A method for constructing a macro model of a MEMS device based on physical field analysis

Abstract

The application discloses a MEMS device macro model construction method based on physical field analysis, and belongs to the technical field of calculation, estimation or counting. The method separates multiple physical field effects of a MEMS device, selects a physical field with the deepest coupling degree with the mechanical structure of the MEMS device as a main physical field, reduces the order of the main physical field through a system identification method based on a step response, and obtains a state space model of the main physical field. Behavior equations are used to respectively construct behavior models of other physical fields of the MEMS device, and finally, the state space model and each behavior model are described and assembled through Verilog-A, and finally, a macro model of the MEMS device is obtained. The application takes a diode type MEMS Pirani vacuum sensor macro model modeling process as an example, introduces the MEMS device macro model modeling method based on physical field analysis, and other types of devices can also be analyzed and modeled in the same way.

Description

Technical Field

[0001] This invention relates to the field of MEMS device simulation, and in particular discloses a method for constructing a macro model of a MEMS device based on physical field analysis, belonging to the technical field of calculation, estimation or counting. Background Technology

[0002] With the development of technology, MEMS are becoming increasingly diverse in form and more complex in function, bringing with them design and analysis challenges. The design of MEMS devices and interface circuits is usually separate. For device analysis, the traditional method is the finite element method (FEM), but the multi-physics coupling and cross-scale structure of MEMS make FEM analysis very time-consuming. For interface circuit analysis, it is usually based on circuit analysis software. However, with current technology, FEM and circuit software cannot be directly connected, meaning that the design of the mechanical and electronic circuit parts is separate. This situation hinders the transmission of data between mechanical devices and circuits, which is detrimental to the development of MEMS and even microsystems. To solve this problem, more than a decade ago, the industry proposed system-level design that combines devices and circuits. This involves describing the mechanical structure of the MEMS using a numerical or analytical model containing accurate information about the original device. The model is then transformed using a hardware description language to form electronic IP units that can be connected to the circuit. Since then, system-level design has become a powerful tool for MEMS optimization design, and systems verified by this method have advantages such as high overall performance and high reliability. However, existing macro-model construction methods are still limited to specific devices or a small number of devices, and the parameterization of the constructed macro-models is low.

[0003] Traditional macro-modeling methods suffer from difficulties in order reduction when dealing with multiphysics. An improved macro-modeling method for MEMS devices addresses this by systematically identifying the linear physical processes of the MEMS device, establishing a linear process model, and then coupling the nonlinear physical processes of the MEMS device into the linear process model using a hardware description language. The implementation of this macro-modeling method relies on decoupling the linear and nonlinear processes. However, most existing devices are strongly coupled, making linear and nonlinear decoupling extremely difficult. Furthermore, the linear and nonlinear factors vary significantly among different MEMS devices, hindering its applicability to other MEMS devices.

[0004] In summary, the present invention aims to propose a method for constructing macro-models of MEMS devices based on physical field analysis to overcome the above-mentioned shortcomings. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing methods for constructing macro-models of MEMS devices by providing a method for constructing macro-models of MEMS devices based on physical field analysis. This method decouples the multiple physical fields that drive the operation of MEMS devices, models each physical field separately, and then describes and assembles them using Verilog-A to form a relatively accurate and complete basic device electronic unit model that can include some behaviors of MEMS devices. This solves the technical problem of the difficulty in constructing macro-models caused by the diversification of MEMS device structures.

[0006] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0007] A method for constructing macro-models of MEMS devices based on physical field analysis, comprising the following steps:

[0008] Step 1: Analyze the physical field interaction mechanism of MEMS devices. Based on the control equations of MEMS devices, decompose the multiple mutually coupled physical fields and select the physical field with the deepest coupling with MEMS devices as the main physical field.

[0009] Step 2: Extract the material, structure, and size parameters of the MEMS device and construct a three-dimensional solid model of the device;

[0010] Step 3: Apply linear boundary conditions to the 3D solid model, freeze other physical fields, and perform transient finite element analysis only on the main physical field to obtain a set of step response datasets that describe the behavior of the main physical field and contain multiple inputs and multiple outputs.

[0011] Step 4: Use the system identification method based on step response to perform system identification on the step response dataset. According to the data characteristics of the step response dataset, select the time domain or frequency domain for system identification. Then, according to the accuracy requirements, choose the order of the state space model obtained by system identification to obtain the matrix or transfer function of the low-dimensional state space model of the main physical field.

[0012] Step 5: Based on the working mechanism of MEMS devices and the interaction between other physical fields and the main physical field, establish a set of behavioral description equations for each of the other physical fields besides the main physical field, and obtain the behavioral model of each physical field.

[0013] Step 6: Based on the interaction between physical fields, use Verilog-A to describe the state-space model of the main physical field and the behavioral models of other physical fields. Assemble the model based on the information transmission relationship between each physical field. Finally, interconnect the interfaces of different models according to the information transmission relationship between each physical field to obtain the macro model of the MEMS device.

[0014] Furthermore, in step 1, the primary physical field most deeply coupled with the MEMS device is usually reflected in the mechanical structure of the MEMS device, while other physical fields affect the MEMS device by influencing the primary physical field. Taking the diode-type MEMS Pirani vacuum sensor as an example, it is affected by three physical fields: thermal, electromagnetic, and fluid. The thermal field is the primary physical field. The electromagnetic field acts on the diode through current, thereby generating the thermal field and carrying away some of the heat in the thermal field through thermal radiation. The fluid field mainly carries away some of the heat in the thermal field through thermal convection. The thermal balance equation of the vacuum sensor with thermal energy as the primary physical field is:

[0015] P e =(T-T0)(G s +G r +G g (p))(1)

[0016] Among them, P e This refers to the heating power of the diode when it is under constant bias, where T is the temperature of the sensitive region, T0 is the ambient temperature, and G is the heating power. s It is solid thermal conductivity, G r It is radiative thermal conductivity, G g (p) represents the thermal conductivity of a gas, and p is the ambient pressure. The thermal conductivity of a solid can be expressed as:

[0017]

[0018] Where, λ s The solid thermal conductivity is given by L, where L is the length of the cantilever beam, w is the width of the cantilever beam, and t is the thickness of the cantilever beam.

[0019] Radiative thermal conductivity can be expressed as:

[0020]

[0021] Where σ is the Boltzmann constant, ε is the emissivity of the sensitive region, and A is the area of ​​the sensitive region.

[0022] Gas thermal conductivity can be expressed as:

[0023]

[0024] Where k0 is the heat transfer coefficient of air at room temperature, T g d is the air temperature, and d is the distance between the sensitive area and the heat dissipation substrate. Therefore, the physical field that dominates the operation of the diode-type MEMS Pirani vacuum sensor is divided into three categories: thermal physical field, electromagnetic physical field, and fluid physical field.

[0025] Furthermore, in step 2, the material, structure, and size parameters in the three-dimensional solid model of the device are constant. Taking the diode-type MEMS Pirani vacuum sensor as an example, its mechanical structure includes a sensitive area composed of diodes and wires, a heat dissipation substrate, and a cantilever beam. The sensitive area is suspended by the cantilever beam and maintains a certain air gap with the heat dissipation substrate.

[0026] Furthermore, the linear boundary conditions and freezing of other physical fields involved in step 3, taking the diode-type MEMS Pirani vacuum sensor as an example, are as follows: after meshing the three-dimensional solid model, a linear boundary condition is applied to the model. The linear boundary condition is constant power, and the flow field and electromagnetic field are frozen. That is, only the thermal field is simulated to obtain a set of step response datasets with power as input and temperature as output.

[0027] In the linear boundary condition of constant power, the constant power is applied to the upper and lower surfaces of the sensitive area and the series diode group in the model. Under each power input, the output is the temperature value of the upper and lower surfaces of the sensitive area and the temperature value of each of the five diodes. After transient simulation, a total of 21 step response data files with 3 inputs and 7 outputs were obtained. The input and output values ​​of the step response data files can be selected according to the specific design.

[0028] Furthermore, in step 4, the step response dataset obtained from the finite element simulation in step 3 is systematically identified; the low-order state-space model of the thermal field obtained through systematic identification has the same output as the original thermal field system under the same input.

[0029] In the model, power of 0.09mW was applied to the upper and lower surfaces of the sensitive area, and power of 0.03576mW was applied to the series diode group. Temperature data T for the upper and lower surfaces of the sensitive area and each of the five diodes were obtained. up (t),T down (t),T d1 (t),T d2 (t),T d3 (t),T d4 (t) and T d5 (t). According to the state-space model equation

[0030]

[0031] y=Cx+Du (5)

[0032] Where x is the state vector. This is the differential form of the state vector, where y is the output vector, u is the input vector, and A, B, C, and D are the system matrix, input matrix, output matrix, and direct feed matrix, respectively. The specific values ​​of these four matrices can be obtained through a system identification method based on step response, leading to the specific state-space model equations of the thermal field.

[0033] Furthermore, in step 5, a set of behavioral description equations is established for each of the physical fields other than the main physical field to obtain a behavioral model for each physical field. The flow field behavioral model can be abstracted as follows:

[0034] Q g =G g (p)×(T i -T0) (6)

[0035] Among them, Q g Convective heat flux, T i It is the temperature at the heat exchange interface. The electromagnetic field behavior model can be abstracted as follows:

[0036]

[0037]

[0038] Among them, Q r I is the radiative heat flux, I is the diode bias current, and R is the diode bias current. j It is the resistance of the j-th diode in a series diode configuration.

[0039] Furthermore, in step 6, the state-space model of the thermal field and the behavioral models of the flow and electromagnetic fields are described using Verilog-A language. The product of the convective heat flux and the interface area of ​​the flow field behavioral model is used as the input to the state-space model. Similarly, the product of the radiative heat flux and the radiative surface area of ​​the electromagnetic field, as well as the heating power, are also used as the input to the state-space model. Then, the output temperature of the thermal field state-space model is fed back into the T value in the formulas for convective and radiative heat flux. i By using the method of multi-physics coupling, a macro model of a diode-type MEMS Pirani vacuum sensor was constructed.

[0040] An electronic device includes a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor executes the steps of the above-described MEMS device macromodel construction method when running the computer program.

[0041] A computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the steps of the above-described method for constructing a macro model of a MEMS device when it is run.

[0042] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0043] (1) This invention proposes a macro model construction method for MEMS devices with multi-physics coupling that is widely applicable. The multi-physics that dominates the operation of MEMS devices is decomposed, and the physical field with the highest coupling degree with the mechanical structure of MEMS devices is selected as the main physical field. The system model of the main physical field is reduced in order to obtain the state space model. Other physical fields are abstracted into a set of behavioral equations to construct the behavioral model of each physical field. Then, based on the coupling relationship between physical fields, Verilog-A is used to describe and assemble the state space model and the behavioral model to obtain the macro model of MEMS devices. Based on the mechanism of decoupling, modeling and reassembling multi-physics coupling, the difficulty of order reduction caused by multi-physics coupling is fundamentally solved, and technology is provided for the co-simulation of MEMS devices and interface circuits.

[0044] (2) The system identification method based on step response in this invention is to identify the dataset obtained based on finite element transient simulation. In the finite element, linear or nonlinear parameters such as material properties can be set for the MEMS device model. Its characteristics will be reflected in the state space matrix. That is, the macro model of the MEMS device will contain some linear and nonlinear effects in the mechanical structure.

[0045] (3) In this invention, the Verilog-A hardware description language is used to describe and assemble the model, which can realize the conversion of digital information to analog signals, thereby directly obtaining electronic IP units that can be called at any time to participate in circuit simulation and realize the data and information transmission between MEMS devices and interface circuits.

[0046] (4) In summary, this invention obtains the macro model of MEMS devices from the perspective of physical field decomposition and coupling. It performs order reduction processing on the main physical field rather than on the overall physical field that dominates the operation of MEMS devices, which can greatly reduce the requirements for the order reduction algorithm. At the same time, the physical field can be reused after being abstracted into different models and then reassembled. That is, the macro model constructed in this application is a gray box model that is widely applicable to MEMS devices with multi-physical field coupling. The parameters are directly integrated into the model describing individual physical fields through the behavioral equation description method, which solves the parameterization problem of macro model and is conducive to extending the macro model construction method to devices with the same physical field. Attached Figure Description

[0047] Figure 1 This is a top view of the structure of a diode-type MEMS Pirani vacuum sensor.

[0048] Figure 2 This is a cross-sectional view of the diode-type MEMS Pirani vacuum sensor.

[0049] Figure 3 This is a flowchart of the method proposed in this invention.

[0050] Figure 4 This is a macro model of a diode-type MEMS Pirani vacuum sensor.

[0051] Figure 5 for Figure 4 The diagram shows the interconnection between the macro model and the interface circuit.

[0052] Figure 6 10 -3 ~10 6 Comparison of macro-model co-simulation and experimental results within the Pa pressure range. Detailed Implementation

[0053] The embodiments of the present invention are described in detail below, and the specific flow of the embodiments is shown in the accompanying drawings.

[0054] When the coupled physical field that drives the operation of a MEMS device can be decoupled into multiple separate physical fields, the MEMS device macro-model construction method based on physical field analysis proposed in this invention can be used. This embodiment uses a typical diode-type MEMS Pirani vacuum sensor as a specific application to illustrate the implementation process of the MEMS device macro-model construction method proposed in this invention. Other MEMS devices can also be modeled and analyzed using this method.

[0055] like Figure 3 As shown, the method for constructing a macro-model of a MEMS device based on physical field analysis includes the following 6 steps.

[0056] Step 1: Decouple the multiphysics fields that dominate the operation of MEMS devices.

[0057] This paper analyzes the physical field interaction mechanism of MEMS devices. Based on the control equations of MEMS devices, multiple mutually coupled physical fields are decomposed, and the physical field with the deepest coupling with the MEMS device is selected as the master physical field. The master physical field with the deepest coupling with the MEMS device is usually reflected in the mechanical structure of the MEMS device, while other physical fields affect the MEMS device by influencing the master physical field.

[0058] The diode-type MEMS Pirani vacuum sensor is a typical nonlinear system with multi-physics coupling, dominated by electromagnetic, thermal, and fluid fields. This type of sensor is a typical thermally based device, with the thermal field being the most deeply coupled to the sensor's mechanical structure. Therefore, the thermal field is chosen as the primary physical field. The electromagnetic field acts on the diode through current, generating a thermal field, and carries away some heat through thermal radiation. The fluid field mainly carries away some heat through thermal convection. The electromagnetic and fluid fields are considered as the other physical fields. Therefore, the physical field interaction process of the diode-type MEMS Pirani vacuum sensor is divided into thermal, fluid, and electromagnetic fields. Each of these three fields is analyzed separately, and their coupling relationship can be expressed by the thermal balance equation of the diode-type MEMS Pirani vacuum sensor.

[0059] P e =(T-T0)(G s +G r +G g (p))(1)

[0060] In equation (1), P e This refers to the heating power of the diode when it is under constant bias, where T is the temperature of the sensitive region, T0 is the ambient temperature, and G is the heating power. s It is solid thermal conductivity, G r It is radiative thermal conductivity, G g (p) is the thermal conductivity of the gas, and p is the ambient pressure.

[0061] Solid thermal conductivity can be expressed as:

[0062]

[0063] In equation (2), λ s t is the solid thermal conductivity, L is the cantilever beam length, w is the cantilever beam width, and t is the cantilever beam thickness.

[0064] Radiative thermal conductivity can be expressed as:

[0065]

[0066] In equation (3), σ is the Boltzmann constant, ε is the emissivity of the sensitive region, and A is the area of ​​the sensitive region.

[0067] Gas thermal conductivity can be expressed as:

[0068]

[0069] In equation (4), k0 is the heat transfer coefficient of air, and T g d is the air temperature, and d is the distance between the sensitive area and the heat dissipation substrate.

[0070] Step 2: Construct a three-dimensional solid model of the MEMS device.

[0071] Because the thermophysical field is deeply coupled with the mechanical structure of the device, after extracting the material, structure, and size parameters of the mechanical structure of the diode-type MEMS Pirani vacuum sensor, a three-dimensional solid model of the mechanical structure of the diode-type MEMS Pirani vacuum sensor is performed.

[0072] like Figure 1 , Figure 2 As shown, the mechanical structure of the diode-type MEMS Pirani vacuum sensor includes a sensitive area composed of diodes and wires, a heat dissipation substrate, and a cantilever beam. The sensitive area is suspended by the cantilever beam and maintains a certain air gap with the heat dissipation substrate.

[0073] The extracted mechanical structure dimensions of the diode-type MEMS Pirani vacuum sensor are as follows: the sensitive area is 150 × 150 μm. 2 The beam thickness is 1.49 μm, the beam width is 16 μm, the beam length is 407 μm, the conductor width is 4 μm, the air gap height is 70 μm, the diode thickness is 0.2 μm, and the central diode area is 100 × 50 μm. 2 The area of ​​the other four diodes is 60×40μm. 2 .

[0074] Step 3: Perform transient finite element analysis on the master physics field to obtain a set of step response datasets describing the behavior of the master physics field and containing multiple inputs and multiple outputs.

[0075] The three-dimensional solid model of the mechanical structure of the diode-type MEMS Pirani vacuum sensor constructed in step 2 is discretized by meshing. Linear boundary conditions are applied to the model with constant power, and the flow field and electromagnetic field are frozen. Constant power is applied to the upper and lower surfaces of the sensitive area and the diode group formed by five diodes connected in series. Temperature probes are applied to the upper and lower surfaces of the sensitive area and the five diodes. Transient simulation analysis of the thermophysical field is performed to obtain the temperature values ​​of the upper and lower surfaces of the sensitive area and each diode under each constant power input. In this way, a time-temperature step response dataset consisting of 3 inputs and 7 outputs is obtained.

[0076] Step 4: Use the system identification method based on step response to perform system identification on the step response dataset from Step 3 to obtain the state-space model of the master physical field.

[0077] In step 3, a power of 0.09mW was applied to the upper and lower surfaces of the sensitive area, and a power of 0.03576mW was applied to the series diode group. The temperature probe measured the temperature values ​​T of the upper and lower surfaces of the sensitive area and each of the five diodes.up (t),T down (t),T d1 (t),T d2 (t),T d3 (t),T d4 (t) and T d5 (t).

[0078] The step response dataset obtained in step 3 is identified using a system identification method based on step response. Based on the data characteristics of the step response dataset, system identification is performed in either the time domain or the frequency domain. Then, according to accuracy requirements, the order of the state-space model obtained from the system identification is autonomously selected, thereby determining the matrix or transfer function of the low-dimensional state-space model of the thermophysical field. This leads to the acquisition of the state-space model of the thermophysical field. The state-space model of the thermophysical field of the diode-type MEMS Pirani vacuum sensor can be represented by the following set of equations:

[0079]

[0080] y=Cx+Du (5)

[0081] In equation (5), x is the state vector. This is the differential form of the state vector, which is the time-dependent temperature quantity; y is the output vector, i.e., the temperature values ​​of the upper and lower surfaces of the sensitive area and the five diodes measured by the temperature probe; u is the input vector, i.e., the constant power applied to the upper and lower surfaces of the sensitive area and the series diode group; A, B, C, and D are the system matrix, input matrix, output matrix, and direct feed matrix, respectively. Here, the state vector is the temperature quantity. Since the initial temperature is 293.15K, matrix D is:

[0082]

[0083] After system identification, the matrix A of the second-order state-space model can be obtained as a 42×42 diagonal matrix:

[0084]

[0085] In equation (7), the element a on the diagonal of matrix A 11 to a 42 42The values ​​are, in order: -1.471358e+02, -3.711099e+00, -1.647523e+02, -3.711108e+00, -7.467515e+01, -5.177785e+00, -1.680463e+02, -3.711124e+00, -1.438031e+02, -3.711085e+00, -7.4 59212e+01, -5.177791e+00, -5.381802e+01, -3.712024e+00, -5.410834e+01, -3.71200 7e+00, -9.648104e+01, -5.178176e+00, -5.428312e+01, -3.712036e+00, -5.446485e+0 1, -3.712027e+00, -9.746173e+01, -5.178246e+00, -5.428716e+01, -3.712036e+00, -5 .441357e+01, -3.712031e+00, -9.745131e+01, -5.178246e+00, -5.385763e+01, -3.712 021e+00, -5.408913e+01, -3.712008e+00, -9.649262e+01, -5.178179e+00, -5.421833e +01, -3.712037e+00, -5.448304e+01, -3.712022e+00, -8.271049e+01, -5.177603e+00.

[0086] The matrix B of the second-order state-space model is a 42×3 matrix:

[0087]

[0088] The element values ​​in the first 6 rows of matrix B are listed from top to bottom as b 11 to b 63 The values ​​are 11111.1111, 11111.1111, 11111.1111, 11111.1111, 27964.206, 27964.206, and the remaining 36 rows repeat the first 6 values ​​every 6 rows.

[0089] The matrix C of the second-order state-space model is a 7×42 matrix:

[0090]

[0091] The first row of matrix C contains the values ​​1.296185e+02, 1.472655e+03, 1.448782e+02, 1.472664e+03, -3.654573e+01, and 4.508429e+02. The second row contains the values ​​1.475205e+02, 1.472676e+03, 1.268919e+02, 1.472644e+03, and -3.6. The values ​​in the third row are 51455e+01, 4.508440e+02, -1.389164e+02, 1.788271e+03, -1.395271e+02, 1.788253e+03, 8.713746e+01, 5.449885e+02. The values ​​in the fourth row are -1.506473e+02, 1.797466e+03, -1.51071. The values ​​in the fifth row are -1.506506e+02, 1.797456e+03, 1.008719e+02, 5.476096e+02, -1.506506e+02, 1.797460e+03, -1.509545e+02, 1.797455e+03, 1.008528e+02, 5.476082e+02, and -1.390025e+02. The values ​​in the seventh row are -1.494077e+02, 1.796513e+03, -1.500049e+02, 1.796496e+03, 7.922303e+01, and 5.473134e+02.

[0092] Step 5: Obtain behavioral models of other physical fields

[0093] Based on the working mechanism of the diode-type MEMS Pirani vacuum sensor and the interaction between other physical fields and the main physical field, we establish a set of behavioral description equations for the other physical fields besides the main physical field, and obtain behavioral models for the electromagnetic field and the flow field respectively.

[0094] The flow field behavior model can be abstracted as follows:

[0095]

[0096]

[0097] In equations (6) to (7), Q g1 It is the convective heat flux on the upper surface of the sensitive area, Q g2Where is the convective heat flux at the lower surface of the sensitive area, k0 = 0.0284 is the air heat transfer coefficient, d1 = 70 is the air gap height from the lower surface of the sensitive area to the heat dissipation substrate, d2 = 2000 is the distance from the upper surface of the sensitive area to the thin air layer at room temperature, and T g =293.15K is room temperature.

[0098] The electromagnetic field behavior model can be abstracted as follows:

[0099]

[0100]

[0101]

[0102] In equations (8) to (10), Q r1 It is the radiative heat flux of the upper surface of the sensitive area, Q r2 It is the radiative heat flux of the lower surface of the sensitive area, P e Where σ = 1 is the heating power, ε = 5.672e-8 is the Boltzmann constant, I = 10μA is the diode bias current, R1, R2, R4, R5 = 72000Ω are the resistances of the four smaller diodes in the series diodes, and R3 = 69600Ω is the resistance of the middle larger diode in the series diodes.

[0103] Step 6: Perform hardware description of the main physical field and other physical field models to construct the macro model of the MEMS device.

[0104] Based on the interaction between physical fields, Verilog-A is used to describe the models of each physical field. Then, the models are assembled based on the information transmission relationship between each physical field. That is, according to the interaction of other physical fields with respect to the main physical field, the interfaces of different models are interconnected, and finally the macro model of the MEMS device is obtained.

[0105] Taking a diode-type MEMS Pirani vacuum sensor as an example, the state-space model of the thermophysical field, the behavioral models of the flow field and the electromagnetic field are described using Verilog-A language. Based on whether the flow field and electromagnetic field are positive or negative energy inputs relative to the thermophysical field, the interfaces of the thermophysical field model, the flow field model, and the electromagnetic field model are interconnected. The convective heat flux Q of the flow field behavioral model is... gi The product of the surface area A of the sensitive region and the electromagnetic field is used as an element of the input vector u in the state-space model equation, i = 1, 2. Similarly, the radiative heat flux Q of the electromagnetic field... ri The product of the surface area A of the sensitive region and the heating power P e It is also used as an element of the input vector u in the state-space model equation, i = 1, 2, and then the output temperature T of the thermophysical field state-space model is... up(t) and T down (t) will be fed back into the convective heat flux formula and the radiative heat flux formula, thereby achieving multi-physics coupling, and thus constructing a macro-model of the diode-type MEMS Pirani vacuum sensor, such as Figure 4 As shown, the macromodel includes 3 input interfaces and 7 output interfaces. The 3 input interfaces input the current I, the ambient temperature Tamb, and the air gap height dgap, respectively. The 7 output ports output the upper surface temperature T of the sensitive area. up (t), lower surface temperature of the sensitive area T down (t) and the temperature T of each of the five diodes. d1 (t)~T d5 Alternatively, the voltages of the five diodes and the total voltage of the sensor can be selected as the output of the macro model.

[0106] Finally, the macro model of the diode-type MEMS Pirani vacuum sensor is connected to the bias interface circuit for co-simulation, such as... Figure 5 As shown. Figure 6 It shows that at a pressure of 10 -3 ~10 6 A comparison chart of co-simulation results and experimental results within the Pa range.

[0107] 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 transformations or substitutions that can be conceived by anyone skilled in the art within the technical scope disclosed in the present invention, such as the flow field model being used by MEMS devices with fluid physical fields, should be covered within the scope of protection of the present invention. It should be noted that the interface specified in the macro model of different MEMS devices is generally different and needs to be set according to the information transmission relationship between the flow field model and other physical field models. However, the main body of the behavioral equations in the flow field model remains unchanged. Therefore, the scope of protection of the present invention should be determined by the scope of protection of the claims.

Claims

1. A method for constructing a macro-model of a MEMS device based on physical field analysis, characterized in that, Includes the following steps: Step 1: Decouple the multiphysics fields that dominate the operation of the diode-type MEMS Pirani vacuum sensor. Select the thermophysics field as the main physical field, and the flow field and electromagnetic field as the other physical fields. The coupling relationship of the multiphysics fields is given by the thermal equilibrium equation. It means that, among them, This represents the heating power of the diode when it is under constant bias. For the temperature of the sensitive area, For ambient temperature, For solid thermal conductivity, For radiative thermal conductivity, For gas thermal conductivity, For environmental pressure, , , , For solid thermal conductivity, For the length of the cantilever beam, For the width of the cantilever beam, For the thickness of the cantilever beam, Boltzmann's constant, For the emissivity of the sensitive area, For the area of ​​the sensitive zone, The heat transfer coefficient of air. For air temperature, This represents the distance between the sensitive area and the heat dissipation substrate. Step 2: Extract the material, structural, and dimensional parameters of the diode-type MEMS Pirani vacuum sensor, and construct a three-dimensional solid model of the mechanical structure of the diode-type MEMS Pirani vacuum sensor; Step 3: Apply linear boundary conditions to the three-dimensional solid model of the diode-type MEMS Pirani vacuum sensor mechanical structure constructed in Step 2, freeze other physical fields, apply constant power to the upper and lower surfaces of the sensitive area and the series diode group respectively, apply temperature probes to the upper and lower surfaces of the sensitive area and each diode respectively, perform transient simulation analysis only on the thermophysical field, and obtain the time-temperature step response dataset characterizing the temperature values ​​of the upper and lower surfaces of the sensitive area and each diode under each constant power input; Step 4: Use the system identification method of step response to perform system identification on the step response dataset obtained in step 3 to obtain the state space model of the master physical field. Step 5: Construct other physical field behavior models; Step 6: Perform hardware description of the main physical field state space model and other physical field behavior models. Based on the information transmission relationship between each physical field, assemble the main physical field state space model and other physical field behavior models to obtain the macro model of the MEMS device.

2. The method for constructing a macro-model of a MEMS device based on physical field analysis according to claim 1, characterized in that, In step 1, the specific method for decoupling the multiple physical fields that dominate the operation of the diode-type MEMS Pirani vacuum sensor is as follows: analyze the physical field action mechanism of the diode-type MEMS Pirani vacuum sensor, and separate the multiple mutually coupled physical fields according to the control equation of the diode-type MEMS Pirani vacuum sensor.

3. The method for constructing a macro-model of a MEMS device based on physical field analysis according to claim 1, characterized in that, The specific method of step 4 is as follows: Based on the data characteristics of the step response dataset, select the time domain or frequency domain for system identification, and obtain the transfer function of the thermophysical field state-space model under the required accuracy. The thermophysical field state-space model is: ， ， in, For state vectors, This is the differential form of the state vector. For the output vector, For the input vector, , , , These are the system matrix, input matrix, output matrix, and direct feed matrix.

4. The method for constructing a macro-model of a MEMS device based on physical field analysis according to claim 3, characterized in that, The specific method for step 5 is as follows: The flow field behavior model is represented as: , , The electromagnetic field behavior model is represented as: , , , in, For the convective heat flux on the upper surface of the sensitive area, For the convective heat flux of the lower surface of the sensitive region, The air gap height from the lower surface of the sensitive area to the heat dissipation substrate. The distance from the upper surface of the sensitive area to the thin layer of air at room temperature. for Temperature value of the upper surface of the time-sensitive area for Temperature value of the lower surface of the time-sensitive region The radiative heat flux on the upper surface of the sensitive area. The radiative heat flux of the lower surface of the sensitive area. =1 represents the emissivity. =5.672e-8 is the Boltzmann constant. =10μA is the diode bias current. Let be the resistance value of the j-th resistor in the series diode group.

5. The method for constructing a macro-model of a MEMS device based on physical field analysis according to claim 4, characterized in that, The specific method of step 6 is as follows: The thermophysical field state-space model, flow field behavior model, and electromagnetic field behavior model are described using Verilog-A language, and the convective heat flux on the upper surface of the sensitive area is... Area of ​​sensitive area The product of the product of the convective heat flux of the lower surface of the sensitive region. Area of ​​sensitive area The product of these two vectors serves as the input vector in the state-space model equations of the physical field. The element will affect the radiative heat flux on the upper surface of the sensitive area. Area of ​​sensitive area The product of the radiative heat flux of the lower surface of the sensitive region Area of ​​sensitive area The product of and heating power It also serves as the input vector in the state-space model equations of the physical field. The elements, the temperature update values ​​of the upper surface of the sensitive area and the lower surface of the sensitive area output by the thermophysical field state space model are fed back to the flow field behavior model and the electromagnetic field behavior model.

6. An electronic device, comprising a memory and a processor, wherein the memory stores a computer program that runs on the processor, and the processor executes the steps of the MEMS device macromodel construction method of claim 1 when running the computer program.

7. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, performs the steps of the MEMS device macromodel construction method of claim 1.

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