Piezoelectric mass sensor based on PT symmetry principle and its use method

Abstract

The present invention discloses a piezoelectric mass sensor based on the PT symmetry principle, comprising a piezoelectric mass sensing unit and a matching circuit, wherein the piezoelectric mass sensing unit and the matching circuit are connected via a coupling capacitor. The equivalent dynamic capacitance and equivalent dynamic inductance of the piezoelectric mass sensing unit are equal to the capacitance and inductance of the matching circuit, and the equivalent dynamic resistance of the piezoelectric mass sensing unit and the equivalent resistance of the matching circuit are equal in magnitude but opposite in sign, forming a PT symmetric resonator system. When the mass of the piezoelectric mass sensing unit undergoes a slight change, the resonant frequency changes, thereby changing the resonant frequency of the PT symmetric resonant system. The mass change of the piezoelectric mass sensing unit can be obtained based on the change in the resonant frequency. By modulating the coupling capacitor, the PT symmetric resonator system operates at a singular point where the coupling coefficient and loss parameter are equal, significantly improving the sensitivity of the sensor.

Description

Technical Field

[0001] The present invention belongs to the field of micro-electromechanical systems (MEMS) technology, discloses the application of the spatial mirror-time reversal (PT) symmetry principle in MEMS, and specifically relates to a piezoelectric mass sensor based on the PT symmetry principle and a method for using the same. Background Art

[0002] In 1959, G.Z. Sauerbrey (Sauerbrey G., Verwendung von Schwingquarzenzur Wagung dunner Schichten und zur Mikrowagung. Zeitschrift fur Physik A Hadrons and Nuclei, 1959. 155(2): 206-222.) derived the relationship between the frequency shift of a quartz crystal resonator with an AT or BT cut and the change in mass attached to the electrode surface. Based on this theory, quartz resonators, also known as quartz crystal microbalances (QCMs), have been applied to vacuum film thickness detection, biomolecular sensors, humidity sensors, and other fields.

[0003] In 1992, Ronald P. O'Toole invented a film bulk acoustic resonator (FBAR) using piezoelectric aluminum nitride film as the piezoelectric material and applied it to methanol gas adsorption mass detection. FBARs made from piezoelectric aluminum nitride, piezoelectric zinc oxide, and piezoelectric ceramics have subsequently been applied to mass detection in fields such as biomolecule sensors and humidity sensors. The key to mass detection using piezoelectric resonators lies in the change in resonant frequency caused by mass. For the same mass change, the greater the frequency change in the resonant system, the better the performance of the resulting piezoelectric mass sensor.

[0004] In 1998, Bender and Boettcher (Bender CM, Boettcher S, Meisinger PN. PT-Symmetric Quantum Mechanics [J]. Journal of Mathematical Physics, 1998, 40(5).) proposed a special family of spatial mirror-time reversal (PT) symmetric Hamiltonians, pointing out that in addition to Hermitian systems, non-Hermitian systems such as PT symmetric systems can also obtain real solutions. This theory was subsequently extended to many fields such as optics, mechanics, and electricity. In 2014, Jan Wiersig et al. (Wiersig J. Enhancing the Sensitivity of Frequency and Energy Splitting Detection by Using Exceptional Points: Application to Microcavity Sensors for Single-Particle Detection [J]. Phys. Rev. Lett, 2014, 112(20): 203901.1-203901.5.) proposed that if a PT symmetric system is biased near a singular point where the coupling coefficient and loss coefficient are equal, and external parameters perturb the system, it will cause the system frequency to split. Sensors designed using this principle have extremely high sensitivity. Therefore, how to integrate the PT symmetry principle into the design and production of sensors has become an issue that urgently needs research and development in the field of microelectromechanical technology. Summary of the Invention

[0005] The present invention addresses the problems in the prior art and, in order to significantly improve the sensitivity of the sensor, proposes a piezoelectric mass sensor based on the PT symmetry principle and a method for using the same. The piezoelectric mass sensor comprises a piezoelectric mass sensitive unit and a matching circuit. The mass sensitive unit and the matching circuit are connected via a coupling capacitor to form a PT symmetric resonator system. By modulating the coupling capacitor, the PT symmetric resonator system operates at a singular point where the coupling coefficient and the loss parameter are equal, thereby significantly improving the sensitivity of the sensor.

[0006] To achieve the above objectives, the present invention adopts a technical solution: a piezoelectric mass sensor based on the PT symmetry principle, comprising a piezoelectric mass sensing unit and a matching circuit, wherein the piezoelectric mass sensing unit and the matching circuit are connected via a coupling capacitor; the equivalent dynamic capacitance and equivalent dynamic inductance of the piezoelectric mass sensing unit are equal to the capacitance and inductance of the matching circuit, and the equivalent dynamic resistance of the piezoelectric mass sensing unit and the equivalent resistance of the matching circuit are equal in magnitude but opposite in sign, thereby forming a PT symmetric resonator system;

[0007] By modulating the coupling capacitance, the coupling coefficient between the piezoelectric mass-sensing unit and the matching circuit is changed, so that the PT-symmetrical resonator system operates at a singular point where the coupling coefficient and loss parameter are equal.

[0008] When a piezoelectric mass-sensing unit is applied to the environment to be measured, changes in mass will cause changes in the equivalent capacitance and resonant frequency of the piezoelectric mass-sensing unit, which in turn causes the resonant frequency of the PT-symmetrical system operating at the singular point to split. The frequency change of the PT-symmetrical system is detected to detect mass changes.

[0009] As an improvement of the present invention, the piezoelectric mass sensitive unit includes but is not limited to a quartz crystal microbalance (QCM) and a film bulk acoustic resonator (FBAR).

[0010] As an improvement to the present invention, a piezoelectric mass sensor unit includes a piezoelectric resonant device and a humidity-sensitive layer covering the surface of the piezoelectric resonant device. Changes in external humidity cause the mass of water adsorbed by the humidity-sensitive material to change, altering the equivalent dynamic inductance and resonant frequency of the piezoelectric mass sensor unit, thereby changing the resonant frequency of the PT-symmetric system operating at a singular point.

[0011] In order to achieve the above object, the present invention also adopts a technical solution: a method for using a piezoelectric mass sensor based on the PT symmetry principle, comprising the following steps:

[0012] S1, by modulating the matching circuit, the dynamic capacitance and dynamic inductance of the piezoelectric mass sensitive unit are equal to the capacitance and inductance in the matching circuit, and the equivalent dynamic resistance of the piezoelectric mass sensitive unit is equal to the equivalent resistance of the matching circuit but has opposite signs, forming a PT symmetrical resonator system;

[0013] S2, modulates the coupling capacitor so that the PT symmetrical resonator system composed of the piezoelectric mass sensitive unit and the matching circuit operates at a singular point where the coupling coefficient and loss parameter are equal;

[0014] S3, the piezoelectric mass sensitive unit is applied to the environment to be tested to detect the change in the resonant frequency of the PT symmetrical resonant system and to measure the mass change.

[0015] Compared with the existing technology, the piezoelectric mass sensor based on the PT symmetry principle proposed in the present invention has extremely high sensitivity, a simple structure, easy operation, and a higher cost-effectiveness, making it more suitable for mass production in the field of micro-electromechanical systems. Since the PT symmetric resonator system operates at a singular point, any perturbation will cause a significant change in the resonant frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the structure of the piezoelectric mass sensor based on the PT symmetry principle of the present invention;

[0017] Figure 2 This is an equivalent circuit model diagram of the piezoelectric mass sensor based on the PT symmetry principle of the present invention;

[0018] Figure 3 This is a comparison diagram of the normalized resonant frequency changes of the PT symmetric resonant system and the piezoelectric mass sensitive unit in Example 1 of the present invention;

[0019] Figure 4 1 is a sensitivity comparison diagram of the PT symmetric resonant system and the piezoelectric mass sensitive unit in Example 1 of the present invention;

[0020] Figure 5 Schematic diagram of the structure of a piezoelectric humidity sensor based on the PT symmetry principle in Example 2 of the present invention;

[0021] Figure 6 This is a comparison diagram of the normalized resonant frequency changes of the PT symmetrical resonant system and the piezoelectric humidity sensitive unit in Example 2 of the present invention;

[0022] Figure 7 2 is a sensitivity comparison diagram of the PT symmetrical resonant system and the piezoelectric humidity sensitive unit in Example 2 of the present invention;

[0023] Among them, 1. Upper electrode, 2. Piezoelectric resonant crystal, 3. Lower electrode, 4. Support layer, 5. Silicon substrate, 6. Adjustable capacitor C x 7. Adjustable inductor L x 8. Adjustable equivalent negative resistance R x 9. Adjustable coupling capacitor C c 10. Equivalent dynamic capacitance C of piezoelectric mass sensitive unit m 11. Equivalent dynamic inductance L of piezoelectric mass sensitive unit m 12. Equivalent dynamic resistance R of piezoelectric mass sensitive unit m , 13. Piezoelectric mass sensitive unit equivalent static capacitance C0, 14. Humidity sensitive layer. DETAILED DESCRIPTION

[0024] The present invention will be described in more detail below with reference to the accompanying drawings and embodiments.

[0025] Example 1

[0026] A piezoelectric mass sensor based on the PT symmetry principle, such as Figure 1 As shown, the piezoelectric mass sensitive unit is composed of an upper electrode 1, a piezoelectric resonant crystal 2, a lower electrode 3, a support layer 4, and a silicon substrate 5; x 6. Adjustable inductor Lx 7. Adjustable equivalent negative resistance R x 8 forms a matching circuit, and the piezoelectric mass sensitive unit and the matching circuit are coupled by a capacitor C c 9 connected together.

[0027] When using the piezoelectric mass sensor based on the PT symmetry principle in this embodiment:

[0028] (1) First, the adjustable capacitor C x 6. Adjustable inductor L x 7. Adjustable equivalent negative resistance R x 8, so that the equivalent dynamic capacitance C in the piezoelectric mass sensitive unit m , equivalent dynamic inductance L m And the adjustable capacitor C in the matching circuit x , adjustable inductor L x Equal, the equivalent dynamic resistance R of the piezoelectric mass sensitive unit m and the equivalent resistance R of the matching circuit x Keeping the magnitudes equal and the signs opposite, a PT symmetric resonator system is formed;

[0029] (2) Adjust the coupling capacitance C between the piezoelectric sensitive unit and the matching circuit c 9. Make the PT symmetric resonator system work at the singular point where the coupling coefficient and loss parameter are equal,

[0030] (3) The piezoelectric sensitive unit is applied to the environment to be measured. The mass on the piezoelectric mass sensitive unit changes, which in turn causes the change of the resonant frequency of the PT symmetric resonant system. The change of the resonant frequency of the PT symmetric resonant system is detected to measure the mass change.

[0031] like Figure 2 As shown, the equivalent circuit model diagram of the piezoelectric mass sensor based on the PT symmetry principle, the equivalent dynamic capacitance C m 10 and adjustable capacitor C x 6 equal, that is, C m =C x ;Equivalent dynamic inductance L m 11 and adjustable inductor L x 7 equal, that is, L m =L x ; Equivalent dynamic resistance R m 12 and adjustable equivalent negative resistance R x 8 are equal in size but opposite in sign, i.e. R = -R x ; Then the natural series resonant frequency of the piezoelectric sensitive unit is The loss parameter is The coupling parameter between the piezoelectric mass sensitive unit and the matching circuit is μ=C m / (C c+C0), the PT symmetric singular point has γ=μ. In this embodiment, the piezoelectric resonant crystal is a (0002) oriented piezoelectric aluminum nitride crystal, the upper and lower electrodes are platinum, and the piezoelectric sensitive unit is made on a (001) oriented silicon wafer with a supporting layer of silicon dioxide. The equivalent dynamic capacitance C of the piezoelectric sensitive unit m =971.3fF, equivalent dynamic inductance L m =3.41nH, equivalent dynamic resistance R = 0.33Ω, static capacitance C0 = 19.1pF, then the inherent series resonant frequency ω0 = 17.4GHz (corresponding to f0 = 2.8GHz), loss parameter γ = 5.57×10 -3 , coupling capacitor C c =155.3pF.

[0032] When the mass of the piezoelectric mass-sensitive unit changes due to the external environment, the equivalent dynamic inductance changes accordingly:

[0033]

[0034] Where f0 is the natural series resonant frequency, A is the electrode area, ρ0 is the density of the piezoelectric resonant crystal, and v0 is the speed of sound in the piezoelectric layer. That is, the equivalent inductance L of the piezoelectric mass sensitive unit m Minor changes:

[0035]

[0036] The natural series frequency of the piezoelectric mass sensitive unit is used to determine the system resonant frequency Normalized. The normalized resonant frequency change of the PT symmetric resonant system is greater than the resonant frequency change of the piezoelectric mass sensitive unit, such as Figure 3 Therefore, the sensitivity of the PT symmetric system to mass changes is also higher than that of a single piezoelectric mass sensitive unit, as shown in Figure 4 shown.

[0037] In summary, at the singular point of the PT-symmetric resonator system, any perturbation will cause a significant change in the resonant frequency. Therefore, the piezoelectric mass sensor of the present invention has extremely high sensitivity.

[0038] Example 2

[0039] The difference between this embodiment and embodiment 1 is that the surface of the piezoelectric sensitive mass unit is covered with a humidity sensitive layer 14, such as Figure 5 As shown, it becomes a piezoelectric humidity sensitive unit. When the external humidity changes, the mass of water molecules contained in the humidity sensitive layer changes, which in turn affects the resonant frequency of the PT symmetric system.

[0040] When using the piezoelectric humidity sensor based on the PT symmetry principle in this embodiment:

[0041] (1) First, under the conditions of constant temperature and constant humidity, adjust the adjustable capacitor C x 6. Adjustable inductor L x 7. Adjustable equivalent negative resistance R x 8, so that the equivalent dynamic capacitance C in the piezoelectric humidity sensitive unit m , equivalent dynamic inductance L m And the adjustable capacitor C in the matching circuit x , adjustable inductor L x Equal, the equivalent dynamic resistance R m and the equivalent resistance R of the matching circuit x Keeping the magnitudes equal and the signs opposite, a PT symmetric resonator system is formed;

[0042] (2) Adjust the coupling capacitance C between the piezoelectric humidity sensitive unit and the matching circuit c 9. Make the PT symmetric resonator system work at the singular point where the coupling coefficient and loss parameter are equal;

[0043] (3) The piezoelectric humidity sensitive unit is applied to the environment to be measured. The mass of water in the humidity sensitive layer changes, which in turn causes the change of the resonant frequency of the PT symmetric resonant system. The change of the resonant frequency of the PT symmetric resonant system is detected to measure the ambient humidity.

[0044] In this embodiment, the piezoelectric resonant crystal is a piezoelectric zinc oxide film with a (0002) orientation, and the upper and lower electrodes are aluminum. The piezoelectric sensitive unit is made on a silicon wafer with a (001) orientation, and the supporting layer is silicon nitride. The humidity sensitive material is graphene oxide. Under the conditions of 20°C and 75% RH, the equivalent dynamic capacitance C of the piezoelectric humidity sensitive unit is m =1.42pF, equivalent dynamic inductance L m =14.80nH, equivalent dynamic resistance R = 0.41Ω, equivalent static capacitance C0 = 16.22pF, then the series resonant frequency ω0 = 6.90GHz (corresponding to f0 = 1.10GHz), loss parameter γ = 4.02×10 -3 , coupling capacitor C c =337.01pF.

[0045] The natural series frequency of the piezoelectric humidity sensor is used to determine the system resonant frequency. Normalized. As the ambient humidity decreases, the mass of water attached to the humidity-sensitive material graphene oxide decreases, which is equivalent to the equivalent inductance L of the piezoelectric mass sensitive unit. m A small change occurs δ = ΔL m / L m When , the normalized resonant frequency change of the PT symmetric resonant system is much greater than the resonant frequency change of the piezoelectric sensitive unit, such as Figure 6The sensitivity of the PT symmetric system to mass changes is also much higher than that of a single piezoelectric mass sensitive unit, such as Figure 7 As shown in the figure, a humidity change of 5% RH corresponds to a perturbation δ = 0.056%.

[0046] In summary, at the singular point of the PT-symmetric resonator system, a perturbation will cause a significant change in the resonant frequency. Therefore, the sensor of the present invention has extremely high sensitivity.

[0047] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A piezoelectric mass sensor based on the PT symmetry principle, characterized by: The piezoelectric mass-sensing unit comprises a piezoelectric mass-sensing unit and a matching circuit, wherein the piezoelectric mass-sensing unit and the matching circuit are connected via a coupling capacitor; the equivalent dynamic capacitance and equivalent dynamic inductance of the piezoelectric mass-sensing unit are equal to the capacitance and inductance of the matching circuit, and the equivalent dynamic resistance of the piezoelectric mass-sensing unit and the equivalent resistance of the matching circuit are equal in magnitude but opposite in sign, thereby forming a PT-symmetrical resonator system; The method for using the piezoelectric mass sensor comprises the following steps: S1, by modulating the matching circuit, the equivalent dynamic capacitance and equivalent dynamic inductance of the piezoelectric mass sensitive unit are equal to the capacitance and inductance of the matching circuit, and the equivalent dynamic resistance of the piezoelectric mass sensitive unit is equal to the equivalent resistance of the matching circuit but has opposite signs, thus forming a PT symmetrical resonator system; S2, modulates the coupling capacitor so that the PT symmetrical resonator system composed of the piezoelectric mass sensitive unit and the matching circuit operates at a singular point where the coupling coefficient and loss parameter are equal; S3, the piezoelectric mass sensitive unit is applied to the environment to be tested to detect the change in the resonant frequency of the PT symmetrical resonant system and to measure the mass change.

2. The piezoelectric mass sensor based on the PT symmetry principle according to claim 1, characterized in that: The matching circuit includes a first adjustable capacitor, an adjustable inductor and an equivalent negative resistance with adjustable resistance; the coupling capacitor includes a second adjustable capacitor.

3. The piezoelectric mass sensor based on the PT symmetry principle according to claim 1, characterized in that: The piezoelectric mass sensitive unit includes but is not limited to a quartz crystal microbalance and a thin film bulk acoustic resonator.

4. The piezoelectric mass sensor based on the PT symmetry principle according to claim 1, characterized in that: The piezoelectric resonant crystal in the piezoelectric mass sensitive unit includes but is not limited to a piezoelectric quartz crystal, a piezoelectric aluminum nitride crystal, a piezoelectric zinc oxide crystal, and a piezoelectric ceramic crystal.

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