Hot-pressing resistance PT symmetrical MEMS pressure sensor

Abstract

The invention discloses a thermocompression resistance PT symmetrical MEMS pressure sensor, which comprises two resonators with identical structures, and the two resonators are connected through a group of coupling spring beams. Each resonator comprises four anchor areas connected with the thin film substrate, narrow beams which are connected with the four anchor areas and have a piezoresistive effect, and a mass block connected with the four narrow beams, and the four anchor areas are symmetrically distributed on the two sides of the mass block. For one of the resonators, a current path is formed through connection of a constant current source in the anchor section on the same side of the mass block. Under the action of a constant current source, hot resistance pressing feedback is generated at narrow beams of the resonators, so that the two coupled resonators form a PT symmetric system, and the PT symmetric resonators are initially arranged at an Exception Point (EP) point. When pressure acts on the lower surface of the substrate, the substrate generates strain, the position of the anchor area is driven to change, the rigidity of the resonator is changed, a PT symmetric system deviates from an EP point, the system eigenfrequency is split and shows pull-ratio oscillation, and the frequency splitting amount depends on the pressure borne by the substrate. Because the EP point has a large response to tiny disturbance, the thermal pressure resistance PT symmetric MEMS pressure sensor can realize accurate measurement of weak pressure change, and has the advantages of high sensitivity and simple manufacturing process.

Description

Technical Field

[0001] The present invention is a thermopiezoresistive PT-symmetric MEMS pressure sensor, belonging to the technical field of sensors. Background Art

[0002] MEMS technology is an advanced technology integrating micro-mechanical and electronic components, which is widely used in the field of sensors. MEMS pressure sensors are based on miniaturized mechanical and electronic components and can detect external pressure changes with high precision. Their working principle is usually to convert the microstructural deformation caused by pressure into an electrical signal for signal processing. Compared with traditional pressure sensors, MEMS pressure sensors have significant advantages such as small size, light weight, low power consumption, and low cost. They are widely used in fields such as automotive, medical, consumer electronics, and industrial automation. For example, automotive tire pressure monitoring systems, blood pressure monitoring devices, gas detection instruments, etc. all use MEMS pressure sensors. However, there are still certain technical challenges in existing MEMS pressure sensors. How to further improve the weak signal detection ability and sensitivity of MEMS pressure sensors remains the focus of current technology research and development. Summary of the Invention

[0003] Technical Problem: In view of the above problems, the present invention provides a thermopiezoresistive parity-time (PT)-symmetric micro-electronic mechanical system (MEMS) pressure sensor. The pressure sensor senses pressure through a substrate to generate strain, thereby affecting the stiffness of the PT-symmetric MEMS resonator, causing the PT-symmetric system to deviate from the EP point and resulting in the splitting of the system's eigenfrequency. In a PT-symmetric system, the amount of frequency splitting is proportional to the square root of the stiffness perturbation received, and it has very high sensitivity to weak pressure. This pressure sensor is fully compatible with the MEMS process and has advantages such as simple process preparation, easy integration, small size, and low cost.

[0004] Technical solution: To achieve the above object, the present invention provides a technical solution for a thermopiezoresistive PT-symmetric MEMS pressure sensor. The pressure sensor includes two resonators with exactly the same structure, and the two resonators are connected by a set of coupling spring beams. Each resonator includes 4 anchor regions connected to the thin film substrate, narrow beams with piezoresistive effect connected to the four anchor regions, and a mass block connecting the four narrow beams. The 4 anchor regions are symmetrically distributed on both sides of the mass block. For one of the resonators, a constant current source is connected between the side anchor regions on the same side of the mass block. Under the action of the constant current source, a thermopiezoresistive feedback is generated at the narrow beam of the resonator, and its specific function is as follows: The displacement of the resonator oscillation causes the narrow beam to undergo strain. Due to the piezoresistive effect, the resistance of the narrow beam changes accordingly. Since the narrow beam is in the path of the constant current source and the current remains unchanged, the Joule heat power generated at the narrow beam will change with the change of the resistance, thus causing the balance of heat diffusion and heat conduction of the narrow beam to be destroyed, and the temperature of the narrow beam changes. Due to the thermal expansion characteristics of the material, the temperature change causes stress on the narrow beam, and the stress ultimately leads to the displacement of the beam. Such a feedback process is the thermopiezoresistive feedback, and the force F feedback generated by the feedback has the following relationship with the moving speed of the resonator

[0005]

[0006] where E, α, and C t are the Young's modulus, thermal expansion coefficient, and heat capacity of silicon respectively; A, L, and R DC are the cross-sectional area, length, and DC impedance of the narrow beam respectively; k is the equivalent stiffness of the resonator, and I DC is the DC current provided by the constant current source. Substituting this feedback force into the vibration equation of the resonator, the equivalent damping of the resonator under the feedback action can be obtained

[0007]

[0008] where c is the intrinsic damping of the resonator. By adjusting the magnitude of I DC to make c s =-c, the action effect of the feedback force is opposite to that of the damping, and it acts as the gain in the PT-symmetric system. There is no constant current source acting on the other resonator, and it has loss characteristics. The two resonators form a PT-symmetric system through the weak coupling of the coupling spring beams. In the initial state, the system is biased at the EP point. When pressure acts on the lower surface of the substrate to cause strain in the substrate, it drives the position of the anchor region to change, thereby causing a change in the stiffness of the resonator Δk, causing the PT-symmetric system to deviate from the EP point, and the eigenfrequency of the system splits, manifested as Rabi oscillation. The frequency splitting amount is

[0009]

[0010] Among them, μ is the coupling coefficient of the resonator, and f0 is the natural frequency of the resonator, both of which are known parameters; δ = Δk / k is the stiffness perturbation, and k is the stiffness of the resonator when it is not perturbed; the frequency splitting amount is proportional to the square root of the change in stiffness perturbation. For a small pressure change, δ << 1, and there is an obvious change in the frequency splitting amount Δf.

[0011] The expression for the system normalized sensitivity is as follows:

[0012]

[0013] Compared with the traditional two-degree-of-freedom resonant system (the normalized sensitivity is 1), there is an improvement in the order of magnitude.

[0014] Specifically as follows:

[0015] A thermally piezoresistive PT-symmetric MEMS pressure sensor, which includes two resonators with exactly the same structure, namely a first resonator (a) and a second resonator (b). The two resonators are connected and fixed on a substrate (7) through a set of coupling spring beams, namely a first coupling spring beam (4a) and a second coupling spring beam (4b). The first resonator (a) includes four anchor regions, namely a first anchor region one (3a1), a first anchor region two (3a2), a first anchor region three (3a3), and a first anchor region four (3a4), four narrow beams with piezoresistive effect, namely a first narrow beam one (1a1), a first narrow beam two (1a2), a first narrow beam three (1a3), and a first narrow beam four (1a4), and a first mass block (1a5); the second resonator (b) includes four anchor regions, namely a second anchor region one (3b1), a second anchor region two (3b2), a second anchor region three (3b3), and a second anchor region four (3b4), four narrow beams with piezoresistive effect, namely a second narrow beam one (1b1), a second narrow beam two (1b2), a second narrow beam three (1b3), and a second narrow beam four (1b4), and a second mass block (1b5). The first anchor region one (3a1) is connected to the first narrow beam one (1a1), the first anchor region two (3a2) is connected to the first narrow beam two (1a2), the first anchor region three (3a3) is connected to the first narrow beam three (1a3), the first anchor region four (3a4) is connected to the first narrow beam four (1a4), and the first mass block (1a5) is connected to the four narrow beams, namely the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4); the second anchor region one (3b1) is connected to the second narrow beam one (1b1), the second anchor region two (3b2) is connected to the second narrow beam two (1b2), the second anchor region three (3b3) is connected to the second narrow beam three (1b3), the second anchor region four (3b4) is connected to the second narrow beam four (1b4), and the second mass block (1b5) is connected to the four narrow beams, namely the second anchor region one (3b1), the second anchor region two (3b2), the second anchor region three (3b3), and the second anchor region four (3b4); a first constant current source (5a1) is connected to the first anchor region one (3a1) and the first anchor region two (3a2) of the first resonator (a), a second constant current source (5a2) is connected to the first anchor region three (3a3) and the first anchor region four (3a4) of the first resonator (a), and a filter capacitor (6) is connected to the first anchor region two (3a2).

[0016] Under the action of the first constant current source (5a1) and the second constant current source (5a2), thermal piezoresistive feedback is generated at the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4) of the resonator, so that the two coupled resonators, namely the first resonator (a) and the second resonator (b), form a PT-symmetric system. The PT-symmetric resonator is initially set at the EP point. When the lower surface of the substrate (7) is subjected to pressure and generates strain, it drives the positions of the anchor regions, namely the first anchor region one (3a1), the first anchor region two (3a2), the first anchor region three (3a3), the first anchor region four, the second anchor region one (3b1), the second anchor region two (3b2), the second anchor region three (3b3), and the second anchor region four (3b4) to change, thereby causing the stiffness of the first resonator (a) and the second resonator (b) to change, causing the PT-symmetric system to deviate from the EP point, and the eigenfrequency of the system to split, manifested as Rabi oscillation. The amount of frequency splitting depends on the magnitude of the pressure applied to the substrate.

[0017] Beneficial effects: The thermopiezoresistive PT-symmetric MEMS pressure sensor of the present invention is based on a PT-symmetric MEMS resonator composed of thermopiezoresistive feedback. The PT-symmetric system is biased at the EP point. When the pressure changes act on the lower surface of the substrate, it causes the stiffness of the MEMS resonator to change, thereby causing the PT-symmetric system to deviate from the EP point, resulting in eigenfrequency splitting. The amount of frequency splitting is proportional to the square root of the stiffness change. Under weak pressure, due to the square root effect, the sensitivity of the frequency splitting relative to the pressure has an order-of-magnitude improvement. This pressure sensor is based on a MEMS resonator and has the advantages of simple process, easy integration, small size, and low cost. Description of the Drawings

[0018] Figure 1 is a top view of the thermopiezoresistive PT-symmetric MEMS pressure sensor.

[0019] Figure 2 is a cross-sectional view of the thermopiezoresistive PT-symmetric MEMS pressure sensor.

[0020] Figure 3 is a schematic diagram of the thermopiezoresistive feedback process.

[0021] Figure 4 is a comparison of the normalized sensitivities of the thermopiezoresistive PT-symmetric MEMS pressure sensor in this embodiment and a traditional two-degree-of-freedom resonant pressure sensor.

[0022] In the figure: a, the first resonator; b, the second resonator; 4a, the first coupling spring beam; 4b, the second coupling spring beam; 6, the filter capacitor; 7, the substrate; 1a5, the first mass; 1b5, the second mass.

[0023] 3a1, the first anchor region 1, 3a2, the first anchor region 2, 3a3, the first anchor region 3, 3a4, the first anchor region 4,

[0024] 1a1, the first narrow beam 1, 1a2, the first narrow beam 2, 1a3, the first narrow beam 3, 1a4, the first narrow beam 4, 3b1, the second anchor region 1, 3b2, the second anchor region 2, 3b3, the second anchor region 3, 3b4, the second anchor region 4, 1b1, the second narrow beam 1, 1b2, the second narrow beam 2, 1b3, the second narrow beam 3, 1b4, the second narrow beam 4. Detailed implementation manner

[0025] To deepen the understanding and recognition of the present invention, the present invention will be further described below with reference to the accompanying drawings.

[0026] Example: The thermally piezoresistive PT-symmetric MEMS pressure sensor involved in the present invention is shown in Figure 1 , Figure 2 , and includes two resonators with exactly the same structure, namely the first resonator a and the second resonator b. The first resonator a includes four narrow beams with piezoresistive effects, namely the first narrow beam 1a1, the first narrow beam 1a2, the first narrow beam 1a3, the first narrow beam 1a4, and the first mass block 1a5; the second resonator b includes four narrow beams with piezoresistive effects, namely the second narrow beam 1b1, the second narrow beam 1b2, the second narrow beam 1b3, the second narrow beam 1b4, and the second mass block 1b5; the two are completely consistent in terms of effective mass and stiffness. The anchor regions of the first resonator a, namely the first anchor region 1 3a1, the first anchor region 2 3a2, the first anchor region 3 3a3, the first anchor region 4 3a4, and the four anchor regions of the second resonator b, namely the second anchor region 1 3b1, the second anchor region 2 3b2, the second anchor region 3 3b3, the second anchor region 4 3b4, are fixed on the thin film substrate 7. The first resonator a and the second resonator b are connected by a set of coupled spring beams 4a and 4b to form a weak coupling. The positive pole of the first constant current source 5a1 is connected to the first anchor region 1 (3a1) of the first resonator a, and the negative pole is connected to the first anchor region 2 3a2. The positive pole of the second constant current source 5a2 is connected to the first anchor region 3 3a3 of the first resonator a, and the negative pole is connected to the first anchor region 4 3a4, forming a thermally piezoresistive feedback on the first resonator a. The filter capacitor 6 is connected to the first anchor region 1 3a1 of the first resonator a.

[0027] The schematic diagram of the thermally piezoresistive feedback process involved in the present invention is shown in Figure 3, the first constant current source 5a1 forms a current path among the first anchor area 1 3a1, the first narrow beam 1 1a1, the second narrow beam 1 1a2, and the second anchor area 3a2; the second constant current source 5a2 forms a current path among the third anchor area 3a3, the third narrow beam 1 1a3, the fourth narrow beam 1 1a4, and the fourth anchor area 3a4; the first constant current source 5a1 and the second constant current source 5a2 apply direct current with the same magnitude to the first resonator a, and the Joule heat power generated by the flowing current will be concentrated on the first narrow beam 1 1a1, the second narrow beam 1 1a2, the third narrow beam 1 1a3, and the fourth narrow beam 1 1a4. When the resonator vibrates, the vibration displacement x of the first mass block 1a5 drives the narrow beams, namely the first narrow beam 1 1a1, the second narrow beam 1 1a2, the third narrow beam 1 1a3, and the fourth narrow beam 1 1a4, to generate strain. Due to the piezoresistive effect, the resistance r of the first narrow beam 1 1a1, the second narrow beam 1 1a2, the third narrow beam 1 1a3, and the fourth narrow beam 1 1a4 changes. Since the current remains unchanged under the action of the constant current source, the Joule heat power P generated at this place changes in direct proportion to the vibration displacement x. According to the thermodynamic heat transfer equation, the change in the Joule heat power P causes a change in the temperature T of the narrow beams, the first narrow beam 1 1a1, the second narrow beam 1 1a2, the third narrow beam 1 1a3, and the fourth narrow beam 1 1a4. Due to the thermal expansion characteristics of the material, the change in temperature T will lead to a change in the thermal expansion force F. The thermal expansion force F acting on the beam, according to Hooke's law, in turn causes a change in the vibration displacement x, forming a feedback. The force F feedback caused by the feedback has the following relationship with the moving speed

[0028]

[0029] where E, α, and C t are the Young's modulus, thermal expansion coefficient, and heat capacity of silicon, respectively; the first narrow beam 1 1a1, the second narrow beam 1 1a2, the third narrow beam 1 1a3, and the fourth narrow beam 1 1a4 have the same cross-sectional area, length, and direct current impedance, which are A, L, and R DC , respectively; k is the equivalent stiffness of the first resonator a, and I DC is the direct current provided by the first constant current source 5a1 and the second constant current source 5a2. Substituting this feedback force into the vibration equation of the resonator, the equivalent damping

[0030]

[0031] of the first resonator a under the feedback action can be obtained, where c is the inherent damping of the first resonator a. Adjust the magnitude of I DC to make c s=-c. The effect produced by the feedback force is opposite to that of the damping, providing gain for the first resonator a. Since the second resonator b is under a loss condition due to its inherent damping, the first resonator a with equivalent gain and the second resonator b with equivalent loss form a PT-symmetric system under the coupling action of the first coupling spring beam 4a and the second coupling spring beam 4b.

[0032] It should be noted that the above is only one embodiment of the present invention. In fact, since the first resonator a and the second resonator b are completely symmetric, the first constant current source 5a1 and the second constant current source 5a2 can also be applied to the first anchor region 1 3a1, the first anchor region 2 3a2, the first anchor region 3 3a3, and the first anchor region 4 3a4 of the second resonator b.

[0033] The process of piezoresistive feedback is equivalent to an action opposite to the damping for the first resonator a, so it can be regarded as the gain in the PT-symmetric system. The second resonator b has no constant current source and is directly affected by the damping, acting as the loss in the PT-symmetric system. The first resonator a and the second resonator b are connected by a set of coupled spring beams 4a and 4b to form a weak coupling, and form a PT-symmetric system under the action of feedback and damping.

[0034] When pressure acts on the lower surface of the thin film substrate 7, it causes the deformation of the thin film substrate 7, thereby driving the anchor regions of the first resonator a fixed on the thin film substrate 7, namely the first anchor region 1 3a1, the first anchor region 2 3a2, the first anchor region 3 3a3, the first anchor region 4 3a4, and the anchor regions of the second resonator b, namely the second anchor region 1 3b1, the second anchor region 2 3b2, the second anchor region 3 3b3, the second anchor region 4 3b4, to change their positions, resulting in a change in the stiffness of the first resonator a and the second resonator b. The change in stiffness causes the state of the PT-symmetric system originally biased at the EP point to change, the system deviates from the EP point, and the eigenfrequency splits, manifested as Rabi oscillations. The frequency splitting amount is proportional to the square root of the stiffness change. The specific relationship is as follows:

[0035]

[0036] Therefore, the change in the stiffness of the resonator can be directly obtained through the frequency splitting amount, and according to the calibrated pressure-induced film deformation and thus the resulting stiffness change, the pressure to be measured can be obtained.

[0037] The frequency splitting amount can be extracted from the vibration signal of the system, and the vibration signal is obtained from the alternating current after filtering out the direct current component by the filter capacitor (6).

[0038] The criteria for distinguishing whether it is this structure are as follows:

[0039] (a) Adopt a PT-symmetric MEMS resonator;

[0040] (b) The gain of the PT - symmetric system is provided by a narrow beam with a thermo - piezoresistive effect;

[0041] (c) Pressure sensitivity is achieved by simultaneously generating perturbations on two resonators through a substrate - thin - film structure.

[0042] A structure that meets the above three conditions should be regarded as the pressure sensor of this structure.

[0043] The above - mentioned is only the preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above - mentioned embodiment. Any equivalent modification or change made by those of ordinary skill in the art according to the disclosure of the present invention should be incorporated into the protection scope recorded in the claims.

Claims

1. A thermopiezoresistive PT-symmetric MEMS pressure sensor, characterized in that, The pressure sensor includes two resonators with exactly the same structure, namely a first resonator (a) and a second resonator (b). The two resonators are connected and fixed on a substrate (7) through a set of coupling spring beams, namely a first coupling spring beam (4a) and a second coupling spring beam (4b).

2. The thermopiezoresistive PT-symmetric MEMS pressure sensor according to claim 1, wherein the first resonator (a) includes four anchor regions, namely a first anchor region 1 (3a1), a first anchor region 2 (3a2), a first anchor region 3 (3a3), and a first anchor region 4 (3a4), four narrow beams with piezoresistive effect, namely a first narrow beam 1 (1a1), a first narrow beam 2 (1a2), a first narrow beam 3 (1a3), and a first narrow beam 4 (1a4), and a first mass block (1a5); the second resonator (b) includes four anchor regions, namely a second anchor region 1 (3b1), a second anchor region 2 (3b2), a second anchor region 3 (3b3), and a second anchor region 4 (3b4), four narrow beams with piezoresistive effect, namely a second narrow beam 1 (1b1), a second narrow beam 2 (1b2), a second narrow beam 3 (1b3), and a second narrow beam 4 (1b4), and a second mass block (1b5). The first anchor region 1 (3a1) is connected to the first narrow beam 1 (1a1), the first anchor region 2 (3a2) is connected to the first narrow beam 2 (1a2), the first anchor region 3 (3a3) is connected to the first narrow beam 3 (1a3), the first anchor region 4 (3a4) is connected to the first narrow beam 4 (1a4), and the first mass block (1a5) is connected to the four narrow beams, namely the first narrow beam 1 (1a1), the first narrow beam 2 (1a2), the first narrow beam 3 (1a3), and the first narrow beam 4 (1a4). The second anchor region 1 (3b1) is connected to the second narrow beam 1 (1b1), the second anchor region 2 (3b2) is connected to the second narrow beam 2 (1b2), the second anchor region 3 (3b3) is connected to the second narrow beam 3 (1b3), the second anchor region 4 (3b4) is connected to the second narrow beam 4 (1b4), and the second mass block (1b5) is connected to the four narrow beams, namely the second anchor region 1 (3b1), the second anchor region 2 (3b2), the second anchor region 3 (3b3), and the second anchor region 4 (3b4). A first constant current source (5a1) is connected to the first anchor region 1 (3a1) and the first anchor region 2 (3a2) of the first resonator (a), a second constant current source (5a2) is connected to the first anchor region 3 (3a3) and the first anchor region 4 (3a4) of the first resonator (a), and a filter capacitor (6) is connected to the first anchor region 2 (3a2).

3. The thermopiezoresistive PT-symmetric MEMS pressure sensor according to claim 1, wherein: Under the action of the first constant current source (5a1) and the second constant current source (5a2), thermal piezoresistive feedback is generated at the first narrow beam 1 (1a1), the first narrow beam 2 (1a2), the first narrow beam 3 (1a3), and the first narrow beam 4 (1a4) of the resonator, so that the two coupled resonators, namely the first resonator (a) and the second resonator (b), form a PT-symmetric system. The PT-symmetric resonator is initially set at the EP point. When the lower surface of the substrate (7) is subjected to pressure and generates strain, it drives the positions of the anchor regions, namely the first anchor region 1 (3a1), the first anchor region 2 (3a2), the first anchor region 3 (3a3), the first anchor region 4, the second anchor region 1 (3b1), the second anchor region 2 (3b2), the second anchor region 3 (3b3), and the second anchor region 4 (3b4) to change, thereby causing the stiffness of the first resonator (a) and the second resonator (b) to change, making the PT-symmetric system deviate from the EP point, and the eigenfrequency of the system splits. The amount of frequency splitting depends on the magnitude of the pressure applied to the substrate.

4. The thermal piezoresistive PT-symmetric MEMS pressure sensor according to claim 3, characterized in that: When pressure acts on the lower surface of the substrate to generate strain, it drives the positions of the anchor regions to change, thereby causing a change in the stiffness Δk of the resonator, making the PT-symmetric system deviate from the EP point, and the eigenfrequency of the system splits, manifested as Rabi oscillation. The amount of frequency splitting is: where μ is the coupling coefficient of the resonator, f0 is the natural frequency of the resonator, both are known parameters; δ = Δk / k is the stiffness perturbation, and k is the stiffness of the resonator when it is not perturbed; the amount of frequency splitting is proportional to the square root of the change in the stiffness perturbation. For a small pressure change, δ << 1, and there is an obvious change in the amount of frequency splitting Δf.

5. The thermopiezoresistive PT-symmetric MEMS pressure sensor according to claim 1, characterized in that: The first constant current source (5a1) forms a current path between the first anchor region 1 (3a1), the first narrow beam 1 (1a1), the first narrow beam 2 (1a2), and the first anchor region 2 (3a2); The second constant current source (5a2) forms a current path between the first anchor region 3 (3a3), the first narrow beam 3 (1a3), the first narrow beam 4 (1a4), and the first anchor region 4 (3a4); The first constant current source (5a1) and the second constant current source (5a2) apply DC currents of the same magnitude to the first resonator (a). The Joule heat power generated by the flowing current will be concentrated on the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4). When the resonator vibrates, the vibration displacement (x) of the first mass block (1a5) drives the narrow beams, namely the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4), to undergo strain. Due to the piezoresistive effect, the resistance (r) of the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4) changes. Since the current remains constant under the action of the constant current source, the Joule heat power (P) at this location changes in proportion to the vibration displacement (x). According to the thermodynamic heat transfer equation, the change in the Joule heat power (P) causes a change in the temperature (T) of the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4). Due to the thermal expansion characteristics of the material, the change in temperature (T) will lead to a change in the thermal expansion force (F). The thermal expansion force (F) acting on the first narrow beam one (1a1), the first narrow beam two (1a2), the first narrow beam three (1a3), and the first narrow beam four (1a4) in turn causes a change in the vibration displacement (x) according to Hooke's law, forming a feedback. The feedback process is equivalent to an action opposite to the damping direction, providing gain for the first resonator (a). The second resonator (b) is under a loss condition due to its inherent damping. The first resonator (a) with equivalent gain and the second resonator (b) with equivalent loss form a PT-symmetric system under the coupling action of the first coupling spring beam (4a) and the second coupling spring beam (4b).

6. The thermopiezoresistive PT-symmetric MEMS pressure sensor according to claim 5, wherein: The force F caused by feedback feedback and the moving speed of the resonator are in the following relationship: where E, α, and C t are Young's modulus, coefficient of thermal expansion, and heat capacity of silicon, respectively; the first narrow beams one (1a1), two (1a2), three (1a3), and four (1a4) have the same cross-sectional area, length, and direct current impedance of A, L, and R, respectively DC ,; k is the equivalent stiffness of the first resonator (a), I DC is the DC current provided by the first constant current source (5a1) and the second constant current source (5a2). Substituting this feedback force into the vibration equation of the resonator, the equivalent damping of the first resonator (a) under the feedback effect can be obtained where c is the inherent damping of the first resonator (a), adjust the magnitude of I DC such that c s = -c, the action effect of the feedback force is opposite to the damping, providing gain for the first resonator (a). The second resonator (b) is under a loss condition due to the inherent damping. The first resonator (a) with equivalent gain and the second resonator (b) with equivalent loss form a PT - symmetric system under the coupling action of the first coupling spring beam (4a) and the second coupling spring beam (4b). In the initial state, the system is biased at the EP point. When pressure acts on the lower surface of the substrate to cause strain in the substrate, driving the positions of the first anchor region one (3a1), the first anchor region two (3a2), the first anchor region three (3a3), the first anchor region four, the second anchor region one (3b1), the second anchor region two (3b2), the second anchor region three (3b3), and the second anchor region four (3b4) to change, thereby causing a change in the stiffness of the resonator Δk, causing the PT - symmetric system to deviate from the EP point, the eigen - frequency of the system splits, manifested as Rabi oscillations, and the frequency splitting amount is: where μ is the coupling coefficient and f0 is the natural frequency of the resonator, both of which are known parameters; δ = Δk / k is the stiffness perturbation, and k is the stiffness of the resonator when it is not perturbed; the frequency splitting amount is proportional to the square root of the change in the stiffness perturbation. For a small pressure change, δ << 1, and an obvious change is shown in the frequency splitting amount Δf. The system normalization sensitivity expression is as follows:

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