Abstract:
A tuning fork quartz crystal resonator has a base and two resonating arms extended in parallel from the same side of the base. Each resonating arm has asymmetric grooves on its upper and bottom surface, and the via-hole to reliably connect the top and bottom electrode. The asymmetric groove design can simplify the manufacturing process and lower the manufacturing cost. The base has continuous concave on both side surfaces and a recess on the main surface. The energy of ultrasonic wave propagating via the base mounting pads into the ceramic package can be reduced. This unique tuning fork quartz crystal resonator can prevent dramatic reduction of the Q value, and retain the outstanding quality of the resonator.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This non-provisional application claims priority under 35 U.S.C. §119(a) on Patent Application No(s). 098139231 filed in Taiwan, R.O.C. on Nov. 18, 2009, the entire contents of which are hereby incorporated by reference. 
       BACKGROUND 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a piezoelectric resonator, particularly to a tuning fork quartz crystal resonator. 
         [0004]    2. Related Art 
         [0005]    A quartz crystal resonator uses its piezoelectric characteristics to generate a periodic constant frequency. It retains a relative high Quality Factor (Q value) to maintain a stable frequency. It has been provided to frequency and timing control for various portable devices such as watches, cell phones, global position system, wireless communications, and medical devices, etc. 
         [0006]      FIG. 15  depicts the electric equivalent circuit of the quartz crystal resonator. In  FIG. 15 , a motional resistance (R 1 ), a motional inductance (L 1 ), and a motional capacitance (C 1 ) form a series arm. This series arm is then connected to a static capacitance (C 0 ) in parallel. 
         [0007]    Based on the electric equivalent circuit shown in  FIG. 15 , the series resonate frequency (Fs) is defined as follows: 
         [0000]    
       
         
           
             Fs 
             = 
             
               1 
               
                 2 
                  
                 π 
                  
                 
                   
                     
                       L 
                       1 
                     
                      
                     
                       C 
                       1 
                     
                   
                 
               
             
           
         
       
     
         [0008]    A tuning fork quartz crystal resonator has the same electric equivalent circuit. A tuning fork quartz crystal resonator is manufactured from a quartz wafer that was cut from a single crystal alpha quartz bar with a designate cutting angle θ. After the resonator was processed and shaped into a tuning fork structure of the desired dimension, two electrodes of opposite polarities are formed on the resonating arms with proper electrical connection paths. By inserting a tuning fork quartz crystal resonator into an oscillation circuit, it induces the resonator to vibrate in flexure mode at constant oscillating frequency. 
         [0009]      FIG. 14  illustrates the X, Y, and Z coordinate for a single crystal alpha quartz bar, and the X, Y′, and Z′ coordinate for a quartz wafer with a designate cutting angle θ. The tuning fork crystal resonator and the quartz wafer have the same X, Y′, and Z′ coordinates. The cutting angle θ is an angle rotating around the +X axis in a range of −6° to +6°. The X axis is interpreted as an electrical axis, the Y axis is a mechanical axis, and the Z axis is an optical axis. 
         [0010]    The resonating frequency (Fs) of the tuning fork quartz crystal resonator is proportional to the width (W) of the resonating arm, and inversely proportional to the square of the length (L) of the resonating arm. The relation of the resonating frequency, resonating arm length, and width is as follow: 
         [0000]    
       
         
           
             Fs 
             = 
             
               k 
               × 
               
                 W 
                 
                   L 
                   2 
                 
               
             
           
         
       
     
         [0000]    where k is a constant. 
         [0011]    An oscillator consists of a tuning fork quartz crystal resonator and an oscillation circuit. In general, an oscillator has a better performance when the resonator has a lower R 1  value. 
         [0012]    The electronic industry has been growing for last thirty years. On demand, most electronic devices and components have been miniaturized. A tuning fork quartz crystal resonator can be miniaturized by reducing the length and width of the resonating arms. In general, reducing the length and width of the resonating arms results in a lower C 1  value and higher R 1  value. 
       SUMMARY 
       [0013]    In order to reduce the R 1  value, a quartz crystal resonator can be designed to increase the C 1  value without degrading the Q value. An effective way to increase the C 1  value of a tuning fork resonator is to strengthen the electrical field along the X axis between two electrodes on the resonating arms. 
         [0014]    Photolithographic etching process has been used to miniaturize the quartz crystal resonator. To increase the C 1  value of a tuning fork resonator, the concept of symmetric grooves on the upper and lower main surfaces of the two resonating arms was introduced in early Nineteen Eighty. To form symmetric grooves and tuning fork structure requires multiple photolithographic etching processes. 
         [0015]    The present invention provides a different approach to the conventional one in the groove design. “Asymmetric grooves” are formed to a desirable range of depth on the upper and lower main surfaces of the two resonating arms of the tuning fork quartz crystal resonator by a photolithographic etching process. The tuning fork structure and the asymmetric grooves can be formed simultaneously in one single etching process. Followed by the metal coating process, one electrode is formed on both side surfaces of the resonating arms, and the other electrode with opposite polarity is formed in the grooves. With proper electrical connection of the two electrodes between the grooves and the side surfaces of the resonating arms, the effective electrical field strength on the resonating arms along the X axis is increased which leads to a higher C 1  value and a lower R 1  value. This invention fully utilizes the physical characteristics of the asymmetric grooves, simplifies the photolithographic etching process, shortens the manufacturing cycle time, reduces the manufacturing cost, and improves the production capacity. 
         [0016]    Furthermore, the present invention also provides an unique structure on the base of the tuning fork resonator by adding a recess to the base, and a continuous curved concave to both side surfaces of the base. This unique structure can reduce the ultrasonic energy from being propagated through the base mounting pads to the ceramic package. The Q value of the resonator is thus retained to ensure the high performance of the resonator. 
         [0017]    The present invention proposes a tuning fork quartz crystal resonator, particularly a miniaturized tuning fork quartz crystal resonator. This tuning fork quartz crystal resonator is produced from quartz wafer. During the same photolithographic etching process, the asymmetric grooves on the resonating arms and the shape of the turning forks are formed simultaneously. Metal films are deposited on the side surfaces and in the grooves of the resonating arms to form two electrodes of opposite polarities. With proper electrical connection between the two electrodes, a miniature tuning fork resonator with low R 1  value can be produced. The frequency of the resonator is in a range of 10 KHz to 200 KHz. 
         [0018]      FIG. 1A  is a schematic three-dimensional view of the present invention, and  FIG. 1B  is a schematic three-dimensional back view of  FIG. 1A . The tuning fork quartz crystal resonator of the present invention comprises a first resonating arm, a second resonating arm, and a base. The first resonating arm and the second resonating arm are connected to same side of the base. 
         [0019]    The first resonating arm has a first main surface, a first side surface, a second main surface, and a second side surface adjacent to each other in sequence. The first resonating arm has at least one first groove and at least one second groove. The first groove is located on the first main surface, and the second groove is located on the second main surface. The first resonating arm has at least one first via-hole. The first via-hole extends from the first main surface to the second main surface. 
         [0020]    The second resonating arm has a third main surface, a third side surface, a fourth main surface, and a fourth side surface adjacent to each other in sequence. The second resonating arm has at least one third groove and at least one fourth groove. The third groove is located on the third main surface, and the fourth groove is located on the fourth main surface. The second resonating arm has at least one second via-hole. The second via-hole extends from the third main surface to the fourth main surface. 
         [0021]    The base has a fifth main surface and a sixth main surface opposite to each other. The base also has a fifth side surface and a sixth side surface opposite to each other. The fifth side surface and the sixth side surface of the base have a concave, and the concave is a continuous curved surface. There is a recess on the fifth main surface or the sixth main surface of the base. 
         [0022]    The present invention has an unique asymmetric grooves design. The asymmetric grooves are formed on the first main surface and the second main surface on the opposite side of the first resonating arm, as well as the third main surface and the fourth main surface on the opposite side of the second resonating arm. In other words, the first and the third groove are asymmetric to the second and the fourth groove. Both the first and the third groove have a first depth, and the second and the fourth groove have a second depth. The first depth and the second depth are substantially different from each other. The characteristics of the asymmetric grooves can be asymmetric in groove number, depth, or width. 
         [0023]    This invention addresses various asymmetric groove designs. The groove designs can be asymmetric in groove number, groove width, or groove depth. For example, the asymmetric grooves can be on the first and the third main surface where there are two first groove and two third groove respectively, and on the second main surface and the fourth main surface where there are two second groove and two fourth groove respectively. In other case, they can be on the first main surface and the third main surface where there are two first groove and two third groove respectively, and on the second main surface and the fourth main surface where there is one second groove and one fourth groove respectively. In other case, they can be on the first main surface and the third main surface where there is one first groove and one third groove respectively, and on the second main surface and the fourth main surface where there are two second groove and two fourth groove respectively. 
         [0024]    Refer to  FIGS. 2A and 2B .  FIG. 2A  is a schematic view of the electrodes and electrical interconnection patterns of  FIG. 1A , and  FIG. 2B  is a schematic view of the electrodes and electrical interconnection patterns of  FIG. 1B . The first main surface and the third main surface are located on the same plane. A thin metal layer is deposited on the surface of the first groove, the surface of the second groove, the surface of the first via-hole, the third side surface, and the fourth side surface. A thin metal layer is also deposited on the surface of the third groove, the surface of the fourth groove, the surface of the second via-hole, the first side surface, and the second side surface. The metal film on the surface of the first groove, the metal film on the surface of the second groove, the metal film on the surface of the first via-hole, the metal film on the third side surface, and the metal film on the fourth side surface are electrically connected to form a first electrode. This first electrode extends to the bottom of the base through a first conducting path on the main surface of the base. The metal film on the surface of the third groove, the metal film on the surface of the fourth groove, the metal film on the surface of the second via-hole, the metal film on the first side surface, and the metal film on the second side surface are electrically connected to form a second electrode. This second electrode extends to the bottom of the base through a second conducting path on the main surfaces of the base. The first electrode and the second electrode have opposite polarities. 
         [0025]    The shape of the first via-hole and the second via-hole of the present invention is not limited to a rectangle. It can be square, round, or elliptic. The size, shape, position, number, and penetrating manner of the first and the second via-hole may be designed in various ways in accordance with the numbers and structures of the first groove, the second groove, the third groove, and the fourth groove. 
         [0026]    The performance of the resonator is effectively improved by implementing the asymmetric grooves on the resonating arms, the via-holes connecting the grooves, the continuous curved surfaces concaves on the side surfaces of the base, and the recess on the main surface of the base. In addition, using the principles of these characteristics, the manufacturing process of the tuning fork quartz crystal resonator is greatly simplified, and the manufacturing cost is lowered. 
         [0027]    A manufacturing process of the present invention is described as follows: 
         [0028]    Step A, a quartz wafer is produced from a single crystal alpha quartz bar cut at a designate angle (θ). 
         [0029]    Step B, a metal layer is deposited on the upper and lower surfaces of the wafer. 
         [0030]    Step C, a first photo resist layer is coated on the metal layers of the upper and lower surfaces of the wafer. Followed by the exposure and development process, some specific areas of the first photo resist layer are removed to expose the metal surfaces underneath. In other words, the first photo resist layer only remains on the main body of the tuning fork which comprises the base, the first resonating arm, and the second resonating arm of the resonator, but excluding the asymmetric grooves and the via-holes on the resonating arms, and the recess on the base. 
         [0031]    Step D, these exposed metal films are removed by metal etching process. 
         [0032]    Step E, the remaining first photo resist layer is then removed from the wafer. 
         [0033]    Step F, a second photo resist layer is coated on the top and bottom surfaces of the wafer. Some specific areas of the second photo resist layer are removed by the exposure and development process. The remaining second photo resist layer only covers the main body of the tuning fork which comprises the base, the first and the second resonating arm, but excluding the asymmetric grooves and the via-holes of the resonating arms, the recess of the base, and the non-electrode areas on the main surfaces of the resonating arms and the base. In other words, the second photo resist layer was partly removed to expose the asymmetric grooves and the via-holes of the resonating arms, the recess of the base, the non-electrode areas on the main surfaces of the resonating arms and the base, and the regions of surfaces other than the main bodies of the tuning forks. 
         [0034]    Step G, the wafer is placed in a quartz etching bath. The quartz surfaces without the metal films covered will be etched to form the tuning fork structure. In the same quartz etching process step, due to the unique asymmetric groove design, not only the tuning fork structure is formed, but also the desirable depths of the asymmetric grooves and via-holes on the resonating arms, and the recess of the base are successfully constructed. 
         [0035]    Step H, a metal etching process is performed on the wafer to remove the metal surface not covered by the second photo resist layer, and therefore expose the quartz surface underneath. The purpose of this step is to form the electrode pattern, including the first electrode, the second electrode, and the necessary electrode connecting paths on the main surfaces of the resonating arms and the base. 
         [0036]    Step I, the remaining second photo resist layer is removed. At this time, the first electrode and the second electrode of the resonator are partially formed. 
         [0037]    Step J, a metal layer is deposited onto the asymmetric grooves, the via-holes, and the side surfaces of the resonating arms. This metal layer is formed to complete the electrodes of the tuning fork resonator. 
         [0038]    The above describes the designs, the manufacturing method, and process of the present invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0039]    The present invention will become more fully understood from the detailed description given herein below for illustration only, and thus are not limitative of the present invention, and wherein: 
           [0040]      FIG. 1A  is a schematic three-dimensional front view of the present invention; 
           [0041]      FIG. 1B  is a schematic three-dimensional back view of the present invention; 
           [0042]      FIG. 2A  is a schematic view of an electrical connection relation of  FIG. 1A ; 
           [0043]      FIG. 2B  is a schematic view of an electrical connection relation of  FIG. 1B ; 
           [0044]      FIG. 3A  is a top view of a first embodiment of the present invention; 
           [0045]      FIG. 3B  is a back view of the first embodiment of the present invention; 
           [0046]      FIG. 4A  is a cross-sectional view taken along Line  4 A- 4 A of  FIG. 3A ; 
           [0047]      FIG. 4B  is a cross-sectional view taken along Line  4 B- 4 B of  FIG. 3A ; 
           [0048]      FIG. 4C  is a partial enlarged view of  FIG. 3A ; 
           [0049]      FIG. 4D  is a partial enlarged view of  FIG. 3B ; 
           [0050]      FIG. 5A  is a schematic view of an electrical connection relation of  FIG. 4A ; 
           [0051]      FIG. 5B  is a schematic view of an electrical connection relation of  FIG. 4B ; 
           [0052]      FIG. 6A  is a schematic curve diagram of Q values of a tuning fork quartz crystal resonator at different groove depths according to the first embodiment of the present invention; 
           [0053]      FIG. 6B  is a schematic curve diagram of C 1  values of the tuning fork quartz crystal resonator at different groove depths according to the first embodiment of the present invention; 
           [0054]      FIG. 6C  is a schematic curve diagram of R 1  values of the tuning fork quartz crystal resonator at different groove depths according to the first embodiment of the present invention; 
           [0055]      FIG. 7A  is a top view of a second embodiment of the present invention; 
           [0056]      FIG. 7B  is a back view of the second embodiment of the present invention; 
           [0057]      FIG. 8A  is a cross-sectional view taken along Line  8 A- 8 A of  FIG. 7A ; 
           [0058]      FIG. 8B  is a cross-sectional view taken along Line  8 B- 8 B of  FIG. 7A ; 
           [0059]      FIG. 9  is a schematic view of an electrical connection relation of  FIG. 8B ; 
           [0060]      FIG. 10A  is a schematic curve diagram of Q values of a tuning fork quartz crystal resonator at different groove depths according to the second embodiment of the present invention; 
           [0061]      FIG. 10B  is a schematic curve diagram of C 1  values of the tuning fork quartz crystal resonator at different groove depths according to the second embodiment of the present invention; 
           [0062]      FIG. 10C  is a schematic curve diagram of R 1  values of the tuning fork quartz crystal resonator at different groove depths according to the second embodiment of the present invention; 
           [0063]      FIG. 11A  is a top view of a third embodiment of the present invention; 
           [0064]      FIG. 11B  is a back view of the third embodiment of the present invention; 
           [0065]      FIG. 12A  is a cross-sectional view taken along Line  12 A- 12 A of  FIG. 11A ; 
           [0066]      FIG. 12B  is a cross-sectional view taken along Line  12 B- 12 B of  FIG. 11A ; 
           [0067]      FIG. 13  is a schematic view of an electrical connection relation of  FIG. 12B ; 
           [0068]      FIG. 14  is a diagram of a relative relation between X, Y, and Z axial directions of a single crystal alpha quartz bar and X, Y′, and Z′ axial directions of a tuning fork quartz crystal resonator in the prior art; and 
           [0069]      FIG. 15  is a diagram of an equivalent circuit of the quartz crystal resonator in the prior art. 
       
    
    
     DETAILED DESCRIPTION 
       [0070]    The features and advantages of the present invention are described in the following detailed embodiments. This allows relative skilled persons understand and implement the content of the present invention. Furthermore, by reference to the contents of the disclosed specification, claims, and drawings, they can easily comprehend the objective and advantage of the present invention. The embodiments below are intended to further describe the views of the present invention but not to limit the scope of the same. 
       First Embodiment 
       [0071]    Refer to  FIGS. 1A ,  1 B,  2 A,  2 B,  3 A, and  3 B.  FIGS. 1A and 1B  are three-dimensional views of the first embodiment of the present invention.  FIGS. 3A  and  3 B are the top and bottom view of the first embodiment.  FIGS. 2A and 2B  are the electrodes and electrical interconnection patterns of the tuning fork quartz crystal resonator of the first embodiment. 
         [0072]      FIGS. 1A and 1B  illustrate a tuning fork quartz crystal resonator which comprises a base  30 , a first resonating arm  10 , and a second resonating arm  20 . The first resonating arm  10  and the second resonating arm  20  are connected to same side of the base  30 . The base  30  has a fifth main surface  351  and a sixth main surface  361  opposite to each other. The base  30  also has a fifth side surface  352  and a sixth side surface  362  opposite to each other. 
         [0073]    The first resonating arm  10  is connected to the base  30 . The first resonating arm  10  is approximately a parallelepiped. The first resonating arm  10  has a first main surface  111 , a first side surface  112 , a second main surface  121 , and a second side surface  122  adjacent to each other in sequence. The first main surface  111  and the second main surface  121  are substantially parallel to each other. The first resonating arm  10  has two first groove  171  and two second groove  172 . The two first groove  171  are located on the first main surface  111 , and the two second groove  172  are located on the second main surface  121 . The two first groove  171  are substantially parallel to each other, and the two second groove  172  are substantially parallel to each other. 
         [0074]    The second resonating arm  20  is connected to the base  30 . The second resonating arm  20  is approximately a parallelepiped. The second resonating arm  20  has a third main surface  231 , a third side surface  232 , a fourth main surface  241 , and a fourth side surface  242  adjacent to each other in sequence. The third main surface  231  and the fourth main surface  241  are substantially parallel to each other. The second resonating arm  20  has two third groove  273  and two fourth groove  274 . The two third groove  273  are located on the third main surface  231 , and the two fourth groove  274  are located on the fourth main surface  241 . The two third groove  273  are substantially parallel to each other, and the two fourth groove  274  are substantially parallel to each other. The first resonating arm  10  and the second resonating arm  20  are approximately parallel to each other. Both resonating arms extend out along the Y′ axis. 
         [0075]    The first main surface  111  and the third main surface  231  are connected to the fifth main surface  351 . The first main surface  111 , the third main surface  231 , and the fifth main surface  351  are substantially coplanar. The second main surface  121  and the fourth main surface  241  are connected to the sixth main surface  361 . The second main surface  121 , the fourth main surface  241 , and the sixth main surface  361  are substantially coplanar. 
         [0076]    Refer to  FIGS. 2A and 2B . The first groove  171 , the second groove  172 , the third side surface  232 , and the fourth side surface  242  have a thin metal layer deposited thereon, and are electrically connected to form a part of a first electrode  81 . The third groove  273 , the fourth groove  274 , the first side surface  112 , and the second side surface  122  have a thin metal layer deposited thereon, and are electrically connected to form a part of a second electrode  82 . The first electrode  81  and the second electrode  82  have opposite polarities. When an AC voltage source which has a frequency close to the natural resonate frequency of the tuning fork is supplied to the first electrode  81  and the second electrode  82 , the first resonating arm  10  and the second resonating arm  20  vibrate at the frequency close to the natural resonate frequency. For the convenience of description and clarity of the drawings, the thin metal layer is not shown in all the drawings except  FIG. 2A ,  FIG. 2B , and all cross-sectional views. However, it should be noted that, the thin metal layer has been deposited on the quartz surface to form electrodes and their interconnection in each embodiment. 
         [0077]    Refer to  FIG. 4A  for a cross-sectional view which is taken along Line  4 A- 4 A of  FIG. 3A . 
         [0078]    The first groove  171 , the second groove  172 , the third groove  273 , and the fourth groove  274  are formed by etching. The depths of the grooves depend on the widths of the grooves, the etching rate, and the etching duration. The wider the groove is and the longer the etching time is, the deeper the groove will be. The similar width and etching direction of the first groove  171  and the third groove  273  lead to form the similar depth of the first groove  171  and the third groove  273 . The similar width and etching direction of the second groove  172  and the fourth groove  274  lead to form the similar depth of the second groove  172  and the fourth groove  274 . 
         [0079]    The first groove  171  is asymmetric to the second groove  172 . The third groove  273  is asymmetric to the fourth groove  274 . The asymmetric structures can be asymmetric in the depth, the width, and the number of the grooves. The first groove  171  and the third groove  273  are asymmetric to the second groove  172  and the fourth groove  274  respectively. 
         [0080]    The R 1  value of the resonator can be reduced by forming proper width and the depth of the first groove  171 , the second groove  172 , the third groove  273 , and the fourth groove  274 . For example, when the width of the first groove  171 , the second groove  172 , the third groove  273 , and the fourth groove  274  is widened, the strength of the electrical field along the X axis on the first resonating arm  10  and the second resonating arm  20  is intensified due to a narrower distance of the two electrodes (the first and second electrodes). A wider groove shortens the distance of the two electrodes on the resonating arms, that intensifies an effective and stronger strength of the electrical field along the X axis, thereby increases the C 1  value and reduces the R 1  value of the resonator. 
         [0081]    The width of the first groove  171  and the third groove  273  is denoted as a first width (W 1 ), and the width of the second groove  172  and the fourth groove  274  is denoted as a second width (W 2 ). The depth of the first groove  171  and the third groove  273  is denoted as a first depth (D 1 ), and the depth of the second groove  172  and the fourth groove  274  is denoted as a second depth (D 2 ). T is the thickness of the resonating arm  10  and  20 . ΔD is the difference of T from the sum of D 1  and D 2  (ΔD=T−D 1 −D 2 ). In other words, ΔD is the residual thickness of the resonating arm after the depth of the first groove  171  (the third groove  273 ) and the depth of the second groove  172  (the fourth groove  274 ) are deducted from the resonating arm thickness T. 
         [0082]    In this embodiment, since the first width W 1  is greater than the second width W 2 . The first depth D 1  is greater than the second depth D 2 . The first groove  171  is asymmetric to the second groove  172 , and the third groove  273  is asymmetric to the fourth groove  274 . The first depth D 1  is substantially different from the second depth D 2 . 
         [0083]      FIG. 4B  is a cross-sectional view which is taken along Line  4 B- 4 B of  FIG. 3A . In order to complete the first electrode  81  and the second electrode  82 , there are two first via-hole  91  on the first resonating arm  10  and two second via-hole  92  on the second resonating arm  20 . The metal film on the surface of the first via-hole  91  connects the metal film on the surface of the first groove  171  to the metal film on the surface of the second groove  172  to form a part of the first electrode  81 . The metal film on the surface of the second via-hole  92  connects the metal film on the surface of the third groove  273  to the metal film on surface of the fourth groove  274  to form a part of the second electrode  82 . 
         [0084]    Refer to  FIGS. 5A and 5B .  FIGS. 5A and 5B  illustrate the electrical interconnection of the electrodes shown on  FIGS. 4A and 4B . The metal film on the surface of the two first groove  171 , the metal film on the surface of the two second groove  172 , the metal film on the surface of the two first via-hole  91 , the metal film on the third side surface  232 , and the metal film on the fourth side surface  242  are electrically connected to form the first electrode  81 . The metal film on the surface of the two third groove  273 , the metal film on surface of the two fourth groove  274 , the metal film on the surface of the two second via-hole  92 , the metal film on the first side surface  112 , and the metal film on the second side surface  122  are electrically connected to form the second electrode  82 . 
         [0085]      FIGS. 4C and 4D  are a partially enlarged view of  FIGS. 3A and 3B . Refer to  FIG. 4C , viewing from the top of the first main surface  111 , one of the two first via-hole  91  is partially embedded in the first groove  171  which is close to the first side surface  112 , and the other first via-hole  91  is partially embedded in the other first groove  171  which is close to the second side surface  122 . Viewing from the top of the third main surface  231 , one of the two second via-hole  92  is partially embedded in the third groove  273  which is close to the third side surface  232 , and the other second via-hole  92  is partially embedded in the other third groove  273  which is close to the fourth side surface  242 . Refer to  FIG. 4D . Viewing from the top of the second main surface  121 , one of the two first via-hole  91  is partially embedded in the second groove  172  which is close to the first side surface  112 , and the other first via-hole  91  is partially embedded in the other second groove  172  which is close to the second side surface  122 . Viewing from the top of the fourth main surface  241 , one of the two second via-hole  92  is partially embedded in the fourth groove  274  which is close to the third side surface  232 , and the other second via-hole  92  is partially embedded in the other fourth groove  274  which is close to the fourth side surface  242 . 
         [0086]    Refer to  FIGS. 1A and 1B . Two concave  95  are formed on the side surfaces of the base  30 , one each on the fifth side surface  352  and the sixth side surface  362  respectively. The concave  95  is a continuous curved surface comprising a turning segment  961 , a first connecting segment  971 , and a second connecting segment  972 . The turning segment  961  connects the first connecting segment  971  with the second connecting segment  972 . The second connecting segment  972  is ended at  359  (the end of base  30 ). The first connecting segment  971  is close to the other end of the base  30  which is opposite to the end  359 . One concave  95  constitutes an integral part of the fifth side surface  352  and the other concave  95  constitutes an integral part of the sixth side surface  362 . The two concaves  95  are substantially symmetric to each other along the Y′ axis. The shortest distance between the fifth side surface  352  and the sixth side surface  362  is the measurement from the turning segment  961  of the concave  95  on the fifth side surface  352  to the turning segment  961  of the concave  95  on the sixth side surface  362 . The longest distance between the fifth side surface  352  and the sixth side surface  362  is the end  359  of the base  30 . The rate of change of slop of the first connecting segment  971  is greater than that of the second connecting segment  972 . The difference of the rate of change of slope between the first connecting segment  971  and the second connecting segment  972  of the concave  95  may be obtained by the finite element analysis and practical experiment according to actual requirements. 
         [0087]    The forming of concave  95  on the base is to minimize the acoustic energy propagating to the mounting areas of the base  30 . This will prevent the decrease of the Q value of the resonator. The detailed design of the concave  95  may be obtained by the finite element analysis and practical experiment according to actual requirements. 
         [0088]    A recess  39  formed on the fifth main surface  351  of the base  30  functions to reduce the acoustic energy propagating to the mounting areas of the base  30 . This will prevent the decrease of the Q value of the resonator. The recess  39  concaves inwards into the base  30  from the fifth main surface  351  along the Z′ axis. Refer to  FIG. 3A . One end of the recess  39  near the first resonating arm  10  and the second resonating arm  20  has a first width G 1  (a width along the X axis), and the other end of the recess  39  away from the first resonating arm  10  and the second resonating arm  20  has a second width G 2  (a width along the X axis). The first width G 1  is greater than the second width G 2 . 
         [0089]    Viewing from the fifth main surface  351 , the shape of the recess  39  is approximately a triangle. However, the recess  39  in the present invention is not limited to a triangle. It can be square, round, or polygonal. Preferably, the recess  39  is an acute triangle with a base line parallel to the end  359  of the base  30 , and each vertex of the polygon has an arc chord angle to eliminate sharp points for accumulating stress. The recess  39  is formed on the fifth main surface  351  in this embodiment. The recess  39  functions the same when it is formed on the sixth main surface  361 . 
         [0090]    The depth of the grooves will affect the Q, C 1 , and R 1  value of the quartz crystal resonator. Their relationships are illustrated respectively in  FIGS. 6A ,  6 B, and  6 C. Referring to  FIGS. 3A ,  3 B, and  4 A, there are two grooves on both main surfaces of the first resonating arm  10  and the second resonating arm  20  respectively. D 1  is the depth of the first groove  171  and the third groove  273 . D 2  is the depth of the second groove  172  and the fourth groove  274 . T is the thickness of the resonating arm  10  and  20 . ΔD is the difference of T from the sum of D 1  and D 2  (ΔD=T−D 1 −D 2 ). ΔD/T is the ratio of ΔD over the thickness of resonating arm T. When forming the grooves on the resonating arms during the manufacturing processes, longer quartz etching time will produce deeper grooves, namely greater D 1  and D 2  value. The deeper the grooves are, the smaller the ΔD value becomes, and the lower the ΔD/T ratio will be. Referring to  FIG. 6A , the vertical axis has the scale value of the ratio of Q(ΔD/T)/Qmax, where Qmax is the maximum of the Q value. The horizontal axis has the scale value of the ratio of ΔD/T. Referring to  FIG. 6B , the vertical axis has the scale value of the ratio of C 1 (ΔD/T)/C 1 max, where C 1 max is the maximum of the C 1  value. The horizontal axis has the scale value of the ratio of ΔD/T. Referring to  FIG. 6C , the vertical axis has the scale value of the ratio of R 1 (ΔD/T)/R 1 min, where R 1 min is the minimum of the R 1  value. The horizontal axis has the scale value of the ratio of ΔD/T.  FIG. 6A  illustrates the relationship of ΔD/T and the Q value of the resonator. When ΔD/T is within the range of 0.4 to 0.05, the Q value of the resonator decreases approximately 20% as the ratio of ΔD/T decreases.  FIG. 6B  shows the relationship between ΔD/T and the C 1  value of the resonator. When ΔD/T is within the range of 0.4 to 0.05, the C 1  value of the resonator gradually increases as the ratio of ΔD/T decreases. This leads to a reduction of the R 1  value of the resonator within the range.  FIG. 6C  illustrates the relationship between ΔD/T and the R 1  value of the resonator. When ΔD/T is within the range of 0.4 to 0.05, the R 1  value of the resonator has relatively low value to ensure the excellent performance of the resonator. When the ratio of ΔD/T is greater than 0.4 due to a smaller and insufficient depth value of D 1  and D 2 , the R 1  value of the resonator increases greatly while the resonator still maintains its high Q value. The usage and application of the resonators with a high Q value and a high R 1  value are quite limited because of practical difficulties in circuit design. When the ratio of ΔD/T is less than 0.05 due to an excessive depth value of D 1  and D 2 , the Q value of the resonator decreases rapidly and therefore causes the R 1  value of the resonator to increase. Thus the performance of the resonator is greatly deteriorated. In summary, when the ratio of ΔD/T is in the range of 0.4 to 0.05, not only the Q value of the resonator is maintained at a relatively high quality level, but also the R 1  value of the resonator is kept at a relatively low value. A resonator with high Q value and low R 1  value in this range ensures its excellent performance. From this experiment, the valid value of ΔD/T falls in the range of 0.05 to 0.4, with an optimum value in the range of 0.1 to 0.32. 
       Second Embodiment 
       [0091]    In the present invention, in addition to the structure of the first embodiment, the following variations may be made. Persons skilled in the art will be able to design or manufacture the quartz crystal resonator of similar structure according to the spirit of the present invention. 
         [0092]      FIGS. 7A and 7B  are the top and bottom view of the second embodiment of the present invention. The tuning fork quartz crystal resonator comprises a base  30 , a first resonating arm  10 , and a second resonating arm  20 . The first resonating arm  10  and the second resonating arm  20  are connected to same side of the base  30 . 
         [0093]    The base  30  has a fifth main surface  351  and a sixth main surface  361  opposite to each other. The base  30  also has a fifth side surface (not shown) and a sixth side surface (not shown) opposite to each other. 
         [0094]    The first resonating arm  10  is connected to the base  30 . The first resonating arm  10  is approximately a parallelepiped. The first resonating arm  10  has a first main surface  111 , a first side surface  112 , a second main surface  121 , and a second side surface  122  adjacent to each other in sequence. The first main surface  111  and the second main surface  121  are substantially parallel to each other. The first resonating arm  10  has two first groove  171  and one second groove  172 . The two first groove  171  are located on the first main surface  111 , and the second groove  172  is located on the second main surface  121 . The two first groove  171  are substantially parallel to each other. 
         [0095]    The second resonating arm  20  is also connected to the base  30 . The second resonating arm  20  is approximately a parallelepiped. The second resonating arm  20  has a third main surface  231 , a third side surface  232 , a fourth main surface  241 , and a fourth side surface  242  adjacent to each other in sequence. The third main surface  231  and the fourth main surface  241  are substantially parallel to each other. The second resonating arm  20  has two third groove  273  and one fourth groove  274 . The two third groove  273  are located on the third main surface  231 , and the fourth groove  274  is located on the fourth main surface  241 . The two third groove  273  are substantially parallel to each other. The first resonating arm  10  and the second resonating arm  20  are approximately parallel to each other. Both resonating arms extend out along the Y′ axis. 
         [0096]    The first main surface  111  and the third main surface  231  are connected to the fifth main surface  351 . The first main surface  111 , the third main surface  231 , and the fifth main surface  351  are substantially coplanar. The second main surface  121  and the fourth main surface  241  are connected to the sixth main surface  361 . The second main surface  121 , the fourth main surface  241 , and the sixth main surface  361  are substantially coplanar. 
         [0097]      FIG. 8A  is a cross-sectional view taken along Line  8 A- 8 A of  FIG. 7A , and  FIG. 8B  is a cross-sectional view taken along Line  8 B- 8 B of  FIG. 7A . The widths of the two first groove  171  on the first main surface  111  are substantially the same, and the depths thereof are also substantially the same. The widths of the two third groove  273  on the third main surface  231  are substantially the same, and the depths thereof are also substantially the same. In this embodiment, the first width W 1  is the width of the first groove  171  and the third groove  273 . The second width W 2  is the width of the second groove  172  and the fourth groove  274 . The second width W 2  is smaller than a distance between the two neighboring flanks of the two first groove  171  (or the two third groove  273 ) in the width direction of the resonating arm. This distance also indicates the separation of the two first groove  171  (or the two third groove  273 ) along the X axis. The first depth D 1  is the depth of the first groove  171  and the third groove  273 . The second depth D 2  is the depth of the second groove  172  and the fourth groove  274 . Since the first width W 1  is greater than the second width W 2 , the first depth D 1  is greater than the second depth D 2 . T is the thickness of the first resonating arm  10  and the second resonating arm  20 . ΔD is the difference of T from the sum of D 1  and D 2  (ΔD=T−D 1 −D 2 ). In other words, ΔD is the residual thickness of the resonating arm after the depth of the first groove  171  (the third groove  273 ) and the depth of the second groove  172  (the fourth groove  274 ) are deducted from the resonating arm thickness T. 
         [0098]    Refer to  FIG. 7A . Viewing from the top of the first main surface  111 , one of the two first via-hole  91  is partially embedded in the first groove  171  which is close to the first side surface  112 , and the other first via-hole  91  is partially embedded in the other first groove  171  which is close to the second side surface  122 . Viewing from the top of the third main surface  231 , one of the two second via-hole  92  is partially embedded in the third groove  273  which is close to the third side surface  232 , and the other second via-hole  92  is partially embedded in the other third groove  273  which is close to the fourth side surface  242 . Refer to  FIG. 7B . Viewing from the top of the second main surface  121 , the two first via-hole  91  starting from the first main surface  111  to the second main surface  121  merge together with a portion of the second groove  172  and form one opening on the second main surface  121 . Viewing from the top of the fourth main surface  241 , the two second via-hole  92  starting from the third main surface  231  to the fourth main surface  241  merge together with a portion of the fourth groove  274  and form one opening on the fourth main surface  241 . 
         [0099]      FIG. 9  illustrates the electrical interconnection of the electrodes shown on  FIG. 8B . The metal film on the surface of the two first groove  171 , the metal film on the surface of the second groove  172 , the metal film on the surface of the two first via-hole  91 , the metal film on the third side surface  232 , and the metal film on the fourth side surface  242  are electrically connected to form a first electrode  81 . The metal film on the surface of the two third groove  273 , the metal film on the surface of the fourth groove  274 , the metal film on the surface of the two second via-hole  92 , the metal film on the first side surface  112 , and the metal film on the second side surface  122  are electrically connected to form a second electrode  82 . 
         [0100]    Referring to  FIGS. 8B and 9 , the metal film on the surface of the two first grooves  171  and the metal film on the surface of the second groove  172  are electrically connected and effectively conducted via the metal film on the surface of the two first via-holes  91 . The metal film on the surface of the two third grooves  273  and the metal film on the surface of the forth groove  274  are electrically connected and effectively conducted via the metal film on the surface of the two second via-holes  92 . 
         [0101]    The depth of the grooves will affect the Q, C 1 , and R 1  value of the quartz crystal resonator. Their relationships are illustrated respectively in  FIGS. 10A ,  10 B, and  10 C. Referring to  FIGS. 7A ,  7 B, and  8 A, there are two first groove  171  on the first main surface  111  of the first resonating arm  10  and two third grooves  273  on the third main surface  231  of the second resonating arm  20 . There is only one second groove  172  on the second main surface  121  of the first resonating arm  10  and one fourth groove  274  on the fourth main surface  241  of the second resonating arm  20 . D 1  is the depth of the first groove  171  and the third groove  273 . D 2  is the depth of the second groove  172  and the fourth groove  274 . T is the thickness of the resonating arm  10  and  20 . ΔD is the difference of T from the sum of D 1  and D 2  (ΔD=T−D 1 −D 2 ). ΔD/T is the ratio of ΔD over the thickness of resonating arm T. When forming the grooves on the resonating arms during the manufacturing processes, longer etching time will produce deeper grooves, namely greater D 1  and D 2  value. The deeper the grooves are, the smaller the ΔD value becomes, and the lower the ΔD/T ratio will be. Referring to  FIG. 10A , the vertical axis has the scale value of the ratio of Q(ΔD/T)/Qmax, where Qmax is the maximum of the Q value. The horizontal axis has the scale value of the ratio of ΔD/T. Referring to  FIG. 10B , the vertical axis has the scale value of the ratio of C 1 (ΔD/T)/C 1 max, where C 1 max is the maximum of the C 1  value. The horizontal axis has the scale value of the ratio of ΔD/T. Referring to  FIG. 10C , the vertical axis has the scale value of the ratio of R 1 (ΔD/T)/R 1 min, where R 1 min is the minimum of the R 1  value. The horizontal axis has the scale value of the ratio of ΔD/T.  FIG. 10A  illustrates the relationship of ΔD/T and the Q value of the resonator. When ΔD/T is within the range of +0.18 to −0.25, the Q value of the resonator decreases approximately 20% as the ratio of ΔD/T decreases.  FIG. 10B  shows the relationship between ΔD/T and the C 1  value of the resonator. When ΔD/T is within the range of +0.18 to −0.25, the C 1  value of the resonator gradually increases as the ratio of ΔD/T decreases. This leads to a reduction of R 1  value of the resonator within the range.  FIG. 10C  illustrates the relationship between ΔD/T and the R 1  value of the resonator. When ΔD/T is within the range of +0.18 to −o.25, the R 1  value of the resonator has relatively low value to ensure the excellent performance of the resonator. When the ratio of ΔD/T is greater than +0.18 due to a smaller and insufficient depth value of D 1  and D 2 , the R 1  value of the resonator increases greatly while the resonator still maintains its high Q value. The usage and application of the resonators with a high Q value and a high R 1  value are quite limited because of practical difficulties in circuit design. When the ratio of ΔD/T is less than −0.25 due to an excessive depth value of D 1  and D 2 , the Q value of the resonator decreases rapidly and therefore causes the R 1  value of the resonator to increase. Thus the performance of the resonator is greatly deteriorated. In summary, when the ratio of ΔD/T is in the range of +0.18 to −0.25, not only the Q value of the resonator is maintained at a relatively high quality level, but also the R 1  value of the resonator is kept at a relatively low value. A resonator with high Q value and low R 1  value in this range ensures its excellent performance. From this experiment, the valid ratio of ΔD/T falls in the range of −0.25 to +0.18, with an optimum value in the range of −0.15 to +0.12. 
       Third Embodiment 
       [0102]      FIGS. 11A and 11B  are the top view and bottom view of the third embodiment of the present invention. The tuning fork quartz crystal resonator comprises a base  30 , a first resonating arm  10 , and a second resonating arm  20 . The first resonating arm  10  and the second resonating arm  20  are connected to same side of the base  30 . 
         [0103]    The base  30  has a fifth main surface  351  and a sixth main surface  361  opposite to each other. The base  30  also has a fifth side surface (not shown) and a sixth side surface (not shown) opposite to each other. 
         [0104]    The first resonating arm  10  is connected to the base  30 . The first resonating arm  10  is approximately a parallelepiped. The first resonating arm  10  has a first main surface  111 , a first side surface  112 , a second main surface  121 , and a second side surface  122  adjacent to each other in sequence. The first main surface  111  and the second main surface  121  are substantially parallel to each other. The first resonating arm  10  has one first groove  171  and two second groove  172 . The first groove  171  is located on the first main surface  111 , and the two second groove  172  are located on the second main surface  121 . The two second groove  172  are substantially parallel to each other. 
         [0105]    The second resonating arm  20  is also connected to the base  30 . The second resonating arm  20  is approximately a parallelepiped. The second resonating arm  20  has a third main surface  231 , a third side surface  232 , a fourth main surface  241 , and a fourth side surface  242  adjacent to each other in sequence. The third main surface  231  and the fourth main surface  241  are substantially parallel to each other. The second resonating arm  20  has one third groove  273  and two fourth groove  274 . The third groove  273  is located on the third main surface  231 , and the two fourth groove  274  are located on the fourth main surface  241 . The two fourth groove  274  are substantially parallel to each other. The first resonating arm  10  and the second resonating arm  20  are approximately parallel to each other. Both resonating arms extend out along the Y′ axis. 
         [0106]    The first main surface  111  and the third main surface  231  are connected to the fifth main surface  351 . The first main surface  111 , the third main surface  231 , and the fifth main surface  351  are substantially coplanar. The second main surface  121  and the fourth main surface  241  are connected to the sixth main surface  361 . The second main surface  121 , the fourth main surface  241 , and the sixth main surface  361  are substantially coplanar. 
         [0107]      FIG. 12A  is a cross-sectional view taken along Line  12 A- 12 A of  FIG. 11A , and  FIG. 12B  is a cross-sectional view taken along Line  12 B- 12 B of  FIG. 11A . The widths of the two second groove  172  on the second main surface  121  are substantially the same, and the depths thereof are also substantially the same. The widths of the two fourth groove  274  on the fourth main surface  241  are substantially the same, and the depths thereof are also substantially the same. In this embodiment, the first width W 1  is the width of the first groove  171  and the third groove  273 . The second width W 2  is the width of the second groove  172  and the fourth groove  274 . The first depth D 1  is the depth of the first groove  171  and the third groove  273 . The second depth D 2  is the depth of the second groove  172  and the fourth groove  274 . Since the first width W 1  is greater than the second width W 2 , the first depth D 1  is greater than the second depth D 2 . 
         [0108]    Refer to  FIG. 11B . Viewing from the top of the second main surface  121 , one of the two first via-hole  91  is partially embedded in the second groove  172  which is close to the first side surface  112 , and the other first via-hole  91  is partially embedded in the other second groove  172  which is close to the second side surface  122 . Viewing from the top of the fourth main surface  241 , one of the two second via-hole  92  is partially embedded in the fourth groove  274  which is close to the third side surface  232 , and the other second via-hole  92  is partially embedded in the other fourth groove  274  which is close to the fourth side surface  242 . Refer to  FIG. 11A . Viewing from the top of the first main surface  111 , the two first via-hole  91  are separately embedded in the first groove  171 , one near the first side surface  112  and the other near the second side surface  122 . Viewing from the top of the third main surface  231 , the two second via-hole  92  are separately embedded in the third groove  273 , one near the third side surface  232  and the other near the fourth side surface  242 . 
         [0109]      FIG. 13  illustrates the electrical interconnection of the electrodes shown on  FIG. 12B . The metal film on the surface of the first groove  171 , the metal film on the surface of the two second groove  172 , the metal film on the surface of the two first via-hole  91 , the metal film on the third side surface  232 , and the metal film on the fourth side surface  242  are electrically connected to form a first electrode  81 . The metal film on the surface of the third groove  273 , the metal film on the surface of the two fourth groove  274 , the metal film on the surface of the two second via-hole  92 , the metal film on the first side surface  112 , and the metal film on the second side surface  122  are electrically connected to form a second electrode  82 . 
         [0110]    In summary, the tuning fork quartz crystal resonator of the present invention has the asymmetric grooves  171 ,  172 ,  273 , and  274 , via-holes  91  and  92  for reliable electrode connection, the concaves  95  in the form of continuous curved surfaces, and the recess  39 , thereby achieving the effects of lowering the R 1  value and improving the Q value of the resonator, alleviating the vibration impact, and also simplifying the manufacturing process.