Patent Publication Number: US-2023134199-A1

Title: Method for Manufacturing Vibration Element

Description:
The present application is based on, and claims priority from JP Application Serial Number 2021-176210, filed Oct. 28, 2021, the disclosure of which is hereby incorporated by reference herein in its entirety. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a method for manufacturing a vibration element. 
     2. Related Art 
     JP-A-2013-175933 describes a method for forming a tuning-fork-type vibrator having a bottomed groove in each vibrating arm in wet and dry etching processes. In the manufacturing method described in JP-A-2013-175933, a quartz crystal substrate is wet-etched to form the outer shape of the tuning-fork-type vibrator, and the resultant structure is then dry-etched to form the grooves. 
     JP-A-2007-013382 describes a method for forming a tuning-fork-type vibrator having a bottomed groove in each vibrating arm in a dry etching process. In the manufacturing method described in JP-A-2007-013382, a substrate made of a piezoelectric material is so dry-etched that the width of the grooves is smaller than the width of the space between the pair of vibrating arms to allow the micro-loading effect to make the etched grooves shallower than the etched space between the pair of vibrating arms. The grooves and the outer shape of the vibrator are thus formed all at once. 
     In the manufacturing method described in JP-A-2013-175933, the wet etching process in which the outer shape is formed and the dry etching process in which the grooves are formed are separate processes, so that the manufacturing processes are complicated, and the grooves are likely to be misaligned with respect to the outer shape. Vibration elements manufactured by this method therefore have potential unwanted vibration and other problems. 
     On the other hand, in the manufacturing method described in JP-A-2007-013382, the outer shape and the grooves are formed all at once in the same step, so that the problem described above does not arise. This manufacturing method, however, uses the micro-loading effect in dry etching to form the outer shape and the grooves all at once, which causes restrictions on dimension setting, such as the width of the vibrating arms and the width and depth of the grooves, resulting in a problem of a decrease in design flexibility. 
     There is therefore a need for a vibration element manufacturing method that allows formation of the outer shape and the grooves of the vibration element all at once and provides a high degree of design flexibility. 
     SUMMARY 
     A method for manufacturing a vibration element according to an aspect of the present disclosure is a method for manufacturing a vibration element including a first vibrating arm and a second vibrating arm that extend along a first direction and are arranged side by side along a second direction intersecting the first direction, the first and second vibrating arms each have a first surface and a second surface arranged side by side in a third direction intersecting the first direction and the second direction in a front and back relationship and a bottomed groove opening to the first surface, the method including a preparation step of preparing a quartz crystal substrate having a first substrate surface and a second substrate surface in a front and back relationship, a first protective film formation step of forming a first protective film at the first substrate surface in a region excluding a groove forming region where the grooves are formed from a first vibrating arm forming region where the first vibrating arm is formed and a second vibrating arm forming region where the second vibrating arm is formed, a first dry etching step of dry-etching the quartz crystal substrate from a first substrate surface side via the first protective film to form the grooves and outer shapes of the first and second vibrating arms, a second protective film formation step of forming a second protective film in the grooves, and a second dry etching step of dry-etching the quartz crystal substrate from the first substrate surface side via the second protective film to form the first surface and the outer shapes of the first and second vibrating arms. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a plan view showing a vibration element according to a first embodiment. 
         FIG.  2    is a cross-sectional view of the vibration element taken along the line A 1 -A 1  in  FIG.  1   . 
         FIG.  3    shows steps of manufacturing the vibration element according to the first embodiment. 
         FIG.  4    is a cross-sectional view for describing a method for manufacturing the vibration element. 
         FIG.  5    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  6    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  7    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  8    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  9    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  10    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  11    is a cross-sectional view for describing a method for manufacturing a vibration element according to a second embodiment. 
         FIG.  12    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  13    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  14    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  15    is a cross-sectional view for describing the method for manufacturing the vibration element. 
         FIG.  16    is a plan view showing a variation of the vibration element. 
         FIG.  17    is a cross-sectional view of the vibration element taken along the line A 3 -A 3  in  FIG.  16   . 
         FIG.  18    is a plan view showing another variation of the vibration element. 
         FIG.  19    is a cross-sectional view of the vibration element taken along the line A 4 -A 4  in  FIG.  18   . 
         FIG.  20    is a cross-sectional view of the vibration element taken along the line A 5 -A 5  in  FIG.  18   . 
         FIG.  21    is a plan view showing another variation of the vibration element. 
         FIG.  22    is a cross-sectional view of the vibration element taken along the line A 6 -A 6  in  FIG.  21   . 
         FIG.  23    is a cross-sectional view of the vibration element taken along the line A 7 -A 7  in  FIG.  21   . 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     1. First Embodiment 
     A method for manufacturing a vibration element  1  according to a first embodiment will be described. 
     The configuration of the vibration element  1  will first be described with reference to  FIGS.  1  and  2   , and the method for manufacturing the vibration element  1  will next be described with reference to  FIGS.  3  to  10   . 
     The figures excluding  FIG.  3    show axes X, Y, and Z, which are three axes perpendicular to one another, for convenience of description. The direction along the axis X as a second direction is also called a direction X, the direction along the axis Y as a first direction is also called a direction Y, and the direction along the axis Z as a third direction is also called a direction Z. The side facing the arrow attached to each of the axes is also called a positive side, and the side opposite from the positive side is also called a negative side. The positive side of the direction Z is also called an “upper side”, and the negative side of the direction Z is also called a “lower side”. A plan view viewed in the direction Z is also simply called a “plan view”. The axes X, Y, and Z correspond to the crystal axes of quartz crystal, as will be described later. 
     The vibration element  1  is a tuning-fork-type vibration element and includes a vibration substrate  2  and an electrode  3  formed at the front surface of the vibration substrate  2 , as shown in  FIGS.  1  and  2   . 
     The vibration substrate  2  is formed by patterning a Z-cut quartz crystal substrate as a Z-cut quartz crystal plate into a desired shape, spreads in the plane X-Y defined by the axes X and Y, which are the crystal axes of quartz crystal, and has a thickness along the direction Z. The axis X is also called an electrical axis, the axis Y is also called a mechanical axis, and the axis Z is also called an optical axis. The thickness along the direction Z is also simply called a “thickness”. 
     The vibration substrate  2  has the shape of a plate and has a first surface  2 A and a second surface  2 B, which are front and rear sides with respect to each other and arranged side by side in the direction Z. The vibration substrate  2  has a base  21 , and a first vibrating arm  22  and a second vibrating arm  23  extending from the base  21  along the direction Y and arranged side by side along the direction X. 
     The first vibrating arm  22  has a bottomed groove  221 , which opens via the first surface  2 A, a bank  225 , which defines the groove  221 , and a side surface  101 , which couples the first surface  2 A and the second surface  2 B to each other. The bank  225  is a portion of the first surface  2 A, the portion sandwiching and disposed alongside the groove  221  along the direction X in the plan view. 
     Similarly, the second vibrating arm  23  has a bottomed groove  231 , which opens via the first surface  2 A, a bank  235 , which defines the groove  231 , and a side surface  103 , which couples the first surface  2 A and the second surface  2 B to each other. The bank  235  is a portion of the first surface  2 A, the portion sandwiching and disposed alongside the groove  231  along the direction X in the plan view. 
     The grooves  221  and  231  each extend along the direction Y. The banks  225  and  235  are formed on opposite sides, in the direction X, of the grooves  221  and  231 , respectively, and extend along the direction Y. The first vibrating arm  22  and the second vibrating arm  23  therefore each have a substantially U-shaped cross-sectional shape. The thus configured vibration element  1  has a reduced thermoelastic loss and excellent vibration characteristics. 
     The electrode  3  includes a signal electrode  31  and a ground electrode  32 . The signal electrode  31  is disposed at the first surface  2 A and the second surface  2 B of the first vibrating arm  22  and the side surface  103  of the second vibrating arm  23 . On the other hand, the ground electrode  32  is disposed at the side surface  101  of the first vibrating arm  22  and the first surface  2 A and the second surface  2 B of the second vibrating arm  23 . When a drive signal is applied to the signal electrode  31  with the ground electrode  32  grounded, the first vibrating arm  22  and the second vibrating arm  23  perform flexural vibration in the direction X, in which the two vibrating arms repeatedly approach each other and separate from each other, as indicated by the arrows in  FIG.  1   . 
     The vibration element  1  has been briefly described above. 
     The method for manufacturing the vibration element  1  will next be described. The method for manufacturing the vibration element  1  includes a preparation step S 1  of preparing a quartz crystal substrate  20 , which is the base material of the vibration substrate  2 , a first protective film formation step S 2  of forming a first protective film  51  at the first substrate surface  20 A of the quartz crystal substrate  20 , a first dry etching step S 3  of dry-etching the quartz crystal substrate  20  via the first protective film  51  to form the grooves  221  and  231 , a second protective film formation step S 4  of forming a second protective film  52  in the grooves  221  and  231 , a second dry etching step S 5  of dry-etching the quartz crystal substrate  20  via the second protective film  52 , a first protective film removal step S 6  of removing the first protective film  51  left at the first substrate surface  20 A, a second protective film removal step S 7  of removing the second protective film  52  left in the grooves  221  and  231 , and an electrode formation step S 8  of forming the electrode  3  at the front surface of the vibration substrate  2  produced by the steps described above, as shown in  FIG.  3   . 
     The first protective film removal step S 6  corresponds to the “protective film removal step” in the present disclosure. 
     The steps described above will be sequentially described below. 
     Preparation Step S 1   
     The quartz crystal substrate  20 , which is the base material of the vibration substrate  2 , is prepared, as shown in  FIG.  4   . A plurality of the vibration elements  1  are formed all at once from the quartz crystal substrate  20 . The quartz crystal substrate  20  has the shape of a plate and has the first substrate surface  20 A and the second substrate surface  20 B, which are front and rear sides with respect to each other and arranged side by side in the direction Z. The thickness of the quartz crystal substrate  20  is adjusted to a desired value through a grinding process, such as lapping and polishing, and the first substrate surface  20 A and the second substrate surface  20 B are sufficiently smoothed. Surface treatment using wet etching may be performed on the quartz crystal substrate  20  as required. 
     In the following description, the region where the first vibrating arm  22  is formed is also called a first vibrating arm forming region Q 2 . The region where the second vibrating arm  23  is formed is also called a second vibrating arm forming region Q 3 . The region located between the first vibrating arm forming region Q 2  and the second vibrating arm forming region Q 3  is also called an inter-arm region Q 4 . The region located between adjacent vibration substrates  2  is also called an inter-element region Q 5 . 
     The first vibrating arm forming region Q 2  and the second vibrating arm forming region Q 3  have a groove forming region Q 1 , where the grooves  221  and  231  are formed, and a bank forming region Qd 1 , where the banks  225  and  235  are formed. In other words, the bank forming region Qd 1  corresponds to the region excluding the groove forming region Q 1  from the first vibrating arm forming region Q 2  and the second vibrating arm forming region Q 3 . The grooves  221  and  231  and the banks  225  and  235  are formed by the first dry etching step S 3 , which will be described later. 
     First Protective Film Formation Step S 2   
     The first protective film  51  is formed at the first substrate surface  20 A of the quartz crystal substrate  20 , as shown in  FIG.  5   . The first protective film  51  is formed at the bank forming regions Qd 1  of the first substrate surface  20 A. 
     In the present embodiment, the first protective film  51  is a resin film made of resin. For example, the first protective film  51  can be formed by applying a resist material, which is a photosensitive resin, onto the first substrate surface  20 A and patterning the resultant structure by using a lithographic technique. For example, the first protective film  51  can instead be formed by selectively applying the resin by using screen printing, imprinting, or any other printing technique. Since a resin film can be readily formed as described above, the first protective film formation step S 2  can be simplified by using a resin film as the first protective film  51 . 
     In the present embodiment, the thus formed first protective film  51  is so thick as to be left in the bank forming region Qd 1  when the first dry etching step S 3  and second dry etching step S 5 , which will be described later, are completed. Note that the formed first protective film  51  may be so thin as to be removed from the bank forming region Qd 1  when the first dry etching step S 3  or the second dry etching step S 5  is completed. 
     In the present embodiment, the first protective film  51  is made of resin and may instead be made of a non-resin material. For example, the first protective film  51  may be a metal film made of metal. 
     First Dry Etching Step S 3   
     The quartz crystal substrate  20  is dry-etched from the side facing the first substrate surface  20 A via the first protective film  51  to simultaneously form the grooves  221  and  231  and the outer shape of the vibration substrate  2 , as shown in  FIG.  6   . The phrase “simultaneously form” means that two features are formed all at once in a single step. The present step is reactive ion etching and is executed by using a reactive ion etching apparatus (RIE apparatus). The reaction gas introduced into the RIE apparatus is not limited to a specific gas and may, for example, be SF 6 , CF 4 , C 2 F 4 , C 2 F 6 , C 3 F 6 , or C 4 F 8 . 
     In the present step, the first protective film  51  formed in the bank forming region Qd 1  is used as a mask, and the regions excluding the bank forming region Qd 1  are etched. The regions excluding the bank forming region Qd 1  are the groove forming region Q 1 , the inter-arm region Q 4 , and the inter-element region Q 5 . The groove forming region Q 1  of the quartz crystal substrate  20  is etched from the side facing the first substrate surface  20 A to form the grooves  221  and  231 . The etching depth in the groove forming region Q 1  corresponds to the depth of the grooves  221  and  231 . The inter-arm region Q 4  and the inter-element region Q 5  of the quartz crystal substrate  20  are etched from the side facing the first substrate surface  20 A to form the outer shape of the vibration substrate  2 . The etching depth in the inter-arm region Q 4  and inter-element region Q 5  corresponds to a depth of the outer shape of the vibration substrate  2 . The “outer shape of the vibration substrate  2 ” is also called the “outer shapes of the first vibrating arm  22  and the second vibrating arm  23 ”. 
     The first dry etching step S 3  ends when the depth of the grooves  221  and  231  reaches a desired depth Wa. In the present embodiment, the depth of the outer shape of the vibration substrate  2  at the end of the present step is approximately equal to the depth Wa of the grooves  221  and  231 . The term “approximately equal” conceptually includes a case where the two depths are not equal to each other in an exact sense due, for example, to variation in the etching conditions. 
     In the present embodiment, the first protective film  51  is formed in the bank forming region Qd 1  of the first substrate surface  20 A but is not formed in the groove forming region Q 1 , the inter-arm region Q 4 , or the inter-element region Q 5 , as described above. That is, the groove forming region Q 1 , the inter-arm region Q 4 , and the inter-element region Q 5  of the first substrate surface  20 A are exposed. Therefore, in the first dry etching step S 3 , etching of the groove forming region Q 1 , the inter-arm region Q 4 , and the inter-element region Q 5  starts as the dry etching starts. The first dry etching step S 3  can therefore be executed in a short period. 
     Second Protective Film Formation Step S 4   
     The second protective film  52  is formed in the grooves  221  and  231 , as shown in  FIG.  7   . 
     In the present embodiment, the second protective film  52  is a resin film made of resin. The second protective film  52  is formed by burying the resin in the grooves  221  and  231 . For example, the second protective film  52  can be formed by applying a resist material, which is a photosensitive resin, onto the quartz crystal substrate  20  from the side facing the first substrate surface  20 A and patterning the resultant structure by using a lithographic technique. For example, the second protective film  52  can instead be formed by selectively applying the resin by using screen printing, imprinting, or any other printing technique. Since a resin film can be readily formed as described above, the second protective film formation step S 4  can be simplified by using a resin film as the second protective film  52 . 
     In the present embodiment, the thus formed second protective film  52  is thicker than or equal to the depth Wa of the grooves  221  and  231  when the second dry etching step S 5 , which will be described later, is completed. Note that the formed second protective film  52  only needs to be so thick as to be left at the bottom surfaces of the grooves  221  and  231  when the second dry etching step S 5  is completed. 
     In the present embodiment, the second protective film  52  is a thick film formed by burying the resin in the grooves  221  and  231 , and may instead be a thin film that covers the sidewalls and the bottom surfaces of the grooves  221  and  231 . 
     In the present embodiment, the second protective film  52  is made of resin, and may instead be made of a non-resin material. For example, the second protective film  52  may be a metal film made of metal. 
     Second Dry Etching Step S 5   
     The quartz crystal substrate  20  is dry-etched from the side facing the first substrate surface  20 A via the second protective film  52  to simultaneously form the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 , and the outer shape of the vibration substrate  2 , as shown in  FIG.  8   . The present step is reactive ion etching and is executed by using an RIE apparatus. 
     In the present step, the second protective film  52  formed in the groove forming region Q 1  is used as a mask, and the regions excluding the groove forming region Q 1  are etched. Note in the present embodiment that the first protective film  51  has been left in the bank forming region Qd 1 , as described above. Therefore, in the present step, the first protective film  51  and the second protective film  52  are used as a mask, and the regions excluding the groove forming region Q 1  and the bank forming region Qd 1  of the quartz crystal substrate  20  are etched. The regions excluding the groove forming region Q 1  and the bank forming region Qd 1  are the inter-arm region Q 4  and the inter-element region Q 5 . 
     The inter-arm region Q 4  and the inter-element region Q 5  of the quartz crystal substrate  20  are thus etched from the side facing the first substrate surface  20 A to form the outer shape of the vibration substrate  2 . 
     The second dry etching step S 5  ends when depths of the outer shape of the vibration substrate  2  reach desired depths Aa and Ba. That is, at the end of the present step, the etching depth in the inter-arm region Q 4  is the depth Aa, and the etching depth in the inter-element region Q 5  is the depth Ba. In the present embodiment, the depth Aa and the depth Ba are approximately equal to each other. 
     In the present embodiment, the depths Aa and Ba of the outer shape of the vibration substrate  2  are each greater than or equal to a thickness Ta of the quartz crystal substrate  20 . That is, Aa≥Ta and Ba≥Ta are satisfied. When the depths Aa and Ba are set at values greater than or equal to the thickness Ta of the quartz crystal substrate  20 , the inter-arm region Q 4  and the inter-element region Q 5  pass through the quartz crystal substrate  20  in the second dry etching step S 5 . The inter-arm region Q 4  and the inter-element region Q 5  passing through the quartz crystal substrate  20  form the first vibrating arm  22  and the second vibrating arm  23 . 
     In the present embodiment, in the second dry etching step S 5 , the dry etching is terminated with the first protective film  51  left at the first substrate surface  20 A of the quartz crystal substrate  20 . That is, the bank forming region Qd 1  of the first substrate surface  20 A is protected by the first protective film  51  and is therefore not etched in the first dry etching step S 3  or the second dry etching step S 5 . The bank forming region Qd 1  of the first substrate surface  20 A forms the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23  in the first protective film removal step S 6 , which will be described later. 
     In the second dry etching step S 5 , the dry etching may be terminated with no first protective film  51  left at the first substrate surface  20 A. That is, the bank forming region Qd 1  may be etched. In this case, the surface etched in the second dry etching step S 5  forms the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 . 
     Etching part of the bank forming region Qd 1  of the first substrate surface  20 A and not etching another part thereof as described above form the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 . 
     The first protective film formation step S 2 , the first dry etching step S 3 , the second protective film formation step S 4 , and the second dry etching step S 5  are summarized below. 
     Dry etching can process quartz crystal without affecting the crystal planes thereof, allowing formation of the grooves  221  and  231  and the outer shapes of the first vibrating arm  22  and the second vibrating arm  23  with excellent dimensional accuracy. 
     Forming the grooves  221  and  231  and the outer shape of the vibration substrate  2  all at once allows reduction in the number of steps of manufacturing the vibration element  1  and the cost thereof. Furthermore, positional shift of the grooves  221  and  231  from the outer shape does not occur, whereby the vibration substrate  2  can be formed with increased accuracy. 
     Since the grooves  221  and  231  and the outer shapes of the first vibrating arm  22  and the second vibrating arm  23  can be formed without using the micro-loading effect, the width of the inter-arm region Q 4 , the width of the inter-element region Q 5 , the widths of the grooves  221  and  231 , and other dimensions can be set without any restrictions, whereby the degree of design flexibility of the vibration element  1  can be improved. For example, adjusting the thickness and width of the first protective film  51  in the first protective film formation step S 2  allows control of the dimensions of the grooves  221  and  231  and the outer shapes of the first vibrating arm  22  and the second vibrating arm  23 . 
     Since the micro-loading effect is not used, restrictions on the dry etching conditions, such as selection of the reaction gas used to perform the dry etching, are relaxed, whereby the vibration element  1  can be more readily manufactured than when the micro-loading effect is used. 
     First Protective Film Removal Step S 6   
     The first protective film  51  left at the first substrate surface  20 A of the quartz crystal substrate  20  is removed, as shown in  FIG.  9   . The first substrate surface  20 A thus forms the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 . Since the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23  has not been etched in the first dry etching step S 3  or the second dry etching step S 5 , the thickness of the first vibrating arm  22  and the second vibrating arm  23  and the surface roughness of the first surface  2 A are maintained equal to the thickness of the quartz crystal substrate  20  and the surface roughness of the first substrate surface  20 A. The accuracy of the thickness of the first vibrating arm  22  and the second vibrating arm  23  is therefore improved, whereby occurrence of unwanted vibration such as torsional vibration is suppressed. 
     In a case where the first protective film  51  is removed from the first substrate surface  20 A and is not left there when the second dry etching step S 5  is completed, the first protective film removal step S 6  may not be provided. 
     Second Protective Film Removal Step S 7   
     The second protective film  52  left in the grooves  221  and  231  is removed, as shown in  FIG.  10   . 
     The order in accordance with which the first protective film removal step S 6  and the second protective film removal step S 7  are executed is not limited to the order described above, and the order of execution may be reversed. Furthermore, the first protective film removal step S 6  and the second protective film removal step S 7  may be executed as a single step to remove the first protective film  51  and the second protective film  52  all at once. 
     A plurality of vibration substrates  2  are collectively formed from the quartz crystal substrate  20  by executing steps S 1  to S 7  described above, as shown in  FIG.  10   . 
     Electrode Formation Step S 8   
     A metal film is deposited at the front surface of the vibration substrate  2 , and the metal film is patterned to form the electrode  3 . 
     The vibration element  1  is thus manufactured. 
     The present embodiment can provide the effects below, as described above. 
     The method for manufacturing the vibration element  1  is a method for manufacturing the vibration element  1 , which includes the first vibrating arm  22  and the second vibrating arm  23 , which extend along the direction Y, which is the first direction, and are arranged along the direction X, which is the second direction that intersects with the direction Y, the first vibrating arm  22  and the second vibrating arm  23  having the first surface  2 A and the second surface  2 B, which are front and rear sides with respect to each other and are arranged in the direction Z, which is the third direction that intersects with the directions X and Y, the first vibrating arm  22  and the second vibrating arm  23  further having the bottomed grooves  221  and  231 , which open via the first surface  2 A, the method including the preparation step S 1  of preparing the quartz crystal substrate  20  having the first substrate surface  20 A and the second substrate surface  20 B, which are front and rear sides with respect to each other, the first protective film formation step S 2  of forming the first protective film  51  at the first substrate surface  20 A in the bank forming region Qd 1 , which is the region excluding the groove forming region Q 1 , where the grooves  221  and  231  are formed, from the first vibrating arm forming region Q 2 , where the first vibrating arm  22  is formed, and the second vibrating arm forming region Q 3 , where the second vibrating arm  23  is formed, the first dry etching step S 3  of dry-etching the quartz crystal substrate  20  from the side facing the first substrate surface  20 A via the first protective film  51  to form the grooves  221  and  231  and the outer shapes of the first vibrating arm  22  and the second vibrating arm  23 , the second protective film formation step S 4  of forming the second protective film  52  in the grooves  221  and  231 , and the second dry etching step S 5  of dry-etching the quartz crystal substrate  20  from the side facing the first substrate surface  20 A via the second protective film  52  to form the first surface  2 A and the outer shapes of the first vibrating arm  22  and the second vibrating arm  23 . 
     Therefore, the outer shapes of the first vibrating arm  22  and the second vibrating arm  23 , and the grooves  221  and  231  can be formed all at once, and the width of the inter-arm region Q 4 , the width of the inter-element region Q 5 , the widths of the grooves  221  and  231 , and other dimensions can be set without any restrictions, whereby a method for manufacturing the vibration element  1  with a high degree of design flexibility can be provided. 
     Furthermore, the configuration in which the first protective film  51 , which is formed in the bank forming region Qd 1 , and the second protective film  52 , which is formed in the groove forming region Q 1 , are each a resin film allows simplification of the first protective film formation step S 2  and the second protective film formation step S 4 . 
     2. Second Embodiment 
     A method for manufacturing the vibration element  1  according to a second embodiment will be described with reference to  FIGS.  11  to  15   . The same components as those in the first embodiment have the same reference characters, and no redundant description of the same components will be made. 
     The second embodiment is the same as the first embodiment except that a first protective film  51   a  formed in the bank forming region Qd 1  in the first protective film formation step S 2  is a metal film, that the first protective film  51   a  has a first metal film  511  and a second metal film  512 , and that the first metal film  511  is formed in regions other than the bank forming region Qd 1  in the first protective film formation step S 2 . 
     The first metal film  511  formed in the groove forming region Q 1  out of the regions excluding the bank forming region Qd 1  corresponds to a third protective film  55  in the present disclosure. The first metal film  511  formed in the inter-arm region Q 4  and the inter-element region Q 5  out of the regions excluding the bank forming region Qd 1  corresponds to a fourth protective film  57  in the present disclosure. 
     The preparation step S 1  is the same as that in the first embodiment and will therefore not be described, and the description will start with the first protective film formation step S 2 . 
     First Protective Film Formation Step S 2   
     The first metal film  511  is first formed at the first substrate surface  20 A of the quartz crystal substrate  20 , as shown in  FIG.  11   . The first metal film  511  is a ground film that facilitates the formation of the second metal film  512 , which will be described later. The first metal film  511  can be made, for example, of copper (Cu) or chromium (Cr). The first metal film  511  can be formed, for example, by using vapor phase deposition, such as sputtering and evaporation. 
     A resist film R 1  is then formed at a surface of the first metal film  511 , the surface opposite from the quartz crystal substrate  20 , by using a photolithography technique. The surface of the first metal film  511  opposite from the quartz crystal substrate  20  is the surface of the first metal film  511  on the positive side of the direction Z. The resist film R 1  has openings in the bank forming region Qd 1 . That is, the resist film R 1  is so patterned that the second metal film  512  can be formed in the bank forming region Qd 1 . 
     The second metal film  512  is then formed on a surface of the first metal film  511 , the surface opposite from the quartz crystal substrate  20 , via the openings in the resist film R 1 . That is, the resist film R 1  is used as a mask, and the second metal film  512  is layered on the first metal film  511 . The first protective film  51   a  including the first metal film  511  and the second metal film  512  is thus formed in the bank forming region Qd 1  of the first substrate surface  20 A. The second metal film  512  can be made, for example, of nickel (Ni). The second metal film  512  can be formed, for example, by using electroless plating. 
     After the formation of the first protective film  51   a , the resist film R 1  is removed.  FIG.  12    shows the resultant structure. 
     The first protective film  51   a  including the first metal film  511  and the second metal film  512  is formed in the bank forming region Qd 1  of the first substrate surface  20 A, as shown in  FIG.  12   . That is, in the present embodiment, the first protective film  51   a  is a metal film made of metal. In general, the etching rates at which metals are etched is lower than the etching rates at which photosensitive resins used as resist materials are etched. The configuration in which the first protective film  51   a  is formed of a metal film therefore allows reduction in the thickness of the first protective film  51   a  as compared with the case where the first protective film  51   a  is formed of a resin film. The dimensional accuracy of the first vibrating arm  22  and the second vibrating arm  23 , the grooves  221  and  231 , and other portions formed in the first dry etching step S 3  can thus be improved. 
     The first metal film  511  as the third protective film  55  is formed in the groove forming region Q 1  of the first substrate surface  20 A. The first metal film  511  as the fourth protective film  57  is formed in the inter-arm region Q 4  and the inter-element region Q 5  of the first substrate surface  20 A. The first metal films  511  as the third protective film  55  and the fourth protective film  57  are thinner than the first protective film  51   a.    
     First Dry Etching Step S 3   
     The quartz crystal substrate  20  is dry-etched from the side facing the first substrate surface  20 A via the first protective film  51   a , as shown in  FIG.  13   . 
     In the present embodiment, the dry etching is initiated with the first metal films  511  formed in the groove forming region Q 1 , the inter-arm region Q 4 , and the inter-element region Q 5  of the first substrate surface  20 A. The first metal film  511  as the third protective film  55  formed in the groove forming region Q 1  and the first metal film  511  as the fourth protective film  57  formed in the inter-arm region Q 4  and the inter-element region Q 5  are thinner than the first protective film  51   a  formed in the bank forming region Qd 1 . The third protective film  55  and the fourth protective film  57  are therefore more readily removed in the first dry etching step S 3  than the first protective film  51   a.    
     Therefore, even when the first metal film  511  as the third protective film  55  is formed in the groove forming region Q 1 , the grooves  221  and  231  and the outer shape of the vibration substrate  2  can be formed all at once. The step of removing the first metal film  511  as the third protective film  55  is therefore unnecessary, whereby the number of steps of manufacturing the vibration substrate  2  can be reduced. 
     Furthermore, even when the first metal film  511  as the fourth protective film  57  is formed in the inter-arm region Q 4  and the inter-element region Q 5 , the grooves  221  and  231  and the outer shape of the vibration substrate  2  can be formed all at once. The step of removing the first metal film  511  as the fourth protective film  57  is therefore unnecessary, whereby the number of steps of manufacturing the vibration substrate  2  can be reduced. 
     Second Protective Film Formation Step S 4   
     The second protective film  52  is formed in the grooves  221  and  231 , as shown in  FIG.  14   . 
     In the present embodiment, the second protective film  52  is a resin film made of resin. The second protective film  52  is formed by burying the resin in the grooves  221  and  231 . 
     Second Dry Etching Step S 5   
     The quartz crystal substrate  20  is dry-etched from the side facing the first substrate surface  20 A via the second protective film  52  to simultaneously form the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 , and the outer shape of the vibration substrate  2 , as shown in  FIG.  15   . 
     In the present embodiment, in the second dry etching step S 5 , the dry etching is terminated with the first protective film  51   a  left at the first substrate surface  20 A of the quartz crystal substrate  20 . That is, the bank forming region Qd 1  of the first substrate surface  20 A is protected by the first protective film  51   a  and has therefore not been etched in the first dry etching step S 3  or the second dry etching step S 5 . The bank forming region Qd 1  of the first substrate surface  20 A forms the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23  in the first protective film removal step S 6 , which will be described later. The sentence “the first protective film  51   a  is left” means that “at least part of the first protective film  51   a  is left”. For example, when the second dry etching step S 5  is completed, the first metal film  511  and second metal film  512 , which form the first protective film  51   a , are left at the first substrate surface  20 A, in the present embodiment, and the second metal film  512  may instead be removed. 
     Completion of the second dry etching step S 5  is followed by the first protective film removal step S 6 . 
     The first protective film removal step S 6 , the second protective film removal step S 7 , and the electrode formation step S 8  are the same as those in the first embodiment and will therefore not be described. 
     The vibration element  1  is thus manufactured. 
     The present embodiment can provide the following effect in addition to the effects provided by the first embodiment. 
     The configuration in which the first protective film  51   a  formed in the bank forming region Qd 1  is a metal film allows improvement in the dimensional accuracy of the first vibrating arm  22 , the second vibrating arm  23 , the grooves  221  and  231 , and other portions. 
     The method for manufacturing the vibration element  1  has been described above based on the first and second embodiments. The present disclosure is, however, not limited thereto, and the configuration of each portion can be replaced with any configuration having the same function. Furthermore, any other constituent element may be added to any of the embodiments of the present disclosure. Moreover, the embodiments may be combined as appropriate with each other. 
     For example, at least one of the first protective film  51  and the second protective film  52  only needs to be a resin film. 
     For example, at least one of the first protective film  51  and the second protective film  52  only needs to be a metal film. 
     For example, the fourth protective film  57  may not be formed in the inter-arm region Q 4  of the first substrate surface  20 A. That is, the inter-arm region Q 4  of the first substrate surface  20 A may be exposed. In other words, no protective film may be formed in the inter-arm region Q 4  of the first substrate surface  20 A. 
     For example, the fourth protective film  57  may not be formed in the inter-element region Q 5  of the first substrate surface  20 A. That is, the inter-element region Q 5  of the first substrate surface  20 A may be exposed. In other words, no protective film may be formed in the inter-element region Q 5  of the first substrate surface  20 A. 
     For example, in addition to the bottomed grooves  221  and  231 , which open via the first surface  2 A of the first vibrating arm  22  and the second vibrating arm  23 , the vibration element  1  may further have bottomed grooves that open via the second surface  2 B. That is, the method for manufacturing the vibration element  1  is also applicable to a vibration element having bottomed grooves in each of the first surface  2 A and the second surface  2 B of the first vibrating arm  22  and the second vibrating arm  23 . 
     The vibration element manufactured in accordance with the vibration element manufacturing method according to the present disclosure is not limited to a specific device. 
     The vibration element manufactured by the vibration element manufacturing method according to the present disclosure may, for example, be a double-tuning-fork-type vibration element  7  shown in  FIGS.  16  and  17   . Note that no electrode is shown in  FIGS.  16  and  17   . The double-tuning-fork-type vibration element  7  includes a pair of bases  711  and  712 , and a first vibrating arm  72  and a second vibrating arm  73 , which link the bases  711  and  712  to each other. The first vibrating arm  72  and the second vibrating arm  73  have a first surface  7 A and a second surface  7 B, which are front and rear sides with respect to each other. The first vibrating arm  72  and the second vibrating arm  73  have bottomed grooves  721  and  731 , which open via the first surface  7 A, and banks  725  and  735 , which define the grooves  721  and  731 . 
     The vibration element may, for example, be a gyro vibration element  8  shown in  FIGS.  18 ,  19 , and  20   . Note that no electrode is shown in  FIGS.  18 ,  19 , and  20   . The gyro vibration element  8  includes a base  81 , a pair of detection vibration arms  82  and  83 , which extend from the base  81  toward opposite sides of the direction Y, a pair of linkage arms  84  and  85 , which extend from the base  81  toward opposite sides of the direction X, drive vibration arms  86  and  87 , which extend from the tip of the linkage arm  84  toward opposite sides of the direction Y, and drive vibration arms  88  and  89 , which extend from the tip of the linkage arm  85  toward opposite sides of the direction Y. When an angular velocity ωz around the axis Z acts on the thus configured gyro vibration element  8  with the drive vibration arms  86 ,  87 ,  88 , and  89  undergoing flexural vibration in the direction labeled with the arrows SD in  FIG.  18   , the Coriolis force newly excites flexural vibration of the detection vibration arms  82  and  83  in the direction labeled with the arrows SS, and the angular velocity ωz is detected based on the electric charges outputted from the detection vibration arms  82  and  83  due to the flexural vibration. 
     The detection vibration arms  82  and  83  and the drive vibration arms  86 ,  87 ,  88 , and  89  have a first surface  8 A and a second surface  8 B, which are front and rear sides with respect to each other. The detection vibration arms  82  and  83  have bottomed grooves  821  and  831 , which open via the first surface  8 A, and banks  825  and  835 , which define the grooves  821  and  831 . The drive vibration arms  86 ,  87 ,  88 , and  89  have bottomed grooves  861 ,  871 ,  881 , and  891 , which open via the first surface  8 A, and banks  865 ,  875 ,  885 , and  895 , which define the grooves  861 ,  871 ,  881 , and  891 . In the thus configured gyro vibration element  8 , for example, the drive vibration arms  86  and  88  or the drive vibration arms  87  and  89  form the first and second vibrating arms. 
     The vibration element may, for example, be a gyro vibration element  9  shown in  FIGS.  21 ,  22 , and  23   . Note that no electrode is shown in  FIGS.  21 ,  22 , and  23   . The gyro vibration element  9  has a base  91 , a pair of drive vibration arms  92  and  93 , which extend from the base  91  toward the positive side of the direction Y and arranged side by side in the direction X, and a pair of detection vibration arms  94  and  95 , which extend from the base  91  toward the negative side of the direction Y and arranged side by side in the direction X. When an angular velocity coy around the axis Y acts on the thus configured gyro vibration element  9  with the drive vibration arms  92  and  93  undergoing flexural vibration in the direction labeled with the arrows SD in  FIG.  21   , the Coriolis force newly excites flexural vibration of the detection vibration arms  94  and  95  in the direction labeled with the arrows SS, and the angular velocity coy is detected based on the electric charges outputted from the detection vibration arms  94  and  95  due to the flexural vibration. 
     The drive vibration arms  92  and  93  and the detection vibration arms  94  and  95  have a first surface  9 A and a second surface  9 B, which are front and rear sides with respect to each other. The drive vibration arms  92  and  93  have bottomed grooves  921  and  931 , which open via the first surface  9 A, and banks  925  and  935 , which define the grooves  921  and  931 . The detection vibration arms  94  and  95  have bottomed grooves  941  and  951 , which open via the first surface  9 A, and banks  945  and  955 , which define the grooves  941  and  951 . In the thus configured gyro vibration element  9 , the drive vibration arms  92  and  93  or the detection vibration arms  94  and  95  form the first and second vibrating arms.