Flexural vibration piece

A resonator includes a base portion and a vibration arm. The vibration arm has first and second main faces opposite each other, the main faces have first and second grooves, the first groove has a plurality of first groove portions which are divided in the longitudinal direction of the vibration arm and arranged to be alternately shifted on both sides with respect to the longitudinal center line of the vibration arm, the second groove has a plurality of second groove portions arranged similar to the first groove portions on an opposite side to the first groove portions with respect to the longitudinal center line. A voltage is applied to excitation electrodes provided at the first and second grooves and second excitation electrodes provided on both side faces of the vibration arm, such that the vibration arm flexural-vibrates in the in-plane direction of the first or second main face.

BACKGROUND

1. Technical Field

The present invention relates to a flexural vibration piece that is used for various piezoelectric devices, such as vibrators or resonators, oscillators, gyroscopes, and various sensors, and other electronic devices, and vibrates in a flexural vibration mode.

2. Related Art

A flexural vibration mode piezoelectric vibration piece, such as a tuning-fork type piezoelectric vibration piece, generally has a structure in which grooves are formed at the front surface and/or the rear surface of the vibration arm in the longitudinal direction, and excitation electrodes are formed at the inner surfaces of the grooves (for example, see International Publication No. WO00/44092). Such a vibration arm is configured such that an electric field is generated between an excitation electrode at the side surface of the vibration arm and the excitation electrodes in the grooves so as to be widely distributed over the cross-section of the vibration arm, thereby significantly improving electric field efficiency. Therefore, even when the vibration piece is reduced in size, vibration loss can be made small, and the CI value can be suppressed at a low value.

In the flexural vibration mode piezoelectric vibration piece, if loss of vibration energy occurs at the time of flexural vibration of the vibration arm, deterioration in performance, such as an increase in the CI value or a decrease in the Q value, may occur. In order to prevent or reduce loss of vibration energy, a tuning-fork type crystal vibration piece is known in which cutout portions or cutout grooves having a predetermined depth are formed at both side portions of a base portion, from which the vibration arm extends (see JP-A-2002-261575 and JP-A-2004-260718). When vibration of the vibration arm includes a component in the vertical direction with respect to the main face of the vibration arm, that is, the out-plane direction, the cutout portions or cutout grooves of the base portion mitigate vibration leaking from the base portion. Thus, the confinement effect of vibration energy is increased, an increase in the CI value is suppressed, and a variation in the CI value between the vibration pieces is prevented.

Loss of vibration energy also is generated due to thermal conduction caused by a difference in temperature between a contracting portion of the vibration arm which flexural-vibrates and an expanding portion of the vibration arm to which tensile stress is applied. The decrease in the Q value due to thermal conduction is called a thermoelastic loss effect. In order to prevent or suppress the decrease in the Q value, a tuning-fork type vibrator is known in which a groove or a hole is formed on the center line of the vibration arm (vibration beam) having a rectangular cross-section (for example, see Japanese Utility Model Application No. 63-110151).

However, as described in Japanese Utility Model Application No. 63-110151, if a through hole is formed in the vibration arm, undesirably, rigidity of the vibration arm is significantly deteriorated. As described in the related art, in the piezoelectric vibration piece in which grooves are formed at the front and rear surface of the vibration arm on the center line, it is difficult to sufficiently prevent or suppress the decrease in the Q value due to the thermoelastic effect.

The inventors have suggested a flexural vibration piece in which a flexural vibration portion having a rectangular sectional shape and extending from a base portion to flexural-vibrate, that is, a vibration arm, has a first face and a second face, which are opposite each other and alternately expanded and contracted due to flexural vibration, and a third face and a fourth face, which are opposite each other and have grooves. In this flexural vibration piece, the grooves have a depth smaller than the distance between the third face and the fourth face, and the sum of the depths of the grooves is greater than the distance between the third face and the fourth face. The grooves are arranged between the first face and the second face. The grooves are provided in the above-described manner, such that the vibration arm has an S-shaped cross-section. Thus, the thermomigration path between the first face and the second face is extended, and the time until the difference in temperature between the expanding portion and the contracting portion of the vibration arm is mitigated by thermal conduction is extended, thereby suppressing the change in the Q value due to the thermoelastic effect.

It has been found that, at the time of flexural vibration of the vibration arm having an S-shaped cross-section, in which the grooves are formed in the above-described manner, the vibration arm may be displaced in the in-plane direction including the main faces at which the grooves are formed and in the vertical direction with respect to the main faces.FIGS. 9A to 10Bschematically show the configuration of a tuning-fork type piezoelectric vibration piece including a vibration arm having an S-shaped cross-section.

A tuning-fork type piezoelectric vibration piece1ofFIG. 9Ahas a pair of vibration arms3and4which extend in parallel from a base portion2. At the front and rear main faces of the respective vibration arms, first grooves5aand6aand second grooves5band6bare formed to extend in the longitudinal direction from the connection portions to the base portion. The first grooves5aand6aand the second grooves5band6bhave the same width, length, and depth. The piezoelectric vibration piece1of the related art is formed integrally of quartz. Of the quartz crystal axes, the electrical axis X is aligned in the width direction of the vibration arms, the mechanical axis Y is aligned in the longitudinal direction of the vibration arm, and the optical axis Z is aligned in the thickness of the vibration piece.

The first grooves5aand6aat the front-side main faces are arranged outside in the width direction with respect to the longitudinal center lines i of the vibration arms3and4. That is, the groove at the front-side main face of one vibration arm is arranged on the opposite side to the other vibration arm. The second grooves5band6bat the rear-side main face are arranged inside in the width direction with respect to the longitudinal center lines i of the vibration arms in the longitudinal direction. That is, the groove at the rear-side main face of one vibration arm is arranged to face the other vibration arm. As shown inFIG. 9B, the first grooves5aand6aand the second grooves5band6bare provided so as to have a depth greater than half of the thickness of the vibration arms3and4. The first grooves5aand6aand the second grooves5band6bare provided so as not to overlap each other when viewed from the front and rear main faces of the vibration arms and so as to overlap each other from when viewed from the side faces. As a result, the vibration arms have an S-shaped cross-section which is line-symmetric with respect to the center line i′ between the vibration arms.

First excitation electrodes (not shown) are respectively formed at the inner surfaces of the first grooves and the second grooves of the vibration arms3and4. Second excitation electrodes (not shown) are respectively formed at both side faces of the vibration arms. The first excitation electrodes of one vibration arm are connected to the second excitation electrodes of the other vibration arm. An alternating-current voltage is applied to the first excitation electrodes and the second excitation electrodes, such that the vibration arms vibrate to approach or move away from each other.

At this time, it has been found that the vibration arms3and4have the vibration components in the in-plane of the front and rear main faces and the out-plane direction, that is, in the ±Z direction. When the vibration arms are bent to move away from each other, as indicated by the arrows A1and A2ofFIG. 9B, the vibration arms are also displaced in the −Z direction. When the vibration arms are bent to approach each other, as indicated by the arrows B1and B2ofFIG. 9B, the vibration arms are also displaced in the +Z direction.

A tuning-fork type piezoelectric vibration piece7ofFIG. 10A, first grooves8aand9aat the front-side main face are arranged on the same sides in the width direction with respect to the longitudinal center lines i of the vibration arms3and4, that is, the left sides in the drawing. Second grooves8band9bat the rear-side main face are arranged on the same sides in the width direction with respect to the longitudinal center lines i of the vibration arms, that is, on the right sides in the drawing. Similarly to the piezoelectric vibration piece1ofFIGS. 9A and 9B, the first grooves and the second grooves have a depth greater than half of the thickness of the vibration arms3and4. The first grooves and the second grooves are provided so as not to overlap each other when viewed from the front and rear main faces of the vibration arms and so as to overlap each other when viewed from the side faces. Thus, as shown inFIG. 10B, the vibration arms of the piezoelectric vibration piece7have an S-shaped cross-section which is point-symmetric with respect to the center point O between the vibration arms.

In the tuning-fork type piezoelectric vibration piece7, it has been found that, when an alternating-current voltage is applied to the first excitation electrodes formed at the first grooves and the second grooves and the second excitation electrodes at both side faces of the vibration arms, and the vibration arms3and4vibrate to approach or move away from each other, the vibration arms have the vibration components in the in-plane direction and the out-plane direction, that is, in the ±Z direction. When the vibration arms are bent to move away from each other, as indicated by the arrows A1and A2ofFIG. 10B, the vibration arm3is also displaced in the −Z direction and the vibration arm4is also displaced in the +Z direction. When the vibration arms are bent to approach each other, as indicated by the arrows B1and B2ofFIG. 10B, the vibration arm3is also displaced in the +Z direction and the vibration arm4is also displaced in the −Z direction.

Referring toFIGS. 9B and 10B, when the cross-sections of each of the vibration arms is divided by the center lines in the X direction and the Z direction, it can be seen that the displacement in the ±Z direction at the time of flexural vibration of the vibration arms is generated to be attracted to a region having a greater mass. Referring toFIG. 9B, in the vibration arm3, the displacement in the ±Z direction is generated from the center toward the −X and −Z region and the +X and +Z region where the first and second grooves5aand5bhave a small occupying area. The same is applied to the vibration arm4in which the first and second grooves6aand6bare arranged to be different from those in the vibration arm3. This is because the bending moment of the vibration arm is applied toward a region having a greater mass.

The vibration component in the ±Z direction of the vibration arm, that is, the out-plane vibration component, causes loss of vibration energy, that is, vibration leakage. For this reason, the Q value of the vibration piece decreases, and the CI value is deteriorated. In the flexural vibration piece, the reduction in size causes a decrease in the Q value, such that the decrease in the Q value due to vibration leakage interferes with reduction in size and thickness of the vibration piece.

SUMMARY

An advantage of some aspects of the invention is that it provides a flexural vibration piece, in which first and second grooves in a longitudinal direction are formed at first and second main faces arranged opposite each other of a vibration arm extending from a base portion, and the first and second grooves are arranged to be shifted to the opposite sides between the first and second main faces in a width direction with respect to a longitudinal center line of the vibration arm, and which is capable of eliminating or suppressing a vibration component in a vertical direction with respect to the first and second main faces at the time of flexural vibration of the vibration arm to eliminate or reduce vibration leakage, thereby improving a Q value, improving a CI value, achieving high performance, and realizing reduction in size and thickness.

According to an aspect of the invention, a flexural vibration piece includes a base portion, and a vibration arm extending from the base portion. The vibration arm has first and second main faces which are arranged to be opposite each other. The first main face have first groove which is formed in the longitudinal direction of the vibration arm. The second main face have second groove which is formed in the longitudinal direction of the vibration arm. The vibration arm further has a longitudinal center line which extends in the longitudinal direction of the vibration arm. The first groove has a plurality of first groove portions which are arranged on both sides with respect to the longitudinal center line. The plurality of first groove portions are shifted from each other in the longitudinal direction of the vibration arm. The second groove has a plurality of second groove portions which are arranged on both sides with respect to the longitudinal center line. The plurality of second groove portions are shifted from each other in the longitudinal direction of the vibration arm and are arranged on an opposite side to the first groove portions with respect to the longitudinal center line.

When the cross-section of the vibration arm, in which a plurality of first groove portions and second groove portions are arranged, is divided by the center lines in the width direction and the thickness direction, the region opposite to the opening of each of the first groove portions or the second groove portions in the width direction and the thickness direction has amass greater than other regions since the occupying area of the first groove portion or the second groove portion is small. The region having a greater mass alternately moves between the opposing diagonal positions at each of the positions corresponding to the next first and second groove portions in the longitudinal direction of the vibration arm. As a result, at the time of flexural vibration of the vibration arm, for each of the positions of the first and second groove portions in the longitudinal direction, the vibration components in the out-plane direction with respect to the first and second main faces occur in the reverse directions and cancel each other. Thus, the displacement in the out-plane direction of the vibration arm is eliminated or sufficiently suppressed as a whole, and vibration energy is confined in the in-plane direction of the first and second main faces, thereby preventing vibration leakage. Therefore, the Q value of the flexural vibration piece can be improved, the CI value can be suppressed, and reduction in size and thickness can be realized.

The plurality of first groove portions and second groove portions may have different widths in the longitudinal direction of the vibration arm, and the width of each of the first and second groove portions at a base end-side portion of the vibration arm may be set to be greater than the width of each of the first and second groove portions at a tip end-side portion of the vibration arm. Stress occurring at the base end-side portion of the vibration arm contributes to the displacement of the vibration arm in the out-plane direction more significantly than stress occurring at the tip end-side portion of the vibration arm. If the width of each of the first and second groove portions is set in such a manner, the displacement of the vibration arm in the out-plane direction can be satisfactorily eliminated or suppressed as a whole.

The plurality of first groove portions and second groove portions may have different lengths in the longitudinal direction of the vibration arm, and the length of each of the first and second groove portions at a base end-side portion of the vibration arm may be set to be smaller than the length of each of the first and second groove portions at a tip end-side portion of the vibration arm. As described above, stress occurring at the base end-side portion of the vibration arm contributes to the displacement of the vibration arm in the out-plane direction more significantly than stress occurring at the tip end-side portion of the vibration arm. If the length of each of the first and second groove portions is set in such a manner, the displacement of the vibration arm in the out-plane direction can be satisfactorily eliminated or suppressed as a whole.

Like a tuning-fork type flexural vibration piece having two vibration arms, the invention may be applied to a flexural vibration piece in which a plurality of vibration arms extend in parallel from the base portion and flexural-vibrate to approach or move away from each other.

The invention may be applied to a flexural vibration piece in which a plurality of vibration arms extend in parallel from the base portion and vibrates in a flexural mode in phases inverse to each other.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, exemplary embodiments of the invention will be described in detail with reference to the accompanying drawings. In the drawings, the same or similar parts are represented by the same or similar reference numerals.

FIG. 1Aschematically shows a flexural vibration piece according to a first embodiment of the invention. A flexural vibration piece11of this embodiment has one vibration arm13which extends in parallel from a base portion12. A first groove and a second groove are formed at front and rear main faces14and15of the vibration arm13so as to extend in the longitudinal direction from a connection portion to the base portion. The piezoelectric vibration piece11is formed integrally of quartz. Of the quartz crystal axes, the electrical axis X is aligned in the width direction of the vibration arm, the mechanical axis Y is aligned in the longitudinal direction of the vibration arm, and the optical axis Z is aligned in the thickness direction of the vibration piece. In another embodiment, a piezoelectric material other than quartz or a semiconductor material, such as silicon, may be used.

The first groove at the front-side main face14is divided into two first groove portions16aand16bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm13. The first groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i of the vibration arm13in the longitudinal direction. Specifically, the first groove portion16awhich is close to the base end, that is, the base portion, is arranged on one side in the width direction with respect to the longitudinal center line i, that is, on the right side in the drawing. The first groove portion16bwhich is away from the tip end, that is, the base portion, is arranged on the opposite side in the width direction with respect to the longitudinal center line i, that is, on the left side in the drawing.

Similarly, the second groove at the rear-side main face15is divided into two second groove portions17aand17bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm13. The second groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i of the vibration arm13in the longitudinal direction. Specifically, the second groove portion17aat the base end is arranged on one side in the width direction with respect to the longitudinal center line i, that is, on the left side in the drawing. The second groove portion17bat the tip end is arranged on the opposite side in the width direction with respect to the longitudinal center line i, that is, on the right side in the drawing.

As shown inFIGS. 1B and 1C, the first groove portions16aand16band the second groove portions17aand17bhave a depth greater than half of the thickness of the vibration arm13. The first groove portions16aand16band the second groove portions17aand17boverlap each other when viewed from the side face of the vibration arm. The first groove portions16aand16band the second groove portions17aand17bwhich are at the corresponding positions in the longitudinal direction of the vibration arm are arranged on the opposite sides in the width direction with respect to the longitudinal center line i so as not to overlap each other when viewed from the front and rear main faces. Therefore, in the vibration arm13, the base end-side portion at which the first and second groove portions16aand17aare provided and the tip end-side portion at which the first and second groove portions16band17bare provided have an S-shaped cross-section which is mirror-symmetric.

If the cross-section of the vibration arm13is divided by the center lines in the width direction and the thickness direction, as shown inFIG. 1B, at the base end-side portion, the mass of each of the −X and +Z region and the +X and −Z region where each of the first and second groove portions16aand17ahas a small occupying area is greater than the mass of each of the −X and −Z region and the +X and +Z region. As shown inFIG. 1C, at the tip end-side portion of the vibration arm13, the mass of the −X and −Z region and the +X and +Z region where the first and second groove portions16band17bhave a small occupying area is greater than the −X and +Z region and the +X and −Z region.

First excitation electrodes (not shown) are formed at the side surfaces of the first groove portions16aand16band the second groove portions17aand17badjacent to the side faces of the vibration arm13. Second excitation electrodes (not shown) are formed on both side faces of the vibration arm. If a predetermined alternating-current voltage is applied to the first excitation electrodes and the second excitation electrodes, the vibration arm13flexural-vibrates in the directions indicated by arrows A and B ofFIG. 1A.

At this time, as indicated by arrows Aa and Ba ofFIG. 1B, the base end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. Meanwhile, as indicated by arrows Ab and Bb ofFIG. 1C, the tip end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass in the same manner. As a result, over the entire vibration arm13, the vibration components in the ±Z direction cancel each other.

Thus, in the vibration arm13, the displacement in the ±Z direction can be eliminated or sufficiently suppressed, and vibration energy can be confined in the in-plane direction of the front and rear main faces14and15. Therefore, the Q value of the flexural vibration piece11can be improved, the CI value can be suppressed, and as a result, reduction in size and thickness can be realized.

FIG. 2Aschematically shows a piezoelectric vibration piece according to a second embodiment of the invention. A flexural vibration piece18of this embodiment is different from the first embodiment ofFIGS. 1A to 1Cin that the width w1of each of first and second groove portions19aand20aat the base end is different from the width w2of each of first and second groove portions19band20bat the tip end, and the condition w1>w2is satisfied.

If the vibration arm13flexural-vibrates in the directions indicated by arrows A and B ofFIG. 2A, as indicated by arrows Aa and Ba ofFIG. 2B, the base end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. Meanwhile, as indicated by arrows Ab and Bb ofFIG. 2C, the tip end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass in the same manner.

It has been confirmed that stress occurring at the base end of the vibration arm contributes to the displacement of the vibration arm13in the out-plane direction more significantly than stress occurring at the tip end of the vibration arm. Thus, as described above, if the widths of the first and second groove portions19a,19b,20a, and20bare set to be different at the base end and the tip end, over the entire vibration arm13, the vibration components in the out-plane direction can satisfactorily cancel each other, and the displacement in the out-plane direction can be eliminated or suppressed. Therefore, the Q value of the flexural vibration piece18can be further improved, and the CI value can be further effectively suppressed.

FIG. 3Aschematically shows a piezoelectric vibration piece according to a third embodiment of the invention. A flexural vibration piece21of this embodiment is different from the first embodiment ofFIGS. 1A to 1Cin that the length L1of each of first and second groove portions22aand23aat the base end is different from the length L2of each of first and second groove portions22band23bat the tip end, and the condition L1<L2is satisfied.

If the vibration arm13flexural-vibrates in the directions indicated by arrows A and B ofFIG. 3A, as indicated by arrows Aa and Ba ofFIG. 3B, the base end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. Meanwhile, as indicated by arrows Ab and Bb ofFIG. 3C, the tip end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass in the same manner.

It has been confirmed that stress occurring at the base end of the vibration arm contributes to the displacement of the vibration arm13in the out-plane direction more significantly than stress occurring at the tip end of the vibration arm. Thus, as described above, if the lengths of the first and second groove portions22a,22b,23a, and23bare set to be different at the base end and the tip end, over the entire vibration arm13, the vibration components in the out-plane direction can cancel each other, and the displacement in the out-plane direction can be eliminated or suppressed. Therefore, the Q value of the flexural vibration piece18can be further improved, and the CI value can be further effectively suppressed.

In another embodiment, the second embodiment may be incorporated into the third embodiment. For example, the width of each of the first and second groove portions22aand23aat the base end may be greater or smaller than the width of each of the first and second groove portions22band23bat the tip end.

FIG. 4Aschematically shows a piezoelectric vibration piece according to a fourth embodiment of the invention. A flexural vibration piece24of this embodiment is different from the first embodiment ofFIGS. 1A to 1Cin that a first groove at the front-side main face14is divided into three first groove portions25ato25cwhich have the same width, length, and depth in the longitudinal direction of the vibration arm13, and similarly, a second groove at the rear-side main face15is divided into three second groove portions26ato26cwhich have the same width, length, and depth in the longitudinal direction of the vibration arm13. The first groove portions25ato25care arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i of the vibration arm13in the longitudinal direction. The second groove portions26ato26care arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i. The second groove portions26ato26care arranged on the opposite sides in the width direction with respect to the longitudinal center line i so as not to overlap the first groove portions25ato25cwhen viewed from the front and rear main faces of the vibration arm.

If the vibration arm13flexural-vibrates in the directions indicated by arrows A and B ofFIG. 4A, as indicated by arrows Aa and Ba ofFIG. 4B, the base end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. As indicated by arrow Ab and Bb ofFIG. 4C, a central portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass. Similarly to the base end-side portion, as indicated by the arrows Ab and Bb ofFIG. 4C, the tip end-side portion of the vibration arm13tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass.

If the number of first and second divided groove portions increases, each time the arrangement of the first and second groove portions in the width direction of the vibration arm changes, the direction of the in-plane vibration component frequently and repeatedly changes reversely in the length direction from the base end of the vibration arm13toward the tip end of the vibration arm13. As a result, the vibration arm can smoothly flexural-vibrate in the in-plane direction as a whole. In another embodiment, the first and second grooves may be divided into four or more first and second groove portions.

In another embodiment, the second and third embodiment may be incorporated into the fourth embodiment separately or together. For example, the first groove portions25ato25cand the second groove portions26aand26cmay be set to have different lengths, different widths, and different lengths and widths in the longitudinal direction of the vibration arm13.

FIG. 5Aschematically shows a piezoelectric vibration piece according to a fifth embodiment of the invention. A flexural vibration piece31of this embodiment is a tuning-fork type flexural vibration piece which has a pair of vibration arms33and34extending in parallel from a base portion32.

A first groove and a second groove are formed at front and rear main faces35and36of the vibration arm33so as to extend in the longitudinal direction from connection portions to the base portion. The first groove at the front-side main face35is divided into two first groove portions37aand37bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm13. The first groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i of the vibration arm33in the longitudinal direction. Similarly, the second groove at the rear-side main face36is divided into two second groove portions38aand38bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm33. The second groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i.

Similarly, a first groove and a second groove are formed at front and rear main faces39and40of the vibration arm34so as to extend in the longitudinal direction from connection portions to the base portion. The first groove at the front-side main face39is divided into two first groove portions41aand41bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm34. The first groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i of the vibration arm33in the longitudinal direction. Similarly, the second groove portions at the rear-side main face40is divided into two second groove portions42aand42bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm34. The second groove portions are arranged to be alternately shifted on both sides in the width direction with respect to the longitudinal center line i.

As shown inFIGS. 5B and 5C, the first grooves at the front-side main faces35and39of both vibration arms33and34are provided to be symmetric with respect to a center line i′ between both vibration arms. The first groove portions37aand41aat the base end are arranged to be adjacent each other, and the first groove portions37band41bat the tip end are arranged on the opposite sides. Similarly, the second grooves at the rear-side main faces36and40of both vibration arms33and34are provided to be symmetric with respect to the center line i′ between both vibration arms. The first groove portions38band42bat the tip end are arranged to be adjacent to each other, and the first groove portions38aand42aare arranged on the opposite sides. Therefore, the base end-side portion and the tip end-side portion of each of both vibration arms33and34have an S-shaped cross-section which is line-symmetric with respect to the center line i′.

As shown inFIG. 5B, if the cross-section of the vibration arm33is divided by the center lines in the width direction and the thickness direction, at the base end-side portion, the mass of each of the −X and +Z region and the +X and −Z region where each of the first and second groove portions36aand38ahas a small occupying area is greater than the mass of each of the −X and −Z region and the +X and +Z region. At the base end-side portion of the vibration arm34having a cross-sectional shape, which is line-symmetric with the vibration arm33, the mass of each of the +X and +Z region and the −X and −Z region where each of the first and second groove portions41aand42ahas a small occupying area is greater than the mass of each of the −X and +Z region and the +X and −Z region.

As shown inFIG. 5C, at the tip end-side portion of the vibration arm33, the mass of each of the −X and −Z region and the +X and +Z region where each of the first and second groove portions37band38bhas a small occupying area is greater than the mass of each of the −X and +Z region and the +X and −Z region. Symmetrically, at the tip end-side portion of the vibration arm34, the mass of each of the +X and −Z region and the −X and +Z region where each of the first and second groove portions41band42bhas a small occupying area is greater than the mass of each of the −X and −Z region and the +X and +Z region.

First excitation electrodes (not shown) are formed at the inner surfaces of the first and second grooves of the vibration arms33and34, and second excitation electrodes (not shown) are formed at both side faces of the vibration arms. The first excitation electrodes of one vibration arm are connected to the second excitation electrodes of the other vibration arm. If an alternating-current voltage is applied to the first excitation electrodes and the second excitation electrodes, both vibration arm vibrates to approach or move away from each other, as indicated by arrows A and B ofFIG. 5A.

At this time, as indicated by arrows Aa1and Ba1ofFIG. 5B, the base end-side portion of the vibration arm33tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. As indicated by arrows Aa2and Ba2ofFIG. 5B, the base end-side portion of the vibration arm34tends to be bent from the cross-sectional center in the directions toward the +X and +Z region and the −X and −Z region having a greater mass. Meanwhile, as indicated by arrows Ab1and Bb1ofFIG. 5C, the tip end-side portion of the vibration arm33tends to be bent from the cross-sectional center in the directions toward the −X and −Z direction and the +X and +Z direction having a greater mass. As indicated by arrows Ab2and Bb2ofFIG. 5C, the tip end-side portion of the vibration arm34tends to be bent from the cross-sectional center in the directions toward the +X and −Z region and the −X and +Z region having a greater mass.

As described above, the base end-side portion of both vibration arms33and34have the out-plane vibration components in the same direction as the Z direction, and the tip end-side portions of both vibration arms33and34have the out-plane vibration components in the same direction as the Z direction and in the reverse direction to the base end-side portions. As a result, in the case of the vibration arms33and34, the vibration components in the ±Z direction cancel each other as a whole, and the displacement in the ±Z direction is eliminated or suppressed. Therefore, in the case of the flexural vibration piece31, the Q value can be improved, the CI value can be suppressed, and as a result, reduction in size and thickness can be realized.

FIG. 6Aschematically shows a piezoelectric vibration piece according to a sixth embodiment of the invention. A flexural vibration piece43of this embodiment is a tuning-fork type flexural vibration piece which is a modification of the fifth embodiment, and has a pair of vibration arms33and34extending in parallel from the base portion32. The vibration arm33has the same configuration as the fifth embodiment. A first groove portion44aat the base end of the front-side main face35is arranged to be adjacent to the vibration arm34and a first groove portion44bat the tip end is arranged on the opposite side to the vibration arm34. A second groove portion45bat the tip end of the rear-side main face36is arranged to be adjacent to the vibration arm34and a second groove portion45aat the base end is arranged on the opposite to the vibration arm34.

In the case of the vibration arm34, the first groove portion46bat the tip end of the front-side main face35is arranged to be adjacent to the vibration arm33and the first groove portion46aat the base end is arranged on the opposite side to the vibration arm33. The second groove portion47aat the base end of the rear-side main face36is arranged to be adjacent to the vibration arm33and the second groove portion47bat the tip end is arranged on the opposite side to the vibration arm33. This is different from the flexural vibration piece31of the fifth embodiment. Thus, as shown inFIGS. 6B and 6C, the base end-side portion and the tip end-side portion of each of both vibration arms33and34have an S-shaped cross section which is point-symmetric with respect to the center O between both vibration arms.

Thus, as indicated by arrows A and B ofFIG. 6A, if the flexural vibration piece43flexural-vibrates to approach or move away from each other, as indicated by arrows Aa1and Ba1ofFIG. 6B, the base end-side portion of the vibration arm33tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass. As indicated by arrows Aa2and Ba2ofFIG. 6B, the base end-side portion of the vibration arm34tends to be bent from the cross-sectional center in the directions toward the +X and −Z region and the −X and +Z region having a greater area. Meanwhile, as indicated by arrows Ab1and Bb1ofFIG. 6C, the tip end-side portion of the vibration arm33tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass. As indicated by arrows Ab2and Bb2ofFIG. 6C, the tip end-side portion of the vibration arm34tends to be bent from the cross-sectional center in the directions toward the +X and +Z region and the −X and −Z region having a greater mass.

As described above, the base end-side portions of both vibration arms33and34have the out-plane vibration components in the reverse direction to the Z direction, and the tip end-side portions of both vibration arms33and34have the out-plane vibration components in the reverse direction to the Z direction and in the reverse direction to the base end-side portion. As a result, in the case of the vibration arms33and34, the vibration components in the ±Z direction cancel each other as a whole, and the displacement in the ±Z direction is eliminated or suppressed. Therefore, in the case of the flexural vibration piece43, the Q value can be improved, the CI value can be suppressed, and as a result, reduction in size and thickness can be realized.

In another embodiment, the flexural vibration pieces31and43ofFIGS. 5A to 5CandFIGS. 6A to 6Cmay have the vibration arms33and34having the same configuration as that in each of the second to fourth embodiments, or may have the vibration arms in the second to fourth embodiments in combination. In yet another embodiment, the invention may be applied to a tuning-fork type flexural vibration piece having three or more vibration arms.

FIG. 7Aschematically shows a piezoelectric vibration piece according to a seventh embodiment of the invention. Similarly to the fifth and sixth embodiments, a flexural vibration piece51of this embodiment is a tuning-fork type flexural vibration piece which has a pair of vibration arms53and54extending in parallel from a base portion52. However, the flexural vibration piece51of this embodiment is different from the tuning-fork type flexural vibration pieces of the fifth and sixth embodiment in that, as indicated by arrows A to D ofFIG. 7A, the vibration arms53and54vibrate in an inverse-phase flexural vibration mode, called walk vibration, in the vertical direction with respect to the front and rear faces of the relevant vibration arm. The piezoelectric vibration piece51is also formed integrally of quartz. However, unlike the foregoing embodiments, of the quartz crystal axes, the electrical axis X is aligned in the thickness direction of the vibration piece, the mechanical axis Y is aligned in the longitudinal direction of the vibration arm, and the optical axis Z is aligned in the width direction of the vibration piece. In another embodiment, a piezoelectric material other than quartz or a semiconductor material, such as silicon, may be used.

The flexural vibration piece51has first and second main faces which are arranged to be opposite each other in the width direction of the vibration arms53and54. The vibration arm53has a first main face55facing the vibration arm54and a second main face56on the opposite side to the vibration arm54. A first groove and a second groove are respectively formed at the first main face55and the second main face56so as to extend in the longitudinal direction from a connection portion to the base portion. The first groove at the first main face55is divided into two first groove portions57aand57bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm53. The first groove portions are arranged to be alternately shifted on both sides with respect to a longitudinal center line i1of the vibration arm53in the longitudinal direction. The second groove at the second main face56is divided into two second groove portions58aand58bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm53. The second groove portions are arranged to be alternately shifted on both sides with respect to a longitudinal center line i2of the vibration arm53in the longitudinal direction.

Similarly, the vibration arm54has a first main face59on the opposite side of the vibration arm53and a second main face60facing the vibration arm53. A first groove and a second groove are respectively formed at the first main face59and the second main face60so as to extend in the longitudinal direction from a connection portion to the base portion. The first groove at the first main face59is divided into two first groove portions61aand61bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm54. The first groove portions are arranged to be alternately shifted on both sides with respect to a longitudinal center line i1of the vibration arm54in the longitudinal direction. The second groove portion at the second main face60is divided into two second groove portions62aand62bwhich have the same width, length, and depth in the longitudinal direction of the vibration arm54. The second groove portions are arranged to be alternately shifted on both sides with respect to a longitudinal center line i2of the vibration arm54in the longitudinal direction.

Thus, as shown inFIGS. 7B and 7C, the base end-side portion and the tip end-side portion of each of both vibration arms53and54have an S-shaped cross-section which is point-symmetric with respect to a center O between both vibration arms. Therefore, if the flexural vibration piece51flexural-vibrates in reverse phase as described above, as indicated by arrows Aa and Ca ofFIG. 7B, the base end-side portion of the vibration arm53tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass. As indicated by arrows Ba and Da ofFIG. 7B, the base end-side portion of the vibration arm54tends to be bent from the cross-sectional center in the directions toward the +X and +Z region and the −X and −Z region having a greater mass. Meanwhile, as indicated by arrows Ab and Cb ofFIG. 7C, the tip end-side portion of the vibration arm53tends to be bent from the cross-sectional center in the directions toward the −X and +Z direction and the +X and −Z direction having a greater mass. As indicated by arrows Bb and Db ofFIG. 7C, the tip end-side portion of the vibration arm54tends to be bent from the cross-sectional center in the directions toward the +X and −Z region and the −X and +Z region having a greater mass.

Thus, the base end-side portion and the tip end-side portion of each of the vibration arms53and54have the out-plane vibration components in the reverse direction to the Z direction. As a result, in the case of the vibration arms53and54, the vibration components in the ±Z direction cancel each other as a whole, and the displacement in the ±Z direction is eliminated or suppressed. Therefore, in the case of the flexural vibration piece51, the Q value can be improved, the CI value can be suppressed, and as a result, reduction in size and thickness can be realized.

FIG. 8Aschematically shows a piezoelectric vibration piece according to an eighth embodiment of the invention. A flexural vibration piece71of this embodiment is a modification of the seventh embodiment, and have three vibration arms73to75extending in parallel from a base portion72. As indicated by arrows A to F ofFIG. 8A, the vibration arms73to75alternately vibrates in an inverse-phase flexural vibration mode in the vertical direction with respect to the surface of the vibration piece. The vibration arms73to75respectively have first main faces76,78, and80and second main faces77,79, and81which are arranged to be opposite each other in the width direction of the vibration arms.

Similarly to the seventh embodiment, first and second grooves are respectively formed at the first and second main faces of the vibration arms73to75so as to extend in the longitudinal direction from connection portions to the base portion. The first and second grooves of the vibration arm73on the left side of the drawing are respectively divided into two first groove portions82aand82band second groove portions83aand83bwhich have the same width, length, and depth in the longitudinal direction. The first groove portions82aand82band the second groove portions83aand83bare respectively arranged to be alternately shifted on both sides with respect to longitudinal center lines i1and i2of the vibration arm73in the longitudinal direction and on the opposite sides with respect to the longitudinal center lines i1and i2.

Similarly, the first and second grooves of the vibration arm74at the center of the drawing are respectively divided into two first groove portions84aand84band second groove portions85aand85bwhich have the same width, length, and depth in the longitudinal direction. The first groove portions84aand84band the second groove portions85aand85bare respectively arranged to be alternately shifted on both sides with respect to longitudinal center lines i1and i2of the vibration arm74in the longitudinal direction and on the opposite sides with respect to the center lines.

The first and second grooves of the vibration arm75on the right side of the drawing are respectively divided into two first groove portions86aand86band second groove portions87aand87bwhich have the same width, length, and depth in the longitudinal direction. The first groove portions86aand86band the second groove portions87aand87bare respectively arranged to be alternately shifted on both sides with respect to longitudinal center lines i1and i2of the vibration arm75and on the opposite sides with respect to the center lines.

Thus, as shown inFIGS. 8B and 8C, the base end-side portion and the tip end-side portion of each of the vibration arms73to75have an S-shaped cross-section which is point-symmetric with respect to a center O1or O2between the adjacent vibration arms. Therefore, if the flexural vibration piece71flexural-vibrates in inverse phase as described above, The base end-side portion of each of the vibration arms73to75tends to be bent from the cross-sectional center in the directions toward the −X and −Z region and the +X and +Z region having a greater mass. The tip end-side portion of each of the vibration arms tends to be bent from the cross-sectional center in the directions toward the −X and +Z region and the +X and −Z region having a greater mass.

Thus, the base end-side portion and the tip end-side portion of each of the vibration arms73to75have the out-plane vibration components in the reverse direction to the Z direction. As a result, in the case of the vibration arms73to75, the vibration components in the ±Z direction cancel each other as a whole, and the displacement in the ±Z direction is eliminated or suppressed. Therefore, in the case of the flexural vibration piece71, the Q value can be improved, the CI value can be suppressed, and as a result, reduction in size and thickness can be realized.

In another embodiment, the flexural vibration pieces51and71ofFIGS. 7A to 7CandFIGS. 8A to 8Cmay have the vibration arms having the same configuration as that in each of the second to fourth embodiments. In yet another embodiment, like the tuning-fork type flexural vibration piece ofFIGS. 5A to 5C, the first and second groove portions at the base end and the first and second groove portion at the tip end may be arranged at the reverse positions with respect to the longitudinal center line of the vibration arm between the vibration arms.

The invention is not limited to the foregoing embodiments, and various modifications or changes may be made without departing from the technical scope of the invention. For example, the depths of the first and second groove portions may vary in the longitudinal direction of the vibration arm insofar as the displacement in the ±Z direction can be eliminated or suppressed over the entire vibration arm.

The entire disclosure of Japanese Patent Application No. 2009-111256, filed Apr. 30, 2009 is expressly incorporated by reference herein.