CN102967522B - Quartz crystal microbalance (QCM) mass sensor - Google Patents
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Abstract
为了提高QCM质量传感器质量灵敏度的均匀性，本发明提供具有一种不对称电极结构的QCM质量传感器，属于电子技术领域。包括圆形石英晶片和分别位于圆形石英晶片上下两面的金属电极，其中下金属电极为一半径为m的圆电极，上金属电极为点-环状电极，由一个环状电极（内半径为n、外半径为m）和与环状电极同心的点电极（半径为g）构成，且g<n。本发明对现有具有环状电极结构的QCM质量传感器的上金属电极进行改进，通过在环状电极中增加一个较小的点电极，将QCM质量传感器的质量灵敏度分布曲线由双峰型改进成三峰型，在保证了较高的绝对质量灵敏度基础上，提高了QCM质量传感器的质量灵敏度分布的均匀性，进而提高其测量结果的重复性。
In order to improve the uniformity of mass sensitivity of a QCM mass sensor, the invention provides a QCM mass sensor with an asymmetric electrode structure, which belongs to the field of electronic technology. It includes a circular quartz wafer and metal electrodes respectively located on the upper and lower sides of the circular quartz wafer, wherein the lower metal electrode is a circular electrode with a radius of m, and the upper metal electrode is a point-ring electrode, consisting of a ring electrode (with an inner radius of n, the outer radius is m) and the point electrode (radius is g) concentric with the ring electrode, and g<n. The present invention improves the upper metal electrode of the existing QCM mass sensor with a ring electrode structure, and improves the mass sensitivity distribution curve of the QCM mass sensor from a bimodal to a The three-peak type, on the basis of ensuring a high absolute mass sensitivity, improves the uniformity of the mass sensitivity distribution of the QCM mass sensor, thereby improving the repeatability of its measurement results.
Description
技术领域 technical field
本发明属于电子技术领域，涉及石英晶体微天平（Quartz Crystal Mircrobalance，QCM），尤其是QCM质量传感器。The invention belongs to the field of electronic technology, and relates to a quartz crystal microbalance (Quartz Crystal Microbalance, QCM), especially a QCM mass sensor.
背景技术 Background technique
石英晶体微天平（Quartz Crystal Mircrobalance，QCM）是一种在20世纪60年代兴起的新型的微小质量检测仪器，其核心部件是QCM质量传感器。QCM质量传感器是一种非常灵敏的质量传感器，它的质量测定可以精确到纳克级，已经在物理、化学、生物、医学等学科的检测问题中得到了应用。在一定的外界条件下，当石英晶振表面吸附其它物质时，根据石英振子的频率变化与晶体表面的所附物质质量变化成正比的这一原理，石英晶振的谐振频率将会随着吸附物质质量的大小而改变。QCM质量传感器其实就是具有上下电极结构的石英晶体谐振器。石英晶体谐振器因为压电效应会在外界激励下以它的谐振频率振荡，QCM质量传感器就是利用石英晶体谐振器这一特性，在石英晶体谐振器电极表面吸附一层待测物质，把待测物质的质量信号转化为频率信号进行检测的。QCM具有很高的灵敏度、优良的选择性、所需成本低廉，而且测试装置简单、易于实现现场连续检测等众多优点，所以受到了世界各国科学家的高度重视，它已经广泛应用于质量、密度、浓度等的检测领域。Quartz Crystal Microbalance (QCM) is a new type of tiny mass detection instrument that emerged in the 1960s, and its core component is the QCM mass sensor. QCM mass sensor is a very sensitive mass sensor, its mass measurement can be accurate to the nanogram level, and it has been applied in the detection problems of physics, chemistry, biology, medicine and other disciplines. Under certain external conditions, when other substances are adsorbed on the surface of the quartz crystal oscillator, according to the principle that the frequency change of the quartz oscillator is proportional to the change in the quality of the substance attached to the crystal surface, the resonance frequency of the quartz crystal oscillator will change with the mass of the adsorbed substance. changes in size. The QCM quality sensor is actually a quartz crystal resonator with an upper and lower electrode structure. Due to the piezoelectric effect, the quartz crystal resonator will oscillate at its resonant frequency under external excitation. The QCM quality sensor uses the characteristic of the quartz crystal resonator to absorb a layer of the substance to be measured on the electrode surface of the quartz crystal resonator. The mass signal of the substance is converted into a frequency signal for detection. QCM has many advantages such as high sensitivity, excellent selectivity, low cost, simple test device, easy to realize on-site continuous detection, etc., so it has been highly valued by scientists all over the world. It has been widely used in quality, density, Concentration detection field.
然而，QCM在应用中存在一个显著问题：测量结果的重复性很低。为获得较高重复性的测量结果，人们提出了许多QCM使用时的注意事项，如使被测样品均匀刚性的分布于QCM的整个电极表面，能够实现样品均匀刚性的分布的方法主要有真空镀膜、电镀等，操作过程不仅繁琐而且效率很低。However, there is a significant problem in the application of QCM: the repeatability of the measurement results is very low. In order to obtain high repeatability measurement results, many precautions have been put forward when using QCM. For example, the uniform rigidity of the sample to be measured is distributed on the entire electrode surface of the QCM. The method that can achieve uniform rigidity distribution of the sample mainly includes vacuum coating. , electroplating, etc., the operation process is not only cumbersome but also inefficient.
目前，人们已认识到，QCM质量传感器质量灵敏度分布曲线的不一致是造成其测量结果重复性低的主要原因。理论和实践都已证明，常规如图1示的具有圆电极结构（m-m型）的QCM质量传感器，其质量灵敏度分布曲线为如图2所示的钟罩型（或高斯型），这就产生了QCM质量传感器质量灵敏度分布曲线的不一致，带来了测量结果重复性低的问题。At present, it has been recognized that the inconsistency of the mass sensitivity distribution curve of the QCM mass sensor is the main reason for the low repeatability of its measurement results. Both theory and practice have proved that the mass sensitivity distribution curve of the conventional QCM mass sensor with a circular electrode structure (m-m type) as shown in Figure 1 is a bell jar type (or Gaussian type) as shown in Figure 2, which results in The inconsistency of the mass sensitivity distribution curve of the QCM mass sensor has brought about the problem of low repeatability of the measurement results.
为了获得质量灵敏度分布均匀的QCM质量传感器，研究人员对QCM质量传感器的电极结构进行了该进，如设计出了不对称的圆形n-m型电极、椭圆形电极等，但这都不能解决由于QCM质量传感器质量灵敏度分布曲线的不一致所带来的测量结果重复性低的问题。In order to obtain a QCM mass sensor with uniform mass sensitivity distribution, researchers have made some improvements to the electrode structure of the QCM mass sensor, such as designing asymmetric circular n-m type electrodes, elliptical electrodes, etc., but this cannot solve the problem due to the QCM The problem of low repeatability of measurement results caused by the inconsistency of mass sensor mass sensitivity distribution curves.
有国外研究者提出了具有一种不对称电极结构的QCM质量传感器，如图3、4所示，其上电极是一种圆环形电极（圆环电极内半径为n，外半径为m），其下电极仍然是一个外半径为m的圆形电极。具有这种电极结构的QCM质量传感器，其质量灵敏度分布曲线为双峰形，双峰间的凹陷是明显的，如果能够将凹陷补平，则可获得局部均匀的质量灵敏度分布。为将双峰间的凹陷补平，科学家们做了很多探讨。1996年，Youbok Lee等人发现，可以通过减小电极质量负载因数，使双峰间的凹陷减小（Y.Lee,F.Josse,“Radial dependence of mass sensitivity formodified-electrode quartz resonators”,Proc.IEEE Ultrason.Symp,vol.1,pp.321-325,1996.），其提供的质量灵敏度分布曲线如图5所示。可见在谐振器镀回频率极小时,其质量灵敏度分布曲线有趋于一致的趋势，但绝对质量灵敏度峰值却有所下降（即分辨率降低），尤其其致命的不足是：由于R值太小（即晶片的镀回频率太小），只有通过减小电极厚度的方法来减小电极质量负载因数，然而，即使电极薄至超过所能实现的工艺极限，双峰间的凹陷仍然比较明显。可见，通过减小电极的厚度将双峰间的凹陷补平，这在实际中是不可行的。Some foreign researchers have proposed a QCM mass sensor with an asymmetric electrode structure, as shown in Figures 3 and 4, the upper electrode is a ring-shaped electrode (the inner radius of the ring electrode is n, and the outer radius is m). , the lower electrode is still a circular electrode with an outer radius of m. The mass sensitivity distribution curve of the QCM mass sensor with this electrode structure is double-peaked, and the depression between the double peaks is obvious. If the depression can be filled up, a locally uniform mass sensitivity distribution can be obtained. In order to fill the depression between the two peaks, scientists have done a lot of research. In 1996, Youbok Lee and others found that the sag between the double peaks can be reduced by reducing the electrode mass load factor (Y.Lee, F.Josse, "Radial dependence of mass sensitivity formodified-electrode quartz resonators", Proc. IEEE Ultrason.Symp,vol.1,pp.321-325,1996.), the mass sensitivity distribution curve provided by it is shown in Figure 5. It can be seen that when the plating back frequency of the resonator is extremely small, the mass sensitivity distribution curve tends to be consistent, but the peak value of the absolute mass sensitivity decreases (that is, the resolution decreases), especially the fatal problem is: due to the small R value (That is, the plating back frequency of the wafer is too small), the only way to reduce the electrode quality load factor is to reduce the electrode thickness. However, even if the electrode is thinner than the process limit that can be achieved, the depression between the double peaks is still relatively obvious. It can be seen that it is not feasible to fill up the depression between the double peaks by reducing the thickness of the electrode.
发明内容 Contents of the invention
为了提高QCM质量传感器质量灵敏度的均匀性，本发明提供具有一种不对称电极结构的QCM质量传感器，该QCM质量传感器可在基本不降低绝对质量灵敏度的基础上,提高质量灵敏度的均匀性，从而提高QCM测量结果的重复性，达到提高QCM测量精度的目的。In order to improve the uniformity of the mass sensitivity of the QCM mass sensor, the present invention provides a QCM mass sensor with an asymmetric electrode structure, the QCM mass sensor can improve the uniformity of the mass sensitivity without substantially reducing the absolute mass sensitivity, thereby Improve the repeatability of QCM measurement results to achieve the purpose of improving QCM measurement accuracy.
本发明技术方案如下：Technical scheme of the present invention is as follows:
一种石英晶体微天平质量传感器，如图6、7所示，包括圆形石英晶片1，所述圆形石英晶片1上下两面分别具有上金属电极2和下金属电极3。经过圆形石英晶片1几何中心的法线与经过上金属电极2几何中心的法线和经过下金属电极3几何中心的法线三者保持重合。所述下金属电极3为一半径为m的圆电极。所述上金属电极2为点-环状电极，由一个环状电极21和与环状电极21同心的点电极22构成。所述环状电极21的内半径为n、外半径为m，所述点电极22的半径为g，且g<n。A quartz crystal microbalance quality sensor, as shown in Figures 6 and 7, includes a circular quartz wafer 1, and the upper and lower sides of the circular quartz wafer 1 have an upper metal electrode 2 and a lower metal electrode 3 respectively. The normal line passing through the geometric center of the circular quartz wafer 1 and the normal line passing through the geometric center of the upper metal electrode 2 and the normal line passing through the geometric center of the lower metal electrode 3 keep coincident. The lower metal electrode 3 is a circular electrode with a radius of m. The upper metal electrode 2 is a point-ring electrode, which is composed of a ring electrode 21 and a point electrode 22 concentric with the ring electrode 21 . The inner radius of the ring electrode 21 is n, the outer radius is m, the radius of the point electrode 22 is g, and g<n.
本发明提供的QCM质量传感器，其实质是将图3、4所示的具有不对称电极结构的QCM质量传感器的圆环状上金属电极改成点-环状上金属电极。其中点-环状上金属电极结构如图7所示，其中g、n、m分别表示中心点电极22的半径、环状电极21的内半径和外半径。从图7中可见它有三类区域：分别为非电极区（U区）、部分电极区（P区）和全电极区（E区），其截止频率分别用fU、fP和fE表示。根据能陷理论要求，该QCM质量传感器的工作频率范围为fE<f<fP<fU。在该工作频率范围下，该QCM质量传感器的质点位移幅度的解为:The essence of the QCM mass sensor provided by the present invention is to change the ring-shaped upper metal electrode of the QCM mass sensor with an asymmetric electrode structure shown in Fig. 3 and 4 into a point-annular upper metal electrode. The dot-annular upper metal electrode structure is shown in FIG. 7 , where g, n, and m represent the radius of the central dot electrode 22, the inner radius and the outer radius of the annular electrode 21, respectively. It can be seen from Figure 7 that it has three types of areas: non-electrode area (U area), partial electrode area (P area) and full electrode area (E area), and their cut-off frequencies are represented by f U , f P and f E respectively. . According to the requirement of energy trapping theory, the working frequency range of the QCM mass sensor is f E <f<f P <f U . Under this operating frequency range, the solution of the particle displacement amplitude of this QCM mass sensor is:
由质点位移和应变在r=g、n、m处连续，可以得到六个线性齐次方程组成的分界连续方程组，选择方程组中的任意五个方程可以得到质点位移幅度常数C1、C2、C3、C4、C5、C6的比例关系。Since the mass point displacement and strain are continuous at r=g, n, m, a boundary continuous equation system composed of six linear homogeneous equations can be obtained, and any five equations in the equation system can be selected to obtain the mass point displacement amplitude constants C 1 , C 2. The proportional relationship of C 3 , C 4 , C 5 , and C 6 .
这样，就得到了A(r)的表示式，由下式即可得到该QCM质量传感器的质量灵敏度Sf(r)的表示：In this way, the expression of A(r) is obtained, and the expression of the mass sensitivity S f (r) of the QCM mass sensor can be obtained from the following formula:
(2)式中Cf是QCM质量传感器的质量灵敏度常数。(2) where C f is the mass sensitivity constant of the QCM mass sensor.
图8为本发明提供的具有点-环电极结构的QCM质量传感器与普通环状电极结构的QCM质量传感器的质量灵敏度的比较示意图。从图8中可以看出，采用点-环电极结构的QCM质量传感器，其质量灵敏度分布曲线的不一致程度减小了一半，这同时意味着其测量的重复性将提高一倍。Fig. 8 is a schematic diagram of mass sensitivity comparison between the QCM mass sensor with point-ring electrode structure and the QCM mass sensor with common ring electrode structure provided by the present invention. It can be seen from Figure 8 that the inconsistency of the mass sensitivity distribution curve of the QCM mass sensor using the point-ring electrode structure is reduced by half, which means that the repeatability of its measurement will be doubled.
综上所述，本发明提供的QCM质量传感器在基本不降低绝对质量灵敏度的基础上,能够提高质量灵敏度的均匀性，从而提高QCM测量结果的重复性，达到提高QCM测量精度的目的。In summary, the QCM mass sensor provided by the present invention can improve the uniformity of mass sensitivity without substantially reducing the absolute mass sensitivity, thereby improving the repeatability of QCM measurement results and achieving the purpose of improving QCM measurement accuracy.
附图说明 Description of drawings
图1是常规具有上下对称圆电极结构（m-m型）的QCM质量传感器的纵向截面示意图。Figure 1 is a schematic longitudinal cross-sectional view of a conventional QCM mass sensor with an up-and-down symmetrical circular electrode structure (m-m type).
图2是图1所示结构的QCM质量传感器的质量灵敏度分布曲线。Fig. 2 is a mass sensitivity distribution curve of the QCM mass sensor with the structure shown in Fig. 1 .
图3是具有环形电极结构的QCM质量传感器的纵向截面示意图。3 is a schematic longitudinal cross-sectional view of a QCM mass sensor with a ring electrode structure.
图4是图3所示具有环形电极结构的QCM质量传感器的上金属电极结构示意图。FIG. 4 is a schematic diagram of the upper metal electrode structure of the QCM mass sensor with the ring electrode structure shown in FIG. 3 .
图5是图3所示具有环形电极结构的QCM质量传感器的质量灵敏度曲线。它在电极中心点周围的分布是双峰形的，随着R的减小，其质量灵敏度分布曲线有趋于一致的趋势，但这时的R值太小，已超出了所能实现的工艺极限。FIG. 5 is a mass sensitivity curve of the QCM mass sensor shown in FIG. 3 with a ring electrode structure. Its distribution around the center point of the electrode is bimodal, and as R decreases, its mass sensitivity distribution curve tends to be consistent, but the R value at this time is too small, which has exceeded the achievable process limit.
图6是本发明提供的具有点-环电极结构的QCM质量传感器的纵向截面示意图。Fig. 6 is a schematic longitudinal cross-sectional view of a QCM mass sensor with a point-ring electrode structure provided by the present invention.
图7是本发明提供的具有点-环电极结构的QCM质量传感器的上金属电极结构示意图。Fig. 7 is a schematic diagram of the structure of the upper metal electrode of the QCM mass sensor with the point-ring electrode structure provided by the present invention.
图8是本发明提供的具有点-环电极结构的QCM质量传感器与图3所示具有环形电极结构的QCM质量传感器的质量灵敏度曲线比较。其中实线为图3所示具有环形电极结构的QCM质量传感器的质量灵敏度曲线，虚线为本发明提供的具有点-环电极结构的QCM质量传感器的质量灵敏度曲线。从图8中可以看出，本发明提供的具有点-环电极结构的QCM质量传感器，在保证较高的绝对质量灵敏度的前提下，通过形成三峰形曲线，提高了QCM质量传感器的质量灵敏度的均匀性。FIG. 8 is a comparison of the mass sensitivity curves of the QCM mass sensor with the point-ring electrode structure provided by the present invention and the QCM mass sensor with the ring electrode structure shown in FIG. 3 . The solid line is the mass sensitivity curve of the QCM mass sensor with the ring electrode structure shown in FIG. 3 , and the dotted line is the mass sensitivity curve of the QCM mass sensor with the point-ring electrode structure provided by the present invention. As can be seen from Fig. 8, the QCM mass sensor with point-ring electrode structure provided by the present invention improves the mass sensitivity of the QCM mass sensor by forming a three-peak curve under the premise of ensuring higher absolute mass sensitivity Uniformity.
注:图4和图7中均只标明了电极区,未标起导电作用的电极引出线。Note: In Figure 4 and Figure 7, only the electrode area is marked, and the lead-out wires of the electrodes that conduct electricity are not marked.
具体实施方式 Detailed ways
下面结合附图和具体实施方式，对本发明进行进一步的描述。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.
一种QCM质量传感器，如图6、7所示，包括圆形石英晶片1，所述圆形石英晶片1上下两面分别具有上金属电极2和下金属电极3。经过圆形石英晶片1几何中心的法线与经过上金属电极2几何中心的法线和经过下金属电极3几何中心的法线三者保持重合。所述下金属电极3为一半径为m的圆电极。所述上金属电极2为点-环状电极，由一个环状电极21和与环状电极21同心的点电极22构成。所述环状电极21的内半径为n、外半径为m，所述点电极22的半径为g，且g<n。A QCM quality sensor, as shown in FIGS. 6 and 7 , includes a circular quartz wafer 1 , and the upper and lower sides of the circular quartz wafer 1 have an upper metal electrode 2 and a lower metal electrode 3 respectively. The normal line passing through the geometric center of the circular quartz wafer 1 and the normal line passing through the geometric center of the upper metal electrode 2 and the normal line passing through the geometric center of the lower metal electrode 3 keep coincident. The lower metal electrode 3 is a circular electrode with a radius of m. The upper metal electrode 2 is a point-ring electrode, which is composed of a ring electrode 21 and a point electrode 22 concentric with the ring electrode 21 . The inner radius of the ring electrode 21 is n, the outer radius is m, the radius of the point electrode 22 is g, and g<n.
所述上金属电极2和下金属电极3材料为金或铬+金（以金属铬层为基层，在金属铬层上再镀金层，以增加金在石英基片上的附着力），厚度为10-7米。The material of the upper metal electrode 2 and the lower metal electrode 3 is gold or chromium+gold (the metal chromium layer is used as the base layer, and a gold layer is plated on the metal chromium layer to increase the adhesion of gold on the quartz substrate), and the thickness is 10 -7 meters.
所述点电极22的半径g在0.4毫米到1.2毫米的范围内；所述环状电极21的内半径n在1.6毫米到3.2毫米的范围内，外半径m在2.5毫米到5.0毫米的范围内。The radius g of the point electrode 22 is in the range of 0.4 mm to 1.2 mm; the inner radius n of the annular electrode 21 is in the range of 1.6 mm to 3.2 mm, and the outer radius m is in the range of 2.5 mm to 5.0 mm .
石英晶片1的直径在8.0mm到14.0mm的范围内。The diameter of the quartz wafer 1 is in the range of 8.0 mm to 14.0 mm.
所述石英晶片1为AT切石英晶片，其切角范围从35°1'到35°12'。The quartz wafer 1 is an AT-cut quartz wafer, and its cutting angle ranges from 35°1' to 35°12'.
所述QCM质量传感器的称频率为5MHz、10MHz或11MHz，工作泛音次数为基频、3次泛音或5次泛音。The weighing frequency of the QCM quality sensor is 5MHz, 10MHz or 11MHz, and the number of working overtones is the fundamental frequency, the third overtone or the fifth overtone.
根据上述技术方案，以切角为AT切35°8'、标称频率为10MHz、泛音次数为基频的石英晶片（厚度约为0.1648mm）制作QCM质量传感器。其中石英晶片直径为8.7mm，上下金属电极材料选择金，上下电极厚度为为10-7米（1000埃）。上金属电极中，点电极22的半径g=0.45mm，环状电极21的内半径n=2.12mm、外半径m=2.85mm。According to the above technical scheme, a QCM quality sensor is made with a quartz wafer (thickness is about 0.1648mm) with a cut angle of AT cut 35°8', a nominal frequency of 10MHz, and an overtone frequency as the fundamental frequency. The diameter of the quartz wafer is 8.7mm, the material of the upper and lower metal electrodes is gold, and the thickness of the upper and lower electrodes is 10 −7 meters (1000 Angstroms). In the upper metal electrode, the point electrode 22 has a radius g=0.45 mm, the ring electrode 21 has an inner radius n=2.12 mm, and an outer radius m=2.85 mm.
选择同样的石英晶片制作另一个具有环状电极结构的QCM质量传感器，作为上述制作的QCM质量传感器的对比实施例（二者的区别仅仅在于上金属电极，本发明在环状电极中增加了一个同心的点电极，其余材料、尺寸等所有参数均相同，且对比实施例的环状电极的上电极环的内、外电极的半径也相同）。Select the same quartz wafer to make another QCM quality sensor with ring electrode structure, as a comparative example of the QCM quality sensor made above (the difference between the two is only the upper metal electrode, the present invention adds a For concentric point electrodes, all parameters such as other materials and dimensions are the same, and the radii of the inner and outer electrodes of the upper electrode ring of the ring electrode of the comparative embodiment are also the same).
按照上述规格参数设计的具有环状电极结构的QCM质量传感器和本发明设计的具有点-环电极结构的QCM质量传感器的质量灵敏度分布曲线如图8所示。The mass sensitivity distribution curves of the QCM mass sensor with a ring electrode structure designed according to the above specification parameters and the QCM mass sensor with a point-ring electrode structure designed in the present invention are shown in FIG. 8 .
由图8可以看出，具有环状电极结构的QCM质量传感器的质量灵敏度分布曲线呈双峰状，双峰之间质量灵敏度的最大差值约为2.5×1011Hz/Kg；本发明提供的具有点-环电极结构的QCM质量传感器的质量灵敏度分布曲线呈三峰状，三峰间质量灵敏度的最大差值缩小到大约1.25×1011Hz/Kg。同时，从图8中也可以看出，本发明提供的具有点-环电极结构的QCM质量传感器，保证了较高的绝对质量灵敏度。因此，本发明提供的具有点-环电极结构的QCM质量传感器，在保证较高的绝对质量灵敏度的前提下，质量灵敏度分布曲线的不一致程度大约减小了一半，换句话说，本发明提供的具有点-环电极结构的QCM质量传感器，其测量的重复性将大约提高一倍。It can be seen from Fig. 8 that the mass sensitivity distribution curve of the QCM mass sensor with ring electrode structure is bimodal, and the maximum difference in mass sensitivity between the bimodal is about 2.5×10 11 Hz/Kg; the present invention provides The mass sensitivity distribution curve of the QCM mass sensor with point-ring electrode structure is in the shape of three peaks, and the maximum difference of mass sensitivity between the three peaks is reduced to about 1.25×10 11 Hz/Kg. At the same time, it can also be seen from FIG. 8 that the QCM mass sensor provided by the present invention has a point-ring electrode structure, which ensures a high absolute mass sensitivity. Therefore, the QCM mass sensor provided by the present invention has a point-ring electrode structure, under the premise of ensuring higher absolute mass sensitivity, the inconsistency of the mass sensitivity distribution curve is approximately reduced by half, in other words, the present invention provides A QCM mass sensor with a point-ring electrode structure will approximately double the measurement repeatability.
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