JP2005197946A - Tuning fork type crystal resonator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a 32 kHz tuning fork type crystal resonator whose secondary temperature coefficient β of a frequency temperature characteristic is reduced from -3.4×10<SP>-8</SP>/°C<SP>2</SP>to ≤-1.6×10<SP>-8</SP>/°C<SP>2</SP>. <P>SOLUTION: This crystal resonator having a tuning fork shape having a width X in an electric axis direction and a length Y' along arm parts of a tuning fork is formed of a crystal flat plate obtained by rotating a crystal Z-cut flat plate, having as a main plane a plane containing an electric axis X and a mechanical axis Y of right crystal, counterclockwise on the electronic axis by 0 to 8°, and top and reverse main planes of the arm parts are grooved to obtain the tuning fork type crystal resonator. The tuning fork type crystal resonator has a vibration mode A in which displacement of the arm parts are in the electric axis direction X and the operating frequency is f0 and a vibration mode B in which the displacement of the arm parts is Z perpendicular to the main planes and the operating frequency is greatly different from f0; and the two vibration modes A and B are coupled together by a nonlinear parametric vibration phenomenon generated at the arm parts to reduce and compensate the secondary temperature coefficient β of the original frequency-temperature characteristic curve that the vibration mode A has, thereby providing the tuning fork type crystal resonator having a flat frequency-temperature characteristic. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

In the present invention, the frequency temperature characteristics of a conventional tuning fork type crystal resonator having a frequency secondary temperature coefficient β of −3.4 × 10 ⁻⁸ / ° C. ² are greatly improved by utilizing a parametric vibration phenomenon. The present invention relates to a tuning fork crystal unit.

  Conventionally, a 32 kHz tuning fork type crystal resonator using a piezoelectric Z-cut plate having piezoelectricity is used as a clock source for time reference of various electronic devices because its frequency temperature characteristic has a zero temperature coefficient and high accuracy. However, this is because a small-sized, low-power and high-precision crystal oscillator can be used at low cost.

  The Z-cut quartz plate is well known, and is orthogonal to the mechanical axis Z in an orthogonal coordinate system comprising the electric axis X, the mechanical axis Y, and the optical axis Z, which are the basic axes of the quartz crystal. In a substrate obtained by rotating the Z plate around the electrical axis X by θ degrees (particularly θ = 0 to 5 degrees at which a zero temperature coefficient can be obtained at room temperature), the electrical axis direction X is θ degrees in the width direction of the tuning fork crystal resonator. The machine axis Y "after rotation is arranged in the longitudinal direction of the tuning-fork-shaped arm portion to form a tuning-fork type crystal piece (see, for example, Patent Document 1,“ Temperature Detection Crystal Vibrator and its Manufacturing Method ”). )

In the conventional product, the vibration mode to be used is one in which the arm portion has a vibration displacement Ux in the electric axis direction X, and a bending that generates a displacement in the main surface extending between the axes X and Y ′. The vibration mode is used. More specifically, only the vibration mode A in FIG. 1 and the vibration mode designated by the X displacement bending vibration (mode A) having the frequency f0 (Hz) in the uppermost frame in FIG. 2 are used. In addition, since other modes existing as natural vibration modes adversely affect the characteristics of the vibrator, they are usually avoided or suppressed as spurious and are not used. In this case, the frequency temperature characteristic of the conventional product has a frequency secondary temperature coefficient β of approximately −3.4 × 10 ⁻⁸ / ° C. ² .

  In addition, recently, the tuning fork crystal unit has been further miniaturized as a result of grooving along the longitudinal direction of the arm on the main plane of the tuning fork crystal unit. It came to do. For details of the shape configuration, refer to Patent Document 2 “Transducer and Electronic Device Mounted with the Vibrator” as an example (the description is later, but the general shape of FIG. 3 corresponds to this).

  As a method for improving the frequency temperature characteristics of the tuning fork type crystal resonator, a method for compensating temperature by linearly combining a unique torsional vibration mode generated in a tuning fork shape and a first-order higher-order bending vibration has been proposed and realized. (For example, Patent Document 3: “Quartz Crystal”).

Japanese Patent Laid-Open No. 06-074834 Japanese Patent Laid-Open No. 12-844092 JP 59-151516 A

However, in the above-described conventional technology, an attempt has been made to improve the frequency temperature characteristics in the 32 kHz tuning fork type crystal resonators that are currently most produced, but the conventional frequency secondary temperature coefficient β is −3. A means for improving to 4 × 10 ⁻⁸ / ° C. ² or more and reducing it to −1.6 × 10 ⁻⁸ / ° C. ² or less is still unknown. However, in the tuning fork-type torsional crystal resonator having a specific cut angle or the prior art according to Patent Document 3, a secondary temperature coefficient of about −1.6 × 10 ⁻⁸ / ° C. ² was obtained, but the resonance frequency In the size of about 32 kHz, it becomes 196 kHz, and there is a problem that the operating current consumption of the oscillation circuit is about 6 times 400 μA for use in a wristwatch or the like, and the battery life of 10 years cannot be maintained.

  Therefore, the present invention utilizes a non-linear parametric vibration phenomenon existing between modes having significantly different natural vibration frequencies existing in a quartz tuning fork type vibration piece, and mainly has a resonance frequency of 32 kHz, To provide the market with tuning fork crystal units that self-compensate the frequency temperature characteristics, which are quadratic functions, and realize a substantially flat frequency temperature characteristic (± 5 ppm) in the operating temperature range of -20 to + 60 ° C. is there.

  The purpose is to realize a situation in which the electronic time of the network society is less distorted by using a tuning-fork type crystal resonator with significantly improved frequency temperature characteristics.

(1) The tuning fork type crystal resonator according to the present invention is a quartz Z-cut flat plate whose main surface is the surface extending between the electric axis X and the mechanical axis Y of the right crystal crystal, and is 0 to 8 degrees counterclockwise around the electric axis. A crystal unit having a tuning fork shape in which the width direction is X in the electric axis direction and the longitudinal direction of the arm portion of the tuning fork is Y ′ is formed from the rotated crystal flat plate, and is formed on the front and back main surfaces of the arm portion. In tuning fork-type crystal units with grooving,
The tuning fork type crystal resonator has a vibration mode A in which the displacement of the arm is in the electric axis direction X and the operating frequency is f0, and the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1. There is a vibration mode B that is significantly different from f0,
The two vibration modes A and B are coupled by a non-linear parametric vibration phenomenon generated through a coupling member formed on the arm portion, and the second-order temperature coefficient of the original frequency-temperature characteristic curve of the vibration mode A It is characterized in that β is reduced and compensated to realize a flat frequency temperature characteristic.

  According to the configuration of (1) above, in the conventional tuning fork type crystal resonator, the temperature temperature characteristic of the operating frequency f0 can be sufficiently compensated for temperature compensation. Thus, if a quartz wristwatch using the tuning fork type crystal resonator of the present invention is manufactured, there is an effect that a high-precision wristwatch with a yearly difference of about 20 seconds and a standard oscillator for electronic devices can be realized.

(2) In the tuning fork type quartz resonator of the present invention, the vibration mode B is a first-order in-phase bending in which the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1 is almost twice f0. It is a vibration mode.

  With the configuration of (2) above, since the vibration mode A and the vibration mode B have a double frequency relationship, they can realize a non-linear mode coupling state due to the closest and strong parametric vibration. Compensation is possible.

(3) In the tuning fork type crystal resonator of the present invention, the vibration mode B is a first-order reversed phase in which the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1 is approximately twice f0. It is characterized by bending vibration mode (so-called primary walk vibration).

  In the configuration of (3) above, since the vibration mode A and the vibration mode B have a double frequency relationship, they can realize a non-linear mode coupling state due to the closest and strong parametric vibration. Compensation is possible. The so-called 'walk' vibration of the anti-phase mode is another stable vibration mode B candidate.

(4) In the tuning fork type crystal resonator according to the present invention, the coupling member formed on the arm portion is made of a metal film or an oxide film having a considerable thickness, and the degree of coupling is increased by a non-linear parametric vibration phenomenon. And

  With the configuration of (4) above, in the main vibration region having the maximum distortion in the tuning fork shape, non-linear parametric vibration occurs between the metal film as the coupling member and its oxide and the crystal member as the base material. Therefore, stable temperature compensation can be realized.

(5) The tuning fork type crystal resonator according to the present invention is characterized in that a metal film or an oxide film as a coupling member formed on the arm portion is formed of Cr metal and its oxide.

(6) The tuning fork type crystal resonator according to the present invention is characterized in that a metal film or an oxide film as a coupling member formed on the arm portion is formed of Ni metal and its oxide.

(7) The tuning fork type crystal resonator of the present invention is characterized in that a metal film or an oxide film, which is a coupling member formed on the arm portion, is formed of Ti metal and its oxide.

  With the above configurations (5), (6), and (7), the main vibration region having the maximum distortion in the tuning fork shape is sufficiently hard against the Young's modulus of the crystal, so even a small amount is effective. Since a non-linear parametric vibration is generated between the metal film and its oxide, which are simple coupling members, and the quartz crystal member which is a base material, stable temperature compensation can be realized. Cr, Ti, and Ni are all metals that are easy to handle as manufactured.

(8) The tuning fork type crystal resonator according to the present invention is characterized in that a metal film or an oxide film as a coupling member formed on the arm portion is formed of Si metal and its oxide.

With the configuration of (8) above, since the oxide of Si is SiO _{2, that} is, a stable oxide, nonlinear parametric vibration is stably generated, stable temperature compensation can be realized, and Cr and Au Since it has an insulating effect between the electrodes, it has an electrical short-circuit preventing effect.

(9) In the tuning fork type crystal resonator according to the present invention, a metal film or an oxide film as a coupling member formed on the arm portion is formed of Cr metal and its oxide, and the tuning fork type is composed of the Cr metal and its oxide. It is characterized in that the frequency increase amount of the crystal resonator is +1000 ppm to +3000 ppm in terms of the rate of change in frequency.

With the configuration of (9) above, the secondary temperature coefficient β = −3.4 × 10 ⁻⁸ / ° C. ² of the frequency temperature characteristic of the conventional 32 kHz tuning fork type crystal resonator is set so that β becomes almost zero. Since compensation can be made, there is an effect that a highly accurate frequency temperature characteristic can be realized.

(10) The tuning fork type crystal resonator according to the present invention is characterized in that a resonance frequency f0 of the tuning fork type crystal resonator is 32768 Hz, and a high order resonance frequency of the f1 is approximately 65536 Hz.

With the configuration of (10) above, the second-order temperature coefficient β = −3.4 × 10 ⁻⁸ / ° C. ² of the frequency temperature characteristic of the conventional 32 kHz tuning fork type crystal resonator is set so that β becomes almost zero. Since compensation can be made, there is an effect that a highly accurate frequency temperature characteristic can be realized.

(11) In the tuning fork type crystal resonator according to the present invention, if the maximum value U0 of the vibration displacement of the resonance frequency f0 of the tuning fork type crystal resonator is 1, the maximum vibration displacement of the higher order resonance frequency of f1. The relative ratio U1 / U0 of the value U1 is approximately in the range of 10 ⁻³ to 10 ⁻² .

With the configuration of (11) above, the secondary temperature coefficient β = −3.4 × 10 ⁻⁸ / ° C. ² of the frequency temperature characteristic of the conventional 32 kHz tuning fork type crystal resonator is set so that β becomes almost zero. Since compensation can be made, there is an effect that a highly accurate frequency temperature characteristic can be realized.

(12) The tuning fork type crystal resonator according to the present invention is characterized in that a vertex temperature θmax of a frequency temperature characteristic of the tuning fork type crystal resonator is in a range of 20 ° C. to 60 ° C.

  With the configuration of (12), the frequency temperature characteristic of the conventional 32 kHz tuning fork type crystal resonator can be compensated so that the frequency accuracy is almost zero of ± 10 ppm in the temperature range of −20 ° C. to 70 ° C. Therefore, there is an effect that a highly accurate watch can be realized.

(13) In the tuning fork type crystal resonator according to the present invention, the direction and size of the tuning fork type crystal resonator element are set so that the rotation angle θ of the crystal rotation Z-cut plate is in the range of 0 degrees to 8 degrees, and is generally an arm. The length of the part is in the range of 1500 to 1600 μm, the arm width is in the range of 90 to 110 μm, the thickness of the arm, that is, the thickness of the crystal Z-cut plate is in the range of 90 to 110 μm, the groove width is in the range of 60% to 80% of the arm width, and the groove length The length is in the range of 40% to 60% of the arm length, the (arm thickness / arm width) ratio is in the range of 0.9 to 1.0, and the length in the Y′-axis direction of the base portion connecting the left and right arm portions is: The thickness is set in the range of 500 to 700 μm, and the film thickness of the Cr metal bonding member formed with the arms is set in the range of 800 to 1000 angstroms.

  According to the configuration of (13) above, a tuning fork type resonator element having a total length of about 2 mm can be obtained, so that a highly accurate and ultra-small tuning fork type crystal resonator can be provided to the market.

  A piezoelectric Z-crystal material made of quartz cuts out a rotating Z-cut rotated by θ degrees around the + X axis, which is the basic axis of quartz, and after mirror-polishing the surface, a tuning fork shape is formed by photolithography technology. A tuning fork type vibrating piece having a tuning fork shape is formed by anisotropic etching using hydrofluoric acid or ammonium fluoride. FIG. 3 illustrates this situation. In the figure, 300 is the optical axis (+ Z axis) of the right crystal crystal, 301 is the mechanical axis (+ Y axis), and 303 is the electrical axis (+ X axis). 302 is a tuning fork type vibration piece made of quartz. Reference numeral 305 denotes a groove portion recently introduced for the purpose of downsizing the tuning fork type crystal resonator. The main surface portion of the arm portion of the tuning fork type resonator element is formed on the arm portion by the photolithography technique described above. It is the state which formed the recessed part which followed. By reducing the equivalent spring constant and increasing the effective electromechanical coupling constant and reducing the equivalent series resistance of the tuning fork crystal unit, we succeeded in reducing the size to half that of the conventional size. Yes. A rectangular cross-sectional shape is ideal for the groove shape, but when an actual photolithography process is performed, a complex shape of a polyhedron is formed by etching anisotropy of quartz (see FIG. 8 which is a schematic diagram). about).

  The tuning fork type crystal vibrating piece obtained by the above-described processing can excite a fundamental wave bending vibration displacement Ux that is symmetrical in the electric axis +/− X axis direction by appropriately forming a conductive metal on the tuning fork type crystal piece. Configure as follows. Thereafter, it is housed in a high vacuum container of 10 −3 torr. The conductor metal film, as the meaning of the letters, constitutes an electrode that mediates between mechanical vibration displacement and electric vibration by applying an electric field to the tuning-fork type quartz vibrating piece and utilizing a piezoelectric phenomenon. In general, the thickness of the conductive metal film is usually thin using a metal such as Au on the Cr base. The above is a general description of the structure and operation of the conventional tuning fork crystal unit and the manufacturing process.

In the present invention, by adding a new configuration to be described in more detail further below in the conventional configuration, the frequency secondary temperature coefficient is a level of conventional ^{β = -3.4 × 10 -8 / ℃} 2 This is a small reduction to −1.6 × 10 ⁻⁸ / ° C. ² or less.

  In order to facilitate understanding of the tuning fork type crystal resonator according to the present invention, the configuration of a specific example will be described with reference to FIG. 1, and then FIGS. 2, 4, and 5 will be used. The operation principle of the present invention will be outlined, and the characteristics of the SAW resonator of the present invention will be described in detail with reference to FIGS.

(Example 1)
FIG. 1 shows an embodiment of a tuning fork type crystal resonator (hereinafter simply referred to as a resonator) according to the main inventions of claims 1 to 4.

The names of the respective parts in FIG. 1 are tuning fork-type crystal vibrating pieces 100 and 101, and represent two states existing in one vibrating piece indispensable for constituting the present invention. 100 represents a resonance frequency f0 = 32 kHz corresponding to the vibration mode A and a state having a fundamental wave bending vibration displacement Ux symmetric with respect to the electric axis direction X (Note: description of 32 kHz and the like is about 32768 Hz. Abbreviated display meaning frequency). Reference numeral 102 denotes left and right arms of the tuning-fork type vibrating piece, 103 is a positive / negative electrode formed on the main surface, and 104 is a negative / positive electrode formed on the X side surface. Incidentally, the positive and negative electrodes are formed in pairs on the opposing surfaces and driven by the voltage applied to the positive and negative electrodes. In order to make the parametric phenomenon used in the present invention more effective, when there is a groove formed on the main surface, the formed electrode is somewhat complicated, but this does not impair the spirit of the present invention (FIG. The groove is not shown in FIG. The outline of the tuning-fork type crystal vibrating piece written with a broken line shows the shape of the stationary state. 106 is the + X-axis direction, and 105 is the + Y "-axis direction.
(Note: As already explained, it is added that the conventional product has only vibration mode A).

  Next, the state of the vibration mode B 101 will be described. The operating frequency of this mode B is f1, which is significantly different from the resonance frequency f0 of the vibration mode A described above. Therefore, it is refused that linear coupled vibration cannot be performed between vibration modes A and B (the meaning of linear coupled vibration is a system described by simultaneous differential equations with constant coefficients).

  In the present invention, a so-called parametric vibration phenomenon is interposed between vibration mode A and vibration mode B, and both operate in a non-linear manner. (See FIG. 2 for details). Reference numerals 110 and 111 denote primary Z bending vibration states in which the vibration mode B has an asymmetrical displacement Uz in the Z direction perpendicular to the primary higher-order main surface. 109 and 108 indicate the direction of vibration displacement. Incidentally, in the vibration mode B, the electrode member 103 and the like are not shown because the coupling phenomenon is mechanical without involving an electric system. The vibration mode B has the same function and effect even in the first-order in-phase bending vibration mode in which the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1 is almost twice f0. . Incidentally, in the parametric phenomenon, when the relationship between the frequencies f1 and f0 is f1 = n (f0 / 2) (n = 1, 2, 3,... Is an integer), the coupling phenomenon between the two systems is It is known to be prominent. Even in the present invention, as a result of various experimental confirmations, it has been found that this parametric phenomenon occurs also in the tuning fork type crystal resonator.

  Further, the electrode member which is the above-mentioned coupling member is preferably made of a metal and a metal oxide which are better and harder than the Young's modulus E11 in the + Y′-axis direction of the crystal. For example, it can be formed of Cr metal and its oxide, Ni metal and its oxide, Ti metal and its oxide, Si metal and its oxide, and the like. Further, the electrode member as the coupling member may be laminated with Au, aluminum or the like to have a coupling function and an electrical conduction function.

  In the present invention, the film thicknesses of the metal and the metal oxide are formed such that the frequency increase amount fup of the tuning fork type crystal resonator is changed from +1000 ppm to +3000 ppm as a frequency change rate. The frequency increase amount fup is set to be significantly larger than the level of +500 ppm or less, which is the increase amount of the conventional product. The frequency increase amount fup increases substantially in proportion to the film thickness of the metal and metal oxide. For example, when Cr metal is used, the film thickness H is about 500 to 1000 angstroms corresponding to the frequency increase amount fup of +1000 ppm to +3000 ppm.

  Furthermore, regarding the operating frequencies f0 and f1 of the vibration modes A and B, for example, the resonance frequency f0 is 32768 Hz, and the high-order resonance frequency of the f1 is approximately 65536 Hz, which is twice that of 32768. Most preferred. However, it is possible to estimate the possibility that it can be realized with other frequency relationships.

  FIG. 10 shows an arrangement relationship of specific resonance frequencies with respect to (arm thickness / arm width) of the tuning fork type crystal resonator. The arm thickness corresponds to the thickness of the crystal Z-cut plate. A curve 1000 in FIG. 10 is a resonance frequency of the fundamental wave X bending vibration mode (corresponding to mode A), and 1001 is a resonance frequency of the primary Z in-phase bending vibration mode (corresponding to mode B). Here, the primary Z in-phase bending vibration is a mode in which the displacement Uz of the left and right arms vibrates in the same direction with the same phase. Further, point P in the figure is a point giving a frequency of 32768 (Hz) in the fundamental wave X bending vibration mode when (arm thickness / arm width) is 0.96, and Q point is the same (arm thickness / arm width). In the width ratio, the frequency is 65536 (Hz). The (arm thickness / arm width) ratio is preferably 0.96, but if it is at least in the range of 0.9 to 1.0, the self-temperature compensation effect of the present invention may be realized.

Next, the vibration displacement actually observed by laser Doppler measurement is such that U0 = Ux displacement at f0 = 32768 kHz is 10 microns, and vibration displacement U1 = Uz displacement perpendicular to the main surface at f1 = 65536 kHz is about several hundred nm. Can be observed. The displacement ratio (U1 / U0) is a combined state in which the ratio is about 10 ⁻³ to 10 ⁻² . The actual Uz displacement observation results are shown in FIG. In FIG. 9, the upper characteristic diagram shows the waveform of the main surface vertical vibration component Uz (901) of the conventional product. In the conventional product, Uz of 901 oscillates at a frequency of 32 kHz, and in this case, the self-temperature compensation of the frequency temperature characteristic does not occur. On the other hand, the lower characteristic diagram of FIG. 9 shows the waveform of the main surface vertical vibration component Uz (902) of the product of the present invention. In the product of the present invention, Uz of 902 vibrates with a frequency component of 65530 Hz that is almost twice 32768 Hz. In this case, the self-temperature compensation of the frequency temperature characteristic occurs. A portion indicated by a broken line 903 is different from the conventional product due to generation of a double harmonic component. Here, it should be noted that the Uz component of 32 kHz does not produce a self-temperature compensation effect. This is proof that temperature compensation has not yet occurred in the linear combination between almost the same frequencies.

  At the end of the description of the embodiment, a specific size and shape of the tuning-fork type crystal vibrating piece will be described in the case where the frequency f0 is 32768 Hz. First, the rotation angle θ of the crystal rotation Z-cut plate is set in the range of 0 to 8 degrees so that the vertex temperature θmax of the frequency temperature characteristic of the tuning fork type crystal resonator is in the range of 20 ° C. to 60 ° C. Thus, the above-described excellent frequency temperature characteristic is realized. Next, regarding the dimensions and shape of the tuning-fork type crystal vibrating piece that realizes the temperature compensation function of the present invention, the length of the arm portion is generally in the range of 1500 to 1600 μm, the arm width is in the range of 90 to 110 μm, the thickness of the arm, that is, the crystal Z Cut plate thickness is in the range of 90 to 110 μm, groove width is in the range of 60% to 80% of arm width, groove length is in the range of 40% to 60% of arm length, Y'-axis direction of the base connecting the left and right arm parts The length of was set in the range of 500 to 700 μm.

  Next, how the frequency temperature characteristic of the conventional product is improved by the above-described configuration of the present invention will be briefly described using the similar model system. In this explanation, the following reference material is considered effective.

  Reference 1) 16.338 Lab Report # 2: Kaptisa's Stable Inverted Pendulum (authors AM Budge, E. Frazzoli December 14, 1997).

  The above-mentioned document 1 investigates a coupling relational expression between frequencies of two high and low vibrations in a parametric vibration phenomenon (parametric vibration phenomenon) which is a nonlinear operation phenomenon of the inverted pendulum of FIG. 5 by theory and experiment.

  In FIG. 5, reference numeral 500 denotes a rotatable bar member, which is fixed so as to be rotatable at a fulcrum 502. Reference numeral 503 denotes the center of gravity of the bar member 500, and the gravity G acts downward in FIG. 5 to generate a rotational force F1. The fulcrum 502 is connected to the second connecting rod member 501, and is inverted by applying a periodic vibration Uz (t) = λ cos (ω 1 · t) having an amplitude λ to the connecting rod member 501. Parametric external force is applied to the pendulum system (comparison with literature is ω1 = ωfast). In this state, assuming that the inverted pendulum vibrates at a stable angular frequency, this frequency is set to ω0 (the comparison with the literature is ω0 = ωslow). At this time, Document 1 suggests that the relationship between ωslow and ωfast is the following equation.

  Using this equation (1), we have deduced and derived some relational expressions that are not important to the present invention. Considering the angular frequency ωslow as a function of the excitation amplitude λ in equation (1) and taking the total derivative,

  On the other hand, in the tuning fork type crystal resonator, the displacement in the Z direction Uz (corresponding to = λ = dλ) leaks vibration energy to the outside of the vibration piece when it is supported and fixed at the base of the vibration piece (112 in FIG. 1). Thus, an energy loss in the vibration mode A (frequency f0) is generated. When this relationship is expressed using the characteristic equation of the crystal resonator, Q = 1 / (ωRC) = 2πE / dE,

  Where Q is the Q value of the vibrator, E is the total energy of vibration, dE is the loss energy, R is the equivalent series resistance, C is the equivalent series capacitance, and ω is the resonance frequency.

  By substituting equation (3) into equation (2) and using the relationship of ω1 = 2ω0, which is said to be able to realize a particularly stable state, if ωslow = 32 kHz and ωfast = 64 kHz,

  Alternatively, when the inverted pendulum system is described by the Mathieu equation, which is the governing equation of parametric vibration (see FIG. 2), the relational expression between the excitation amplitude λ and q described above is

(Y represents the rotation angle θ of the pendulum, and z corresponds to a time variable.)
Since there is a relation q = − (3λ / L), in the equation (2), λ is replaced with q,

Is obtained.

  The meaning of equation (6) means that the frequency ωslow = ω0 = 32 kHz of the vibration mode A increases according to the square of the amplitude q. That is, frequency temperature compensation can be realized. Further explanation is needed to make this conclusion clearer.

Before proceeding to the next description, the meaning of the Mathieu equation is applied to a tuning fork type crystal resonator and a description is added. Without wherein time variation claim 2Qcos2z (corresponding to z in the time variable t) in (5), equation (5) is a harmonic oscillator with a second-order differential equation to simple constant a = .omega.0 ² coefficients It becomes the governing equation. The cause of the occurrence of the time change term 2qcos2z is that the coupling member and electrode film formed on the arm portion of the tuning fork type crystal resonator is deformed by the deformation of the Uz component due to the vibration displacement Ux and Ux, and the electrode member is slightly deformed. In other words, a non-negligible stress T that periodically changes with time is generated. This is the time change term 2qcos2z. The principle of this side is theorized in detail in Document 2.

Reference 2) HFTiersten: “Perturbation theory for linear electroelastic equations for small fieldes superposed on a bias”, Acoustic Society of
America, pp. 832-837 (1978).

According to Document 2, the generated stress T is equivalent to an elastic constant or an increment of the Young's modulus E11 of the arm. FIG. 8 shows a cross-sectional view of the arm of the tuning fork type crystal resonator of the present invention. This will be described in more detail with reference to FIG. In FIG. 8, the hatched area 800 in the upper stage is a crystal part, 801 is a groove formed by removing the crystal part with hydrofluoric acid or the like, and a film 802 laminated on the crystal is a coupling member / electrode made of a metal and its oxide. It is a member. The crystal arm portion 800 is formed with a groove and thus has a reduced overall rigidity. The lower characteristic diagram shows the increase / decrease dG characteristic from the steady value G of the elastic constant, that is, the effective spring constant of the crystal, the metal as the coupling member, and its oxide film. The increase in spring constant dGm0 due to the formation of the metal and its oxide film can be converted by the frequency increase amount fup of the vibrator, and therefore appears as an effect of about +1000 ppm to +3000 ppm at the temperature θmax. G0 is an effective spring constant of the quartz part. The increase dGm0 (θmax) of this small spring constant varies depending on the temperature (803). Since the first order temperature coefficient is about 10 ⁻⁴ / ° C., the amount of this change is (1000 to 3000) ppm × 10 ⁻⁴ × 100 (° C.) = (10 to 30) ppm in the temperature range of 100 degrees. It becomes.

  On the other hand, G0 of only quartz also changes with temperature (increment dG0), but changes about twice the frequency change amount of the frequency temperature characteristic. When the temperature difference between the frequency change rate 0 ppm and θmax at the temperature θmax is 54 ° C., the change is about dG0 = 2 × 100 ppm. The difference dG = dGm−dG0 between the two is considered to be q which appears in the above-described equation (5) or an amount proportional to the excitation amplitude λ (q∝λ∝dG). Therefore, it can be estimated that the temperature compensation degree of the frequency temperature characteristic increases as the electrode film becomes thicker. However, it can be easily understood from the above explanation that the metal needs to be larger than the Young's modulus E11 of the crystal, and therefore, must be a hard metal.

  Next, FIG. 4 shows the conventional series equivalent resistance R1 and the tuning-fork type crystal resonator of the present invention with respect to the low temperature side region from the vertex temperature θmax for the purpose of verifying the relational expression given by the above-mentioned formula (4). The horizontal axis represents the difference dR1 of the series equivalent resistance R1 ′, and the vertical axis represents the difference df0 between the resonance frequency f0 of the conventional product and the resonance frequency f0 ′ of the tuning-fork type crystal resonator of the present invention as a frequency change rate. It is. 401 in the figure is the actual measurement result, 400 is the correlation function, and the correlation coefficient r is 0.9842, which is a high degree of correlation. As described above, it can be said that the relationship of Expression (4) is established. Considering that the equation (4) is derived from the equations (2) and (3), it is considered that the parametric vibration phenomenon is proved to be an operation principle.

The contents described above are illustrated in FIG. Use Figure 2 will be briefly described together that d (ωslow) α dq ² is a conclusion of the foregoing is intended to realize a frequency temperature compensation.

  In FIG. 2, reference numeral 200 surrounded by a broken line in the upper stage denotes an X-displacement bending tuning fork vibration (mode A) having a frequency f 0 that forms the configuration of the conventional product. Also, the lower broken lines 201, 202, 203, and 204 are newly added portions as the configuration of the present invention. The meaning of 'nonlinear phenomenon due to stress elasticity effect of crystal shape + hard metal film, that is, parametric vibration phenomenon' shown in 201 is simply explained by coupling with the electrode film by the vibration displacement of 32 kHz of the crystal itself. The metal film also serving as a member is deformed, and vibration stress T (t) = Acos (2πf0t) of f0 = 32 kHz is generated. According to the literature 2, the vibration stress T is equivalent to an elastic constant C, a Young's modulus E, and further a spring constant K. Therefore, the spring constant K is a time t-dependent term K = a (constant) + A cos (2πf0t). This is why this is called parametric vibration. Mode B having a resonance frequency of f1 = 2 · f0 is excited through the vibration stress T (that is, a parametric vibration phenomenon). The Mathieu equation describing this case is:

However, Uz is a vibration displacement of mode B and has a first-order in-phase or anti-phase vibration state, Uz (t), tt is a second-order time differential term of Uz, and a (constant) has mode B. Uz's own natural frequency a = (2π · f1) ² , A is an amplitude constant, f0 is the frequency of mode A, 32 kHz, and t is time.

  The inverted pendulum system is a model similar to the parametric vibration phenomenon used in the above-described tuning-fork type crystal resonator according to the present invention. Therefore, the inverted pendulum system is used for explanation as the operation principle of the present invention. The meaning of the similar model is that it can be described by a so-called Mathieu equation. The lower part in 201 of FIG. 2 is a Mathieu equation obtained by converting 2πf0t = 2z.

  Next, the frequency temperature characteristics of the tuning fork type crystal resonator of the present invention and the temperature characteristics of the series equivalent resistance R1 will be described with reference to FIGS.

  First, with respect to FIG. 6, the upper characteristic diagram is the frequency temperature characteristic diagram, and the lower graph is the temperature characteristic of the equivalent series resistance R1. In the figure, the horizontal axis represents the ambient temperature (unit: ° C) to be measured, and the vertical axis represents the equivalent series resistance R1 (Ω) and the frequency change rate df / f (ppm). Curves 603 and 613 in the figure are the frequency temperature characteristics of the conventional product and the temperature variation of the equivalent series resistance, respectively, and 602 and 612 are the same characteristics to which the effect of the present invention (setting of the film of the coupling member) is moderately added. is there. Reference numerals 601 and 611 denote frequency temperature characteristics and equivalent series resistance when the film thickness condition of the coupling member is appropriately set. For example, when Cr metal is used, the film thickness H is about 500 to 1000 angstroms corresponding to a frequency increase amount fup of +1000 ppm to +3000 ppm.

  Next, FIG. 7 shows another embodiment of the frequency temperature characteristic of the tuning fork type crystal resonator according to the present invention. 700 in the figure indicates a state in which self-temperature compensation is performed by the configuration of the present invention, and a curve 702 which is a top-order quadratic function is a state before temperature compensation. The state in the figure is the case where the apex temperature θmax is 60 ° C. Under this condition, the frequency temperature characteristic achieves a frequency accuracy of about 10 ppm in the −20 to 70 ° C. range. The method of changing the apex temperature θmax can be realized by setting the cut angle θ in FIG. 3 by rotating it counterclockwise in the range of 0 ° to + 8 °.

  As described above, the resonance frequency f0 is mainly described for 32 kHz, but it is added that it is clear that the technique of the present invention is effective even if f0 is different from 32 kHz.

  The tuning fork type crystal resonator of the present invention has a resonance frequency of 32 kHz utilizing a nonlinear parametric vibration phenomenon existing between modes having significantly different natural vibration frequencies existing in a crystal tuning fork type vibration piece, Tuning fork crystal units that have a self-compensating frequency temperature characteristic, which is a low-order quadratic function, and have achieved an almost flat frequency temperature characteristic (± 5ppm) in the operating temperature range of -10 to + 60 ° C. Can be provided. Therefore, it is possible to realize a social situation in which the electronic time of the quartz wristwatch and the network society is less distorted by using the tuning fork type crystal resonator with significantly improved frequency temperature characteristics. Time accuracy can be maintained.

The perspective view which shows the vibration displacement state of the vibration mode which one Example of the tuning fork type crystal resonator of this invention has. The explanatory view showing the coupled vibration operation situation of the tuning fork type crystal vibrator of the present invention. The angle orientation figure which mounts the tuning fork type crystal vibrating piece of the present invention from the crystal. The characteristic view which the tuning fork type crystal unit of the present invention has. The system block diagram of the inverted pendulum for demonstrating the operation | movement principle of this invention. The characteristic view which the tuning fork type crystal unit of the present invention has. The other characteristic view which the tuning fork type crystal unit of the present invention has. FIG. 3 is an explanatory diagram relating to a tuning fork type crystal resonator according to the present invention. The other characteristic view which the tuning fork type crystal unit of the present invention has. The other characteristic view which the tuning fork type crystal unit of the present invention has.

Explanation of symbols

100 Tuning fork type crystal resonator (mode A: fundamental wave X bending vibration state)
101 Tuning fork type crystal resonator (mode B: primary Z bending vibration)
102 Arm 103 Positive electrode / Non-linear coupling member (arranged on the main surface)
104 Negative electrode and non-linear coupling member (located on the side)
112 Base

Claims (13)

A crystal Z-cut plate whose main surface is the surface between the electric axis X and the mechanical axis Y of the right crystal crystal is rotated from 0 to 8 degrees counterclockwise around the electric axis. In the tuning fork type crystal resonator in which a crystal resonator having a tuning fork shape in which the longitudinal direction of the arm portion of the tuning fork is Y ′ is formed and grooving processing is performed on the front and back main surfaces of the arm portion,
The tuning fork type crystal resonator has a vibration mode A in which the displacement of the arm portion is in the electric axis direction X and the operating frequency is f0, and the displacement of the arm portion is Z perpendicular to the main surface and operates. There is a vibration mode B in which the frequency f1 is significantly different from f0,
The two vibration modes A and B are coupled by a non-linear parametric vibration phenomenon generated through a coupling member formed with an arm, and the second-order temperature coefficient β of the original frequency-temperature characteristic curve of the vibration mode A. Tuning-fork type quartz crystal resonator that has been compensated for by realizing a flat frequency temperature characteristic.   2. The vibration mode B is a first-order in-phase bending vibration mode in which the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1 is approximately twice f0. Tuning fork type quartz crystal.   The vibration mode B is a primary anti-phase bending vibration mode (so-called primary walk vibration) in which the displacement of the arm is Z perpendicular to the main surface and the operating frequency f1 is almost twice f0. The tuning fork type crystal resonator according to claim 1.   In the arm portion, the coupling member formed on the arm portion is formed with a metal film or an oxide film having a considerable thickness, so that the degree of coupling is increased by a non-linear parametric vibration phenomenon. The tuning fork type crystal resonator according to Item 1.   5. The tuning fork type crystal resonator according to claim 4, wherein a metal film or an oxide film as a coupling member formed on the arm portion is formed of Cr metal and its oxide.   5. The tuning fork type crystal resonator according to claim 4, wherein a metal film or an oxide film as a coupling member formed on the arm portion is formed of Ni metal and its oxide.   5. The tuning fork type crystal resonator according to claim 4, wherein a metal film or an oxide film which is a coupling member formed on the arm portion is formed of Ti metal and its oxide.   5. The tuning fork type crystal resonator according to claim 4, wherein a metal film or an oxide film, which is a coupling member formed on the arm portion, is formed of Si metal and its oxide.   A metal film or an oxide film, which is a coupling member formed on the arm portion, is formed of Cr metal and its oxide, and the frequency increase amount of the tuning fork type crystal resonator by the Cr metal and its oxide becomes the frequency change rate. 5. The tuning fork type crystal resonator according to claim 4, wherein the tuning fork type crystal resonator is from +1000 ppm to +3000 ppm.   The tuning fork type crystal resonator according to claim 1, wherein a resonance frequency f0 of the tuning fork type crystal resonator is 32768 Hz, and a high order resonance frequency of the f1 is approximately 65536 Hz. If the maximum value U0 of the vibration displacement of the resonance frequency f0 of the tuning fork type crystal resonator is 1, the relative ratio U1 / U0 of the vibration displacement maximum value U1 of the higher-order resonance frequency of the f1 is approximately 10 ^−3. The tuning fork type crystal resonator according to claim 1, wherein the tuning fork type crystal resonator is in a range of from 10 to ^2.sup.-2 .   2. The tuning fork type crystal resonator according to claim 1, wherein the peak temperature θmax of the frequency temperature characteristic of the tuning fork type crystal resonator is in a range of 20 ° C. to 60 ° C.   The direction and dimensions of the tuning-fork type crystal vibrating piece are set such that the rotation angle θ of the crystal rotation Z-cut plate is set in the range of 0 to 8 degrees, the length of the arm portion is generally in the range of 1500 to 1600 μm, and the arm width is In the range of 90 to 110 μm, the thickness of the arm, that is, the thickness of the quartz Z-cut plate is in the range of 90 to 110 μm, the groove width is in the range of 60% to 80% of the arm width, and the groove length is in the range of 40% to 60% of the arm length. The ratio of (arm thickness / arm width) is in the range of 0.9 to 1.0, and the length in the Y′-axis direction of the base that joins the left and right arms is set in the range of 500 to 700 μm. 2. A tuning fork type crystal resonator according to claim 1, wherein the thickness of the formed Cr metal bonding member is in the range of 800 to 1000 angstroms.

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