Piezoelectric vibration element

Abstract

This piezoelectric vibration element comprises a piezoelectric piece and an excitation electrode that overlap in the thickness direction, and includes a high acoustic velocity region and a low acoustic velocity region having a lower acoustic velocity than the high acoustic velocity region. In a plan view in the thickness direction, the high acoustic velocity region is provided in a region overlapping the center portion of the excitation electrode, and the low acoustic velocity region is provided in at least a portion of a region overlapping an end of the excitation electrode. A plurality of holes that make the mass per unit area of the high acoustic velocity region smaller than the mass per unit area of the low acoustic velocity region are formed on the excitation electrode in the high acoustic velocity region. In one direction intersecting the thickness direction, the size in one direction of a section of the low acoustic velocity region adjacent to the high acoustic velocity region is smaller than the size of the high acoustic velocity region in one direction. In a plan view in the thickness direction, the surface area of the low acoustic velocity region is smaller than the surface area of the high acoustic velocity region.

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 configuration in which the mesa thickness ratio of the inverted mesa shape of the excitation electrode is changed while the shape of the vibration displacement is flattened, thereby reducing spurious oscillations, which are vibrations occurring at frequencies other than the main vibration.

[0004] International Publication No. 98 / 38736

[0005] However, it is desirable to further reduce spurious oscillations and improve the electromechanical coupling coefficient.

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

[0007] A piezoelectric vibration element according to one embodiment of the present invention is a piezoelectric vibration element comprising a piezoelectric piece and an excitation electrode that overlap in the thickness direction, and has a high acoustic velocity region and a low acoustic velocity region in which the acoustic velocity is lower than that of the high acoustic velocity region, and when viewed in a plane in the thickness direction, the high acoustic velocity region is provided in a region that overlaps with the center of the excitation electrode, and the low acoustic velocity region is provided in at least a part of a region that overlaps with the end of the excitation electrode, and the excitation electrode in the high acoustic velocity region has a plurality of holes formed therein that make the mass per unit area of ​​the high acoustic velocity region smaller than the mass per unit area of ​​the low acoustic velocity region, and in one direction intersecting the thickness direction, the dimension in one direction of the portion of the low acoustic velocity region adjacent to the high acoustic velocity region is smaller than the dimension in one direction of the high acoustic velocity region, and when viewed in a plane in the thickness direction, the area of ​​the low acoustic velocity region is smaller than the area of ​​the high acoustic velocity region.

[0008] According to the present invention, it is possible to provide a piezoelectric vibration element that can improve the electromechanical coupling coefficient.

[0009] 1 is an exploded perspective view of a quartz crystal resonator according to the first embodiment; FIG. 2 is a cross-sectional view of a quartz crystal oscillator according to the first embodiment; FIG. 3 is a cross-sectional view of a quartz crystal resonator according to the first embodiment; FIG. 4 is a cross-sectional view of a quartz crystal resonator element according to the first embodiment; FIG. 5 is a plan view of a quartz crystal resonator element according to the first embodiment; FIG. 6 is a diagram showing simulation results based on an example; FIG. 7 is a diagram showing simulation results based on an example; FIG. 8 is a diagram showing simulation results based on an example; FIG. 9 is a cross-sectional view of a quartz crystal resonator element according to a first comparative example; FIG. 10 is a diagram showing simulation results based on the first comparative example; FIG. 11 is a diagram showing simulation results based on the first comparative example; FIG. 12 is a diagram showing simulation results based on the first comparative example; FIG. 13 is a cross-sectional view of a quartz crystal resonator element according to a second comparative example; FIG. 14 is a diagram showing simulation results based on the second comparative example; FIG. 15 is a diagram showing simulation results based on the second comparative example; FIG. 16 is a graph showing the influence of the dimensions of the low acoustic velocity region in the first embodiment; FIG. 17 is a graph showing the influence of the dimensions of the low acoustic velocity region in the first embodiment; 1 is a graph showing the influence of the dimensions of the low acoustic velocity region in the first embodiment; FIG. 2 is a graph showing the influence of the planar dimensions of the hole in the first embodiment; FIG. 3 is a graph showing the influence of the planar dimensions of the hole in the first embodiment; FIG. 4 is a graph showing the influence of the planar dimensions of the hole in the first embodiment; FIG. 5 is a graph showing the influence of the aperture ratio of the hole in the first embodiment; FIG. 6 is a graph showing the influence of the aperture ratio of the hole in the first embodiment; FIG. 7 is a plan view of a quartz crystal vibration element according to a second embodiment; FIG. 8 is a graph showing the influence of the dimensions of the low acoustic velocity region in the second embodiment; FIG. 9 is a graph showing the influence of the dimensions of the low acoustic velocity region in the second embodiment;FIG. 1 is a plan view of a quartz vibrating element according to a third embodiment. FIG. 2 is a graph showing the influence of the dimensions of the low acoustic velocity region in the third embodiment. FIG. 3 is a graph showing the influence of the dimensions of the low acoustic velocity region in the third embodiment. FIG. 4 is a cross-sectional view of a quartz vibrating element according to a fourth embodiment. FIG. 5 is a cross-sectional view of a quartz vibrating element according to a fifth embodiment. FIG. 6 is a cross-sectional view of a quartz vibrating element according to a sixth embodiment. FIG. 7 is a cross-sectional view of a quartz vibrating element according to a seventh embodiment. FIG. 8 is a cross-sectional view of a quartz vibrating element according to an eighth embodiment. FIG. 9 is a plan view of a modified example of the high acoustic velocity region. FIG. 10 is a plan view of a modified example of the high acoustic velocity region. FIG. 11 is a plan view of a modified example of the high acoustic velocity region.

[0010] 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.

[0011] 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 each component. The X-axis, Y'-axis, and Z'-axis correspond to each other in each drawing. The X-axis, Y'-axis, and Z'-axis correspond to the crystalline 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 around the X-axis by 35 degrees 15 minutes ± 1 minute 30 seconds in the direction from the Y-axis to the Z-axis.

[0012] In the following description, the direction parallel to the X-axis is referred to as the "X-axis direction," the direction parallel to the Y'-axis is referred to as the "Y'-axis direction," and the direction parallel to the Z'-axis is referred to as the "Z'-axis direction." The directions of the 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 resonator element 10, the quartz resonator 1, and the quartz oscillator 100 is not limited to this. The plane defined by the X-axis and Z'-axis is referred to as the Z'X plane, and the same applies to planes defined by the other axes. The Y'-axis direction is an example of the "thickness direction."

[0013] First Embodiment

[0014] First, a schematic configuration of a crystal oscillator 100 according to an embodiment will be described with reference to Fig. 1. Fig. 1 is a cross-sectional view of the crystal oscillator 100 according to the first embodiment.

[0015] In the following description, a crystal oscillator (XO) equipped with a quartz crystal resonator unit will be used as an example of a piezoelectric oscillator. Furthermore, a crystal resonator unit equipped with a quartz crystal resonator will be used as an example of a piezoelectric resonator unit. Furthermore, a crystal resonator element equipped with a quartz crystal element will be used as an example of a piezoelectric resonator element. A quartz crystal element is a type of piezoelectric material (piezoelectric piece) that vibrates in response to an applied voltage. Note that the piezoelectric resonator element according to one embodiment of the present invention is not limited to a quartz crystal resonator element, and may utilize other piezoelectric materials such as ceramic.

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

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

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

[0019] The crystal unit 1 is provided on one surface (the upper surface in FIG. 1 ) of the mounting substrate 130. More specifically, the crystal unit 1 is electrically connected to the wiring layer of the mounting substrate 130 by solder 153.

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

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

[0022] The electronic component 156 is electrically connected to the crystal unit 1 through a wiring layer of the mounting substrate 130. The electronic component 156 includes, for example, a capacitor, an IC chip, etc. The electronic component 156 is, for example, part of an oscillation circuit that causes the crystal unit 1 to oscillate, or part of a temperature compensation circuit that compensates for the temperature characteristics of the crystal unit 1. When the electronic component 156 includes a temperature compensation circuit, the crystal oscillator 100 corresponds to an example of a temperature compensated crystal oscillator (TCXO). The crystal oscillator 100 may correspond to an example of a voltage controlled crystal oscillator (VCXO) or an example of an oven controlled crystal oscillator (OCXO).

[0023] Next, the configuration of the crystal resonator 1 according to the first embodiment will be described with reference to Figures 2 and 3. Figure 2 is an exploded perspective view of the crystal resonator according to the first embodiment. Figure 3 is a cross-sectional view of the crystal resonator according to the first embodiment.

[0024] 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 .

[0025] The quartz crystal vibrating element 10 is an electromechanical energy conversion element that converts electrical energy into mechanical energy and vice versa through the piezoelectric effect. The main mode frequency of the quartz crystal vibrating element 10 is, for example, approximately 0.8 GHz to 2.0 GHz, e.g., approximately 0.95 GHz. The inharmonic mode frequency of the quartz crystal vibrating element 10 is, for example, within a range of approximately 1% of the main mode frequency. The quartz crystal vibrating element 10 includes a thin quartz crystal piece (quartz crystal element) 11, a first excitation electrode 14a and a second excitation electrode 14b that constitute a pair of excitation electrodes, a first extraction electrode 15a and a second extraction electrode 15b that constitute a pair of extraction electrodes, and a first connection electrode 16a and a second connection electrode 16b that constitute a pair of connection electrodes.

[0026] 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 cover 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.

[0027] 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 a square with a pair of sides extending in the Z'-axis direction and a pair of sides extending in the X-axis direction. Furthermore, the quartz crystal blank 11 has a thickness in the Y'-axis direction. As an example, the shape of the quartz crystal blank 11 is a flat plate with a uniform thickness.

[0028] 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 may be rectangular with short sides extending in the Z'-axis direction and long sides extending in the X-axis direction. The planar shape of the crystal blank may be polygonal, circular, elliptical, or a combination thereof. Furthermore, the crystal blank is not limited to a flat plate. The crystal blank may have a mesa structure or an inverted mesa structure with irregularities on at least one of the upper surface 11A and the lower surface 11B. The crystal blank may have a convex structure in which the thickness changes continuously, or a bevel structure in which the thickness changes discontinuously.

[0029] 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.

[0030] 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.

[0031] The cut angle of the quartz crystal blank is not limited to the above. The rotation angle of the Y'-axis and Z'-axis of the AT-cut quartz crystal blank 11 may be in the range of -5 degrees or more or +15 degrees or less from 35 degrees 15 minutes. Furthermore, the cut angle of the quartz crystal blank may be a different cut than the AT cut, such as a BT cut, a GT cut, or an SC cut.

[0032] 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 planar 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. The first excitation electrode 14a is an example of an "excitation electrode."

[0033] The planar shape of the first excitation electrode 14 is a rectangle 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.

[0034] 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 with short sides extending in the X-axis direction. The planar shapes of the first excitation electrode and the second excitation electrode may also be square, polygonal, circular, elliptical, or a combination thereof.

[0035] 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.

[0036] 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.

[0037] 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. These electrodes of the quartz crystal vibrating element 10 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 quartz crystal blank 11, and the surface layer is a gold (Au) layer that has good chemical stability. The electrodes of the quartz crystal vibrating element 10 may contain silver (Ag), copper (Cu), palladium (Pd), platinum (Pt), titanium (Ti), nickel (Ni), aluminum (Al), molybdenum (Mo), tungsten (W), or an alloy containing at least one of these. The electrodes of the quartz crystal vibrating element 10 may also have a single-layer structure.

[0038] 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.

[0039] 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.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] The external electrodes 35a and 35b are external terminals for electrically connecting the quartz crystal vibrating element 10 to an external substrate. The external electrode 35a electrically connects the first excitation electrode 14a of the quartz crystal vibrating element 10 to the mounting substrate 130, and the external electrode 35b electrically connects the second excitation electrode 14b of the quartz crystal vibrating element 10 to the mounting substrate 130. One of the external electrodes 35c and 35d is a ground electrode that grounds the lid member 40, and the other is a dummy electrode that is not electrically connected to the quartz crystal vibrating element 10 or the lid member 40. The external electrodes 35a, 35b, 35c, and 35d are each continuously provided from the cutout side surfaces provided at four corners of the base 31 to the bottom surface 31B. In the example shown in FIG. 2 , 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. However, the external electrodes 35a, 35b, 35c, and 35d are not limited to those described above. Both the 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.

[0044] 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).

[0045] 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.

[0046] The lid member 40 forms an internal space 20 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 edge of the top wall 41 toward the base member 30, and a flange 43 extending outward from the tip of the mounting substrate 130. 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 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 is imparted to the lid member 40, reducing the amount of electromagnetic waves entering and leaving the internal space 20. 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).

[0047] The joint 50 joins the base member 30 and the lid member 40 and seals the internal space 20. 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).

[0048] Next, the configuration of the quartz crystal vibrating element 10 according to the first embodiment will be described with reference to Fig. 4 and Fig. 5. Fig. 4 is a cross-sectional view of the quartz crystal vibrating element 10 according to the first embodiment. Fig. 5 is a plan view of the quartz crystal vibrating element 10 according to the first embodiment. Note that, for simplicity of explanation, the first extraction electrode 15a, the second extraction electrode 15b, the first connection electrode 16a, and the second connection electrode 16b are not shown in Figs. 4 and 5.

[0049] The quartz crystal vibrating element 10 has a high acoustic velocity region 17 and a low acoustic velocity region 18 in the region overlapping with the first excitation electrode 14a in a planar view. The high acoustic velocity region 17 is a region of the excitation region where the quartz crystal blank 11 is excited by the first excitation electrode 14a and the second excitation electrode 14b, where the acoustic velocity is high. The low acoustic velocity region 18 is a region of the excitation region where the acoustic velocity is low. In other words, the acoustic velocity in the low acoustic velocity region 18 is lower than that in the high acoustic velocity region 17.

[0050] 4, the thickness of the crystal blank 11 in the high acoustic velocity region 17 is the same as the thickness of the crystal blank 11 in the low acoustic velocity region 18. In addition, the thickness of the second excitation electrode 14b in the high acoustic velocity region 17 is the same as the thickness of the second excitation electrode 14b in the low acoustic velocity region 18. In other words, the mass per unit area of ​​the crystal blank 11 and the second excitation electrode 14b in the high acoustic velocity region 17 (hereinafter simply referred to as "mass") is the same as the mass of the crystal blank 11 and the second excitation electrode 14b in the low acoustic velocity region 18.

[0051] A plurality of holes H are formed in the first excitation electrode 14a in the high acoustic velocity region 17. The holes H are through holes that penetrate the first excitation electrode 14a in the Y'-axis direction. However, the holes are not limited to through holes, and the holes may be grooves with bottoms that open in the Y'-axis direction. The plurality of holes H make the mass of the high acoustic velocity region 17 smaller than the mass of the low acoustic velocity region 18. Due to the mass difference caused by the plurality of holes H, the acoustic velocity in the high acoustic velocity region 17 is greater than the acoustic velocity in the low acoustic velocity region 18.

[0052] 5, in a plan view, the high acoustic velocity region 17 is provided in a region overlapping the central portion of the first excitation electrode 14a. The planar shape of the high acoustic velocity region 17 is a rectangle having long sides extending along the X-axis direction and short sides extending along the Z′-axis direction.

[0053] 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 a rectangle having a short side extending along the X-axis direction and a long side extending along the Z'-axis direction. The planar shape of the high sound velocity region may also be a square, polygon, circle, ellipse, or a combination thereof.

[0054] 5, in a plan view, the low acoustic velocity region 18 is provided in a region overlapping an end portion of the first excitation electrode 14 a. The low acoustic velocity region 18 is provided in the shape of a rectangular frame that is continuous in the circumferential direction and surrounds the center portion of the first excitation electrode 14 a.

[0055] The planar shape of the low acoustic velocity region is not limited to a rectangular frame shape that is continuous in the circumferential direction. The planar shape of the low acoustic velocity region may be a frame shape that extends along the contour of a polygonal shape, a circle, an ellipse, or a shape that is a combination of these. The low acoustic velocity region may also be a frame shape that is discontinuous in the circumferential direction. For example, the low acoustic velocity region may be a rail shape, a horseshoe shape, or the like.

[0056] The low sound velocity region 18 has a first low sound velocity region 18A, a second low sound velocity region 18B, a third low sound velocity region 18C, and a fourth low sound velocity region 18D.

[0057] The first low acoustic velocity region 18A is adjacent to the high acoustic velocity region 17 on the negative 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 positive 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 negative 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 positive Z'-axis side and extends along the X-axis direction. The end of the first low acoustic velocity region 18A on the negative Z'-axis side is connected to the end of the third low acoustic velocity region 18C on the negative X-axis side, and the end of the first low acoustic velocity region 18A on the positive Z'-axis side is connected to the end of the fourth low acoustic velocity region 18D on the negative X-axis side. 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 third low sound speed region 18C on the positive side of the X axis, and 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 fourth low sound speed region 18D on the positive side of the X axis.

[0058] In a plan view, the end of first low sound speed region 18A on the negative Z'-axis side overlaps with the end of third low sound speed region 18C on the negative X-axis side, and the end of first low sound speed region 18A on the positive Z'-axis side overlaps with the end of fourth low sound speed region 18D on the negative X-axis side. The end of second low sound speed region 18B on the negative Z'-axis side overlaps with the end of third low sound speed region 18C on the positive X-axis side, and the end of second low sound speed region 18B on the positive Z'-axis side overlaps with the end of fourth low sound speed region 18D on the positive X-axis side.

[0059] The configuration of the low acoustic velocity region is not limited to the above. The third and fourth low acoustic velocity regions may be omitted. That is, the high acoustic velocity region, the first and second low acoustic velocity regions may extend parallel to the Z'-axis direction and be provided in a strip shape from the end of the first excitation electrode on the negative side of the Z'-axis to the end on the positive side of the Z'-axis in a plan view. The first and second low acoustic velocity regions may be omitted. That is, the high acoustic velocity region, the third and fourth low acoustic velocity regions may extend parallel to the X-axis direction and be provided in a strip shape from the end of the first excitation electrode on the negative side of the X-axis to the end on the positive side of the X-axis in a plan view. The end of the first low acoustic velocity region on the negative 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 positive 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 negative 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 positive side of the Z' axis may be spaced apart from the fourth low sound velocity region.

[0060] As shown in Figures 4 and 5, the dimension of the crystal blank 11 along the Y'-axis direction is defined as thickness Tp. The dimension of the first excitation electrode 14a in the high acoustic velocity region 17 along the Y'-axis direction is defined as thickness Te1. The dimension of the second excitation electrode 14b along the Y'-axis direction is defined as thickness Te2. The dimension of the crystal blank 11 along the X-axis direction is defined as length Px, and the dimension of the crystal blank 11 along the Z'-axis direction is defined as length Pz. The dimension of the first excitation electrode 14a along the X-axis direction is defined as length Ex, and the dimension of the first excitation electrode 14a along the Z'-axis direction is defined as length Ez. The dimension of the first low acoustic velocity region 18A along the X-axis direction is defined as length Wx1. The dimension of the second low acoustic velocity region 18B along the X-axis direction is defined as length Wx2. The dimension of the third low acoustic velocity region 18C along the Z'-axis direction is defined as length Wz1. The dimension of the fourth low acoustic velocity region 18D along the Z'-axis direction is defined as length Wz2.

[0061] 5 , when the first low acoustic velocity region 18A has a pair of ends parallel to the Z′-axis direction in a plan view, the length Wx1 is determined by measuring the distance in the X-axis direction between the pair of ends parallel to the Z′-axis direction of the first low acoustic velocity region 18A. One of the pair of ends parallel to the Z′-axis direction of the first low acoustic velocity region 18A is the boundary between the high acoustic velocity region 17 and the first low acoustic velocity region 18A, and the other end is the outer edge of the first excitation electrode 14a on the negative side of the X-axis.

[0062] Similarly, the length Wx2 is determined by measuring the distance in the X-axis direction between a pair of ends of the second low acoustic velocity region 18B that are parallel to the Z'-axis direction. One of the pair of ends of the second low acoustic velocity region 18B that are parallel to the Z'-axis direction is the boundary between the high acoustic velocity region 17 and the second low acoustic velocity region 18B, and the other end is the outer edge of the first excitation electrode 14a on the positive side of the X-axis.

[0063] Similarly, the length Wz1 is determined by measuring the distance in the Z'-axis direction between a pair of ends of the third low acoustic velocity region 18C that are parallel to the X-axis direction. One of the pair of ends of the third low acoustic velocity region 18C that are parallel to the X-axis direction is the boundary between the high acoustic velocity region 17 and the third low acoustic velocity region 18C, and the other end is the outer edge of the first excitation electrode 14a on the negative side of the Z'-axis.

[0064] Similarly, the length Wz2 is determined by measuring the distance in the Z'-axis direction between a pair of ends of the fourth low acoustic velocity region 18D that are parallel to the X-axis direction. One of the pair of ends of the fourth low acoustic velocity region 18D that are parallel to the X-axis direction is the boundary between the high acoustic velocity region 17 and the fourth low acoustic velocity region 18D, and the other end is the outer edge of the first excitation electrode 14a on the positive side of the Z'-axis.

[0065] However, when the planar shape of the high acoustic velocity region 17 is polygonal, circular, elliptical, or a combination thereof, or when the planar shape of the first excitation electrode 14a is polygonal, circular, elliptical, or a combination thereof, and the first low acoustic velocity region 18A does not have a pair of ends parallel to the Z'-axis direction in a planar view, the length Wx1 can be determined by a method other than the above. For example, the length Wx1 may be determined by dividing the area of ​​the first low acoustic velocity region 18A in a planar view by the dimension of the first low acoustic velocity region 18A in the Z'-axis direction. Alternatively, the length Wx1 may be determined by measuring multiple dimensions of the first low acoustic velocity region 18A in the X-axis direction at multiple positions in the Z'-axis direction and calculating the average value of these multiple dimensions. When measuring multiple dimensions in the X-axis direction, the measurement positions for the dimensions in the X-axis direction may be determined, for example, at equal intervals in the Z'-axis direction or may be determined arbitrarily. The number of measurement positions for the dimensions in the X-axis direction may be determined arbitrarily. When calculating the average value of multiple dimensions in the X-axis direction, the average value of the remaining dimensions may be calculated by excluding at least one of the maximum and minimum values. The lengths Wx2, Wz1, and Wz2 may also be specified in the same manner as the length Wx1.

[0066] As described above, the thickness Tp of the crystal blank 11 is the same in the high acoustic velocity region 17 and the low acoustic velocity region 18. Similarly, the thickness Te2 of the second excitation electrode 14b is the same in the high acoustic velocity region 17 and the low acoustic velocity region 18. The thickness Te1 of the first excitation electrode 14a is the same in the high acoustic velocity region 17 and the low acoustic velocity region 18. In other words, the thickness Te1 of the first excitation electrode 14a in the low acoustic velocity region 18 is the same as the thickness Te1 of the first excitation electrode 14a excluding the multiple holes H in the high acoustic velocity region 17. The thickness Te1 is the minimum value, minimum value, or average value of the thickness of the first excitation electrode 14a. The thickness of the first excitation electrode 14a in the low acoustic velocity region 18 is the minimum value, minimum value, or average value of the thickness of the first excitation electrode 14a in the low acoustic velocity region 18. The thickness of the first excitation electrode 14a excluding the multiple holes H in the high acoustic velocity region 17 is the minimum, minimum, or average value of the thickness of the first excitation electrode 14a excluding the multiple holes H in the high acoustic velocity region 17. Similarly, the thickness Tp is the minimum, minimum, or average value of the thickness of the crystal blank 11, and the thickness Te2 is the minimum, minimum, or average value of the thickness of the second excitation electrode 14b.

[0067] The thickness of the first excitation electrode may be different between the high acoustic velocity region and the low acoustic velocity region. For example, the thickness of the first excitation electrode in the low acoustic velocity region may be greater than the thickness of the first excitation electrode in the high acoustic velocity region. In this case, the thickness of the first excitation electrode may change discontinuously in a stepwise manner at the boundary between the high acoustic velocity region and the low acoustic velocity region. That is, the first excitation electrode may have an inverted mesa structure. Furthermore, the first excitation electrode may have a bevel structure or a convex structure in which the thickness changes continuously at the boundary between the high acoustic velocity region and the low acoustic velocity region. The second excitation electrode is also not limited to a flat plate with a uniform thickness, and may have a mesa structure, a bevel structure, or a convex structure.

[0068] In addition, when the first excitation electrode in the low acoustic velocity region is provided with a sub-hole portion described below, the thickness of the first excitation electrode in the low acoustic velocity region is the minimum value, minimum value, or average value of the thickness of the first excitation electrode excluding the multiple sub-hole portions in the low acoustic velocity region.

[0069] 5, the length Wx1 of the first low sound velocity region 18A in the X-axis direction is approximately equal to the length Wx2 of the second low sound velocity region 18B in the X-axis direction (Wx1≈Wx2). The sum of the lengths Wx1 and Wx2 is smaller than the length Ex - (Wx1 + Wx2) of the high sound velocity region 17 in the X-axis direction (Wx1 + Wx2 < Ex - (Wx1 + Wx2)). In other words, the sum of the lengths Wx1 and Wx2 satisfies the relationship (Wx1 + Wx2) / Ex < 0.5. Preferably, the relationship (Wx1 + Wx2) / Ex ≦ 0.29.

[0070] Furthermore, the lengths Wx1 and Wx2 satisfy the relationships 2×Wx1<Ex−(Wx1+Wx2) and 2×Wx2<Ex−(Wx1+Wx2). Preferably, the relationships 0<Wx1 / Ex≦0.10 and 0<Wx2 / Ex≦0.10 hold. More preferably, the relationships 0<Wx1 / Ex≦0.07 and 0<Wx2 / Ex≦0.07 hold.

[0071] As long as the above relationship is established, it is not limited to the case where the relationship Wx1 = Wx2 is established, and the relationship Wx1 ≠ Wx2 may also be established. However, in order to achieve a good balance between mechanical strength, vibration distribution, etc., it is desirable that the relationship Wx1 = Wx2 is established.

[0072] Similarly, the length Wz1 of the third low sound velocity region 18C in the Z'-axis direction is approximately equal to the length Wz2 of the fourth low sound velocity region 18D in the Z'-axis direction (Wz1 ≒ Wz2). The sum of the lengths Wz1 and Wz2 is smaller than the length Ez - (Wz1 + Wz2) of the high sound velocity region 17 in the Z'-axis direction (Wz1 + Wz2 < Ez - (Wz1 + Wz2)). In other words, the sum of the lengths Wz1 and Wz2 satisfies the relationship (Wz1 + Wz2) / Ez < 0.5. Preferably, the relationship (Wx1 + Wx2) / Ex ≦ 0.29 holds.

[0073] Furthermore, the lengths Wz1 and Wz2 satisfy the relationships 2×Wz1<Ez−(Wz1+Wz2) and 2×Wz2<Ez−(Wz1+Wz2). Preferably, the relationships 0<Wz1 / Ez≦0.10 and 0<Wz2 / Ez≦0.10 hold. More preferably, the relationships 0<Wz1 / Ez≦0.08 and 0<Wz2 / Ez≦0.08 hold.

[0074] As long as the above relationship is established, it is not limited to the case where the relationship Wz1 = Wz2 is established, and the relationship Wz1 ≠ Wz2 may also be established. However, in order to achieve a good balance between mechanical strength, vibration distribution, etc., it is desirable that the relationship Wz1 = Wz2 is established.

[0075] The area of ​​the low sound velocity region 18 is defined as S18, and the area of ​​the high sound velocity region 17 is defined as S17. In the example shown in Fig. 5, the area S18 is calculated by the following formula: S18 = Ex x Ez - [{Ex - (Wx1 + Wx2)} x {Ez - (Wz1 + Wz2)}], and the area S17 is calculated by the following formula: S17 = {Ex - (Wx1 + Wx2)} x {Ez - (Wz1 + Wz2)}. The area S18 of the low sound velocity region 18 is smaller than the area S17 of the high sound velocity region 17 (S18 < S17). The area S18 of the low sound velocity region 18 is preferably smaller than 75% of the area S17 of the high sound velocity region 17 (S18 < S17 x 0.75), more preferably smaller than 50% (S18 < S17 x 0.50), and even more preferably smaller than 25% (S18 < S17 x 0.25).

[0076] 5, the length of the first low acoustic velocity region 18A in the Z'-axis direction and the length of the second low acoustic velocity region 18B in the Z'-axis direction are substantially equal to the length Ez of the first excitation electrode 14a in the Z'-axis direction. Also, the length of the third low acoustic velocity region 18C in the X-axis direction and the length of the fourth low acoustic velocity region 18D in the X-axis direction are substantially equal to the length Ex of the first excitation electrode 14a in the X-axis direction.

[0077] As long as the low acoustic velocity regions function sufficiently, the length of the first low acoustic velocity region in the Z'-axis direction and the length of the second low acoustic velocity region in the Z'-axis direction may be smaller than the length Ez. Furthermore, the length of the third low acoustic velocity region in the X-axis direction and the length of the fourth low acoustic velocity region in the X-axis direction may be smaller than the length Ex. That is, in a plan view, the first low acoustic velocity region and the second low acoustic velocity region may be spaced apart from at least one of the end of the first excitation electrode on the positive side of the Z'-axis and the end of the first excitation electrode on the negative side of the Z'-axis. Furthermore, the third low acoustic velocity region and the fourth low acoustic velocity region may be spaced apart from at least one of the end of the first excitation electrode on the positive side of the X-axis and the end of the first excitation electrode on the negative side of the X-axis. However, in order to prevent the first and second low acoustic velocity regions from disrupting the vibration mode and splitting the waveform, it is desirable that the length of the first low acoustic velocity region in the Z'-axis direction and the length of the second low acoustic velocity region in the Z'-axis direction are both 80% or more of the length Ez. It is also desirable that the length of the third low acoustic velocity region in the X-axis direction and the length of the fourth low acoustic velocity region in the X-axis direction are both 80% or more of the length Ex.

[0078] 5, the dimension of hole H in the Z'-axis direction is Hz, and the dimension of hole H in the X-axis direction is Hx. The planar shape of hole H is a square having a side extending along the Z'-axis direction and a side extending along the X-axis direction. In other words, Hz = Hx.

[0079] The planar shape of the hole H is not limited to a square shape having sides extending in the X-axis direction and the Z'-axis direction. For example, the planar shape of the hole H may be a square shape having sides extending in a direction intersecting the X-axis direction and the Z'-axis direction, or a rectangular shape where Hz < Hx or Hx < Hz. As shown in FIG. 47, the planar shape of the hole H may be a circle. As shown in FIG. 48, the planar shape of the hole H may be an ellipse. As shown in FIG. 49, the planar shape of the hole H may be a square shape with arc-shaped corners. Thus, the planar shape of the hole H may be a polygon, a circle, an ellipse, or a combination thereof.

[0080] As shown in Figure 5, the multiple holes H are arranged in a matrix in the X-axis direction and the X'-axis direction. The pitch 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 pitch 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.

[0081] The pitch 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. As shown in Figures 46 to 49, the multiple holes H may be arranged in a staggered pattern. As shown in Figure 50, the multiple holes H may be arranged randomly.

[0082] Next, the simulation results of an example based on the first embodiment will be described with reference to Figures 6 to 20. Figures 15 to 20 are diagrams showing the simulation results based on a second comparative example.

[0083] 6 to 9 are diagrams showing simulation results based on the embodiment. FIG. 6 is a graph showing frequency distribution in the embodiment. The horizontal axis of FIG. 6 represents frequency (Frequency [Hz]), and the vertical axis of FIG. 6 represents impedance (Impedance [ohm]). FIG. 7 shows the vibration distribution of the main S0 mode in the embodiment. FIG. 8 shows the vibration distribution of the S1Z mode, which is a type of inharmonic spurious, in the embodiment. FIG. 9 shows the vibration distribution of the S1X mode, which is a type of inharmonic spurious, in the embodiment.

[0084] FIG. 10 is a cross-sectional view of a quartz crystal vibrating element 70 according to a first comparative example. The first excitation electrode 74a of the quartz crystal vibrating element 70 is flat, similar to the second excitation electrode 14b. The acoustic velocity is substantially uniform throughout the area overlapping the first excitation electrode 74a in a planar view. In other words, the quartz crystal vibrating element 70 does not have high or low acoustic velocity regions. FIGS. 11 to 14 are diagrams showing simulation results based on the first comparative example. FIG. 11 is a graph showing frequency distribution in the first comparative example. The horizontal and vertical axes of the graph in FIG. 11 are the same as those of the graph in FIG. 6 . FIG. 12 shows the vibration distribution of the main S0 mode in the first comparative example. FIG. 13 shows the vibration distribution of the S1Z mode, which is a type of inharmonic spurious, in the first comparative example. FIG. 14 shows the vibration distribution of the S1X mode, which is a type of inharmonic spurious, in the first comparative example.

[0085] FIG. 15 is a cross-sectional view of a quartz crystal vibrating element 80 according to a second comparative example. The first excitation electrode 84a of the quartz crystal vibrating element 80 has an inverted mesa structure, and the thickness of the first excitation electrode 84a in the low acoustic velocity region 88 is greater than the thickness of the first excitation electrode 84a in the high acoustic velocity region 87. The shape of the first excitation electrode 84a in the low acoustic velocity region 88 is a flat plate with a uniform thickness, and the shape of the first excitation electrode 84a in the low acoustic velocity region 88 is a flat plate with a uniform thickness. FIGS. 16 to 20 are diagrams showing simulation results based on the second comparative example. FIG. 16 is a graph showing frequency distribution in the second comparative example. The horizontal and vertical axes of the graph in FIG. 16 are the same as the horizontal and vertical axes of the graph in FIG. 6. FIG. 17 shows the vibration distribution of the main S0 mode in the second comparative example. FIG. 18 shows the vibration distribution of the S1Z mode, a type of inharmonic spurious, in the second comparative example. Fig. 19 shows the vibration distribution of the S1X mode, which is a type of inharmonic spurious, in the first comparative example. Fig. 20 is a graph showing the distribution of the electromechanical coupling coefficient k (hereinafter also simply referred to as "k_S0") in the S0 mode of the second comparative example, with the horizontal axis representing Wx / Ex and the vertical axis representing Wz / Ez. Note that, hereinafter, like k_S0, the electromechanical coupling coefficient k in the S1Z mode will also be simply referred to as "k_S1Z," and the electromechanical coupling coefficient k in the S1X mode will also be simply referred to as "k_S1X."

[0086] The configurations of the example, first comparative example, and second comparative example are as follows: (Example) Tp = 1.52 μm Te1 = Te2 = 0.08 μm Px = Pz = 140 μm Ex = 100 μm Ez = 80 μm Wx1 = Wx2 = Wx = 6.5 μm Wz1 = Wz2 = Wz = 5.5 μm PHx = PHz = 3 μm Hx = Hz = 2 μm Number of H: 30 × 24 = 720 (First comparative example) Tp = 1.52 μm Te1 = Te2 = 0.08 μm Px = Pz = 140 μm Ex = 100 μm Ez = 80 μm Wx1 = Wx2 = Wx = 0 μm Wz1 = Wz2 = Wz = 0 μm (Second comparative example) Tp = 1.52 μm Thickness of the first excitation electrode in the high sound velocity region = 0.08 μm Thickness of the first excitation electrode in the low sound velocity region = 0.08 + 0.032 μm Te2 = 0.08 μm Px = Pz = 140 μm Ex = 100 μm Ez = 80 μm Wx1 = Wx2 = Wx = 6.5 μm Wz1 = Wz2 = Wz = 5.5 μm

[0087] As shown in Fig. 11, the frequency of the S0 mode in the first comparative example is approximately 965 MHz. As shown in Fig. 6, the frequency of the S0 mode in the example is approximately 988 MHz. The reason why the resonant frequency in the example is higher than the resonant frequency in the comparative example is because the mass of the first excitation electrode is reduced by forming multiple holes in the first excitation electrode in the high acoustic velocity region. In other words, compared to the second comparative example in which the mass of the low acoustic velocity region is increased to achieve a difference in acoustic velocity between the high acoustic velocity region and the low acoustic velocity region, the example in which the mass of the high acoustic velocity region is reduced to achieve a difference in acoustic velocity between the high acoustic velocity region and the low acoustic velocity region is advantageous in increasing the frequency of the quartz crystal vibrating element.

[0088] As shown in Fig. 12, the S-mode vibration in the first comparative example increases from the end to the center of the first excitation electrode. As shown in Fig. 17, the S0-mode vibration in the second comparative example spreads across the entire first excitation electrode compared to the S0-mode amplitude in the first comparative example. As shown in Fig. 7, the S0-mode vibration in the example is larger across the entire first excitation electrode compared to the second comparative example. In the first comparative example, k_S0 = 6.87%, in the second comparative example, k_S0 = 7.99%, and in the example, k_S0 = 8.46%. The electromechanical coupling coefficient of the S0 mode in the second comparative example is larger than that of the first comparative example, but the electromechanical coupling coefficient of the S0 mode in the example is even larger.

[0089] As shown in FIG. 13 , in the S1Z mode of the first comparative example, anti-phase vibrations are aligned in the Z′-axis direction. As shown in FIG. 18 , in the S1Z mode of the second comparative example, some of the anti-phase vibrations cancel each other out. As shown in FIG. 8 , in the S1Z mode of the example, the anti-phase vibrations are further canceled out, reducing vibrations across the entire first excitation electrode. In the first comparative example, k_S1Z = 2.44%, in the second comparative example, k_S1Z = 0.47%, and in the example, k_S1Z = 0.00%. The electromechanical coupling coefficient of the S1Z mode of the second comparative example is smaller than that of the first comparative example, but the electromechanical coupling coefficient of the S1Z mode of the example is even smaller.

[0090] As shown in FIG. 14 , in the S1X mode of the first comparative example, anti-phase vibrations are aligned in the X-axis direction. As shown in FIG. 19 , in the S1X mode of the second comparative example, some of the anti-phase vibrations cancel each other out. As shown in FIG. 9 , in the S1X mode of the example, the anti-phase vibrations are further canceled out, reducing vibrations across the entire first excitation electrode. In the first comparative example, k_S1X = 2.17%, in the second comparative example, k_S1X = 1.32%, and in the example, k_S1X = 0.46%. The electromechanical coupling coefficient of the S1X mode of the second comparative example is smaller than that of the first comparative example, but the electromechanical coupling coefficient of the S1X mode of the example is even smaller.

[0091] 20 , in the second comparative example, k_S0 peaks when Wx / Ex and Wz / Ez, which are the ratios of the width of the low acoustic velocity region 88 to the width of the first excitation electrode 84a, are in the ranges of 0<Wx / Ex≦0.10 and 0<Wz / Ez≦0.10. That is, in a configuration in which the width of the low acoustic velocity region 88 is smaller than the width of the high acoustic velocity region 87, there are Wx / Ex and Wz / Ez at which k_S0 peaks. Such a tendency of the electromechanical coupling coefficient k_S0 of the S0 mode with respect to the ratios Wx / Ex and Wz / Ez of the width of the low acoustic velocity region is also confirmed in the examples.

[0092] Next, the influence of the dimensions of the low acoustic velocity region 18 on the electromechanical coupling coefficient will be described with reference to Fig. 21 to Fig. 26. Fig. 21 to Fig. 26 are graphs showing the influence of the dimensions of the low acoustic velocity region 18 in the first embodiment.

[0093] 21 to 23 are graphs showing the change in the electromechanical coupling coefficient when Wx1 / Ex = Wx2 / Ex = Wx / Ex are variables and Wz1 / Ez = Wz2 / Ez = Wz / Ez = 0.070 (constant) in the above-mentioned embodiment. The horizontal axis of the graphs in Fig. 21 to 23 represents Wx / Ex. The vertical axis of the graph in Fig. 21 represents k_S0, the vertical axis of the graph in Fig. 22 represents k_S1X, and the vertical axis of the graph in Fig. 23 represents k_S1Z.

[0094] The plot for Wx / Ex = 0 in the graph of Figure 21 is not for Wx / Ex = 0 and Wz / Ez = 0.070, but for k_S0 = 6.87% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above). Although not shown in Figure 22, the comparison for k_S1X is for k_S1X = 2.17% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above). Furthermore, although not shown in Figure 23, the comparison for k_S1Z is for k_S1Z = 2.44% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above).

[0095] As shown in FIG. 21 , when the relationship 0<Wx / Ex≦0.070 holds, k_S0 increases, and k_S0 becomes 6.87%<k_S0. To further increase k_S0, it is desirable that the relationship 0.050≦Wx / Ex≦0.070 holds. As shown in FIG. 22 , when the relationship 0.040≦Wx / Ex≦0.075 holds, k_S1X decreases, and k_S1X<2.17% holds. To further decrease k_S1X, it is desirable that the relationship 0.050≦Wx / Ex≦0.074 holds, and it is even more desirable that the relationship 0.060≦Wx / Ex≦0.072 holds. As shown in FIG. 23 , when the relationship 0<Wx / Ex≦0.070 holds, k_S1Z decreases, and k_S1Z<2.44% holds. To further reduce k_S1Z, it is desirable that the relationship 0.030≦Wx / Ex≦0.068 be satisfied, and it is even more desirable that the relationship 0.050≦Wx / Ex≦0.066 be satisfied.

[0096] Even when the relationship Wx1≠Wx2 holds, k_S0 increases if the relationships 0<Wx1 / Ex≦0.07 and 0<Wx2 / Ex≦0.07 hold. If the relationships 0.050≦Wx1 / Ex≦0.070 and 0.050≦Wx2 / Ex≦0.070 hold, k_S0 further increases. Similarly, even when the relationship Wx1≠Wx2 holds, k_S1X decreases if the relationships 0.040≦Wx1 / Ex≦0.075 and 0.040≦Wx2 / Ex≦0.075 hold. If the relationships 0.050≦Wx1 / Ex≦0.074 and 0.050≦Wx2 / Ex≦0.074 hold, k_S1X further decreases. If the relationships 0.060≦Wx1 / Ex≦0.072 and 0.060≦Wx2 / Ex≦0.072 hold, k_S1X will further decrease. Similarly, even if the relationship Wx1≠Wx2 holds, if the relationships 0<Wx1 / Ex≦0.070 and 0<Wx2 / Ex≦0.070 hold, k_S1Z will further decrease. If the relationships 0.30≦Wx1 / Ex≦0.068 and 0.30≦Wx2 / Ex≦0.068 hold, k_S1Z will further decrease. If the relationships 0.50≦Wx1 / Ex≦0.066 and 0.50≦Wx2 / Ex≦0.066 hold, k_S1Z will further decrease.

[0097] When the relationship Wx / Ex = 0.062 ± 0.006 holds, k_S0 further increases, and k_S1X and k_S1Z further decrease. In particular, k_S0 is maximized when the relationship Wx / Ex = 0.062 holds, k_S1X is minimized when the relationship Wx / Ex = 0.066 holds, and k_S1Z is minimized when the relationship Wx / Ex = 0.062 holds.

[0098] Even if the relationship Wx1≠Wx2 holds, if the relationships Wx1 / Ex=0.062±0.006 and Wx2 / Ex=0.062±0.006 hold, k_S0 will further increase and k_S1X and k_S1Z will further decrease.

[0099] 24 to 26 are graphs showing changes in the electromechanical coupling coefficient when Wx1 / Ex = Wx2 / Ex = Wx / Ex = 0.062 (constant) and Wz1 / Ez = Wz2 / Ez = Wz / Ez are variables. The horizontal axes of the graphs in Fig. 24 to 26 represent Wz / Ez. The vertical axes of the graph in Fig. 24 represent k_S0, the vertical axes of the graph in Fig. 25 represent k_S1X, and the vertical axes of the graph in Fig. 26 represent k_S1Z.

[0100] The plot for Wz / Ez = 0 in the graph of Figure 24 is a comparison of k_S0 = 6.87% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above), rather than when Wx / Ex = 0.062 and Wz / Ez = 0. Note that, although not shown in Figure 25, the comparison for k_S1X is k_S1X = 2.17% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above). Furthermore, although not shown in Figure 26, the comparison for k_S1Z is k_S1Z = 2.44% when Wx / Ex = 0 and Wx / Ex = 0 (the first comparative example described above).

[0101] As shown in FIG. 24, when the relationship 0<Wz / Ez≦0.080 holds, k_S0 increases, and k_S0 becomes 6.87%<k_S0. To further increase k_S0, it is desirable that the relationship 0.060≦Wz / Ez≦0.075 holds. As shown in FIG. 25, when the relationship 0<Wz / Ez≦0.082 holds, k_S1X decreases, and k_S1X becomes <2.17%. To further decrease k_S1X, it is desirable that the relationship 0.035≦Wz / Ez≦0.080 holds, and it is even more desirable that the relationship 0.065≦Wz / Ez≦0.080 holds. As shown in FIG. 26, when the relationship 0.04≦Wz / Ez≦0.076 holds, k_S1Z decreases, and k_S1Z becomes <2.44%. To further reduce k_S1Z, it is desirable that the relationship 0.052≦Wz / Ez≦0.074 be satisfied, and it is even more desirable that the relationship 0.062≦Wz / Ez≦0.072 be satisfied.

[0102] Even when the relationship Wz1≠Wz2 holds, k_S0 increases if the relationships 0<Wz1 / Ez≦0.080 and 0<Wz2 / Ez≦0.080 hold. If the relationships 0.060≦Wz1 / Ez≦0.075 and 0.060≦Wz2 / Ez≦0.075 hold, k_S0 further increases. Similarly, even when the relationship Wz1≠Wz2 holds, k_S1X decreases if the relationships 0<Wz1 / Ez≦0.082 and 0<Wz2 / Ez≦0.082 hold. If the relationships 0.035≦Wz1 / Ez≦0.080 and 0.0352≦Wz / Ez≦0.080 hold, k_S1X further decreases. If the relationships 0.065≦Wz1 / Ez≦0.080 and 0.065≦Wz2 / Ez≦0.080 hold, k_S1X will further decrease. Similarly, even if the relationship Wz1 ≠ Wz2 holds, if the relationships 0.04≦Wz1 / Ez≦0.076 and 0.04≦Wz2 / Ez≦0.076 hold, k_S1Z will further decrease. If the relationships 0.052≦Wz1 / Ez≦0.074 and 0.052≦Wz2 / Ez≦0.074 hold, k_S1Z will further decrease. If the relationships 0.062≦Wz1 / Ez≦0.072 and 0.062≦Wz2 / Ez≦0.072 hold, k_S1Z will further decrease.

[0103] When the relationship Wz / Ez = 0.070 ± 0.006 holds, k_S0 further increases, and k_S1X and k_S1Z further decrease. In particular, k_S0 is maximized when the relationship Wz / Ez = 0.072 holds, k_S1X is minimized when the relationship Wz / Ez = 0.079 holds, and k_S1Z is minimized when the relationship Wz / Ez = 0.069 holds.

[0104] Even when the relationship Wz1≠Wz2 holds, if the relationships Wz1 / Ez=0.070±0.006 and Wz2 / Ez=0.070±0.006 hold, k_S0 will further increase and k_S1X and k_S1Z will further decrease.

[0105] Next, the influence of the dimensions of the hole H on the electromechanical coupling coefficient will be described with reference to FIGS. 27 to 29 . FIGS. 27 to 29 are graphs showing the influence of the planar dimensions of the hole H in the first embodiment. FIGS. 27 to 29 are graphs showing the change in the electromechanical coupling coefficient when Hx / Tp = Hz / Tp = Hr / Tp is used as a variable in the above-described example. Hx / Tp is determined by fixing Tp and varying Hx. The horizontal axes of FIGS. 27 to 29 represent Hx / Tp (= Hr / Tp). The vertical axis of the graph in FIG. 27 represents k_S0, the vertical axis of the graph in FIG. 28 represents k_S1X, and the vertical axis of the graph in FIG. 29 represents k_S1Z. Note that Hr is the length of one side of the hole H when the shape is square. When the shape of the hole H is other than square, it is the length of one side when the hole H is converted to a square while maintaining a constant area.

[0106] When the relationship 0<Hr / Tp≦2.0 is satisfied, the capacitance reduction rate due to the influence of the hole H is suppressed to 1% or less. Therefore, the first excitation electrode 14a in the high acoustic velocity region 17 can function sufficiently as an excitation electrode. Preferably, the relationship 0<Hr / Tp≦1.5 is satisfied, and more preferably, the relationship 0<Hr / Tp≦1.0 is satisfied. If 0<Hr / Tp≦1.5, the capacitance reduction rate can be suppressed to 0.5% or less. If 0<Hr / Tp≦1.0, the capacitance reduction rate can be suppressed to 0.1% or less. Note that, in order to form the hole H with sufficient processing precision, it is preferable that 0.1≦Hr / Tp, and it is even more preferable that 0.5≦Hr / Tp.

[0107] As shown in FIG. 27 , when the relationship 0<Hx / Tp≦1.45 holds, k_S0 is greater than k_S0=6.87% when Hx / Tp=0. That is, 6.87%<k_S0. To further increase k_S0, it is desirable that the relationship 1.00≦Hx / Tp≦1.43 holds, and it is even more desirable that the relationship 1.20≦Hx / Tp≦1.41 holds. As shown in FIG. 28 , when the relationship 0.8≦Hx / Tp≦1.45 holds, k_S1X is smaller than k_S1X=2.17% when Hx / Tp=0. That is, k_S1X<2.17%. To further reduce k_S1X, it is desirable that the relationship 1.10≦Hx / Tp≦1.40 be satisfied, and it is even more desirable that the relationship 1.20≦Hx / Tp≦1.38 be satisfied. As shown in FIG. 29 , when the relationship 0<Hx / Tp≦1.45 is satisfied, k_S1Z becomes smaller than k_S1Z=2.44% when Hx / Tp=0. In other words, k_S1Z<2.44%. To further reduce k_S1Z, it is desirable that the relationship 1.00≦Hx / Tp≦1.42 be satisfied, and it is even more desirable that the relationship 1.20≦Hx / Tp≦1.40 be satisfied.

[0108] When the relationship Hx / Tp = 1.3 ± 0.1 holds, k_S0 further increases, and k_S1X and k_S1Z further decrease. In particular, k_S0 is maximized when the relationship Hx / Tp = 1.3 holds, and k_S1X and k_S1Z are minimized when the relationship Hx / Tp = 1.3 holds.

[0109] Next, the influence of the aperture ratio Har of the hole H on the electromechanical coupling coefficient will be described with reference to Fig. 30 to Fig. 32. Fig. 30 to Fig. 32 are graphs showing the influence of the aperture ratio Har of the hole H in the first embodiment. Fig. 30 to Fig. 32 are graphs showing the change in the electromechanical coupling coefficient when Hx ≠ Hz is set and the aperture ratio Har expressed by the following formula is used as a variable in the above-mentioned example. Har = (Hx / PHx) × (Hz / PHz) Hx = 1.6 μm, 1.8 μm, 2.0 μm, 2.2 μm, and 2.4 μm

[0110] The horizontal axis of the graphs in Figures 30 to 32 represents Har. The vertical axis of the graph in Figure 30 represents k_S0, the vertical axis of the graph in Figure 31 represents k_S1X, and the vertical axis of the graph in Figure 32 represents k_S1Z. The plots in the graph in Figure 30 show that Har is changed by changing Hz at Hx = 1.6 μm, 1.8 μm, 2.0 μm, 2.2 μm, and 2.4 μm. The plots in the graphs in Figures 31 and 32 show that Har is changed by changing Hz at Hx = 1.6 μm, 2.0 μm, and 2.4 μm.

[0111] As shown in FIG. 30 , when the relationship 0<Har≦0.50 holds, k_S0 increases, and k_S0 becomes 6.87%<k_S0. To further increase k_S0, it is desirable that the relationship 0.10≦Har≦0.48 holds, and it is even more desirable that the relationship 0.28≦Har≦0.46 holds, and it is even more desirable that the relationship 0.28≦Har≦0.46 holds. As shown in FIG. 31 , when the relationship 0<Har≦0.55 holds, k_S1X decreases, and k_S1X becomes <2.17%. To further decrease k_S1X, it is desirable that the relationship 0.10≦Har≦0.53 holds, and it is even more desirable that the relationship 0.32≦Har≦0.53 holds, and it is even more desirable that the relationship 0.36≦Har≦0.50 holds. 32, when the relationship 0<Har≦0.50 holds, k_S1Z decreases, and k_S1Z<2.44%. To further reduce k_S1Z, it is desirable that the relationship 0.10≦Har≦0.46 holds, it is even more desirable that the relationship 0.33≦Har≦0.46 holds, and it is even more desirable that the relationship 0.36≦Har≦0.43 holds.

[0112] When the relationship Har=0.40±0.06 holds, k_S0 further increases, and k_S1X and k_S1Z further decrease. In particular, k_S0 is maximum at Har=0.42, k_S1X is minimum at Har=0.42, and k_S1Z is minimum at Har=0.40.

[0113] As described above, according to this embodiment, the dimensions Wx1+Wx2 in the X-axis direction of the first low sound speed region 18A and the second low sound speed region 18B, which are adjacent to the high sound speed region 17 in the X-axis direction within the low sound speed region 18, are smaller than the dimension Ex-(Wx1+Wx2) in the X-axis direction of the high sound speed region 17. Furthermore, the dimensions Wz1+Wz2 in the Z'-axis direction of the third low sound speed region 18C and the fourth low sound speed region 18D, which are adjacent to the high sound speed region 17 in the Z'-axis direction within the low sound speed region 18, are smaller than the dimension Ez-(Wz1+Wz2) in the Z'-axis direction of the high sound speed region 17. Furthermore, in a plan view, the area S18 of the low sound speed region 18 is smaller than the area S17 of the high sound speed region 17.

[0114] This reduces the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and increases the electromechanical coupling coefficient k_S0 of the main mode, thereby providing a quartz crystal vibrating element 10 that can improve the electromechanical coupling coefficient.

[0115] Furthermore, the high acoustic velocity region 17 and the low acoustic velocity region 18 can be formed by the single-layer first excitation electrode 14a. In a configuration in which a first metal film of uniform thickness is provided in the high acoustic velocity region and the low acoustic velocity region, and then a second metal film is provided to form the low acoustic velocity region, or in a configuration in which an insulating mass-addition film is provided to form the low acoustic velocity region, k_S0 may decrease due to manufacturing variations caused by misalignment of the second metal film or the mass-addition film. In contrast, according to this embodiment, the first excitation electrode 14a can be provided with higher manufacturing precision than a multi-layer first excitation electrode. Furthermore, the impact of misalignment of the multiple holes H on k_S0 is smaller than the impact of misalignment of the second metal film or the mass-addition film on k_S0. Therefore, a quartz crystal vibrating element 10 that is less susceptible to manufacturing variations can be provided.

[0116] Furthermore, by forming the plurality of holes H, the mass of the first excitation electrode 14 a can be reduced compared to when the plurality of holes H is not formed. Therefore, the resonant frequency of the quartz-crystal vibrating element 10 can be increased by the amount of the reduction in the mass of the first excitation electrode 14 a.

[0117] As one aspect of this embodiment, the relationships 0<Wx1 / Ex≦0.07, 0<Wx2 / Ex≦0.07, 0<Wz1 / Ez≦0.08, and 0<Wz2 / Ez≦0.08 hold.

[0118] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0119] In one aspect of this embodiment, the relationships Wx1 / Ex = 0.062 ± 0.006, Wx2 / Ex = 0.062 ± 0.006, Wz1 / Ez = 0.070 ± 0.006, and Wz2 / Ez = 0.070 ± 0.006 hold.

[0120] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0121] In one aspect of this embodiment, the relationship 0<Hr / Tp≦2.0 holds.

[0122] This makes it possible to suppress the rate of decrease in capacitance due to the influence of the hole H to 1% or less, and allows the first excitation electrode 14a in the high acoustic velocity region 17 to function satisfactorily as an excitation electrode.

[0123] In one aspect of this embodiment, the relationship 0<Hr / Tp≦1.45 holds.

[0124] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0125] In one aspect of this embodiment, the relationship Hr / Tp=1.3±0.1 holds.

[0126] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0127] In one aspect of this embodiment, the relationship 0<Har≦0.5 holds.

[0128] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0129] In one aspect of this embodiment, the relationship Har=0.4±0.06 holds.

[0130] This makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0131] 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.

[0132] Second Embodiment Next, the configuration of a quartz crystal vibrating element 210 according to a second embodiment will be described with reference to Fig. 33. Fig. 33 is a cross-sectional view of the quartz crystal vibrating element 210 according to the second embodiment.

[0133] As shown in FIG. 33 , the quartz crystal vibrating element 210 has a high acoustic velocity region 217, a first low acoustic velocity region 218A, and a second low acoustic velocity region 218B. In a plan view, the high acoustic velocity region 217 is located in the center of the first excitation electrode 214a in the X-axis direction and is provided in a strip-shaped region extending in the Z'-axis direction. The first low acoustic velocity region 218A is adjacent to the high acoustic velocity region 217 on the negative X-axis side and is provided in a strip-shaped region extending in the Z'-axis direction. The second low acoustic velocity region 218B is adjacent to the high acoustic velocity region 217 on the positive X-axis side and is provided in a strip-shaped region extending in the Z'-axis direction. In a plan view, the high acoustic velocity region 217, the first low acoustic velocity region 218A, and the second low acoustic velocity region 218B are provided across the entire width of the first excitation electrode 214a, from the end on the negative Z'-axis side to the end on the positive Z'-axis side.

[0134] Next, the influence of the dimensions of the low acoustic velocity region 218 on the electromechanical coupling coefficient will be described with reference to Fig. 34 to Fig. 36. Fig. 34 to Fig. 36 are graphs showing the influence of the dimensions of the low acoustic velocity region 218 in the second embodiment.

[0135] 34 to 36 are graphs showing changes in the electromechanical coupling coefficient when Wx1 / Ex = Wx2 / Ex = Wx / Ex are variables and Wz1 / Ez = Wz2 / Ez = Wz / Ez = 0 (constant) in an example according to the first embodiment. The horizontal axes of the graphs in Fig. 34 to 36 represent Wx / Ex. The vertical axes of the graph in Fig. 34 represent k_S0, the vertical axes of the graph in Fig. 35 represent k_S1X, and the vertical axes of the graph in Fig. 36 represent k_S1Z.

[0136] As shown in Figure 34, when the relationship 0 < Wx / Ex ≤ 0.074 holds, k_S0 increases, and k_S0 becomes 6.87% < k_S0. To further increase k_S0, it is desirable that the relationship 0.040 ≤ Wx / Ex ≤ 0.074 holds. As shown in Figure 35, when the relationship 0 < Wx / Ex ≤ 0.076 holds, k_S1X decreases, and k_S1X becomes < 2.17%. To further decrease k_S1X, it is desirable that the relationship 0.052 ≤ Wx / Ex ≤ 0.076 holds, and it is even more desirable that the relationship 0.064 ≤ Wx / Ex ≤ 0.073 holds. As shown in FIG. 36, when the relationship 0.030≦Wx / Ex≦0.060 or 0.070≦Wx / Ex≦0.080 holds, k_S1Z decreases and becomes k_S1Z<2.44%.

[0137] Even when the relationship Wx1≠Wx2 holds, k_S0 increases if the relationships 0<Wx1 / Ex≦0.074 and 0<Wx2 / Ex≦0.074 hold. If the relationships 0.04≦Wx1 / Ex≦0.074 and 0.04≦Wx2 / Ex≦0.074 hold, k_S0 further increases. Similarly, even when the relationship Wx1≠Wx2 holds, k_S1X decreases if the relationships 0.00<Wx1 / Ex≦0.076 and 0.00<Wx2 / Ex≦0.076 hold. If the relationships 0.052≦Wx1 / Ex≦0.076 and 0.052≦Wx2 / Ex≦0.076 hold, k_S1X further decreases. If the relationships 0.064≦Wx1 / Ex≦0.073 and 0.064≦Wx2 / Ex≦0.073 are satisfied, k_S1X will be further reduced. Similarly, even when the relationship Wx1 ≠ Wx2 holds, k_S1Z decreases when the relationship 0.030≦Wx1 / Ex≦0.060 and 0.030≦Wx2 / Ex≦0.060 holds, when the relationship 0.030≦Wx1 / Ex≦0.060 and 0.070≦Wx2 / Ex≦0.080 holds, when the relationship 0.070≦Wx1 / Ex≦0.080 and 0.030≦Wx2 / Ex≦0.060 holds, or when the relationship 0.070≦Wx1 / Ex≦0.080 and 0.070≦Wx2 / Ex≦0.080 holds.

[0138] When the relationship Wx / Ex = 0.066 ± 0.006 holds, k_S0 further increases and k_S1X further decreases. In particular, k_S0 is maximum when Wx / Ex = 0.068, and k_S1X is minimum when Wx / Ex = 0.07.

[0139] Even if the relationship Wx1≠Wx2 holds, if the relationships Wx1 / Ex=0.066±0.006 and Wx2 / Ex=0.066±0.006 hold, k_S0 will further increase and k_S1X and k_S1Z will further decrease.

[0140] As described above, according to this embodiment, the relationships Wz1=Wz2=0, 0<Wx1 / Ex≦0.074, and 0<Wx2 / Ex≦0.074 hold true.

[0141] This makes it possible to decrease the electromechanical coupling coefficient k_S1X of the inharmonic spurious mode and increase the electromechanical coupling coefficient k_S0 of the main mode.

[0142] In one aspect of this embodiment, the relationships Wx1 / Ex = 0.066 ± 0.006 and Wx2 / Ex = 0.066 ± 0.006 hold.

[0143] This makes it possible to further reduce the electromechanical coupling coefficient k_S1X of the inharmonic spurious mode and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0144] Third Embodiment Next, the configuration of a quartz crystal vibrating element 310 according to a third embodiment will be described with reference to Fig. 37. Fig. 37 is a cross-sectional view of the quartz crystal vibrating element 310 according to the third embodiment.

[0145] As shown in FIG. 37 , the quartz-crystal vibrating element 310 has a high acoustic velocity region 317, a third low acoustic velocity region 318C, and a fourth low acoustic velocity region 318D. In a plan view, the high acoustic velocity region 317 is located in the center of the first excitation electrode 314a in the Z′-axis direction and is provided in a strip-shaped region extending in the X-axis direction. The third low acoustic velocity region 318C is adjacent to the high acoustic velocity region 317 on the negative Z′-axis side and is provided in a strip-shaped region extending in the X-axis direction. The fourth low acoustic velocity region 318D is adjacent to the high acoustic velocity region 317 on the positive X-axis side and is provided in a strip-shaped region extending in the X-axis direction. In a plan view, the high acoustic velocity region 317, the third low acoustic velocity region 318C, and the fourth low acoustic velocity region 318D are provided across the entire width of the first excitation electrode 314a, from the end on the negative X-axis side to the end on the positive X-axis side.

[0146] Next, the influence of the dimensions of the low acoustic velocity region 318 on the electromechanical coupling coefficient will be described with reference to Fig. 38 to Fig. 40. Fig. 38 to Fig. 40 are graphs showing the influence of the dimensions of the low acoustic velocity region 318 in the third embodiment.

[0147] 38 to 40 are graphs showing changes in the electromechanical coupling coefficient in an example according to the first embodiment, where Wx1 / Ex = Wx2 / Ex = Wx / Ex = 0 (constant) and Wz1 / Ez = Wz2 / Ez = Wz / Ez are variables. The horizontal axes of the graphs in Fig. 38 to 40 represent Wz / Ez. The vertical axes of the graph in Fig. 38 represent k_S0, the vertical axes of the graph in Fig. 39 represent k_S1X, and the vertical axes of the graph in Fig. 40 represent k_S1Z.

[0148] As shown in FIG. 38, when the relationship 0<Wz / Ez≦0.082 holds, k_S0 increases, and k_S0 becomes 6.87%<k_S0. To further increase k_S0, it is desirable to hold the relationship 0.050≦Wz / Ez≦0.082. As shown in FIG. 39, when the relationship 0<Wz / Ez≦0.050 or 0.078≦Wz / Ez≦0.82 holds, k_S1X decreases, and k_S1X<2.17%. As shown in FIG. 40, when the relationship 0.040≦Wz / Ez≦0.082 holds, k_S1Z decreases, and k_S1Z<2.44%. To further reduce k_S1Z, it is desirable that the relationship 0.06≦Wz / Ez≦0.08 be satisfied, and it is even more desirable that the relationship 0.068≦Wz / Ez≦0.078 be satisfied.

[0149] Even when the relationship Wz1≠Wz2 holds, k_S0 increases if the relationships 0<Wz1 / Ez≦0.082 and 0<Wz2 / Ez≦0.082 hold. If the relationships 0.050≦Wz1 / Ez≦0.082 and 0.050≦Wz2 / Ez≦0.082 hold, k_S0 increases further. Similarly, even when the relationship Wz1≠Wz2 holds, k_S1X decreases when the relationship 0<Wz1 / Ez≦0.050 and 0<Wz2 / Ez≦0.050 holds, when the relationship 0<Wz1 / Ez≦0.050 and 0.078≦Wz2 / Ez≦0.82 holds, when the relationship 0.078≦Wz1 / Ez≦0.82 and 0<Wz2 / Ez≦0.050 holds, or when the relationship 0.078≦Wz1 / Ez≦0.82 and 0.078≦Wz2 / Ez≦0.82 holds. Similarly, even if the relationship Wx1 ≠ Wx2 holds, k_S1Z decreases if the relationships 0.040 ≦ Wz1 / Ez ≦ 0.082 and 0.040 ≦ Wz2 / Ez ≦ 0.082 hold. If the relationships 0.060 ≦ Wz1 / Ez ≦ 0.080 and 0.060 ≦ Wz2 / Ez ≦ 0.080 hold, k_S1Z decreases further.

[0150] When the relationship Wz / Ez=0.074±0.006 holds, k_S0 further increases and k_S1Z further decreases. In particular, k_S0 is maximized when Wz / Ez=0.076, and k_S1Z is minimized when Wz / Ez=0.075.

[0151] Even when the relationship Wz1≠Wz2 holds, if the relationships Wx1 / Ex=0.074±0.006 and Wx2 / Ex=0.074±0.006 hold, k_S0 will further increase and k_S1Z will further decrease.

[0152] As described above, according to this embodiment, the relationships Wx1=Wx2=0, 0<Wx1 / Ex≦0.082, and 0<Wx2 / Ex≦0.082 hold true.

[0153] This makes it possible to reduce the electromechanical coupling coefficient k_S1Z of the inharmonic spurious mode and increase the electromechanical coupling coefficient k_S0 of the main mode.

[0154] In one aspect of this embodiment, the relationships Wz1 / Ez=0.074±0.006 and Wz2 / Ez=0.074±0.006 hold.

[0155] This makes it possible to further reduce the electromechanical coupling coefficient k_S1Z of the inharmonic spurious mode and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0156] Fourth Embodiment Next, the configuration of a quartz crystal vibrating element 410 according to a fourth embodiment will be described with reference to Fig. 41. Fig. 41 is a cross-sectional view of the quartz crystal vibrating element 410 according to the fourth embodiment.

[0157] The thickness Te1+Tf of the first excitation electrode 414a in the low acoustic velocity region 418 is greater than the thickness Te1 of the portion of the first excitation electrode 414a excluding the hole H in the high acoustic velocity region 417. A first metal film having a thickness Te1 and a second metal film having a thickness Tf are stacked on the first excitation electrode 414a in the low acoustic velocity region 418. The first metal film extends from the low acoustic velocity region 418 to the high acoustic velocity region 417. The material of the second metal film is, for example, the same as the material of the first metal film. The thickness Tf of the second metal film is, for example, smaller than the thickness Te1 of the first metal film.

[0158] As described above, according to this embodiment, the thickness Te1+Tf of the first excitation electrode 414a in the low acoustic velocity region 418 is greater than the thickness Te1 of the first excitation electrode 414a excluding the multiple holes H in the high acoustic velocity region 417.

[0159] This further increases the difference in mass between the low acoustic velocity region 418 and the high acoustic velocity region 417 by the thickness Tf, thereby further reducing the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increasing the electromechanical coupling coefficient k_S0 of the main mode.

[0160] The thickness and material of the second metal film are not limited to those described above. The thickness of the second metal film may be the same as or greater than the thickness of the first metal film. The material of the second metal film may be different from the material of the first metal film. For example, by using a material with a higher specific gravity for the second metal film than the material of the first metal film, the mass difference between the low acoustic velocity region and the high acoustic velocity region can be further increased. Alternatively, a mass-adding film made of a non-metallic conductive or insulating material may be provided instead of the second metal film. The second metal film or mass-adding film may be provided between the crystal blank and the first metal film. A multilayer film including at least one of a metal film and a mass-adding film may be provided on at least one of the crystal blank side and the opposite side of the first metal film in the low acoustic velocity region.

[0161] Fifth Embodiment Next, the configuration of a quartz crystal vibrating element 510 according to a fifth embodiment will be described with reference to Fig. 42. Fig. 42 is a cross-sectional view of the quartz crystal vibrating element 510 according to the fifth embodiment.

[0162] A plurality of sub-holes h are formed in the first excitation electrode 514a in the low acoustic velocity region 518. The sub-holes h are through-holes that penetrate the first excitation electrode 514a in the Y'-axis direction. However, the sub-holes h are not limited to through-holes, and may be grooves with a bottom that open in the Y'-axis direction.

[0163] The dimension of the sub-hole h in the Z'-axis direction is defined as hz, and the dimension of the sub-hole h in the X-axis direction is defined as hx. The planar shape of the sub-hole h is a square having a side extending along the Z'-axis direction and a side extending along the X-axis direction. In other words, hz = hx. In Figure 42, hx is not shown.

[0164] The planar shape of the sub-holes h is not limited to a square, but may be a rectangle with hz<hx or a rectangle with hx<hz. The planar shape of the sub-holes h may be a rectangle with sides extending in directions intersecting the X-axis direction and the Y'-axis direction. The planar shape of the sub-holes h may also be a polygon, a circle, an ellipse, or a combination thereof.

[0165] The pitch of the multiple sub-holes h in the Z'-axis direction, i.e., the distance between the ends of two adjacent sub-holes h in the Z'-axis direction on the negative side of the Z'-axis, is defined as Phz. The pitch of the sub-holes h in the X-axis direction, i.e., the distance between the ends of two adjacent sub-holes h in the X-axis direction on the negative side of the X-axis, is defined as Phx. The multiple sub-holes h are arranged at equal intervals in both the Z'-axis direction and the X-axis direction. In other words, Phz = Phx. Phx is not shown in Figure 42.

[0166] The pitch of the multiple sub-holes h is not limited to the above, and may be Phz<Phx, or may be Phx<Phz. Furthermore, the direction in which the multiple sub-holes h are arranged is not limited to the Z'-axis direction and the X-axis direction, and they may be arranged in a direction intersecting the Z'-axis direction and the X-axis direction. The multiple sub-holes h may be arranged in a staggered pattern. Furthermore, the multiple sub-holes h may be arranged randomly.

[0167] In this embodiment, the length hx=hz of one side of the sub-hole h is smaller than the length Hx=Hz of one side of the hole H (hx=hz<Hx=Hz). Furthermore, in this embodiment, the pitch Phz of the multiple sub-holes h is the same as the pitch PHz of the multiple holes H (Phz≈PHz), and the pitch Phx of the multiple sub-holes h is the same as the pitch PHx of the multiple holes H (Phx≈PHx). As a result, the opening ratio har of the sub-holes h, expressed by the formula har=(hx / Phx)×(hz / Phz), is smaller than the opening ratio Har of the hole H (har<Har).

[0168] According to this, the total mass of the first excitation electrode 514a is further reduced by forming the sub-holes h in the first excitation electrode 514a in the low acoustic velocity region 518. As a result, the resonant frequency of the quartz crystal vibrating element 510 can be further increased.

[0169] Sixth Embodiment Next, the configuration of a quartz crystal vibrating element 610 according to a sixth embodiment will be described with reference to Fig. 43. Fig. 43 is a cross-sectional view of the quartz crystal vibrating element 610 according to the sixth embodiment.

[0170] In this embodiment, the length hx=hz of one side of the sub-hole h is the same as the length Hx=Hz of one side of the hole H (hx=hz=Hx=Hz). Furthermore, in this embodiment, the pitch Phz of the multiple sub-holes h is larger than the pitch PHz of the multiple holes H (PHz<Phz), and the pitch Phx of the multiple sub-holes h is larger than the pitch PHx of the multiple holes H (PHx<Phx). As a result, the aperture ratio har of the sub-holes h is smaller than the aperture ratio Har of the hole H (har<Har). Note that hx and Phx are not shown in FIG.

[0171] Although the fifth embodiment has been described with an example of a configuration in which the relationship hx = hz < Hx = Hz holds, and the sixth embodiment has been described with an example of a configuration in which the relationships PHz < Phz and PHx < Phx hold, the present invention is not limited to these as long as the relationship har < Har holds. For example, the pitch Phz of the sub-holes h may be smaller than the pitch PHz of the holes H (Phz < PHz), and the pitch Phx of the sub-holes h may be smaller than the pitch PHx of the holes H (Phx < PHx). In this case, for the relationship har < Har to hold, the area hz × hx of the sub-holes h must be smaller than the area Hz × Hx of the holes H (hz × hx < Hz × Hx).

[0172] Furthermore, if the relationship har<Har is established, the area hz×hx of the sub-holes h may be equal to or larger than the area Hz×Hx of the holes H (Hz×Hx≦hz×hx). In this case, for the relationship har<Har to be established, at least one of the following relationships must be established: the pitch Phz of the sub-holes h is larger than the pitch PHz of the holes H (PHz<Phz), and the pitch Phx of the sub-holes h is larger than the pitch PHx of the holes H (PHx<Phx).

[0173] However, even if the area hz × hx of the sub-hole h is larger than the area Hz × Hx of the hole H (Hz × Hx < hz × hx), the relationship between the side length hz = hx = hr of the sub-hole h, similar to the side length Hz = Hx = Hr of the hole H, is 0 < hr / Tp ≦ 2.0. This allows the capacitance reduction rate to be kept to 1% or less, allowing the low acoustic velocity region 518 to function as an excitation electrode. If 0 < hr / Tp ≦ 1.5, the capacitance reduction rate can be kept to 0.5% or less. If 0 < Hr / Tp ≦ 1.0, the capacitance reduction rate can be kept to 0.1% or less. Note that hr is the length of one side of the sub-hole h when the planar shape is square. If the planar shape of the sub-hole h is other than square, it is the length of one side when the sub-hole h is converted to a square while maintaining its area constant.

[0174] Seventh Embodiment Next, the configuration of a quartz crystal vibrating element 710 according to a seventh embodiment will be described with reference to Fig. 44. Fig. 44 is a cross-sectional view of the quartz crystal vibrating element 710 according to the seventh embodiment.

[0175] A plurality of holes Ha are formed in the first excitation electrode 714a in the high acoustic velocity region 717, and a plurality of holes Hb are formed in the second excitation electrode 714b in the high acoustic velocity region 717. The holes Ha and Hb have the same configuration as the hole H described above.

[0176] According to this embodiment, the mass difference between the low acoustic velocity region 418 and the high acoustic velocity region 417 is further increased, which makes it possible to further reduce the electromechanical coupling coefficients k_S1X and k_S1Z of the inharmonic spurious modes and further increase the electromechanical coupling coefficient k_S0 of the main mode.

[0177] The diameters of the holes formed in the first excitation electrode may be different from the diameters of the holes formed in the second excitation electrode, and the pitches of the holes formed in the first excitation electrode may be different from the pitches of the holes formed in the second excitation electrode.

[0178] Eighth Embodiment Next, the configuration of a quartz crystal vibrating element 810 according to an eighth embodiment will be described with reference to Fig. 45. Fig. 45 is a cross-sectional view of the quartz crystal vibrating element 810 according to the eighth embodiment.

[0179] The plurality of holes HB formed in the first excitation electrode 814a in the high acoustic velocity region 817 are groove-shaped blind holes with bottoms.

[0180] According to this, even if the length hr of one side of the hole HB is greater than 2.0 μm, the capacitance does not decrease, and therefore the degree of freedom in designing the hole HB is improved.

[0181] 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.

[0182] <1> A piezoelectric vibration element including a piezoelectric piece and an excitation electrode that overlap in the thickness direction, the piezoelectric vibration element having a high acoustic velocity region and a low acoustic velocity region in which the acoustic velocity is lower than that of the high acoustic velocity region, wherein, in a planar view in the thickness direction, the high acoustic velocity region is provided in a region that overlaps with a central portion of the excitation electrode, and the low acoustic velocity region is provided in at least a part of a region that overlaps with an end portion of the excitation electrode, the excitation electrode in the high acoustic velocity region has a plurality of holes that make the mass per unit area of ​​the high acoustic velocity region smaller than the mass per unit area of ​​the low acoustic velocity region, and in one direction intersecting the thickness direction, the dimension in one direction of a portion of the low acoustic velocity region adjacent to the high acoustic velocity region is smaller than the dimension in one direction of the high acoustic velocity region, and in a planar view in the thickness direction, the piezoelectric vibration element has an area that is smaller than the area of ​​the high acoustic velocity region.

[0183] <2> The piezoelectric element according to <1>, wherein the piezoelectric piece is an AT-cut quartz crystal piece having crystal axes consisting of an X-axis, a Y-axis, and a Z-axis, a thickness direction being a Y'-axis direction obtained by rotating the Y-axis around the X-axis, and a main surface defined by a Z'-axis direction obtained by rotating the Z-axis around the X-axis and an X-axis direction parallel to the X-axis.

[0184] <3> The low acoustic velocity region includes a first low acoustic velocity region adjacent to the high acoustic velocity region in the X-axis direction, a second low acoustic velocity region adjacent to the high acoustic velocity region on the opposite side to the first low acoustic velocity region, a third low acoustic velocity region adjacent to the high acoustic velocity region in the Z'-axis direction, and a fourth low acoustic velocity region adjacent to the high acoustic velocity region on the opposite side to the third low acoustic velocity region, wherein, when the dimension of the excitation electrode in the X-axis direction is Ex, the dimension of the excitation electrode in the Z'-axis direction is Ez, the dimension of the first low acoustic velocity region in the X-axis direction is Wx1, the dimension of the second low acoustic velocity region in the X-axis direction is Wx2, the dimension of the third low acoustic velocity region in the Z'-axis direction is Wz1, and the dimension of the third low acoustic velocity region in the Z'-axis direction is Wz2, 0<Wx1 / Ex≦0.07 and 0<Wx2 / Ex≦0.07 and 0<Wz1 / Ez≦0.08 and The piezoelectric vibration element according to <2>, wherein the relationship: 0<Wz2 / Ez≦0.08 holds.

[0185] <4> The piezoelectric vibration element according to <3>, wherein the following relationships hold: Wx1 / Ex = 0.062±0.00, Wx2 / Ex = 0.062±0.006, Wz1 / Ez = 0.070±0.006, and Wz2 / Ez = 0.070±0.006.

[0186] <5> The piezoelectric vibration element according to <2>, wherein the low acoustic velocity region includes a first low acoustic velocity region adjacent to the high acoustic velocity region in the X-axis direction and a second low acoustic velocity region adjacent to the high acoustic velocity region on the opposite side to the first low acoustic velocity region, the high acoustic velocity region, the first low acoustic velocity region, and the second low acoustic velocity region are provided across the entire width of the excitation electrode from one end to the other end in the Z'-axis direction, and wherein, when the dimension of the excitation electrode in the X-axis direction is Ex, the dimension of the first low acoustic velocity region in the X-axis direction is Wx1, and the dimension of the second low acoustic velocity region in the X-axis direction is Wx2, the relationships 0<Wx1 / Ex≦0.074 and 0<Wx2 / Ex≦0.074 hold.

[0187] <6> The piezoelectric vibration element according to <5>, wherein the relationships Wx1 / Ex = 0.066 ± 0.006 and Wx2 / Ex = 0.066 ± 0.006 are satisfied.

[0188] <7> The piezoelectric vibration element according to <2>, wherein the low acoustic velocity region includes a third low acoustic velocity region adjacent to the high acoustic velocity region in the Z'-axis direction and a fourth low acoustic velocity region adjacent to the high acoustic velocity region on the opposite side to the third low acoustic velocity region, the high acoustic velocity region, the third low acoustic velocity region and the fourth low acoustic velocity region are provided across the entire width of the excitation electrode from one end to the other end in the Z'-axis direction, and wherein, when the dimension of the excitation electrode in the Z'-axis direction is Ez, the dimension of the third low acoustic velocity region in the Z'-axis direction is Wz1, and the dimension of the fourth low acoustic velocity region in the Z'-axis direction is Wz2, the relationships 0<Wz1 / Ez≦0.082 and 0<Wz2 / Ez≦0.082 hold.

[0189] <8> The piezoelectric vibration element according to <7>, wherein the relationships Wz1 / Ez=0.074±0.006 and Wz2 / Ez=0.074±0.006 hold.

[0190] <9> The piezoelectric vibration element according to any one of <1> to <8>, wherein the plurality of holes are through holes that penetrate the excitation electrode in the thickness direction, the thickness of the piezoelectric piece is Tp, and when the shape of the plurality of holes is square in plan view, the length of one side of the square is Hr, and when the shape of the plurality of holes is other than square, the length of one side when the shape is converted to a square while keeping the area constant is Hr, the relationship 0<Hr / Tp≦2.0 holds.

[0191] <10> The piezoelectric vibration element according to <9>, wherein the relationship 0<Hr / Tp≦1.45 holds.

[0192] <11> The piezoelectric vibration element according to <10>, wherein a relationship of Hr / Tp=1.3±0.1 holds.

[0193] <12> The piezoelectric vibration element according to any one of <1> to <11>, wherein the plurality of holes are through holes that penetrate the excitation electrode in the thickness direction, and when an aperture ratio of the plurality of holes is Har, a relationship of 0<Har≦0.5 is satisfied.

[0194] <13> The piezoelectric vibration element according to <12>, wherein a relationship of Har=0.4±0.06 holds.

[0195] <14> The piezoelectric vibration element according to any one of <1> to <8>, wherein the plurality of holes are groove-shaped with a bottom.

[0196] <15> The piezoelectric vibration element according to any one of <1> to <14>, wherein the thickness of the excitation electrode in the low acoustic velocity region is equal to the thickness of the excitation electrode excluding the plurality of holes in the high acoustic velocity region.

[0197] <16> The piezoelectric vibration element according to any one of <1> to <14>, wherein the thickness of the excitation electrode in the low acoustic velocity region is greater than the thickness of the excitation electrode excluding the plurality of holes in the high acoustic velocity region.

[0198] <17> The piezoelectric vibration element according to any one of <1> to <16>, wherein in a low acoustic velocity region, a plurality of sub-holes are formed in the excitation electrode, the aperture ratio of the plurality of sub-holes is smaller than the aperture ratio of the plurality of holes, the thickness of the piezoelectric piece is Tp, 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 shape while keeping the area constant is hr, the relationship 0<hr / Tp≦2.0 holds.

[0199] In this specification, a quartz crystal resonator having a quartz crystal substrate as a piezoelectric substrate has been described as an example, but the piezoelectric resonator is not limited to this. Examples of piezoelectric substrates 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 substrate is not limited to these and can be selected as appropriate.

[0200] The embodiments according to the present invention are not particularly limited and can be appropriately applied to any device that performs electromechanical energy conversion using the piezoelectric effect, such as a timing device, a sound generator, an oscillator, or a load sensor.

[0201] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibration element that can improve the electromechanical coupling coefficient.

[0202] 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.

[0203] DESCRIPTION OF SYMBOLS 100... Crystal oscillator 130... Mounting substrate 140... Cover 1... Crystal vibrator 10... Crystal vibrating element 11... 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 18A... First low acoustic velocity region 18B... Second low acoustic velocity region 18C... Third low acoustic velocity region 18D... Fourth low acoustic velocity region 30... Base member 40... Cover member 50... Joint portion H... Hole portion

Claims

1. A piezoelectric vibration element including a piezoelectric piece and an excitation electrode overlapping in a thickness direction, A high sound speed region and a low sound speed region in which the sound speed is slower than that of the high sound speed region, In a plan view in the thickness direction, the high sound velocity region is provided in a region overlapping a central portion of the excitation electrode, and the low sound velocity region is provided in at least a part of a region overlapping an end portion of the excitation electrode, A plurality of holes are formed in the excitation electrode in the high sound velocity region, which makes the mass per unit area of ​​the high sound velocity region smaller than the mass per unit area of ​​the low sound velocity region, In one direction intersecting the thickness direction, a dimension of a portion of the low sound speed region adjacent to the high sound speed region in the one direction is smaller than a dimension of the high sound speed region in the one direction, In a plan view in the thickness direction, the area of ​​the low sound velocity region is smaller than the area of ​​the high sound velocity region. Piezoelectric vibration element.

2. The piezoelectric piece is an AT-cut quartz crystal piece having crystal axes consisting of an X-axis, a Y-axis, and a Z-axis, a Y'-axis direction obtained by rotating the Y-axis around the X-axis being the thickness direction, and a main surface defined by a Z'-axis direction obtained by rotating the Z-axis around the X-axis and an X-axis direction parallel to the X-axis. The piezoelectric vibration element according to claim 1 .

3. The low sound speed region includes a first low sound speed region adjacent to the high sound speed region in the X-axis direction, a second low sound speed region adjacent to the high sound speed region on the opposite side to the first low sound speed region, a third low sound speed region adjacent to the high sound speed region in the Z'-axis direction, and a fourth low sound speed region adjacent to the high sound speed region on the opposite side to the third low sound speed region, When the dimension of the excitation electrode in the X-axis direction is Ex, the dimension of the excitation electrode in the Z'-axis direction is Ez, the dimension of the first low sound velocity region in the X-axis direction is Wx1, the dimension of the second low sound velocity region in the X-axis direction is Wx2, the dimension of the third low sound velocity region in the Z'-axis direction is Wz1, and the dimension of the third low sound velocity region in the Z'-axis direction is Wz2, 0<Wx1 / Ex≦0.07 and, 0<Wx2 / Ex≦0.07 and, 0<Wz1 / Ez≦0.08 and, 0<Wz2 / Ez≦0.08 The relationship is established as follows: The piezoelectric vibration element according to claim 2 .

4. Wx1 / Ex=0.062±0.006 and, Wx2 / Ex=0.062±0.006 and, Wz1 / Ez=0.070±0.006 and, Wz2 / Ez=0.070±0.006 The relationship is established as follows: The piezoelectric vibration element according to claim 3 .

5. The low sound speed region includes a first low sound speed region adjacent to the high sound speed region in the X-axis direction, and a second low sound speed region adjacent to the high sound speed region on the opposite side to the first low sound speed region, The high acoustic velocity region, the first low acoustic velocity region, and the second low acoustic velocity region are provided over an entire width of the excitation electrode from one end to the other end in the Z′-axis direction, When the dimension of the excitation electrode in the X-axis direction is Ex, the dimension of the first low sound velocity region in the X-axis direction is Wx1, and the dimension of the second low sound velocity region in the X-axis direction is Wx2, 0<Wx1 / Ex≦0.074 and, 0<Wx2 / Ex≦0.074 The relationship is established as follows: The piezoelectric vibration element according to claim 2 .

6. Wx1 / Ex=0.066±0.006 and Wx2 / Ex=0.066±0.006 The relationship is established as follows: The piezoelectric vibration element according to claim 5 .

7. The low sound speed region includes a third low sound speed region adjacent to the high sound speed region in the Z'-axis direction, and a fourth low sound speed region adjacent to the high sound speed region on the opposite side to the third low sound speed region, The high acoustic velocity region, the third low acoustic velocity region, and the fourth low acoustic velocity region are provided over the entire width of the excitation electrode from one end to the other end in the Z′-axis direction, When the dimension of the excitation electrode in the Z'-axis direction is Ez, the dimension of the third low sound velocity region in the Z'-axis direction is Wz1, and the dimension of the fourth low sound velocity region in the Z'-axis direction is Wz2, 0<Wz1 / Ez≦0.082 and, 0<Wz2 / Ez≦0.082 The relationship is established as follows: The piezoelectric vibration element according to claim 2 .

8. Wz1 / Ez=0.074±0.006 and, Wz2 / Ez=0.074±0.006 The relationship is established as follows: The piezoelectric vibration element according to claim 7 .

9. the plurality of holes are through holes penetrating the excitation electrode in the thickness direction, The thickness of the piezoelectric piece is Tp, In a plan view, when the shape of the plurality of holes is a square, the length of one side of the square is defined as Hr. When the shape of the plurality of holes is other than a square, the length of one side of the square shape when the shape is converted to a square shape while keeping the area constant is defined as Hr. 0<Hr / Tp≦2.0 The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

10. 0<Hr / Tp≦1.45 The relationship is established as follows: The piezoelectric vibration element according to claim 9 .

11. Hr / Tp=1.3±0.1 The relationship is established as follows: The piezoelectric vibration element according to claim 10.

12. the plurality of holes are through holes penetrating the excitation electrode in the thickness direction, When the aperture ratio of the plurality of holes is Har, 0<Har≦0.5 The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

13. Har=0.4±0.06 The relationship is established as follows: The piezoelectric vibration element according to claim 12.

14. The plurality of holes are groove-shaped with a bottom. The piezoelectric vibration element according to claim 1 .

15. The thickness of the excitation electrode in the low sound velocity region is equal to the thickness of the excitation electrode excluding the plurality of holes in the high sound velocity region. The piezoelectric vibration element according to claim 1 .

16. A thickness of the excitation electrode in the low sound velocity region is greater than a thickness of the excitation electrode excluding the plurality of holes in the high sound velocity region. The piezoelectric vibration element according to claim 1 .

17. In the low sound velocity region, a plurality of sub-holes are formed in the excitation electrode, an aperture ratio of the plurality of sub-holes is smaller than an aperture ratio of the plurality of holes; The thickness of the piezoelectric piece is Tp, In a plan view, when the shape of the plurality of holes is a square, the length of one side of the square is defined as hr, and when the shape of the plurality of holes is other than a square, the length of one side of the square shape when the shape is converted to a square shape while keeping the area constant is defined as hr. The relationship 0<hr / Tp≦2.0 is satisfied. The piezoelectric vibration element according to claim 1 .