Piezoelectric vibrator piece, piezoelectric resonator, and oscillator

Abstract

To provide a piezoelectric vibrator piece whose shape is optimized so as to suppress vibration leakage.SOLUTION: A piezoelectric plate 30 includes a base portion 35, an arm portion 36, and a weight portion 37. Grooves 60 are formed on both surfaces of the arm portion 36. In this structure, the width in the X-axis direction of the weight portion 37 is defined as Wh (μm), the length in the Y' direction of the weight portion 37 as Lh (μm), the thickness of the piezoelectric plate 30 as t (μm), the length in the Y' direction of the groove 60 as Lt (μm), the width in the X-axis direction of the arm portion 36 as Wa (μm), the width in the X-axis direction of the groove 60 as Wt (μm), and the thickness at a portion of the arm portion 36 corresponding to the groove 60 as t' (μm). When Ix is a variable satisfying the following expression (1), and X is a variable satisfying the following expression (2), the width Wb (μm) of the base portion 35 in the X-axis direction satisfies the relational expression (3) below. (1) Ix=Wt×t'3 / 12+(Wa-Wt)×t3 / 12, (2) X=Wh×Lh×t×Lt×Wa / Ix, (3) Wb≥197X+271.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a piezoelectric vibrating piece, a piezoelectric vibrator, and an oscillator. [Background technology]

[0002] For example, in electronic devices such as mobile phones and personal digital assistants, piezoelectric vibrators using quartz crystal or the like are used as devices used as time sources, timing sources for control signals, etc., reference signal sources, etc. A known piezoelectric vibrator of this type is one in which a piezoelectric vibrating reed equipped with a piezoelectric plate made of a piezoelectric material such as quartz crystal and two excitation electrodes arranged on the outer surface of the piezoelectric plate to apply an excitation drive voltage to the piezoelectric plate is hermetically sealed in a package having a cavity formed therein.

[0003] Some piezoelectric vibrating reeds include a piezoelectric plate having a pair of vibrating arms arranged side by side and a base connecting the base ends of the pair of vibrating arms. In such piezoelectric vibrating reeds, excitation electrodes are arranged on the outer surfaces of the vibrating arms, and when a drive voltage is applied between the two excitation electrodes, the vibrating arms vibrate at a predetermined resonance frequency in directions approaching or separating from each other, starting from the connection point with the base. In this type of piezoelectric vibrating reed, in order to reduce its size, wide weights are sometimes attached to the tips of the vibrating arms to shorten the overall length (see, for example, Patent Documents 1 and 2).

[0004] Furthermore, in the piezoelectric vibrating piece having the above configuration, grooves are formed in the vibrating arms to reduce the crystal impedance. In the piezoelectric vibrating piece having grooves formed in the vibrating arms, two excitation electrodes are arranged separately on the side of the vibrating arms and in the grooves, and the electric field efficiency inside the vibrating arms is increased when a drive voltage is applied between the two excitation electrodes.

[0005] However, when a pair of vibrating arms of a piezoelectric vibrating piece vibrates, the vibrations are transmitted to the base and may leak into the package, etc. This is known as vibration leakage. Techniques for suppressing this vibration leakage are described in Patent Documents 1 and 2.

[0006] Patent document 1 discloses a vibrating element that includes a base, a pair of vibrating arms extending from a first end of the base along a first direction, and a protrusion that is integral with the base, wherein the base has a second end and a reduced width portion on the opposite side of the first end in the first direction from the first end, the reduced width portion is arranged so that the distance along the first direction from a second direction virtual line that passes between the first end and the second end and runs along a second direction perpendicular to the first direction to at least one of the first end and the second end becomes shorter as it moves away from the first direction virtual line that passes through the center between the pair of vibrating arms and runs along the first direction, and the protrusion is provided on at least one of the third end and the fourth end that respectively connect both ends of the first end and both ends of the second end.

[0007] Patent document 2 discloses a piezoelectric vibrator that vibrates in a bending mode and has a pair of vibrating arms having upper and lower surfaces and side surfaces, a base formed integrally with one end of the vibrating arms, and a pair of side bases formed integrally with the base and extending along the side surfaces of the vibrating arms, wherein a second gap narrower than the first gap between the vibrating arms and side bases is formed between the base and the side bases, continuing from the first gap, and the vibrating arms, base and side bases are formed integrally by etching a crystal piece, and the second gap is the minimum width that can be etched through. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-121039 [Patent Document 2] Japanese Patent Application Laid-Open No. 2007-13910 Summary of the Invention [Problem to be solved by the invention]

[0009] However, conventional methods for evaluating the vibration leakage characteristics of piezoelectric vibrating reeds have been limited to measuring the vibration leakage characteristics while the piezoelectric vibrating reed is fixed in a package. This has meant that it has taken time from designing the piezoelectric vibrating reed to evaluating it, and there has been a challenge in efficiently optimizing the shape of the piezoelectric vibrating reed.

[0010] SUMMARY OF THE INVENTION Accordingly, the present invention provides a piezoelectric vibrating piece whose shape is optimized to suppress vibration leakage, and a piezoelectric vibrator and oscillator that include the piezoelectric vibrating piece. [Means for solving the problem]

[0011] A piezoelectric vibrating piece according to a first aspect of the present invention includes a piezoelectric plate formed of a quartz substrate, and defines a first direction and a second direction orthogonal to each other as a direction orthogonal to a thickness direction of the piezoelectric plate, the piezoelectric plate having a base portion, and a pair of vibrating arms extending from the base portion in the first direction and arranged side by side in the second direction, the pair of vibrating arms having arm portions connected to the base portion and weight portions connected to the tip ends of the arm portions and formed wider in the second direction than the arm portions, and groove portions extending along the first direction are formed on both sides of the arm portions in the thickness direction, and the Let the width of the weight portion in the second direction be Wh (μm), the length of the weight portion in the first direction be Lh (μm), the thickness of the piezoelectric plate be t (μm), the length of the groove portion in the first direction be Lt (μm), the width of the arm portion in the second direction be Wa (μm), the width of the groove portion in the second direction be Wt (μm), and the thickness of the arm portion at the location corresponding to the groove portion be t' (μm); Ix be a variable that satisfies the following equation (1); and X be a variable that satisfies the following equation (2), then the width of the base portion in the second direction is Wb (μm), which satisfies the following relational equation (3). Ix=Wt×t' 3 / 12+(Wa-Wt)×t 3 / 12 ···(1) X=Wh×Lh×t×Lt×Wa / Ix (2) Wb≧197X+271 (3)

[0012] According to the first aspect, it is possible to prevent the stress generated on the side surface of the base facing the second direction from reaching 0.41 MPa. A separate evaluation of the relationship between the side surface of the base and vibration leakage confirmed that vibration leakage increases when the stress generated on the side surface of the base is 0.41 MPa or higher. Therefore, a piezoelectric vibrating piece with an optimized shape can be obtained to suppress vibration leakage.

[0013] A piezoelectric vibrating piece according to a second aspect of the present invention is a piezoelectric vibrating piece according to the first aspect, wherein the piezoelectric plate further comprises a pair of support arms extending from the base and extending along the first direction at positions outward in the second direction from the base, and when the spacing between the pair of support arms in the second direction is W (μm), the distance between the base and the support arms may be Wg (μm) that satisfies the following relational expression (4): W-Wg ≥ Wb (4)

[0014] According to the second aspect, a space of Wg / 2 or more can be secured between the base and the support arm to prevent an electrical short circuit between the base and the support arm.

[0015] A piezoelectric vibrating reed according to a third aspect of the present invention may be the piezoelectric vibrating reed according to the first or second aspect, and may satisfy the following relational expression (5). Wb≧207X+274 (5)

[0016] According to the third aspect, the stress generated on the side surface of the base is reliably smaller than 0.35 MPa. A separate evaluation of the relationship between the side surface of the base and vibration leakage confirmed that good vibration leakage characteristics can be obtained if the stress generated on the side surface of the base is 0.35 MPa or less. Therefore, a piezoelectric vibrating piece with more reliably suppressed vibration leakage can be obtained.

[0017] A piezoelectric vibrator according to a fourth aspect of the present invention includes the piezoelectric vibrating piece according to any one of the first to third aspects, and a package that hermetically seals the piezoelectric vibrating piece.

[0018] According to the fourth aspect, it is possible to provide a piezoelectric vibrator that suppresses vibration leakage from the piezoelectric vibrating reed and has excellent vibration characteristics.

[0019] An oscillator according to a fifth aspect of the present invention includes the piezoelectric vibrator according to the fourth aspect, and the piezoelectric vibrator is electrically connected to an integrated circuit as an oscillator.

[0020] According to the fifth aspect, it is possible to obtain an oscillator that outputs a highly accurate frequency signal. [Effects of the Invention]

[0021] According to the present invention, it is possible to provide a piezoelectric vibrating reed whose shape is optimized so as to suppress vibration leakage. [Brief explanation of the drawings]

[0022] [Figure 1] FIG. 1 is a diagram illustrating an oscillator according to an embodiment. [Figure 2] 1 is a perspective view of the appearance of a piezoelectric vibrator according to an embodiment; [Figure 3] FIG. 2 is an exploded perspective view of the piezoelectric vibrator according to the embodiment. [Figure 4] FIG. 2 is a plan view of the piezoelectric vibrating reed according to the embodiment. [Figure 5] FIG. 5 is a cross-sectional view taken along line VV in FIG. [Figure 6] 10 is a graph showing the relationship between the width of the base in the X-axis direction and the stress generated on the side surface of the base. [Figure 7] 10 is a graph showing the relationship between a variable X and the width of the base in the X-axis direction. DETAILED DESCRIPTION OF THE INVENTION

[0023] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the following description, components having the same or similar functions will be denoted by the same reference numerals, and redundant descriptions of those components may be omitted.

[0024] (oscillator) FIG. 1 is a diagram showing an oscillator according to an embodiment. As shown in FIG. 1, the oscillator 100 includes a substrate 101, an electronic component 102, an integrated circuit 103, and a piezoelectric vibrator 1. The electronic component 102 is, for example, a capacitor, and is mounted on the substrate 101. The integrated circuit 103 is for the oscillator and is also mounted on the substrate 101. The integrated circuit 103 is electrically connected to the piezoelectric vibrator 1 and the electronic component 102 via wiring (not shown). The piezoelectric vibrator 1 is mounted, for example, on the substrate 101 near the integrated circuit 103. The piezoelectric vibrator 1 functions as an oscillator. The piezoelectric vibrator 1 will be described later. At least a portion of the oscillator 100 may be molded with a resin (not shown) as appropriate.

[0025] In the oscillator 100, when power is supplied to the piezoelectric vibrator 1, the piezoelectric vibrating piece 3 (see FIG. 3) of the piezoelectric vibrator 1 vibrates. The vibration of the piezoelectric vibrating piece 3 is converted into an electric signal by the piezoelectric characteristics of the piezoelectric vibrating piece 3. This electric signal is output from the piezoelectric vibrator 1 to the integrated circuit 103. The integrated circuit 103 performs various processes on the electric signal output from the piezoelectric vibrator 1 to generate a frequency signal.

[0026] The oscillator 100 can be used, for example, as a single-function oscillator for a clock, a timing control device that controls the operation timing of various devices such as a computer, or a device that provides time or a calendar. The integrated circuit 103 is configured according to the functions required of the oscillator 100, and may include a so-called RTC (real-time clock) module.

[0027] (piezoelectric vibrator) Fig. 2 is an external perspective view of the piezoelectric vibrator according to the embodiment, and Fig. 3 is an exploded perspective view of the piezoelectric vibrator according to the embodiment. As shown in Figures 2 and 3, the piezoelectric vibrator 1 is a so-called ceramic package type surface-mount vibrator. The piezoelectric vibrator 1 includes a package 2 having an airtightly sealed cavity therein, and a piezoelectric vibrating piece 3 housed in the cavity. The piezoelectric vibrator 1 has a rectangular parallelepiped shape. In this embodiment, the longitudinal direction of the piezoelectric vibrator 1 in a plan view is referred to as the longitudinal direction L, the lateral direction is referred to as the width direction W, and the direction perpendicular to the longitudinal direction L and the width direction W is referred to as the thickness direction T.

[0028] The package 2 includes a package body 5 and a sealing plate 6 that is joined to the package body 5 and forms a cavity between the package body 5 and the sealing plate 6. The package body 5 includes a first base substrate 10 and a second base substrate 11 that are bonded together in a stacked state, and a seal ring 12 that is bonded onto the second base substrate 11.

[0029] The first base substrate 10 is a ceramic substrate having a rectangular shape in a plan view seen in the thickness direction T. The upper surface of the first base substrate 10 forms the bottom of the cavity. A pair of external electrodes 21A, 21B are formed on the lower surface of the first base substrate 10 with a gap between them in the longitudinal direction L. The external electrodes 21A, 21B are formed of a single-layer film made of a single metal formed by, for example, vapor deposition or sputtering, or a laminated film made of a laminate of different metals.

[0030] The second base substrate 11 is a ceramic substrate having the same outer shape as the first base substrate 10 in a plan view, and is integrally bonded to the first base substrate 10 by sintering or the like while being stacked on top of the first base substrate 10. Note that the ceramic material used for each of the base substrates 10, 11 can be, for example, HTCC (High Temperature Co-Fired Ceramic) made of alumina or LTCC (Low Temperature Co-Fired Ceramic) made of glass ceramic.

[0031] As shown in FIG. 3, the second base substrate 11 has a through-hole 11a that penetrates the second base substrate 11 in the thickness direction T. The through-hole 11a has a rounded rectangular shape in a plan view. Mounting portions 14A and 14B that protrude inward in the width direction W are formed on the inner surface of the through-hole 11a at portions located on both sides in the width direction W. The mounting portions 14A and 14B are located in the center of the second base substrate 11 in the longitudinal direction L.

[0032] A pair of electrode pads 20A, 20B are formed on the mounting portions 14A, 14B as connection electrodes with the piezoelectric vibrating reed 3. Like the external electrodes 21A, 21B described above, the electrode pads 20A, 20B are formed of a single-layer film made of a single metal, formed by, for example, vapor deposition or sputtering, or a laminated film made of laminated layers of different metals. The electrode pads 20A, 20B and the external electrodes 21A, 21B are electrically connected to each other via through-wiring (not shown) that penetrates each of the base substrates 10, 11 in the thickness direction T.

[0033] At the four corners of each of the base substrates 10, 11, cutout portions 15 having a quarter-circular arc shape in plan view are formed over the entire thickness direction T of both base substrates 10, 11. Each of the base substrates 10, 11 is fabricated, for example, by stacking and bonding two wafer-like ceramic substrates, forming a plurality of through-holes penetrating both ceramic substrates in a matrix pattern, and cutting both ceramic substrates in a grid pattern using each through-hole as a reference. At this time, the through-holes are divided into four to form the above-mentioned cutout portions 15.

[0034] The seal ring 12 is a conductive frame-shaped member that is slightly smaller than the outer shape of each of the base substrates 10, 11, and is bonded to the upper surface of the second base substrate 11. Specifically, the seal ring 12 is bonded to the second base substrate 11 by baking with a brazing material such as silver brazing or a solder material, or by welding to a metal bonding layer formed on the second base substrate 11. The seal ring 12 forms a side wall of the cavity together with the inner surface of the second base substrate 11 (through portion 11a). In the illustrated example, the inner surface of the seal ring 12 is disposed flush with the inner surface of the second base substrate 11.

[0035] The material of the seal ring 12 may be, for example, a nickel-based alloy, and specifically may be selected from Kovar, Elinvar, Invar, 42-alloy, etc. In particular, it is preferable to select a material for the seal ring 12 that has a thermal expansion coefficient close to that of the base substrates 10 and 11, which are made of ceramics. For example, the base substrates 10 and 11 may have a thermal expansion coefficient of 6.8×10 -6 When alumina with a thermal expansion coefficient of 5.2×10 / °C is used, the seal ring 12 has a thermal expansion coefficient of 5.2×10 -6 / ℃ Kovar and thermal expansion coefficient 4.5~6.5×10 -6 It is preferable to use 42-alloy with a temperature of 1000 K / °C.

[0036] The sealing plate 6 is made of a conductive substrate and is joined onto the seal ring 12 to airtightly seal the inside of the package body 5. The space defined by the seal ring 12, the sealing plate 6, and each of the base substrates 10 and 11 constitutes an airtightly sealed cavity.

[0037] The piezoelectric vibrating reed 3 is housed in a cavity of a hermetically sealed package 2. The piezoelectric vibrating reed 3 includes a piezoelectric plate 30 made of a piezoelectric material such as quartz crystal, lithium tantalate, or lithium niobate. The piezoelectric plate 30 has a pair of vibrating arms 31 and 32 and a pair of support arms 33 and 34. The piezoelectric vibrating reed 3 is mounted to the package 2 within the cavity by supporting the support arms 33 and 34 on mounting sections 14A and 14B of the package 2 with a conductive adhesive. This allows the piezoelectric vibrating reed 3 to be supported within the cavity with the vibrating arms 31 and 32 floating above the base substrates 10 and 11. Two excitation electrodes (not shown) are arranged on the outer surfaces of the vibrating arms 31 and 32, causing the pair of vibrating arms 31 and 32 to vibrate when a predetermined voltage is applied.

[0038] To operate the piezoelectric vibrator 1, a predetermined voltage is applied to the external electrodes 21A and 21B. This causes a current to flow through the excitation electrodes of the piezoelectric vibrating piece 3, generating an electric field between the excitation electrodes. The vibrating arms 31 and 32 vibrate at a predetermined resonance frequency, for example, in directions approaching or separating from each other, due to the inverse piezoelectric effect caused by the electric field generated between the excitation electrodes. The vibrations of the vibrating arms 31 and 32 are used as a time source, a timing source for control signals, a reference signal source, etc.

[0039] (Piezoelectric vibrating piece) The piezoelectric vibrating reed 3 of the embodiment will be described in detail. FIG. 4 is a plan view of the piezoelectric vibrating reed according to the embodiment. As shown in FIG. 4, the piezoelectric vibrating piece 3 includes a piezoelectric plate 30 and an electrode film (not shown) disposed on the outer surface of the piezoelectric plate 30.

[0040] The piezoelectric plate 30 is formed by slicing a Lambertian quartz crystal ore at a predetermined angle relative to the X-axis (electrical axis), Y-axis (mechanical axis), and Z-axis (optical axis), which are orthogonal to each other as quartz crystal axes, into wafers, and then etching the wafers to form them. In the following description, when describing the configuration of the piezoelectric vibrating reed 3, a coordinate system is used in which the X-axis, Y'-axis, and Z'-axis are orthogonal to each other. The Z'-axis is the axis obtained by rotating the Z-axis around the X-axis within a range of -5° to +10°. The Y'-axis is the axis obtained by rotating the Y-axis at the same angle as the Z-axis within a plane containing the Z-axis and Y-axis, with the X-axis as the rotation axis. The X-axis direction (second direction), Y'-axis direction (first direction), and Z'-axis direction will be described with the arrow direction in the figure as the positive side and the direction opposite the arrow as the negative side. In the piezoelectric plate 30 of this embodiment, the Z'-axis direction coincides with the thickness direction of the piezoelectric plate 30. The term "width" used in the following description means the size of a portion extending in any direction in a plan view seen from the Z'-axis direction, in a direction perpendicular to the any direction in a plan view.

[0041] The piezoelectric plate 30 includes a base 35, a pair of vibrating arms 31, 32 (first vibrating arm 31 and second vibrating arm 32) extending from the base 35 to the positive side in the Y'-axis direction, and a pair of support arms 33, 34 (first support arm 33 and second support arm 34) located on the positive and negative sides in the X-axis direction relative to the base 35. Except for etching residues, the piezoelectric plate 30 is formed symmetrically on both sides in the front and back directions and line-symmetrically with respect to an imaginary line extending in the Y'-axis direction through its center in the X-axis direction in a plan view.

[0042] The base 35 is formed in a rectangular shape in a plan view. The base 35 has a first end face 35a facing the positive side in the Y'-axis direction, a second end face 35b facing the negative side in the Y'-axis direction, and a pair of side faces 35c facing outward in the X-axis direction. The first end face 35a and the second end face 35b each extend in the X-axis direction in a plan view. A recess is formed in an intermediate portion of the second end face 35b in the X-axis direction, recessed toward the positive side in the Y'-axis direction in a plan view. The pair of side faces 35c each extend in the Y'-axis direction in a plan view.

[0043] The pair of vibrating arms 31, 32 are arranged parallel to each other in the X-axis direction. The pair of vibrating arms 31, 32 are connected to the ends of the first end surface 35a of the base 35 in the X-axis direction. Each of the vibrating arms 31, 32 vibrates in a direction approaching or separating from each other, with the base end on the base 35 side as a fixed end and the tip end as a free end. Each of the vibrating arms 31, 32 has an arm portion 36 extending from the first end surface 35a of the base 35, and a weight portion 37 connected to the tip of the arm portion 36 and formed wider than the arm portion 36.

[0044] The arm portion 36 comprises a straight portion 361 extending with a constant width in the Y'-axis direction, a tip portion 362 extending from the end of the straight portion 361 on the positive side in the Y'-axis direction toward the positive side in the Y'-axis direction toward the weight portion 37 and connecting to the weight portion 37, and a base portion 363 extending from the end of the straight portion 361 on the negative side in the Y'-axis direction toward the base portion 35 and connecting to the base portion 35 while widening in width as it moves toward the negative side in the Y'-axis direction.

[0045] The base end portion 363 has an outer surface 363a that faces the space on the outside of the arm portion 36 in the X-axis direction, and an inner surface 363b that faces the space on the inside of the arm portion 36 in the X-axis direction.

[0046] The outer surface 363a is connected to the side surface 35c of the base 35. A first half of the outer surface 363a on the base 35 side is formed flush with the side surface 35c of the base 35 and extends in the Y'-axis direction in a plan view. A second half of the outer surface 363a on the arm 36 side is a concave curved surface that is recessed inward in the X-axis direction and toward the negative side in the Y'-axis direction. The second half bends from the end of the straight portion 361 side of the first half toward the inside in the X-axis direction and the positive side in the Y'-axis direction, and then extends toward the positive side in the Y'-axis direction as it heads inward in the X-axis direction.

[0047] The inner surface 363b is connected to the first end surface 35a of the base 35. The inner surface 363b is a concave curved surface that is recessed outward in the X-axis direction and toward the negative side in the Y'-axis direction. The inner surface 363b extends toward the positive side in the Y'-axis direction as it moves outward in the X-axis direction from the first end surface 35a of the base 35. In the Y'-axis direction, the position of the positive side end of the inner surface 363b coincides with the position of the positive side end of the outer surface 363a.

[0048] The straight portion 361 has a pair of side surfaces 361a facing the X-axis direction. The pair of side surfaces 361a are connected to the outer side surface 363a and the inner side surface 363b of the base end portion 363 in a one-to-one relationship. Each side surface 361a is smoothly connected to the outer side surface 363a or the inner side surface 363b of the base end portion 363 so that the tangent to the outer side surface 363a or the inner side surface 363b of the base end portion 363 is continuous. However, each side surface 361a may be connected to the outer side surface 363a or the inner side surface 363b of the base end portion 363 so that the tangent to the outer side surface 363a or the inner side surface 363b of the base end portion 363 is discontinuous.

[0049] The tip portion 362 has an outer surface 362a that faces the space outside the X-axis direction of the arm portion 36, and an inner surface 362b that faces the space inside the X-axis direction of the arm portion 36. The outer surface 362a and the inner surface 362b are flat surfaces. The outer surface 362a extends from the end of the side surface 361a of the straight portion 361 outward in the X-axis direction and toward the positive side in the Y'-axis direction. The inner surface 362b extends from the end of the side surface 361a of the straight portion 361 inward in the X-axis direction and toward the positive side in the Y'-axis direction.

[0050] Plummet 37 is located at the tip of vibrating arms 31, 32. Plummet 37 extends from the tip of each arm 36 to the positive side in the Y'-axis direction. Plummet 37 is formed symmetrically with respect to the center line of straight portion 361 in a plan view. Plummet 37 as a whole is formed larger on both sides in the X-axis direction than tip 362 of arm 36.

[0051] Each support arm 33, 34 has an L-shape in plan view and surrounds the base 35 and the vibrating arms 31, 32 from the outside in the X-axis direction. Specifically, each support arm 33, 34 includes a root portion 38 that protrudes outward in the X-axis direction from an end of the side surface 35c of the base 35 on the negative side in the Y'-axis direction, and a tip portion 39 that extends from an end of the root portion 38 opposite the base 35 to the positive side in the Y'-axis direction. The tip portion 39 extends in the Y'-axis direction with a constant width. The end of the tip portion 39 on the positive side in the Y'-axis direction is located closer to the positive side in the Y'-axis direction than the base 35 and closer to the negative side in the Y'-axis direction than the weight portion 37. The first support arm 33 is disposed on the opposite side of the second vibrating arm 32 with respect to the first vibrating arm 31. The second support arm 34 is disposed on the opposite side of the second vibrating arm 32 with respect to the first vibrating arm 31.

[0052] FIG. 5 is a cross-sectional view taken along line VV in FIG. As shown in FIGS. 4 and 5, grooves 60 are formed in each of the vibrating arms 31 and 32. The grooves 60 are recessed in the Z'-axis direction on both main surfaces of the piezoelectric plate 30 facing the Z'-axis direction. The grooves 60 extend in the Y'-axis direction with a constant width through the arm 36. The positions of both ends of the grooves 60 in the Y'-axis direction coincide with the positions of both ends of the arm 36. The grooves 60 extend so that the center line passing through the center of their width substantially coincides with the center line of the straight portion 361. Note that the grooves 60 may be formed so that their center lines are shifted toward the positive side in the X-axis direction with respect to the center line of the straight portion 361.

[0053] Two excitation electrodes, which are part of the electrode film, are formed on the outer surfaces of the vibrating arms 31 and 32. The two excitation electrodes are electrically insulated from each other. When a predetermined driving voltage is applied between the excitation electrodes, the excitation electrodes generate an electric field in each vibrating arm 31 and 32, causing each vibrating arm 31 and 32 to vibrate in the X-axis direction. The excitation electrodes are, for example, a laminated film of chromium (Cr) and gold (Au). A chromium film, which has good adhesion to quartz crystal, is formed as a base, and then a thin gold film is laminated on the chromium film. However, the film configuration of the electrode film is not limited to this. For example, a thin gold film may be laminated on a laminated film of chromium and nichrome (NiCr), or a single-layer film of chromium, nickel, aluminum (Al), titanium (Ti), or the like may be used. Each excitation electrode is connected to a wiring film (not shown) which is part of the electrode film. The wiring film is electrically connected to the electrode pads 20A and 20B of the package 2 via a conductive adhesive.

[0054] The dimensions and functions of each part of the piezoelectric vibrating reed 3 of the embodiment will be described in detail. 4 and 5, the width of weight 37 in the X-axis direction is Wh (μm), the length of weight 37 in the Y'-axis direction is Lh (μm), the thickness of piezoelectric plate 30 is t (μm), the length of groove 60 in the Y'-axis direction is Lt (μm), the width of arm 36 in the X-axis direction is Wa (μm), the width of groove 60 in the X-axis direction is Wt (μm), and the thickness of arm 36 at a location corresponding to groove 60 is t' (μm). Furthermore, Ix is a variable that satisfies the following equation (1), and X is a variable that satisfies the following equation (2). Ix is the second moment of area in the bending direction of arm 36. Ix=Wt×t' 3 / 12+(Wa-Wt)×t 3 / 12 ···(1) X=Wh×Lh×t×Lt×Wa / Ix (2)

[0055] If the width of the base 35 in the X-axis direction is Wb (μm), Wb satisfies the following relational expression (3). Wb≧197X+271 (3)

[0056] Furthermore, if the distance between the pair of support arms 33, 34 in the X-axis direction is W (μm) and the distance between the base 35 and the tip 39 of the support arms 33, 34 is Wg (μm), it is desirable that Wg satisfy the following relational expression (4). W-Wg ≥ Wb (4)

[0057] It is desirable that Wb satisfy the following relational expression (5). Wb≧207X+274 (5)

[0058] Fig. 6 is a graph showing the relationship between the width of the base in the X-axis direction and the stress generated on the side surface of the base. The horizontal axis in Fig. 6 represents the width of base 35 in the X-axis direction. The vertical axis in Fig. 6 represents the stress generated on side surface 35c of base 35. As shown in Figure 6, when the variable X is between 0.07 and 0.113, the stress generated on the side surface 35c of the base 35 decreases as the width of the base 35 in the X-axis direction increases. Simulations using finite element analysis software from Ansys, Inc. confirmed that vibration leakage is not sufficiently suppressed when the stress generated on the side surface 35c of the base 35 is 0.41 MPa, but is sufficiently suppressed when the stress is 0.35 MPa or less. The location of the side surface 35c of the base 35 where the stress was evaluated is specified as the end of the side surface 35c on the support arm 33, 34 side.

[0059] 7 is a graph showing the relationship between the variable X and the width of the base in the X-axis direction. The horizontal axis shown in FIG. 7 represents the variable X. The vertical axis shown in FIG. 7 represents the width of the base 35 in the X-axis direction. Each data group plotted in Figure 7 represents the width value of base 35 in the X-axis direction when the stress generated on side surface 35c of base 35 is 0.35 MPa, 0.315 MPa, and 0.41 MPa as the variable X is changed. The straight lines shown in Figure 7 are obtained by approximating each data group to a linear function using the least squares method. Specifically, line L1 corresponds to the data group for a stress of 0.35 MPa and represents a function of variable X expressed by equation (6) below, line L2 corresponds to the data group for a stress of 0.315 MPa and represents a function of variable X expressed by equation (7) below, and line L3 corresponds to the data group for a stress of 0.41 MPa and represents a function of variable X expressed by equation (8) below. Wb=197X+271 (6) Wb=207X+274 (7) Wb=180X+265 (8)

[0060] 7, by making the width of the base 35 in the X-axis direction at least a function of the variable X indicated by the line L1, it is possible to prevent the stress generated on the side surface 35c of the base 35 from exceeding 0.41 MPa, at which point vibration leakage increases. Therefore, it can be seen that vibration leakage can be suppressed by making Wb satisfy the above relational expression (3).

[0061] Furthermore, by making the width of the base 35 in the X-axis direction equal to or greater than the function of the variable X indicated by the line L2, the stress generated on the side surface 35c of the base 35 is reliably reduced to less than 0.35 MPa, which is the stress required to obtain good vibration leakage characteristics. Therefore, it can be seen that vibration leakage can be more reliably suppressed by making Wb satisfy the above relational expression (5).

[0062] As described above, by setting the width of the base 35 in the X-axis direction so as to satisfy the above relational expression (3), a piezoelectric vibrating reed 3 whose shape is optimized to suppress vibration leakage can be obtained.

[0063] Furthermore, when Wg satisfies the above relational expression (4), a space of Wg / 2 or more can be secured between the base 35 and the support arms 33, 34 to prevent an electrical short circuit between the base 35 and the support arms 33, 34.

[0064] The present invention is not limited to the above-described embodiment explained with reference to the drawings, and various modifications are possible within the technical scope of the present invention. For example, in the above embodiment, the piezoelectric vibrating piece 3 is a so-called side arm type vibrating piece in which the support arms 33 and 34 are arranged outside the vibrating arms 31 and 32. However, the present invention is not limited to this configuration, and the piezoelectric vibrating piece may be a vibrating piece that does not have a support arm.

[0065] In addition, the components in the above-described embodiments can be replaced with well-known components as appropriate, without departing from the spirit of the present invention. [Explanation of symbols]

[0066] REFERENCE SIGNS LIST 1... piezoelectric vibrator 2... package 3... piezoelectric vibrating piece 30... piezoelectric plate 31, 32... vibrating arms 33, 34... supporting arms 35... base 36... arms 37... weights 60... grooves 100... oscillator 103... integrated circuit

Claims

1. a piezoelectric plate formed by a quartz crystal substrate; a first direction and a second direction perpendicular to each other are defined as directions perpendicular to the thickness direction of the piezoelectric plate; The piezoelectric plate is A base and a pair of vibrating arms extending from the base in the first direction and arranged side by side in the second direction, each having an arm connected to the base and a weight connected to a tip of the arm and formed wider in the second direction than the arm; and Groove portions extending along the first direction are formed on both surfaces of the arm portion in the thickness direction, The width of the weight portion in the second direction is Wh (μm), The length of the weight portion in the first direction is Lh (μm), The thickness of the piezoelectric plate is t (μm), The length of the groove portion in the first direction is Lt (μm), The width of the arm portion in the second direction is Wa (μm), The width of the groove portion in the second direction is Wt (μm), The thickness of the arm portion at a portion corresponding to the groove portion is defined as t′ (μm), Ix is a variable that satisfies the following formula (1): Let X be a variable that satisfies the following formula (2): A piezoelectric vibrating piece in which the width of the base in the second direction is Wb (μm) that satisfies the following relational expression (3). Ix=Wt×t' ３ / 12+(Waa−Wt)×t ３ / 12 ・・・(1) X=Wh×Lh×t×Lt×Wa / Ix...(2) Wb≧197X+271 (3)

2. the piezoelectric plate further includes a pair of support arms extending from the base and extending along the first direction at positions outward of the base in the second direction; When the distance between the pair of support arms in the second direction is W (μm), 2. The piezoelectric vibrating piece according to claim 1, wherein the distance between the base and the support arm is Wg (μm) that satisfies the following relational expression (4). W-Wg≧Wb...(4)

3. 3. The piezoelectric vibrating piece according to claim 1, wherein the following relational expression (5) is satisfied: Wb≧207X+274 (5)

4. The piezoelectric vibrating piece according to claim 1 or 2, a package that hermetically seals the piezoelectric vibrating piece; A piezoelectric vibrator comprising:

5. A piezoelectric vibrator according to claim 4, The piezoelectric vibrator is electrically connected to an integrated circuit as an oscillator. Oscillator.

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