37% and Fr_S0 is 985.13 MHz in one example of the seventh embodiment. As shown in Fig. 36, k_A0Z is 0.03% and Fr_A0Z is 985.62 MHz in one example of the seventh embodiment. As shown in Fig. 37, k_A0X is 0.01% and Fr_A0X is 985.66 MHz in one example of the seventh embodiment.

[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 opening 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 opening 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 and 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 desirable that Wh2 / Wp be ≦0.90, and it is even more desirable that Wh2 / Wp be ≦0.80.

[0155] Eighth Embodiment Next, the configuration of a quartz crystal vibrating element 108 according to an 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 opening 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 is 7.36% and Fr_S0 is 985.63 MHz in one example of the eighth embodiment. As shown in Fig. 43, k_A0Z is 0.02% and Fr_A0Z is 985.63 MHz in one example of the eighth embodiment. As shown in Fig. 44, k_A0X is 0.01% and Fr_A0X is 985.67 MHz in one example of the eighth embodiment.

[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 a quartz crystal vibrating element 109 according to a 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 14 a and the first extraction electrode 15 a are shown, but the second excitation electrode 14 b and the second extraction electrode 15 b 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 a quartz crystal vibrating element 110 according to a 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 Fig. 50, k_S0 is 7.25% and Fr_S0 is 985.20 MHz in one example of the tenth embodiment. As shown in Fig. 51, k_A0Z is 0.07% and Fr_A0Z is 985.71 MHz in one example of the tenth embodiment. As shown in Fig. 52, k_A0X is 0.01% and Fr_A0X is 985.75 MHz in one example of the tenth embodiment.

[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 a quartz crystal vibrating element 111 according to an 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. In the X-axis direction, the dimension from the boundary B to the end of the opening farthest from the boundary B among the plurality of openings h21 on the negative X-axis side 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 the boundary B to the end of the opening located farthest from the boundary B 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 an 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 to the 11th embodiment. FIG. 55 shows the vibration distribution of the S0 mode as a simulation result based on the comparative example to the 11th embodiment. FIG. 56 shows the vibration distribution of the A0Z mode as a simulation result based on the comparative example to the 11th embodiment. FIG. 57 shows the vibration distribution of the A0X mode as a simulation result based on the comparative example to the 11th embodiment. In FIGS. 55 to 57, 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.

[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 openings 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 openings are provided. The reason why the A0 mode is less suppressed in the comparative example for the eleventh embodiment than when no openings are provided is because, in the comparative example for the eleventh embodiment, a maximum of six openings h21 are arranged in the X-axis direction, and Lx is << -5 μm. When the length Wh2 of the openings h21 along the X-axis direction is 2 μm and the distance Wp between the ends of two adjacent openings h2 on the negative X-axis direction side is 3 μm, Lx = -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 openings are provided.

[0189] Twelfth Embodiment Next, the configuration of a quartz crystal vibrating element 112 according to a 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 centered on the high acoustic velocity region 17. 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 14 a and the first extraction electrode 15 a are shown, but the second excitation electrode 14 b and the second extraction electrode 15 b are not shown.

[0193] As shown in Fig. 59, k_S0 in one example of the twelfth embodiment is 7.17%, and Fr_S0 is 985.33 MHz. As shown in Fig. 60, k_A0Z in one example of the twelfth embodiment is 0.02%, and Fr_A0Z is 985.91 MHz. As shown in Fig. 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 k_S0 is smaller 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 k_A0Z and k_A0X are smaller 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 cancel each other out.

[0195] Thirteenth Embodiment Next, the configuration of a quartz crystal vibrating element 113 according to a 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 multiple 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, and the second excitation electrode 14b and the second extraction electrode 15b are not shown.

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

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

[0200] Fourteenth Embodiment Next, the configuration of a quartz crystal vibrating element 114 according to a 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 of openings h21 increases in distance from the end of the first excitation electrode 14a on the positive X-axis direction as it moves toward the positive Z'-axis direction. The line of openings h21 increases in distance from the end of the first excitation electrode 14a on the negative X-axis direction as it moves toward the negative Z'-axis direction. The line of openings h23 increases in distance from the end of the first excitation electrode 14a on the positive X-axis direction as it moves toward the negative Z'-axis direction. The line of openings h24 increases in distance from the end of the first excitation electrode 14a on the negative X-axis direction as it moves toward the positive Z'-axis direction. The angle formed by the direction in which the multiple openings h21, h22, h23, and h24 are aligned and the Z'-axis direction is, for example, 30°.

[0202] Fifteenth Embodiment Next, the configuration of a quartz crystal vibrating element 115 according to a 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 extending in a straight line, with its 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 with 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. In the case of 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. In the case of 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 the opening h23 counterclockwise, i.e., toward the negative X-axis direction, around the end of the 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 the opening h24 counterclockwise, i.e., toward the positive X-axis direction, around the end of the 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] In the range where the angle between the longitudinal direction of the opening and the Z'-axis direction is 0° or more and 90° or less, 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 in a direction intersecting with the boundary B, the A0 mode can be sufficiently suppressed.

[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 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 direction of the multiple openings h23 counterclockwise, i.e., toward the negative X-axis direction, around the opening furthest in the Z'-axis positive direction among the multiple openings h23 as the rotation center. This angle is the angle obtained by rotating the arrangement direction of the multiple openings h24 counterclockwise, i.e., toward the positive X-axis direction, around the opening furthest in the Z'-axis negative direction among the multiple openings h24 as the rotation center.

[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 formed by the direction in which the openings are arranged and the Z'-axis direction is a variable.

[0212] In the range of 0° to 90° inclusive, the larger the angle (Lh2 / Tq) × (Wh2 / Wp) between the direction in which the openings are arranged and the Z'-axis direction, the smaller k_A0Z becomes, regardless of the angle. When 0.6≦(Lh2 / Tq) × (Wh2 / Wp), k_A0Z becomes sufficiently small. Even when the angle (Lh2 / Tq) × (Wh2 / Wp) 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 intersecting the 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 simulation results based on the fourteenth embodiment. In Fig. 71 , the horizontal axis represents (Lh2 / Tq) × (Wh2 / Wp), and the vertical axis represents k_S0. k_S0 is plotted when the angle formed by 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] In the range of 0° to 90° inclusive, the smaller the angle formed by the direction in which the openings are arranged with respect to the Z′-axis direction, the larger k_S0 becomes. When (Lh2 / Tq)×(Wh2 / Wp)≦2.3, k_S0 in the fourteenth embodiment becomes larger than k_S0 in the comparative example. Even when the angle formed by the direction in which the openings are arranged with respect to the Z′-axis direction is 90°, k_S0 becomes larger when (Lh2 / Tq)×(Wh2 / Wp)≦2.3. Therefore, even if the row of openings is arranged in a direction intersecting the 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 a quartz crystal vibrating element 116 according to a 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 14 a and the first extraction electrode 15 a are shown, while the second excitation electrode 14 b and the second extraction electrode 15 b are omitted.

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

[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, the provision of the opening h1 suppresses the A0 mode and improves the vibration characteristics of the S0 mode.

[0222] Seventeenth Embodiment Next, the configuration of a quartz crystal vibrating element 117 according to a 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 14 a and the first extraction electrode 15 a are shown, but the second excitation electrode 14 b and the second extraction electrode 15 b are not shown.

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

[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 14 a and the first extraction electrode 15 a are shown, but the second excitation electrode 14 b and the second extraction electrode 15 b are not shown.

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

[0231] k_S0 in an example of the eighteenth embodiment is substantially the same as k_S0 in an example of the first embodiment. k_A0Z in an example of the eighteenth embodiment is substantially the same as k_A0Z in an example of the first embodiment. k_A0X in an example of the eighteenth 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 a quartz crystal vibrating element 119 according to a 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 is provided with 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, is provided with 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 14 b is shown, and the first excitation electrode 14 a, the first extraction electrode 15 a, and the second extraction electrode 15 b are not shown.

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

[0236] In one example of the 19th embodiment, k_S0 is approximately the same as k_S0 in the comparative example. In one example of the 19th embodiment, k_A0Z is smaller than k_A0Z in the comparative example. In one example of the 19th embodiment, k_A0X 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 a 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 is provided with 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, is provided with 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 14 b is shown, and the first excitation electrode 14 a, the first extraction electrode 15 a, and the second extraction electrode 15 b are not shown.

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

[0241] k_S0 in one example of the twentieth embodiment is substantially the same as k_S0 in one example of the nineteenth embodiment. k_A0Z in one example of the twentieth embodiment is substantially the same as k_A0Z in one example of the nineteenth embodiment. k_A0X in one example of the twentieth embodiment is substantially the same as k_A0X in one example of the nineteenth 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 a quartz crystal vibrating element 121 according to the twenty-first embodiment will be described with reference to Fig. 92. Fig. 92 is a plan view of the quartz crystal vibrating element according to the twenty-first embodiment.

[0243] The second excitation electrode 14b, which has the larger area of ​​the first excitation electrode 14a and the second excitation electrode 14b, has a plurality of holes H. 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 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 Fig. 93, k_S0 in one example of the 21st embodiment is 7.36%, and Fr_S0 is 985.14 MHz. As shown in Fig. 94, k_A0Z in one example of the 21st embodiment is 0.06%, and Fr_A0Z is 985.64 MHz. As shown in Fig. 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 twenty-first embodiment is substantially the same as k_S0 in one example of the nineteenth and twentieth embodiments. k_A0Z in one example of the twenty-first embodiment is substantially the same as k_A0Z in one example of the nineteenth and twentieth embodiments. k_A0X in one example of the twenty-first embodiment is substantially the same as k_A0X in one example of the nineteenth and twentieth 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 twenty-second embodiment will be described with reference to Fig. 96. Fig. 96 is a plan view of the quartz crystal vibrating element according to the twenty-second 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 Fig. 97, k_S0 in one example of the 22nd embodiment is 7.33%, and Fr_S0 is 985.21 MHz. As shown in Fig. 98, k_A0Z in one example of the 22nd embodiment is 0.03%, and Fr_A0Z is 985.64 MHz. As shown in Fig. 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 the figure, 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] In one example of the 22nd embodiment, k_S0 is approximately the same as k_S0 in the comparative example. In one example of the 22nd embodiment, k_A0Z is approximately the same as k_A0Z in the comparative example. In one example of the 22nd embodiment, k_A0X 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 a 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 vibration element including: a piezoelectric piece having a first principal surface and a second principal surface opposing 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 an area 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 area where the first excitation electrode and the second excitation electrode overlap, and the low acoustic velocity region has a lower acoustic velocity than the high acoustic velocity region; a first outer periphery of the first excitation electrode is provided more inward than a second outer periphery of the second excitation electrode; the acoustic velocity in the area where the first extraction electrode and the second excitation electrode overlap is lower than the acoustic velocity in the high acoustic velocity region and is equal to or higher than the acoustic velocity in the low acoustic velocity region; and at least one opening is provided in at least one of the first electrode and the second excitation electrode in the area where the first electrode and the second excitation electrode overlap, A piezoelectric vibration element, wherein 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.

[0255] <2> The piezoelectric vibration element according to <1>, wherein a plurality of holes are provided in at least one of the first excitation electrode and the second excitation electrode in the high acoustic velocity region.

[0256] <3> The piezoelectric vibration element according to <1> or <2>, wherein the first excitation electrode has a rectangular shape in a plan view, and the first extraction electrodes are connected to corners of the first excitation electrode.

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

[0258] <5> The piezoelectric vibration element according to any one of <1> to <4>, wherein 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.

[0259] <6> The piezoelectric vibration element described in any one of <1> to <5>, wherein at least one opening has at least one of a slit-shaped opening having a length extending in a direction parallel to the boundary and a row-shaped opening aligned in a direction parallel to the boundary, and the total length of the at least one opening in the direction parallel to the boundary is 50% to 90% of the length of the first extraction electrode in the direction parallel to the boundary.

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

[0261] <8> A piezoelectric vibration element according to any one of <1> to <7>, wherein the relationship 2<Lh / Tq holds when Tq is the thickness of the piezoelectric piece, Wh is the length of one of the at least one opening in a direction along the boundary in a planar view, and Lh is the length of one of the at least one opening in a direction perpendicular to the length Wh along the boundary.

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

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

[0264] <11> The piezoelectric vibration element according to any one of <1> to <10>, wherein at least one opening is a single slit-shaped opening having a longitudinal direction.

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

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

[0267] <14> The piezoelectric vibration element according to any one of <1> to <13>, wherein the at least one opening is formed in the first extraction electrode, and the relationship Ls≦Ws / Rs holds, where Ws is 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, Ls is a length of the at least one opening in a direction perpendicular to the boundary, and Rs is 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.

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

[0269] <16> The piezoelectric vibration element according to any one of <1> to <15>, wherein at least one opening has a plurality of openings arranged in a row, and a relationship of 0.6≦(Lh2 / Tq)×(Wh2 / Wp)≦2.3 holds, where Wp is an arrangement period of the plurality of openings, Wh2 is a length of each of the plurality of openings in a direction in which the plurality of openings are arranged, Lh2 is a length of each of the plurality of openings in a direction perpendicular to the direction in which the plurality of openings are arranged, and Tq is a thickness of the piezoelectric piece.

[0270] <17> The piezoelectric vibration element according to <2>, wherein 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.

[0271] <18> A piezoelectric vibration element including: a piezoelectric piece having a first principal surface and a second principal surface opposing 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 an area 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 area where the first excitation electrode and the second excitation electrode overlap, and the low acoustic velocity region has a lower acoustic velocity than 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; and the acoustic velocity in the area where the first extraction electrode and the second excitation electrode overlap 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, A piezoelectric vibration element, wherein 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, and 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 that is on the opposite side of the high acoustic velocity region from the first extraction electrode.

[0272] <19> The piezoelectric vibration element according to <18>, wherein a plurality of holes are provided in at least one of the first excitation electrode and the second excitation electrode in the high acoustic velocity region.

[0273] <20> The piezoelectric vibration element according to <18> or <19>, wherein 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 that is four times or less the thickness of the piezoelectric piece.

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

[0275] <22> The piezoelectric vibration element described in <21>, wherein the first excitation electrode further has a third corner and a fourth corner 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, and 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.

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

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

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

[0279] <26> The piezoelectric vibration element according to any one of <1> to <25>, wherein, in the high acoustic 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 penetrating the excitation electrode in the thickness direction, and the thickness of the piezoelectric piece is Tq, and when the shape of the plurality of holes is square in plan view, the length of one side of the plurality of holes is Hr, and when the shape of the plurality of holes is other than square, the length of one side when the holes are converted into a square while keeping the area constant is Hr, the relationship 0<Hr / Tq≦2.0 holds.

[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 included within the scope of the present invention. In other words, designs modified by those skilled in the art as appropriate 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 and their arrangements, materials, conditions, shapes, sizes, etc. of the embodiments and / or modifications are not limited to those illustrated and can be modified as appropriate. Furthermore, the embodiments and modifications are merely examples, and it goes without saying that partial substitutions or combinations of the components shown in different embodiments and / or modifications are possible. These are also encompassed within the scope of the present invention as long as they incorporate the characteristics of the present invention.

[0284] DESCRIPTION OF SYMBOLS 1... quartz crystal vibrator 10... quartz crystal vibrating element 30... base member 40... lid member 50... bonding portion 11... quartz crystal blank 11A... upper surface 11B... lower surface 14a... first excitation electrode 14b... second excitation electrode 15a... first extraction electrode 15b... second extraction electrode 16a... first connection electrode 16b... second connection electrode 17... high acoustic velocity region 18... low acoustic 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 vibration element comprising a piezoelectric piece 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 lead-out electrode connected to the first excitation electrode, and a second excitation electrode provided on the second main surface, wherein in a plan view, a high sound velocity region is located at a central portion within a region where the first excitation electrode and the second excitation electrode overlap, and a low sound velocity region is located at a peripheral portion within the region where the first excitation electrode and the second excitation electrode overlap and has a lower sound velocity than the high sound velocity region; the first outer peripheral portion of the first excitation electrode is provided inside the second outer peripheral portion of the second excitation electrode; the sound velocity in a region where the first lead-out 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 a region where the first electrode and the second excitation electrode overlap; and the at least one opening is provided substantially within a range of a distance of 4 times or less the thickness of the piezoelectric piece from a boundary between the first excitation electrode and the first lead-out electrode.

2. The piezoelectric vibration element according to claim 1, wherein 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.

3. The piezoelectric vibration element according to claim 1 or 2, wherein in a plan view, the shape of the first excitation electrode is rectangular, and the first lead-out electrode is connected to a corner of the first excitation electrode.

4. The piezoelectric vibration element according to claim 3, wherein the first lead-out electrode is connected to only one side of the first excitation electrode.

5. The piezoelectric vibration element according to any one of claims 1 to 4, wherein 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 column-shaped opening arranged in a row in the direction along the boundary.

6. The at least one opening has at least one of a slit-shaped opening having a length extending in a direction parallel to the boundary and a column-shaped opening arranged in a row in a direction parallel to the boundary, and a sum of lengths of the at least one opening in the direction parallel to the boundary is 50% or more and 90% or less of a length of the first extraction electrode in the direction parallel to the boundary. The piezoelectric vibration element according to any one of claims 1 to 5.

7. The at least one opening has a column-shaped opening arranged in a row in a direction parallel to the boundary. When a length of one opening is Wh2 and a period in which the openings are arranged is Wp in a direction in which the column-shaped openings are arranged, a relationship of 0.50 ≤ Wh2 / Wp ≤ 0.90 holds. The piezoelectric vibration element according to any one of claims 1 to 6.

8. When a thickness of the piezoelectric sheet is Tq, a length of one of the at least one opening in a direction along the boundary is Wh, and a length of one of the at least one opening in a direction orthogonal to the length Wh along the boundary is Lh in a plan view, a relationship of 2 < Lh / Tq holds. The piezoelectric vibration element according to any one of claims 1 to 7.

9. The at least one opening has a plurality of openings arranged in a direction intersecting the boundary. The piezoelectric vibration element according to any one of claims 1 to 8.

10. A sum of lengths of the at least one opening in a direction orthogonal to the boundary is 2 times or more the thickness of the piezoelectric sheet. The piezoelectric vibration element according to any one of claims 1 to 9.

11. The at least one opening is one slit-shaped opening having a length. The piezoelectric vibration element according to any one of claims 1 to 10.

12. The at least one opening has a plurality of slit-shaped openings having lengths, and the lengths of the plurality of slit-shaped openings extend in parallel to each other. The piezoelectric vibration element according to any one of claims 1 to 10.

13. When 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 Ws and a length of the first excitation electrode in the direction parallel to the boundary is We, a relationship of Ws / We ≤ 0.15 holds. The piezoelectric vibration element according to any one of claims 1 to 12.

14. The at least one opening is formed in the first extraction electrode. When the difference between the length of the first extraction electrode in the 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 the direction orthogonal to the boundary is defined as Ls, and the sheet resistance of the portion of the first extraction electrode that aligns with the at least one opening in the direction parallel to the boundary is defined as Rs, the relationship Ls ≦ Ws / Rs holds. The piezoelectric vibration element according to any one of claims 1 to 13.

15. When the distance between the boundary and the at least one opening in the direction orthogonal to the boundary is defined as Lx, and the difference between the length of the first extraction electrode in the direction parallel to the boundary and the length of the at least one opening is defined as Ws, the relationship Lx = 0.48 × Ls - 1.88 ± 1.70 holds. The piezoelectric vibration element according to any one of claims 1 to 14.

16. The at least one opening has a plurality of openings arranged in a row. When the arrangement period of the plurality of openings is defined as Wp, the length of each of the plurality of openings in the direction in which the plurality of openings are arranged is defined as Wh2, the length of each of the plurality of openings in the direction orthogonal to the direction in which the plurality of openings are arranged is defined as Lh2, and the thickness of the piezoelectric sheet is defined as Tq, the relationship 0.6 ≦ (Lh2 / Tq) × (Wh2 / Wp) ≦ 2.3 holds. The piezoelectric vibration element according to any one of claims 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 sheet. The piezoelectric vibration element according to claim 2.

18. A piezoelectric vibration element comprising: a piezoelectric piece 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 lead-out electrode connected to the first excitation electrode; and a second excitation electrode provided on the second main surface. In a plan view, a high sound velocity region is located at the center within a region where the first excitation electrode and the second excitation electrode overlap, and a low sound velocity region is located at the periphery within the region where the first excitation electrode and the second excitation electrode overlap and has a lower sound velocity than the high sound velocity region. The first outer peripheral portion of the first excitation electrode is provided inside the second outer peripheral portion of the second excitation electrode. The sound velocity in the region where the first lead-out 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. In the region of the low sound velocity region on the first lead-out electrode side with respect to the high 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 the region of the low sound velocity region on the side opposite to the first lead-out electrode with the high sound velocity region interposed therebetween, at least one second opening is provided in at least one of the first excitation electrode and the second excitation electrode.

19. The piezoelectric vibration element according to claim 18, wherein 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.

20. The piezoelectric vibration element according to claim 18 or 19, wherein the at least one first opening and the at least one second opening are provided substantially within a range of a distance of 4 times or less the thickness of the piezoelectric piece from the first outer peripheral portion of the first excitation electrode.

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

22. The first exciting electrode further has a third corner portion and a fourth corner portion that are diagonally positioned with respect to each other. In a region of the low sound velocity region that overlaps with the third corner portion, at least one third opening is provided in at least one of the first exciting electrode and the second exciting electrode. In a region of the low sound velocity region that overlaps with the fourth corner portion, at least one fourth opening is provided in at least one of the first exciting electrode and the second exciting electrode. 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-symmetrical with respect to the center of the first exciting 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-symmetrical with respect to the center of the first exciting 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 exciting electrode among the first exciting electrode and the second exciting electrode. The piezoelectric vibration element according to any one of claims 18 to 24.

26. In the high sound velocity region, a plurality of holes are provided in at least one of the first exciting electrode and the second exciting electrode. The plurality of holes are holes that penetrate the first exciting electrode or the second exciting 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 to a square shape while keeping the area constant be Hr. The relationship 0 < Hr / Tq ≤ 2.0 holds. The piezoelectric vibration element according to any one of claims 1 to 25.

Images