Patent Publication Number: US-2019190486-A1

Title: Piezoelectric resonator unit

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of International application No. PCT/JP2017/030561, filed Aug. 25, 2017, which claims priority to Japanese Patent Application No. 2016-169901, filed Aug. 31, 2016, the entire contents of each of which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a piezoelectric resonator unit, and, in particular, to a piezoelectric resonator unit in which a piezoelectric resonator is held on a substrate by an electroconductive holding member. 
     BACKGROUND OF THE INVENTION 
     A structure in which a piezoelectric resonator is placed on a main surface of a substrate is known as a type of piezoelectric resonator unit. In such a structure, it is desirable to maintain the distance between the piezoelectric resonator and the main surface of the substrate constant so that variation in parasitic capacity, which is generated between an electrode formed on the piezoelectric resonator and an electrode formed on the substrate, can be suppressed. For example, Patent Document 1 discloses a piezoelectric device in which spherical spacers are mixed in an adhesive, which serves as a holding member for holding a piezoelectric element, and a gap between a substrate and the piezoelectric element is maintained due to the diameter of the spherical spacers. Metal particles having an outer diameter of ¼ or smaller of the diameter of the spherical spacers are mixed in the adhesive so that the adhesive can conduct electricity. 
     Patent Document 1: Japanese Unexamined Patent Application Publication No. 2014-150452 
     SUMMARY OF THE INVENTION 
     However, the piezoelectric device disclosed in Patent Document 1 has a problem in that the electroconductivity of the adhesive is low because the metal particles do not sufficiently enter gaps in the holding member that are formed by the spherical spacers. 
     The present invention has been made in consideration of the above circumstances, and an object thereof is to provide a piezoelectric resonator unit in which the electroconductivity of a holding portion that holds a piezoelectric resonator is improved while maintaining the distance between the piezoelectric resonator and a substrate main surface constant. 
     A piezoelectric resonator unit according to an aspect of the present invention includes a piezoelectric resonator, a substrate that has a first main surface and a second main surface that face each other, and an electroconductive holding member that holds the piezoelectric resonator on the first main surface of the substrate. The electroconductive holding member includes a plurality of metal particles and a plurality of spherical spacers, the plurality of spherical spacers positioning the piezoelectric resonator at a predetermined distance from the first main surface of the substrate. A relationship W ave &lt;{(2/√3)−1}×V ave  is satisfied, where V ave  is an average particle diameter of the spherical spacers and W ave  is an average particle diameter of the metal particles. 
     With the structure described above, in a holding portion that holds the piezoelectric resonator, the metal particles can sufficiently enter gaps formed between the spherical spacers. Accordingly, the electroconductivity of the holding portion is improved. 
     With the present invention, it is possible to provide a piezoelectric resonator unit in which the electroconductivity of a holding portion that holds a piezoelectric resonator is improved while maintaining the distance between the piezoelectric resonator and a substrate main surface constant. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an exploded perspective view of a piezoelectric resonator unit according to an embodiment of the present invention. 
         FIG. 2  is a sectional view taken along line II-II of  FIG. 1 . 
         FIG. 3  is a schematic top view of an electroconductive holding member, specifically illustrating a state in which an adhesive  400 , a plurality of spherical spacers  410 , and a plurality of metal particles  420  are included in an electroconductive holding member  342 . 
         FIG. 4  is a conceptual diagram illustrating the relationship between the size of spherical spacers and the size of metal particles, specifically illustrating a state in which one metal particle enters a gap that is formed by three spherical spacers. 
         FIG. 5  is a conceptual diagram illustrating the relationship between the size of spherical spacers and the size of metal particles, specifically illustrating a state in which three metal particles enter a gap that is formed by three spherical spacers. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of the present invention will be described. In the following description related to the drawings, elements that are the same as or similar to each other will be denoted by the same or similar numerals. The drawings are exemplary, the dimensions and shapes of elements are schematic, and the technical scope of the present invention is not limited to the embodiments. 
     Referring to  FIGS. 1 and 2 , a piezoelectric resonator unit  1  according to an embodiment of the present invention will be described.  FIG. 1  is an exploded perspective view of a piezoelectric resonator unit according to an embodiment of the present invention.  FIG. 2  is a sectional view taken along line II-II of  FIG. 1 . 
     As illustrated in  FIG. 1 , the piezoelectric resonator unit  1  according to the present embodiment includes a piezoelectric resonator  100 , a lid member  200 , and a substrate  300 . The lid member  200  and the substrate  300  are parts of a structure of a holding unit (case or package) for accommodating the piezoelectric resonator  100 . 
     The piezoelectric resonator  100  includes a piezoelectric substrate  110  and excitation electrodes  120  and  130  (hereinafter, also referred to as “first excitation electrode  120 ” and “second excitation electrode  130 ”) that are respectively disposed on front and back surfaces of the piezoelectric substrate  110 . 
     The piezoelectric substrate  110  is made of a predetermined piezoelectric material, and the material is not particularly limited. In the example shown in  FIG. 1 , the piezoelectric substrate  110  is made of a synthetic quartz crystal having a predetermined crystal orientation. The piezoelectric substrate  110  is, for example, an AT-cut quartz crystal element. An AT-cut quartz crystal element is cut so that, when an X-axis, a Y-axis, and a Z-axis are the crystal axes of a synthetic quartz crystal and a Y′-axis and a Z′-axis are respectively axes that are obtained by rotating the Y-axis and the Z-axis around the X-axis by 35 degrees 15 minutes±1 minute 30 seconds in a direction from the Y-axis toward the Z-axis, the quartz crystal element has a main surface that is parallel to a plane defined by the X-axis and the Z′-axis (hereinafter, referred to as “XZ′-plane”, and the same applies to planes defined by the other axes). In the example illustrated in  FIG. 1 , the piezoelectric substrate  110 , which is an AT-cut quartz crystal element, has long sides that extend along the X-axis, short sides that extend along the Z′-axis, and sides in the thickness direction that extend along the Y′-axis. The piezoelectric substrate  110  has a substantially rectangular shape in the XZ′-plane. A quartz crystal resonator using an AT-cut quartz crystal element has high frequency stability in a wide temperature range and has high durability. A piezoelectric resonator (that is, a quartz crystal resonator) using an AT-cut quartz crystal element includes a thickness shear mode as main vibration. Hereinafter, elements of the piezoelectric resonator unit  1  will be described with reference to the axial directions of AT-cut. 
     A piezoelectric substrate is not limited to a substrate having the structure described above. For example, a rectangular AT-cut quartz crystal element that has long sides extending along the Z′-axis and short sides extending along the X-axis may be used as the piezoelectric substrate. Alternatively, the piezoelectric substrate may be a quartz crystal element that is not an AT-cut quartz crystal element, such as a BT-cut quartz crystal element, as long as the main vibration thereof includes a thickness shear mode. The material of the piezoelectric substrate is not limited to quartz and may be another piezoelectric material that is, for example, a piezoelectric ceramic such as PZT or zinc oxide. The piezoelectric resonator may be, for example, a microelectromechanical system (MEMS). To be specific, a Si-MEMS, in which a MEMS is formed in a silicon substrate, may be used. Further, the piezoelectric resonator may be a piezoelectric MEMS that is formed by using a predetermined piezoelectric material, such as AIN, LiTaO 3 , LiNbO 3 , or PZT. 
     The first excitation electrode  120  is formed on a first main surface  112  of the piezoelectric substrate  110 , and the second excitation electrode  130  is formed on a second main surface  114  of the piezoelectric substrate  110 . The first excitation electrode  120  and the second excitation electrode  130 , which are a pair of electrodes, are disposed so that substantially the entireties thereof overlap when the XZ′-plane is seen in a plan view. 
     A connection electrode  124  and a connection electrode  134  are formed on the piezoelectric substrate  110 . The connection electrode  124  is electrically connected to the first excitation electrode  120  via an extension electrode  122 , and the connection electrode  134  is electrically connected to the second excitation electrode  130  via an extension electrode  132 . To be specific, the extension electrode  122  extends on the first main surface  112  from the first excitation electrode  120  toward a short side on the negative X side, passes along a side surface of the piezoelectric substrate  110  on the positive Z′ side, and is connected to the connection electrode  124  formed on the second main surface  114 . The extension electrode  132  extends on the second main surface  114  from the second excitation electrode  130  toward a short side on the negative X side, and is connected to the connection electrode  134  formed on the second main surface  114 . The connection electrodes  124  and  134  are disposed along the short side on the negative X side, are electrically connected to and mechanically held by the substrate  300  via electroconductive holding members  340  and  342  (holding portion). The dispositions and the patterns of the connection electrodes  124  and  134  and the extension electrodes  122  and  132  are not limited and may be appropriately modified in consideration of electrical connection with other members. 
     The electrodes described above, including the first excitation electrode  120  and the second excitation electrode  130 , for example, each include a chromium (Cr) underlying layer, which is formed on a surface of the piezoelectric substrate  110  to increase the bonding strength, and a gold (Au) layer formed on the surface of the chromium layer. The materials of these electrodes are not limited. 
     As illustrated in  FIG. 2 , the lid member  200  has a recess that has an opening that faces a first main surface  302  of the substrate  300 . The lid member  200  has a side wall  202  that is formed so as to stand on a bottom surface of the recess along the entire periphery of the opening. The side wall  202  has an end surface  204  that faces the first main surface  302  of the substrate  300 . The end surface  204  is joined to the first main surface  302  of the substrate  300  via a joining material  250 . The shape of the lid member  200  is not particularly limited, as long as the lid member  200  can accommodate the piezoelectric resonator  100  in an inner space thereof when the lid member  200  is joined to the substrate  300 . Although the material of the lid member  200  is not particularly limited, the material may include an electroconductive material such as a metal. In this case, by electrically connecting the lid member  200  to a ground potential, it is possible to additionally provide a shielding function to the lid member  200 . When forming the lid member  200  from a metal, for example, the lid member  200  may be formed from an alloy including iron (Fe) and nickel (Ni) (such as 42 alloy). A surface layer, such as a gold (Au) layer, may be further formed on the surface of the lid member  200 . By forming a gold layer on the surface, oxidation of the lid member  200  can be prevented. Alternatively, the lid member  200  may have a composite structure made from an insulating material or an electroconductive material and an insulating material. 
     Referring back to  FIG. 1 , the substrate  300  holds the piezoelectric resonator  100 . In the example shown in  FIG. 1 , the piezoelectric resonator  100  is excitably held on the first main surface  302  of the substrate  300  via the electroconductive holding members  340  and  342 . 
     The substrate  300  has long sides that extend along the X-axis, short sides that extend along the Z′-axis, and sides in the thickness direction that extend along the Y′-axis. The substrate  300  has a substantially rectangular shape in the XZ′-plane. The substrate  300  is formed from, for example, a single-layer insulating ceramic. As another embodiment, the substrate  300  may be formed by stacking a plurality of insulating ceramic sheets and by firing the ceramic sheets. Preferably, the substrate  300  is made of a heat-resistant material. The substrate  300  may have a flat-plate like shape as illustrated in  FIG. 1 , or may have a recessed shape that has an opening that faces the lid member  200 . 
     Connection electrodes  320  and  322 , corner electrodes  324  and  326 , and extension electrodes  320   a  and  322   a  are formed on the first main surface  302  of the substrate  300 . Side electrodes  330 ,  332 ,  334 , and  336  are formed on side surfaces of the substrate  300 . Outer electrodes  360 ,  362 ,  364 , and  366  are formed on a second main surface  304  of the substrate  300 . 
     The connection electrodes  320  and  322  are formed on the first main surface  302  of the substrate  300  along a short side on the negative X side and at a distance from the short side. The connection electrode  320  is connected to the connection electrode  124  of the piezoelectric resonator  100  via the electroconductive holding member  340 . The connection electrode  322  is connected to the connection electrode  134  of the piezoelectric resonator  100  via the electroconductive holding member  342 . Although the material of the connection electrodes  320  and  322  is not particularly limited, for example, the connection electrodes  320  and  322  are formed by stacking molybdenum (Mo), nickel (Ni), and gold (Au) layers. The electroconductive holding members  340  and  342  are formed, for example, by thermally solidifying an adhesive. Details of the structure of the electroconductive holding members  340  and  342  will be described below. 
     The extension electrode  320   a  extends from the connection electrode  320  to a side electrode  330  disposed at a corner of the substrate  300 . The extension electrode  322   a  extends in the X-axis direction from the connection electrode  322  to the side electrode  332  disposed at a corner of the substrate  300  diagonal to the side electrode  330 . 
     In the present embodiment, corner electrodes  324  and  326  are formed at the remaining corners (corners where the extension electrodes  320   a  and  322   a,  which are electrically connected to the connection electrodes  320  and  322 , are not disposed). The corner electrodes  324  and  326  are not connected to any of the first excitation electrode  120  and the second excitation electrode  130 . 
     The plurality of side electrodes  330 ,  332 ,  334 , and  336  are respectively formed on side surfaces near the corners of the substrate  300 . The plurality of outer electrodes  360 ,  362 ,  364 , and  366  are respectively formed on the second main surface  304  at positions near the corners of the substrate  300 . To be specific, the side electrode  330  and the outer electrode  360  are disposed at a corner on the negative X and positive Z′ side, the side electrode  332  and the outer electrode  362  are disposed at a corner on the positive X and negative Z′ side, the side electrode  334  and the outer electrode  364  are disposed at a corner on the positive X and positive Z′ side, and the side electrode  336  and the outer electrode  366  are disposed at a corner on the negative X and negative Z′ side. 
     The side electrodes  330 ,  332 ,  334 , and  336  are formed to electrically connect electrodes on the first main surface  302  to electrodes on the second main surface  304 . In the example shown in  FIG. 1 , each of the corners of the substrate  300  has a cutout side surface that is formed by partially cutting out the corner in a cylindrically-curved shape (also referred to as a castellation shape). The side electrodes  330 ,  332 ,  334 , and  336  are formed on the cutout side surfaces. The shape of the each of the corners of the substrate  300  is not limited to this. Each of the corners may be planer, or may have a rectangular shape with four right-angled corners without being cut out in a plan view. 
     The outer electrodes  360 ,  362 ,  364 , and  366  are to be electrically connected to a mounting board (not shown). The outer electrodes  360 ,  362 ,  364 , and  366  are respectively connected to the side electrodes  330 ,  332 ,  334 , and  336  that are formed on side surfaces of corresponding corners. Thus, the outer electrodes  360 ,  362 ,  364 , and  366  can be connected to electrodes on the first main surface  302  of the substrate  300  via the side electrodes  330 ,  332 ,  334 , and  336 . 
     To be specific, among the plurality of outer electrodes, the outer electrode  360  is electrically connected to the first excitation electrode  120  via the side electrode  330 , the extension electrode  320   a,  the connection electrode  320 , and the electroconductive holding member  340 ; and the outer electrode  362  is electrically connected to the second excitation electrode  130  via the side electrode  332 , the extension electrode  322   a,  the connection electrode  322 , and the electroconductive holding member  342 . That is, the outer electrodes  360  and  362  are input/output terminals that are electrically connected to the first excitation electrode  120  or the second excitation electrode  130 . 
     The remaining outer electrodes  364  and  366  are dummy electrodes that are not electrically connected to the first excitation electrode  120  or the second excitation electrode  130  of the piezoelectric resonator  100 . Because outer electrodes can be formed on all corners by forming the outer electrodes  364  and  366 , it becomes easy to perform an operation of electrically connecting the piezoelectric resonator unit  1  to other members. The outer electrodes  364  and  366  may have a function as a ground electrode to which a ground potential is supplied. For example, if the lid member  200  is made of an electroconductive material, it is possible to additionally provide the lid member  200  with a shielding function by electrically connecting the lid member  200  to the outer electrodes  364  and  366 . 
     The structures of the connection electrodes, the corner electrodes, the extension electrodes, the side electrodes, and the outer electrodes, which are formed on the substrate  300 , are not limited to those described above and may be modified in various ways. For example, the number of outer electrodes is not limited to four, and, for example, the outer electrodes may be only two input/output terminals that are disposed at diagonal corners. The side electrodes are not limited to those disposed at the corners, and may be formed at any of the side surfaces of the substrate  300  excluding the corners. In this case, as already described, cutout side surfaces may be formed by cutting a part of each of the side surfaces in a cylindrical shape, and the side electrodes may be formed on the side surfaces excluding the corners. Moreover, the corner electrodes  324  and  326 , the side electrodes  334  and  336 , and the outer electrodes  364  and  366  need not be formed. A through-hole may be formed in the substrate  300  so as to extend from the first main surface  302  to the second main surface  304 , and the through-hole may be used to electrically connect a connection electrode formed on the first main surface  302  to the second main surface  304 . 
     The joining material  250  is disposed along the entire periphery of each of the lid member  200  and the substrate  300 , and joins the end surface  204  of the side wall  202  of the lid member  200  and the first main surface  302  of the substrate  300  to each other. Although the material of the joining material  250  is not particularly limited, the material may be, for example, gold-tin (Au—Sn) eutectic alloy. By joining the lid member and the substrate via a metal, if the lid member is made of an electroconductive material, the lid member and the substrate can be electrical connected to each other. Moreover, sealability can be improved. 
     When the lid member  200  and the substrate  300  are joined to each other via the joining material  250 , the piezoelectric resonator  100  is hermetically sealed in an inner space (cavity) that is surrounded by the recess of the lid member  200  and the substrate  300 . In this case, preferably, the inner space is in a vacuum state in which the pressure therein is lower than the atmospheric pressure. In this case, for example, ageing of the first excitation electrode  120  and the second excitation electrode  130  due to oxidation is reduced. 
     With the structure described above, in the piezoelectric resonator unit  1 , an alternating electric field is applied between the pair of the first excitation electrodes  120  and the second excitation electrode  130  of the piezoelectric resonator  100  via the outer electrodes  360  and  362  of the substrate  300 . Thus, the piezoelectric substrate  110  vibrates in a vibration mode including a thickness shear mode, and resonance characteristics due to the vibration are obtained. 
     Next, referring to  FIGS. 2 and 3 , the electroconductive holding members  340  and  342  will be described in detail.  FIG. 3  is a schematic top view of an electroconductive holding member, specifically illustrating a state in which an adhesive  400 , a plurality of spherical spacers  410 , and a plurality of metal particles  420  are included in the electroconductive holding member  342 .  FIG. 3  schematically illustrates the electroconductive holding member  342 , which is disposed on the connection electrode  322 , in a plan view of the substrate  300  (that is, a plan view of the XZ′-plane), while omitting the lid member  200  and the piezoelectric resonator  100 . The following description will be with reference to holding member  342 . Since the detailed description of the electroconductive holding member  340  is similar to the electroconductive holding member  342 , a description thereof will be omitted. 
     As illustrated in  FIGS. 2 and 3 , the electroconductive holding member  342  includes the adhesive (binder)  400 , the plurality of spherical spacers  410 , and the plurality of metal particles  420 . The adhesive  400  is mainly composed of, for example, a resin. 
     Each of the plurality of spherical spacers  410  is mainly composed of, for example, a resin. Examples of the resin include an elastic rubber and a plastic such as a silicone resin. In the present embodiment, a silicone resin is used for the plurality of spherical spacers  410 . If the adhesive  400  and the spherical spacers  410  are each mainly composed of a resin, the adhesive  400  and the spherical spacers  410  may be differentiated by, for example, using different resins as the materials thereof. If the main component of the adhesive  400  and the material of the spherical spacers  410  are each a silicone resin, preferably, the spherical spacers  410  that have been solidified beforehand are added to the adhesive  400 , whose main component is a silicone resin, so that outgas released from an unbridged resin is not generated. With a structure in which the main component of the adhesive  400  and the spherical spacers  410  include a silicone resin in common, the differences in Young&#39;s modulus and linear expansion coefficient between the adhesive  400  and the spherical spacers  410  are small (e.g., Young&#39;s modulus of Silicon: 0.01˜0.1, Au: 78, and Cu: 130 [GPa]; and linear expansion coefficient of Silicon: 25˜400, Au: 14, and Cu: 17 [10 −6 /K]) , such that stress that is generated at boundary surfaces between the adhesive  400  and the spherical spacers  410  can be reduced. Due to the reduction of the stress, it is possible to prevent a problem of detachment of boundary portions of the adhesive  400  and the spherical spacers  410  or to prevent a problem of removal of the spherical spacers  410  from the adhesive  400 . Moreover, because the structure includes the spherical spacers  410  that have been solidified beforehand, release of outgas, such as siloxane, from the adhesive  400  in an unbridged state can be reduced. The plurality of spherical spacers  410  each has, for example, a substantially spherical shape. Here, the term “substantially spherical shape” includes not only a spherical shape but also an elliptical shape, a slightly deformed elliptical shape, and the like. In the present embodiment, each of the plurality of spherical spacers  410  is not covered with a metal, and a silicone resin material, which is an insulator and which is a material of the spherical spacers  410 , is exposed on the surface. With the structure in which the surface of each of the spherical spacers  410  is an insulator, even if the spherical spacers  410  are removed from the adhesive  400 , a problem of causing a short circuit can be prevented, such as when spacers having a conductive surface are used. The spherical spacers  410  have smaller differences in Young&#39;s modulus and acoustic impedance compared with spherical spacers that are covered with a metal. 
     The plurality of spherical spacers  410  each have a particle diameter V, and the average value of the particle diameter V will be represented as the average particle diameter V ave . In the present description, the particle diameter V of a spherical spacer is defined as an equivalent circle diameter obtained from the cross-sectional area of the spherical spacer in a cross sectional view. The cross-sectional view is, for example, an image of a cross section of the electroconductive holding member that is obtained by using a scanning ion microscope using a focused ion beam (FIB) at 10000 times magnification. The average particle diameter V ave  is the average value of the particle diameters of one hundred spherical spacers that are obtained by selecting ten particles, each of which is estimated to have the largest length, in each of ten cross sectional images of the electroconductive holding member that are taken along different cross sections. If it is possible to measure the spherical spacers before being added to the electroconductive holding member, the average particle diameter may be measured by using a particle-diameter-distribution measuring device that uses a laser diffraction-scattering method. The definitions of the particle diameter and the average particle diameter also apply to the particle diameter and the average particle diameter of metal particles described below. 
     In relation to the distance L between the surface of the second excitation electrode  130  formed on the second main surface  114  of the piezoelectric resonator  100  and the surface of the connection electrode  322  formed on the first main surface  302  of the substrate  300 , the particle diameter V of the spherical spacers  410  is equal to the distance L or smaller than the distance L (that is, V≤L is satisfied) (see  FIG. 2 ). The piezoelectric resonator  100  is placed on the surface of the connection electrode  322  so that the plurality of spherical spacers  410  are interposed therebetween. Thus, in a direction normal to the first main surface  302  of the substrate  300 , that is, in the Y′-axis direction shown in  FIG. 2 , the piezoelectric resonator  100  is held at a distance, which is determined in accordance with the particle diameter V of the spherical spacers, from the surface of the connection electrode  322 . To be specific, for example, if the spherical spacers  410  are arranged in one tier in the Y′-axis direction as illustrated in  FIG. 2 , the piezoelectric resonator  100  is held at a distance corresponding to the particle diameter V of the spherical spacers  410  (for example, about 5 to 6 μm). Alternatively, for example, if the spherical spacers  410  are stacked in two tiers in the Y′-axis direction, the piezoelectric resonator  100  is held at a distance corresponding to twice the particle diameter V of the spherical spacers  410  (for example, about 10 to 11 μm). The spherical spacers  410  may be slightly deformed by being interposed between the connection electrode  322  and the piezoelectric resonator  100 , and the length of the spherical spacers  410  in the Y-axis direction may be smaller than the particle diameter V before bonding. In this way, the distance between the second main surface  114  of the piezoelectric resonator  100  and the first main surface  302  of the substrate  300  is maintained constant, and parasitic capacity generated between the two main surfaces can be maintained constant. 
     In a plan view of the XZ′-plane, for example, the plurality of spherical spacers  410  are closely packed on the connection electrode  322  (see  FIG. 3 ). Here, the phrase “closely packed” refers to a state in which the spherical spacers  410  that are adjacent to each other are disposed so that the surfaces thereof are in contact with each other, as illustrated in  FIG. 3 . At this time, as illustrated in  FIG. 3 , a plurality of spherical-spacer sets, each of which is composed of three spherical spacers  410   a,    410   b,  and  410   c  that are adjacent to each other, are disposed on the first main surface of the substrate. A gap is formed in a region surrounded by the three spherical spacers  410   a  to  410   c  that are adjacent to each other. When a plurality of spherical-spacer sets are stacked in the Y′-axis direction, a gap similar to this gap is formed between spherical-spacer sets that are stacked in the Y′-axis direction. 
     Each of the plurality of metal particles  420  is a particle in which a plurality of metal atoms are bonded. Although the material of the plurality of metal particles  420  is not particularly limited, the material is mainly composed of, for example, silver (Ag) or the like. When the adhesive  400  solidifies while the plurality of metal particles  420  are in contact with each other in the adhesive  400 , the electroconductive holding member  342  becomes an adhesive that functions as a holding member while having electroconductivity. The plurality of metal particles  420  each have a particle diameter W, and the average value of the particle diameter W will be represented as the average particle diameter W ave . Variation in particle diameter of the plurality of metal particles  420  (that is, particle diameter distribution) can be approximated to, for example, a normal distribution function having a standard deviation σ. The plurality of metal particles  420  are each disposed so as to enter a gap formed by the plurality of spherical spacers  410 , which are closely packed on the connection electrode  322 , and are continuously arranged in contact with each other in the Y′-axis direction. That is, the particle diameter W of the metal particles  420  is smaller than a gap formed by the three spherical spacers  410   a  to  410   c  included in the spherical-spacer set. Referring to  FIGS. 4 and 5 , this point will be described. In  FIGS. 4 and 5 , it is assumed that the spherical spacers and the metal particle are spheres that circumscribe each other. 
       FIG. 4  is a conceptual diagram illustrating the relationship between the size of spherical spacers and the size of metal particle, specifically illustrating a state in which one metal particle enters a gap that is formed by three spherical spacers that are arranged adjacent to each other on the first main surface  302  of the substrate  300 .  FIG. 5  is a conceptual diagram illustrating the relationship between the size of spherical spacers and the size of metal particles, specifically illustrating a state in which three metal particles enter a gap that is formed by three spherical spacers.  FIGS. 4 and 5  each schematically illustrate a cross section that is parallel to the XZ′-plane and that is at a height such that the surfaces of a plurality of spherical spacers that are adjacent to each other are in contact with each other when the plurality of spherical spacers are evenly packed as illustrated in  FIG. 3 . That is, at this height, a gap that is formed by a plurality of spherical spacers is the smallest. The radius of large circles  10   a,    10   b,  and  10   c  of cross sections of spheres corresponding to the spherical spacers will be denoted by R (corresponding to V/2), and the radius of small circles  20   a ,  20   b,    20   c  of cross sections of spheres corresponding to the metal particles will be denoted by r (corresponding to W/2). 
       FIG. 4  is a conceptual diagram illustrating a case where one metal particle enters a gap formed by three spherical spacers of a spherical-spacer set. A line segment OQ=R and a line segment OP=(R+r), where O is the center of the large circle  10   a,  P is the center of the small circle  20   a,  and Q is the point of contact between the large circle  10   a  and the large circle  10   b.  (the line segment OQ):(the line segment OP)=R:(R+r)=√3:2, because an angle OQP=90 degrees and an angle OPQ=60 degrees in a triangle OPQ. Accordingly, the following equation (1) holds. 
         r ={(2/√3)−1 }×R    (1)
 
     From equation (1), a condition that allows one metal particle having a particle diameter W to enter a gap formed by three spherical spacers having a particle diameter V is represented by the following inequality (2). 
         W &lt;{(2/√3)−1 }×V    (2)
 
     Accordingly, if the following inequality (3) is satisfied, some of a plurality of metal particles having the average particle diameter W ave  can each enter a corresponding one of gaps that are formed by a plurality of spherical spacers having the average particle diameter V ave . If, for example, the average particle diameter W ave  of the metal particles satisfies W ave ={(2/√3)−1}×V ave , metal particles whose particle diameter W is smaller than the average particle diameter W ave  can enter the gaps, and the proportion of such metal particles is about a half of metal particles included in the electroconductive holding member. 
       W ave &lt;{(2√3)−1 }×V   ave (≈0.15 ×V   ave )   (3)
 
     When the particle diameter distribution of metal particles included in the electroconductive holding member is approximated to a normal distribution function having a standard deviation σ, if any of the following inequalities (4) to (6) is further satisfied, most of (for example, if the inequality (5) is satisfied, about 95% of) a plurality of metal particles having the average particle diameter W ave  can enter gaps formed by a plurality of spherical spacers having the average particle diameter V ave . 
         W   ave +σ&lt;{(2/√3)−1 }ΔV   ave    (4)
 
         W   ave +2σ&lt;{(2/√3)−1 }ΔV   ave    (5)
 
         W   ave +3σ&lt;{(2/√3)−1 }ΔV   ave    (6)
 
       FIG. 5  is a conceptual diagram illustrating a case where three metal particles enter a gap formed by three spacers in a spherical-spacer set. Regarding each of the large circles  10   a,    10   b,  and  10   c,  a part of an arc thereof is illustrated. A line segment OQ=R, a line segment OP=(R+r), and a line segment PT=r, where O is the center of the large circle  10   a,  P is the center of the small circle  20   a,  Q is the point of contact between the large circle  10   a  and the large circle  10   b,  S is the point of contact between the large circle  10   a  and the small circle  20   a,  T is the point of contact between the small circle  20   a  and the small circle  20   c,  and U is the intersection of a straight line OT and a straight line QP. A line segment OT=√{(R+r) 2 −r 2 } from the Pythagorean theorem, because an angle PTO=90 degrees in a triangle POT. A line segment TU=(1/√3)×r, because an angle PTU=90 degrees and an angle PUT=60 degrees in a triangle PTU. Accordingly, a line segment OU=√{(R+r) 2 −r 2 }+(1/√3)×r. (the line segment OQ):(the line segment OU)=R:√{(R+r) 2 −r 2 }+(1/√3)×r=√3:2, because the angle OQU=90 degrees and an angle OUQ=60 degrees in the triangle OQU. Accordingly, the following equation (7) holds. 
         r =(   5 − 2 √ 6   )× R    (7)
 
     From the equation (7), a condition that allows three metal particles having a particle diameter W to enter a gap formed by three spherical spacers having a particle diameter V is represented by the following inequality (8). 
         W &lt;(5−2√6)× V    (8)
 
     Accordingly, if the following inequality (9) is satisfied, some sets of three metal particles included in a plurality of metal particles having the average particle diameter W ave  (for example, about a half of metal particles included in the electroconductive holding member) can each simultaneously enter a corresponding one of gaps that are each formed by three spherical spacers having the average particle diameter V ave . 
         W   ave &lt;(5−2√6)× V   ave (≈0.10× V   ave )   (9)
 
     With the structure described above, in the piezoelectric resonator unit  1 , for example, the metal particles can sufficiently enter the gaps formed by the spherical spacers, compared with an existing adhesive as disclosed in Patent Document 1. Therefore, even though the spherical spacers are mixed therein, the electroconductivity of the electroconductive holding member can be maintained appropriately high. Accordingly, with the piezoelectric resonator unit  1 , the electroconductivity of the electroconductive holding member (holding portion), which holds the piezoelectric resonator, is improved while maintaining the distance between the piezoelectric resonator  100  and the main surface of the substrate  300  constant. Moreover, because it is not necessary to cover the spherical spacers with a metal, the manufacturing cost can be reduced, compared with a structure in which spherical spacers are covered with a metal. 
     Moreover, because spherical spacers that are not covered with a metal are used, for example, the electroconductive holding members  340  and  342  each have small Young&#39;s modulus and low acoustic impedance, compared with an existing piezoelectric resonator unit as disclosed in Patent Document 1. Thus, the difference in acoustic impedance between the piezoelectric resonator  100  and the substrate  300 , whose acoustic impedances are comparatively high, and the acoustic impedance of the electroconductive holding member, whose acoustic impedance is comparatively low, is large. Here, regarding transmission of vibrations between different objects, reflection waves of vibrations at the boundary surfaces between the objects increase and transmitted waves decrease, as the difference in acoustic impedance between the objects increases. That is, among vibrations that are transmitted from the piezoelectric resonator  100 , reflection waves at the boundary surfaces between the piezoelectric resonator  100  and the electroconductive holding members  340  and  342  increase, and transmitted waves to the substrate  300  decrease. Accordingly, vibrations that leak from the piezoelectric resonator  100  via the electroconductive holding members  340  and  342  to the substrate  300  decrease, and decrease of the CI (crystal impedance) value of the piezoelectric resonator unit  1  is suppressed. 
     Furthermore, when the metal particles have a size such that three metal particles can simultaneously enter a gap formed by three spherical spacers as illustrated in  FIG. 5 , blocking of the gap by the metal particles due to contact between the metal particles is reduced. Thus, compared with the case shown in  FIG. 4 , metal particles can more easily enter the gap, and the electroconductivity of the electroconductive holding member is further improved. 
     The average particle diameter W ave  of the plurality of metal particles may satisfy the following inequality (10). In this case, at least six metal particles can simultaneously enter a gap formed by three spherical spacers. Accordingly, occurrence of powder bridge of metal particles is suppressed, and therefore metal particles can more easily enter the gaps and the electroconductivity of the electroconductive holding member is improved. 
         W   ave &lt;[{(2/√3)−1}/6 ]×V   ave (≈0.03 ×V   ave )   (10)
 
     In the example illustrated in  FIG. 1 , one end of the piezoelectric resonator  100  is fixed by the electroconductive holding members  340  and  342  and the other end is free. However, the piezoelectric resonator  100  may be fixed to the substrate  300  at both ends thereof. That is, the connection electrodes  320  and  322  may be disposed on different sides on the first main surface  302  of the substrate  300 . For example, one of the connection electrodes  320  and  322  may be formed on the positive X side, and the other may be formed on the negative X side. 
     In  FIG. 2 , the spherical spacers are arranged in one tier in the height direction (Y′-axis direction). However, the number of tiers of the spherical spacers is not limited to one, and two or more tiers may be stacked in the height direction. 
     In order that, for example, six metal particles can simultaneously enter a gap formed by three spherical spacers, the metal particles need to be small relative to the spherical spacers. However, when the size of the metal particles is reduced, the proportion of the metal particles in the electroconductive holding member increases. As a result, the acoustic impedance of the electroconductive holding member increases. Thus, the difference in acoustic impedance between the electroconductive holding member, and the piezoelectric resonator  100  and the substrate  300  tends to decrease. Accordingly, in order to prevent decrease of the difference in acoustic impedance, preferably, the average particle diameter of the metal particles W ave  satisfies the following inequality (11), so that the number of metal particles that can enter a gap formed by three spherical spacers having the average particle diameter V ave  is, for example, at most six. 
         W   ave ≥[{(2/√3)−1}/6 ]×V   ave (≈0.03 ×V   ave )   (11)
 
     The piezoelectric resonator unit  1  need not include the lid member  200 . 
     Heretofore, exemplary embodiments of the present invention have been described. In the piezoelectric resonator unit  1 , the electroconductive holding members  340  and  342  each include the plurality of metal particles  420  and the plurality of spherical spacers  410 , the spherical spacers  410  positioning the piezoelectric resonator  100  at a predetermined distance from the first main surface  302  of the substrate  300 ; and a relationship W ave &lt;{(2/√3)−1}×V ave  is satisfied, where V ave  is the average particle diameter of the spherical spacers  410  and W ave  is the average particle diameter of the metal particles  420 . Thus, the metal particles  420  sufficiently enter the gaps formed by the spherical spacers  410 , and therefore the electroconductivity of the electroconductive holding members  340  and  342  is improved. Moreover, because it is not necessary to cover the spherical spacers with a metal, the manufacturing cost is reduced. Furthermore, because spherical spacers that are not covered with a metal are used, the electroconductive holding members  340  and  342  each have small Young&#39;s modulus and low acoustic impedance. Thus, vibrations that leak from the piezoelectric resonator  100  via the electroconductive holding members  340  and  342  to the substrate  300  decrease, and decrease of the CI value of the piezoelectric resonator unit  1  is suppressed. 
     In the piezoelectric resonator unit  1 , a relationship W ave +2σ&lt;{(2/√3)−1}×V ave  may be further satisfied, where σ is a standard deviation of a normal distribution function to which a particle diameter distribution of the metal particles is approximated. In this case, most of (for example, if the inequality (5) is satisfied, about 95% of) the metal particles  420  can enter the gaps formed by the plurality of spherical spacers  410 . Accordingly, the electroconductivity of the electroconductive holding members  340  and  342  is further improved. 
     In the piezoelectric resonator unit  1 , a relationship W ave &lt;(5−2√6)×V ave  may be further satisfied. In this case, the metal particles  420  can more easily enter the gaps formed by the spherical spacers  410 . Accordingly, the electroconductivity of the electroconductive holding members  340  and  342  is further improved. When the surface of each of the spherical spacers  410  is an insulator, if entry of the metal particles  420  into the gaps between adjacent spherical spacers  410  is blocked, electrical resistance increases. If the additive rate of the spherical spacers  410  is reduced so that gaps are formed in such a way that the spherical spacers  410  are separated from each other without becoming adjacent to each other, it is necessary to increase the additive rate of the metal particles  420  in order to obtain electrical conductivity by allowing the metal particles  420  to contact each other. As the additive rate of the metal particles  420  increases, the rigidity of the electroconductive holding member becomes close to that of the metal, and the influence of the electroconductive holding member on excitation of the piezoelectric resonator increases. A structure that satisfies a relationship W ave &lt;[{(2/√3)−1}/6]×V ave , and more preferably a relationship W ave &lt;&lt;(5−2√6)×V ave  can suppress the increase of electrical resistance of the electroconductive holding member and can suppress the increase of the influence of the electroconductive holding member on excitation of the piezoelectric resonator, even if the additive rate of the spherical spacers in the electroconductive holding member is at a high level such that the spherical spacers  410  contact each other. 
     Although the material of the spherical spacers  410  is not particularly limited, the material may be mainly composed of, for example, a resin. 
     For example, the surface of each of the spherical spacers  410  may be an insulator. In this case, the acoustic impedance of the spherical spacers  410  is low, compared with spherical spacers that are covered with a metal. Accordingly, vibrations that leak from the piezoelectric resonator  100  via the electroconductive holding members  340  and  342  to the substrate  300  decrease, and therefore decrease of the CI value of the piezoelectric resonator unit  1  is suppressed. 
     Although the material of the metal particles  420  is not particularly limited, the material may be mainly composed of, for example, silver. 
     The plurality of spherical spacers  410  may include a spherical-spacer set that is composed of three spherical spacers  410   a  to  410   c  that are arranged on the first main surface  302  of the substrate  300  and that are adjacent to each other, and the plurality of metal particles  420  may include a plurality of particles that pass through a gap surrounded by the three spherical spacers  410   a  to  410   c  and that are continuously arranged in contact with each other in a direction normal to the first main surface  302 . 
     The three spherical spacers  410   a  to  410   c  may be in contact with each other. 
     A plurality of the spherical-spacer sets may be disposed on the first main surface  302  of the substrate  300 . 
     The piezoelectric resonator unit  1  further includes the lid member  200  that is joined to the substrate  300  and that accommodates the piezoelectric resonator  100 . In this case, the piezoelectric resonator  100  can be accommodated in an inner space. 
     The embodiments, which have been described above in order to facilitate understanding the present invention do not limit the scope of the present invention. The present invention may be modified within the spirit and scope thereof and includes the equivalents thereof. That is, a modification of each of the embodiments that is appropriately modified in design by a person having ordinary skill in the art is included in the scope of the present invention as long as the modification has the features of the present invention. For example, elements of each of the embodiments; and the arrangement, the materials, the shapes, and the sizes of the elements are not limited to those described above as examples and may be modified as appropriate. Elements of the embodiments may be used in a combination as long as the combination is technologically feasible, and such combination is also included in the scope of the present invention as long as the combination has the features of the present invention. 
     REFERENCE SIGNS LIST 
     
         
           1  piezoelectric resonator unit 
           100  piezoelectric resonator 
           110  piezoelectric substrate 
           120 ,  130  excitation electrode 
           122 ,  132  extension electrode 
           124 ,  134  connection electrode 
           200  lid member 
           250  joining material 
           300  substrate 
           320 ,  322  connection electrode 
           320   a,    322   a  extension electrode 
           324 ,  326  corner electrode 
           330 ,  332 ,  334 ,  336  side electrode 
           340 ,  342  electroconductive holding member 
           360 ,  362 ,  364 ,  366  outer electrode 
           400  adhesive 
           410  spherical spacer 
           420  metal particle 
           10   a,    10   b,    10   c  large circle 
           20   a,    20   b,    20   c  small circle