Quartz crystal plate for quartz crystal resonator thermometer and preparation method thereof

Abstract

The present invention discloses a quartz crystal plate for a quartz crystal resonator thermometer and a preparation method thereof, wherein the quartz crystal plate has a cut shape represented by (yxwl)φ l / θ l , where: y represents the thickness direction of the initial plate parallel to the y-axis, x represents the length direction of the initial plate parallel to the x-axis, and w represents the counterclockwise rotation φ around the plate width axis l Angle, get the plate after the first rotation, l represents the counterclockwise rotation θ around the length direction of the plate after the first rotation l The angle of the second rotation is 14.7°<φ l <17.8°,5.6°<θ l <11.5°. The advantage is that by selecting a specific cut type of quartz crystal plate, the cut quartz crystal plate has a good linear temperature-frequency relationship in a wide range and can be used to prepare a quartz crystal resonator thermometer.

Description

Technical Field

[0001] The invention relates to a quartz crystal plate, in particular to a quartz crystal plate used for a quartz crystal resonator thermometer and a preparation method thereof. Background Art

[0002] A quartz resonator is an electronic device that uses the inverse piezoelectric properties of quartz crystal to convert mechanical vibrations into a precise, stable-frequency alternating current signal. It is equivalent to an electronic oscillator circuit and is commonly used for precise timing and frequency control. The core component of a quartz crystal resonator is a quartz crystal plate, which is obtained by precisely cutting artificially grown quartz crystal. Because quartz crystal is a typical anisotropic material, different cutting angles will cause the crystal plate's properties to change. Specifically, the specific cutting angle is called the cut type.

[0003] Since the mechanical vibration of the quartz crystal plate is very stable and quartz has a piezoelectric effect, its mechanical vibration can be stimulated by applying an alternating current of a specific frequency, thereby outputting a stable AC signal source.

[0004] The frequency of the signal generated by a quartz resonator is very precise, and even slight changes in the conditions will cause the resonator's frequency to shift. When the ambient temperature fluctuates, the resonator's frequency will drift slightly, a phenomenon known as the temperature-frequency relationship, which is very easy to detect. Resonators with different quartz crystal cuts have different temperature-frequency relationships. For resonators used for timing and frequency control, it is desirable to have an operating frequency that is unaffected by ambient temperature, thus achieving a resonator with stable frequency and performance. Common cuts for such quartz crystal resonators include AT cut and SC cut.

[0005] However, there are certain quartz crystal cuts that produce resonators whose frequency varies significantly and linearly with temperature. Clearly, these resonators can be used as temperature sensors. By measuring the change in the resonator's frequency as the ambient temperature changes, the known temperature-frequency relationship can be used to infer the temperature change, ultimately providing a precise reading of the actual temperature.

[0006] Based on this concept, researchers have discovered several quartz crystal cuts with excellent linear temperature-frequency relationships. These include the LC cut discovered by D.L. Hammond and A. Benjaminsson in their paper "The Linear Quartz Thermometer—a New Tool for Measuring Absolute and Difference Temperatures," Hewlett-Packard Journal, Vol. 16, No. 7, pp. 1-7, 1965, and the NLSC cut discovered by M. Nakazawa in his paper "Studies of Stress Compensated Quartz Resonators with Ultralinear Frequency-temperature Responses," Journal of Applied Physics, Vol. 60, No. 10, pp. 3765-3771, 1986. Because quartz crystal resonators have high frequency accuracy, the resulting thermometers also exhibit high measurement precision. Taking the LC cut thermometer as an example, the temperature measurement accuracy reaches 0.0001°C, which is a high accuracy that other temperature testing technologies cannot achieve.

[0007] The core component of a quartz resonator is a quartz crystal plate. The resonant frequency of the resonator is equal to the vibration frequency f of the plate's operating mode. Quartz crystal plates can be cut from quartz crystal. Quartz crystal resonators made with quartz crystal plates cut at different angles have different performance characteristics. These cutting angles are called cut profiles. To describe a cut profile, one first needs to define a coordinate system, and then define the cut profile based on the plate's rotation angle. According to the IRE-1949 / IEEE standard "IRE standards on piezoelectric crystals, Proceedings of the IRE, vol. 37, pp. 1378-1395, 1949," taking right-handed quartz and a right-handed coordinate system as an example (left-handed quartz and its cut profile in a left-handed coordinate system are mirror-symmetrical), the x-axis of the standard coordinate system is parallel to the electrical axis of the right-handed quartz, the z-axis is parallel to the optical axis of the right-handed quartz, and the y-axis is the vector direction determined by the x- and z-axis unit vectors. Initially, the thickness of a quartz crystal plate is parallel to the y-axis. Quartz crystal plates cut in this state are called Y-cut quartz. For a double-twisted quartz crystal plate, the initial plate is rotated counterclockwise about the z-axis by φ degrees. A new body coordinate system is then established on the rotated plate, with the length, width, and thickness of the plate corresponding to the x′, z′, and y′ axes, respectively. In this new coordinate system, the plate is then rotated counterclockwise by θ degrees about the x′ axis. The resulting double-twisted quartz crystal plate is then called a double-twisted plate. The two rotation angles φ and θ are called the cut shape. The cut shape is (yxwl)φ,θ. The first letter y indicates that the initial plate's thickness is parallel to the y-axis, the second letter x indicates that the initial plate's length is parallel to the x-axis, the third letter w indicates that the plate is rotated counterclockwise by φ degrees about its width (width) axis to obtain the first rotated plate. The fourth letter l indicates that the plate is rotated counterclockwise by θ degrees about its length to obtain the second rotated plate. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a quartz crystal plate having a linear temperature-frequency relationship and a cut shape that can be used for a quartz crystal resonator thermometer, and a preparation method thereof.

[0009] The technical solution adopted by the present invention to solve the above technical problems is: a quartz crystal plate for a quartz crystal resonator thermometer, the cut shape of which is represented by (yxwl)φ l / θ l , where: y represents the thickness direction of the initial plate parallel to the y-axis, x represents the length direction of the initial plate parallel to the x-axis, and w represents the counterclockwise rotation φ around the plate width axis l Angle, get the plate after the first rotation, l represents the counterclockwise rotation θ around the length direction of the plate after the first rotation lThe angle of the second rotation is 14.7°<φ l <17.8°, 5.6°<θ l <11.5°.

[0010] The best solution is: l =17.69°,θ l =11.33°.

[0011] The above-mentioned method for manufacturing the quartz crystal plate specifically comprises the following steps:

[0012] First, grow a piece of artificial quartz and establish a three-dimensional coordinate system. Define the length direction of the original plate as x, the thickness direction as y, and the width direction as z. Rotate φ counterclockwise around the z axis. l Angle, then rotate counterclockwise around the length of the plate after the first rotation θ l The tool is rotated at an angle of φ, and then cut to obtain a cut shape of (yxwl)φ l / θ l quartz crystal plate;

[0013] The cut crystal plate is then placed in a frequency grinder, and operated with grinding sand and grinding liquid to obtain a quartz crystal plate with a thickness that meets the requirements.

[0014] The ground large wafer plates can be glued together with glass glue, and the long sides of the wafers can be uniformly cut using a wire saw. After the long sides are cut, they are ground using a grinder, and the short side dimensions of the wafers are obtained in the same way. Finally, the wafers are debonded by heating and debonding agents to obtain the three important parameters of the wafer's geometric dimensions: length, thickness, and width.

[0015] A resonator can be made using the above-mentioned quartz crystal plate.

[0016] A high-precision thermometer can be made using the resonator described above.

[0017] Compared with the prior art, the advantage of the present invention is that by selecting a specific cut shape of the quartz crystal plate, the cut quartz crystal plate has a good linear temperature-frequency relationship in a wide range and can be used to prepare a quartz crystal resonator thermometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic structural diagram of the cut type of the present invention;

[0019] Figure 2 The roots of the tangent type equations with linear temperature-frequency relationship under double rotation form a solution curve in the three-dimensional parameter space in φ l and θ l Schematic diagram of the projection of the plane;

[0020] Figure 3 The temperature-frequency curve of the present invention is compared with the temperature-frequency curves of LC cut and NLSC cut;

[0021] Figure 4 The graphs are temperature-frequency curves of three specific cut types obtained by the method of the present invention. DETAILED DESCRIPTION

[0022] The technical solution of the present invention will be described in detail below with reference to the embodiments of the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0023] Example 1: First, grow an artificial quartz crystal and establish a three-dimensional coordinate system using the standard published by IRE / IEEE in 1949. Define the length direction of the original plate as x, the thickness direction as y, and the width direction as z. Rotate φ counterclockwise around the z axis. l Angle, then rotate counterclockwise around the length of the plate after the first rotation θ l The tool is rotated at an angle of φ, and then cut to obtain a cut shape of (yxwl)φ l / θ l quartz crystal plate, where: y represents the thickness direction of the initial plate parallel to the y-axis, x represents the length direction of the initial plate parallel to the x-axis, and w represents the counterclockwise rotation φ around the plate width axis l Angle, get the plate after the first rotation, l represents the counterclockwise rotation θ around the length direction of the plate after the first rotation l Angle, get the plate after the second rotation, rotate the tool so that the tool and Figure 1 After two rotations, the plates are parallel and then cut to obtain Figure 1 The quartz crystal plate that rotates twice.

[0024] The cut crystal plate is then placed in a frequency grinder, and the desired chip thickness is obtained by using grinding sand and grinding liquid.

[0025] The ground large wafers are bonded together with glass glue. A wire saw is used to uniformly cut the long edges of the wafers. To ensure a smooth, burr-free cut surface, the long edges are then ground with a grinder. Similarly, the short edges of the wafers are processed in the same manner. Finally, the wafers are debonded using heat and a debonding agent. This provides the three key wafer geometry parameters: length, thickness, and width.

[0026] Usually 14.7°<φ l <17.8°, .6°<θ l <11.5°.

[0027] The best solution is: l =17.69°,θl =11.33°.

[0028] To optimize the wafer's performance, the chamfering effect of the crystal plate is exploited and a rounding machine is used to round the wafer's edges, thereby reducing impedance and improving the quality factor. Due to the previous series of mechanical processes, the wafer has a certain amount of damage layer. The chemical reaction between hydrofluoric acid and quartz is used to etch the wafer surface, and the etching progress is controlled with a frequency meter. This results in a precise wafer thickness and a smooth surface.

[0029] Sputtering is used to obtain a conductive metal electrode surface in a designated area on the surface of the wafer. Conductive glue is used to bond the sputtered wafer to the resonator base. The conductive glue is cured in a high-temperature oven to fix the wafer position. Subsequently, a layer of the electrode surface is appropriately scraped off by spraying argon particles in a vacuum environment in conjunction with synchronized frequency testing to achieve the purpose of frequency fine-tuning and obtain an accurate resonator frequency. Finally, the upper cover is bonded to the resonator base by electric welding to complete the weld seal, thereby ensuring the airtightness of the resonator. In this way, a complete quartz crystal resonator is obtained.

[0030] By using the quartz crystal plate, a resonator can be produced according to the process for producing a resonator, and the obtained resonator can be used as a high-precision thermometer.

[0031] Temperature affects the plate vibration frequency, so the frequency f is a function of temperature T, and this function is called the temperature-frequency relationship. However, because the vibration theory is relatively complex, the temperature-frequency relationship is not expressed explicitly, but appears implicitly. The process of deriving the temperature-frequency relationship can be referred to the paper "Optimal orientations of quartz crystals for bulk acoustic wave resonators with the consideration of thermal properties, Proceedings of Meetings on Acoustics, 32(1), 2017." by J. Wang et al. Here we directly list the temperature-frequency relationship.

[0032]

[0033] Among them, f i is the frequency, 2b is the thickness of the plate, ρ is the density of quartz, and n is the order of the vibration frequency. We take f1>f2>f3 and call them A mode, B mode and C mode of plate vibration respectively. The thermometer corresponding to this patent works in C mode, c iIt is a function of temperature, cutting angle, elastic constant and thermal expansion coefficient, which is obtained by solving the following characteristic equation

[0034] KA=cA, (2)

[0035] Where A=(A1,A2,A3) T is the eigenvector, and the three roots of the characteristic equation are c i , K is

[0036]

[0037] in

[0038]

[0039] In the above formula, T0 is the reference temperature, which is set to room temperature 25℃, and δ ij is the Kronickel symbol, They are the first-order, second-order, and third-order thermal expansion coefficients of the double rotation, and their values ​​need to be obtained through coordinate transformation through the values ​​in the standard coordinate system (which is obtained by experimental measurement).

[0040]

[0041] are the first three order thermal expansion coefficients in the standard coordinate system. Their values ​​are given in the appendix of the article by R. Bechmann et al., “Higher-Order Temperature Coefficients of the Elastic Stiffnesses and Compliances of Alpha-Quartz, Proceedings of the IRE, 50, 1812, 1962”. M and N are the coordinate transformation matrices, respectively, and their forms are as follows:

[0042]

[0043]

[0044] where φ and θ represent the rotation angles, see Figure 1 As shown, the cut type is represented by the IRE-1949 standard as (yxwl)φ,θ.

[0045] D in formula (3) pq Defined as

[0046]

[0047] Among them, C pq is the double-spin elastic constant, They are the first-order, second-order, and third-order thermoelastic constants of the double rotation, which are obtained by coordinate transformation from the values ​​in the standard coordinate system.

[0048]

[0049]

[0050] in, is the elastic constant value in the standard coordinate system, refer to R.Bechmann's paper "Elastic and Piezoelectric Constants of Alpha-Quartz Physical Review 10(5)1958". are the values ​​of the first three order thermoelastic constants in the standard coordinate system, referring to the article by PCY Lee et al. “Frequency Temperature behavior of thickness vibrations of doubly rotated quartz plates affected by plate dimensions and orientations, Journal of Applied Physics, 60(7)1986”. P and Q are Bond transformation matrices, respectively, and their forms are as follows

[0051]

[0052]

[0053] Where φ and θ represent the rotation angles, see example Figure 1 As shown, the cut type is represented by the IRE-1949 standard as (yxwl)φ,θ.

[0054] Experiments show that frequency drift often presents a cubic function as temperature changes, so the temperature-frequency relationship (1) can be expressed at a specific temperature T s Perform Taylor expansion at (the specific value is obtained by solving the equation later) and retain it to the third order, then we have

[0055]

[0056] In the above formula, f is the frequency at a certain actual temperature, f s It's T s Frequency at temperature, The definition of

[0057]

[0058] For the thermometer, we hope that the temperature-frequency relationship (13) changes linearly.

[0059]

[0060] Then, the root φ of the system of equations (15) l ,θ l ,T l The temperature-frequency relationship (13) of the resonator produced by the corresponding cutting is

[0061]

[0062] That is, in T l The temperature shows a linear frequency relationship near the temperature, that is, this cut type can be used to manufacture quartz crystal resonator thermometers, and its measuring temperature range is T l Within a certain range nearby.

[0063] The solution of equation (15) can be first transformed into the following objective function F(φ,θ,T s ) minimum value problem,

[0064]

[0065] This extreme value problem can be solved using the commonly used extreme value solving methods (such as gradient method or Newton method). After obtaining the minimum value, we can then judge and Is the error from 0 less than a very small number ε (for example, 10 -6 ). If yes, the angle corresponding to the minimum is considered to be the root of equation (15). If not, it is discarded. When solving the extreme value using the optimization method, the derivative of the temperature-frequency relationship needs to be calculated in (14), which can be calculated using the finite difference method.

[0066] By numerically solving the equation group (15), we obtain the shear type with linear temperature-frequency relationship under double rotation. The equation group (15) has three unknowns and two equations, so its roots form a solution curve in the three-dimensional parameter space. This curve is in φ l and θ l The projection of the plane is Figure 2 . Figure 2 There is an inflection point in the middle curve, so the polynomial is fitted piecewise. Their specific expressions are as follows

[0067]

[0068] Where 14.7°<φ l <17.8°, and

[0069]

[0070] where 5.6°<θ l <11.5°.

[0071] In particular, for T l The cutting type at 25℃ has the highest linearity near room temperature and the best practical application performance, so the angle of the cutting type is deliberately calculated, and the corresponding values ​​are φ l =17.69°,θ l =11.33°, and the cut corresponding to this set of angles is named WL cut. The angle value of LC cut calculated by Hammond et al. is φ l =8.44°,θ l =13°, and the angle used in the final experiment is φ l = 11.17°,θ l =9.39°. By comparison, it is found that the closest distances to the angles calculated theoretically are 6.5° and 4.2°, which are quite different.

[0072] In order to illustrate the reliability of the theory, we specially selected the experimental data on NLSC cut in the paper "Studies of stress compensated quartz resonators with ultralinear frequency-temperature responses, Journal of Applied Physics, 60(10), 1986" by M. Nakazawa et al., which corresponds to Figure 3 Then the temperature-frequency curve under this cut is drawn using the theory, as shown in Figure 3 As shown by the black solid line in the middle, it can be seen that the theoretically calculated curve is consistent with the experimental data, which illustrates the reliability of the theory.

[0073] In addition, the temperature-frequency curves corresponding to the WL cut, LC cut experimental angles and LC cut theoretical angles were calculated theoretically, as shown in Figure 2. Figure 3 As shown in the figure, it can be seen that the linearity of the temperature-frequency curve obtained through theoretical calculation is significantly better than the two curves obtained by LC cutting. In other words, the linear temperature range of the curve is wider, and the temperature range that can be measured is wider.

[0074] The temperature-frequency curves of the cut type and WL cut at both ends of the cut type curve are also drawn, and it is found that the T l The temperature is relatively low, at -150℃, which means that this type of cut is suitable for working around -150℃ and is suitable for making low-temperature thermometers. lThe linear temperature range of the middle WL cut is very wide, almost covering the two cuts mentioned above, making it able to operate in a very wide temperature range.

[0075] The following describes in detail some performance parameters of the WL cut. First, the WL cut shows almost perfect linear changes in the temperature range of -200℃ to 300℃, and its linear correlation coefficient after fitting with a linear curve is 1.0000, indicating that the measurement range of the thermometer is at least in the temperature range of -200℃ to 300℃. Secondly, the slope of the temperature-frequency curve of the WL cut is 25.4ppm / ℃, that is, for every 1 degree change in ambient temperature, the resonator frequency drifts by 25.4ppm. The greater the slope of the temperature-frequency curve, the greater the frequency drift caused by changing the same temperature, and the easier it is to measure the frequency drift under the same measurement equipment. In practice, there is a certain error in the cutting angle of the chip, which will cause changes in the temperature-frequency curve. Calculations show that the change in the cutting angle mainly causes the temperature-frequency curve to rotate a certain angle, that is, to change the slope of the temperature-frequency curve, and the linear correlation is still 1.0000. So we calculated the change in the slope of the temperature-frequency line when the cutting angle changes by one degree, φ l ,θ l When the angle error is 1 degree, the corresponding slope changes are 0.02ppm / ℃ / ° and 1.55ppm / ℃ / ° respectively. For example, for the temperature measurement at 100℃ from the measurement origin, if the angle error is 1 degree, the frequency drift errors are 2ppm and 155ppm respectively. The corresponding temperature errors need to be divided by the slope of 25.4ppm / ℃, which is 0.08℃ and 6.10℃. l The effect of variations in the crystal thickness on measurement accuracy is somewhat significant, but this can be corrected during the actual manufacturing process to reduce the error. Finally, we calculated the frequency constant of the WL-cut crystal. The frequency constant divided by the crystal thickness gives the resonator's actual operating frequency. The value of this frequency constant is 1668 Hz·m, which is close to that of an AT-cut quartz crystal resonator.

Claims

1. A quartz crystal plate for a quartz crystal resonator thermometer, the cut shape of which is represented by in: y indicates that the thickness direction of the initial plate is parallel to the y-axis, x indicates that the length direction of the initial plate is parallel to the x-axis, and w indicates the counterclockwise rotation φ around the plate width axis l Angle, get the plate after the first rotation, l represents the counterclockwise rotation θ around the length direction of the plate after the first rotation l The angle of the second rotation is obtained, and the plate is characterized by: 14.7°<φ l <17.8°,5.6°<θ l <11.5°, the cut quartz crystal plate has a good linear temperature-frequency relationship in a wide range.

2. The quartz crystal plate for a quartz crystal resonator thermometer according to claim 1, wherein: f l =17.69°,θ l = 11.33°.

3. The method for manufacturing the quartz crystal plate according to claim 1, characterized in that The specific steps include: First, grow an artificial quartz crystal and establish a three-dimensional coordinate system. Define the length direction of the original plate as x, the thickness direction as y, and the width direction as z. Rotate φ counterclockwise around the z axis. l Angle, then rotate counterclockwise around the length of the plate after the first rotation θ l The cutter is rotated at an angle of quartz crystal plate; The cut crystal plate is then placed in a frequency grinder, and operated with grinding sand and grinding liquid to obtain a quartz crystal plate with a thickness that meets the requirements.

4. The method for manufacturing a quartz crystal plate according to claim 3, wherein The ground large wafer plates are bonded together with glass glue, and the long sides of the wafers are uniformly cut using a wire saw. After the long sides are cut, they are ground using a grinder, and the short side dimensions of the wafers are obtained in the same way. Finally, the wafers are debonded by heating and debonding agents to obtain the three important parameters of the wafer's geometric dimensions: length, thickness, and width.

5. A resonator manufactured using the quartz crystal plate according to claim 1.

6. A thermometer manufactured using the resonator according to claim 5.

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