Method for manufacturing a quartz crystal unit

Abstract

In a method for manufacturing a quartz crystal unit, a quartz crystal tuning fork resonator is formed by etching a quartz crystal wafer to form a quartz crystal tuning fork base, quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, and a groove having stepped portions in at least one of opposite main surfaces of each of the quartz crystal tuning fork tines. A, and by disposing a first electrode is disposed on at least one of the stepped portions of each of the grooves and a second electrode is disposed on each of side surfaces at least one side surface of each of the quartz crystal tuning fork tines. A frequency of oscillation of the quartz crystal tuning fork resonator is adjusted at least twice and in different steps. The quartz crystal tuning fork resonator is then mounted in a case and an open end of the case is covered with a lid. An overall length of the resonator and a length of the groove are determined so that a series resistance R 1 of a fundamental mode of vibration of the resonator is less than a series resistance R 2 of a second overtone mode of vibration thereof or less than a series resistance R 3 of a third overtone mode of vibration thereof.

What is claimed is: 
     
       1. A method for manufacturing a quartz crystal unit, comprising the steps of:
 forming at least one quartz crystal tuning fork resonator by etching a quartz crystal wafer to form a quartz crystal tuning fork base, a plurality of quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, and at least one groove having a plurality of stepped portions in at least one of opposite main surfaces of each of the quartz crystal tuning fork tines, and disposing a first electrode on at least one of the stepped portions of at least one of the grooves and a second electrode on at least one side surface of each of the quartz crystal tuning fork tines;   adjusting at least twice and in different steps a frequency of oscillation of the quartz crystal tuning fork resonator;   providing a case having an interior space and an open end communicating with the interior space;   providing a lid for covering the open end of the case;   mounting the quartz crystal tuning fork resonator in the interior space of the case; and   connecting the lid to the case to cover the open end thereof.   
     
     
       2. A method according to  claim 1 ; wherein the step of forming the groove comprises the step of forming a through-hole in each of the quartz crystal tuning fork tines extending through the opposite main surfaces thereof. 
     
     
       3. A method according to  claim 1 ; wherein the step of forming a plurality of quartz crystal tuning fork tines comprises the step of forming a first quartz crystal tuning fork tine and a second quartz crystal tuning fork tine; wherein the step of forming the first and second electrodes comprises the steps of forming the first electrode on each of two of the stepped portions of the groove in at least one of the opposite main surfaces of each of the first and second quartz crystal tuning fork tines and forming the second electrode on each of two of the side surfaces of each of the first and second quartz crystal tuning fork tines; and wherein the first electrode disposed on each of two of the stepped portions of the groove of the first quartz crystal tuning fork tine is connected to the second electrode disposed on each of two of the side surfaces of the second quartz crystal tuning fork tine to form a first electrode terminal, and the second electrode disposed on each of two of the side surfaces of the first quartz crystal tuning fork tine is connected to the first electrode disposed on each of two of the stepped portions of the groove of the second quartz crystal tuning fork tine to form a second electrode terminal so that the quartz crystal tuning fork resonator vibrates in a flexural mode of an inverse phase when an alternating current voltage is applied between the first electrode terminal and the second electrode terminal. 
     
     
       4. A method according to  claim 3 ; wherein the at least one groove is formed in each of the first main surface and the second main surface of each of the quartz crystal tuning fork tines so that a ratio W 2 /W is in the range of 0.35 to 0.85, where W 2  represents a width of the groove and W represents a width of each of the quartz crystal tuning fork tines. 
     
     
       5. A method according to  claim 3 ; wherein the adjusting step comprises the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by at least one of a laser method and evaporation and etching methods so that the frequency of oscillation of the quartz crystal tuning fork resonator is about 32.768 Hz with a frequency deviation within the range of −9000 PPM to +5000 PPM. 
     
     
       6. A method according to  claim 3 ; wherein the side surfaces of the first and second quartz crystal tuning fork tines comprise a first side surface and a second side surface, the first side surface of the first quartz crystal tuning fork tine confronting the first side surface of the second quartz crystal tuning fork tine; and wherein the stepped portions of the groove comprises a first stepped portion, a second stepped portion, and a third stepped portion connecting the first stepped portion to the second stepped portion, each of the first and second stepped portions being formed opposite to the first side surface of each of the first and second quartz crystal tuning fork tines. 
     
     
       7. A method according to  claim 3 ; wherein the step of forming at least one quartz crystal tuning fork resonator comprises the steps of forming two of the quartz crystal tuning fork resonators and integrally connecting together the two quartz crystal tuning fork resonators at their respective quartz crystal tuning fork bases at an angle of 30° or less. 
     
     
       8. A method according to  claim 3 ; wherein the adjusting step comprises the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by at least one of a laser method and evaporation and etching methods after the quartz crystal tuning fork resonator is mounted in the interior space of the case so that the frequency of oscillation of the resonator is about 32.768 kHz with a frequency deviation within the range of −100 PPM to +100 PPM. 
     
     
       9. A method according to  claim 8 ; wherein the step of forming at least one quartz crystal tuning fork resonator comprises the step of forming one quartz crystal tuning fork resonator capable of vibrating in a flexural mode of an inverse phase; and further comprising the step of forming one quartz crystal resonator capable of vibrating in a mode different from the flexural mode of an inverse phase. 
     
     
       10. A method according to  claim 8 ; wherein the connecting step comprises the step of connecting the lid to the case using at least one of a metal and a glass with a low melting point. 
     
     
       11. A method according to  claim 10 ; wherein the adjusting step comprises the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by a laser method after the connecting step so that the frequency of oscillation of the quartz crystal tuning fork resonator is about 32.768 kHz with a frequency deviation within the range of −30 ppm to +30 ppm. 
     
     
       12. A method according to  claim 10 ; wherein the adjusting step comprises the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by a laser method after the connecting step so that the frequency of oscillation of the resonator is about 32.768 kHz with a frequency deviation within the range of −50 ppm to +50 ppm. 
     
     
       13. A method according to  claim 12 ; wherein one of the case and the lid has a through-hole; and further comprising the step of disposing at least one of a metal and a glass into the through hole to maintain the interior space of the case in a vacuum. 
     
     
       14. A method according to  claim 13 ; wherein the adjusting step comprises the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by a laser method after the disposing step so that the frequency of oscillation of the resonator is about 32.768 kHz with a frequency deviation within the range of −30 ppm to +30 ppm. 
     
     
       15. A method according to  claim 3 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines in a first etching process and forming the corresponding grooves in a second etching process different from the first etching process; and wherein the step of forming the quartz crystal tuning fork tines is performed before the step of forming the corresponding grooves. 
     
     
       16. A method according to  claim 3 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines in a first etching process and forming the corresponding grooves in a second etching process different from the first etching process; and wherein the step of forming the corresponding grooves is performed before the step of forming the quartz crystal tuning fork tines. 
     
     
       17. A method according to  claim 1 ; wherein the adjusting step comprises the step of adjusting a frequency of oscillation of the quartz crystal tuning fork resonator to a preselected frequency with a frequency deviation within the range of −100 ppm to +100 ppm. 
     
     
       18. A method according to  claim 17 ; wherein the preselected frequency is about 32.768 kHz. 
     
     
       19. A method according to  claim 17 ; wherein a width of the groove formed in at least one of the opposite main surfaces of each of the quartz crystal tuning fork tines is greater than a distance in the width direction of the groove measured from an outer edge of the groove to an outer edge of the quartz crystal tuning fork tine. 
     
     
       20. A method according to  claim 19 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines in a first etching process and forming the corresponding grooves in a second etching process different from the first etching process; and wherein the step of forming the quartz crystal tuning fork tines is performed before the step of forming the corresponding grooves. 
     
     
       21. A method according to  claim 19 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines in a first etching process and forming the corresponding grooves in a second etching process different from the first etching process; and wherein the step of forming the corresponding grooves is performed before the step of forming the quartz crystal tuning fork tines. 
     
     
       22. A method according to  claim 19 ; wherein the groove formed in at least one of the main surfaces of each of the quartz crystal tuning fork tines comprises a through hole. 
     
     
       23. A method according to  claim 19 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines into a first quartz crystal tuning fork tine and a second quartz crystal tuning fork tine; forming a groove in each of opposite main surfaces of each of the first and second quartz crystal tuning fork tines; forming a first electrode on each of at least two of the stepped portions of the groove in each of the opposite main surfaces of the first and second quartz crystal tuning fork tines; forming a second electrode on each of two of side surfaces of each of the first and second quartz crystal tuning fork tines; connecting the first electrodes disposed on at least two of the stepped portions of the groove of the first quartz crystal tuning fork tine to the second electrodes disposed on two of the side surfaces of the second quartz crystal tuning fork tine to form a first electrode terminal; and connecting the second electrodes disposed on two of the side surfaces of the first quartz crystal tuning fork tine to the first electrodes disposed on at least two of the stepped portions of the groove of the second quartz crystal tuning fork tine to form a second electrode terminal; and further comprising the step of applying an alternating current voltage between the first electrode terminal and the second electrode terminal to vibrate the quartz crystal tuning fork resonator in a flexural mode of an inverse phase. 
     
     
       24. A method according to  claim 23 ; wherein the forming step comprises the step of forming the first and second quartz crystal tuning fork tines simultaneously with the corresponding grooves. 
     
     
       25. A method according to  claim 23 ; wherein a ratio W 2 /W is in the range of 0.35 to 0.85, where W 2  represents a width of the groove and W represents a width of each of the first and second quartz crystal tuning fork tines. 
     
     
       26. A method according to  claim 25 ; wherein the connecting step comprises the step of connecting the lid to the case using at least one of a metal and a glass with a low melting point. 
     
     
       27. A method according to  claim 25 ; wherein the quartz crystal tuning fork resonator has a fundamental mode of vibration and a second overtone mode of vibration; and wherein a series resistance R 1  of the fundamental mode of vibration is less than a series resistance R 2  of the second overtone mode of vibration. 
     
     
       28. A method according to  claim 27 ; wherein one of the case and the lid has a through-hole; and further comprising the step of disposing at least one of a metal and a glass into the through-hole to maintain the interior space of the case in a vacuum. 
     
     
       29. A method according to  claim 27 ; further comprising the step of providing a CMOS inverter, a plurality of capacitors, and a plurality of resistors to form an oscillator having the quartz crystal tuning fork resonator. 
     
     
       30. A method according to  claim 1 ; wherein the adjusting step comprises the steps of adjusting a frequency of oscillation of the quartz crystal tuning fork resonator to a first preselected frequency of oscillation, and adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to a second preselected frequency of oscillation different from the first preselected frequency of oscillation. 
     
     
       31. A method according to  claim 30 ; wherein the first preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within the range of −9000 ppm to +5000 ppm; and wherein the second preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within the range of −100 ppm to +100 ppm. 
     
     
       32. A method according to  claim 30 ; wherein the at least one groove is formed in each of the opposite main surfaces of each of the quartz crystal tuning fork tines so that a ratio W 2  /W is in the range of 0.35 to 0.85, where W 2  represents a width of the groove and W represents a width of each of the first and second quartz crystal tuning fork tines. 
     
     
       33. A method according to  claim 30 , further comprising the step of etching the quartz crystal wafer to simultaneously form the quartz crystal tuning fork tines and the corresponding grooves by a single etching process. 
     
     
       34. A method according to  claim 30 , wherein the quartz crystal tuning fork resonator has a fundamental mode of vibration and a second overtone mode of vibration; and wherein a series resistance R 1  of the fundamental mode of vibration is less than a series resistance R 2  of the second overtone mode of vibration. 
     
     
       35. A method according to  claim 34 ; wherein the at least one groove is formed in each of the opposite main surfaces of each of the quartz crystal tuning fork tines so that a width of at least one of the grooves in each of the opposite main surfaces of each of the quartz crystal tuning fork tines is greater than a distance in the width direction of the groove measured from an outer edge of the groove to an outer edge of the quartz crystal tuning fork tine; and wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines into a first quartz crystal tuning fork tine and a second quartz crystal tuning fork tine; forming at least one groove in each of opposite main surfaces of each of the first and second quartz crystal tuning fork tines; forming a plurality of first electrodes on at least two of the stepped portions of the grooves in the opposite main surfaces of the first and second quartz crystal tuning fork tines; forming a plurality of second electrodes on side surfaces of each of the first and second quartz crystal tuning fork tines; connecting the first electrodes disposed on at least two of the stepped portions of the grooves of the first quartz crystal tuning fork tine to the second electrodes disposed on the side surfaces of the second quartz crystal tuning fork tine to form a first electrode terminal; and connecting the second electrodes disposed on the side surfaces of the first quartz crystal tuning fork tine to the first electrodes disposed on at least two of the stepped portions of the grooves of the second quartz crystal tuning fork tine to form a second electrode terminal; and further comprising the step of applying an alternating current voltage between the first electrode terminal and the second electrode terminal to vibrate the quartz crystal tuning fork resonator in a flexural mode of an inverse phase. 
     
     
       36. A method according to  claim 35 ; wherein the forming step comprises the steps of forming the quartz crystal tuning fork tines in a first etching process and forming the corresponding grooves in a second etching process different from the first etching process; and wherein the step of forming the quartz crystal tuning fork tines is performed before the step of forming the corresponding grooves. 
     
     
       37. A method for manufacturing a quartz crystal unit, comprising the steps of:
 forming at least one quartz crystal tuning fork resonator having an overall length by etching a quartz crystal wafer to form a quartz crystal tuning fork base, a plurality of quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, and at least one groove having a length and a plurality of stepped portions in at least one of opposite main surfaces of each of the quartz crystal tuning fork tines, and disposing a first electrode on at least one of the stepped portions of at least one of the grooves and a second electrode on at least one side surface of each of the quartz crystal tuning fork tines;   determining the overall length of the quartz crystal tuning fork resonator and the length of the at least one groove formed in the at least one of the opposite main surfaces of each of the quartz crystal tuning fork tines so that a series resistance R 1  of a fundamental mode of vibration of the quartz crystal tuning fork resonator is less than a series resistance R 2  of a second overtone mode of vibration thereof or less than a series resistance R 3  of a third overtone mode of vibration thereof;   adjusting at least twice and in different steps a frequency of oscillation of the quartz crystal tuning fork resonator;   providing a case having an interior space and an open end communicating with the interior space;   providing a lid for covering the open end of the case;   mounting the quartz crystal tuning fork resonator in the interior space of the case; and   connecting the lid to the case to cover the open end thereof.    
     
     
       38. A method according to claim 37; wherein each of the quartz crystal tuning fork tines has a length; wherein the stepped portions of the at least one groove formed in the at least one of the opposite main surfaces of at least one of the quartz crystal tuning fork tines comprise a first stepped portion, a second stepped portion and a third stepped portion, each of the first and second stepped portions being formed along the length of the at least one quartz crystal tuning fork tine and being formed directly opposite the at least one side surface of the at least one quartz crystal tuning fork tine so that the at least one groove formed in the at least one of the opposite main surfaces of the at least one quartz crystal tuning fork tine has a first width and a second width greater than the first width and the first stepped portion is not opposite the second stepped portion in the width direction, the third stepped portion being directly connected to each of the first and second stepped portions; and wherein each of the first and second widths of the at least one groove formed in the at least one of the opposite main surfaces of the at least one quartz crystal tuning fork tine is greater than each of a first distance in the width direction of the at least one groove measured from a first outer edge of the first stepped portion of the at least one groove to a first outer edge of the at least one side surface of the at least one quartz crystal tuning fork tine and a second distance less than the first distance in the width direction of the at least one groove measured from a second outer edge of the second stepped portion of the at least one groove to a second outer edge of the at least one side surface of the at least one quartz crystal tuning fork tine.  
     
     
       39. A method according to claim 28; wherein the stepped portions of the at least one groove formed in the at least one of the opposite main surfaces of the at least one quartz crystal tuning fork tine comprise a fourth stepped portion opposite a fifth stepped portion in the length direction; wherein the fourth stepped portion is directly connected to the first stepped portion; wherein the fifth stepped portion is directly connected to the second stepped portion; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines, each of the first and second quartz crystal tuning fork tines having a first main surface and a second main surface opposite the first main surface; wherein the forming step of the at least one groove comprises the step of forming a groove having a length in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein the determining step comprises the step of determining each of the overall length of the quartz crystal tuning fork resonator and the length of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that the series resistance R 1  of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R 2  of the second overtone mode of vibration thereof or less than the series resistance R 3  of the third overtone mode of vibration thereof.  
     
     
       40. A method according to claim 37; wherein the adjusting step comprises the steps of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator after the forming step of the at least one groove and before the mounting step so that the frequency of oscillation thereof comprises a first preselected frequency of oscillation, and adjusting the frequency of oscillation of the quartz crystal tuning fork resonator after the mounting step so that the frequency of oscillation thereof comprises a second frequency of oscillation.  
     
     
       41. A method according to claim 38; wherein the first preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; and wherein the second preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −100 ppm to +100 ppm.  
     
     
       42. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines, each of the first and second quartz crystal tuning fork tines having a length, and a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface; wherein the forming step of the at least one groove comprises the step of forming a groove having a first width and a second width greater than the first width, and first, second and third stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; wherein the case has a through-hole and a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and further comprising the sequential steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming the groove in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that each of the first and second stepped portions is formed along the length of the corresponding one of the first and second quartz crystal tuning fork tines and formed directly opposite the first side surface of the corresponding one of the first and second quartz crystal tuning fork tines, the third stepped portion being directly connected to each of the first and second stepped portions, and so that the first width of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than a first distance in the width direction of the groove measured from a first outer edge of the first stepped portion of the groove to a first outer edge of the first side surface of the corresponding one of the first and second quartz crystal tuning fork tines and the second width of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than a second distance less than the first distance in the width direction of the groove measured from a second outer edge of the second stepped portion of the groove to a second outer edge of the first side surface of the corresponding one of the first and second quartz crystal tuning fork tines; forming a first electrode on a surface of each of the first and second stepped portions of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines so that the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the second quartz crystal tuning fork tine, and the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the at least one of the first and second main surfaces of the second quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the first quartz crystal tuning fork tine; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator so that the frequency of oscillation thereof comprises a preselected frequency of oscillation; mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; connecting the lid to the case to cover the open end thereof; and disposing a metal or a glass into the through-hole of the case to close the through-hole thereof in a vacuum.  
     
     
       43. A method according to claim 40; wherein the preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; and further comprising the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator after the mounting step so that the frequency of oscillation thereof is about 32.768 kHz with a frequency deviation within a range of −50 ppm to +50 ppm.  
     
     
       44. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines, each of the first and second quartz crystal tuning fork tines having a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface; wherein the forming step of the at least one groove comprises the step of forming a groove in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; wherein the case has a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and further comprising the sequential steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming the groove in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; forming a metal film on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines; forming a resist on the metal film; forming a first electrode on a surface of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines so that the first electrode formed on the surface of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the second quartz crystal tuning fork tine, and the first electrode formed on the surface of the groove formed in the at least one of the first and second main surfaces of the second quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the first quartz crystal tuning fork tine; removing the resist formed on the metal film; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator so that the frequency of oscillation thereof is about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator so that the frequency of oscillation thereof is about 32.768 kHz with a frequency deviation within a range of −100 ppm to +100 ppm; and connecting the lid to the case to cover the open end thereof.  
     
     
       45. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines, each of the first and second quartz crystal tuning fork tines having a length, a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface; wherein the forming step of the at least one groove comprises the step of forming a groove having a length, and first, second and third stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that each of the first and second stepped portions is formed along the length of the corresponding one of the first and second quartz crystal tuning fork tines and is formed directly opposite the first side surface of the corresponding one of the first and second quartz crystal tuning fork tines, the third stepped portion being formed in a direction different from that of each of the first and second stepped portions and the first stepped portion being connected to the second stepped portion through the third stepped portion, and so that each of the first and second stepped portions is directly connected to the third stepped portion; wherein the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a fourth stepped portion opposite a fifth stepped portion in the length direction, the fourth stepped portion being directly connected to the first stepped portion and the fifth stepped portion being directly connected to the second stepped portion; and wherein the determining step comprises the step of determining each of the overall length of the quartz crystal tuning fork resonator and the length of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that the series resistance R 1  of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R 2  of the second overtone mode of vibration thereof or less than the series resistance R 3  of the third overtone mode of vibration thereof. 
     
     
       46. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, each of the first and second quartz crystal tuning fork tines having a length, a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface; wherein the forming step of the at least one groove comprises the steps of forming a groove having at least two stepped portions including first and second stepped portions in the first main surface of the first quartz crystal tuning fork tine so that each of the first and second stepped portions is formed along the length of the first quartz crystal tuning fork tine and is formed directly opposite the first side surface of the first quartz crystal tuning fork tine, the first stepped portion being connected to the second stepped portion through a third stepped portion formed in a direction different from that of each of the first and second stepped portions, and so that each of the first and second stepped portions is directly connected to the third stepped portion, and forming a groove having at least three stepped portions including first, second and third stepped portions in the second main surface of the first quartz crystal tuning fork tine so that each of the first, second and third stepped portions is formed along the length of the first quartz crystal tuning fork tine and the first stepped portion is connected to the second stepped portion through a fourth stepped portion; wherein the groove formed in the first main surface of the first quartz crystal tuning fork tine has a first width and a second width greater than the first width; wherein a first distance in the width direction of the groove measured from a first outer edge of the first stepped portion of the groove to a first outer edge of the first side surface of the first quartz crystal tuning fork tine is greater than a second distance in the width direction of the groove measured from a second outer edge of the second stepped portion of the groove to a second outer edge of the first side surface of the first quartz crystal tuning fork tine; and wherein the first width of the groove formed in the first main surface of the first quartz crystal tuning fork tine is greater than the first distance and the second width of the groove formed in the first main surface of the first quartz crystal tuning fork tine is greater than the second distance.  
     
     
       47. A method according to claim 44; wherein the first side surface of the second quartz crystal tuning fork tine confronts the first side surface of the first quartz crystal tuning fork tine; wherein the forming step of the at least one groove comprises the steps of forming a groove having at least two stepped portions including first and second stepped portions in the first main surface of the second quartz crystal tuning fork tine so that each of the first and second stepped portions is formed along the length of the second quartz crystal tuning fork tine and the first stepped portion is connected to the second stepped portion through a third stepped portion formed in a direction different from that of each of the first and second stepped portions, and so that each of the first and second stepped portions is directly connected to the third stepped portion, and forming a groove having at least three stepped portions including first, second and third stepped portions in the second main surface of the second quartz crystal tuning fork tine so that each of the first, second and third stepped portions is formed along the length of the second quartz crystal tuning fork tine and the first stepped portion is connected to the second stepped portion through a fourth stepped portion; wherein the groove formed in the first main surface of the second quartz crystal tuning fork tine has a first width and a second width greater than the first width; wherein a first distance in the width direction of the groove measured from a first outer edge of the first stepped portion of the groove to a first outer edge of the first side surface of the second quartz crystal tuning fork tine is greater than a second distance in the width direction of the groove measured from a second outer edge of the second stepped portion of the groove to a second outer edge of the first side surface of the second quartz crystal tuning fork tine; and wherein the first width of the groove formed in the first main surface of the second quartz crystal tuning fork tine is greater than the first distance and the second width of the groove formed in the first main surface of the second quartz crystal tuning fork tine is greater than the second distance.  
     
     
       48. A method according to claim 45; wherein the case has a through-hole and a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and further comprising the sequential steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming each of the groove having the first and second widths and the first and second distances in the first main surface of each of the first and second quartz crystal tuning fork tines so that the first width is greater than the first distance and the second width is greater than the second distance, and the groove having the first, second and third stepped portions in the second main surface of each of the first and second quartz crystal tuning fork tines so that each of the first, second and third stepped portions is formed along the length of the corresponding one of the first and second quartz crystal tuning fork tines; forming a first electrode on a surface of each of the first and second stepped portions of the groove formed in the second main surface of each of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines so that the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the second main surface of the first quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the second quartz crystal tuning fork tine, and the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the second main surface of the second quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the first quartz crystal tuning fork tine; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −50 ppm to +50 ppm; connecting the lid to the case to cover the open end thereof; and disposing a metal or a glass into the through-hole of the case to close the through-hole thereof in a vacuum.  
     
     
       49. A method according to claim 45; wherein the case has a through-hole and a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and further comprising the sequential steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming each of the groove having the first and second widths and the first and second distances in the first main surface of each of the first and second quartz crystal tuning fork tines so that the first width is greater than the first distance and the second width is greater than the second distance, and the groove having the first, second and third stepped portions in the second main surface of each of the first and second quartz crystal tuning fork tines so that each of the first, second and third stepped portions is formed along the length of the corresponding one of the first and second quartz crystal tuning fork tines; forming a first electrode on a surface of each of the first and second stepped portions of the groove formed in the second main surface of each of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines so that the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the second main surface of the first quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the second quartz crystal tuning fork tine, and the first electrode formed on the surface of each of the first and second stepped portions of the groove formed in the second main surface of the second quartz crystal tuning fork tine is connected to the second electrode formed on each of the first and second side surfaces of the first quartz crystal tuning fork tine; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; connecting the lid to the case to cover the open end thereof; disposing a metal or a glass into the through-hole of the case to close the through-hole thereof in a vacuum; and adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −30 ppm to +30 ppm.  
     
     
       50. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, each of the first and second quartz crystal tuning fork tines having a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface, the first side surface of the first quartz crystal tuning fork tine confronting the first side surface of the second quartz crystal tuning fork tine; and wherein the forming step of the at least one groove comprises the step of forming a groove having a first width and a second width greater than the first width, and first, second and third surfaces in at least one of the first and second main surfaces of the first quartz crystal tuning fork tine so that the first surface is connected to the second surface through the third surface, and each of the first and second surfaces is directly opposite the first side surface of the first quartz crystal tuning fork tine and directly connected to the third surface, a distance in the width direction of the groove measured from a first outer edge of the first surface of the groove to a first outer edge of the first side surface of the first quartz crystal tuning fork tine being defined by a first distance and a distance in the width direction of the groove measured from a second outer edge of the second surface of the groove to a second outer edge of the first side surface of the first quartz crystal tuning fork tine being defined by a second distance, the first distance being greater than the second distance, and so that the first width of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine is greater than the first distance and the second width of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine is greater than the second distance.  
     
     
       51. A method according to claim 48; wherein the forming step of the at least one groove comprises the step of forming a groove having a first width and a second width greater than the first width, and first, second and third surfaces in at least one of the first and second main surfaces of the second quartz crystal tuning fork tine so that the first surface is connected to the second surface through the third surface, and each of the first and second surfaces is directly opposite the first side surface of the second quartz crystal tuning fork tine and directly connected to the third surface, a distance in the width direction of the groove measured from a first outer edge of the first surface of the groove to a first outer edge of the first side surface of the second quartz crystal tuning fork tine being defined by a third distance and a distance in the width direction of the groove measured from a second outer edge of the second surface of the groove to a second outer edge of the first side surface of the second quartz crystal tuning fork tine being defined by a fourth distance, the third distance being greater than the fourth distance, and so that the first width of the groove formed in the at least one of the first and second main surfaces of the second quartz crystal tuning fork tine is greater than the third distance and the second width of the groove formed in the at least one of the first and second main surfaces of the second quartz crystal tuning fork tine is greater than the fourth distance.  
     
     
       52. A method according to claim 48; wherein the case has a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and further comprising the sequential steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming the groove having the first and second widths, and the first, second and third surfaces in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine so that each of the first and second surfaces is directly opposite the first side surface of the first quartz crystal tuning fork tine and directly connected to the third surface, and each of the first and second widths of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine is greater than each of the first distance and the second distance; forming a first electrode on each of the first and second surfaces of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine and a second electrode on each of the first and second side surfaces of the first quartz crystal tuning fork tine so that the first electrode formed on each of the first and second surfaces of the groove formed in the at least one of the first and second main surfaces of the first quartz crystal tuning fork tine has an electrical polarity opposite to an electrical polarity of the second electrode formed on each of the first and second side surfaces of the first quartz crystal tuning fork tine; adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to a first preselected frequency of oscillation; mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; and adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to a second preselected frequency of oscillation.  
     
     
       53. A method according to claim 50; wherein the first preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm; and wherein the second preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −100 ppm to +100 ppm.  
     
     
       54. A method according to claim 50; wherein the second preselected frequency of oscillation is about 32.768 kHz with a frequency deviation within a range of −100 ppm to +100 ppm; and further comprising the step of connecting the lid to the case to cover the open end thereof after the adjusting step of the second preselected frequency of oscillation.  
     
     
       55. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, each of the first and second quartz crystal tuning fork tines having a first main surface and a second main surface opposite the first main surface, and an inner side surface and an outer side surface opposite the inner side surface, the inner side surface of the first quartz crystal tuning fork tine confronting the inner side surface of the second quartz crystal tuning fork tine, the inner side surface of each of the first and second quartz crystal tuning fork tines having a first outer edge and a second outer edge; wherein the forming step of the at least one groove comprises the step of forming a groove having a length, and a first outer edge and a second outer edge in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that a first distance in the width direction of the groove measured from the first outer edge of the groove to the first outer edge of the inner side surface of the first quartz crystal tuning fork tine is different from or greater than a second distance in the width direction of the groove measured from the second outer edge of the groove to the second outer edge of the inner side surface of the first quartz crystal tuning fork tine, and so that a third distance in the width direction of the groove measured from the first outer edge of the groove to the first outer edge of the inner side surface of the second quartz crystal tuning fork tine is different from or greater than a fourth distance in the width direction of the groove measured from the second outer edge of the groove to the second outer edge of the inner side surface of the second quartz crystal tuning fork tine; and wherein the determining step comprises the step of determining the overall length of the quartz crystal tuning fork resonator and the length of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that the series resistance R 1  of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R 2  of the second overtone mode of vibration thereof or less than the series resistance R 3  of the third overtone mode of vibration thereof.  
     
     
       56. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, each of the first and second quartz crystal tuning fork tines having a first main surface and a second main surface opposite the first main surface, and an inner side surface and an outer side surface opposite the inner side surface, the inner side surface of the first quartz crystal tuning fork tine confronting the inner side surface of the second quartz crystal tuning fork tine; wherein the forming step of the at least one groove comprises the step of forming a groove in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that a width W 2  of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than distances in the width direction of the groove measured from a first outer edge of the groove to a first outer edge of the inner side surface of the corresponding one of the first and second quartz crystal tuning fork tines and measured from a second outer edge different from the first outer edge of the groove to a second outer edge different from the first outer edge of the inner side surface of the corresponding one of the first and second quartz crystal tuning fork tines, and the ratio (W 2 /W) is within a range of 0.35 to 0.85, where W represents a width of each of the first and second quartz crystal tuning fork tines; wherein the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a first groove portion including a first surface, a second groove portion including a second surface and a third groove portion including a third surface, the first surface being connected to the second surface through the third surface, and each of the first and second surfaces being opposite the inner side surface of the corresponding one of the first and second quartz crystal tuning fork tines and directly connected to the third surface not opposite the inner side surface; wherein a first distance in the width direction of the first groove portion of the groove measured from a first outer edge of the first surface of the first groove portion of the groove to a first outer edge of the inner side surface of the corresponding one of the first and second quartz crystal tuning fork tines is different from or greater than a second distance in the width direction of the second groove portion of the groove measured from a second outer edge of the second surface of the second groove portion of the groove to a second outer edge of the inner side surface of the corresponding one of the first and second quartz crystal tuning fork tines; and wherein the distances in the width direction of the groove comprises the first distance in the width direction of the first groove portion and the second distance in the width direction of the second groove portion.  
     
     
       57. A method according to claim 54; wherein the first groove portion of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a first width and the second groove portion of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a second width greater than the first width; and wherein the first width of the first groove portion of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than the first distance in the width direction of the first groove portion of the groove and the second width of the second groove portion of the groove formed in the at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than the second distance in the width direction of the second groove portion of the groove.  
     
     
       58. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise the first and second quartz crystal tuning fork tines, each of the first and second quartz crystal tuning fork tines having a length, and a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface, the first side surface of the first quartz crystal tuning fork tine confronting the first side surface of the second quartz crystal tuning fork tine; wherein the case has a through-hole and a mounting portion in the interior space; wherein the mounting step comprises the step of mounting the quartz crystal tuning fork resonator on the mounting portion in the interior space of the case; wherein the forming step of the at least one groove comprises the steps of forming a groove having at least two stepped portions including first and second stepped portions in the first main surface of at least one of the first and second quartz crystal tuning fork tines so that each of the first and second stepped portions is formed along the length of the at least one of the first and second quartz crystal tuning fork tines and formed directly opposite the first side surface of the at least one of the first and second quartz crystal tuning fork tines, the first stepped portion being connected to the second stepped portion through a third stepped portion formed in a direction different from that of each of the first and second stepped portions, and so that each of the first and second stepped portions is directly connected to the third stepped portion, the groove formed in the first main surface of the at least one of the first and second quartz crystal tuning fork tines having a first width and a second width greater than the first width, a first distance in the width direction of the groove measured from a first outer edge of the first stepped portion of the groove to a first outer edge of the first side surface of the at least one of the first and second quartz crystal tuning fork tines being greater than a second distance in the width direction of the groove measured from a second outer edge of the second stepped portion of the groove to a second outer edge of the first side surface of the at least one of the first and second quartz crystal tuning fork tines, and so that each of the first and second widths of the groove formed in the first main surface of the at least one of the first and second quartz crystal tuning fork tines is greater than each of the first distance and the second distance, and forming a groove having at least three stepped portion including first, second and third stepped portions in the second main surface of the at least one of the first and second quartz crystal tuning fork tines so that each of the first, second and third stepped portions is formed along the length of the corresponding one of the first and second quartz crystal tuning fork tines; wherein the adjusting step comprises the steps of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −9000 ppm to +5000 ppm, and adjusting the frequency of oscillation of the quartz crystal tuning fork resonator to about 32.768 kHz with a frequency deviation within a range of −50 ppm to +50 ppm; and further comprising the steps of forming a quartz crystal tuning fork shape having the quartz crystal tuning fork base, and the first and second quartz crystal tuning fork tines; forming a metal film on a surface of the groove formed in each of the first and second main surfaces of the at least one of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of the at least one of the first and second quartz crystal tuning fork tines; forming a first electrode on the surface of the groove formed in each of the first and second main surfaces of the at least one of the first and second quartz crystal tuning fork tines and a second electrode on each of the first and second side surfaces of the at least one of the first and second quartz crystal tuning fork tines so that the first electrode formed on the surface of the groove formed in each of the first and second main surfaces of the at least one of the first and second quartz crystal tuning fork tines has an electrical polarity opposite to an electrical polarity of the second electrode formed on the each of the first and second side surfaces of the at least one of the first and second quartz crystal tuning fork tines; and disposing a metal or a glass into the through-hole of the case to close the through-hole thereof in a vacuum.  
     
     
       59. A method according to claim 37; wherein the quartz crystal tuning fork tines comprise first and second quartz crystal tuning fork tines connected to the quartz crystal tuning fork base, each of the first and second quartz crystal tuning fork tines having a length, and a first main surface and a second main surface opposite the first main surface, and a first side surface and a second side surface opposite the first side surface, the first side surface of the first quartz crystal tuning fork tine confronting the first side surface of the second quartz crystal tuning fork tine; wherein the forming step of the at least one groove comprises the step of forming a groove in at least one of the first and second main surfaces of at least one of the first and second quartz crystal tuning fork tines so that the groove comprises a first groove portion having a first width and a first surface, a second groove portion having a second width greater than the first width and a second surface, and a third groove portion having a third surface and each of the first and second surfaces is formed along the length of the at least one of the first and second quartz crystal tuning fork tines, the third surface being formed in a direction different from each of the first and second surfaces and the first surface being connected to the second surface through the third surface, and so that each of the first and second surfaces is directly opposite the first side surface of the at least one of the first and second quartz crystal tuning fork tines and directly connected to the third surface; wherein a first distance in the width direction of the first groove portion of the groove measured from a first outer edge of the first surface of the first groove portion of the groove to a first outer edge of the first side surface of the at least one of the first and second quartz crystal tuning fork tines is greater than a second distance in the width direction of the second groove portion of the groove measured from a second outer edge of the second surface of the second groove portion of the groove to a second outer edge of the first side surface of the at least one of the first and second quartz crystal tuning fork tines; and wherein the first width of the first groove portion of the groove formed in the at least one of the first and second main surfaces of the at least one of the first and second quartz crystal tuning fork tines is greater than the first distance in the width direction of the first groove portion of the groove and the second width of the second groove portion of the groove formed in the at least one of the first and second main surfaces of the at least one of the first and second quartz crystal tuning fork tines is greater than the second distance in the width direction of the second groove portion of the groove.