JP3109596B2 - Piezoelectric resonator with ring-shaped electrode - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial application field) The present invention is provided with a piezoelectric resonator, particularly a ring-shaped electrode for suppressing the generation of spurious components while suppressing the equivalent resistance thereof sufficiently low in a high frequency range. The present invention relates to a piezoelectric resonator.

(Prior Art) Conventionally, a piezoelectric resonator utilizing thickness vibration is generally designed to minimize its equivalent resistance as much as possible.

That is, since the equivalent resistance of the piezoelectric resonator is generally inversely proportional to the electrode area, the electrode area should be as large as possible. However, if the electrode area is too large, it is well known that the symmetric zero-order mode (harmonic mode, harmoni
c mode or also called So called mode) and referred mainly vibration in addition to anharmonic higher-order mode and collectively to antisymmetric or anti-symmetric zero-order mode (a ₀ mode), symmetrical primary mode (S ₁ mode ), Anti-symmetric first-order mode (a ₁ mode),... Oscillations appear sequentially and become spurious, so that the electrode film thickness is reduced to suppress them, but if the electrode film thickness is too small, the electrode becomes thin. Has a defect that the ohmic loss increases, so that the Q of the resonator decreases and oscillation becomes difficult.

As described above, the electrode area and the electrode thickness of the piezoelectric resonator are in a trade-off relationship with each other in terms of spurious suppression, equivalent resistance, and reduction of ohmic loss of the electrode. However, there has been no solution yet.

(Object of the Invention) The present invention has been made to fundamentally remove the defects of the conventional piezoelectric resonator as described above, and in particular, does not generate spurious in principle in a high frequency band. It is an object of the present invention to provide a piezoelectric resonator capable of suppressing equivalent resistance and ohmic loss of an electrode to sufficiently low values.

(Summary of the Invention) In order to achieve the above object, the present invention relates to a thickness vibrating piezoelectric vibrator having a pair of ring-shaped electrodes arranged symmetrically on the front and back surfaces of a piezoelectric substrate on both flat surfaces. The difference between the diameter of the outer circumference and the diameter of the inner circumference is set so that the ring electrode excites the symmetric zero-order mode and hardly excites other nonharmonic higher-order modes. The ring electrode is a circular or elliptical electrode.

(Examples) Hereinafter, the present invention will be described in detail based on theoretical analysis and experimental data.

First, before describing the theory relating to the present invention and the analysis thereof, the relationship between various parameters of a piezoelectric resonator generally used in the past and spurious generation factors will be briefly described to assist understanding of the present invention.

FIG. 3 shows, as is well known, the frequency spectrum of a conventional general piezoelectric resonator (when quartz is used as the piezoelectric substrate). In order to simplify the explanation, it is theoretically mechanically excited, but electrically. Antisymmetric modes that do not appear are ignored (indicated by dotted lines in this figure).

In this figure, the horizontal axis represents the parameters when the thickness H of the piezoelectric substrate, the representative dimension a of the electrode, the overtone order m, and the amount of frequency decrease 基 づ く based on the mass addition effect of the electrode are used as parameters. The vertical axis corresponds to the vibration energy confinement ratio of the vibration of each excited mode.

By the way, a general piezoelectric resonator is designed to excite only the zeroth-order symmetric mode of vibration and not to excite other nonharmonic higher-order modes of vibration. Is inversely proportional to the square of the electrode size a, that is, the electrode area. Therefore, if the value of a is increased to reduce the equivalent resistance, the horizontal axis of FIG. Becomes large, and the design point of the resonator enters a region that excites anharmonic mode vibration, resulting in spurious (or increasing spurious). To avoid this, there is a dilemma that if the frequency decrease amount 周波 数 is set small, the ohmic loss of the electrode increases, the Q of the resonator decreases, and oscillation becomes difficult.

Such a problem is that when the resonator is an overtone piezoelectric resonator, the value of m takes a value such as 3, 5,.
There is no point in adjusting the value of the above, so there is no other way than to design the electrode size sufficiently large to reduce the equivalent resistance of the piezoelectric resonator simply by closing the eyes and simply reducing the equivalent resistance of the piezoelectric resonator due to the relationship with the oscillation circuit As described above, this was the actual situation.

In order to solve the above-mentioned defects of the conventional piezoelectric resonator, the present inventor made the following considerations. (1) Assuming that the electrodes of the piezoelectric resonator have a concentric ring shape, the vibration energy is confined in the width of the ring, and the generation of anharmonic higher-order mode vibration is a ring width dimension a−
b (a and b are the outer and inner radii of the ring, respectively) and the frequency reduction amount △.

(2) It is considered that non-axisymmetric vibration is not excited piezoelectrically by making the ring-shaped electrode generally an elliptical ring in consideration of the in-plane anisotropy of the substrate.

(3) If the above estimations (1) and (2) are correct, the ring width is set to a value within a range in which an axisymmetric nonharmonic higher-order mode oscillation does not appear on the frequency spectrum, and the ring inner radius is set. If b is selected to a large value, it is easy to increase the electrode area, so that a piezoelectric resonator having sufficiently low equivalent resistance and free from spurious spurious harmonic mode oscillations will be obtained.

Based on the above inference, a theoretical analysis was performed on a resonator having a ring electrode to obtain a frequency spectrum.

First, the resonance of the vibration energy confinement type occurs near the cutoff frequency of the thickness vibration propagating in the plane of the plate, but the propagation constant in the plane of the plate is generally different in the crystal axis direction. Is about 25% in the Z and X directions, and about 3% in the third overtone oscillation.)
Therefore, it is generally assumed that the electrode structure is not a circle but an ellipse, and considering the coordinate system as shown in FIG. 1A, the wave of the thickness vibration near the cutoff frequency can be treated as a potential wave.

Now, FIG. 1 (a) to at by x ₁ direction and the x ₃ respectively a ₁ a correction constant for the substrate anisotropic because the propagation constant is to that a generally different with respect to the axial direction of both these in the direction, a Assuming ₃ , a ₁ p ₁ = a ₃ q ₁ , a ₁ p ₂ = a ₃ q ₂ ... (1) For an in-plane isotropic piezoelectric substrate, a ₁ = a ₃ Needless to say.

Therefore, the above-described wave equation of the potential wave is approximately expressed as follows.

Where U is the displacement of the thickness vibration wave, [nu is the speed of a plane wave propagating in the thickness direction, omega is the angular frequency, omega _c denotes a cut-off angular frequency, the electrode portions ω _{c =} ω _o, the electrodeless portion omega _o '.

Since then when the the (1) is established is considered the degree of confinement vibration energy near elliptical ring of FIG. 1 (a) is similar in chi ₁ direction and the chi ₃ directions, such as the following The coordinate transformation will make vibration analysis extremely easy.

In other words, the (扱₁ , _{３ 3} ) coordinate plane of FIG. 1A is changed to (a _{1 1} ) as shown in FIG. 1B so that wave propagation in the え る₁ direction and that in the χ ₃ direction can be treated equivalently. ₁ , a _{3 ３ 3} ) plane, which is further converted to a polar coordinate (r, θ) plane.

Here, a and b are the outer and inner radii of the electrode in the polar coordinates, respectively, and the inner and outer radii p ₁ and p ₂ of the ellipse are b / a ₁ and a / b, respectively.
a ₁ , q ₁ , and q ₂ are given by b / a ₃ and a / a ₃ , respectively.

By the above coordinate transformation, the above equation (2) can be rewritten as follows.

Here, k _ro in the electrode part and the non-electrode part, respectively. Given by

The solution of equation (3) is as follows, considering that the displacement U at infinity is zero and the displacement of the electrode portion is finite.

Where n is an integer representing the order in the circumferential direction (circumferential order),
A, B, C and D are constants, Jn and Yn are Bessel functions, and In and Kn are modified Bessel functions.

On the other hand, the boundary conditions at the boundary between the electrode portion and the non-electrode portion are as follows: r = a, r = b, and U and ∂U / ∂r are continuous (7), (6), (7) more _{sin (χ 2 ω o / ν} ) ≒ sin
Using the approximation of (χ ₂ ω _o '/ ν), the following equation is derived.

The frequency equation that determines the resonance frequency is the determinant | Mij | =
The vibration mode is obtained by setting to 0
The ratio between An, Bn, Cn, and Dn can be obtained by substituting the ratio into Expression (6).

Therefore, when the circumferential order n is 1 or more, considering the symmetry of the ring-shaped electrode, non-axisymmetric vibration is mechanically excited but is canceled electrically and does not appear.
Numerical calculations were performed only for the mode of n = 0, which is the axially symmetric vibration in the (r, θ) coordinate, and the frequency spectrum was obtained. As a result, FIG. 1 (c) was obtained.

It should be noted here that the correction constant relating to the anisotropy of the piezoelectric material described above is a constant between the values of a and b on the horizontal axis of the frequency spectrum and the actual electrode dimensions [a] and [b]. a = a ₁ · for the example chi ₁ direction [a], a-b = a ₁
・ {[A]-[b]}, χ For ₃ directions, b = a ₃
[B], a−b = a ₃ · {[a] − [b]}.

Incidentally, the values of a ₁ and a ₃ are a ₁ (a direction) = 1.888 and a ₃ (z direction) = 1.94 for the fundamental wave vibration of the AT-cut quartz, respectively.
6 and a ₁ = 1.8 respectively for m-th overtone oscillation
88 / m, a ₃ = 1.946 / m, and the value of ceramics, which is an isotropic piezoelectric material, does not vary depending on the composition, but Nepec-8 (trademark; Tohoku) used to verify the theory of the present invention described later. A ₁ = a ₃ ≒ 1.0 for the piezoelectric ceramics sold by Metal Industry Co., Ltd.).

Note that the above-mentioned correction constants related to the anisotropy of the piezoelectric material are described in the following documents, and therefore, explanations thereof will be omitted to avoid complication of the description. Sekimoto, Ihara, Nakata, Miura: "Spurious Suppression of Quartz Crystal Resonator by Adding Mass to Electrode Edge and Charge Cancellation", IEICE Transactions, J69-A, P.90
4 (1976). Based on the results of the theoretical analysis described above, a prototype of a ceramics piezoelectric resonator having a ring-shaped electrode was fabricated, and the results of comparing various characteristics with a circular electrode resonator having the same electrode area are shown in FIGS. 2 (a) to 2 (e). It will be described using FIG.

FIGS. 2 (a) and 2 (b) are experimental data showing spurious characteristics of a ceramics resonator manufactured based on the design shown in FIG. 2 (e) except that the shape of the electrodes is substantially the same. In contrast, the resonator having a circular electrode clearly generates a symmetric first-order mode vibration as spurious (see FIG. 7A), whereas the ring-shaped electrode shown in FIG. In this case, no spurious due to anharmonic higher-order mode vibration was generated, and a piezoelectric resonator having good spurious characteristics was obtained.

Regarding the Q and equivalent resistance of the resonator, the resonator with a ring-shaped electrode was considerably deteriorated compared to that of a circular electrode, even though the electrode area was the same. However, this can be sufficiently understood that the degree of confinement of the vibration energy of the ring-shaped electrode is somewhat inferior to that of the circular electrode, and this problem can be understood if the electrode area is greatly increased. That is, ring electrode representative dimensions ab
Is fixed to a value that does not cause spurious, while the inner and outer radii [a] and [b] of the ring are slightly increased to greatly increase the electrode area.

From the experimental results and considerations described above, the validity of the above-described basic theory and analysis results of the present invention was confirmed.

It should be noted that the comparison between FIGS. 9C and 9D is the same as that described above, so that the description of the experimental results will be omitted to avoid complication of the description.

In the above, the experimental example of the resonator using the piezoelectric ceramics as the isotropic material as the substrate and, therefore, the resonator with the circular ring electrode has been described. It will be necessary to attach an elliptical ring electrode.

For example, in the case of an AT-cut quartz substrate, the propagation constant in the χ direction for the fundamental vibration is about 25% larger than that in the z direction, so the ring electrode also has a corresponding inner and outer radius in the χ direction as compared to that in the z direction. It is better to use an elliptical ring electrode that is 25% larger.

Based on the above concept, a circular electrode resonator for tertiary overtone and an elliptical ring electrode resonator using an AT-cut quartz substrate were prototyped and compared.

The sample used in this experiment has parameters as shown in FIG. 4 (c), and the ratio between the inner and outer radius of the electrode in the χ direction and the z direction is the difference between the propagation constants in these two directions (for the third order overtone oscillation, (A difference of about 3%).

In this experiment, the limit of oscillations of the symmetric first-order mode on the frequency spectrum did not appear as spurs in the resonator having a circular electrode and an elliptical ring electrode. Or Is selected and Q, equivalent resistance and capacitance ratio of the two are compared.

Examination of this result with FIG. 9C shows that the equivalent resistance of the resonator having the circular electrode is extremely large and Q is extremely small, and is not practically practical. This is because the resonators having circular electrodes used in the experiments were completely different from those actually used today, and various parameters were selected only with a view to not generating spurs. If the equivalent resistance, Q, etc. are designed so as to satisfy any value as in the case of the next overtone crystal resonator, it means that spurious will always occur.

On the other hand, the piezoelectric resonator of the present invention having an elliptical ring electrode can increase the outer diameter of the electrode relatively freely, so that it is possible to use a large-area electrode. It will be understood that it is possible to obtain a resonator having a small Q and an extremely small equivalent resistance and capacitance ratio.

By the way, as a conclusion of the theoretical analysis and experimental results of the present invention described above, the relationship between the excitation of anharmonic higher-order mode vibration of the symmetric first-order mode and the second-order mode and the inner diameter of the ring electrode will be briefly described with reference to FIG. I do.

This figure shows, for example, the frequency spectrum shown in FIG. If the value of is slightly smaller than 1, no spurious in the symmetric first-order mode will appear, and as long as the ring inner diameter dimension b is selected, no spurious will be generated. The occurrence of the mode is substantially independent of the ring inner diameter and is determined by the ring width ab. Therefore, the value of ab is set to a value at which no spurious appears, and the ring inner diameter b is adjusted to reduce the electrode area. It is shown that if it is made sufficiently large, a resonator having sufficiently small equivalent resistance and no spurious can be obtained.

Next, a method for manufacturing a piezoelectric resonator having the above-described ring electrode will be briefly described.

In order to mass-produce a piezoelectric resonator, it is general to deposit a material for an electrode by contacting a mask having a hole corresponding to an electrode portion having a desired shape with a piezoelectric substrate.

If such a general method is applied to the formation of the ring electrode according to the present invention, the problem is how to fix the mask covering the non-electrode portion at the center of the ring to the mask frame. Is expected to be a little difficult.

In order to solve this problem, in the present invention, FIG.
As shown in FIG. 2B, a mask 2 corresponding to the shape of the electrodeless portion is fixed and held at the center of the mask frame 1 using a strip 3 having an appropriate width. The electrode 5 is formed. That is, an electrode having a slit 6 in at least a part of the ring electrode.

In this way, if the width of the slit 6 is small, there is no significant effect on the confinement of vibration energy.
Is provided so as to divide the electrode lead portion 7, FIG.
Even if a slit 8 is further added to the ring electrode 5 as shown in FIG. 5, the electrode lead portion 7 has a special problem because both sides of the slit 6 are electrically connected with a lead wire (not shown) by a conductive adhesive or the like. Does not occur.

In the above, the theory, theoretical analysis, experimental examples and electrode configuration methods of the present invention have been described. Mention the differences.

Conventionally, as shown in FIG. 7, there is an example in which an extremely thin (small frequency drop △) ring electrode 11 is provided on a piezoelectric substrate 9 or 10 having a convex or bevel-shaped cross section.

The purpose of this purpose is to greatly increase the Q of the piezoelectric vibrator in the low frequency band.
Or, because the cut-off frequency at the center of 10 is low and the electrode 11 is thin, the vibration energy is confined inside the ring as shown in this figure, and Q is improved because there is no mass of the electrode that interferes with vibration in this part. It does not significantly reduce the equivalent resistance and is completely independent of spurious suppression.

It is especially noted that, above all, this idea can only be applied to piezoelectric resonators in the low frequency band (the piezoelectric resonator in the high frequency band has a very thin substrate and cannot be made into a convex section). I want to.

(Effects of the Invention) Since the present invention is constructed as described above, the spurious of a piezoelectric resonator that oscillates a high frequency band, especially an overtone frequency, for which no conventional solution exists, is completely prevented. Since the equivalent resistance can be suppressed to a low level, the frequency is increased, and there is a remarkable effect in responding to the design of a piezoelectric resonator in which the strictness of various characteristics such as oscillation conditions and high Q is further increased.

[Brief description of the drawings]

FIGS. 1 (a) and 1 (b) are diagrams for explaining parameter setting for performing a theoretical analysis of a vibration mode of a resonator having a ring electrode according to the present invention, and FIG. 1 (c) is a diagram showing a result of the theoretical analysis. FIGS. 2 (a) to 2 (e) show frequency spectrum diagrams, and FIG. 2 (a) to FIG. 2 (e) show comparison experimental data of a piezoelectric resonator having a circular ring electrode according to the present invention and a conventional piezoelectric resonator having a circular electrode, respectively. FIG. 4 (a) to FIG. 4 (c) are frequency spectrum diagrams of a general piezoelectric resonator having a circular electrode, and FIGS. 4 (a) to 4 (c) are comparative experiments of a piezoelectric resonator having an elliptical ring electrode according to another embodiment of the present invention and a conventional general piezoelectric resonator. Diagram showing data, fifth
FIGS. 6A to 6C are diagrams illustrating the dependence of spurious characteristics on the inner diameter of a ring electrode in the piezoelectric resonator according to the present invention, and FIGS. 6A to 6C are diagrams respectively illustrating an electrode forming mask and a piezoelectric resonator according to the present invention. FIGS. 7A and 7B are views for explaining the shape of the formed electrode, and FIGS. 7A and 7B are views for explaining a conventional piezoelectric resonator having a ring electrode. 4 ... Piezoelectric substrate, 5 ... Ring-shaped electrode, 6,8 ... Slit.

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Pasuyoshi Nakamura 3-18-2 Minaminakayama, Sendai City, Miyagi Prefecture (72) Inventor Ryoichi Yasike 1816 Tsuchiya, Hiratsuka City, Kanagawa Prefecture

Claims (3)

(57) [Claims] 1. A thickness vibrating piezoelectric vibrator having a pair of ring-shaped electrodes arranged symmetrically on both sides of a piezoelectric substrate in flat and front-back parallel regions, wherein the ring electrodes excite a symmetric zero-order mode, A piezoelectric resonator having a ring-shaped electrode, wherein a difference between an outer diameter and an inner diameter is set so as to hardly excite other nonharmonic higher-order modes. 2. A piezoelectric device having a ring-shaped electrode according to claim 1, wherein a slit for cutting said ring-shaped electrode is provided in at least one desired position of said conductor ring constituting said ring-shaped electrode. Resonator. 3. The ring-shaped electrode according to claim 1, wherein said ring-shaped electrode is an elliptical ring-shaped electrode having a ratio of a short axis to a long axis corresponding to anisotropy of thickness vibration wave propagation in a plane of said piezoelectric substrate. A piezoelectric resonator having the ring-shaped electrode according to the range (1) or (2).