Piezoelectric vibration element

Abstract

A piezoelectric vibration element 10 comprises: a piezoelectric piece 11; a first excitation electrode 14a provided on a first principal surface 11A of the piezoelectric piece 11; a second excitation electrode 14b provided on a second principal surface 11B of the piezoelectric piece 11; and a mass addition film 20 at least partially overlapping the first excitation electrode 14a. The mass addition film 20 includes a first portion 21 and a second portion 22 that are provided so as to avoid a central portion of the first excitation electrode 14a; the first excitation electrode 14a has a first outer edge portion 71 and a second outer edge portion 72 in plan view; the second excitation electrode 14b has a third outer edge portion 81 and a fourth outer edge portion 82; the first portion 21 is provided along the first outer edge portion 71; the second portion 22 is provided along the second outer edge portion 72; and when a region in which the piezoelectric piece 11, the first excitation electrode 14a, and the second excitation electrode 14b overlap one another is defined as a high acoustic velocity region 17, and regions in which the mass addition film 20 further overlaps the piezoelectric piece 11, the first excitation electrode 14a, and the second excitation electrode 14b are defined as first and second low acoustic velocity regions 18A, 18B, the third outer edge portion 81 and the fourth outer edge portion 82 are further away from the central portion than the first low acoustic velocity region 18A and the second low acoustic velocity region 18B, respectively, in plan view.

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 quartz crystal vibration element comprising a quartz crystal piece having a first main surface and a second main surface, a first excitation electrode provided on the first main surface, and a second excitation electrode provided on the second main surface, wherein the first excitation electrode and the second excitation electrode have a film thickness portion at the electrode end that is thicker than other portions.

[0004] International Publication No. 2022 / 080426

[0005] However, in the crystal vibration element described in Patent Document 1, the electromechanical coupling coefficient may be deteriorated due to misalignment of the film-thickness portion caused by manufacturing variations.

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

[0007] A piezoelectric vibration element according to one aspect of the present invention includes a piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface, a first excitation electrode provided on the first main surface of the piezoelectric piece, a second excitation electrode provided on the second main surface of the piezoelectric piece, and a mass-adding film at least partially overlapping the first excitation electrode, wherein the mass-adding film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode having, in a plan view, a first outer edge portion located on one side of the central portion in the first direction and a second outer edge portion located on the other side of the central portion in the first direction, and the second excitation electrode having, in a plan view, a first outer edge portion located on the other side of the central portion in the first direction. the piezoelectric element has a third outer edge portion located on one side of the piezoelectric element and a fourth outer edge portion located on the other side in the first direction relative to the central portion, the first portion being provided along the first outer edge portion, and the second portion being provided along the second outer edge portion, and when a region where the piezoelectric element, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric element, the first excitation electrode, and the second excitation electrode are further overlapped by a first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric element, the first excitation electrode, and the second excitation electrode are further overlapped by a second portion of the mass adding film is defined as a second low acoustic velocity region, in a planar view, the third outer edge portion is farther from the central portion than the first low acoustic velocity region, and in a planar view, the fourth outer edge portion is farther from the central portion than the second low acoustic velocity region.

[0008] A piezoelectric vibration element according to one aspect of the present invention includes a piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface, a first excitation electrode provided on the first main surface of the piezoelectric piece, a second excitation electrode provided on the second main surface of the piezoelectric piece, and a mass-adding film at least a portion of which overlaps the first excitation electrode, wherein the mass-adding film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode having, in a plan view, a first outer edge portion located on one side of the central portion in the first direction and a second outer edge portion located on the other side of the central portion in the first direction, the second excitation electrode having, in a plan view, a third outer edge portion located on one side of the central portion in the first direction and a fourth outer edge portion located on the other side of the central portion in the first direction, the first portion being provided along the first outer edge portion, and the second portion being provided along the second outer edge portion a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is a high acoustic velocity region; a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap with a first portion of the mass adding film is a first low acoustic velocity region; a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap with a second portion of the mass adding film is a second low acoustic velocity region; and a region between an end of the first portion of the mass adding film opposite to the second portion and an end of the second portion opposite to the first portion When the dimension along the first direction is A, the dimension of the first excitation electrode along the first direction is B, and the dimension of the second excitation electrode along the first direction is C, the relationship A=C<B holds, and when viewed in a plane, the outer edge of the first low acoustic velocity region opposite the second low acoustic velocity region and the outer edge of the second low acoustic velocity region opposite the first low acoustic velocity region overlap the first excitation electrode, and when viewed in a plane, the third outer edge and fourth outer edge of the second excitation electrode overlap the first excitation electrode.

[0009] According to the present invention, it is possible to provide a piezoelectric vibration element that can suppress deterioration of the electromechanical coupling coefficient.

[0010] FIG. 1 is a cross-sectional view of a crystal oscillator according to a first embodiment. FIG. 2 is an exploded perspective view of a crystal resonator according to a first embodiment. FIG. 3 is a cross-sectional view of a crystal resonator according to a first embodiment. FIG. 4 is a cross-sectional view of a crystal resonator element according to a first embodiment. FIG. 5 is a plan view of a crystal resonator element according to a first embodiment. FIG. 6 is a table showing conditions for a simulation based on the first embodiment. FIG. 7 is a graph showing a simulation result based on the first embodiment. FIG. 8 is a graph showing a simulation result based on the first embodiment. FIG. 9 is a graph showing a simulation result based on the first embodiment. FIG. 10 is a graph showing a simulation result based on the first embodiment. FIG. 11 is a graph showing a simulation result based on the first embodiment. FIG. 12 is a graph showing a simulation result based on the first embodiment. FIG. 13 is a graph showing a simulation result based on the first embodiment. FIG. 14 is a graph showing a simulation result based on the first embodiment. FIG. 15 is a graph showing a simulation result based on the first embodiment. FIG. 16 is a graph showing a simulation result based on the first embodiment. FIG. 17 is a graph showing a simulation result based on the first embodiment. FIG. 10 is a diagram for explaining the influence of misalignment in the fifth embodiment. FIG. 11 is a diagram for explaining the influence of misalignment in the fifth embodiment. FIG. 12 is a cross-sectional view of a quartz crystal vibrating element according to a sixth embodiment. FIG. 13 is a diagram for explaining the influence of misalignment in the sixth embodiment. FIG. 14 is a diagram for explaining the influence of misalignment in the sixth embodiment. FIG. 15 is a cross-sectional view of a quartz crystal vibrating element according to a seventh embodiment. FIG. 16 is a cross-sectional view of a quartz crystal vibrating element according to an eighth embodiment. FIG. 17 is a table showing simulation results of comparative examples and examples based on the first to eighth embodiments. FIG. 18 is a table showing simulation conditions of comparative examples and examples based on the first to eighth embodiments. FIG. 19 is a cross-sectional view of a quartz crystal vibrating element according to a ninth embodiment. FIG. 11 is a plan view of a quartz crystal vibrating element according to a tenth embodiment. FIG. 12 is a plan view of a quartz crystal vibrating element according to an eleventh embodiment.

[0011] An embodiment of the present invention will be described below. In the following description of the drawings, identical or similar components are denoted by identical or similar reference numerals. The drawings are illustrative, and the dimensions and shapes of each part are schematic, and the technical scope of the present invention should not be interpreted as being limited to the embodiment. In the following description, "dimension" means the length of an object, and "distance" means the distance between two objects.

[0012] For the sake of clarity, each drawing may be accompanied by a Cartesian coordinate system consisting of an X-axis, a Y'-axis, and a Z'-axis to clarify the interrelationships between the drawings and to aid in understanding the positional relationships of 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.

[0013] In the following description, the direction parallel to the X-axis is referred to as the "X-axis direction," the direction parallel to the Y'-axis is referred to as the "Y'-axis direction," and the direction parallel to the Z'-axis is referred to as the "Z'-axis direction." The directions of the arrows on the X-axis, Y'-axis, and Z'-axis are referred to as "positive" or "+ (plus)," and the directions opposite the arrows are referred to as "negative" or "- (minus)." For convenience, the +Y'-axis direction will be described as the upward direction, and the -Y'-axis direction will be described as the downward direction, but the up-down orientation of the quartz resonator element 10, the quartz resonator 1, and the quartz oscillator 100 is not limited to this. The plane specified by the X-axis and Z'-axis is referred to as the Z'X plane, and the same applies to planes specified by the other axes.

[0014] First Embodiment

[0015] First, a schematic configuration of a crystal oscillator according to an embodiment will be described with reference to Fig. 1. Fig. 1 is a cross-sectional view of the crystal oscillator according to the first embodiment.

[0016] 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 oscillator is not limited to a quartz crystal resonator, and may utilize other piezoelectric materials such as ceramic. Similarly, the piezoelectric vibrator is not limited to a quartz crystal vibrator, but may be one that uses other piezoelectric materials such as ceramics, etc. Similarly, the piezoelectric vibrating element is not limited to a quartz crystal vibrating element, but may be one that uses other piezoelectric materials such as ceramics, etc.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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).

[0024] 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.

[0025] The Z'-axis direction corresponds to an example of the "first direction", the X-axis direction corresponds to an example of the "second direction", and the Y'-axis direction corresponds to an example of the "third direction". The Y'-axis direction corresponds to an example of the "thickness direction". However, the first direction, second direction, and third direction are not limited to the above. For example, the X-axis direction may be the first direction, and the Z'-axis direction may be the second direction.

[0026] 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 .

[0027] The quartz crystal vibrating element 10 is an electromechanical energy conversion element that converts electrical energy and mechanical energy mutually using 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, for example, 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, a first connection electrode 16a and a second connection electrode 16b that constitute a pair of connection electrodes, and a mass addition film 20.

[0028] 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.

[0029] 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.

[0030] 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 amount of change in thickness changes continuously, or a bevel structure in which the amount of change in thickness changes discontinuously.

[0031] 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.

[0032] 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.

[0033] The cut angle of the quartz crystal blank is not limited to the above. The rotation angle of the Y'-axis and Z'-axis in the AT-cut quartz crystal blank 11 may be inclined within a range of -5 degrees or more or +15 degrees or less from 35 degrees 15 minutes. The cut angle of the quartz crystal blank may also be a cut other than the AT cut, such as a BT cut, a GT cut, or an SC cut. The primary vibration mode of the quartz crystal vibrating element is not limited to the thickness-shear vibration mode, and may be, for example, thickness-extensional vibration, diaphragm vibration, longitudinal vibration, or flexural vibration.

[0034] 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."

[0035] 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.

[0036] 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.

[0037] 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.

[0038] 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.

[0039] 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 titanium (Ti), aluminum (Al), molybdenum (Mo), or an aluminum-copper alloy (AlCu) primarily composed of aluminum (Al). The electrodes of the quartz crystal vibrating element 10 may also have a single-layer structure.

[0040] The mass addition film 20 reduces the sound velocity in a portion of the region where the first excitation electrode 14a and the second excitation electrode 14b face each other due to its mass addition effect. The mass addition film 20 is provided on the side of the first excitation electrode 14a opposite the crystal blank 11. At least a portion of the mass addition film 20 overlaps the first excitation electrode 14a. The material of the mass addition film 20 is an electrical conductor, and is, for example, the same as the material of the first excitation electrode 14a.

[0041] When the first excitation electrode 14a and the mass-adding film 20 are made of the same material and the boundary is unclear, the portion located on the opposite side of the crystal blank 11 with respect to the XZ' plane including the surface of the first excitation electrode 14a in the high acoustic velocity region 17 (see Figure 4) is designated as the mass-adding film 20.

[0042] The mass-adding film may be provided on the opposite side of the second excitation electrode from the crystal blank 11, rather than on the opposite side of the first excitation electrode from the crystal blank 11. The material of the mass-adding film 20 may be a metal different from that of the first excitation electrode, or may be an insulator.

[0043] 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.

[0044] 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.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] 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).

[0050] 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.

[0051] The lid member 40 forms an internal space 39 between itself and the base member 30, in which the quartz-crystal vibrating element 10 is housed. The lid member 40 has a top wall 41, a side wall 42 extending from the outer 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 39. 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).

[0052] The joint 50 joins the base member 30 and the lid member 40 and seals the internal space 39. The joint 50 is provided in a frame shape around the entire periphery of the flange portion 43 of the base member 30 and is sandwiched between the lower surface of the flange portion 43 of the lid member 40 and the upper surface 31A of the base member 30. The joint 50 is made of an insulating material. The joint 50 is provided with an organic adhesive, for example, an epoxy-based, vinyl-based, acrylic-based, urethane-based, or silicone-based resin. The material of the joint 50 is not limited to organic adhesives, and may be an inorganic adhesive, such as a silicon-based adhesive containing water glass or a calcium-based adhesive containing cement. The material of the joint 50 may also be low-melting-point glass (e.g., lead borate-based or tin phosphate-based).

[0053] 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 according to the first embodiment. Fig. 5 is a plan view of the quartz crystal vibrating element according to the first embodiment. Note that, for the sake of simplicity, 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.

[0054] The quartz crystal vibrating element 10 has, in an excitation region where a voltage is applied to cause excitation, a high acoustic velocity region 17, a low acoustic velocity region 18, and an outer high acoustic velocity region 19. The low acoustic velocity region 18 is a region where the acoustic velocity is reduced due to the mass addition effect caused by the provision of a mass addition film 20. The acoustic velocities in the high acoustic velocity region 17 and the outer high acoustic velocity region 19 are higher than the acoustic velocity in the low acoustic velocity region 18. The acoustic velocity in the high acoustic velocity region 17 is approximately equal to the acoustic velocity in the outer high acoustic velocity region 19.

[0055] 5, in a plan view, the high acoustic velocity region 17 is provided in a region overlapping the center 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.

[0056] 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.

[0057] 5, in a plan view, the low acoustic velocity region 18 is provided along the outer edge of the first excitation electrode 14a in a region inside the outer edge of the first excitation electrode 14a. The low acoustic velocity region 18 is provided in a frame shape surrounding the center of the first excitation electrode 14a. The low acoustic velocity region 18 has a first low acoustic velocity region 18A, a second low acoustic velocity region 18B, a third low acoustic velocity region 18C, and a fourth low acoustic velocity region 18D.

[0058] The first low acoustic velocity region 18A is adjacent to the high acoustic velocity region 17 on the negative side of the Z' axis and extends along the X axis. The second low acoustic velocity region 18B is adjacent to the high acoustic velocity region 17 on the positive side of the Z' axis and extends along the X axis. The third low acoustic velocity region 18C is adjacent to the high acoustic velocity region 17 on the positive side of the X axis and extends along the Z' axis. The fourth low acoustic velocity region 18D is adjacent to the high acoustic velocity region 17 on the negative side of the X axis and extends along the Z' axis. The end of the first low acoustic velocity region 18A on the positive side of the X axis connects to the end of the third low acoustic velocity region 18C on the negative side of the Z' axis, and the end of the first low acoustic velocity region 18A on the positive side of the X axis connects to the end of the fourth low acoustic velocity region 18D on the negative side of the Z' axis. The end of the second low sound speed region 18B on the positive side of the X-axis is connected to the end of the third low sound speed region 18C on the positive side of the Z'-axis, and the end of the second low sound speed region 18B on the negative side of the X-axis is connected to the end of the fourth low sound speed region 18D on the positive side of the Z'-axis.

[0059] In a plan view, the end of first low sound speed region 18A on the positive X-axis side overlaps the end of third low sound speed region 18C on the negative Z'-axis side, and the end of first low sound speed region 18A on the negative X-axis side overlaps the end of fourth low sound speed region 18D on the negative Z'-axis side. The end of second low sound speed region 18B on the positive X-axis side overlaps the end of third low sound speed region 18C on the positive Z'-axis side, and the end of second low sound speed region 18B on the negative X-axis side overlaps the end of fourth low sound speed region 18D on the positive Z'-axis side.

[0060] In a plan view, an outer edge portion located on the opposite side to the center of the first excitation electrode 14 a in the first low acoustic velocity region 18A overlaps with an outer edge portion (outer edge portion 21A) located on the opposite side to the center of the first excitation electrode 14 a in a first portion 21 (described later) of the mass adding film 20. An outer edge portion located on the opposite side to the center of the first excitation electrode 14 a in the second low acoustic velocity region 18B overlaps with an outer edge portion (outer edge portion 22A) located on the opposite side to the center of the first excitation electrode 14 a in a second portion 22 (described later) of the mass adding film 20. An outer edge portion located on the opposite side to the center of the first excitation electrode 14 a in the third low acoustic velocity region 18C overlaps with an outer edge portion (outer edge portion 23A) located on the opposite side to the center of the first excitation electrode 14 a in a third portion 23 (described later) of the mass adding film 20. The outer edge portion located on the opposite side of the center of the first excitation electrode 14a in the fourth low acoustic velocity region 18D overlaps with the outer edge portion (outer edge portion 24A described later) located on the opposite side of the center of the first excitation electrode 14a in the fourth part 24 of the mass-adding film 20 described later.

[0061] In a plan view, an inner edge portion located on the central side of the first excitation electrode 14 a in the first low acoustic velocity region 18A overlaps with an inner edge portion (inner edge portion 21B described later) located on the central side of the first excitation electrode 14 a in a first portion 21 described later of the mass adding film 20. An inner edge portion located on the central side of the first excitation electrode 14 a in the second low acoustic velocity region 18B overlaps with an inner edge portion (inner edge portion 22B described later) located on the central side of the first excitation electrode 14 a in a second portion 22 described later of the mass adding film 20. An inner edge portion located on the central side of the first excitation electrode 14 a in the third low acoustic velocity region 18C overlaps with an inner edge portion (inner edge portion 23B described later) located on the central side of the first excitation electrode 14 a in a third portion 23 described later of the mass adding film 20. The inner edge portion located on the central side of the first excitation electrode 14a in the fourth low acoustic velocity region 18D overlaps with the inner edge portion (inner edge portion 24B described later) located on the central side of the first excitation electrode 14a in the fourth part 24 of the mass-adding film 20 described later.

[0062] In a plan view, both an outer edge portion 71 (described later) of the first excitation electrode 14a and an outer edge portion 81 (described later) of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the first low acoustic velocity region 18A. The outer edge portion 81 is farther from the center of the first excitation electrode 14a than the outer edge portion 71. Both an outer edge portion 72 (described later) of the first excitation electrode 14a and an outer edge portion 82 (described later) of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the second low acoustic velocity region 18B. The outer edge portion 82 is farther from the center of the first excitation electrode 14a than the outer edge portion 72. An outer edge portion 73 (to be described later) of the first excitation electrode 14a and an outer edge portion 83 (to be described later) of the second excitation electrode 14b are both farther from the center of the first excitation electrode 14a than the outer edge portion of the third low acoustic velocity region 18C. The outer edge portion 83 is farther from the center of the first excitation electrode 14a than the outer edge portion 73. An outer edge portion 74 (to be described later) of the first excitation electrode 14a and an outer edge portion 84 (to be described later) of the second excitation electrode 14b are both farther from the center of the first excitation electrode 14a than the outer edge portion of the fourth low acoustic velocity region 18D. The outer edge portion 84 is farther from the center of the first excitation electrode 14a than the outer edge portion 73.

[0063] The shape 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 be arranged in strips extending parallel to each other along the X-axis direction. Alternatively, the first and second low acoustic velocity regions may be omitted, and the high acoustic velocity region, the third and fourth low acoustic velocity regions may be arranged in strips extending parallel to each other along the Z'-axis direction. Furthermore, the end of the first low acoustic velocity region on the positive X-axis side may be spaced apart from the third low acoustic velocity region, and the end of the first low acoustic velocity region on the negative X-axis side may be spaced apart from the fourth low acoustic velocity region. The end of the second low acoustic velocity region on the positive X-axis side may be spaced apart from the third low acoustic velocity region, and the end of the second low acoustic velocity region on the negative X-axis side may be spaced apart from the fourth low acoustic velocity region.

[0064] Furthermore, the positional relationship between the first, second, third, and fourth low acoustic velocity regions is not limited to the above. The first low acoustic velocity region may be adjacent to the high acoustic velocity region on the positive side of the Z'-axis, and the second low acoustic velocity region may be adjacent to the high acoustic velocity region on the negative side of the Z'-axis. The third low acoustic velocity region may be adjacent to the high acoustic velocity region on the negative side of the X-axis, and the fourth low acoustic velocity region may be adjacent to the high acoustic velocity region on the positive side of the X-axis. One of the first and second low acoustic velocity regions may be adjacent to the high acoustic velocity region on the negative side of the X-axis, and the other may be adjacent to the high acoustic velocity region on the positive side of the X-axis. One of the third and fourth low acoustic velocity regions may be adjacent to the high acoustic velocity region on the negative side of the Z'-axis, and the other may be adjacent to the high acoustic velocity region on the positive side of the Z'-axis.

[0065] 5, in a plan view, the outer high acoustic velocity region 19 is provided along the outer edge of the first excitation electrode 14a in a region between the outer edge of the mass addition film 20 and the outer edge of the first excitation electrode 14a. The outer high acoustic velocity region 19 is provided in a frame shape surrounding the low acoustic velocity region 18. The outer high acoustic velocity region 19 has a first outer high acoustic velocity region 19A, a second outer high acoustic velocity region 19B, a third outer high acoustic velocity region 19C, and a fourth outer high acoustic velocity region 19D.

[0066] The first outer high acoustic velocity region 19A is adjacent to the first low acoustic velocity region 18A on the negative side of the Z' axis and extends along the X axis. The second outer high acoustic velocity region 19B is adjacent to the second low acoustic velocity region 18B on the positive side of the Z' axis and extends along the X axis. The third outer high acoustic velocity region 19C is adjacent to the third low acoustic velocity region 18C on the positive side of the X axis and extends along the Z' axis. The fourth outer high acoustic velocity region 19D is adjacent to the fourth low acoustic velocity region 18D on the negative side of the X axis and extends along the Z' axis. The end of the first outer high acoustic velocity region 19A on the positive side of the X axis connects to the end of the third outer high acoustic velocity region 19C on the negative side of the Z' axis, and the end of the first outer high acoustic velocity region 19A on the negative side of the X axis connects to the end of the fourth outer high acoustic velocity region 19D on the negative side of the Z' axis. The end of the second outer high sound velocity region 19B on the positive side of the X-axis is connected to the end of the third outer high sound velocity region 19C on the positive side of the Z'-axis, and the end of the second outer high sound velocity region 19B on the negative side of the X-axis is connected to the end of the fourth outer high sound velocity region 19D on the positive side of the Z'-axis.

[0067] In a plan view, the end of first outer high sound velocity region 19A on the positive X-axis side overlaps with the end of third outer high sound velocity region 19C on the negative Z'-axis side, and the end of first outer high sound velocity region 19A on the negative X-axis side overlaps with the end of fourth outer high sound velocity region 19D on the negative Z'-axis side. The end of second outer high sound velocity region 19B on the positive X-axis side overlaps with the end of third outer high sound velocity region 19C on the positive Z'-axis side, and the end of second outer high sound velocity region 19B on the negative X-axis side overlaps with the end of fourth outer high sound velocity region 19D on the positive Z'-axis side.

[0068] The shape of the outer high acoustic velocity regions is not limited to the above. The third outer high acoustic velocity region and the fourth outer high acoustic velocity region may be omitted. That is, the first outer high acoustic velocity region and the second outer high acoustic velocity region may be provided in a strip shape extending parallel to each other along the X-axis direction. In this case, the first outer high acoustic velocity region and the second outer high acoustic velocity region may be provided from the end of the first excitation electrode on the negative X-axis side to the end on the positive X-axis side in a plan view. Alternatively, the first outer high acoustic velocity region and the second outer high acoustic velocity region may be omitted, and the third outer high acoustic velocity region and the fourth outer high acoustic velocity region may be provided in a strip shape extending parallel to each other along the Z'-axis direction. In this case, the third outer high acoustic velocity region and the fourth outer high acoustic velocity region may be provided from the end of the first excitation electrode on the negative Z'-axis side to the end on the positive Z'-axis side in a plan view. Furthermore, the first outer high acoustic velocity region may be separated from the third outer high acoustic velocity region or the fourth outer high acoustic velocity region. The second outer high sound velocity region may be spaced apart from the third outer high sound velocity region and may be spaced apart from the fourth outer high sound velocity region.

[0069] The crystal blank 11, the first excitation electrode 14a, and the second excitation electrode 14b are provided in the high acoustic velocity region 17, the low acoustic velocity region 18, and the outer high acoustic velocity region 19. A mass adding film 20 is further provided in the low acoustic velocity region 18. The mass adding film 20 is provided so as to avoid the high acoustic velocity region 17 and the outer high acoustic velocity region 19. In other words, the planar shape of the mass adding film 20 is a frame shape that overlaps the low acoustic velocity region 18.

[0070] The first excitation electrode 14a has outer edge portions 71, 72, 73, and 74. The outer edge portion 71 is an edge portion of one side of the four edges of the first excitation electrode 14a in a plan view that extends along the X-axis on the negative Z'-axis side. The outer edge portion 72 is an edge portion of one side that extends along the X-axis on the positive Z'-axis side. The outer edge portion 73 is an edge portion of one side that extends along the Z'-axis on the positive X-axis side. The outer edge portion 74 is an edge portion of one side that extends along the Z'-axis on the negative X-axis side.

[0071] The second excitation electrode 14b has outer edge portions 81, 82, 83, and 84. The outer edge portion 81 is an edge portion of one side of the four edges of the first excitation electrode 14a in a plan view that extends along the X-axis on the negative Z'-axis side. The outer edge portion 82 is an edge portion of one side that extends along the X-axis on the positive Z'-axis side. The outer edge portion 83 is an edge portion of one side that extends along the Z'-axis on the positive X-axis side. The outer edge portion 84 is an edge portion of one side that extends along the Z'-axis on the negative X-axis side.

[0072] The mass addition film 20 includes a first portion 21, a second portion 22, a third portion 23, and a fourth portion 24. The first portion 21 is provided on the first excitation electrode 14a in the first low acoustic velocity region 18A. The second portion 22 is provided on the first excitation electrode 14a in the second low acoustic velocity region 18B. The third portion 23 is provided on the first excitation electrode 14a in the third low acoustic velocity region 18C. The fourth portion 24 is provided on the first excitation electrode 14a in the fourth low acoustic velocity region 18D.

[0073] The first portion 21 is provided along an outer edge 71 of the first excitation electrode 14a located on the negative side of the high acoustic velocity region 17 in the Z'-axis direction, avoiding the high acoustic velocity region 17. The second portion 22 is provided along an outer edge 72 of the first excitation electrode 14a located on the positive side of the high acoustic velocity region 17 in the Z'-axis direction, avoiding the high acoustic velocity region 17. The third portion 23 is provided along an outer edge 73 of the first excitation electrode 14a located on the positive side of the high acoustic velocity region 17 in the X-axis direction, avoiding the high acoustic velocity region 17. The fourth portion 24 is provided along an outer edge 74 of the first excitation electrode 14a located on the negative side of the high acoustic velocity region 17 in the X-axis direction, avoiding the high acoustic velocity region 17. In a plan view, the first portion 21 is spaced apart from the outer edge portion 71 , the second portion 22 is spaced apart from the outer edge portion 72 , the third portion 23 is spaced apart from the outer edge portion 73 , and the fourth portion 24 is spaced apart from the outer edge portion 74 .

[0074] The first portion 21 has an outer edge 21A located on the side of the outer high sound velocity region 19 and an inner edge 21B located on the side of the high sound velocity region 17. The second portion 22 has an outer edge 22A located on the side of the outer high sound velocity region 19 and an inner edge 22B located on the side of the high sound velocity region 17. The third portion 23 has an outer edge 23A located on the side of the outer high sound velocity region 19 and an inner edge 23B located on the side of the high sound velocity region 17. The fourth portion 24 has an outer edge 24A located on the side of the outer high sound velocity region 19 and an inner edge 24B located on the side of the high sound velocity region 17.

[0075] Outer edge portions 21A, 22A, 23A, and 24A are located at the boundary between low sound velocity region 18 and outer high sound velocity region 19. Inner edge portions 21B, 22B, 23B, and 24B are located at the boundary between high sound velocity region 17 and low sound velocity region 18. The end of outer edge portion 21A on the positive X-axis side is connected to the end of outer edge portion 23A on the negative Z'-axis side, and the end of outer edge portion 21A on the negative X-axis side is connected to the end of outer edge portion 24A on the negative Z'-axis side. The end of outer edge portion 22A on the positive X-axis side is connected to the end of outer edge portion 23A on the positive Z'-axis side, and the end of outer edge portion 22A on the negative X-axis side is connected to the end of outer edge portion 24A on the positive Z'-axis side. The end of inner edge 21B on the positive X-axis side is connected to the end of inner edge 23B on the negative Z'-axis side, and the end of inner edge 21B on the negative X-axis side is connected to the end of inner edge 24B on the negative Z'-axis side. The end of inner edge 22B on the positive X-axis side is connected to the end of inner edge 23B on the positive Z'-axis side, and the end of inner edge 22B on the negative X-axis side is connected to the end of inner edge 24B on the positive Z'-axis side.

[0076] 5 , in a plan view, the outer edge portions 71 and 72 of the first excitation electrode 14a overlap the second excitation electrode 14b. The outer edge portions 71 and 72 of the first excitation electrode 14a are located between the outer edge portions 81 and 82 of the second excitation electrode 14b. The outer edge portion 71 of the first excitation electrode 14a is located between the outer edge portion 81 of the second excitation electrode 14b and the outer edge portion 21A of the first portion 21 of the mass addition film 20. The outer edge portion 72 of the first excitation electrode 14a is located between the outer edge portion 82 of the second excitation electrode 14b and the outer edge portion 22A of the second portion 22 of the mass addition film 20. Similarly, the outer edge portions 73 and 74 of the first excitation electrode 14a overlap the second excitation electrode 14b. The outer edge portions 73 and 74 of the first excitation electrode 14a are located between the outer edge portions 83 and 84 of the second excitation electrode 14b. The outer edge portion 73 of the first excitation electrode 14a is located between the outer edge portion 83 of the second excitation electrode 14b and the outer edge portion 23A of the third portion 23 of the mass adding film 20. The outer edge portion 74 of the first excitation electrode 14a is located between the outer edge portion 84 of the second excitation electrode 14b and the outer edge portion 24A of the fourth portion 24 of the mass adding film 20.

[0077] As shown in FIG. 4 , the distance along the Z′-axis direction between the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 22A of the second portion 22 is defined as length A. The distance along the Z′-axis direction between the inner edge 21B of the first portion 21 of the mass addition film 20 and the inner edge 22B of the second portion 22 is defined as length A'. The distance along the Z′-axis direction between the outer edge 71 and the outer edge 72 of the first excitation electrode 14a is defined as length B. The distance along the Z′-axis direction between the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 71 of the first excitation electrode 14a is defined as length B1. The distance along the Z′-axis direction between the outer edge 22A of the second portion 22 of the mass addition film 20 and the outer edge 72 of the first excitation electrode 14a is defined as length B2. The distance along the Z′-axis direction between the outer edge 81 and the outer edge 82 of the second excitation electrode 14b is defined as length C. The distance along the Z'-axis direction between the outer edge 71 of the first excitation electrode 14a and the outer edge 81 of the second excitation electrode 14b is defined as length C1. The distance along the Z'-axis direction between the outer edge 72 of the first excitation electrode 14a and the outer edge 82 of the second excitation electrode 14b is defined as length C2. The distance along the Z'-axis direction between the outer edge 21A and the inner edge 21B of the first portion 21 of the mass addition film 20 is defined as length D1, and the distance along the Z'-axis direction between the outer edge 22A and the inner edge 22B of the second portion 22 of the mass addition film 20 is defined as length D2. The distance along the Z'-axis direction between the outer edge of the first low acoustic velocity region 18A on the opposite side to the second low acoustic velocity region 18B and the outer edge of the second low acoustic velocity region 18B on the opposite side to the first low acoustic velocity region 18A is defined as length E. The distance along the Z'-axis direction between the outer edge of the high sonic velocity region 17 on the first low sonic velocity region 18A side and the outer edge of the high sonic velocity region 17 on the second low sonic velocity region 18B side is defined as length E'. In other words, length E' is the distance along the Z'-axis direction between the inner edge of the first low sonic velocity region 18A on the second low sonic velocity region 18B side and the inner edge of the second low sonic velocity region 18B on the first low sonic velocity region 18A side. The distance along the Z'-axis direction between the outer edge of the first low sonic velocity region 18A on the opposite side to the second low sonic velocity region 18B and the outer edge of the second low sonic velocity region 18B side is defined as length E1. The distance along the Z'-axis direction between the outer edge of the second low sonic velocity region 18B on the opposite side to the first low sonic velocity region 18A and the outer edge of the first low sonic velocity region 18A side is defined as length E2.

[0078] The length A corresponds to the dimension of the mass addition film 20 along the Z'-axis direction. The length A' corresponds to the dimension of the high acoustic velocity region 17 along the Z'-axis direction. The length B corresponds to the dimension of the first excitation electrode 14a along the Z'-axis direction, and corresponds to the sum of the dimensions of the high acoustic velocity region 17, the first low acoustic velocity region 18A, the second low acoustic velocity region 18B, the first outer high acoustic velocity region 19A, and the second outer high acoustic velocity region 19B along the Z'-axis direction. The length B1 corresponds to the dimension of the first outer high acoustic velocity region 19A along the Z'-axis direction, and the length B2 corresponds to the dimension of the second outer high acoustic velocity region 19B along the Z'-axis direction. The length C corresponds to the dimension of the second excitation electrode 14b along the Z'-axis direction. The length C1 corresponds to the dimension of the portion of the second excitation electrode 14b extending from the first excitation electrode 14a toward the negative Z'-axis direction in a plan view. The length C2 corresponds to the dimension along the Z'-axis direction of the portion of the second excitation electrode 14b that extends from the first excitation electrode 14a toward the positive side of the Z'-axis in a plan view. The length D1 corresponds to the dimension along the Z'-axis direction of the first portion 21 of the mass adding film 20, and the length D2 corresponds to the dimension along the Z'-axis direction of the second portion 22 of the mass adding film 20. The length E corresponds to the sum of the dimensions along the Z'-axis direction of the high acoustic velocity region 17 and the low acoustic velocity region 18. The length E' corresponds to the dimension along the Z'-axis direction of the high acoustic velocity region 17. The length E1 corresponds to the dimension along the Z'-axis direction of the first low acoustic velocity region 18A. The length E2 corresponds to the dimension along the Z'-axis direction of the second low acoustic velocity region 18B.

[0079] 5, when the outer edge portions 21A and 22A of the mass adding film 20 are parallel to the X-axis direction in a plan view, the length A is determined by measuring the distance in the Z'-axis direction between the outer edge portion 21A and the outer edge portion 22A. When the inner edge portions 21B and 22B of the mass adding film 20 are parallel to the X-axis direction in a plan view, the length A' is determined by measuring the distance in the Z'-axis direction between the inner edge portion 21B and the inner edge portion 22B.

[0080] 5 , when the outer edge portions 71 and 72 of the first excitation electrode 14a are parallel to the X-axis direction in a plan view, the length B is determined by measuring the distance in the Z′-axis direction between the outer edge portion 71 and the outer edge portion 72. When the outer edge portions 21A and 22A of the mass addition film 20 and the outer edge portions 71 and 72 of the first excitation electrode 14a are parallel to the X-axis direction in a plan view, the length B1 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 21A and the outer edge portion 71, and the length B2 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 22A and the outer edge portion 72.

[0081] 5 , when the outer edge portions 81 and 82 of the second excitation electrode 14b are parallel to the X-axis direction in a plan view, the length C is determined by measuring the distance in the Z′-axis direction between the outer edge portion 81 and the outer edge portion 82. When the outer edge portions 71 and 72 of the first excitation electrode 14a and the outer edge portions 81 and 82 of the second excitation electrode 14b are parallel to the X-axis direction in a plan view, the length C1 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 71 and the outer edge portion 81, and the length C2 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 72 and the outer edge portion 82.

[0082] As shown in Figure 5, when the outer edge portions 21A, 22A and inner edge portions 21B, 22B of the mass-adding film 20 are parallel to the X-axis direction in a planar view, the length D1 is determined by measuring the distance in the Z'-axis direction between the outer edge portion 21A and the inner edge portion 21B, and the length D2 is determined by measuring the distance in the Z'-axis direction between the outer edge portion 22A and the inner edge portion 22B.

[0083] 5 , when the outer edge portions 21A, 22A and the inner edge portions 21B, 22B of the mass addition film 20 are parallel to the X-axis direction in a plan view, the length E is determined by measuring the distance in the Z′-axis direction between the outer edge portion 21A and the outer edge portion 22A. Furthermore, the length E′ is determined by measuring the distance in the Z′-axis direction between the inner edge portion 21B and the inner edge portion 22B. The length E1 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 21A and the inner edge portion 21B. The length E2 is determined by measuring the distance in the Z′-axis direction between the outer edge portion 21A and the inner edge portion 21B.

[0084] However, when the outer edges 21A and 22A of the mass adding film 20 are not parallel in plan view, such as when the planar shape of the mass adding film 20 is polygonal, circular, elliptical, or a combination thereof, the length A can be determined by a method other than the above. For example, the length A may be determined as the maximum value of the distance between the outer edges 21A and 22A. The length A may also be determined as the average or minimum value of the distance between the outer edges 21A and 22A. The length A may also be determined by dividing the area of ​​the region surrounded by the outer edges 21A, 22A, 23A, and 24A of the mass adding film 20 by the distance in the X-axis direction between the outer edges 23A and 24A. The length A may also be determined by measuring the distance between the outer edges 21A and 22A of the inner edge 23B of the mass adding film 20 in plan view or on a tangent line that is tangent to the inner edge 23B and extends in the Z'-axis direction. The lengths A', B, B1, B2, C, C1, C2, D1, D2, E, E', E1, and E2 may also be specified in the same manner as the length A.

[0085] In this embodiment, length E and length A are approximately equal (E=A), and length E' and length A' are approximately equal (E'=A'). Length E1 and length D1 are approximately equal (E1=D1), and length E2 and length D2 are approximately equal (E2=D2). Length E1 and length E2 are approximately equal (E1=E2). Specifically, the relationship E1=E2=(1±0.04)×(E-E') / 2 holds. Lengths E1 and E2 are greater than length A' (A'<E1 and A'<E2). However, lengths E1 and E2 may be approximately equal to length A' or may be smaller than length A'.

[0086] In this embodiment, length A is smaller than length B, and length B is smaller than length C (A<B<C). Lengths B1 and B2 are approximately equal (B1=B2). Specifically, the relationship B1=B2=(1±0.10)×(B-A) / 2 holds. Lengths C1 and C2 are approximately equal (C1=C2). Specifically, the relationship C1=C2=(1±0.10)×(C-B) / 2 holds. As an example, length C1 is larger than length B1 (B1<C1), and length C2 is larger than length B2 (B2<C2). Lengths D1 and D2 are approximately equal (D1=D2). Specifically, the relationship D1=D2=(1±0.04)×(A-A') / 2 holds. As an example, length D1 is greater than length A' (A'≦D1), and length D2 is greater than length A' (A'≦D2). The ratio A' / B of the length A' to the length B is, for example, 0.02 or more (0.02≦A' / B). Preferably, the relationship 0.05≦A' / B≦0.5 holds. More preferably, the relationship 0.20≦A' / B≦0.47 holds.

[0087] Note that, as long as the relationship A<B<C holds, the magnitude relationship between the lengths A, A', B, B1, B2, C, C1, C2, D1, and D2 is not limited to the above. For example, the relationship B1<B2 or B2<B1 may hold, or the relationship C1<C2 or C2<C1 may hold. The relationship C1≦B1 may hold, or the relationship C2≦B2 may hold. The relationship D1<D2 or D2<D1 may hold. The relationship D1<A' may hold, or the relationship D2<A' may hold.

[0088] 4 , the thickness of the crystal blank 11 is Tp, the thickness of the first excitation electrode 14a is Te1, the thickness of the second excitation electrode 14b is Te2, and the thickness of the mass adding film 20 is Tf. When the first excitation electrode 14a and the mass adding film 20 are made of the same material and the boundary between them is unclear, the thickness Tf of the mass adding film 20 may be specified as the distance along the Y′-axis direction between the surface of the first excitation electrode 14a in the high acoustic velocity region 17 and the surface of the mass adding film 20 in the low acoustic velocity region 18. Furthermore, the thickness Tf of the mass adding film 20 may be specified as the height of the steps at the outer edge portions 21A, 22A, 23A, and 24A of the mass adding film 20, or as the height of the steps at the inner edge portions 21B, 22B, 23B, and 24B of the mass adding film 20. However, if the height of the steps at the outer edge portions 21A, 22A, 23A, and 24A is different from the height of the steps at the inner edge portions 21B, 22B, 23B, and 24B, the thickness Tf of the mass-adding film 20 is determined as the height of the steps at the inner edge portions 21B, 22B, 23B, and 24B.

[0089] The thickness Tp is approximately constant throughout the high acoustic velocity region 17, the low acoustic velocity region 18, and the outer high acoustic velocity region 19. Similarly, the thicknesses Te1 and Te2 are approximately constant throughout the high acoustic velocity region 17, the low acoustic velocity region 18, and the outer high acoustic velocity region 19. The thickness Tf is approximately constant throughout the entire low acoustic velocity region 18. In other words, the first portion 21, the second portion 22, the third portion 23, and the fourth portion 24 are approximately equal in thickness. The thickness Te1 and the thickness Te2 are approximately equal (Te1 = Te2), and the thickness Tf is smaller than the thickness Te1 (Tf < Te1). For example, the thicknesses Te1 and Te2 are approximately 0.05 μm, and the thickness Tf is approximately 0.02 μm.

[0090] The relationship between the thicknesses is not limited to the above. For example, the thickness Tf may be equal to or greater than the thickness Te1 (Te1≦Tf). The thickness Te1 may be smaller than the thickness Te2 (Te1<Te2), or the thickness Te1 may be larger than the thickness Te2 (Te2<Te1).

[0091] As shown in FIG. 5 , 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 Xe1, and the dimension of the first excitation electrode 14a along the Z'-axis direction is defined as length Ze1. The dimension of the second excitation electrode 14b along the X-axis direction is defined as length Xe2, and the dimension of the second excitation electrode 14b along the Z'-axis direction is defined as length Ze2. The distance along the Z'-axis direction between the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 71 of the first excitation electrode 14a is defined as length Wgz. The distance along the Z'-axis direction between the outer edge 22A of the second portion 22 of the mass addition film 20 and the outer edge 72 of the first excitation electrode 14a is defined as length Wgz. The distance along the Z'-axis direction between the inner edge 21B of the first portion 21 of the mass addition film 20 and the outer edge 71 of the first excitation electrode 14a is defined as length Wz. The distance along the Z'-axis direction between the inner edge 22B of the second portion 22 of the mass addition film 20 and the outer edge 72 of the first excitation electrode 14a is defined as length Wz. The distance along the X-axis direction between the outer edge 23A of the third portion 23 of the mass addition film 20 and the outer edge 73 of the first excitation electrode 14a is defined as length Wgx. The distance along the X-axis direction between the outer edge 24A of the fourth portion 24 of the mass addition film 20 and the outer edge 74 of the first excitation electrode 14a is defined as length Wgx. The distance along the X-axis direction between the inner edge 23B of the third portion 23 of the mass addition film 20 and the outer edge 73 of the first excitation electrode 14a is defined as length Wx. The distance along the X-axis direction between the inner edge 24B of the fourth portion 24 of the mass adding film 20 and the outer edge 74 of the first excitation electrode 14a is defined as length Wx. The distance along the Z′-axis direction between the first portion 21 and the second portion 22 of the mass adding film 20 is defined as length Zf, and the distance along the X-axis direction between the third portion 23 and the fourth portion 24 of the mass adding film 20 is defined as length Xf.

[0092] The length Ze2 corresponds to the length C (Ze2 = C). The length Ze1 corresponds to the length B (Ze1 = B). The length Wgz corresponds to the lengths B1 and B2 (Wgz = B1 = B2). The length Wz corresponds to the sum of the lengths B1 and D1 and the sum of the lengths B2 and D2 (Wz = B1 + D1 = B2 + D2). The length Zf corresponds to the length A' (Zf = A'). The dimension of the mass addition film 20 along the Z'-axis direction can be expressed as 2 × Wz + Zf - 2 × Wgz, which is equal to or less than the dimension Ze2 of the second excitation electrode 14b along the Z'-axis direction (2 × Wz + Zf - 2 × Wgz ≦ Ze2). The dimension of the mass addition film 20 along the X-axis direction can be expressed as 2×Wx+Xf−2×Wgx, which is equal to or less than the dimension Xe2 of the second excitation electrode 14b along the X-axis direction (2×Wx+Xf−2×Wgx≦Xe2). The length Wgz is, for example, approximately equal to the length Wgx (Wgz=Wgx). However, the length Wgz may be smaller than the length Wgx (Wgz<Wgx), or may be larger than the length Wgx (Wgx<Wgz).

[0093] Next, simulation results of examples based on the first embodiment will be described with reference to Fig. 6 to Fig. 16. Fig. 6 is a table showing the conditions for the simulation based on the first embodiment. Fig. 7 to Fig. 16 are graphs showing the simulation results based on the first embodiment.

[0094] (First Example) Tp = 1.52 μm Tf = 0.02 μm Te1 = Te2 = 0.08 μm Px = Pz = 120 μm Xf = Zf = 20 μm Wx = 40 μm Wz = 30 μm Wgx: variable Wgz: variable Xe1 = 100 μm Ze1 = 80 μm Xe2 = 104 μm Ze2 = 84 μm (First' Example) Wgx = Wgz = 2 μm Xe2: variable Ze2: variable Other than the above, the same as the first example.

[0095] (Second Example) Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 12 μm Zf = 28 μm Wx = 24 μm Wz = 16 μm Wgx: variable Wgz: variable Xe1 = Ze1 = 60 μm Xe2 = Ze2 = 64 μm (Second' Example) Wgx = Wgz = 2 μm Xe2: variable Ze2: variable Other than the above, the example is the same as the second example.

[0096] (Third Example) Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 19 μm Zf = 30 μm Wx = 28 μm Wz = 20 μm Wgx: variable Wgz: variable Xe1 = 75 μm Ze1 = 70 μm Xe2 = 79 μm Ze2 = 74 μm (Third' Example) Wgx = Wgz = 2 μm Xe2: variable Ze2: variable Other than the above, the example is the same as the third example.

[0097] FIG. 7 shows simulation results based on the first embodiment. The vertical axis represents the electromechanical coupling coefficient k (hereinafter also referred to as "k_S0") of the main S0 mode, and the horizontal axis represents Wgx = Wgz. The graph plots the k_S0 simulation results for the first embodiment (Wx = 40 μm, Wz = 30 μm), the k_S0 simulation results for a configuration based on the first embodiment with Wx = 30 μm and Wz = 25 μm, and the k_S0 simulation results for a configuration based on the first embodiment with Wx = 25 μm and Wz = 20 μm. For a configuration with Tf = 0, i.e., without the mass-adding film 20, k_S0 is approximately 6.8%. Since Xf and Zf are determined by the following equations, Xf = Xe1 - Wx × 2 and Zf = Ze1 - Wz × 2, Xf and Zf change in conjunction with Wx and Wz.

[0098] In the first embodiment, when B' = Wgx = Wgz ≦ 8 μm, k_S0 is improved over 6.8% when Tf = 0. Even when Wx and Wz are changed based on the configuration of the first embodiment, a similar trend is obtained. At least when the ratio of Wx to Xe1 is 25% or more and 40% or less, and the ratio of Wz to Ze1 is 25% or more and 37.5% or less, k_S0 is 6.8% < when B' = Wgx = Wgz < 8 μm, and 6.8% < k_S0 is 6.8% < when B' = Wgx = Wgz ≦ 7 μm, regardless of the magnitude of Wx and Wz.

[0099] When the planar shape of the mass-adding film is a circumferentially continuous rectangular frame, the condition for 6.8% < k_S0 when B' = Wgx = Wgz < 8 μm, regardless of the sizes of Wx and Wz, is that the area ratio of the mass-adding film to the area of ​​the first excitation electrode is 75% or more and 95% or less. When the planar shape of the mass-adding film is two strips parallel to the X-axis direction, the condition for 6.8% < k_S0 when B' = Wgz < 8 μm, regardless of the size of Wz, is that the area ratio is 50% or more and 80% or less. Similarly, when the planar shape of the mass-adding film is two strips parallel to the Z'-axis direction, the condition for 6.8% < k_S0 when B' = Wgx < 8 μm, regardless of the size of Wx, is that the area ratio is 50% or more and 80% or less.

[0100] FIG. 8 shows simulation results based on the first embodiment. FIG. 9 shows simulation results based on the second embodiment. In FIGS. 8 and 9 , the vertical axis represents the electromechanical coupling coefficient k (hereinafter also referred to as “k_A0”) of the spurious A0 mode, and the horizontal axis represents Wgx = Wgz. The graphs in FIGS. 8 and 9 plot the simulation results of k_A0Z for a configuration in which there is no misalignment between the mass addition film 20 and the second excitation electrode 14b, as well as the simulation results of k_A0Z for a configuration in which there is a misalignment. The simulation results of k_A0Z for a configuration in which there is a misalignment were performed under the assumption that the mass addition film 20 is misaligned by 0.5 μm in the positive X-axis direction and the positive Z′-axis direction, and the second excitation electrode 14b is misaligned by 0.5 μm in the negative X-axis direction and the negative Z′-axis direction.

[0101] 8 and 9, in the range of 2 μm≦B′=Wgx=Wgz≦10 μm, k_A0Z in the configuration with misalignment is substantially equal to k_A0Z in the configuration without misalignment. In other words, in the range of 2 μm≦B′=Wgx=Wgz≦10 μm, an increase in k_A0Z is suppressed regardless of the dimensions and misalignment of the first excitation electrode 14 a, the second excitation electrode 14 b, and the mass addition film 20.

[0102] 10 shows the simulation results based on the first embodiment. The vertical axis represents the Q value, and the horizontal axis represents Wgx = Wgz. The graph plots the simulation results of the Q value in a configuration without misalignment of the mass addition film 20 and the second excitation electrode 14b, and the simulation results of the Q value in a configuration with misalignment. The direction and amount of misalignment in the configuration with misalignment in FIG. 10 are the same as the direction and amount of misalignment in the configuration with misalignment in FIGS. 8 and 9.

[0103] In a configuration without misalignment, the Q value does not change substantially in the range of 0<B'=Wgx=Wgz≦10 μm. Also, the Q value in a configuration with misalignment is substantially equal to the Q value in a configuration without misalignment. In other words, the Q value is substantially constant regardless of the magnitude of B'=Wgx=Wgz and whether or not there is misalignment.

[0104] 11 shows the simulation results based on the first embodiment. The vertical axis represents k_S0, and the horizontal axis represents x = C - B = Ze2 - Ze1. The graph plots the simulation results of k_S0 in a configuration where there is no misalignment of the mass addition film 20 and the second excitation electrode 14b, as well as the simulation results of k_S0 in a configuration where there is a misalignment. The direction and amount of misalignment in the configuration with misalignment in FIG. 11 are the same as the direction and amount of misalignment in the configuration with misalignment in FIGS. 8 and 9.

[0105] In a configuration without misalignment, k_S0 does not change substantially in the range of 0<x≦10 μm. Furthermore, in the range of 0<x≦10 μm, k_S0 in a configuration with misalignment is substantially equal to k_S0 in a configuration without misalignment. In other words, k_S0 is substantially constant regardless of the magnitude of x or the presence or absence of misalignment.

[0106] FIG. 12 shows simulation results based on the first' embodiment, FIG. 13 shows simulation results based on the second' embodiment, and FIG. 14 shows simulation results based on the third' embodiment. In FIGS. 12 to 14, the vertical axis represents k_A0, and the horizontal axis represents x = C - B = Ze2 - Ze1. The graphs in FIGS. 12 to 14 plot simulation results of k_A0X and k_A0Z in a configuration where there is no misalignment of the mass addition film 20 and the second excitation electrode 14b, as well as simulation results of k_A0X and k_A0Z in a configuration where there is a misalignment. The direction and amount of misalignment in the configuration with misalignment in FIGS. 12 to 14 are the same as the direction and amount of misalignment in the configuration with misalignment in FIGS. 8 and 9.

[0107] In FIG. 12 , both k_A0X and k_A0Z are sufficiently reduced and substantially constant in the range of 3 μm≦x≦10 μm. That is, the excitation suppression effect of the A0 mode is stable in the range of 3 μm≦x≦10 μm. Furthermore, in the range of 3 μm≦x≦10 μm, k_A0X and k_A0Z in the configuration with misalignment are substantially equal to k_A0X and k_A0Z in the configuration without misalignment. That is, in the range of 3 μm≦x≦10 μm, k_A0X and k_A0Z are substantially constant regardless of the magnitude of x and whether or not there is misalignment. In FIGS. 13 and 14 , k_A0X and k_A0Z show a similar tendency. That is, the increase in k_A0 is suppressed regardless of the dimensions and misalignment of the first excitation electrode 14 a, the second excitation electrode 14 b, and the mass addition film 20.

[0108] 15 and 16 show simulation results based on the first embodiment. In FIGS. 15 and 16, the vertical axis represents the Q value, and the horizontal axis represents x = C - B = Ze2 - Ze1. The graph in FIG. 15 plots the simulation results of the Q value for a configuration without misalignment of the mass addition film 20 and the second excitation electrode 14b, as well as the simulation results of the Q value for a configuration with misalignment. The direction and amount of misalignment in the configuration with misalignment in FIG. 15 are the same as the direction and amount of misalignment in the configuration with misalignment in FIGS. 8 and 9. The graph in FIG. 16 plots the simulation results of the Q value for the first embodiment (Wx = 40 μm, Wz = 30 μm), the simulation results of the Q value for a configuration based on the first embodiment with Wx = 30 μm, Wz = 25 μm, and the simulation results of the Q value for a configuration based on the first embodiment with Wx = 45 μm, Wz = 30 μm.

[0109] 15, the Q value in the configuration without misalignment is 80% or more of the Q value when x = 0 μm in the range of 0 < x ≦ 8 μm. The Q value in the configuration with misalignment shows a similar trend to the Q value in the configuration without misalignment and is approximately equal to the Q value in the configuration without misalignment. In other words, in the range of 0 < x ≦ 8 μm, the decrease in the Q value is suppressed regardless of the presence or absence of misalignment.

[0110] 16, even when Wx and Wz are changed based on Example 1, the Q value shows a similar tendency. That is, in the range of 0<x≦8 μm, the decrease in the Q value is suppressed regardless of the dimensions of the first excitation electrode 14 a, the second excitation electrode 14 b, and the mass addition film 20.

[0111] Next, the influence of misalignment will be described with reference to FIGS. 17 and 18. FIG. 17 is a diagram for explaining the influence of misalignment in the first embodiment. FIG. 18 is a diagram for explaining the influence of misalignment in the first embodiment. FIG. 17 is a cross-sectional view of the quartz crystal vibrating element 10 when the mass addition film 20 is misaligned by dz in the positive direction of the Z' axis. FIG. 18 is a cross-sectional view of the quartz crystal vibrating element 10 when the second excitation electrode 14b is misaligned by dz in the negative direction of the Z' axis.

[0112] 17, when the mass adding film 20 is shifted by dz in the positive direction of the Z' axis, the length of the first outer high sound velocity region 19A along the Z' axis direction is defined as B1d1. The length B1d1 is greater than the length B1 by the amount of shift dz. That is, it can be expressed as B1d1 = B1 + dz. When the mass adding film 20 is shifted by dz in the positive direction of the Z' axis, the length of the second outer high sound velocity region 19B along the Z' axis direction is defined as B2d1. The length B2d1 is less than the length B2 by the amount of shift dz. That is, it can be expressed as B2d1 = B2 - dz.

[0113] As shown in FIG. 17 , when the mass adding film 20 is shifted by dz in the positive direction of the Z' axis, the length of the first low acoustic velocity region 18A along the Z' axis direction is defined as E1d1. The length E1d1 does not change from the length E1. That is, E1d1 = E1 = D1. When the mass adding film 20 is shifted by dz in the positive direction of the Z' axis, the length of the second low acoustic velocity region 18B along the Z' axis direction is defined as E2d1. The length E2d1 does not change from the length E2. That is, E2d1 = E2 = D2. Therefore, in this embodiment, even when the mass adding film 20 is shifted by dz in the positive direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction does not change, and the relationship E1d1 = E2d1 holds. Therefore, even if the mass adding film 20 is displaced by dz in the positive direction of the Z' axis, an increase in k_A0 is suppressed and a decrease in k_S0 is suppressed.

[0114] Note that when B2<dz, the second portion 22 of the mass addition film 20 extends from the first excitation electrode 14a toward the positive Z'-axis direction in a plan view. As a result, there are portions of the second portion 22 of the mass addition film 20 that do not overlap with the first excitation electrode 14a, which changes the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z'-axis direction. To maintain the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z'-axis direction, it is desirable to satisfy the relationship dz≦B'=B1=B2. Since the maximum positional deviation on the same plane is, for example, approximately 0.3 μm, it is desirable to satisfy 0.5 μm≦B', more desirably 1 μm≦B', and even more desirably 2 μm≦B'.

[0115] As shown in FIG. 18 , when the second excitation electrode 14b is shifted by dz in the negative direction of the Z' axis, the length of the first low acoustic velocity region 18A along the Z' axis direction is defined as E1d2. The length E1d2 does not change from the length E1. That is, E1d2 = E1 = D1. When the second excitation electrode 14b is shifted by dz in the negative direction of the Z' axis, the length of the second low acoustic velocity region 18B along the Z' axis direction is defined as E2d2. That is, E2d2 = E2 = D2. Therefore, in this embodiment, even when the second excitation electrode 14b is shifted by dz in the negative direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction does not change, and the relationship E1d2 = E2d2 holds. Therefore, even if the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, an increase in k_A0 is suppressed and a decrease in k_S0 is suppressed.

[0116] Note that when C2<dz, the second excitation electrode 14b extends from the first excitation electrode 14a toward the positive Z'-axis direction in plan view. As a result, a portion of the first excitation electrode 14a does not overlap with the second excitation electrode 14b, changing the balance in the lengths of the first outer high acoustic velocity region 19A and the second outer high acoustic velocity region 19B along the Z'-axis direction. To maintain the balance in the lengths of the first outer high acoustic velocity region 19A and the second outer high acoustic velocity region 19B along the Z'-axis direction, it is desirable to satisfy the relationship dz≦C'=C1=C2. Since the positional misalignment between the different surfaces is, for example, a maximum of approximately 0.7 μm, it is desirable for 1 μm≦C' to be satisfied, more desirably 2 μm≦C', and even more desirably 4 μm≦C'.

[0117] As described above, according to this embodiment, the mass adding film 20 is provided on the first excitation electrode 14a. The mass adding film 20 is provided along the outer edge of the first excitation electrode 14a, and when the dimension of the mass adding film 20 along the Z'-axis direction is A and the dimension of the second excitation electrode 14b along the Z'-axis direction is C, the relationship A≦C holds. Furthermore, the outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass adding film 20 overlap the second excitation electrode 14b.

[0118] This makes it possible to prevent the dimensional balance between the first low acoustic velocity region 18A and the second low acoustic velocity region 18B from deteriorating even when the positions of the mass addition film 20 and the second excitation electrode 14b are misaligned, thereby preventing an increase in the electromechanical coupling coefficient k_A0 of the spurious mode and a decrease in the electromechanical coupling coefficient k_S0 of the main mode.

[0119] Furthermore, in this embodiment, when the dimension of the first portion 21 of the mass adding film 20 along the Z'-axis direction is D1, the dimension of the second portion 22 of the mass adding film 20 along the Z'-axis direction is D2, and the distance along the Z'-axis direction between the first portion 21 and the second portion 22 of the mass adding film 20 is A, D1 and D2 are approximately equal, for example, D1 = (1 ± 0.04) × (A - A') / 2 μm, D2 = (1 ± 0.04) × (A - A') / 2 μm.

[0120] This makes it possible to suppress spurious vibrations in the A0 mode.

[0121] Furthermore, in this embodiment, when the distance along the Z'-axis direction between the first part 21 and the second part 22 of the mass-adding film 20 is A' and the dimension along the Z'-axis direction of the first excitation electrode 14a is B, the relationship A' / B≦0.5 holds.

[0122] This makes it possible to prevent the effect of the mass adding film 20 in reducing spurious vibrations from being reduced due to the first portion 21 or the second portion 22 of the mass adding film 20 being too large.

[0123] In this embodiment, the relationship 0.05≦A′ / B holds.

[0124] This prevents most of the first portion 21 or the second portion 22 of the mass adding film 20 from extending outside the first excitation electrode 14a in a plan view when the mass adding film 20 is misaligned with respect to the first excitation electrode 14a. That is, it is possible to prevent the dimensional balance between the first low acoustic velocity region 18A and the second low acoustic velocity region 18B from becoming unbalanced. Therefore, it is possible to sufficiently prevent an increase in k_A0 and a decrease in k_S0.

[0125] Furthermore, in this embodiment, when the distance along the Z'-axis direction between the outer edge 21A of the first part 21 of the mass adding film 20 and the outer edge 71 of the first excitation electrode 14a is defined as B', and the distance along the Z'-axis direction between the outer edge 22A of the second part 22 of the mass adding film 20 and the outer edge 72 of the first excitation electrode 14a is defined as B', the relationship 2 μm≦B' holds.

[0126] This makes it possible to suppress an increase in k_A0.

[0127] In this embodiment, the relationship B'≦8 μm holds.

[0128] This makes it possible to suppress the decrease in k_S0.

[0129] In this embodiment, when the dimension of the second excitation electrode 14b along the Z'-axis direction is C, the relationship 3 μm≦C−B holds.

[0130] This makes it possible to suppress an increase in k_A0.

[0131] In this embodiment, the relationship CB≦10 μm holds true.

[0132] This makes it possible to suppress a decrease in the Q value.

[0133] Other embodiments will be described below. 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 in detail.

[0134] Second Embodiment Next, the configuration of a quartz crystal vibrating element 210 according to a second embodiment will be described with reference to Fig. 19. Fig. 19 is a cross-sectional view of the quartz crystal vibrating element according to the second embodiment.

[0135] In a plan view, the outer edge 71 of the first excitation electrode 14a overlaps the outer edge 81 of the second excitation electrode 14b, and the outer edge 72 of the first excitation electrode 14a overlaps the outer edge 82 of the second excitation electrode 14b. The outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass addition film 20 are located between the outer edge 71 and the outer edge 72 of the first excitation electrode 14a. The length B is approximately equal to the length C and is greater than the length A (A<B=C). The length E1 is approximately equal to the length D1 (E1=D1), the length E1 is approximately equal to the length D1 (E2=D2), and the length E1 is approximately equal to the length E2 (E1=E2).

[0136] In a plan view, both the outer edge portion 71 of the first excitation electrode 14a and the outer edge portion 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the first low acoustic velocity region 18A. The outer edge portion 71 and the outer edge portion 81 are equally far from the center of the first excitation electrode 14a. Both the outer edge portion 71 of the first excitation electrode 14a and the outer edge portion 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the second low acoustic velocity region 18B. The outer edge portion 72 and the outer edge portion 82 are equally far from the center of the first excitation electrode 14a.

[0137] Third Embodiment Next, the configuration of a quartz crystal vibrating element 310 according to a third embodiment will be described with reference to Fig. 20. Fig. 20 is a cross-sectional view of the quartz crystal vibrating element according to the third embodiment.

[0138] In a plan view, an outer edge portion 81 of the second excitation electrode 14b is located between an outer edge portion 71 of the first excitation electrode 14a and an outer edge portion 21A of the first portion 21 of the mass adding film 20. An outer edge portion 82 of the second excitation electrode 14b is located between the outer edge portion 72 of the first excitation electrode 14a and an outer edge portion 22A of the second portion 22 of the mass adding film 20. The outer edge portions 21A of the first portion 21 and the outer edge portion 22A of the second portion 22 of the mass adding film 20 are located between the outer edge portions 81 and 82 of the second excitation electrode 14b. The outer edge portions 81 and 82 of the second excitation electrode 14b are located between the outer edge portions 71 and 72 of the first excitation electrode 14a. Length B is greater than length C, and length C is greater than length A (A<C<B). The length E1 is approximately equal to the length D1 (E1=D1), the length E1 is approximately equal to the length D1 (E2=D2), and the length E1 is approximately equal to the length E2 (E1=E2).

[0139] In a plan view, both the outer edge portion 71 of the first excitation electrode 14a and the outer edge portion 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the first low acoustic velocity region 18A. The outer edge portion 71 is farther from the center of the first excitation electrode 14a than the outer edge portion 81. Both the outer edge portion 71 of the first excitation electrode 14a and the outer edge portion 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge portion of the second low acoustic velocity region 18B. The outer edge portion 72 is farther from the center of the first excitation electrode 14a than the outer edge portion 82.

[0140] Fourth Embodiment Next, the configuration of a quartz crystal vibrating element 410 according to a fourth embodiment will be described with reference to Fig. 21. Fig. 21 is a cross-sectional view of the quartz crystal vibrating element according to the fourth embodiment.

[0141] In a plan view, the outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass adding film 20 overlap the outer edge 81 of the second excitation electrode 14b. The outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass adding film 20 are located between the outer edges 71 and 72 of the first excitation electrode 14a. The length A is approximately equal to the length C and is smaller than the length B (A=C<B). The length E1 is approximately equal to the length D1 (E1=D1), the length E1 is approximately equal to the length D1 (E2=D2), and the length E1 is approximately equal to the length E2 (E1=E2).

[0142] In a plan view, the outer edge of the first low acoustic velocity region 18A overlaps not only the outer edge 21A of the first portion 21 of the mass adding film 20 but also the outer edge 81 of the second excitation electrode 14b. The outer edge of the second low acoustic velocity region 18B overlaps not only the outer edge 22A of the second portion 22 of the mass adding film 20 but also the outer edge 82 of the second excitation electrode 14b.

[0143] In a plan view, of the outer edge portion 71 of the first excitation electrode 14 a and the outer edge portion 81 of the second excitation electrode 14 b, one outer edge portion 71 is farther from the center of the first excitation electrode 14 a than the outer edge portion of the first low acoustic velocity region 18 A. Of the outer edge portion 72 of the first excitation electrode 14 a and the outer edge portion 82 of the second excitation electrode 14 b, one outer edge portion 72 is farther from the center of the first excitation electrode 14 a than the outer edge portion of the second low acoustic velocity region 18 B.

[0144] Next, the influence of misalignment in the fourth embodiment will be described with reference to Fig. 22 and Fig. 23. Fig. 22 and Fig. 23 are diagrams for explaining the influence of misalignment in the fourth embodiment. Fig. 22 is a cross-sectional view of the quartz crystal vibrating element 410 when the mass addition film 20 is misaligned by dz in the positive direction of the Z' axis. Fig. 23 is a cross-sectional view of the quartz crystal vibrating element 410 when the second excitation electrode 14b is misaligned by dz in the negative direction of the Z' axis.

[0145] In both cases, when the mass adding film 20 is displaced by dz in the positive direction of the Z' axis as shown in FIG. 22 and when the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis as shown in FIG. 23, the second portion 22 of the mass adding film 20 extends from the second excitation electrode 14b in the positive direction of the Z' axis by the amount of displacement dz in a plan view. Therefore, the overlapping area of ​​the first excitation electrode 14a, the second excitation electrode 14b, and the second portion 22 of the mass adding film 20 is reduced by the amount of displacement dz. In other words, the lengths E2d1 and E2d2 are expressed as E2d1 = E2d2 = E2 - dz = D2 - dz. The lengths E1d1 and E2d2 do not change from the length E1. In other words, the lengths E1d1 = E1d2 = E1 = D1. Therefore, in this embodiment, when the mass adding film 20 is displaced by dz in the positive direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction changes, and the relationship E2d1 < E1d1 holds. Similarly, when the second excitation electrode 14b is displaced by dz in the positive direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction changes, and the relationship E2d2 < E1d2 holds. However, the outer edge 22A of the second portion 22 of the mass adding film 20 is located on the positive Z' side of the second low acoustic velocity region 18B, and the outer edge 72 of the first excitation electrode 14a is located further on the positive Z' side. In other words, as one moves from the second low acoustic velocity region 18B toward the Z' positive direction, the total thickness of the quartz-crystal vibrating element 410 changes from Tp + Te1 + Te2 + Tf to Tp + Te1 + Tf, then to Tp + Te1, and finally to Tp. On the Z' positive side of the second low acoustic velocity region 18B, the total thickness of the quartz-crystal vibrating element 410 gradually decreases, accelerating the phase change. This alleviates problems caused by a change in the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis.

[0146] Fifth Embodiment Next, the configuration of a quartz crystal vibrating element 510 according to a fifth embodiment will be described with reference to Fig. 24. Fig. 24 is a cross-sectional view of the quartz crystal vibrating element according to the fifth embodiment.

[0147] In a plan view, an outer edge 21A of the first portion 21 of the mass adding film 20 overlaps an outer edge 71 of the first excitation electrode 14a, and an outer edge 22A of the second portion 22 of the mass adding film 20 overlaps an outer edge 72 of the first excitation electrode 14a. The outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass adding film 20 are located between the outer edges 81 and 82 of the second excitation electrode 14b. The length A is approximately equal to the length B and is smaller than the length C (A=B<C). The length E1 is approximately equal to the length D1 (E1=D1), the length E1 is approximately equal to the length D1 (E2=D2), and the length E1 is approximately equal to the length E2 (E1=E2).

[0148] In a plan view, the outer edge of the first low acoustic velocity region 18A overlaps not only the outer edge 21A of the first portion 21 of the mass adding film 20 but also the outer edge 71 of the first excitation electrode 14a. The outer edge of the second low acoustic velocity region 18B overlaps not only the outer edge 22A of the second portion 22 of the mass adding film 20 but also the outer edge 72 of the first excitation electrode 14a.

[0149] In a plan view, one of the outer edge portions 71 of the first excitation electrode 14a and the outer edge portion 81 of the second excitation electrode 14b is farther from the center of the first excitation electrode 14a than the outer edge portion of the first low acoustic velocity region 18A. One of the outer edge portions 72 of the first excitation electrode 14a and the outer edge portion 82 of the second excitation electrode 14b is farther from the center of the first excitation electrode 14a than the outer edge portion of the second low acoustic velocity region 18B.

[0150] Next, the influence of misalignment in the fifth embodiment will be described with reference to Fig. 25 and Fig. 26. Fig. 25 and Fig. 26 are diagrams for explaining the influence of misalignment in the fifth embodiment. Fig. 25 is a cross-sectional view of the quartz crystal vibrating element 510 when the mass addition film 20 is misaligned by dz in the positive direction of the Z' axis. Fig. 26 is a cross-sectional view of the quartz crystal vibrating element 510 when the second excitation electrode 14b is misaligned by dz in the negative direction of the Z' axis.

[0151] As shown in FIG. 25 , when the mass addition film 20 is displaced by dz in the positive direction of the Z′ axis, the outer edge 22A of the second portion 22 of the mass addition film 20 is located between the outer edge 72 of the first excitation electrode 14a and the outer edge 82 of the second excitation electrode 14b in a planar view. The outer edge 71 of the first excitation electrode 14a is located between the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 81 of the second excitation electrode 14b. The second portion 22 of the mass addition film 20 extends from the first excitation electrode 14a in the positive direction of the Z′ axis by the amount of displacement dz. Therefore, the overlapping region of the first excitation electrode 14a, the second excitation electrode 14b, and the second portion 22 of the mass addition film 20 is reduced by the amount of displacement dz. In other words, the length E2d1 is expressed as E2d1 = E2 - dz = D2 - dz. Furthermore, the area of ​​the region where the first excitation electrode 14a, the second excitation electrode 14b, and the first portion 21 of the mass adding film 20 overlap does not change. That is, the length E1d1 is expressed as E1d1 = E1 = D1. Therefore, in this embodiment, when the mass adding film 20 is displaced by dz in the positive direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction changes, and the relationship E2d1 < E1d1 holds. In this embodiment, when D1 = D2, the difference in the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction when the mass adding film 20 is displaced by dz in the positive direction of the Z' axis is dz. On the other hand, in a comparative example in which the outer edge of the mass adding film, the outer edge of the first excitation electrode, and the outer edge of the second excitation electrode overlap, the difference in length along the Z'-axis direction between the first low acoustic velocity region and the second low acoustic velocity region when the mass adding film is displaced by dz in the positive direction of the Z'-axis in the comparative example is dz. Therefore, in this embodiment, the deterioration of the electromechanical coupling coefficient k when a positional displacement occurs in the mass adding film 20 is equivalent to the deterioration of the electromechanical coupling coefficient k when a positional displacement occurs in the comparative example.

[0152] As shown in FIG. 26 , when the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, the length E1d2 does not change from the length E1. That is, E1d2 = E1 = D1. Furthermore, the length E2d2 does not change from the length E2. That is, the length E2d2 is expressed as E2d2 = E2 = D2. Therefore, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction does not change, and the relationship E1d2 = E2d2 holds. On the other hand, when the second excitation electrode is displaced by dz in the negative direction of the Z' axis in the comparative example, the difference in the lengths of the first low acoustic velocity region and the second low acoustic velocity region along the Z' axis direction is dz. Therefore, in this embodiment, the deterioration of the electromechanical coupling coefficient k when the second excitation electrode is displaced is more suppressed than the deterioration of the electromechanical coupling coefficient k when the second excitation electrode is displaced in the comparative example. That is, even if the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, an increase in k_A0 is suppressed and a decrease in k_S0 is suppressed.

[0153] Sixth Embodiment Next, the configuration of a quartz crystal vibrating element 610 according to a sixth embodiment will be described with reference to Fig. 27. Fig. 27 is a cross-sectional view of the quartz crystal vibrating element according to the sixth embodiment.

[0154] The mass addition film 20 is made of an insulating material, such as silicon oxide or silicon nitride. In a plan view, an outer edge 21A of the first portion 21 of the mass addition film 20 overlaps an outer edge 81 of the second excitation electrode 14b, and an outer edge 22A of the second portion 22 of the mass addition film 20 overlaps an outer edge 82 of the second excitation electrode 14b. The outer edges 71 and 72 of the first excitation electrode 14a are located between the outer edges 21A and 22A of the first portion 21 of the mass addition film 20. The length A is approximately equal to the length C and greater than the length B (B<A=C). The length E1 is smaller than the length D1 (D1<E1), the length E2 is smaller than the length D2 (D2<E2), and the length E1 is approximately equal to the length E2 (E1=E2).

[0155] In a plan view, the outer edge of the first low acoustic velocity region 18A overlaps with the outer edge 71 of the first excitation electrode 14a. The outer edge of the second low acoustic velocity region 18B overlaps with the outer edge 72 of the first excitation electrode 14a.

[0156] In a plan view, both the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the first low acoustic velocity region 18A. The outer edge 21A and the outer edge 81 are equally far from the center of the first excitation electrode 14a. Both the outer edge 22A of the second portion 22 of the mass addition film 20 and the outer edge 82 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the second low acoustic velocity region 18B. The outer edge 22A and the outer edge 82 are equally far from the center of the first excitation electrode 14a.

[0157] When the dimension along the Z'-axis direction of the portion of the first portion 21 of the mass adding film 20 that protrudes from the first excitation electrode 14a to the negative side of the Z'-axis is defined as D'1, the length E1 is expressed as E1 = D1 - D'1. When the dimension along the Z'-axis direction of the portion of the second portion 22 of the mass adding film 20 that protrudes from the first excitation electrode 14a to the negative-positive side of the Z'-axis is defined as D'2, the length E2 is expressed as E2 = D2 - D'2.

[0158] Next, the influence of misalignment in the sixth embodiment will be described with reference to Fig. 28 and Fig. 29. Fig. 28 and Fig. 29 are diagrams for explaining the influence of misalignment in the sixth embodiment. Fig. 28 is a cross-sectional view of the quartz crystal vibrating element 610 when the mass addition film 20 is misaligned by dz in the positive direction of the Z' axis. Fig. 29 is a cross-sectional view of the quartz crystal vibrating element 610 when the second excitation electrode 14b is misaligned by dz in the negative direction of the Z' axis.

[0159] 28, when the mass addition film 20 is shifted by dz in the positive direction of the Z' axis, the first low acoustic velocity region 18A expands by the amount of shift dz. That is, the length E1d1 is expressed as E1d1 = E1 + dz = (D1 - D'1) + dz. The second low acoustic velocity region 18B contracts by the amount of shift dz. That is, the length E2d1 is expressed as E2d1 = E2 - dz = (D2 - D'2) - dz. Therefore, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction changes, and the relationship E2d1 < E1d1 holds. In this embodiment, when D1 = D2 and D'1 = D'2, that is, E1 = E2, when the mass-adding film 20 is shifted by dz in the positive direction of the Z' axis, the difference in length along the Z' axis direction between the first low acoustic velocity region 18A and the second low acoustic velocity region 18B is 2dz.

[0160] As shown in FIG. 29 , when the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, the length E1d2 does not change from the length E1. That is, E1d2 = E1 = D1 - D'1. Furthermore, the length E2d2 does not change from the length E2. That is, E2d2 = E2 = D2 - D'2. In this embodiment, when D1 = D2 and D'1 = D'2, i.e., E1 = E2, even when the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, the balance of the lengths of the first low acoustic velocity region 18A and the second low acoustic velocity region 18B along the Z' axis direction does not change, and the relationship E1d2 = E2d2 holds. Therefore, even when the second excitation electrode 14b is displaced by dz in the negative direction of the Z' axis, an increase in k_A0 is suppressed and a decrease in k_S0 is suppressed.

[0161] Seventh Embodiment Next, the configuration of a quartz crystal vibrating element 710 according to a seventh embodiment will be described with reference to Fig. 30. Fig. 30 is a cross-sectional view of the quartz crystal vibrating element according to the seventh embodiment.

[0162] The mass adding film 20 is made of an electrically conductive material, for example, the same material as the first excitation electrode 14a. In a plan view, an outer edge 21A of the first portion 21 of the mass adding film 20 overlaps an outer edge 81 of the second excitation electrode 14b, and an outer edge 22A of the second portion 22 of the mass adding film 20 overlaps an outer edge 82 of the second excitation electrode 14b. The outer edges 71 and 72 of the first excitation electrode 14a are located between the outer edges 21A and 22A of the first portion 21 of the mass adding film 20. The length A is approximately equal to the length C and greater than the length B (B<A=C). The length E1 is smaller than the length D1 (D1<E1), the length E2 is smaller than the length D2 (D2<E2), and the length E1 is approximately equal to the length E2 (E1=E2). The length E1 is expressed as E1=D1-D'1, and the length E2 is expressed as E2=D2-D'2.

[0163] In a plan view, the outer edge of the first low acoustic velocity region 18A overlaps with the outer edge 71 of the first excitation electrode 14a. The outer edge of the second low acoustic velocity region 18B overlaps with the outer edge 72 of the first excitation electrode 14a.

[0164] In a plan view, both the outer edge 21A of the first portion 21 of the mass addition film 20 and the outer edge 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the first low acoustic velocity region 18A. The outer edge 21A and the outer edge 81 are equally far from the center of the first excitation electrode 14a. Both the outer edge 22A of the second portion 22 of the mass addition film 20 and the outer edge 82 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the second low acoustic velocity region 18B. The outer edge 22A and the outer edge 82 are equally far from the center of the first excitation electrode 14a.

[0165] The first portion 21 of the mass addition film 2 extends from the first excitation electrode 14a in the negative Z' direction. The second portion 22 of the mass addition film 2 extends from the first excitation electrode 14a in the positive Z' direction. Because the mass addition film 20 has the same potential as the first excitation electrode 14a, the portion of the mass addition film 20 extending from the first excitation electrode 14a functions as an excitation electrode. Therefore, in a plan view, the region outside the first excitation electrode 14a where the first portion 21 of the mass addition film 20 and the second excitation electrode 14b overlap is a first outer high acoustic velocity region 191A, and the region outside the first excitation electrode 14a where the second portion 22 of the mass addition film 20 and the second excitation electrode 14b overlap is a second outer high acoustic velocity region 191B. The sum of the thicknesses in the high acoustic velocity region 17 is Tp + Te1 + Te2, and the sum of the thicknesses in each of the first outer high acoustic velocity region 191A and the second outer high acoustic velocity region 191B is Tp + Tf + Te2. Therefore, when the material of the mass addition film 20 is the same as the material of the first excitation electrode 14a and the relationship Tf < Te1 holds, the acoustic velocity in the first outer high acoustic velocity region 191A and the second outer high acoustic velocity region 191B is greater than the acoustic velocity in the high acoustic velocity region 17. In other words, the acoustic velocity in the high acoustic velocity region 17 is smaller than the acoustic velocity in the outer high acoustic velocity region 191, and the acoustic velocity in the low acoustic velocity region 18 is smaller than the acoustic velocity in the high acoustic velocity region 17. When the material of the mass adding film 20 is the same as the material of the first excitation electrode 14a and the relationship Tf = Te1 holds, the sound speed in the first outer high acoustic velocity region 191A and the second outer high acoustic velocity region 191B is approximately equal to the sound speed in the high acoustic velocity region 17. That is, the sound speed in the outer high acoustic velocity region 191 and the sound speed in the high acoustic velocity region 17 are approximately equal and are greater than the sound speed in the low acoustic velocity region 18. When the material of the mass adding film 20 is the same as the material of the first excitation electrode 14a and Te1 < Tf, the sound speed in the first outer high acoustic velocity region 191A and the second outer high acoustic velocity region 191B is smaller than the sound speed in the high acoustic velocity region 17. That is, the sound speed in the outer high acoustic velocity region 191 is smaller than the sound speed in the high acoustic velocity region 17, and the sound speed in the low acoustic velocity region 18 is smaller than the sound speed in the outer high acoustic velocity region 191.

[0166] Note that, when the material of the mass adding film 20 is different from the material of the first excitation electrode 14a, even when the relationship Tf<Te1 is established, the sound velocity in the outer high acoustic velocity region 191 may be smaller than the sound velocity in the high acoustic velocity region 17. For example, when the mass per unit area of ​​the mass adding film 20 is larger than the mass per unit area of ​​the first excitation electrode 14a, the sound velocity in the outer high acoustic velocity region 191 will be smaller than the sound velocity in the high acoustic velocity region 17. When the mass per unit area of ​​the mass adding film 20 is equivalent to the mass per unit area of ​​the first excitation electrode 14a, the sound velocity in the outer high acoustic velocity region 191 will be equivalent to the sound velocity in the high acoustic velocity region 17. When the mass per unit area of ​​the mass adding film 20 is smaller than the mass per unit area of ​​the first excitation electrode 14a, the sound velocity in the outer high acoustic velocity region 191 will be larger than the sound velocity in the high acoustic velocity region 17.

[0167] In the quartz crystal vibrating element 610 according to the sixth embodiment and the quartz crystal vibrating element 710 according to the seventh embodiment, the relationship B<A=C holds, but if the relationship B<C holds, the relationship C<A may also hold. In other words, the relationship B<C<A may also hold.

[0168] Eighth Embodiment Next, the configuration of a quartz crystal vibrating element 810 according to an eighth embodiment will be described with reference to Fig. 31. Fig. 31 is a cross-sectional view of the quartz crystal vibrating element according to the eighth embodiment.

[0169] In a plan view, the outer edge 21A of the first portion 21 and the outer edge 22A of the second portion 22 of the mass adding film 20 are located between the outer edge 81 and the outer edge 82 of the second excitation electrode 14b. The outer edge 71 of the first excitation electrode 14a is located between the outer edge 21A of the first portion 21 of the mass adding film 20 and the outer edge 81 of the second excitation electrode 14b. The outer edge 72 of the first excitation electrode 14a is located between the outer edge 22A of the second portion 22 of the mass adding film 20 and the outer edge 82 of the second excitation electrode 14b. The length A is greater than the length B and less than the length C (B<A<C). The length E1 is less than the length D1 (D1<E1), the length E2 is less than the length D2 (D2<E2), and the length E1 is approximately equal to the length E2 (E1=E2). The length E1 is expressed as E1=D1-D'1, and the length E2 is expressed as E2=D2-D'2.

[0170] In a plan view, the outer edge of the first low acoustic velocity region 18A overlaps with the outer edge 71 of the first excitation electrode 14a. The outer edge of the second low acoustic velocity region 18B overlaps with the outer edge 72 of the first excitation electrode 14a.

[0171] In a plan view, both the outer edge 21A of the first portion 21 of the mass adding film 20 and the outer edge 81 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the first low acoustic velocity region 18A. The outer edge 81 is farther from the center of the first excitation electrode 14a than the outer edge 21A. Both the outer edge 22A of the second portion 22 of the mass adding film 20 and the outer edge 82 of the second excitation electrode 14b are farther from the center of the first excitation electrode 14a than the outer edge of the second low acoustic velocity region 18B. The outer edge 82 is farther from the center of the first excitation electrode 14a by the same amount as the outer edge 22A.

[0172] Changes in the electromechanical coupling coefficient k in the comparative example and examples based on the first to eighth embodiments will be described with reference to Fig. 32 and Fig. 33. Fig. 32 is a table showing simulation results for the comparative example and examples based on the first to eighth embodiments. Fig. 33 is a table showing simulation conditions for the comparative example and examples based on the first to eighth embodiments.

[0173] (Comparative example) A=B=C Tp=1.00μm Tf=0.02μm Te1=Te2=0.05μm Px=Pz=100μm Xf=19μm Zf=30μm Wx=28μm Wz=20μm Wgx=Wgz=0μm Xe1=75μm Ze1=70μm Xe2=75μm Ze2=70μm (Example based on the first embodiment) A<B<C Tp=1.00μm Tf=0.02μm Te1=Te2=0.05μm Px=Pz=100μm Xf=27μm Zf=38μm Wx=24μm Wz=16μm Wgx=Wgz=4μm Xe1 = 75 μm Ze1 = 70 μm Xe2 = 79 μm Ze2 = 74 μm (Example based on second embodiment) A < B = C Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 27 μm Zf = 38 μm Wx = 24 μm Wz = 16 μm Wgx = Wgz = 4 μm Xe1 = 75 μm Ze1 = 70 μm Xe2 = 75 μm Ze2 = 70 μm (Example based on third embodiment) A < C < B Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 27 μm Zf = 38 μm Wx = 26 μm Wz = 18 μm Wgx = Wgz = 4 μm Xe1 = 79 μm Ze2 = 74 μm Xe2 = 75 μm Ze2 = 70 μm (Example based on the fourth embodiment) A = C < B Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 27 μm Zf = 38 μm Wx = 26 μm Wz = 18 μm Wgx = Wgz = 2 μm Xe1 = 79 μm Ze2 = 74 μm Xe2 = 75 μm Ze2 = 70 μm (Example based on the fifth embodiment) A = B < C Tp = 1.00 μm Tf=0.02μm Te1=Te2=0.05μm Px=Pz=100μm Xf=19μm Zf=30μm Wx=28μm Wz=20μm Wgx=Wgz=0μm Xe1=75μm Ze2=70μm Xe2=79μm Ze2=74μm (Example based on the sixth embodiment) B<A=C Tp=1.00μm Tf=0.02μm Te1=Te2=0.05μm Px=Pz=100μm Xf=11μm Zf=22μm Wx=32μm Wz=24μm Wgx=Wgz=-4μmXe1 = 75 μm Ze2 = 70 μm Xe2 = 79 μm Ze2 = 74 μm (Example based on seventh embodiment) B < A = C Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf = 11 μm Zf = 22 μm Wx = 32 μm Wz = 24 μm Wgx = Wgz = -4 μm Xe1 = 75 μm Ze2 = 70 μm Xe2 = 79 μm Ze2 = 74 μm (Example based on eighth embodiment) B < A < C Tp = 1.00 μm Tf = 0.02 μm Te1 = Te2 = 0.05 μm Px = Pz = 100 μm Xf=11μm Zf=22μm Wx=32μm Wz=24μm Wgx=Wgz=-4μm Xe1=75μm Ze2=70μm Xe2=87μm Ze2=82μm

[0174] 32 , "Frame misalignment" means a state in which the position of the mass adding film 20 is misaligned with respect to the positions of the first excitation electrode 14 a and the second excitation electrode 14 b. "Back surface misalignment" means a state in which the position of the second excitation electrode 14 b is misaligned with respect to the positions of the mass adding film 20 and the first excitation electrode 14 a. "Both misalignments" means a state in which the position of the mass adding film 20 is misaligned with respect to the position of the first excitation electrode 14 a, and the position of the second excitation electrode 14 b is misaligned with respect to the position of the first excitation electrode 14 a in the direction opposite to the misalignment of the mass adding film 20.

[0175] In the comparative example, the change in k Δk due to frame misalignment in S0 mode is −0.15%, the change in k Δk due to back surface misalignment in S0 mode is −0.04%, and the change in k Δk due to both misalignments in S0 mode is −0.28%. In the comparative example, the change in k Δk due to frame misalignment in A0Z mode is 1.07%, the change in k Δk due to back surface misalignment in A0Z mode is 0.69%, and the change in k Δk due to both misalignments in A0Z mode is 1.43%.

[0176] In the example based on the first embodiment, the change in k Δk due to frame misalignment in the S0 mode is 0.00%, the change in k Δk due to back surface misalignment in the S0 mode is 0.00%, and the change in k Δk due to both side misalignment in the S0 mode is 0.00%. The Δk in the S0 mode in the example based on the first embodiment is smaller than the Δk in the S0 mode in the comparative example. That is, in the example based on the first embodiment, the decrease in k in the S0 mode due to positional misalignment is suppressed.

[0177] In the example based on the first embodiment, the change in k Δk due to frame misalignment in the A0Z mode is 0.02%, the change in k Δk due to backside misalignment in the A0Z mode is 0.05%, and the change in k Δk due to both side misalignment in the A0Z mode is 0.02%. The Δk in the A0Z mode in the example based on the first embodiment is smaller than the Δk in the A0Z mode in the comparative example. That is, in the example based on the first embodiment, the increase in k in the A0Z mode due to position misalignment is suppressed.

[0178] In an example based on the second embodiment, the change in k Δk due to frame misalignment in S0 mode is 0.00%, the change in k Δk due to backside misalignment in S0 mode is 0.01%, and the change in k Δk due to both side misalignment in S0 mode is 0.01%. The change in k Δk due to frame misalignment in A0Z mode is 0.03%, the change in k Δk due to backside misalignment in A0Z mode is 0.06%, and the change in k Δk due to both side misalignment in A0Z mode is 0.05%.

[0179] In an example based on the third embodiment, the change in k Δk due to frame misalignment in S0 mode is −0.01%, the change in k Δk due to backside misalignment in S0 mode is −0.02%, and the change in k Δk due to both side misalignment in S0 mode is −0.06%. The change in k Δk due to frame misalignment in A0Z mode is 0.17%, the change in k Δk due to backside misalignment in A0Z mode is 0.19%, and the change in k Δk due to both side misalignment in A0Z mode is 0.35%.

[0180] In an example based on the fourth embodiment, the change in k Δk due to frame misalignment in S0 mode is −0.01%, the change in k Δk due to backside misalignment in S0 mode is −0.02%, and the change in k Δk due to both side misalignment in S0 mode is −0.06%. The change in k Δk due to frame misalignment in A0Z mode is 0.34%, the change in k Δk due to backside misalignment in A0Z mode is 0.36%, and the change in k Δk due to both side misalignment in A0Z mode is 0.51%.

[0181] As with the example based on the first embodiment, the examples based on the second to fourth embodiments suppress a decrease in k in the S0 mode due to misalignment, and as with the example based on the first embodiment, the example based on the second embodiment suppresses an increase in k in the A0Z mode due to misalignment.

[0182] In an example based on the fifth embodiment, the change in k Δk due to frame misalignment in S0 mode is −0.13%, the change in k Δk due to backside misalignment in S0 mode is 0.00%, and the change in k Δk due to both side misalignment in S0 mode is −0.14%. The change in k Δk due to frame misalignment in A0Z mode is 0.89%, the change in k Δk due to backside misalignment in A0Z mode is 0.02%, and the change in k Δk due to both side misalignment in A0Z mode is 0.96%.

[0183] In an example based on the sixth embodiment, the change in k Δk due to frame misalignment in the S0 mode is −0.13%, the change in k Δk due to backside misalignment in the S0 mode is 0.00%, and the change in k Δk due to both side misalignment in the S0 mode is −0.15%. The change in k Δk due to frame misalignment in the A0Z mode is 1.01%, the change in k Δk due to backside misalignment in the A0Z mode is 0.03%, and the change in k Δk due to both side misalignment in the A0Z mode is 1.06%.

[0184] In the examples based on the fifth and sixth embodiments, the Δk of the S0 mode and the Δk of the A0Z mode in the frame misalignment are substantially equivalent to the Δk of the S0 mode and the Δk of the A0Z mode in the comparative example. In the examples based on the fifth and sixth embodiments, the decrease in Δk of the S0 mode in the back surface misalignment and the both surface misalignment is suppressed, and the increase in Δk of the A0Z mode in the back surface misalignment and the both surface misalignment is suppressed.

[0185] In an example based on the seventh embodiment, the change in k Δk due to frame misalignment in S0 mode is −0.20%, the change in k Δk due to backside misalignment in S0 mode is 0.00%, and the change in k Δk due to both side misalignment in S0 mode is −0.22%. The change in k Δk due to frame misalignment in A0Z mode is 1.27%, the change in k Δk due to backside misalignment in A0Z mode is 0.11%, and the change in k Δk due to both side misalignment in A0Z mode is 1.31%.

[0186] In an example based on the eighth embodiment, the change in k Δk due to frame misalignment in S0 mode is −0.18%, the change in k Δk due to backside misalignment in S0 mode is 0.00%, and the change in k Δk due to both side misalignment in S0 mode is −0.19%. The change in k Δk due to frame misalignment in A0Z mode is 1.29%, the change in k Δk due to backside misalignment in A0Z mode is 0.07%, and the change in k Δk due to both side misalignment in A0Z mode is 1.31%.

[0187] In the examples based on the seventh and eighth embodiments, the Δk of the S0 mode and the Δk of the A0Z mode in the frame misalignment are slightly worse than the Δk of the S0 mode and the Δk of the A0Z mode in the comparative example. However, in the examples based on the seventh and eighth embodiments, the decrease in Δk of the S0 mode in the back surface misalignment and the both surface misalignment is suppressed, and the increase in Δk of the A0Z mode in the back surface misalignment and the both surface misalignment is suppressed.

[0188] Next, the configuration of a quartz crystal vibrating element 910 according to the ninth embodiment will be described with reference to Fig. 34. Fig. 34 is a cross-sectional view of the quartz crystal vibrating element according to the ninth embodiment.

[0189] In this embodiment, the mass-adding film 20 is made of a metal different from that of the first excitation electrode 14a. From the viewpoint of efficiently adding mass and reducing the sound velocity in the low sound velocity region 18, it is desirable that the specific gravity of the mass-adding film 20 be greater than that of the first excitation electrode 14a. This can shorten the film formation process of the mass-adding film 20 and improve manufacturing efficiency.

[0190] Next, the configuration of a quartz crystal vibrating element 1010 according to the tenth embodiment will be described with reference to Fig. 35. Fig. 35 is a plan view of the quartz crystal vibrating element according to the tenth embodiment.

[0191] The third portion 23 and the fourth portion 24 of the mass adding film 20 are omitted. The first portion 21 and the second portion 22 of the mass adding film 20 are spaced apart from each other and are provided in the shape of bands extending along the X-axis direction.

[0192] Next, the configuration of a quartz crystal vibrating element 1110 according to the eleventh embodiment will be described with reference to Fig. 36. Fig. 36 is a plan view of the quartz crystal vibrating element according to the eleventh embodiment.

[0193] The first portion 21 and the second portion 22 of the mass adding film 20 are omitted. The third portion 23 and the fourth portion 24 of the mass adding film 20 are spaced apart from each other and are provided in the shape of bands extending along the Z′-axis direction.

[0194] 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.

[0195] <1> A piezoelectric element includes a piezoelectric strip having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface; a first excitation electrode provided on the first main surface of the piezoelectric strip; a second excitation electrode provided on the second main surface of the piezoelectric strip; and a mass-adding film at least a portion of which overlaps the first excitation electrode, wherein the mass-adding film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, wherein the first excitation electrode has, in a plan view, a first outer edge portion located on one side of the central portion in the first direction and a second outer edge portion located on the other side of the central portion in the first direction, wherein the second excitation electrode has, in a plan view, a third outer edge portion located on one side of the central portion in the first direction and a fourth outer edge portion located on the other side of the central portion in the first direction, wherein the first portion is provided along the first outer edge portion and the second portion is provided along the second outer edge portion, A piezoelectric vibration element, wherein a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with a first portion of a mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with a second portion of the mass adding film is defined as a second low acoustic velocity region, wherein, in a planar view, a third outer edge portion is farther from the center than the first low acoustic velocity region, and, in a planar view, a fourth outer edge portion is farther from the center than the second low acoustic velocity region.

[0196] <2> A piezoelectric element includes a piezoelectric strip having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface; a first excitation electrode provided on the first main surface of the piezoelectric strip; a second excitation electrode provided on the second main surface of the piezoelectric strip; and a mass-adding film at least a portion of which overlaps the first excitation electrode, wherein the mass-adding film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, wherein the first excitation electrode has, in a plan view, a first outer edge portion located on one side of the central portion in the first direction and a second outer edge portion located on the other side of the central portion in the first direction, wherein the second excitation electrode has, in a plan view, a third outer edge portion located on one side of the central portion in the first direction and a fourth outer edge portion located on the other side of the central portion in the first direction, wherein the first portion is provided along the first outer edge portion, and the second portion is provided along the second outer edge portion, a high acoustic velocity region is defined as a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap; a first low acoustic velocity region is defined as a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap with a first portion of the mass adding film; and a second low acoustic velocity region is defined as a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap with a second portion of the mass adding film; when the dimension along the first direction between the end of the first portion of the mass adding film opposite the second portion and the end of the second portion opposite the first portion is defined as A, the dimension along the first direction of the first excitation electrode is defined as B, and the dimension along the first direction of the second excitation electrode is defined as C, the relationship A=C<B holds; when viewed in a plane, the outer edge of the first low acoustic velocity region opposite the second low acoustic velocity region and the outer edge of the second low acoustic velocity region opposite the first low acoustic velocity region overlap with the first excitation electrode; A piezoelectric vibration element, wherein a third outer edge portion and a fourth outer edge portion of the second excitation electrode overlap with the first excitation electrode in a plan view.

[0197] <3> The piezoelectric vibration element according to <1>, wherein the first outer edge portion and the second outer edge portion overlap the second excitation electrode in plan view.

[0198] <4> The piezoelectric vibration element according to any one of <1> to <3>, wherein, when the dimension along the first direction between the outer edge on the opposite side to the center of the first low acoustic velocity region and the outer edge on the opposite side to the center of the second low acoustic velocity region is E, and the distance along the first direction between the outer edge on the first low acoustic velocity region side in the high acoustic velocity region and the outer edge on the second low acoustic velocity region side is E', the dimension along the first direction of the first low acoustic velocity region and the dimension along the first direction of the second low acoustic velocity region are (1±0.04)×(E-E') / 2.

[0199] <5> The piezoelectric vibration element described in <1>, wherein when the dimension along the first direction between the end of the first portion of the mass-adding film opposite the second portion and the end of the second portion opposite the first portion is A and the dimension along the first direction of the first excitation electrode is B, the relationship A<B holds.

[0200] <6> The piezoelectric vibration element according to <5>, wherein when the dimension of the second excitation electrode along the first direction is C, a relationship of A<B<C is established.

[0201] <7> The piezoelectric vibration element according to <5>, wherein when the dimension of the second excitation electrode along the first direction is C, the relationship A<B=C holds.

[0202] <8> The piezoelectric vibration element according to <5>, wherein when the dimension of the second excitation electrode along the first direction is C, the relationship A=C<B holds.

[0203] <9> The piezoelectric vibration element according to <5>, wherein when the dimension of the second excitation electrode along the first direction is C, a relationship of A<C<B holds.

[0204] <10> The piezoelectric vibration element described in <1>, wherein the relationship A=B<C holds when the dimension along the first direction between the end of the first portion of the mass-adding film opposite the second portion and the end of the second portion opposite the first portion is A, the dimension along the first direction of the first excitation electrode is B, and the dimension along the first direction of the second excitation electrode is C.

[0205] <11> The piezoelectric vibration element described in <1>, wherein the relationship B<A=C holds when the dimension along the first direction between the end of the first portion of the mass-adding film opposite the second portion and the end of the second portion opposite the first portion is A, the dimension along the first direction of the first excitation electrode is B, and the dimension along the first direction of the second excitation electrode is C.

[0206] <12> The piezoelectric vibration element described in <1>, wherein when the dimension along the first direction between the end of the first portion of the mass-adding film opposite the second portion and the end of the second portion opposite the first portion is A, the dimension along the first direction of the first excitation electrode is B, and the dimension along the first direction of the second excitation electrode is C, the relationship B<A<C holds.

[0207] <13> The piezoelectric vibration element according to any one of <1> to <12>, wherein the mass-adding film is made of an electrical conductor.

[0208] <14> The piezoelectric vibration element according to any one of <1> to <12>, wherein the mass-adding film is made of an insulating material.

[0209] <15> The piezoelectric vibration element according to any one of <1> to <14>, wherein, when A' is the distance along the first direction between the end of the first portion opposite the second portion side and the end of the second portion opposite the first portion side in the mass-adding film, and B is the dimension of the first excitation electrode along the first direction, the relationship A' / B≦0.5 holds.

[0210] <16> The piezoelectric vibration element according to <15>, wherein the relationship 0.05≦A′ / B holds.

[0211] <17> The piezoelectric vibration element described in <1>, wherein the distance along the first direction between an outer edge portion located on one side of the first part of the mass-adding film and the first outer edge portion of the first excitation electrode, and the distance along the first direction between an outer edge portion located on the other side of the second part of the mass-adding film and the second outer edge portion of the first excitation electrode are 0.5 μm or more.

[0212] <18> The piezoelectric vibration element described in <17>, wherein the distance along the first direction between the outer edge portion located on one side of the first part of the mass-adding film and the first outer edge portion of the first excitation electrode, and the distance along the first direction between the outer edge portion located on the other side of the second part of the mass-adding film and the second outer edge portion of the first excitation electrode are 8 μm or less.

[0213] <19> The piezoelectric vibration element according to <1>, wherein, when the dimension of the first excitation electrode along the first direction is B and the dimension of the second excitation electrode along the first direction is C, a relationship of 3 μm≦C−B holds.

[0214] <20> The piezoelectric vibration element according to <19>, wherein, when the dimension of the first excitation electrode along the first direction is B and the dimension of the second excitation electrode along the first direction is C, the relationship C-B≦8 μm holds.

[0215] <21> The mass adding film includes a third portion and a fourth portion provided so as to avoid a central portion of the first excitation electrode, and the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side of the central portion in the second direction and a sixth outer edge portion located on the other side of the central portion in the second direction, and the second excitation electrode has, in a plan view, a seventh outer edge portion located on one side of the central portion in the second direction and an eighth outer edge portion located on the other side of the central portion in the second direction, and the third portion is provided along the fifth outer edge portion, and the fourth portion is provided along the sixth outer edge portion, and when a region in which the third portion of the mass adding film overlaps the piezoelectric piece, the first excitation electrode, and the second excitation electrode is defined as a third low acoustic velocity region, and a region in which the fourth portion of the mass adding film overlaps the piezoelectric piece, the first excitation electrode, and the second excitation electrode is defined as a fourth low acoustic velocity region, in a plan view, the seventh outer edge portion is farther from the central portion than the third low acoustic velocity region, The piezoelectric vibration element according to any one of <1> to <20>, wherein, in a plan view, the eighth outer edge portion is farther from the center portion than the fourth low acoustic velocity region.

[0216] <22> The mass adding film includes a third portion and a fourth portion that are provided to avoid a central portion of the first excitation electrode, and the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side of the central portion in the second direction and a sixth outer edge portion located on the other side of the central portion in the second direction, and the second excitation electrode has, in a plan view, a seventh outer edge portion located on one side of the central portion in the second direction and an eighth outer edge portion located on the other side of the central portion in the second direction, and the third portion is provided along the fifth outer edge portion, and the fourth portion is provided along the sixth outer edge portion, and a region where the third portion of the mass adding film overlaps with the piezoelectric piece, the first excitation electrode, and the second excitation electrode is defined as a third low acoustic velocity region, and a region where the fourth portion of the mass adding film overlaps with the piezoelectric piece, the first excitation electrode, and the second excitation electrode is defined as a fourth low acoustic velocity region, <21>. The piezoelectric vibration element according to any one of <1> to <21>, wherein a dimension along the second direction between an end of the third portion opposite the fourth portion in the mass-adding film and an end of the fourth portion opposite the third portion is equal to a dimension along the second direction of the second excitation electrode and is smaller than a dimension along the second direction of the first excitation electrode; when viewed in a plane, an outer edge of the third low acoustic velocity region opposite the fourth low acoustic velocity region and an outer edge of the fourth low acoustic velocity region opposite the third low acoustic velocity region overlap with the first excitation electrode; when viewed in a plane, a seventh outer edge and an eighth outer edge of the second excitation electrode overlap with the first excitation electrode.

[0217] <23> The piezoelectric vibration element according to any one of <1> to <22>, wherein the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side in the second direction relative to the center portion and a sixth outer edge portion located on the other side in the second direction relative to the center portion, and the fifth outer edge portion and the sixth outer edge portion overlap the second excitation electrode in a plan view.

[0218] <24> The piezoelectric vibration element according to any one of <1> to <23>, wherein the piezoelectric piece is a quartz crystal piece.

[0219] <25> The piezoelectric vibration element according to <24>, wherein the cut angle of the quartz crystal piece is AT cut, BT cut, or ST cut.

[0220] <26> The piezoelectric vibration element according to any one of <1> to <25>, wherein a main vibration mode is thickness-shear vibration.

[0221] It should be noted that the embodiment of the present invention is not limited to a quartz crystal resonator, and can also be applied to other piezoelectric resonators (piezoelectric resonator units). Examples of piezoelectric pieces suitable for use in the piezoelectric resonator according to the present embodiment include piezoelectric ceramics such as lead zirconate titanate (PZT) and aluminum nitride, and piezoelectric single crystals such as lithium niobate and lithium tantalate, but the present invention is not limited to these and can be selected as appropriate.

[0222] 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.

[0223] As described above, according to one aspect of the present invention, it is possible to provide a piezoelectric vibration element that can suppress deterioration of the electromechanical coupling coefficient.

[0224] 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.

[0225] 100... Crystal Oscillator 1... Crystal Vibrator 10... Crystal Vibration Element 11... Crystal Plate 11A... Top 11B... Bottom 14a... First Excitation Electrode 14b... Second Excitation Electrode 17... High-Sonic Velocity Range 18... Low-Sonic Velocity Range 18A... First Low-Sonic Velocity Range 18B... Second Low-Sonic Velocity Range 18C... Third Low-Sonic Velocity Range 18D... Fourth Low-Sonic Velocity Range 19... Outer High-Sonic Velocity Range 19A... First Outer High-Sonic Velocity Range 9B...2nd outer high-speed region 19C...3rd outer high-speed region 19D...4th outer high-speed region 20...Mass-added membrane 21...1st portion 21A...Outer edge 21B...Inner edge 22...2nd portion 22A...Outer edge 22B...Inner edge 23...3rd portion 23A...Outer edge 23B...Inner edge 24...4th portion 24A...Outer edge 24B...Inner edge 71, 72...Outer edge 81, 82...Outer edge

Claims

1. a piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, In a plan view, the third outer edge portion is farther from the central portion than the first low sound velocity region, In a plan view, the fourth outer edge portion is farther from the central portion than the second low sound velocity region, When a dimension in the first direction between an end of the first portion of the mass addition film opposite to the second portion and an end of the second portion opposite to the first portion is A, and a dimension in the first direction of the first excitation electrode is B, A < B The relationship is established as follows: Piezoelectric vibration element.

2. A piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface opposite the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, In a plan view, the third outer edge portion is farther from the central portion than the first low sound velocity region, In a plan view, the fourth outer edge portion is farther from the central portion than the second low sound velocity region, When a dimension in the first direction between an end of the first portion of the mass addition film opposite to the second portion and an end of the second portion opposite to the first portion is A, a dimension of the first excitation electrode in the first direction is B, and a dimension of the second excitation electrode in the first direction is C, B<A=C The relationship is established as follows: Piezoelectric vibration element.

3. A piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface opposite the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, In a plan view, the third outer edge portion is farther from the central portion than the first low sound velocity region, In a plan view, the fourth outer edge portion is farther from the central portion than the second low sound velocity region, When a dimension in the first direction between an end of the first portion of the mass addition film opposite to the second portion and an end of the second portion opposite to the first portion is A, a dimension of the first excitation electrode in the first direction is B, and a dimension of the second excitation electrode in the first direction is C, B<A<C The relationship is established as follows: Piezoelectric vibration element.

4. A piezoelectric strip having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface opposite the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, In a plan view, the third outer edge portion is farther from the central portion than the first low sound velocity region, In a plan view, the fourth outer edge portion is farther from the central portion than the second low sound velocity region, a distance along the first direction between an outer edge portion located on the one side of the first portion of the mass addition film and the first outer edge portion of the first excitation electrode, and a distance along the first direction between an outer edge portion located on the other side of the second portion of the mass addition film and the second outer edge portion of the first excitation electrode are 0.5 μm or more. Piezoelectric vibration element.

5. A piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface opposite the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, In a plan view, the third outer edge portion is farther from the central portion than the first low sound velocity region, In a plan view, the fourth outer edge portion is farther from the central portion than the second low sound velocity region, the mass addition film includes a third portion and a fourth portion provided to avoid the central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side in the second direction with respect to the central portion, and a sixth outer edge portion located on the other side in the second direction with respect to the central portion, the second excitation electrode has, in a plan view, a seventh outer edge portion located on one side in the second direction with respect to the central portion, and an eighth outer edge portion located on the other side in the second direction with respect to the central portion, The third portion is provided along the fifth outer edge portion, The fourth portion is provided along the sixth outer edge portion, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the third portion of the mass adding film is defined as a third low sound velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the fourth portion of the mass adding film is defined as a fourth low sound velocity region, a dimension along the second direction between an end of the third portion opposite to the fourth portion in the mass addition film and an end of the fourth portion opposite to the third portion is equal to a dimension along the second direction of the second excitation electrode and smaller than a dimension along the second direction of the first excitation electrode, When viewed in a plan view, an outer edge portion of the third low sound velocity region opposite to the fourth low sound velocity region and an outer edge portion of the fourth low sound velocity region opposite to the third low sound velocity region overlap with the first excitation electrode, When viewed in a plan view, the seventh outer edge portion and the eighth outer edge portion of the second excitation electrode overlap with the first excitation electrode. Piezoelectric vibration element.

6. a piezoelectric piece having a first main surface extending in a first direction and a second direction intersecting the first direction, and a second main surface facing the first main surface; A first excitation electrode provided on the first main surface of the piezoelectric piece; a second excitation electrode provided on the second main surface of the piezoelectric piece; a mass-adding film at least partially overlapping the first excitation electrode; Equipped with the mass addition film includes a first portion and a second portion provided to avoid a central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a first outer edge portion located on one side in the first direction with respect to the central portion, and a second outer edge portion located on the other side in the first direction with respect to the central portion, the second excitation electrode has, in a plan view, a third outer edge portion located on one side in the first direction with respect to the central portion, and a fourth outer edge portion located on the other side in the first direction with respect to the central portion, The first portion is provided along the first outer edge portion, The second portion is provided along the second outer edge portion, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode overlap is defined as a high acoustic velocity region, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the first portion of the mass adding film is defined as a first low acoustic velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode further overlap with the second portion of the mass adding film is defined as a second low acoustic velocity region, When a dimension in the first direction between an end of the first portion of the mass addition film opposite to the second portion and an end of the second portion opposite to the first portion is A, a dimension of the first excitation electrode in the first direction is B, and a dimension of the second excitation electrode in the first direction is C, A=C<B The relationship is established, When viewed in a plan view, an outer edge portion of the first low sound speed region opposite to the second low sound speed region and an outer edge of the second low sound speed region opposite to the first low sound speed region overlap the first excitation electrode, When viewed in a plan view, the third outer edge portion and the fourth outer edge portion of the second excitation electrode overlap with the first excitation electrode, the mass addition film includes a third portion and a fourth portion provided to avoid the central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side in the second direction with respect to the central portion, and a sixth outer edge portion located on the other side in the second direction with respect to the central portion, the second excitation electrode has, in a plan view, a seventh outer edge portion located on one side in the second direction with respect to the central portion, and an eighth outer edge portion located on the other side in the second direction with respect to the central portion, The third portion is provided along the fifth outer edge portion, The fourth portion is provided along the sixth outer edge portion, a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the third portion of the mass adding film is defined as a third low sound velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the fourth portion of the mass adding film is defined as a fourth low sound velocity region, a dimension along the second direction between an end of the third portion opposite to the fourth portion in the mass addition film and an end of the fourth portion opposite to the third portion is equal to a dimension along the second direction of the second excitation electrode and smaller than a dimension along the second direction of the first excitation electrode, When viewed in a plan view, an outer edge portion of the third low sound velocity region opposite to the fourth low sound velocity region and an outer edge portion of the fourth low sound velocity region opposite to the third low sound velocity region overlap with the first excitation electrode, When viewed in a plan view, the seventh outer edge portion and the eighth outer edge portion of the second excitation electrode overlap with the first excitation electrode. Piezoelectric vibration element.

7. When viewed in a plan view, the first outer edge portion and the second outer edge portion overlap the second excitation electrode. The piezoelectric vibration element according to claim 1 .

8. When a dimension along the first direction between an outer edge portion of the first low sound speed region opposite to the central portion and an outer edge portion of the second low sound speed region opposite to the central portion is E, and a distance along the first direction between an outer edge portion of the high sound speed region on the first low sound speed region side and an outer edge portion of the second low sound speed region side is E', The dimension of the first low sound velocity region along the first direction and the dimension of the second low sound velocity region along the first direction are (1±0.04)×(E−E′) / 2. The piezoelectric vibration element according to claim 1 .

9. When the dimension of the second excitation electrode along the first direction is C, A < B < C The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

10. When the dimension of the second excitation electrode along the first direction is C, A < B = C The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

11. When the dimension of the second excitation electrode along the first direction is C, A=C<B The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

12. When the dimension of the second excitation electrode along the first direction is C, A < C < B The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

13. When a dimension in the first direction between an end of the first portion of the mass addition film opposite to the second portion and an end of the second portion opposite to the first portion is A, a dimension of the first excitation electrode in the first direction is B, and a dimension of the second excitation electrode in the first direction is C, A=B<C The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

14. The material of the mass-adding film is an electrical conductor. The piezoelectric vibration element according to claim 1 .

15. The material of the mass-adding film is an insulator. The piezoelectric vibration element according to claim 1 .

16. In the mass addition film, a distance along the first direction between an end of the first portion opposite to the second portion side and an end of the second portion opposite to the first portion side is defined as A', and a dimension of the first excitation electrode along the first direction is defined as B. A' / B≦0.5 The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

17. 0.05≦A′ / B The relationship is established as follows: The piezoelectric vibration element according to claim 16.

18. a distance along the first direction between an outer edge portion located on the one side of the first portion of the mass addition film and the first outer edge portion of the first excitation electrode, and a distance along the first direction between an outer edge portion located on the other side of the second portion of the mass addition film and the second outer edge portion of the first excitation electrode are 8 μm or less. The piezoelectric vibration element according to claim 4 .

19. When the dimension of the first excitation electrode along the first direction is B and the dimension of the second excitation electrode along the first direction is C, 3μm≦C-B The relationship is established as follows: The piezoelectric vibration element according to claim 1 .

20. When the dimension of the first excitation electrode along the first direction is B and the dimension of the second excitation electrode along the first direction is C, C-B≦8μm The relationship is established as follows:

20. The piezoelectric vibration element according to claim 19.

21. the mass addition film includes a third portion and a fourth portion provided to avoid the central portion of the first excitation electrode, the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side in the second direction with respect to the central portion, and a sixth outer edge portion located on the other side in the second direction with respect to the central portion, the second excitation electrode has, in a plan view, a seventh outer edge portion located on one side in the second direction with respect to the central portion, and an eighth outer edge portion located on the other side in the second direction with respect to the central portion, The third portion is provided along the fifth outer edge portion, The fourth portion is provided along the sixth outer edge portion, When a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the third portion of the mass adding film is defined as a third low sound velocity region, and a region where the piezoelectric piece, the first excitation electrode, and the second excitation electrode are further overlapped with the fourth portion of the mass adding film is defined as a fourth low sound velocity region, In a plan view, the seventh outer edge portion is farther from the central portion than the third low sound velocity region, In a plan view, the eighth outer edge portion is farther from the central portion than the fourth low sound velocity region. The piezoelectric vibration element according to claim 1 .

22. the first excitation electrode has, in a plan view, a fifth outer edge portion located on one side in the second direction with respect to the central portion, and a sixth outer edge portion located on the other side in the second direction with respect to the central portion, When viewed in a plan view, the fifth outer edge portion and the sixth outer edge portion overlap the second excitation electrode. The piezoelectric vibration element according to claim 1 .

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

24. The cut angle of the quartz crystal piece is an AT cut, a BT cut, or an ST cut. The piezoelectric vibration element according to claim 23.

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