WO2003010887A1 - Piezoelectric single-crystal element - Google Patents

Abstract

The invention relates to a piezoelectric single-crystal element, which has excitation electrodes situated on at least one surface or on opposing surfaces and can be exited to a thickness shear oscillation. According to the invention, the single-crystal element has a crystal cut having an excitable fundamental tone resonance frequency in the thickness shear mode in which the effectively active electromechanical coupling factor keff lies between 0.05 % and 2 % and the linear temperature coefficient of the fundamental tone resonance frequency is zero at at least one location in the range of the working temperature of the piezoelectric single-crystal element, preferably ranging from 10 DEG C to 100 DEG C. This enables the production of resonators that have a high oscillation quality.

Description

Piezoelectric single crystal element

The invention relates to a piezoelectric single crystal element which has excitation electrodes on at least one surface or on opposite surfaces and can be excited to a thickness shear vibration, as well as different applications and a method for producing such a piezoelectric single crystal element or resonator element.

In addition to the effective material constants and the physical dimensions, the resonance frequency of a piezoelectric resonator is largely dependent on the interaction with its environment (e.g. pressure, temperature, mass loading). This naturally results in two fundamentally different areas of application. On the one hand, piezoelectric resonators are used as the frequency standard, the resonator usually being located in the feedback branch of an oscillator, thereby stabilizing the oscillator frequency in the vicinity of the resonance frequency. In this application, the influences of the environment on the resonance frequency are kept as constant as possible by hermetically sealed housings, which are either filled with protective gas or evacuated. On the other hand, piezoelectric resonators are used as the sensor element, conclusions being drawn from the measured changes in the resonance properties of the physical or chemical properties or their change over time in the environment. In both areas of application, the highest possible vibration quality of the resonance frequency in question is desirable in order to achieve particularly high short-term stability on the one hand and particularly high measurement resolution or measurement sensitivity on the other.

Definition of quality:

with φ ... phase f ..... frequency f _m .... frequency with maximum admittance

where φ in radians and f, f _m in Hz. The quality can be measured by measuring the change in phase Δφ which occurs in a frequency interval Δf in the immediate vicinity of the maximum admittance, for example using a network analyzer. The quality values, which are shown in FIG. 2, were also determined by this method.

The effective electromechanical coupling _factor k _eff for the fundamental resonance frequency or series resonance frequency f _s is defined by:

with e _e ... effective piezoelectric module

^ ... effective elastic shear constant (D = constant) ε ... effective dielectric constant (S = constant) D, S .. Dielectric shift, distortion tensor

The effective material constants ^ -, c ^ andε ^ are dependent on the cutting angle and can be calculated from the material constants of the relevant crystal material (see for example S. Haussühl, Kristallphysik, Physik Verlag, ISBN 3-87664-587-5).

The effective electromechanical coupling _factor k _eff can be determined, for example, by a network analysis. The resonance behavior of the piezoelectric resonator is based on the model of a series resonance circuit with parallel capacitance. The effective electromechanical coupling factor k _e results from the distance between the series resonance frequency f _s ≤ f _m (for definition see FIG. 1) and the parallel resonance frequency f _p = f _n (f _n .... frequency with minimal admittance, see FIG. 1) ff with:

Alle angegebenen Werte für den effektiv wirkenden elektromechanischen Kopplungsfaktor k_eff beziehen sich auf die Grundtonresonanzfrequenz f_s des jeweiligen piezoelektrischen Kristallschnitt bzw. piezoelektrischen Resonators.

All specified values for the effective electromechanical coupling factor k _eff relate to the fundamental _{resonance frequency} f _{s of} the respective piezoelectric crystal section or piezoelectric resonator.

For example, it is known from Warner AW, "Design and Performance of Ultraprecise 2.5-mc Quartz Crystal Units", Bell Sys. Tech. J., Sept., 1960, pp. 1193-1215, that a quartz AT-cut resonator (effective electromechanical coupling factor k _ef = 8% ... 9%), with a diameter of 30 mm, plano-convex surfaces, with gold electrodes, at room temperature and in vacuum (p = l, 33 * 10 ^{~ 9} bar), in the 5th overtone at a resonance frequency of 2.5 MHz, a quality Q of 5 to 6 million was reached, and an inverse relationship between the resonance frequency f _s (for definition, see FIG. 1) and the maximum achievable quality Q was found AT-cut resonator this empirically found relationship can be expressed by specifying the product of Q * f _s = 16 * 10 ⁶ MHz.

Furthermore, from Ch. Longet, G. Robichon, EFTF, 1995, pp. 141-145, an electrodeless arrangement is known with which - based on a quartz BT-cut resonator - a product Q * f _s = 30 * 10 ⁶ MHz is achieved. The excitation electrodes are not located directly on the resonator surfaces, but at a distance of a few μrπ (so-called PVA resonators). Quartz resonators of this type, which are known, for example, from US Pat. No. 4,135,108, require complex production and have large sizes.

Also from RC Smythe, RC Helmbold, GE Hague, & KA Snow, Joint Meeting EFTF - IEEE IFCS, 1999, pp. 816-820, known that a Y-cut Lananit (LGT) resonator (effective electromechanical coupling factor k _eff > 10%) with a diameter of 14 mm, plane-convex surfaces, gold electrodes, at room temperature and in vacuum (p = 1.33 * 10 ^"7 bar), in the 7th overtone at a resonance frequency of 14.058 MHz, a quality Q of 1.8 million is reached. This corresponds to a product Q * f _s = 25.6 * 10 ⁶ MHz ,

No. 4,754,187 A describes so-called SKI and SK2 sections of a quartz crystal, which are temperature-compensated and have different excitation modes a to c. The crystal cuts are double-rotated cuts, with the angle Φ = 13 ° and the angle θ = -27.5 ° for the SKl cut, for example. The aim is to excite only the b-mode and to substantially suppress the c-mode occurring at the same excitation frequency. For this purpose, an electrode arrangement is chosen which has an angle ψ with respect to the crystal axis X ¹ .

The angle ψ is first calculated theoretically for the SKl section at -75.96 °, but experimental results show one of the theoretical value very different measuring value for ψ at -15 °. The value for the electro-mechanical coupling factor is 4.1%. The aim is only a fashionable excitation and not the achievement of particularly high quality values.

The object of the invention is to propose a piezoelectric single crystal or a method for its production, in which the quality Q - particularly at vacuum pressures below 10 mbar - assumes particularly high values.

The present invention solves this problem in that the single-crystal element has a crystal cut with a stimulable fundamental tone resonance frequency in the thickness shear mode, in which the effective electromechanical coupling factor k _ef f is between 0.05% and 2%, and in that the linear temperature coefficient of the fundamental tone resonance frequency is zero at at least one point in the range of the operating temperature of the piezoelectric single crystal element, preferably in the range between 10 ° C. and 100 ° C. A crystal cut with a relatively low electromechanical coupling is therefore preferably selected in which the temperature response of the resonance frequency of the thickness shear vibration to be excited is as low as possible in the application temperature range (temperature-compensated cut). For this purpose, the temperature response of the resonance frequency must have a parabolic or a cubic frequency response, so that the linear temperature coefficient becomes zero within the application temperature range.

Advantageously, crystal materials with an effective elastic shear constant c ^ in a range from 10 to 100 GNm ^"2 are used. It is also advantageous to choose crystal materials in which, for the selected crystal cut, no hysteresis between the electric field E. Generated by the excitation electrodes and the field of dielectric displacement D arises.

It has surprisingly turned out that, for example, a piezoelectric resonator based on gallium orthophosphate (GaPO ₄ ) with a diameter of 7.4 mm and gold electrodes, which has a relatively low, effective electromechanical coupling _factor k _eff of approx. 0.2% has a very high quality value at an absolute pressure of 5 * 10 ^"5 bar. Compared to a quartz resonator, the GaPO ₄ resonator is considerably more compact (diameter of 7.4 mm, for example) and has a thickness of 0.2 mm (at a resonance frequency of approx. 10 MHz) a better diameter / thickness ratio.

In particular, if the crystal element is subjected to a thermal treatment above 150 ° C. after the application of the excitation electrodes, quality values of over 8.7 million with a resonance frequency f _s of approx. 9.816 MHz can be achieved in the fundamental tone. This results in the product Q * f _s = 85 * 10 ⁶ MHz. Furthermore, it is also possible to heat the crystal element to temperatures of over 150 ° C. during the application of the excitation electrodes. The electrodes can be applied by a CVD method (chemical vapor deposition) or a PVD method (physical vapor deposition), preferably by sputtering.

It is particularly advantageous to heat the piezoelectric resonator to temperatures of over 150 ° C. for several hours after the electrodes have been applied. For example, a GaPO ₄ resonator (f _s = 5.903 MHz) tempered for approx. 10 hours at approx. 350 ° C shows an increase in quality from approx. 350,000 under normal pressure to approx. 13 million at an absolute pressure p = 40 μbar. In contrast, a non-annealed GaPO ₄ resonator (f = 5.872 MHz), which has a quality of approx. 350,000 at normal pressure and a quality of approx. 1.75 million at an absolute pressure of 30 μbar.

The method according to the invention is thus characterized by the following steps:

• Production of a crystal cut with a stimulable basic resonance frequency, at which the effective electromechanical coupling factor k _eff lies between 0.05% and 2%, and the linear temperature coefficient of the fundamental tone resonance frequency at at least one point in the range of the operating temperature of the piezoelectric single crystal element, preferably in Range between 10 ° C and 100 ° C, zero; such as

• application of excitation electrodes on at least one surface or on opposite surfaces of the single crystal element; as well as possibly

• Annealing the crystal cut at temperatures above 150 ° C

Another characteristic of the invention is that the frequency distance from the nearest excitable secondary resonance frequency is> 80 kHz, preferably> 100 kHz. In addition, the maximum admittance of the harmonics should only reach <10%, preferably <5% relative to the fundamental resonance frequency, i.e. the nth overtone (n = 3.5, ...) should no longer be clearly excitable.

The thermal expansion behavior in the plane of the crystal section, for example in the case of crystals of point group 32, can be completely described by two linearly independent expansion coefficients an = a ₂₂ and a ₃ . It has proven to be particularly advantageous to choose a crystal cut in which the effective thermal expansion coefficient deviate (α ι and ₃₃ ) in the plane of the crystal section only by a factor <1.5.

According to a first embodiment variant of the invention, the crystal material belongs to the crystallographic point group 32, the crystal element preferably consisting of quartz-homotypic gallium orthophosphate (GaPO ₄ ).

A combination of the particularly favorable properties such as extremely high quality values, temperature compensation of the resonance frequency and a large distance between the fundamental resonance frequency and its secondary modes can be achieved by using a piezoelectric resonator based on GaPO ₄ , whereby a simply rotated Y-cut is used and the Cutting angle Φ is in a range between -80 ° and -88 °, in particular between -82 ° and -86 °.

The indication of the sign of the cutting angle Φ with respect to their direction of rotation about the crystallographic axes is made according to the “IEEE Standard on Piezo-electricity; ANSI / IEEE hours 176-1987.

According to an embodiment variant of the invention, it is provided to use piezoelectric crystal elements which belong to the crystallographic space group P321, which are described, for example, in “INTERNATIONAL TABLES FOR X-RAY CRYSTAL-LOGRAPHY, The Kynoch Press, 1969, pp. 255 is mentioned. Crystals in this space group have a Ca ₃ Ga ₂ Ge ₄ O ₄ - analog crystal structure, such as, for example, langasite (La ₃ Ga ₅ SiO ₄ ), langanite (La ₃ Ga _{5 (5} Nb _0/5 θι ₄ ), langatate (La ₃ Ga ₅ , ₅ Ta _0.5 θι) or strontium gallium germanate (Sr ₃ Ga ₂ Ge ₄ Oι ₄ ) single crystals, further examples are, for example, from BV Mill, Yu.V. Pisarevsky, EL Belokoneva, “Synthesis, Growth and some Properties of Single Crystals with the Ca ₃ Ga ₂ Ge ₄ Oι ₄ Structure ", Joint Meeting EFTF - IEEE IFCS, 1999, pp. 829-834.

In particular with langasite (La ₃ Ga ₅ SiOι ₄ ) single crystals is a combination of by choosing a simply rotated Y-cut, the angle of rotation Φ between -55 ° and -85 °, preferably between -60 ° and -70 ° low coupling and temperature compensation achievable.

Electrical vacuum gauges measure the pressure indirectly via the particle number density, which depends on the type of gas at a given pressure. The pressure scales of these devices are usually related to nitrogen pressures. If the pressure of another gas (mixture) is to be determined, the displayed pressure must be multiplied by a factor. In addition, these factors are also pressure-dependent in the case of thermal conductivity vacuum gauges (Pirani). Because of the particularly sensitive pressure dependency of the quality, in particular at vacuum pressures below 10 mbar, the crystal elements according to the invention can therefore be used excellently for pressure measurement, pressure measurement being possible regardless of the type of gas or gas composition.

Due to the possible combination of temperature compensation of the resonance frequency and low electromechanical coupling, for example in GaPO ₄ and langasite, the crystal element according to the invention can be used as a frequency-determining component (frequency standard) in oven-controlled or thermostatted oscillators.

Another advantageous application is to use the crystal element according to the invention in a vacuum (p <10 mbar) as a microbalance sensor element, in which an extremely high sensitivity to mass loading can be achieved.

Finally, the crystal element according to the invention can be used as an electronic filter with a particularly high slope.

The present invention is explained in more detail below with reference to drawings. They show

1 shows a diagram of the admittance in which the conductance is plotted on the abscissa and the susceptance is plotted on the ordinate

Fig. 2 is a diagram of the quality Q as a function of pressure for GaPO ₄ and

Fig. 3 shows the first temperature coefficient of the resonance frequency of a GaPO ₄ density shear resonator as a function of the cutting angle Φ.

Fig. 1 shows the local circle of the admittance, which is used for the description of the electrical behavior of a piezoelectric resonator. The relevant definitions of the series resonance frequency f _s , the frequency with maximum admittance f _m , the parallel resonance frequency f _p and the frequency with minimum admittance f _n can also be seen. The distance of the center of the local circle from the abscissa is proportional to the parallel capacitance C ₀ , which is formed by the resonator together with the applied excitation electrodes.

2 shows, for example, the increase in quality of a GaPO ₄ resonator (simply rotated Y-cut with k _eff between 0.2 and 0.4%), which was annealed after the application of the excitation electrodes in comparison to one annealed resonator (fundamental resonance frequency approx. 6MHz). At normal pressure, the quality values are approximately at the same high level in both cases. During the pressure reduction, the quality values of the annealed resonator increase significantly more than in the case of the unannealed resonator.

Fig. 3 shows the dependence of the linear temperature coefficient (l.TCF) of the resonance frequency of a simply rotated Y-cut of a GaPO ₄ Dickenscher resonator (C-mode) as a function of the angle of rotation Φ at a temperature of approximately 85 ° C.

Claims

PATENT CLAIMS 1. Piezoelectric single crystal element which has excitation electrodes on at least one surface or on opposite surfaces and can be excited to a thickness shear oscillation, characterized in that the single crystal element has a crystal section with an excitable fundamental tone resonance frequency in thickness shear mode, in which the effectively acting electromechanical coupling _factor k _eff between 0 , 05% and 2%, and that the linear temperature coefficient of the fundamental resonance frequency is zero at least at one point in the range of the operating temperature of the piezoelectric single crystal element, preferably in the range between 10 ° C. and 100 ° C. 2. Piezoelectric single crystal element according to claim 1, characterized in that the frequency distance from the nearest excitable secondary resonance frequency is> 80 kHz, preferably> 100 kHz. 3. Piezoelectric single crystal element according to claim 1 or 2, characterized in that the maximum admittance of the harmonic harmonics reaches only <10%, preferably <5% relative to the fundamental resonance frequency. 4. Piezoelectric single crystal element according to one of claims 1 to 3, characterized in that the single crystal element is annealed at temperatures above 150 ° C. 5. Piezoelectric single crystal element according to one of claims 1 to 4, characterized in that the effective thermal expansion coefficients in the plane of the crystal section only differ from one another by a factor <1.5. 6. Piezoelectric single crystal element according to one of claims 1 to 5, characterized in that the single crystal element consists of a crystal of the crystallographic point group 32. 7. Piezoelectric single crystal element according to claim 6, characterized in that the crystal element consists of quartz-homo-type gallium orthophosphate (GaPO ₄ ). 8. Piezoelectric single crystal element according to claim 7, characterized in that the crystal element is a single rotated Y-cut, the angle of rotation Φ being between -80 ° and -88 °, preferably between -82 ° and -86 °. 9. Piezoelectric single crystal element according to one of claims 1 to 6, characterized in that the single crystal element consists of a crystal of the crystallographic space group P321. 10. Piezoelectric single crystal element according to claim 9, characterized in that the crystal element made of langasite (La ₃ Ga ₅ SiO ₁₄ ), langanite (La ₃ Ga _5.5 Nbo _{, 5} θι ₄ ), langatate (La ₃ Ga _{5 (5} Tao _{( S} Oι ₄ ) or strontium-gallium-Germanat (Sr ₃ Ga ₂ Ge ₄ O _i4 ). 11. Piezoelectric single crystal element according to claim 10, characterized in that the crystal element is a single-rotated Y-cut from Langasite (La ₃ Ga ₅ SiO ₁₄ ), the angle of rotation Φ between -55 ° and -85 °, preferably between -60 ° and is -70 °. 12. A method for producing a piezoelectric single crystal element that can be excited to a thickness shear vibration, characterized by the following steps: • Production of a crystal cut with a stimulable basic resonance frequency, at which the effective electromechanical coupling factor k _eff lies between 0.05% and 2%, and the linear temperature coefficient of the fundamental tone resonance frequency at at least one point in the range of the operating temperature of the piezoelectric single crystal element, preferably in Range between 10 ° C and 100 ° C, zero; such as • Application of excitation electrodes on at least one surface or on opposite surfaces of the single crystal element. 13. The method according to claim 12, characterized in that the crystal element is heated to temperatures of over 150 ° C during the application of the excitation electrodes. 14. The method according to claim 12 or 13, characterized in that the crystal element is subjected to a thermal treatment above 150 ° C after the application of the excitation electrodes. 15. Use of a piezoelectric crystal element according to one of claims 1 to 14, as a pressure measuring element, in particular at vacuum pressures <10 mbar. 16. Use of a piezoelectric crystal element according to one of claims 1 to 14, as a frequency-determining component in oven-controlled or thermostated oscillators. 17. Use of a piezoelectric crystal element according to one of claims 1 to 14, as a microbalance sensor element, in particular at vacuum pressures <10 mbar. 18. Use of a piezoelectric crystal element according to one of claims 1 to 14, as an electronic filter with high slope.