Elliptical double ring quartz crystal microbalance mass sensor

Abstract

The present invention discloses an elliptical double-ring quartz crystal microbalance mass sensor, comprising a circular quartz crystal and metal electrodes respectively located on the upper and lower sides of the circular quartz crystal, wherein the lower metal electrode is an elliptical electrode structure, and the upper metal electrode is composed of an elliptical double-ring electrode, and the long axis direction of the two electrodes is the direction of the vibration displacement of the quartz crystal microbalance. The elliptical double-ring electrode is composed of an elliptical inner ring electrode and an elliptical outer ring electrode concentric with the elliptical inner ring electrode. The present invention improves the design of the metal electrode of the QCM mass sensor, and the mass sensitivity curves in all directions on the surface of the QCM mass sensor are kept consistent through the elliptical double-ring electrode. This specially designed electrode improves the uniformity of the mass sensitivity distribution of the QCM mass sensor, which is conducive to improving the repeatability of its measurement results.

Description

Technical Field

[0001] The invention belongs to the technical field of sensor detection, in particular to an elliptical double-ring quartz crystal microbalance mass sensor. Background Art

[0002] Quartz Crystal Microbalance (QCM) is an analytical instrument that uses the piezoelectric effect of quartz crystal to detect tiny changes in surface mass. The core component is the QCM mass sensor. The QCM mass sensor is a high-precision mass sensor that converts tiny changes in mass on the electrode surface into changes in vibration frequency. It has many advantages such as high sensitivity, high measurement accuracy, simple structure, low cost, and real-time online monitoring. It is widely used in clinical testing, environmental testing, food safety testing, life sciences, and drug research and development.

[0003] The mass sensitivity of the QCM surface plays a vital role in the quantitative analysis of QCM applications, but the low repeatability of the measurement results in QCM applications can lead to large deviations in the measurement results. This low repeatability problem is mainly attributed to the uneven distribution of mass sensitivity across the sensor surface. The mass sensitivity distribution function of the QCM is defined as follows

[0004]

[0005] Where A(r) is the particle displacement amplitude function, r is the distance from the particle to the electrode center, C f is the mass sensitivity constant, S f (r) is the mass sensitivity distribution function.

[0006] The structure of a general QCM with a circular electrode shape is shown in the figure below. Figure 1 As shown, its mass sensitivity distribution is Gaussian, and the vibration distribution diagram is as follows Figure 2 As shown. Figure 2 It can be seen that the vibration in the center of the circular electrode is larger, but it is not evenly distributed across the entire electrode. Therefore, different locations on the sensor surface will cause deviations in the frequency offset, resulting in low repeatability of the measurement results.

[0007] The shape, thickness, size and material of the metal electrodes of the QCM have a great influence on the mass sensitivity. Therefore, in order to solve the problem of uneven mass sensitivity distribution of the QCM mass sensor, researchers have studied the mass sensitivity of QCM with different electrode structures. Josse and Lee proposed a QCM mass sensor in the shape of a circular ring electrode, and its mass sensitivity distribution curve presents a bimodal shape curve. Richardson compared the mass sensitivity distribution of the ring electrodes through experimental measurements and theoretical calculations, and found that the difference in the depression of the bimodal curve is obvious. If the depression can be filled, a uniform mass sensitivity distribution can be obtained. In order to fill the depression between the two peaks, domestic researchers proposed a QCM mass sensor in the shape of a double-ring electrode in order to eliminate the depression in the mass sensitivity curve of the ring electrode structure. Its mass sensitivity curve presents a four-peak shape curve, which reduces the depression of the double peak, such as Figure 3 However, there is a phenomenon in the surface sensitivity distribution of the QCM mass sensor with double-ring electrodes: in the mass sensitivity distribution of the QCM, the mass sensitivity of the QCM sensor surface perpendicular to the displacement direction will be enhanced, resulting in an uneven sensitivity distribution on the sensor surface, as shown in Figure 2. Figure 4 Therefore, it is necessary to improve the mass sensitivity in this direction so that the mass sensitivity distribution of the entire electrode area tends to be consistent. Summary of the invention

[0008] Aiming at the problem of uneven distribution of mass sensitivity on the surface of the existing quartz crystal microbalance with a circular double-ring electrode structure, the present invention provides an elliptical double-ring quartz crystal microbalance mass sensor to improve the uniformity of mass sensitivity distribution in all directions on the surface of the QCM mass sensor, thereby reducing the repeatability error of the QCM measurement result and improving the QCM measurement accuracy.

[0009] The technical solution for achieving the purpose of the present invention is: an elliptical double-ring quartz crystal microbalance mass sensor, including a circular quartz wafer, with an upper metal electrode and a lower metal electrode attached to the upper and lower surfaces of the circular quartz wafer, respectively, and divided into a full electrode area, a partial electrode area and a non-electrode area; the lower metal electrode is an elliptical electrode; the upper metal electrode is an elliptical double-ring electrode, consisting of an elliptical inner ring electrode and an elliptical outer ring electrode concentric with the elliptical inner ring electrode.

[0010] Furthermore, the long axis of the electrode is at x 1 direction, with the minor axis in x 3 direction, where x 1 The direction is the direction of vibration displacement of the quartz crystal microbalance.

[0011] Furthermore, the inner radius of the major axis of the elliptical inner ring electrode is P 1 , the outer radius of the major axis is P 2 , the inner radius of the minor axis is Q1 , the outer radius of the minor axis is Q 2 , the inner radius of the major axis of the elliptical outer ring electrode is P 3 , the outer radius of the major axis is P 4 , the inner radius of the minor axis is Q 3 , the outer radius of the minor axis is Q 4 , satisfying P 1 :P 2 :P 3 :P 4 =Q 1 :Q 2 :Q 3 :Q 4 =1:3:4:8.

[0012] Furthermore, the minor axis diameter of the elliptical electrode and the elliptical double-ring metal electrode is 80% of the major axis diameter.

[0013] Furthermore, the outer diameter P of the major axis of the elliptical double-ring metal electrode is 4 In the range of 1.375mm to 1.625mm, the short axis outer diameter Q 4 In the range of 1.1mm to 1.3mm.

[0014] Furthermore, the lower metal electrode and the upper metal electrode are made of gold with a thickness of 100 nm.

[0015] Furthermore, the radius of the quartz wafer is 3.25 mm.

[0016] Furthermore, the quartz wafer is an AT-cut quartz wafer.

[0017] Furthermore, the frequency of the quartz crystal microbalance mass sensor is 20 MHz, and the working overtone number is the fundamental frequency

[0018] Compared with the prior art, the present invention has the following significant advantages: the present invention improves the design of the metal electrode of the QCM mass sensor, and maintains the consistency of the mass sensitivity curves in all directions on the surface of the QCM mass sensor through the elliptical double-ring electrode. This specially designed electrode improves the uniformity of the mass sensitivity distribution of the QCM mass sensor, which is conducive to improving the repeatability of its measurement results, thereby achieving the purpose of improving the measurement accuracy of the QCM. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a diagram of the structure of a QCM with a circular electrode shape.

[0020] Figure 2 It is the sensitivity distribution diagram of the QCM with circular electrode shape.

[0021] Figure 3 It is a structural diagram of a QCM in the shape of a circular double-ring electrode.

[0022] Figure 4 It is the sensitivity distribution diagram of the QCM with circular double-ring electrode shape.

[0023] Figure 5 It is a structural diagram of a QCM in the shape of an elliptical double-ring electrode.

[0024] Figure 6 It is the structural diagram of the QCM with elliptical double-ring electrodes after the equivalent coordinate system.

[0025] Figure 7 This is a QCM structure diagram of an elliptical double-ring electrode with specific dimensions marked.

[0026] Figure 8 It is the sensitivity distribution diagram of the QCM with elliptical double-ring electrode shape.

[0027] Fig. 9 It is a bar graph of the QCM surface sensitivity variation data for the two electrodes. DETAILED DESCRIPTION

[0028] In view of the problem of uneven mass sensitivity distribution on the surface of a quartz crystal microbalance with an existing circular double-ring electrode structure, the present invention provides an electrode structure for improving the uniformity of mass sensitivity distribution in all directions on the surface of a QCM mass sensor, wherein the uniformity of mass sensitivity distribution in all directions tends to be consistent, thereby reducing the repeatability error of the QCM measurement result and improving the QCM measurement accuracy.

[0029] like Figure 5 As shown, a quartz crystal microbalance sensor with uniform mass sensitivity distribution includes modifying an elliptical double-ring metal electrode and an elliptical metal electrode in sequence on the working electrode of the quartz crystal microbalance sensor, wherein the electrode material is gold; the lower metal electrode is an elliptical electrode, and the upper metal electrode is an elliptical double-ring electrode, wherein the long axis direction of the two electrodes is the direction of the vibration displacement of the quartz crystal microbalance, and the elliptical double-ring electrode is composed of an elliptical inner ring electrode and an elliptical outer ring electrode, and the inner radius of the long axis of the elliptical inner ring electrode is P 1 , the outer radius of the major axis is P 2 , the inner radius of the minor axis is Q 1 , the outer radius of the minor axis is Q 2 , the inner radius of the major axis of the elliptical outer ring electrode is P 3 , the outer radius of the major axis is P 4 , the inner radius of the minor axis is Q 3 , the outer radius of the minor axis is Q 4 , and P 1 :P 2 :P 3 :P 4 =Q 1 :Q2 :Q 3 :Q 4 =1:3:4:8;

[0030] The electrode structure for improving the uniformity of sensitivity of the QCM mass sensor provided by the present invention is essentially to combine an elliptical structure with a double-ring electrode structure to form an elliptical double-ring electrode QCM mass sensor, wherein the long axes of the two electrodes are at x 1 direction, with the minor axis in x 3 Direction, such as Figure 5 As shown. Its characteristic is that the quartz crystal is 1 A displacement occurs in the axial direction, and the sound wave propagates along the thickness direction of the crystal.

[0031] Considering that the elastic constants are different on the surface of the plate, 1 and x 3 The directional propagation constant is different, and the thickness shear acoustic wave can be written as

[0032]

[0033] Where A is the particle vibration displacement, is the wave number of the excitation frequency, is the wave number of the cutoff frequency, ω and ω c are the excitation angular frequency and the cutoff angular frequency respectively, and v is the propagation wave velocity in the crystal. In formula (2), the anisotropy constant a 1 and a 3 The value depends on the material of the crystal. In the case of AT-cut quartz crystals

[0034]

[0035] In the formula, γ 11 , γ 55 are the bending stiffness and torsional stiffness of the quartz crystal, c 66 is the elastic constant of the quartz crystal.

[0036] The size of the elliptical double ring electrode is 1 , P 2 , P 3 , P 4 , Q 1 , Q 2 , Q 3 , Q 4 The relationship between 1 and x 3 The energy trapping effect in the direction is the same, that is,

[0037] a 1 P 1 =a 3 Q 1 ,a1 P 2 =a 3 Q 2 ,a 1 P 3 =a 3 Q 3 ,a 1 P 4 =a 3 Q 4 , (4)

[0038] In order to treat x equivalently 1 and x 3 ,Will Figure 5 The coordinate plane (x 1 ,x 3 ) is transformed into Figure 6 As shown in (a 1 x 1 ,a 3 x 3 ) plane. Here, R 1 and R 2 Represents the inner radius and outer radius of the inner ring electrode of the elliptical double ring electrode after the inner ring electrode coordinates are converted to polar coordinates, R 3 and R 4 Represents the inner radius and outer radius of the electrode after the outer ring electrode coordinates of the elliptical double ring electrode are converted into polar coordinates.

[0039] According to the energy trap theory, when sound waves propagate on the chip, there is a minimum frequency called the cutoff frequency. Only when the operating frequency is higher than the cutoff frequency can the sound waves propagate freely on the chip and may produce standing waves and resonance. Sound waves below this frequency cannot propagate and show exponential decay around the wave source. The vibration energy is confined to the electrode area. Figure 6 It can be seen that the surface of the QCM mass sensor is divided into three regions, the non-electrode region (U region), the partial electrode region (P region) and the full electrode region (E region), and their cutoff frequencies are respectively denoted by f U 、f P and f E When the vibration energy is confined to the entire electrode area, the operating frequency f of the QCM mass sensor satisfies f E <f<f P <f U , the solution of the particle displacement amplitude function of the elliptical double-ring electrode QCM mass sensor is:

[0040]

[0041] In the formula, k r is the shear horizontal acoustic wave number in the crystal thickness direction, and They are k r In different regions, J0 、N 0 ,I 0 and K 0 They are called the 0th order first kind Bessel function, the 0th order second kind Bessel function, the 0th order first kind improved Bessel function and the 0th order second kind improved Bessel function respectively. When the QCM resonates, the shear stress on the surface of the quartz crystal is zero. Therefore, according to the continuity of the particle displacement and strain at the electrode boundary, a boundary continuity equation system consisting of eight linear homogeneous equations can be obtained, and the particle displacement amplitude constants A, B, C, D, E, F, G, and H can be obtained. Thus, the expression of A(r) is obtained, and the mass sensitivity S of the QCM mass sensor can be obtained from equation (1): f (r).

[0042] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Example

[0044] QCM quality sensor Figure 5 As shown, it includes a circular quartz crystal and metal electrodes located on the upper and lower sides of the circular quartz crystal, which are divided into a full electrode area (E area), a partial electrode area (P area) and a non-electrode area (U area). The lower metal electrode is an elliptical electrode structure, and the upper metal electrode is composed of an elliptical double-ring electrode. The long axes of the two electrodes are in the QCM vibration displacement direction. The elliptical double-ring electrode is composed of a point electrode concentric with an elliptical inner ring electrode and an elliptical outer ring electrode. The inner radius of the long axis of the elliptical inner ring electrode is P. 1 , the outer radius of the major axis is P 2 , the inner radius of the minor axis is Q 1 , the outer radius of the minor axis is Q 2 , the inner radius of the major axis of the elliptical outer ring electrode is P 3 , the outer radius of the major axis is P 4 , the inner radius of the minor axis is Q 3 , the outer radius of the minor axis is Q 4 , and P 1 :P 2 :P 3 :P 4 =Q 1 :Q 2 :Q 3 :Q 4 =1:3:4:8.

[0045] The lower elliptical metal electrode and the upper elliptical double-ring metal electrode are made of gold with a thickness of 100 nm, and the radius of the quartz wafer is 3.25 mm.

[0046] The minor axis diameter of the elliptical electrode and the elliptical double-ring gold electrode of the QCM mass sensor is 80% of the major axis diameter.

[0047] The outer diameter P of the major axis of the elliptical double-ring metal electrode 4 In the range of 1.375mm to 1.625mm, the short axis outer diameter Q 4 In the range of 1.1mm to 1.3mm.

[0048] The quartz wafer is an AT-cut quartz wafer, and the nominal frequency of the QCM sensor is 20 MHz, and the working overtone number is the fundamental frequency.

[0049] According to the above scheme, the designed 20MHz fundamental frequency AT-cut QCM mass sensor is theoretically calculated and simulated, wherein the radius of the quartz wafer is 3.25mm, the thickness is 0.008mm, the upper electrode is in the shape of an elliptical double ring, the lower electrode is in the shape of an elliptical shape, and the electrode thickness is 100nm. The inner radius of the long axis of the elliptical inner ring electrode of the upper elliptical double ring electrode is 0.21875mm, the outer radius of the long axis is 0.65625mm, the inner radius of the short axis is 0.175mm, and the outer radius of the short axis is 0.525mm, the inner radius of the long axis of the elliptical outer ring electrode is 0.875mm, the outer radius of the long axis is 1.75mm, the inner radius of the short axis is 0.7mm, and the outer radius of the short axis is 1.4mm, as shown in FIG. Figure 7 shown.

[0050] As a comparison with the QCM mass sensor produced above, a circular double-ring electrode QCM mass sensor with the same quartz crystal as the elliptical double-ring electrode was produced. The difference between the two is that the upper metal electrode is a circular double ring, and the lower metal electrode is a circular electrode. All other parameters such as materials and dimensions are the same, and the radius of the electrode of the compared QCM mass sensor is the same as the long axis radius of the elliptical double-ring electrode of the present invention.

[0051] Since the repeatability of QCM is closely related to the uniformity of the sensitivity distribution on the electrode surface, we use the coefficient of variation (c v ) is used to represent the uniformity of the mass sensitivity distribution in the electrode area, where the coefficient of variation is the standard deviation of the sensitivity data on the measured electrode surface divided by its mean value.

[0052] The QCM mass sensor with a circular double-ring electrode structure designed according to the above-mentioned specifications and the QCM mass sensor with an elliptical double-ring electrode structure designed by the present invention are x 1 Axis and x 3 The shaft mass sensitivity distribution curve is as follows: Figure 8 As shown in the figure, the coefficient of variation of the electrode surface sensitivity data measured by both is as follows Fig. 9 shown.

[0053] from Figure 4 , Figure 8 It can be seen that the outer ring area x of the circular double-ring electrode QCM3 The sensitivity of the elliptical double-ring QCM in all directions is higher, while the sensitivity distribution of the elliptical double-ring QCM in all directions on the sensor surface is more uniform. Fig. 9 It can be seen that the coefficient of variation of the elliptical double-ring electrode is smaller than that of the circular double-ring electrode. The results show that the QCM mass sensor with the elliptical double-ring electrode provided by the present invention has an approximately uniform mass sensitivity distribution.

Claims

1. An elliptical double-ring quartz crystal microbalance mass sensor, comprising a circular quartz wafer, with upper and lower metal electrodes attached to the upper and lower surfaces of the circular quartz wafer, respectively, and divided into a full electrode area, a partial electrode area and a non-electrode area; characterized in that: The lower metal electrode is an elliptical electrode; the upper metal electrode is an elliptical double-ring electrode, consisting of an elliptical inner ring electrode and an elliptical outer ring electrode concentric with the elliptical inner ring electrode; the major axis of the electrode is in the x1 direction, and the minor axis is in the x3 direction, wherein the x1 direction is the direction of vibration displacement of the quartz crystal microbalance; the major axis inner radius of the elliptical inner ring electrode is P1, the major axis outer radius is P2, the minor axis inner radius is Q1, and the minor axis outer radius is Q2; the major axis inner radius of the elliptical outer ring electrode is P3, the major axis outer radius is P4, the minor axis inner radius is Q3, and the minor axis outer radius is Q4, satisfying P1:P2:P3:P4=Q1:Q2:Q3:Q4=1:3:4:

8.

2. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 1, characterized in that: The minor axis diameter of the elliptical electrode and the elliptical double ring electrode is 80% of the major axis diameter.

3. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 1, characterized in that: The major axis outer radius P4 of the elliptical double-ring electrode is in the range of 1.375 mm to 1.625 mm, and the minor axis outer radius Q4 is in the range of 1.1 mm to 1.3 mm.

4. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 1, characterized in that: The lower metal electrode and the upper metal electrode are made of gold with a thickness of 100 nm.

5. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 4, characterized in that: The radius of the circular quartz wafer is 3.25 mm.

6. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 1 or 5, characterized in that: The circular quartz wafer is an AT-cut quartz wafer.

7. The elliptical double-ring quartz crystal microbalance mass sensor according to claim 1, characterized in that: The frequency of the quartz crystal microbalance mass sensor is 20MHz, and the working overtone number is the fundamental frequency.

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