JP2013042388A - Piezoelectric vibration piece and piezoelectric device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a piezoelectric vibration piece and a piezoelectric device in which the impact of stress on a vibration part is minimized.SOLUTION: The piezoelectric vibration piece includes a vibration part having a first side of length WS and a second side of length LS, a frame having a first frame of length WA and a second frame of length LA and surrounding the vibration part, and one coupling part which couples the first side of the vibration part and the first frame of the frame in the middle of the first side and first frame with a width WR and a length LR, and satisfies at least one of formula 1, formula 2, formula 3 or formula 4. (0.1471×LS-0.004)×0.75<LR<(0.1471×LS-0.004)×1.25...formula 1, (0.3545×WS+0.044)×0.8<WR<(0.3545×WS+0.044)×1.2...formula 2, (0.85×LA-0.3125)×0.94<LS<(0.85×LA-0.3125)×1.06...formula 3, (0.7237×WA-0.272)×0.88<WS<(0.7237×WA-0.272)×1.12...formula 4.

Description

  The present invention relates to a piezoelectric vibrating piece or a piezoelectric device in which the influence of stress on a vibrating part is suppressed.

  There is known a piezoelectric vibrating piece having a vibrating part that vibrates at a predetermined frequency and a frame part surrounding the vibrating part. In such a piezoelectric vibrating piece, a lid plate and a base plate are joined to the front and back surfaces of the frame portion to form a piezoelectric device, and the piezoelectric device is mounted on a printed board or the like. Such a piezoelectric device may receive a stress applied to the printed circuit board. The stress applied to the piezoelectric device affects the piezoelectric vibrating piece and changes the characteristics of the vibration frequency of the vibration part.

  As a method for preventing the vibration part from receiving such stress that affects the vibration frequency of the vibration part, for example, Patent Document 1 discloses that a vibration part and an adhesive part of a piezoelectric vibrating piece are notched. A piezoelectric vibrating piece is disclosed in which stress is prevented from being transmitted to the vibrating portion by dividing the vibration portion, and changes in vibration frequency characteristics are suppressed.

JP 2011-66779 A

  However, even in Patent Document 1, it is not sufficient to suppress the change in the vibration frequency characteristics of the piezoelectric vibrating piece. Further, the piezoelectric vibrating piece of Patent Document 1 does not have a frame portion. It is desired that the piezoelectric vibrating piece further prevents stress from being applied to the vibrating portion and suppresses changes in the characteristics of the vibration frequency.

  The present invention provides a piezoelectric vibrating piece and a piezoelectric device in which the influence of the stress on the vibrating part is suppressed by forming the vibrating part, the frame part, and the connecting part so that the dimensional relationship is appropriate. With the goal.

A piezoelectric vibrating piece according to a first aspect includes a rectangular vibrating portion having a first side having a length WS extending in a first direction and a second side having a length LS extending in a second direction orthogonal to the first direction; A frame portion having a first frame having a length WA extending in the first direction and a second frame having a length LA extending in the second direction and surrounding the vibration portion, a first side of the vibration portion, and a first frame of the frame portion And a connecting portion that connects the first side and the first frame with a width WR in the first direction and a length LR in the second direction, and Formula 1, Formula 2, Formula 3, Or, at least one of Expression 4 is satisfied.
(0.1471 × LS−0.004) × 0.75 <LR <(0.1471 × LS−0.004) × 1.25 Formula 1
(0.3545 × WS + 0.044) × 0.8 <WR <(0.3545 × WS + 0.044) × 1.2 Formula 2
(0.85 × LA−0.3125) × 0.94 <LS <(0.85 × LA−0.3125) × 1.06 Equation 3
(0.7237 × WA−0.272) × 0.88 <WS <(0.7237 × WA−0.272) × 1.12 Equation 4

  The piezoelectric vibrating piece according to the second aspect is the first aspect, in which the vibrating portion has a mesa region and a peripheral region formed around the mesa region and is thinner than the mesa region, and an excitation electrode is formed in the mesa region. An extraction electrode extracted from the excitation electrode is formed on the part and the frame part.

  In the piezoelectric vibrating piece according to the third aspect, in the second aspect, the peripheral area of the vibrating part and the connecting part have the same thickness.

  A piezoelectric device according to a fourth aspect includes a piezoelectric vibrating piece according to the first to third aspects, a lid plate connected to one surface of the frame portion, and a base having an external electrode connected to the other surface of the frame portion. A board.

  According to the piezoelectric vibrating piece of the present invention, the influence of the stress on the vibrating portion can be suppressed by forming the relationship between the dimensions of the vibrating portion, the frame portion, and the connecting portion to be an appropriate relationship.

1 is an exploded perspective view of a piezoelectric device 100. FIG. (A) is sectional drawing of the AA cross section of FIG. FIG. 4B is a plan view of the piezoelectric vibrating piece 130. (A) is a top view of the piezoelectric vibrating piece 130 in which no electrode is formed. (B) is BB sectional drawing of FIG.2 (b). (A) is a simulation result of a piezoelectric vibrating piece having a width WR of the connecting portion 133 of 0.32 mm. (B) is a simulation result of the piezoelectric vibrating piece in which the width WR of the connecting portion 133 is 0.35 mm. (C) is a simulation result of a piezoelectric vibrating piece having a width WR of the connecting portion 133 of 0.45 mm. (D) is a simulation result of a piezoelectric vibrating piece having a width WR of the connecting portion 133 of 0.55 mm. It is the graph which showed distribution of the stress value of the X-axis direction of a piezoelectric vibrating piece. 6 is a graph showing a relationship between a length LS in the X-axis direction of a vibrating portion of a piezoelectric vibrating piece and a length LR in the X-axis direction of a connecting portion. 5 is a graph showing a relationship between a width WS of a vibrating portion of a piezoelectric vibrating piece in a Z′-axis direction and a width WR of a connecting portion in a Z′-axis direction. 6 is a graph showing a relationship between a length LS in the X-axis direction of a vibrating portion of a piezoelectric vibrating piece and a length LA in the X-axis direction of a frame portion. 4 is a graph showing the relationship between the width WS of the vibrating portion of the piezoelectric vibrating piece in the Z′-axis direction and the width WA of the frame portion in the Z′-axis direction. FIG. 6A is a plan view of the piezoelectric vibrating piece 230. (B) is CC sectional drawing of Fig.10 (a).

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. It should be noted that the scope of the present invention is not limited to these forms unless otherwise specified in the following description.

(First embodiment)
<Configuration of Piezoelectric Device 100>
FIG. 1 is an exploded perspective view of the piezoelectric device 100. The piezoelectric device 100 includes a lid plate 110, a base plate 120, and a piezoelectric vibrating piece 130. As the piezoelectric vibrating piece 130, for example, an AT-cut crystal vibrating piece is used. The AT-cut quartz crystal resonator element has a principal surface (YZ plane) inclined with respect to the Y axis of the crystal axis (XYZ) by 35 degrees 15 minutes from the Z axis in the Y axis direction around the X axis. In the following description, the new axes tilted with respect to the axial direction of the AT-cut quartz crystal vibrating piece are used as the Y ′ axis and the Z ′ axis. That is, in the piezoelectric device 100, the long side direction of the piezoelectric device 100 is described as the X-axis direction, the height direction of the piezoelectric device 100 is defined as the Y′-axis direction, and the direction perpendicular to the X and Y′-axis directions is described as the Z′-axis direction. .

  The piezoelectric vibrating piece 130 includes a vibrating part 131 that vibrates at a predetermined vibration frequency, a frame part 132 that surrounds the vibrating part 131, and a connecting part 133 that connects the vibrating part 131 and the frame part 132. The excitation electrode 134 is formed on the surface on the + Y′-axis side and the surface on the −Y′-axis side of the vibration unit 131. An extraction electrode 135 is extracted from each excitation electrode 134 to the frame portion 132 through the connecting portion 133.

  The base plate 120 is disposed on the −Y′-axis side of the piezoelectric vibrating piece 130. The base plate 120 is formed in a rectangular shape having a long side in the X-axis direction and a short side in the Z′-axis direction. A pair of external electrodes 124 is formed on the surface at the −Y′-axis side of the base plate 120. The external device 124 is fixed to and electrically connected to a printed circuit board or the like via solder, whereby the piezoelectric device 100 is mounted on the printed circuit board or the like. Further, castellations 126 are formed on the side surfaces of the four corners of the base plate 120, and castellation electrodes 125 are formed on the castellations 126. A recess 121 is formed on the surface of the base plate 120 on the + Y′-axis side, and a bonding surface 122 is formed around the recess 121. In addition, connection electrodes 123 are formed around the castellations 126 at the four corners of the joint surface 122. The connection electrode 123 is electrically connected to the external electrode 124 via a castellation electrode 125 formed on the castellation 126. The base plate 120 is bonded to the surface at the −Y′-axis side of the frame portion 132 of the piezoelectric vibrating piece 130 via the sealing material 141 (see FIG. 2) at the bonding surface 122. Further, the connection electrode 123 and the extraction electrode 135 of the piezoelectric vibrating piece 130 are electrically connected.

  The lid plate 110 is disposed on the + Y′-axis side of the piezoelectric vibrating piece 130. A concave portion 111 is formed on the surface of the lid plate 110 on the −Y′-axis side, and a bonding surface 112 is formed around the concave portion 111. The lid plate 110 is bonded to the surface on the + Y′-axis side of the frame portion 132 of the piezoelectric vibrating piece 130 via the sealing material 141 (see FIG. 2) at the bonding surface 112.

  FIG. 2A is a cross-sectional view taken along the line AA in FIG. In the piezoelectric device 100, the bonding surface 112 of the lid plate 110 is bonded to the surface on the + Y′-axis side of the frame portion 132 of the piezoelectric vibrating piece 130 via the sealing material 141, and the surface on the −Y′-axis side of the frame portion 132. The joining surface 122 of the base plate 120 is joined via the sealing material 141. When the piezoelectric vibrating piece 130 and the base plate 120 are bonded, the connection formed on the extraction electrode 135 formed on the surface at the −Y′-axis side of the frame portion 132 and the bonding surface 122 of the base plate 120. The electrode 123 is electrically connected. As a result, the excitation electrodes 134 formed on the + Y′-axis side and the −Y′-axis side of the mesa region 131a are electrically connected to the external electrode 124 via the extraction electrode 135, the connection electrode 123, and the castellation electrode 125. Connected.

  FIG. 2B is a plan view of the piezoelectric vibrating piece 130. The piezoelectric vibrating piece 130 includes a vibrating portion 131 that is formed in a rectangular shape, a frame portion 132 that surrounds the vibrating portion 131, and a single connecting portion 133 that connects the vibrating portion 131 and the frame portion 132. Yes. The vibration unit 131 includes a first side 138a that is a side on the −X axis side of the vibration unit 131, and a second side 138b that is a side on the + Z ′ axis side and the −Z ′ axis side of the vibration unit 131. ing. The frame portion 132 is formed of a first frame 132a extending in the Z′-axis direction and a second frame 132b extending in the X-axis direction. The first frame 132a is disposed on the + X axis side and the −X axis side of the vibration unit 131, and the second frame 132b is disposed on the + Z ′ axis side and the −Z ′ axis side of the vibration unit 131. The connecting portion 133 is connected to the center of the first side 138a of the vibration portion 131, and extends in the −X axis direction therefrom and is connected to the center of the first frame 132a on the −X axis side. Further, a region other than the coupling portion 133 between the vibrating portion 131 and the frame portion 132 is a through hole 136 that penetrates the piezoelectric vibrating piece 130 in the Y′-axis direction. The vibration part 131 includes a mesa region 131a where the excitation electrode 134 is formed, a peripheral region 131b formed around the mesa region 131a, and a connection region 131c that is directly connected to the connection part 133. . A peripheral region 131b is formed between the mesa region 131a and the connection region 131c, and the mesa region 131a and the connection region 131c are not in contact with each other. From the excitation electrode 134 formed on the surface on the + Y′-axis side of the mesa region 131a, the peripheral region 131b, the connecting region 131c, the surface on the + Y′-axis side of the connecting portion 133, and the side surface on the + Z′-axis side of the connecting portion 133 The extraction electrode 135 is led out to the corner on the −Z ′ axis side on the −X ′ side of the −Y ′ axis side surface of the frame portion 132 through the surface on the −Y ′ axis side of the coupling portion 133 and 133a. Yes. Further, from the excitation electrode 134 (see FIG. 2A) formed on the surface of the mesa region 131a on the −Y′-axis side, the peripheral region 131b, the connection region 131c, and the connection portion 133 on the −Y′-axis side. The extraction electrode 135 is extracted to the frame portion 132 through the surface of the frame portion 132, and the extraction electrode 135 further extends on the −Y′-axis side surface of the frame portion 132 in the −Z′-axis direction and the + X-axis direction. It is drawn out to the corner of the surface on the Y′-axis side on the + Z-axis side on the + X-axis side. Since the extraction electrode 135 extracted from the excitation electrode 134 formed on the surface on the −Y′-axis side is extracted to the + X-axis side of the frame portion 132, the excitation formed on the surface on the + Y′-axis side. The formation distance is longer than that of the extraction electrode 135 extracted from the electrode 134.

  FIG. 3A is a plan view of the piezoelectric vibrating piece 130 on which no electrode is formed. The length of the first side 138a of the vibration part 131 is the length WS, and the second side 138b is formed to the length LS. Further, the entire length of the first frame 132a of the frame portion 132 of the piezoelectric vibrating piece 130 is the length WA, and the entire length of the second frame 132b of the frame portion 132 is the length of the X-axis direction. LA, the width in the Z′-axis direction of the connecting portion 133 is the width WR, and the length of the connecting portion 133 in the X-axis direction is the length LR.

  FIG.3 (b) is BB sectional drawing of FIG.2 (b). The piezoelectric vibrating piece 130 has a thickness T1 in the Y′-axis direction of the frame portion 132, and a thickness T2 in the Y′-axis direction of the connecting portion 133, the connecting region 131c of the vibrating portion 131, and the mesa region 131a. The thickness in the Y′-axis direction of the peripheral region 131b of the vibration part 131 is formed to a thickness T3. That is, the connecting portion 133 and the connecting region 131c are directly connected to each other with a thickness T2. In the piezoelectric vibrating piece 130, the thickness T1 is formed to be thicker than the thickness T2 and the thickness T3, and the thickness T2 is formed to be thicker than the thickness T3.

<< Measurement of Stress Characteristics of Piezoelectric Vibrating Piece >>
Obtain the appropriate dimensions of the piezoelectric vibrating piece that can suppress the stress applied to the vibrating part of the piezoelectric vibrating piece by predicting the stress applied to the piezoelectric vibrating piece by simulation and measuring the characteristics of the piezoelectric vibrating piece by fabricating a piezoelectric device. An experiment was conducted. Below, the simulation result of a piezoelectric vibrating piece and the measurement result of the characteristic of a piezoelectric vibrating piece are demonstrated.

<Simulation results>
In a state where the piezoelectric device is mounted on the printed board, a simulation was performed to obtain the stress applied to the piezoelectric vibrating piece when the printed board was bent. The simulation results will be described with reference to FIGS. In the following simulation, the dimensions of the piezoelectric vibrating piece are as follows: length LA is 2.0 mm, length WA is 1.6 mm, length LS is 1.4 mm, length WS is 1.375 mm, and length LR is The difference in stress applied to the piezoelectric vibrating piece when the width WR of the connecting portion 133 is changed to 0.15 mm is examined.

  FIG. 4A shows a simulation result of the piezoelectric vibrating piece in which the width WR of the connecting portion 133 is 0.32 mm. In FIG. 4A, the simulation result is shown in a plan view of the vibrating part 131 and the connecting part 133. In the simulation results, the gray area indicates that almost no stress in the X-axis direction is applied to the piezoelectric vibrating piece. As the color increases from gray to black, the tensile stress in the X-axis direction of the piezoelectric vibrating piece increases. The state is shown in which the compressive stress in the X-axis direction of the piezoelectric vibrating piece becomes stronger as the color becomes lighter from gray to white. In the piezoelectric vibrating piece shown in FIG. 4A, it can be seen that stress is applied to a region in the vicinity of the connecting portion 133 of the vibrating portion 131 connected thereto. Further, since the mesa region 131a is a substantially gray region, it can be seen that the mesa region 131a is hardly stressed.

  FIG. 4B shows a simulation result of the piezoelectric vibrating piece in which the width WR of the connecting portion 133 is 0.35 mm. In the piezoelectric vibrating piece shown in FIG. 4B, the color of the connecting portion 133 near the + Z′-axis side, the −Z′-axis side, and the center is darker or lighter than gray, and stress is applied to these regions. It turns out that it takes. Further, since the mesa region 131a is a substantially gray region, it can be seen that the mesa region 131a is hardly stressed.

  FIG. 4C shows a simulation result of the piezoelectric vibrating piece in which the width WR of the connecting portion 133 is 0.45 mm. In the piezoelectric vibrating piece shown in FIG. 4C, the region between the connecting portion 133 and the mesa region 131a is darker than gray, and it can be seen that strong stress is applied to this region. In the mesa region 131a, a color lighter than gray is seen, so that some stress is also applied to the mesa region 131a.

  FIG. 4D shows a simulation result of the piezoelectric vibrating piece in which the width WR of the connecting portion 133 is 0.55 mm. In the piezoelectric vibrating piece shown in FIG. 4D, it can be seen that strong stress is applied between the connecting portion 133 and the mesa region 131 a and on the −X axis side of the side parallel to the X axis of the vibrating portion 131. Since the mesa region 131a is darker and lighter than gray, the mesa region 131a is also somewhat stressed.

  FIG. 5 is a graph showing the distribution of stress values in the X-axis direction of the piezoelectric vibrating piece. The horizontal axis of the graph indicates the position on the straight line 142 (see FIG. 4A) passing through the center of the connecting portion 133 of the piezoelectric vibrating piece and parallel to the X axis. Further, with reference to FIG. 4A, FIG. 5 shows a position where the end on the −X axis side of the frame portion 132 on the −X axis side is 0 mm, and the position advances in the + X axis direction therefrom. Yes. The vertical axis in FIG. 5 indicates the stress applied in the X-axis direction of the piezoelectric vibrating piece. When the stress is a positive value, a tensile stress is applied, and when the stress is a negative value, a compressive stress is applied. In FIG. 5, a black diamond indicates a piezoelectric vibrating piece having a width WR of 0.32 mm, a white triangle indicates a piezoelectric vibrating piece having a width WR of 0.35 mm, and a white circle has a width WR of 0. A 45 mm piezoelectric vibrating piece is shown, and a black square represents a piezoelectric vibrating piece having a width WR of 0.55 mm.

  The piezoelectric vibrating piece having a width WR of 0.55 mm has a maximum stress value of about 0.19 MPa when it advances 0.67 mm in the X-axis direction. The piezoelectric vibrating piece having a width WR of 0.45 mm has a maximum stress value of about 0.16 MPa when it advances 0.48 mm in the X-axis direction. A piezoelectric vibrating piece having a width WR of 0.35 mm has a maximum stress value of about 0.09 MPa when it advances 0.40 mm in the X-axis direction. The piezoelectric vibrating piece having a width WR of 0.32 mm has a maximum stress value of about 0.07 MPa when it advances 0.48 mm in the X-axis direction.

  The stress applied to the piezoelectric vibrating piece is preferably 0.1 MPa or less in consideration of the change in the vibration frequency of the piezoelectric vibrating piece. According to FIG. 5, in the piezoelectric vibrating piece having the width WR of 0.55 mm and 0.45 mm, the maximum stress value applied to the piezoelectric vibrating piece exceeds 0.1 MPa. On the other hand, it can be seen that the piezoelectric vibrating reeds having the width WR of 0.35 mm and 0.32 mm are preferable because the maximum stress applied to the piezoelectric vibrating reed is smaller than 0.1 MPa. That is, the width WR of the piezoelectric vibrating piece is 0.40 mm or less which is an intermediate value between 0.45 mm where the maximum stress value exceeds 0.1 MPa and 0.35 mm where the maximum stress value is 0.1 MPa or less. Is considered preferable.

<Measurement result of characteristics of piezoelectric vibrating piece>
A piezoelectric device was manufactured, and the piezoelectric device was mounted on a printed board, and characteristics such as a vibration frequency and a crystal impedance (CI) value of the piezoelectric vibrating piece were measured. Based on the measurement result of this characteristic, a preferable dimension of the piezoelectric vibrating piece is obtained. In the following description, the deterioration of the characteristics of the piezoelectric vibrating piece means that the vibration frequency of the piezoelectric vibrating piece fluctuates or the CI value increases. The manufactured piezoelectric device uses a piezoelectric vibrating piece having a width WR of 0.4 or less, which is considered preferable based on the result of simulation. Hereinafter, the measurement results of the characteristics of the piezoelectric vibrating piece will be described with reference to FIGS.

  FIG. 6 is a graph showing the relationship between the length LS of the piezoelectric vibrating piece 131 in the X-axis direction and the length LR of the connecting portion 133 in the X-axis direction. In FIG. 6, the dimensions of the piezoelectric vibrating piece are as follows: length LA is 2.0 mm, length WA is 1.6 mm, length WS is 1.375 mm, length LR is 0.15 mm, and width WR is 0.32 mm. Piezoelectric vibrating piece AS1 and piezoelectric vibrating piece AS2 having a length LA of 2.0 mm, a length WA of 1.6 mm, a length WS of 0.872 mm, a length LR of 0.2 mm, and a width WR of 0.37 mm , The characteristics of the piezoelectric vibrating piece are measured by changing the length LS of the vibrating portion 131. In the graph of FIG. 6, the length LS is set on the horizontal axis, and the length LR is set on the vertical axis. In FIG. 6, black diamonds and black circles indicate actual measurement values, and black triangles indicate average values calculated based on the actual measurement values of black diamonds.

In the piezoelectric vibrating piece AS1, the characteristics of the piezoelectric vibrating piece are examined when the length LS of the vibrating portion 131 is 0.99 mm (point AS1a in FIG. 6) and 1.105 mm (point AS1b in FIG. 6). Good characteristics are obtained in the resonator element. Therefore, it is considered that the piezoelectric vibrating piece AS1 has preferable characteristics when the length LS of the vibrating portion 131 is 1.0475 mm (point AS1c in FIG. 6), which is an intermediate value between the two points. Further, in the piezoelectric vibrating piece AS2, the characteristics of the piezoelectric vibrating piece are investigated when the length LS of the vibrating portion 131 is 1.375 mm (point AS2a in FIG. 6) and 1.4 mm (point AS2b in FIG. 6). Good characteristics are obtained in the piezoelectric vibrating piece. Therefore, it is considered that the piezoelectric vibrating piece AS2 has preferable characteristics when the length LS of the vibrating portion 131 is 1.3875 mm (point AS2c in FIG. 6), which is an intermediate value between the two points. That is, it is considered that the piezoelectric vibrating piece preferably satisfies the relationship in which the length LR and the length LS are represented by the straight line LN1 passing through the points AS1c and AS2c in FIG. The straight line LN1 is expressed by the following formula 1.
LR = 0.1471 × LS−0.004 Equation 1

  On the other hand, regarding the piezoelectric vibrating piece AS1, when the length LS is 1.0475 mm (point AS1c in FIG. 6) and the value of the length LR is increased from 1.5 mm, the value of the length LR is 0.19 mm (FIG. The piezoelectric vibrating piece was damaged in the drop test of the piezoelectric device when the point 6 (AS1d) was reached. Similarly, regarding the piezoelectric vibrating piece AS2, when the length LS is 1.3875 mm (point AS2c in FIG. 6) and the value of the length LR is increased from 0.2 mm, the value of the length LR is 0.25 mm ( When the point AS2d) in FIG. 6 was reached, the piezoelectric vibrating piece was damaged in the drop test of the piezoelectric device. That is, the length LR of the piezoelectric vibrating piece is preferably smaller than the length LR derived from the straight line LN1a passing through the points AS1d and AS2d. The length LR derived from the straight line LN1a is approximately + 25% of the length LR derived from the straight line LN1.

  In addition, a substrate bending test was performed on the piezoelectric vibrating piece. The board bending test is a test in which the printed circuit board is bent in a state where the piezoelectric device is mounted on the printed board, and the change in the vibration frequency of the piezoelectric vibrating piece is examined. Regarding the piezoelectric vibrating piece AS1, when the length LS is 1.0475 mm (point AS1c in FIG. 6) and the value of the length LR is decreased from 1.5 mm, the value of the length LR is 1.125 mm (in FIG. 6). When the point AS1e) was reached, the vibration frequency of the piezoelectric vibrating piece changed greatly. Similarly, regarding the piezoelectric vibrating piece AS2, when the length LS is 1.3875 mm (point AS2c in FIG. 6) and the value of the length LR is decreased from 0.2 mm, the value of the length LR is 0.15 mm ( When the point AS2e) in FIG. 6 was reached, the vibration frequency of the piezoelectric vibrating piece changed greatly. The change in the vibration frequency of the piezoelectric vibrating piece is considered to be due to the fact that the stress transmitted from the printed circuit board to the mesa region 131a via the frame portion 132 is increased by shortening the length LR of the connecting portion 133. That is, the piezoelectric vibrating piece is preferably larger than the length LR derived from the straight line LN1b passing through the points AS1e and AS2e. The length LR derived from the straight line LN1b is about −25% of the length LR derived from the straight line LN1.

As described above, the relationship between the length LS and the length LR of the piezoelectric vibrating piece is desirably smaller than + 25% and larger than −25% of the length LR derived from the straight line LN1. That is, it is desirable that the relationship between the length LS and the length LR of the piezoelectric vibrating piece satisfies the following formula 2.
(0.1471 × LS−0.004) × 0.75 <LR <(0.1471 × LS−0.004) × 1.25 (2)

  FIG. 7 is a graph showing the relationship between the length WS in the Z′-axis direction of the vibrating portion 131 of the piezoelectric vibrating piece and the width WR in the Z′-axis direction of the connecting portion 133. In FIG. 7, the piezoelectric vibrating piece has a length LA of 2.0 mm, a length WA of 1.6 mm, a length LS of 0.9 mm, a length LR of 0.2 mm, and a width WR of 0.35 mm. Piezoelectric vibrating piece AS3, length LA is 1.6mm, length WA is 1.2mm, length LS is 0.668mm, length LR is 0.14mm, width WR is 0.25mm, and piezoelectric vibrating piece AS4. , The characteristics of the piezoelectric vibrating piece are measured by changing the length WS of the vibrating portion 131. In the graph of FIG. 7, the length WS is set on the horizontal axis and the width WR is set on the vertical axis. In FIG. 7, black diamonds and black circles indicate actual measurement values, and black triangles indicate average values calculated based on the actual measurement values of black diamonds.

In the piezoelectric vibrating piece AS3, when the length WS of the vibrating portion 131 is 0.525 mm (point AS3a in FIG. 7) and 0.668 mm (point AS3b in FIG. 7), the characteristics of the piezoelectric vibrating piece are investigated. Good characteristics are obtained in the resonator element. Therefore, it is considered that the piezoelectric vibrating piece AS3 has preferable characteristics when the length WS of the vibrating portion 131 is 0.5965 mm (point AS3c in FIG. 7), which is an intermediate value between the two points. Further, in the piezoelectric vibrating piece AS4, the characteristics of the piezoelectric vibrating piece are investigated when the length WS of the vibrating portion 131 is 0.872 mm (point AS4a in FIG. 7) and 0.9 mm (point AS4b in FIG. 7). Good characteristics are obtained in the piezoelectric vibrating piece. Therefore, it is considered that the piezoelectric vibrating piece AS4 has preferable characteristics when the length WS of the vibrating portion 131 is 0.886 mm (point AS4c in FIG. 7), which is an intermediate value between the two points. That is, it is considered that the piezoelectric vibrating piece preferably satisfies the relationship in which the width WR and the length WS are represented by the straight line LN2 passing through the points AS3c and AS4c in FIG. The straight line LN2 is expressed by the following formula 3.
WR = 0.3545 × WS + 0.044 Formula 3

  On the other hand, regarding the piezoelectric vibrating piece AS3, when the length WS is 0.5965 mm (point AS3c in FIG. 7) and the value of the width WR is increased from 0.25 mm, the value of the width WR is 0.3 mm (in FIG. 7). When the point becomes AS3d), the vibration frequency of the piezoelectric vibrating piece greatly changed in the substrate bending test. Similarly, regarding the piezoelectric vibrating piece AS4, when the length WS is 0.886 mm (point AS4c in FIG. 7) and the value of the width WR is increased from 0.35 mm, the value of the width WR is 0.42 mm (FIG. 7). When the point becomes AS4d), the vibration frequency of the piezoelectric vibrating piece greatly changed in the substrate bending test. The change in the vibration frequency of the piezoelectric vibrating piece is considered to be due to an increase in the stress transmitted from the printed circuit board to the mesa region 131a through the frame portion 132 by increasing the width WR of the connecting portion 133. That is, the width WR of the piezoelectric vibrating piece is preferably smaller than the width WR derived from the straight line LN2a passing through the points AS3d and AS4d. The width WR derived from the straight line LN2a is approximately + 20% of the width WR derived from the straight line LN2.

  Further, regarding the piezoelectric vibrating piece AS3, when the length WS is 0.5965 mm (point AS3c in FIG. 7) and the value of the width WR is decreased from 0.25 mm, the value of the width WR is 0.2 mm (in FIG. 7). When the point AS3e) was reached, the piezoelectric vibrating piece was damaged in the drop test of the piezoelectric device. Similarly, regarding the piezoelectric vibrating piece AS4, when the length WS is 0.886 mm (point AS4c in FIG. 7) and the value of the width WR is decreased from 0.35 mm, the value of the width WR is 0.28 mm (FIG. 7). When the point becomes AS4e), the piezoelectric vibrating piece was damaged in the drop test of the piezoelectric device. That is, the piezoelectric vibrating piece is preferably larger than the width WR derived from the straight line LN2b passing through the points AS3e and AS4e. The width WR derived from the straight line LN2b is about −20% of the width WR derived from the straight line LN2.

From the above, it is desirable that the relationship between the length WS and the width WR of the piezoelectric vibrating piece is smaller than + 20% and larger than −20% of the width WR derived from the straight line LN2. That is, it is desirable that the relationship between the length WS and the width WR of the piezoelectric vibrating piece satisfies the following formula 4.
(0.3545 × WS + 0.044) × 0.8 <WR <(0.3545 × WS + 0.044) × 1.2 Formula 4

  FIG. 8 is a graph showing the relationship between the length LS of the vibrating portion 131 of the piezoelectric vibrating piece 131 in the X-axis direction and the length LA of the frame portion 132 in the X-axis direction. In FIG. 8, the dimensions of the piezoelectric vibrating piece are as follows: length LA is 2.0 mm, length WA is 1.6 mm, length WS is 1.375 mm, length LR is 0.15 mm, and width WR is 0.32 mm. A piezoelectric vibrating piece AS5 having a length LA of 1.6 mm, a length WA of 1.2 mm, a length WS of 0.99 mm, a length LR of 0.12 mm, and a width WR of 0.22 mm In AS6, the characteristic of the piezoelectric vibrating piece is measured by changing the length LS of the vibrating part 131. In the graph of FIG. 8, a length LA is set on the horizontal axis, and a length LS is set on the vertical axis. In FIG. 8, black diamonds and black circles indicate actual measurement values, and black triangles indicate average values calculated based on the actual measurement values of black diamonds.

In the piezoelectric vibrating piece AS5, when the length LS of the vibrating portion 131 is 1.105 mm (point AS5a in FIG. 8) and 0.99 mm (point AS5b in FIG. 8), the characteristics of the piezoelectric vibrating piece are investigated, and both piezoelectric elements are examined. Good characteristics are obtained in the resonator element. Therefore, it is considered that the piezoelectric vibrating piece AS5 has preferable characteristics when the length LS of the vibrating portion 131 is 1.0475 mm (point AS5c in FIG. 8), which is an intermediate value between the two points. In the piezoelectric vibrating piece AS6, the characteristics of the piezoelectric vibrating piece were investigated when the length LS of the vibrating portion 131 was 1.4 mm (point AS6a in FIG. 8) and 1.375 mm (point AS6b in FIG. 8). Good characteristics are obtained in the piezoelectric vibrating piece. Therefore, it is considered that the piezoelectric vibrating piece AS6 has preferable characteristics when the length LS of the vibrating portion 131 is 1.3875 mm (point AS6c in FIG. 8), which is an intermediate value between the two points. That is, it is considered that the piezoelectric vibrating piece preferably satisfies the relationship in which the length LA and the length LS are represented by the straight line LN3 passing through the points AS5c and AS6c in FIG. The straight line LN3 is expressed by the following formula 5.
LS = 0.85 × LA−0.3125 (5)

  On the other hand, regarding the piezoelectric vibrating piece AS5, when the value of the length LS is increased from 1.0475 mm (point AS5c in FIG. 8), the through hole is obtained when the value of the length LS becomes larger than 1.1104 mm (point AS5d in FIG. 8). Since the width of 136 (see FIG. 2B) is narrowed, it becomes difficult to form the through hole 136 by wet etching. Similarly, regarding the piezoelectric vibrating piece AS6, when the value of the length LS is increased from 1.3875 mm (point AS6c in FIG. 8), the penetration occurs when the value of the length LS becomes larger than 1.4708 mm (point AS6d in FIG. 8). Since the width of the hole 136 (see FIG. 2B) is narrowed, it is difficult to form the through hole 136 by wet etching. That is, the length LS of the piezoelectric vibrating piece is preferably smaller than the length LS derived from the straight line LN3a passing through the points AS5d and AS6d. The length LS derived from the straight line LN3a is about + 6% of the length LS derived from the straight line LN3.

  Further, regarding the piezoelectric vibrating piece AS5, when the value of the length LS is decreased from 1.0475 mm (point AS5c in FIG. 8), the value of the length LS becomes smaller than 0.9846 mm (point AS5e in FIG. 8). In other words, the CI value in a range preferable as a product is exceeded. Similarly, regarding the piezoelectric vibrating piece AS6, when the value of the length LS is decreased from 1.3875 mm (point AS6c in FIG. 8), the value of the length LS becomes smaller than 1.3042 mm (point AS6e in FIG. 8). In other words, the CI value in a range preferable as a product is exceeded. That is, the length LS of the piezoelectric vibrating piece is preferably larger than the length LS derived from the straight line LN3b passing through the point AS5d and the point AS6d. The length LS derived from the straight line LN3b is about −6% of the length LS derived from the straight line LN3.

From the above, it is desirable that the relationship between the length LS and the length LA of the piezoelectric vibrating piece is smaller than + 6% and larger than −6% of the length LS derived from the straight line LN3. That is, it is desirable that the relationship between the length LS and the length LA of the piezoelectric vibrating piece satisfies the following Expression 6.
(0.85 × LA−0.3125) × 0.94 <LS <(0.85 × LA−0.3125) × 1.06 Equation 6

  FIG. 9 is a graph showing the relationship between the length WS of the vibrating portion 131 of the piezoelectric vibrating piece 131 in the Z′-axis direction and the length WA of the frame portion 132 in the Z′-axis direction. In FIG. 9, the dimensions of the piezoelectric vibrating piece are as follows: length LA is 2.0 mm, length WA is 1.6 mm, length LS is 0.9 mm, length LR is 0.2 mm, and width WR is 0.37 mm. A piezoelectric vibrating piece AS7 having a length LA of 1.6 mm, a length WA of 1.2 mm, a length LS of 0.668 mm, a length LR of 0.14 mm, and a width WR of 0.24 In AS8, the characteristic of the piezoelectric vibrating piece is measured by changing the length WS of the vibrating part 131. In the graph of FIG. 9, the length WA is set on the horizontal axis, and the length WS is set on the vertical axis. In FIG. 9, black diamonds and white circles indicate actual measurement values, and black triangles indicate average values calculated based on the actual measurement values of black diamonds.

In the piezoelectric vibrating piece AS7, when the length WS of the vibrating portion 131 is 0.668 mm (point AS7a in FIG. 9) and 0.525 mm (point AS7b in FIG. 9), the characteristics of the piezoelectric vibrating piece are investigated. Good characteristics are obtained in the resonator element. Therefore, it is considered that the piezoelectric vibrating piece AS7 has preferable characteristics when the length WS of the vibrating portion 131 is 0.597 mm (point AS7c in FIG. 9), which is an intermediate value between the two points. Further, in the piezoelectric vibrating piece AS8, the characteristics of the piezoelectric vibrating piece were investigated when the length WS of the vibrating portion 131 was 0.9 mm (point AS8a in FIG. 9) and 0.872 mm (point AS8b in FIG. 9). Good characteristics are obtained in the piezoelectric vibrating piece. Therefore, it is considered that the piezoelectric vibrating piece AS8 has preferable characteristics when the length WS of the vibrating portion 131 is 0.886 mm (point AS8c in FIG. 9), which is an intermediate value between the two points. That is, it is considered that the piezoelectric vibrating piece preferably satisfies the relationship in which the length WA and the length WS are represented by a straight line LN4 passing through the points AS7c and AS8c in FIG. The straight line LN4 is expressed by the following formula 7.
WS = 0.7237 × WA−0.272 Expression 7

  On the other hand, regarding the piezoelectric vibrating piece AS7, when the value of the length WS is increased from 0.597 mm (point AS7c in FIG. 9), the through hole is obtained when the value of the length WS becomes larger than 0.6687 mm (point AS7d in FIG. 9). Since the width of 136 (see FIG. 2B) is narrowed, it becomes difficult to form the through hole 136 by wet etching. Similarly, regarding the piezoelectric vibrating piece AS8, when the value of the length WS is increased from 0.886 mm (point AS8c in FIG. 9), the penetration occurs when the value of the length WS becomes larger than 0.9924 mm (point AS8d in FIG. 9). Since the width of the hole 136 (see FIG. 2B) is narrowed, it is difficult to form the through hole 136 by wet etching. That is, the length WS of the piezoelectric vibrating piece is preferably smaller than the length WS derived from the straight line LN4a passing through the point AS7d and the point AS8d. The length WS derived from the straight line LN4a is approximately + 12% of the length WS derived from the straight line LN4.

  Further, regarding the piezoelectric vibrating piece AS7, when the value of the length WS is decreased from 0.597 mm (point AS7c in FIG. 9), the value of the length WS becomes smaller than 0.525 mm (point AS7e in FIG. 9). In other words, the CI value in a range preferable as a product is exceeded. Similarly, regarding the piezoelectric vibrating piece AS8, when the value of the length WS is decreased from 0.886 mm (point AS8c in FIG. 9), the value of the length WS becomes smaller than 0.7796 mm (point AS8e in FIG. 9). In some cases, the CI value in a preferable range as a product is exceeded. That is, the length WS of the piezoelectric vibrating piece is preferably larger than the length WS derived from the straight line LN4b passing through the points AS7e and AS8e. The length WS derived from the straight line LN4b is about -12% of the length WS derived from the straight line LN4.

As described above, the relationship between the length WS and the length WA of the piezoelectric vibrating piece is desirably smaller than + 12% and larger than −12% of the length WS derived from the straight line LN4. That is, it is desirable that the relationship between the length WS and the length WA of the piezoelectric vibrating piece satisfies the following Expression 8.
(0.7237 × WA−0.272) × 0.88 <WS <(0.7237 × WA−0.272) × 1.12 Expression 8

(Second Embodiment)
The piezoelectric vibrating piece may be formed such that the thickness of the connecting portion is the same as that of the peripheral area of the vibrating portion. Hereinafter, the piezoelectric vibrating piece 230 in which the thickness of the connecting portion is the same as that of the peripheral area of the vibrating portion will be described. Moreover, in the following description, the same part as 1st Embodiment is represented using the same code | symbol as 1st Embodiment, and the description is abbreviate | omitted.

<Configuration of Piezoelectric Vibrating Piece 230>
FIG. 10A is a plan view of the piezoelectric vibrating piece 230. The piezoelectric vibrating piece 230 vibrates at a predetermined vibration frequency and is formed in a rectangular shape, a frame portion 132 that surrounds the vibrating portion 231, and one connecting portion that connects the vibrating portion 231 and the frame portion 132. 233. A region other than the connecting portion 233 between the vibrating portion 231 and the frame portion 132 is a through hole 136 that penetrates the piezoelectric vibrating piece 230 in the Y′-axis direction. The vibration part 231 is formed by a mesa region 231a where the excitation electrode 134 is formed, and a peripheral region 231b that is formed around the mesa region 231a and is thinner in the Y′-axis direction than the mesa region 231a. The vibration unit 131 includes a first side 138a that is a short side of the vibration unit 131 and a side on the −X axis side of the vibration unit 131, a long side of the vibration unit 131 that is the + Z′-axis side of the vibration unit 131, and −Z. And a second side 138b which is a side on the axis side. The frame portion 132 is formed by a first frame 132a extending in the Z′-axis direction and a second frame 132b extending in the X-axis direction. The connecting portion 233 is connected to the center of the first side 138a of the vibrating portion 231, and extends from the connecting portion 233 in the −X axis direction to be connected to the center of the first frame 132a on the −X axis side. The excitation electrode 134 formed in the mesa region 231a is formed on the surface on the + Y′-axis side and the surface on the −Y′-axis side of the mesa region 231a. From the excitation electrode 134 formed on the surface on the + Y′-axis side of the mesa region 231a, the peripheral region 231b, the surface on the + Y′-axis side of the connecting portion 233, the side surface 233a on the + Z′-axis side of the connecting portion 233, and the connection The extraction electrode 135 is led out through the surface on the −Y′-axis side of the portion 233 to the corner on the + Z′-axis side on the −X-axis side of the surface on the −Y′-axis side of the frame portion 132. Further, from the excitation electrode 134 (see FIG. 10B) formed on the surface on the −Y′-axis side of the mesa region 231a, the peripheral region 231b and the surface on the −Y′-axis side of the connecting portion 233 are interposed. The lead electrode 135 is drawn out to the frame portion 132, and the lead electrode 135 further extends on the −Y′-axis side surface of the frame portion 132 in the −Z′-axis direction and the + X-axis direction to the −Y′-axis side of the frame portion 132. To the corner on the −Z′-axis side on the + X-axis side. Since the extraction electrode 135 extracted from the excitation electrode 134 formed on the surface on the −Y′-axis side is extracted to the + X-axis side of the frame portion 132, the excitation formed on the surface on the + Y′-axis side. The formation distance is longer than that of the extraction electrode 135 extracted from the electrode 134.

  FIG.10 (b) is CC sectional drawing of Fig.10 (a). The piezoelectric vibrating piece 230 has a thickness T1 in the Y′-axis direction of the frame portion 132, a thickness T2 in the Y′-axis direction of the mesa region 231a, a peripheral region 231b of the connecting portion 233 and the vibrating portion 231. The thickness in the Y′-axis direction is formed to a thickness T3. That is, the connecting portion 233 and the peripheral region 231b are directly connected to each other with a thickness T3. In the piezoelectric vibrating piece 230, the thickness T1 is formed to be thicker than the thickness T2 and the thickness T3, and the thickness T2 is formed to be thicker than the thickness T3.

  As described above, the optimal embodiment of the present invention has been described in detail. However, as will be apparent to those skilled in the art, the present invention can be implemented with various modifications and variations within the technical scope thereof.

  For example, in the above-described embodiment, the case where the piezoelectric vibrating piece is an AT-cut quartz vibrating piece is shown. However, the same applies to a BT cut that vibrates in the thickness-slip mode or a tuning-fork type quartz vibrating piece. Applicable. Further, the piezoelectric vibrating piece can be basically applied not only to a crystal material but also to a piezoelectric material including lithium tantalate, lithium niobate, or piezoelectric ceramic.

DESCRIPTION OF SYMBOLS 100 ... Piezoelectric device 110 ... Lid board 111, 121 ... Recessed part 112 ... Bonding surface 120 ... Base board 122 ... Bonding surface 123 ... Connection electrode 124 ... External electrode 125 ... Castellation electrode 126 ... Castellation 130, 230 ... Piezoelectric vibrating piece 131 231 ... Vibration part 131a, 231a ... Mesa area 131b, 231b ... Peripheral area 131c ... Connection area 132 ... Frame part 132a ... 1st frame 132b ... 2nd frame 133, 233 ... Connection part 133a ... + Z 'axis of connection part 133 Side surface 134 ... Excitation electrode 135 ... Extraction electrode 136 ... Through hole 138a ... First side 138b ... Second side 141 ... Sealing material

Claims (4)

A quadrangular vibrating portion having a first side having a length WS extending in a first direction and a second side having a length LS extending in a second direction orthogonal to the first direction;
A frame portion having a first frame having a length WA extending in the first direction and a second frame having a length LA extending in the second direction and surrounding the vibrating portion;
The first side of the vibration part and the first frame of the frame part are connected at the center of the first side and the first frame with a width WR in the first direction and a length LR in the second direction. And a single connecting part
A piezoelectric vibrating piece satisfying at least one of Formula 1, Formula 2, Formula 3, or Formula 4.
(0.1471 × LS−0.004) × 0.75 <LR <(0.1471 × LS−0.004) × 1.25 Formula 1
(0.3545 × WS + 0.044) × 0.8 <WR <(0.3545 × WS + 0.044) × 1.2 Formula 2
(0.85 × LA−0.3125) × 0.94 <LS <(0.85 × LA−0.3125) × 1.06 Equation 3
(0.7237 × WA−0.272) × 0.88 <WS <(0.7237 × WA−0.272) × 1.12 Equation 4 The vibrating portion has a mesa region and a peripheral region formed around the mesa region and thinner than the mesa region,
2. The piezoelectric vibrating piece according to claim 1, wherein an excitation electrode is formed in the mesa region, and an extraction electrode extracted from the excitation electrode is formed in the connection portion and the frame portion.   The piezoelectric vibrating piece according to claim 2, wherein a peripheral region of the vibrating part and the connecting part have the same thickness. The piezoelectric vibrating piece according to any one of claims 1 to 3,
A lid plate connected to one surface of the frame portion;
A base plate connected to the other surface of the frame portion and having an external electrode;
Piezoelectric device with