Patent Publication Number: US-2013241363-A1

Title: Method of manufacturing resonator element, method of manufacturing resonator, resonator, oscillator, and electronic apparatus

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to a method of manufacturing a resonator element, a method of manufacturing a resonator, a resonator, an oscillator, and an electronic apparatus. 
     2. Related Art 
     In the past, there has been known a resonator element (a resonator and an oscillator) using a quartz crystal. Such a resonator element is superior in the frequency-temperature characteristic, and is therefore widely used as a reference frequency source and an oscillation source of a variety of electronic apparatuses. In particular, a resonator element using a quartz crystal substrate carved out at a cutting angle called AT cut has a frequency-temperature characteristic showing a cubic curve, and is therefore widely used also for mobile communication equipment such as a cellular phone (see, e.g., JP-A-2010-147625 (Document 1)). 
     As disclosed in Document 1, as the resonator element using the AT-cut quartz crystal substrate, a resonator element having a structure called bi-mesa structure is known to the public. The bi-mesa structure denotes a shape having a vibrating section with a large thickness and a small-thickness section disposed along an outer edge of the vibrating section and thinner than the vibrating section wherein the vibrating section has a first protruding section protruding from the small-thickness section toward a +Y′-axis side, and a second protruding section protruding toward a −Y′-axis side. Since the vibration can efficiently be confined in the vibrating section, such a shape has an advantage that a superior vibration characteristic can be obtained. 
     Here, as a method of forming the bi-mesa-structure quartz crystal substrate, there can be cited a method of, for example, patterning a plate-like quartz crystal substrate using a photolithography technique and an etching technique. 
     Specifically, the plate-like quartz crystal substrate carved out with AT-cut is firstly prepared, and a first mask corresponding to the first protruding section is formed on one surface of the quartz crystal substrate, and a second mask corresponding to the second protruding section is formed on the other surface thereof. It should be noted that it is assumed that the first and second masks have the same shape, and are formed to have the respective contours overlapping each other. Subsequently, the quartz crystal substrate is etched on the both sides thereof via the first and second masks to thereby form a quartz crystal substrate having the vibration section with the first and second protruding sections and a peripheral edge section located in the periphery of the vibration section. Then, by forming electrodes on the surface of the quartz crystal substrate, the quartz crystal resonator element can be obtained. 
     Here, in some cases, a relative shift between the first mask and the second mask occurs in the etching process of the quarts crystal substrate, and the quartz crystal resonator element having the shape shown in  FIG. 14  is manufactured depending on how the relative shift occurs. It should be noted that due to the crystal face of the quartz crystal, a side surface  512  on a +Z′-axis side of the first protruding section  51  becomes a surface roughly perpendicular to a principal surface  511 , and a side surface  513  on a −Z′-axis side thereof becomes a surface oblique to the principal surface  511 . Further, a side surface  522  on a −Z′-axis side of the second protruding section  52  becomes a surface roughly perpendicular to a principal surface  521 , and a side surface  523  on a +Z′-axis side thereof becomes a surface oblique to the principal surface  521 . 
     Here, since the width (the length in the Z′-axis direction) of an effective vibrating region  53  of a mesa part is important for controlling the vibration characteristics (quality) of the quartz crystal resonator element, it is necessary to obtain and then control the width. It should be noted that the effective vibrating region  53  denotes a region where the principal surface  511  of the first protruding section  51  and the principal surface  521  of the second protruding section  52  overlap each other. 
     There are various methods for obtaining the width W 1 ′ of the effective vibrating region  53  in the shape shown in  FIG. 14 . As a relatively easy method, it is possible to obtain the width W 1 ′ of the effective vibrating region  53  by, for example, obtaining the total width W 2 ′ of the quartz crystal resonator element, a distance L 1 ′ between an end A 2 ′ on the −Z′-axis side of the principal surface  511  of the first protruding section  51  and an end B 2 ′ on the −Z′-axis side of the quartz crystal resonator element, and a distance L 2 ′ between an end A 4 ′ on the +Z′-axis side of the principal surface  521  of the second protruding section  52  and an end B 1 ′ on the +Z′-axis side of the quartz crystal resonator element, and then substituting the values to the following formula. 
         W 1 ′=W 2′−( L 1 ′+L 2′)
 
     However, in the configuration shown in  FIG. 14 , there is a problem that it is not achievable to accurately measure the distances L 1 ′, L 2 ′. Specifically, in the case of measuring the distance L 1 ′, it is necessary to observe the quartz crystal resonator element from the Y′ direction to identify the end A 2 ′ of the principal surface  511  of the first protruding section  51 . However, since a boundary C 3 ′ between the side surface  513  of the first protruding section  51  and the peripheral part is located next to the end A 2 ′, the two boundary lines parallel to each other are observed extremely close to each other, and might be observed integrally, and therefore it is not achievable to accurately identify the end A 2 ′. Therefore, it is not achievable to accurately measure the distance L 1 ′. The same applies to the measurement of the distance L 2 ′. 
     As described above, in the method of manufacturing the quartz crystal resonator element according to the related art, there is a problem that there is manufactured the quartz crystal resonator element having the effective vibrating region the width of which cannot accurately be measured, and having the vibration characteristics (the quality) difficult to control. 
     JP-A-2008-067345 is an example of a related art document. 
     SUMMARY 
     An advantage of some aspects of the invention is to provide a method of manufacturing a resonator element having the effective vibrating region of the vibrating section the width of which can easily and accurately be measured, and having the vibration characteristics easy to control, a method of manufacturing a resonator having the vibration characteristics easy to control, a resonator, an oscillator, and an electronic apparatus each superior in reliability and equipped with the resonator element. 
     The invention can be implemented as the following application examples. 
     Application Example 1 
     This application example of the invention is directed to a method of manufacturing a resonator element including: providing a rotated Y-cut quartz crystal substrate, forming a mesa substrate by disposing a first mask on a principal surface located on a +Y′-axis side of the quartz crystal substrate, disposing a second mask on a principal surface located on a −Y′-axis side so as to be located at a position shifted toward a +Z′-axis side from the first mask, and etching the quartz crystal substrate via the first mask and the second mask, the mesa substrate including a vibrating section including a first protruding section protruding toward the +Y′-axis side from the quartz crystal substrate and a second protruding section protruding toward the −Y′-axis side, and a small-thickness section disposed along an outer edge of the vibrating section and having a thickness smaller than a thickness of the vibrating section, and providing a conductive pattern to the mesa substrate. 
     Thus, the width of the effective vibrating region of the vibrating section can easily and accurately be measured, and it is possible to manufacture the resonator element the vibration characteristics of which can easily be controlled. 
     Application Example 2 
     In the method of manufacturing a resonator element according to the above application example of the invention, it is preferable that an end on the +Z′-axis side of the first mask is located on the +Z′-axis side with respect to a center of the mesa substrate in a Z′-axis direction, and an end on the −Z′-axis side of the second mask is located on the −Z′-axis side with respect to the center of the mesa substrate in the Z′-axis direction. 
     Thus, it is possible to form the effective vibrating region, in which the principal surface of the first protruding section and the principal surface of the second protruding section overlap each other, in the central portion of the resonator element in the Z′-axis direction while keeping the effective vibrating region relatively large in size. Therefore, it is possible to vibrate the vibrating section in a balanced manner, and thus the resonator element superior in vibration characteristics can be manufactured. 
     Application Example 3 
     In the method of manufacturing a resonator element according to the above application examples of the invention, it is preferable that assuming that a shift amount in the Z′-axis direction between the first mask and the second mask is D, and a sum of a height of the principal surface of the first protruding section from a principal surface on the +Y′-axis side of the small-thickness section and a height of the principal surface of the second protruding section from a principal surface on the −Y′-axis side of the small thickness section is t, a relationship between the shift amount D and the sum t satisfies 0&lt;D≦t/2. 
     Thus, it is possible to keep the size of the effective vibrating region relatively large. 
     Application Example 4 
     In the method of manufacturing a resonator element according to the above application examples of the invention, it is preferable that a side surface connecting the end on the +Z′-axis side of the principal surface of the first protruding section and the small-thickness section to each other is perpendicular to the principal surface of the first protruding section, and a side surface connecting the end on the −Z′-axis side of the principal surface of the second protruding section and the small-thickness section to each other is perpendicular to the principal surface of the second protruding section. 
     Thus, the width of the effective vibrating region of the vibrating section can accurately be measured. 
     Application Example 5 
     In the method of manufacturing a resonator element according to the above application examples of the invention, it is preferable that the quartz crystal substrate is an AT-cut quartz crystal substrate. 
     Thus, the resonator element having superior frequency characteristics can be manufactured. 
     Application Example 6 
     It is preferable that the method of manufacturing a resonator according to the above application example of the invention includes housing the resonator element, which is manufactured using the method of manufacturing a resonator element according to the above application examples, in a package. 
     Thus, the resonator having excellent reliability can be obtained. 
     Application Example 7 
     This application example of the invention is directed to a resonator element including a rotated Y-cut quartz crystal substrate including a vibrating section including a first protruding section protruding toward a +Y′-axis side and a second protruding section protruding toward a −Y′-axis side, and a small-thickness section disposed along an outer edge of the vibrating section and having a thickness smaller than a thickness of the vibrating section, and a conductive pattern provided to the quartz crystal substrate, an end on a +Z′-axis side of a principal surface of the first protruding section is disposed so as to overlap a principal surface of the second protruding section in a plan view in a Y′-axis direction, and an end on a −Z′-axis side of the principal surface of the second protruding section overlaps the principal surface of the first protruding section in the plan view in the Y′-axis direction. 
     Thus, the width of the effective vibrating region of the vibrating section can easily and accurately be measured, and it is possible to obtain the resonator element the vibration characteristics of which can easily be controlled. 
     Application Example 8 
     This application example of the invention is directed to a resonator including the resonator element according to the above application example of the invention, and a package adapted to house the resonator element. 
     Thus, the resonator having excellent reliability can be obtained. 
     Application Example 9 
     This application example of the invention is directed to an oscillator including the resonator element according to the above application example of the invention, and an oscillation circuit electrically connected to the resonator element. 
     Thus, the oscillator having excellent reliability can be obtained. 
     Application Example 10 
     This application example of the invention is directed to an electronic apparatus including the resonator element according to the above application example of the invention. 
     Thus, the electronic apparatus having excellent reliability can be obtained. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1  is a plan view of a resonator according to a first embodiment of the invention. 
         FIG. 2  is a cross-sectional view along the A-A line in  FIG. 1 . 
         FIGS. 3A and 3B  are plan views of a resonator element provided to the resonator shown in  FIG. 1 , wherein  FIG. 3A  is a top view and  FIG. 3B  is a bottom view. 
         FIG. 4  is a cross-sectional view along the B-B line in  FIG. 1 . 
         FIGS. 5A and 5B  are partial enlarged views of the resonator element provided to the resonator shown in  FIG. 1 , wherein  FIG. 5A  is a top enlarged view and  FIG. 5B  is a bottom enlarged view. 
         FIGS. 6A through 6C  are cross-sectional views for explaining a method of manufacturing the resonator element shown in  FIGS. 3A and 3B . 
         FIG. 7  is a cross-sectional view for explaining the method of manufacturing the resonator element shown in  FIGS. 3A and 3B . 
         FIG. 8  is a cross-sectional view of a resonator according to a second embodiment of the invention. 
         FIG. 9  is a cross-sectional view of a resonator according to a third embodiment of the invention. 
         FIG. 10  is a cross-sectional view showing an example of an oscillator according to an embodiment of the invention. 
         FIG. 11  is a diagram showing an electronic apparatus (a laptop personal computer) equipped with the resonator element according to an embodiment of the invention. 
         FIG. 12  is a diagram showing an electronic apparatus (a cellular phone) equipped with the resonator element according to an embodiment of the invention. 
         FIG. 13  is a diagram showing an electronic apparatus (a digital still camera) equipped with the resonator element according to an embodiment of the invention. 
         FIG. 14  is a cross-sectional view for explaining the related art. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, a method of manufacturing a resonator element, a method of manufacturing a resonator, a resonator, an oscillator, and an electronic apparatus according to the invention will be explained in detail based on the preferred embodiments shown in the accompanying drawings. 
     Firstly, the resonator (the resonator according to the invention) to which the resonator element according to the invention is applied will be explained. 
     First Embodiment 
       FIG. 1  is a plan view of the resonator according to a first embodiment,  FIG. 2  is a cross-sectional view along the A-A line in  FIG. 1 ,  FIGS. 3A and 3B  are plan views of the resonator element provided to the resonator shown in  FIG. 1 , wherein  FIG. 3A  is a top view and  FIG. 3B  is a bottom view,  FIG. 4  is a cross-sectional view along the B-B line in  FIG. 1 ,  FIGS. 5A and 5B  are partial enlarged views of the resonator element provided to the resonator shown in  FIG. 1 , wherein  FIG. 5A  is a top enlarged view and  FIG. 5B  is a bottom enlarged view, and  FIGS. 6A through 6C , and  7  are cross-sectional views for explaining the method of manufacturing the resonator element shown in  FIGS. 3A and 3B . It should be noted that the upper side of  FIG. 2  is referred to as an “upper side” and the lower side thereof is referred to as a “lower side” in the following descriptions for the sake of convenience of explanation. 
     1. Resonator 
     The resonator  1  shown in  FIGS. 1 and 2  has a resonator element  2  (the resonator element according to the embodiment of the invention) and a package  9  housing the resonator element  2 . Hereinafter, the resonator element  2 , and the package  9  will sequentially be explained in detail. 
     Package 
     The package  9  has a base  91  having a box shape provided with a recessed section  911  opened upward, and a lid  92  having a plate shape and bonded to the base  91  so as to block the opening of the recessed section  911 . Such a package  9  has a housing space S formed by the recessed section  911  blocked by the lid  92 , and the resonator element  2  is airtightly housed and installed in the housing space S. It should be noted that the housing space S can be kept in, for example, a reduced-pressure (preferably vacuum) state, or filled with an inert gas such as nitrogen, helium, or argon. Thus, the vibration characteristics of the resonator element  2  can be improved. 
     The constituent material of the base  91  is not particularly limited, but a variety of types of ceramics such as aluminum oxide can be used therefor. Further, the constituent material of the lid  92  is not particularly limited, but a member with a linear expansion coefficient similar to that of the constituent material of the base  91  is preferable. For example, if the ceramics described above is used as the constituent material of the base  91 , an alloy such as kovar is preferably used. It should be noted that bonding between the base  91  and the lid  92  is not particularly limited, but it is possible to adopt bonding with an adhesive, or to adopt bonding with seam welding. 
     The bottom surface of the recessed section  911  is provided with a first connection terminal  95  and a second connection terminal  96 . The first connection terminal  95  is formed so as to be opposed to a first connection electrode  421  described later provided to the resonator element  2 , and the first connection terminal  95  and the first connection electrode  421  are electrically connected to each other via an electrically conductive fixation member  71 . Further, the second connection terminal  96  is formed so as to be opposed to a second connection electrode  422  described later provided to the resonator element  2 , and the second connection terminal  96  and the second connection electrode  422  are electrically connected to each other via an electrically conductive fixation member  72 . 
     The electrically conductive fixation members  71 ,  72  are not particularly limited, but solder, silver paste, an electrically conductive adhesive (an adhesive obtained by dispersing electrically conductive filler such as metal particles in a resin material), and so on can be used therefor. 
     Further, the first connection terminal  95  is electrically connected to an external terminal (a mounting terminal)  94  provided to the bottom surface of the package  9  via a through hole not shown, and the second connection terminal is electrically connected to an external terminal (a mounting terminal)  97  provided to the bottom surface of the package  9  via a through hole not shown. 
     The configurations of the first and second connection terminals  95 ,  96  and the external terminals  94 ,  97  are not particularly limited providing each of the configurations has an electrical conductivity, but each of the terminals can be formed of a metal coating obtained by stacking a coat made of, for example, Ni (nickel), Au (gold), Ag (silver), or Cu (copper) on a metalization layer (a foundation layer) made of, for example, Cr (chromium), or W (tungsten). 
     Resonator Element  2   
     As shown in  FIGS. 1 ,  2 ,  3 A, and  3 B, the resonator element  2  according to the present embodiment is composed of a quartz crystal substrate  3 , and a conductive pattern  4  formed on the quartz crystal substrate  3 . 
     The quartz crystal substrate  3  is a so-called rotated Y-cut quartz crystal substrate vibrating with a vibration mode of a thickness-shear vibration, and is formed of, for example, an AT-cut quartz crystal substrate. Thus, the resonator element  2  capable of exerting superior frequency characteristics can be obtained. It should be noted that the rotated Y-cut quartz crystal substrate denotes the quartz crystal substrate carved out so as to have a principal surface (a principal surface including the X-axis and the Z′-axis) obtained by rotating the plane (the Y-plane) including the X-axis (electrical axis) and the Z-axis (optical axis) as the crystal axes of the quartz crystal around the X axis counterclockwise (in a −Y-axis (the mechanical axis) direction) by a predetermined angle α from the Z axis. In the quartz crystal substrate  3  with such a configuration, it is possible to determine that the longitudinal direction of the quartz crystal substrate  3  is the X axis, the direction along the shorter side thereof is the Z′ axis, and the thickness direction thereof is the Y′ axis. In the case of the AT-cut quartz crystal substrate, the angle α is about 35°15′. 
     Such a quartz crystal substrate  3  has a vibrating section  31  with a large thickness, and a peripheral section (a small-thickness section)  32  with a small thickness formed in the periphery of the vibrating section  31 . The vibrating section  31  has a first protruding section  35  protruding from the peripheral section  32  toward the +Y′-axis side, and a second protruding section  37  protruding toward the −Y′-axis side. In other words, the quartz crystal substrate  3  forms the bi-mesa structure having the mesa sections formed on the both sides. According to such a shape, since the vibration can effectively be confined in the vibrating section  31 , the frequency characteristics such as a CI value and a Q value can be improved. 
     The principal surface  351  of the first protruding section  35  is provided with a first excitation electrode  411 , and the principal surface  371  of the second protruding section  37  is provided with a second excitation electrode  412 . It should be noted that the first excitation electrode  411  and the second excitation electrode  412  are formed so as to have the respective contours overlapping each other in a plan view of the resonator element  2 . 
     Further, the lower surface of the peripheral section  32  is provided with the first connection electrode  421  and the second connection electrode  422  formed side by side. The first excitation electrode  411  is electrically connected to the first connection electrode  421  via a first connection wiring line  431  formed on the upper surface and a side surface of the quartz crystal substrate  3 , and the second excitation electrode  412  is electrically connected to the second connection electrode  422  via a second connection wiring line  432  formed on the lower surface of the quartz crystal substrate  3 . 
     The first excitation electrode  411 , the second excitation electrode  412 , the first connection electrode  421 , the second connection electrode  422 , the first connection wiring line  431  and the second connection wiring line  432  described above constitute a conductive pattern  4 . 
     The configurations of the first and second excitation electrodes  411 ,  412 , the first and second connection electrodes  421 ,  422 , and the first and second connection wiring lines  431 ,  432  are not particularly limited providing each of the configurations has an electrical conductivity, but each of these members can be formed of a metal coating obtained by stacking an electrode layer made of, for example, Ni (nickel), Au (gold), Ag (silver), or Cu (copper) on a metalization layer (a foundation layer) made of, for example, Cr (chromium), or W (tungsten). 
     Such a resonator element  2  as described above is supported by the electrically conductive fixation members  71 ,  72  to the package  9 . Specifically, as described above, the first connection electrode  421  is fixed to the first connection terminal  95  via the electrically conductive fixation member  71 , and the second connection electrode  422  is fixed to the second connection terminal  96  via the electrically conductive fixation member  72 . 
     Then, the shape of the vibrating section  31  will be explained in detail with reference to  FIG. 4 .  FIG. 4  is a cross-sectional view along the B-B line in  FIG. 1 . 
     As shown in  FIG. 4 , the first protruding section  35  has a principal surface  351 , a side surface  352  located on the +Z′-axis side to the principal surface  351 , and a side surface  353  located on the −Z′-axis side to the principal surface  351 . The side surface  352  is a first crystal face of the quartz crystal, and is a plane (i.e., a plane roughly parallel to the Y′ axis) roughly perpendicular to the principal surface  351 . In contrast, the side surface  353  is a second crystal face of the quartz crystal, and is a plane oblique to the principal surface  351 . 
     Similarly to the above, the second protruding section  37  has a principal surface  371 , a side surface  372  located on the −Z′-axis side to the principal surface  371 , and aside surface  373  located on the +Z′-axis side to the principal surface  371 . The side surface  372  is a first crystal face of the quartz crystal, and is a plane (i.e., a plane roughly parallel to the Y′ axis) roughly perpendicular to the principal surface  371 . In contrast, the side surface  373  is a second crystal face of the quartz crystal, and is a plane oblique to the principal surface  371 . 
     It should be noted that the fact that the side surface  353  is roughly perpendicular to the principal surface  351  denotes that an angle θ formed between the principal surface  351  and the side surface  353  is included in a range of 85°≦θ≦95°. Similarly, the fact that the side surface  373  is roughly perpendicular to the principal surface  371  denotes that an angle θ formed between the principal surface  371  and the side surface  373  is included in a range of 85°≦θ≦95°. 
     Further, an end (a boundary between the principal surface  351  and the side surface  352 ) A 1  on the +Z′-axis side of the principal surface  351  of the first protruding section  35  is located so as to overlap the principal surface  371  of the second protruding section  37 . In other words, the end A 1  is located between an end (a boundary between the principal surface  371  and the side surface  372 ) A 3  on the −Z′-axis side of the principal surface  371  of the second protruding section  37  and an end (a boundary between the principal surface  371  and the side surface  373 ) A 4  on the +Z′-axis side thereof in the Z′-axis direction. 
     Further, the end A 3  on the −Z′-axis side of the principal surface  371  of the second protruding section  37  is located so as to overlap the principal surface  351  of the first protruding section  35  in a plan view. In other words, the end A 3  is located between the end A 1  on the +Z′-axis side of the principal surface  351  of the first protruding section  35  and an end (a boundary between the principal surface  351  and the side surface  353 ) A 2  on the −Z′-axis side thereof in a plan view in the Z′-axis direction. Further, the end A 3  is located away from the end A 1  in the −Z-axis direction. 
     By arranging the ends A 1 , A 3  as described above, the resonator element  2  quality control of which is easy can be obtained. Hereinafter, the specific explanation will be presented. Firstly, as one of the factors for determining the frequency characteristics of the resonator element  2 , there can be cited the width (the length in the Z′-axis direction) W 1  of an effective vibrating region  39  of the vibrating section  31 . It should be noted that the effective vibrating region  39  denotes a region where the principal surface  351  of the first protruding section  35  of the vibrating section  31  and the principal surface  371  of the second protruding section  37  overlap each other in a plan view. Therefore, by measuring and then controlling the width W 1  of the effective vibrating region  39 , the controller (e.g., the manufacturer) can perform sorting by determining those having the width W 1  within a predetermined numerical range as non-defective elements and those having the width W 1  out of the predetermined numerical range as defective elements, or can select the purpose of use depending on the value of the width W 1 . 
     A method of measuring the width W 1  of the effective vibrating region  39  is not particularly limited, but there are various methods. As a relatively easy and accurate method, the following method can be cited. Specifically, the width W 1  can easily be obtained by measuring the total width (the length in the Z′-axis direction) of the quartz crystal substrate  3  as W 2 , measuring the distance between an end B 1  on the +Z′-axis direction of the quartz crystal substrate  3  and the end A 1  on the +Z′-axis side of the principal surface  351  of the first protruding section  35  as L 1 , measuring the distance between an end B 2  on the −Z′-axis side of the quartz crystal substrate  3  and the end A 3  on the −Z′-axis side of the principal surface  371  of the second protruding section  37  as L 2 , and then substituting the values of W 2 , L 1 , and L 2  thus measured to the following formula. 
         W 1 =W 2−( L 1 +L 2)
 
     Here, the measurement of the distance L 1  is performed using the end A 1  as a reference. The end A 1  is the boundary between the principal surface  351  and the side surface  352  of the first protruding section  35 . Since the side surface  352  is a surface roughly perpendicular to the principal surface  351 , the boundary C 1  between the side surface  352  and the peripheral section  32  overlaps the end A 1  when viewing the resonator element  2  from the upper side (the +Y′-axis side), and is therefore not visually recognized as shown in  FIG. 5A . Therefore, since no line segments or the like hindering the visual recognition of the end A 1  appear around the end A 1 , the end A 1  can accurately be identified, and thus the distance L 1  can accurately be measured. 
     Similarly, the measurement of the distance L 2  is performed using the end A 3  as a reference. The end A 3  is the boundary between the principal surface  371  and the side surface  372  of the second protruding section  37 . Since the side surface  372  is a surface roughly perpendicular to the principal surface  371 , the boundary C 2  between the side surface  372  and the peripheral section  32  overlaps the end A 3  when viewing the resonator element  2  from the lower side (the −Y′-axis side), and is therefore not visually recognized as shown in  FIG. 5B . Therefore, since no line segments or the like hindering the visual recognition of the end A 3  appear around the end A 3 , the end A 3  can accurately be identified, and thus the distance L 2  can accurately be measured. 
     As described above, according to the resonator element  2 , it is possible to accurately measure the distances L 1 , L 2 , and thus, the width W 1  can accurately be obtained. Therefore, it is possible to easily perform the highly accurate quality control based on the value of the width W 1 . 
     It should be noted that when assuming that the distance between the end A 1  of the principal surface  351  of the first protruding section  35  and the end A 4  of the principal surface  371  of the second protruding section  37  is D 1 , the distance between the end A 3  of the principal surface  371  of the second protruding section  37  and the end A 2  of the principal surface  351  of the first protruding section  35  is D 2 , and the sum of the height t 1  from a principal surface  32   a  of the peripheral section to the principal surface of the first protruding section  35  and the height t 2  from a principal surface  32   b  of the peripheral section to the principal surface of the second protruding section  37  is t in a plan view, it is preferable to satisfy both of the following conditions. 
       0 &lt;D 1 ≦t/ 2 
       0 &lt;D 2 ≦t/ 2 
     Thus, it is possible to obtain the width W 1  using the method described above while keeping the effective vibrating region  39  larger in size. Therefore, it is possible to obtain the resonator element  2  easily controlled while exerting superior vibration characteristics. 
     Further, the distances D 1 , D 2  can be different from each other, but are preferably equal to each other. Thus, it is possible to roughly match the center of the quartz crystal substrate  3  in the Z′-axis direction and the center of the effective vibrating region  39  in the Z′-axis direction each other. In other words, it is possible to suppress the displacement of the center of the effective vibrating region  39  in the Z′-axis direction from the center of the quartz crystal substrate  3  in the Z′-axis direction. Therefore, since it is possible to vibrate the vibrating section  31  (the effective vibrating region  39 ) in a balanced manner, superior vibration characteristics can be exerted. 
     Further, the height t 1  and the height t 2  can be different from each other, but are preferably equal to each other. Thus, since it is possible to vibrate the vibrating section  31  (the effective vibrating region  39 ) in a balanced manner, superior vibration characteristics can be exerted. 
     Further, since the end A 1  of the principal surface  351  of the first protruding section  35  is located on the +Z′-axis side and the end A 3  of the principal surface  371  of the second protruding section  37  is located on the −Z′-axis side with respect to the center O 1  of the quartz crystal substrate  3  in the Z′-axis direction as in the present embodiment, the effective vibrating region  39  can be formed at the central portion in the Z′-axis direction of the quartz crystal substrate  3  in a balanced manner. Therefore, it is possible to vibrate the vibrating section  31  in a balanced manner. 
     2. Method of Manufacturing Resonator Element 
     Then, a method of manufacturing the resonator element  2  (the manufacturing method according to the embodiment of the invention) will be explained with reference to  FIGS. 6A through 6C , and  7 . 
     The method of manufacturing the resonator element  2  has a first process of preparing an AT-cut quartz crystal substrate  30 , a second process of providing the quartz crystal substrate  30  with the vibrating section  31  and the peripheral section  32  to thereby obtain the quartz crystal substrate  3 , and a third process of providing the quartz crystal substrate  3  with the conductive pattern  4 . Further, the second process includes a mask forming process of forming the first mask M 1  corresponding to the first protruding section  35  on the principal surface on the +Y′-axis side of the quartz crystal substrate  30 , and at the same time forming the second mask M 2  corresponding to the second protruding section  37  on the principal surface on the −Y′-axis side, and an etching process of etching the quartz crystal substrate  30  via the first mask M 1  and the second mask M 2 . 
     Hereinafter, each of these processes will sequentially be explained in detail. 
     First Process 
     Firstly, as shown in  FIG. 6A , the quartz crystal substrate  30  carved out with AT-cut is prepared. The quartz crystal substrate  30  is a member, which turns out the quartz crystal substrate  3  after passing through the processes described later. 
     Second Process 
     Mask Forming Process 
     Firstly, as shown in  FIG. 6B , the first mask M 1  is formed on the upper surface of the quartz crystal substrate  30 , and at the same time the second mask M 2  is formed on the lower surface thereof using a photolithography method or the like. The first mask M 1  is formed so as to correspond to the first protruding section  35  provided to the vibrating section  31 , and the second mask M 2  is formed so as to correspond to the second protruding section  37 . It should be noted that the first mask M 1  and the second mask M 2  have the same shape (including the size) as each other. 
     Further, as shown in  FIG. 6B , the first mask M 1  and the second mask M 2  are shifted from each other in the Z′-axis direction. Specifically, the first and second masks M 1 , M 2  are formed so that the first mask M 1  is located on the −Z′-axis side of the second mask M 2 . 
     Further, the first mask M 1  is formed so that the center O 2  thereof in the Z′-axis direction is located on the −Z′-axis side of the center O 1  of the quartz crystal substrate  30  in the Z′-axis direction, and the second mask M 2  is formed so that the center O 3  thereof in the Z′-axis direction is located on the +Z′-axis side of the center O 1 . 
     Further, it is arranged that the distance D 3  between the center O 1  and the center O 2  and the distance D 4  between the center O 1  and the center O 3  are roughly equal to each other. The displacement amount (a distance D 5  between the center O 2  and the center O 3 ) between the first and second masks M 1 , M 2  in the Z′-axis direction is not particularly limited, but preferably satisfies the following condition assuming that the sum of the height t 1  of the first protruding section  35  to be formed and the height t 2  of the second protruding section  37  is t. 
       0 &lt;D 5 ≦t/ 2 
     Etching Process 
     Subsequently, the quartz crystal substrate  30  is etched via the first and second masks M 1 , M 2 . The etching method is not particularly limited, but a wet-etching method can be used. Thus, as shown in  FIG. 6C , there can be obtained the quartz crystal substrate  3  having the vibrating section  31  having the first protruding section  35  and the second protruding section  37 , and the peripheral section  32  formed in the periphery of the vibrating section  31 . 
     Since the quartz crystal substrate  30  is side-etched in the −Z′-axis direction, the side surface  352  of the first protruding section  35  is formed at a position where the quartz crystal substrate  30  is eroded inward (toward the −Z′-axis side) from the end on the +Z′-axis side of the first mask M 1 . Further, the side surface  352  appears as a vertical surface roughly perpendicular to the principal surface  351  of the first protruding section  35 . In contrast, the side surface  353  of the first protruding section  35  appears as a tilted surface tilted toward the −Z′-axis side from the end on the −Z′-axis side of the first mask M 1 . 
     Similarly, since the quartz crystal substrate  30  is side-etched in the +Z′-axis direction, the side surface  372  of the second protruding section  37  is formed at a position where the quartz crystal substrate  30  is eroded inward (toward the +Z′-axis side) from the end on the −Z′-axis side of the second mask M 2 . Further, the side surface  372  appears as a vertical surface roughly perpendicular to the principal surface  371  of the second protruding section  37 . In contrast, the side surface  373  of the second protruding section  37  appears as a tilted surface tilted toward the +Z′-axis side from the end on the +Z′-axis side of the second mask M 2 . 
     Further, the end A 1  of the principal surface  351  of the first protruding section  35  is located so as to overlap the principal surface  371  of the second protruding section  37  in the Y′-axis direction. In other words, the end A 1  is located between the both ends A 3 , A 4  of the principal surface  371  of the second protruding section  37  in the Z′-axis direction. Further, the end A 3  of the principal surface  371  of the second protruding section  37  is located so as to overlap the principal surface  351  of the first protruding section  35  in the Y′-axis direction. In other words, the end A 3  is located between the both ends A 1 , A 2  of the principal surface  351  of the first protruding section  35  in the Z′-axis direction. 
     Further, the end A 3  is located away from the end A 1  toward the −Z′-axis side. Further, the end A 1  is located on the +Z′-axis side of the center O 1  of the quartz crystal substrate  30  (the quartz crystal substrate  3 ), and the end A 3  is located on the −Z′-axis side of the center O 1 . 
     Third Process 
     After removing the first and second masks M 1 , M 2 , the conductive pattern  4  (the first and second excitation electrodes  411 ,  412 , the first and second connection electrodes  421 ,  422 , and first and second connection wiring lines  431 ,  432 ) is formed on the quartz crystal substrate  3  as shown in  FIG. 7 . Specifically, the conductive pattern  4  can be formed by, for example, firstly depositing films of Cr (chromium) and Au (gold) in this order on the quartz crystal substrate  3  using a vapor phase deposition method such as evaporation, sputtering, ion plating, PVD, or CVD, then forming a mask corresponding to the conductive pattern  4  on the film using the photolithography method or the like, then patterning the film using a dry-etching method or the like, and then removing the mask. 
     The resonator element  2  can be obtained through the process described above. 
     In particular, since in the manufacturing method described above the displacement amount D 5  between the first and second masks satisfies the following relationship, it is possible to surely position the end A 1  of the principal surface  351  of the first protruding section  35  so as to overlap the principal surface  371  of the second protruding section  37  in the Y′-axis direction, and to surely position the end A 3  of the principal surface  371  of the second protruding section  37  so as to overlap the principal surface  351  of the first protruding section  35  in the Y′-axis direction. 
       0 &lt;D 5 ≦t/ 2 
     Further, it is possible to prevent the ends A 1 , A 3  from coming too closer to each other to thereby keep the effective vibrating region  39  large in size. 
     Further, in the manufacturing method described above, since the first mask M 1  is formed so that the center O 2  thereof is located on the −Z′-axis side of the center O 1  of the quartz crystal substrate  30 , and the second mask M 2  is formed so that the center O 3  thereof is located on the +Z′-axis side of the center O 1 , it is possible to form the effective vibrating region  39  at the center portion of the quartz crystal substrate  3  in the Z′-axis direction. Therefore, it is possible to vibrate the vibrating section  31  in a balanced manner. 
     It should be noted that by housing the resonator element  2  obtained in such a manner as described above in the package  9 , the resonator  1  can be obtained. Specifically, the base  91  provided with the first and second connection terminals  95 ,  96 , the external terminals  94 ,  97 , and the through holes is prepared, and the resonator element  2  is fixed to the base  91  via the electrically conductive fixation sections  71 ,  72 . Subsequently, the lid  92  and the base  91  are bonded to each other so as to block the upper opening of the base  91  with the lid  92 . Thus, the resonator  1  can be obtained. 
     Second Embodiment 
     Then, another resonator according to a second embodiment of the invention will be explained. 
       FIG. 8  is a cross-sectional view of the resonator according to the second embodiment of the invention. 
     Hereinafter, the resonator according to the second embodiment will be described with a focus mainly on the differences from the first embodiment described above, and the explanation regarding substantially the same matters will be omitted. 
     The resonator according to the second embodiment of the invention is substantially the same as that of the first embodiment described above except the point that the configuration of the package is different. It should be noted that the constituents substantially the same as those of the first embodiment described above are denoted with the same reference symbols. 
     As shown in  FIG. 8 , the package  9 A has a base  91 A having a plate shape (flat plate shape), and a lid  92 A having a cap-like shape with a recessed section  921  opening downward. Such a package  9 A forms the housing space S with the base  91 A blocking the opening of the recessed section  921 , and airtightly houses the resonator element  2  in the housing space S. 
     According also to the second embodiment described above, substantially the same advantages as in the first embodiment described above can be obtained. 
     Third Embodiment 
     Then, another resonator according to a third embodiment of the invention will be explained. 
       FIG. 9  is a cross-sectional view of the resonator according to the third embodiment of the invention. 
     Hereinafter, the resonator according to the third embodiment will be described with a focus mainly on the differences from the first embodiment described above, and the explanation regarding substantially the same matters will be omitted. 
     The resonator according to the third embodiment of the invention is substantially the same as that of the first embodiment described above except the point that the configuration of the package is different, and further, an electronic component is provided. It should be noted that the constituents substantially the same as those of the first embodiment described above are denoted with the same reference symbols. 
     As shown in  FIG. 9 , the resonator  1  according to the present embodiment has the resonator element  2 , the package  9  for housing the resonator element  2 , and a thermosensing component (the electronic component)  6  for detecting the temperature of the resonator element  2 . 
     Further, the package  9  has a housing section  991  for housing the thermosensing component  6 . The housing section  991  can be formed by, for example, disposing a frame-like member  99  on the bottom side of the base  91 . 
     As the thermosensing component  6 , there can be used, for example, a thermistor having a physical quantity such as an electrical resistance varying in accordance with the temperature variation. Further, by detecting the electrical resistance of the thermistor with an external circuit, the detected temperature of the thermistor can be measured. 
     According also to the third embodiment described above, substantially the same advantages as in the first embodiment described above can be obtained. 
     Hereinabove, the resonator element and the resonator according to the embodiment of the invention are explained. It should be noted that although the configuration of housing the resonator element alone in the housing space S is explained as the configuration of the resonator described above, it is also possible to additionally house other electronic components in the housing space S. As such electronic components, there can be cited, for example, a temperature detection element such as a thermistor for detecting the temperature of the resonator element, and an IC chip  8  described later for controlling drive of the resonator element  2 . 
     Oscillator 
     Then, the oscillator (the oscillator according to the embodiment of the invention) to which the resonator element according to the embodiment of the invention is applied will be explained. 
     The oscillator  10  shown in  FIG. 10  has the resonator  1  and the IC chip (a chip part)  8  for driving the resonator element  2 . Hereinafter, the oscillator  10  will be explained with a focus mainly on the differences from the resonator described above, and the explanations regarding substantially the same matters will be omitted. 
     The package  9  has the base  91  having a box shape provided with the recessed section  911 , and the lid  92  having a plate shape for blocking the opening of the recessed section  911 . 
     The recessed section  911  of the base  91  has a first recessed section  911   a  opened in the upper surface of the base  91 , a second recessed section  911   b  opened in a center portion of the bottom surface of the first recessed section  911   a , and a third recessed section  911   c  opened in a center portion of the bottom surface of the second recessed section  911   b.    
     On the bottom surface of the first recessed section  911   a , there are formed the first connection terminal  95  and the second connection terminal  96 . Further, on the bottom surface of the third recessed section  911   c , there is disposed the IC chip  8 . The IC chip  8  has a drive circuit (an oscillation circuit) for controlling drive of the resonator element  2 . By driving the resonator element  2  with the IC chip  8 , a signal with a predetermined frequency can be taken out. 
     Further, on the bottom surface of the second recessed section  911   b , there is formed a plurality of internal terminals  93  electrically connected to the IC chip  8  via wires. The plurality of internal terminals  93  includes a terminal electrically connected to the external terminal (the mounting terminal)  94  formed on the bottom surface of the package  9  via a through hole not shown provided to the base  91 , a terminal electrically connected to the first connection terminal  95  via a through hole and a wire not shown, and a terminal electrically connected to the second connection terminal  96  via a through hole and a wire not shown. 
     It should be noted that although the configuration having the IC chip  8  disposed in the housing space S is explained with reference to  FIG. 10 , the arrangement of the IC chip  8  is not particularly limited, but it is also possible to dispose the IC chip  8 , for example, outside (on the bottom surface of) the package  9 . 
     Electronic Apparatuses 
     Then, the electronic apparatuses (the electronic apparatuses according to the embodiment of the invention) to which the resonator element according to the embodiment of the invention is applied will be explained in detail with reference to  FIGS. 11 through 13 . 
       FIG. 11  is a perspective view showing a configuration of a mobile type (or laptop type) of personal computer as an example of the electronic apparatus equipped with the resonator element according to the embodiment of the invention. In the drawing, the personal computer  1100  is composed of a main body section  1104  provided with a keyboard  1102 , and a display unit  1106  provided with a display section  100 , and the display unit  1106  is pivotally supported with respect to the main body section  1104  via a hinge structure. Such a personal computer  1100  incorporates the resonator  1  functioning as a filter, a resonator, a reference clock, and so on. 
       FIG. 12  is a perspective view showing a configuration of a cellular phone (including PHS) as an example of the electronic apparatus equipped with the resonator element according to the embodiment of the invention. In this drawing, the cellular phone  1200  is provided with a plurality of operation buttons  1202 , an ear piece  1204 , and a mouthpiece  1206 , and the display section  100  is disposed between the operation buttons  1202  and the ear piece  1204 . Such a cellular phone  1200  incorporates the resonator  1  functioning as a filter, a resonator, and so on. 
       FIG. 13  is a perspective view showing a configuration of a digital still camera as an example of the electronic apparatus equipped with the resonator element according to the embodiment of the invention. It should be noted that connection with external equipment is also shown schematically in this drawing. Here, existing cameras expose a silver salt film to an optical image of an object, while the digital still camera  1300  performs photoelectric conversion on an optical image of an object by an imaging element such as a CCD (a charge coupled device) to generate an imaging signal (an image signal). 
     The case (body)  1302  of the digital still camera  1300  is provided with a display section on the back surface thereof to be configured to display an image in accordance with the imaging signal from the CCD, wherein the display section functions as a viewfinder for displaying the object as an electronic image. Further, the front surface (the back side in the drawing) of the case  1302  is provided with a light receiving unit  1304  including an optical lens (an imaging optical system), the CCD, and so on. 
     When the photographer confirms an object image displayed on the display section, and then pushes a shutter button  1306  down, the imaging signal from the CCD at that moment is transferred to and stored in the memory device  1308 . Further, the digital still camera  1300  is provided with video signal output terminals  1312  and an input-output terminal  1314  for data communication disposed on a side surface of the case  1302 . Further, as shown in the drawing, a television monitor  1430  and a personal computer  1440  are respectively connected to the video signal output terminals  1312  and the input-output terminal  1314  for data communication according to needs. Further, there is adopted the configuration in which the imaging signal stored in the memory device  1308  is output to the television monitor  1430  or the personal computer  1440  in accordance with a predetermined operation. Such a digital still camera  1300  incorporates the resonator  1  functioning as a filter, a resonator, and so on. 
     It should be noted that, as the electronic apparatus equipped with the resonator element according to the embodiment of the invention, there can be cited, for example, an inkjet ejection device (e.g., an inkjet printer), a laptop personal computer, a television set, a video camera, a video cassette recorder, a car navigation system, a pager, a personal digital assistance (including one with communication function), an electronic dictionary, an electric calculator, a computerized game machine, a word processor, a workstation, a video phone, a security video monitor, a pair of electronic binoculars, a POS terminal, a medical device (e.g., an electronic thermometer, an electronic manometer, an electronic blood sugar meter, an electrocardiogram measurement instrument, an ultrasonograph, and an electronic endoscope), a fish detector, various types of measurement instruments, various types of gauges (e.g., gauges for a vehicle, an aircraft, or a ship), and a flight simulator besides the personal computer (the mobile personal computer) shown in  FIG. 11 , the cellular phone shown in  FIG. 12 , and the digital still camera shown in  FIG. 13 . 
     Although the resonator element, the resonator, the oscillator, and the electronic apparatus according to the embodiment of the invention are hereinabove explained based on the embodiments shown in the accompanying drawings, the invention is not limited thereto, but the configuration of each of the constituents can be replaced with one having an arbitrary configuration with an equivalent function. Further, it is possible to add any other constituents to the invention. Further, it is also possible to arbitrarily combine any of the embodiments. 
     The entire disclosure of Japanese Patent Application No. 2012-059329, filed Mar. 15, 2012 is expressly incorporated by reference herein.