MEMS device process error simulation and feedback control system

Abstract

The invention relates to the technical field of intelligent manufacturing control, in particular to an MEMS device process error simulation and feedback control system which comprises a response data acquisition module, a coupling relation analysis module, a change parameter extraction module, a model construction module and an instruction generation module. According to the method, dynamic time sequence data of multi-point displacement and stress in the device are collected in real time in the whole process of the manufacturing process, the response relation between the dynamic time sequence data is deeply analyzed, traditional macroscopic measurement of static geometric errors can be exceeded, and in other words, the dynamic time sequence data are obtained from mechanical behaviors in the device. By calculating the ratio of the direction consistency to the change rate of stress vectors among different structural parts, the coupling effect strength among the stress vectors is quantified, the key transmission path of the process stress is identified, and the internal mechanism of how local stress finally causes performance deviation of a core functional area through structural coupling is revealed. For example, how stress concentration on the supporting arm specifically causes displacement and angle inclination of the boundary of the capacitor plate can be determined.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing control technology, and in particular to a simulation and feedback control system for MEMS device process errors. Background Technology

[0002] The field of intelligent manufacturing control technology mainly involves automated management of manufacturing processes, equipment operation monitoring, data acquisition and analysis, production process optimization, and adaptive scheduling of manufacturing resources based on cyber-physical fusion systems.

[0003] Among them, the MEMS device process error simulation and feedback control system refers to the geometric dimension deviation and performance fluctuation caused by sub-process steps such as photolithography, etching and deposition during the manufacturing process of microelectromechanical system devices. It establishes a physical model to simulate and calculate the structural errors introduced by each sub-process, and uses the measurement results as the basis for model correction to form a closed-loop manufacturing control strategy.

[0004] Existing technologies primarily rely on model correction of the final measurement results. This process fails to delve into the internal mechanical response of devices during dynamic process changes, limiting their ability to handle complex issues caused by thermal mismatch and packaging stress. Due to a lack of analytical methods for stress transmission and coupling relationships between various internal structures, the system mainly attributes process errors to static geometric deviations, ignoring the dynamic processes and root causes of these deviations. For example, when abnormal spacing between capacitor plates is detected in the final product, existing technologies struggle to distinguish whether the problem stems from deviations in the initial etching process or from stress transmission caused by asynchronous thermal expansion coefficients between the support and sensitive structures during the later packaging cooling stage. This is because it does not track and analyze the stress distribution and evolution throughout the entire thermal cycle. This vague understanding of the root cause of errors leads to feedback control strategies that are often general and indirect, unable to specifically adjust key dynamic process parameters such as packaging pressure sequence and heating / cooling rates. Consequently, their optimization effectiveness and problem-solving efficiency are significantly constrained. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a simulation and feedback control system for MEMS device manufacturing process errors.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A MEMS device process error simulation and feedback control system includes:

[0007] The response data acquisition module collects displacement and stress change data of each part of the MEMS device under process temperature changes and packaging stress, analyzes the corresponding relationships, and constructs a structural response dataset.

[0008] The coupling relationship analysis module determines the consistency of the direction of stress transmission from one part to other parts based on the displacement-stress correspondence data of each part of the MEMS device in the structural response dataset, calculates the coupling strength value between the parts with consistent directions, and constructs a stress transmission strength parameter group.

[0009] The variable parameter extraction module, based on the stress transmission intensity parameter group, filters the MEMS device parts connected to the capacitance detection structure, and calculates the boundary offset based on the displacement change of each part of the MEMS device connected to the capacitance detection structure, based on the centering of the filtered MEMS device parts, and constructs a boundary change parameter set.

[0010] The model building module constructs an initial simulation model of the MEMS device during the manufacturing process based on the structural response dataset and the boundary change parameter set.

[0011] The instruction generation module calls the initial simulation model and the boundary change parameter set, adjusts the stress loading and detection window settings of each part of the MEMS device during the MEMS device packaging stage, and generates a feedback control instruction set.

[0012] As a further aspect of the present invention, the structural response dataset includes displacement change curves, stress change sequences, and time synchronization labels; the stress transfer strength parameter set specifically includes coupling strength value distribution, direction consistency identifier, and location mapping index; the boundary change parameter set includes capacitor gap change, boundary offset direction angle, and change time period; the initial simulation model includes three-dimensional structural coordinates, stress loading boundary conditions, and electrode spacing definition; and the feedback control instruction set specifically includes stress loading adjustment value, loading time period setting value, and detection window boundary coordinates.

[0013] As a further aspect of the present invention, the response data acquisition module includes:

[0014] The real-time data acquisition submodule sets measurement points for each part of the MEMS device, including the sensitive beam, support arm, capacitor plate, electrode edge and packaging cavity wall. During the entire process of process heating, isothermal, cooling and sealing, it collects the displacement change value and corresponding stress change value of each measurement point under the action of process temperature and packaging stress in real time, and obtains the multi-point displacement stress time sequence.

[0015] The dynamic trajectory construction submodule calls the multi-point displacement-stress time sequence, calculates the rate of change and direction vector between the recorded values ​​at each time point along the time axis for the displacement and stress data sequence of each measurement point, and fits them to form a continuous stress change curve and a continuous displacement change curve, thereby establishing the dynamic response trajectory of the structural part.

[0016] The response relationship mapping submodule separates the stress change curve and displacement change curve of each part of the MEMS device from the dynamic response trajectory of the structural parts. It extracts the peak value and valley value of the stress change curve and the maximum and minimum offset points of the displacement change curve, calculates the correspondence and numerical difference of the two sets of feature points in the time dimension, and establishes a structural response dataset.

[0017] As a further aspect of the present invention, the coupling relationship analysis module includes:

[0018] The orientation consistency determination submodule calls the stress change data of each part of the MEMS device in the structural response dataset in the same time period, calculates the angle between the stress vectors of any two parts, compares the angle with the orientation consistency determination threshold, filters all part pairs with stress vector angles less than the orientation consistency determination threshold, and establishes a list of orientation consistent part pairs.

[0019] The coupling strength calculation submodule extracts the stress change rate of the corresponding parts in the list of parts with consistent orientation, calculates the ratio of stress change rate of each pair of parts, filters out parts pairs with stress change rate ratio less than the rate consistency judgment threshold, integrates the orientation angle and rate ratio of the filtered parts pairs to calculate the coupling strength value, and obtains the coupling strength between parts.

[0020] The stress transfer strength construction submodule summarizes the coupling strength between all the parts, classifies and arranges them according to the identifier of the part pair, and constructs a stress transfer strength parameter group.

[0021] As a further aspect of the present invention, the variable parameter extraction module includes:

[0022] The target part selection submodule calls the stress transfer strength parameter group to identify part pairs that have a mechanical connection with the capacitance detection structure, extracts the coupling strength value of the part pairs with mechanical connection and compares it with the coupling strength judgment threshold, selects part pairs with coupling strength values ​​greater than the coupling strength judgment threshold as target analysis objects, and establishes target analysis part pairs;

[0023] The boundary offset calculation submodule calls the target analysis part pair and extracts the displacement change curve of the corresponding part from the structural response dataset. For each part of the MEMS device, it calculates the maximum coordinate change value along the direction axis perpendicular to the capacitor detection surface as the capacitor gap change, and calculates the boundary offset direction angle based on the angle between the displacement vector in the direction and the normal vector of the packaging front boundary to obtain the boundary offset quantization value.

[0024] The variable parameter construction submodule extracts the capacitance gap change and boundary offset direction angle of each part of the MEMS device based on the boundary offset quantization value, and associates them with the change time period in the process to construct a boundary change parameter set.

[0025] As a further aspect of the present invention, the model building module includes:

[0026] The geometric relationship definition submodule obtains the original structural dimensions and boundary conditions of each part of the MEMS device, sets a three-dimensional coordinate reference system, and combines the displacement data of each part of the MEMS device in the structural response dataset to define the initial geometric shape and mutual position of each part of the MEMS device and establish initial geometric relationship parameters.

[0027] The boundary condition setting submodule, based on the initial geometric relationship parameters, calls the capacitance gap change and boundary offset direction angle from the boundary change parameter set to set the initial value and change range of the electrode spacing, and determines the stress loading boundary based on the stress input value in the structural response dataset to obtain the model boundary constraint conditions;

[0028] The simulation model building submodule integrates the geometric relationships, electrode spacing, and stress input paths of each part of the MEMS device based on the initial geometric relationship parameters and the model boundary constraints, covering all structural parts of the MEMS device, and constructs the initial simulation model of the MEMS device in the process stage.

[0029] As a further aspect of the present invention, the setting of the initial value and variation range of the electrode spacing specifically involves taking the electrode spacing recorded in the original structural dimensions as the initial value, and combining the capacitance gap change and the boundary offset direction angle in the boundary change parameter set to calculate the maximum and minimum offset of the electrode spacing during the manufacturing process, and defining the numerical interval between the maximum and minimum offset as the variation range.

[0030] As a further aspect of the present invention, determining the stress loading boundary based on the stress input value in the structural response dataset specifically involves extracting the stress input values ​​of all parts from the structural response dataset, identifying and locating structural parts whose stress input values ​​exceed a preset stress threshold, and setting the geometric surface of the structural parts as the stress loading boundary.

[0031] As a further aspect of the present invention, the instruction generation module includes:

[0032] The boundary parameter correction submodule calls the original structural boundary values ​​of each part of the MEMS device in the initial simulation model and the capacitance gap change and boundary offset direction angle in the boundary change parameter set to correct the electrode gap value, and performs directional replacement on the corresponding boundary coordinates according to the boundary offset direction angle to establish the corrected boundary parameters.

[0033] The stress loading adjustment submodule re-plans the stress application sequence during the packaging stage based on the corrected boundary parameters, calculates the loading duration for each part of the MEMS device, and generates stress loading sequence parameters.

[0034] The control instruction integration submodule calculates the detection window position, width, and scanning cycle required for monitoring the capacitance detection structure based on the corrected boundary parameters, and constructs a feedback control instruction set.

[0035] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0036] This invention, by acquiring dynamic time-series data on displacement and stress at multiple points within the device in real time throughout the entire manufacturing process and deeply analyzing the response relationships, transcends traditional macroscopic measurements of static geometric errors. Instead, it starts from the mechanical behavior within the device, quantifying the coupling strength between different structural parts by calculating the ratio of the direction consistency and rate of change of stress vectors. This allows for precise identification of critical stress transmission paths and reveals the intrinsic mechanism by which local stress, through structural coupling, ultimately leads to performance deviations in core functional areas. For example, it clarifies how stress concentration on the support arm specifically causes displacement and angular tilting of the capacitor plate boundary. This analysis based on internal dynamic response allows the simulation model to be built beyond ideal geometry and boundaries, incorporating boundary offsets and stress loading distributions generated in the actual manufacturing process. This enables the model to more realistically reflect the actual state of the device during manufacturing. Finally, feedback control commands generated based on this highly accurate model can specifically adjust the sequence and duration of packaging pressure and optimize the window parameters of online monitoring. This achieves a shift from passive model correction to proactive process intervention, significantly improving the accuracy and foresight of process control. Attached Figure Description

[0037] Figure 1 This is a system flowchart of the present invention;

[0038] Figure 2 This is a flowchart of the response data acquisition module of the present invention;

[0039] Figure 3 This is a flowchart of the coupling relationship analysis module of the present invention;

[0040] Figure 4 This is a flowchart of the variable parameter extraction module of the present invention;

[0041] Figure 5 This is a flowchart of the model construction module of the present invention;

[0042] Figure 6 This is a flowchart of the instruction generation module of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0044] Please see Figure 1 The MEMS device manufacturing process error simulation and feedback control system includes:

[0045] The response data acquisition module collects displacement and stress change data of each part of the MEMS device under process temperature changes and packaging stress, analyzes the corresponding relationships, and constructs a structural response dataset.

[0046] The coupling relationship analysis module determines the consistency of the direction of stress transmission from one part to other parts based on the displacement-stress correspondence data of each part of the MEMS device in the structural response dataset, calculates the coupling strength value between parts with consistent direction, and constructs a stress transmission strength parameter group.

[0047] The variable parameter extraction module, based on the stress transmission intensity parameter group, filters the MEMS device parts connected to the capacitance detection structure, and calculates the boundary offset based on the displacement change of each part of the MEMS device connected to the capacitance detection structure, and constructs a boundary change parameter set.

[0048] The model building module constructs an initial simulation model of the MEMS device during the manufacturing process based on the structural response dataset and the boundary change parameter set.

[0049] The instruction generation module calls the initial simulation model and boundary change parameter set, adjusts the stress loading and detection window settings of each part of the MEMS device during the MEMS device packaging stage, and generates a feedback control instruction set.

[0050] The structural response dataset includes displacement change curves, stress change sequences, and time synchronization labels. The stress transfer strength parameter set specifically includes coupling strength value distribution, direction consistency identifier, and location mapping index. The boundary change parameter set includes capacitor gap change, boundary offset direction angle, and change time period. The initial simulation model includes three-dimensional structural coordinates, stress loading boundary conditions, and electrode spacing definition. The feedback control instruction set specifically includes stress loading adjustment value, loading time period setting value, and detection window boundary coordinates.

[0051] Please see Figure 2 The response data acquisition module includes:

[0052] The real-time data acquisition submodule sets measurement points for each part of the MEMS device, including the sensitive beam, support arm, capacitor plate, electrode edge and packaging cavity wall. During the entire process of process heating, isothermal, cooling and sealing, it collects the displacement change value and corresponding stress change value of each measurement point under the action of process temperature and packaging stress in real time, and obtains the multi-point displacement stress time sequence.

[0053] First, for the internal structure of MEMS devices, a series of discrete measurement points are set in key functional areas and stress concentration areas. Taking a MEMS accelerometer as an example, measurement points are set at the center point, root, and free end of the sensitive beam constituting the core detection structure, a total of 3 points; at the two endpoints of the support arm connecting the sensitive beam and the substrate, a total of 2 points; at the geometric center of the fixed capacitor plate and the movable capacitor plate constituting the variable capacitor, a total of 2 points; and at the edge area of ​​the electrode structure, 4 corner points are selected; finally, on the inner wall of the sealed cavity formed by the package, 4 corresponding points closest to the internal structure are selected. In the device packaging process, this process is divided into 3 main stages: the heating stage, where the temperature is linearly increased from room temperature (25 degrees Celsius) to 150 degrees Celsius; the isothermal stage, where the temperature is maintained at 150 degrees Celsius; and the cooling and sealing stage, where the temperature is linearly decreased from 150 degrees Celsius to room temperature (25 degrees Celsius) and sealing is completed. Throughout the time span, a miniature sensor array deployed at each measurement point synchronously acquires and records the displacement change and the six components of the stress tensor at each point in a 3D coordinate system at fixed time intervals, such as every 0.1 seconds. The displacement change data format is (x-axis displacement, y-axis displacement, z-axis displacement), with units of nanometers; the stress change data format is (x-direction normal stress, y-direction normal stress, z-direction normal stress, xy-plane shear stress, yz-plane shear stress, xz-plane shear stress), with units of megapascals (MPa). Thus, for each measurement point, a set of displacement data sequences and a set of stress data sequences varying over time are obtained. The data sequences from all measurement points together constitute a multi-point displacement-stress time series.

[0054] The dynamic trajectory construction submodule calls a multi-point displacement-stress time sequence. For the displacement and stress data sequence of each measurement point, it calculates the rate of change and direction vector between the recorded values ​​at each time point along the time axis, and fits them to form a continuous stress change curve and a continuous displacement change curve, thus establishing the dynamic response trajectory of the structural part.

[0055] The system calls upon the multi-point displacement-stress time series acquired by the real-time data acquisition submodule. For one measurement point, such as the displacement data sequence of the center point of a sensitive beam, the displacement records at two consecutive time points, time point A and time point B, are extracted. The displacement value at time point A is (5.0, 2.0, 1.0) nanometers, and the displacement value at time point B is (5.2, 2.1, 1.1) nanometers, with a time interval of 0.1 seconds. First, the displacement change between the two time point records is calculated, i.e., subtracting the corresponding coordinate value of time point A from the coordinate values ​​of time point B, resulting in a displacement change of (0.2, 0.1, 0.1) nanometers. Then, each component of the displacement change is divided by the time interval of 0.1 seconds to obtain the displacement change rate within that time interval, which is (2, 1, 1) nanometers per second. Simultaneously, the displacement change of (0.2, 0.1, 0.1) nanometers itself constitutes a direction vector describing the direction of displacement change. The aforementioned calculation is repeated for all adjacent time points in the entire displacement data sequence of this measurement point to obtain a series of continuous displacement change rates and direction vectors. Using cubic spline interpolation, these discrete rates are fitted to vector data points to form a continuous displacement change curve along the entire process time axis. The stress data sequence for this measurement point is processed using the same method. For example, if the normal stress in the x-direction at time point A is 50 MPa and at time point B is 52 MPa, the calculated stress change rate is 20 MPa per second. The direction vector of the stress change is then calculated by combining this with the changes in other stress components. A continuous stress change curve is formed through fitting. This process is repeated for all measurement points to establish a dynamic response trajectory for each structural component.

[0056] The response relationship mapping submodule separates the stress change curve and displacement change curve of each part of the MEMS device from the dynamic response trajectory of the structural parts. It extracts the peak value and valley value of the stress change curve and the maximum and minimum offset points of the displacement change curve, calculates the correspondence and numerical difference of the two sets of feature points in the time dimension, and establishes a structural response dataset.

[0057] From the dynamic response trajectory of the structural parts established by the dynamic trajectory construction submodule, the stress change curve and displacement change curve corresponding to each measurement point are separated. Taking the dynamic response trajectory of the center point of the sensitive beam as an example, its stress change curve is extracted. By traversing all data points on the curve, the local maxima of stress value are identified as peak values, and the local minima are identified as valley values. For example, at the 10th second of the heating stage, a stress peak of 80 MPa is identified, and at the 50th second of the cooling stage, a stress valley of 10 MPa is identified. Similarly, the maximum and minimum offset points are extracted from the displacement change curve. For example, at the 30th second of the isothermal stage, the maximum displacement offset point in the z-direction is identified as 15 nm, and at the 70th second after cooling is completed, the minimum offset point in the z-direction is identified as -2 nm, indicating that a reverse displacement has occurred. Next, the correspondence and numerical differences between these two sets of feature points, namely stress feature points (peak and valley values) and displacement feature points (maximum and minimum offset points), are calculated in the time dimension. Calculate the time difference between the time of peak stress occurrence (10 seconds) and the time of maximum displacement occurrence (30 seconds), which is 20 seconds. Calculate the values ​​corresponding to the valley stress (10 MPa) and the minimum displacement (-2 nm). Integrate this information—location identifier (center point of sensitive beam), stress characteristics (peak 80 MPa, valley 10 MPa), displacement characteristics (maximum offset 15 nm, minimum offset -2 nm), and time difference (20 seconds)—into a single record. Repeat this process for the dynamic response trajectory of all measurement points to build a structural response dataset.

[0058] Please see Figure 3 The coupling relationship analysis module includes:

[0059] The orientation consistency determination submodule calls the stress change data of each part of the MEMS device in the structural response dataset in the same time period, calculates the angle between the stress vectors of any two parts, compares the angle with the orientation consistency determination threshold, filters all part pairs with stress vector angles less than the orientation consistency determination threshold, and establishes a list of orientation consistent part pairs.

[0060] The stress variation data of each part of the MEMS device recorded in the structural response dataset within the same time period is retrieved. Two arbitrary parts are selected, such as the root of the sensitive beam and the end of the support arm near the substrate, and stress data is collected during the time period from the 15th to the 16th second of the process. The stress vector at the root of the sensitive beam consists of stress components in three directions, with values ​​of (60, 20, 5) MPa. The stress vector at the end of the support arm is (55, 18, 4) MPa. The angle between these two 3D vectors is calculated. The calculation process is as follows: first, the magnitudes of the two vectors are calculated separately; then, the dot product of the two vectors is calculated; then, the result of the dot product is divided by the product of the two magnitudes; finally, the inverse cosine of the quotient is taken to obtain the specific value of the angle. After calculation, the angle between the two stress vectors is found to be 8.7 degrees. Subsequently, the calculated angle of 8.7 degrees is compared with the directional consistency judgment threshold. The directional consistency judgment threshold is set based on statistical analysis of historical process data of similar devices. Analysis of 300 batches of devices revealed that in 95% of cases where structural failure occurred, the stress vector angle between the failure site and its adjacent critical components was consistently less than 15 degrees. Therefore, a directional consistency threshold of 15 degrees was set. This value was validated in subsequent experiments across 50 batches, with data showing that this threshold effectively identified over 90% of potential high-stress coupling areas. Since the calculated angle of 8.7 degrees was less than the directional consistency threshold of 15 degrees, the root of the sensitive beam and the end point of the support arm were considered a directional consistency pair, and their identification and angle data were stored in a directional consistency pair list. All components in the structural response dataset were paired, and the angle calculation and comparison process was repeated to filter out all pairs of components with stress vector angles less than 15 degrees, ultimately establishing a complete list of directional consistency pairs.

[0061] The coupling strength calculation submodule extracts the stress change rate of corresponding parts in the list of parts with consistent orientation, calculates the ratio of stress change rate of each pair of parts, filters out parts pairs with stress change rate ratio less than the rate consistency judgment threshold, integrates the orientation angle and rate ratio of the filtered parts pairs to calculate the coupling strength value, and obtains the coupling strength between parts.

[0062] From the list of directionally consistent parts established by the directional consistency determination submodule, the stress change rate corresponding to each pair of parts is extracted. Taking the sensitive beam root and the support arm end point as an example, their stress change rates during the time interval from the 15th to the 16th second are obtained from the dynamic response trajectory of the structural parts. The stress change rate modulus at the sensitive beam root is 50 MPa per second, and the stress change rate modulus at the support arm end point is 48 MPa per second. The ratio of these two rates is calculated, i.e., 48 divided by 50, resulting in a rate ratio of 0.96. Next, the calculated rate ratio of 0.96 is compared with the rate consistency determination threshold. The rate consistency determination threshold is set based on the elastic transfer theory of materials and a large number of finite element simulation experiments. Experiments show that when the absolute value of the difference between the ratio of the stress change rates of the two mechanical connection parts and 1 is less than 0.15, the stress transfer efficiency between the two parts exceeds 85%, exhibiting strong coupling characteristics. Therefore, the rate consistency determination threshold is set to 0.15. This setting was verified through tensile and vibration experiments on physical samples. The actual stress transfer efficiency measured by strain gauges in the experiments showed a 97% agreement rate with the threshold judgment result. In this example, the absolute value of the difference between the rate ratio and 1, i.e., the absolute value of 0.96 minus 1, was calculated, resulting in 0.04. Because 0.04 is less than the rate consistency judgment threshold of 0.15, this part pair passed the screening. Finally, the directional angle of 8.7 degrees and the rate ratio of 0.96 of the screened part pair were integrated to calculate the coupling strength value. The coupling strength calculation process is achieved through the following formula:

[0063] ;

[0064] in, : Represents the coupling strength value, which is a dimensionless parameter. Its value directly reflects the degree of coupling between parts. : Represents the basic value of coupling strength, which is set to 100 in this embodiment as a starting benchmark for calculation. : This represents the weighting coefficient for the directional angle, set to 10. This coefficient is used to adjust the influence of directional consistency deviation in the calculation of total coupling strength, and its value is determined through regression analysis of historical failure data. : Represents the actual angle between the stress vectors of the two analyzed parts, in degrees (°). This value is obtained through vector dot product operation, such as the angle between the root of the sensitive beam and the end point of the support arm in the previous example, which is 8.7 degrees. : Indicates the threshold for determining directional consistency, in degrees (°). Based on a large amount of process data statistics and experimental verification, it is set to 15 degrees as the critical value for judging whether the stress direction is consistent. : Represents the direction angle penalty factor, a dimensionless improvement parameter greater than 1, set to 1.2 in this embodiment. The innovation of introducing this parameter lies in that it makes the reduction of the coupling strength with respect to the direction angle non-linear. Compared to linear reduction, when the angle... When the value is small and far below the threshold, the deduction increases slowly; while when Approaching the threshold When the exponential effect is applied, the deduction amount increases sharply, thereby imposing a stronger penalty on the critical mismatch state and improving the model's sensitivity to potential risks. : This represents the weighting coefficient for the rate ratio, set to 20. This coefficient is used to adjust the weighting of rate consistency deviation in the overall coupling strength calculation. The setting is based on the stress change rate (…). This directly reflects the efficiency and synchronicity of dynamic stress transmission, compared to stress direction ( Static alignment issues and rate mismatches are more revealing of dynamic inconsistencies within a structure, potentially leading to faster fatigue or failure. Therefore, the weight of rate consistency is set to twice that of directional consistency. This is to emphasize its importance in assessing coupling strength. : This represents the ratio of the rate modulus of stress change at two locations, and is a dimensionless parameter. For example, in the calculation example, the ratio of the rate modulus at the end of the support arm to that at the root of the sensitive beam is 0.96. : Represents the threshold for rate consistency judgment. It is a dimensionless parameter, set to 0.15 based on simulation and experimental data. It defines the maximum acceptable deviation range between the rate ratio and the ideal value of 1.

[0065] 1. Parameter assignment: 2. Substitute into the formula:

[0066] ;

[0067] The calculated coupling strength is approximately 89.62. This calculation is repeated for all filtered part pairs in the list of parts with the same orientation to obtain the coupling strength between each pair.

[0068] The stress transfer strength construction submodule summarizes the coupling strength between all parts, classifies and arranges them according to the identification of the parts, and constructs a stress transfer strength parameter group.

[0069] The coupling strength values ​​calculated by the coupling strength calculation submodule are summarized. These data items contain a unique identifier for each part pair and its corresponding coupling strength value. For example, the coupling strength value for (sensitive beam root, support arm end point) is 89.62; the coupling strength value for (sensitive beam center, movable capacitor plate center) is 92.14; and the coupling strength value for (fixed capacitor plate center, encapsulation cavity wall point A) is 35.21. Next, the parts are categorized and arranged according to their identifiers. The categorization is based on one part within each part pair. For example, all coupling strength values ​​related to the sensitive beam root are grouped into one category, and all coupling strength values ​​related to the movable capacitor plate center are grouped into another category. Within each category, the values ​​are further sorted in descending order of coupling strength. For example, in the category related to the movable capacitor plate center, the coupling strength of (sensitive beam center, movable capacitor plate center) is 92.14, which is ranked first, and the coupling strength of (support arm end point, movable capacitor plate center) is 75.66, which is ranked second. By classifying and arranging all the coupling strength data in this way, a structured and ordered dataset is finally formed, which is the stress transfer strength parameter set.

[0070] Please see Figure 4 The variable parameter extraction module includes:

[0071] The target part selection submodule calls the stress transfer strength parameter group to identify part pairs that have a mechanical connection with the capacitance detection structure. It extracts the coupling strength value of the part pairs with mechanical connection and compares it with the coupling strength judgment threshold. It selects part pairs with coupling strength values ​​greater than the coupling strength judgment threshold as target analysis objects and establishes target analysis part pairs.

[0072] The stress transfer strength parameter set constructed by the stress transfer strength construction submodule is invoked. First, all pairs of parts that have a mechanical connection with the capacitance sensing structure are identified from the parameter set. The capacitance sensing structure mainly consists of a movable capacitor plate and a fixed capacitor plate. Therefore, it is necessary to identify all entries in the pair that contain at least one measurement point on either the movable or fixed capacitor plate. For example, the pair (center of the sensitive beam, center of the movable capacitor plate) is identified because it contains the center of the movable capacitor plate. The pair (endpoint of the support arm, point A on the encapsulation cavity wall) is not identified. Next, the coupling strength values ​​of these identified pair of parts are extracted and compared with the coupling strength judgment threshold. The coupling strength judgment threshold was determined through a series of device-level functional simulation experiments. In the simulation, different stress transfer intensities were applied to different pair of parts, and the changes in the output signal of the capacitance sensing structure were observed. Experimental results show that when the coupling strength value is greater than 70, the capacitance gap change caused by stress transfer leads to an error of more than 5% in the capacitance reading, exceeding the accuracy requirements of the device design. To ensure the effectiveness of the screening, 50 physical prototypes were selected for encapsulation stress testing. The test results confirmed that for all locations with coupling strength values ​​exceeding 70, the impact on capacitor accuracy exceeded the design tolerance. Therefore, the coupling strength judgment threshold was set to 70. Taking the aforementioned location (center of the sensitive beam, center of the movable capacitor plate) as an example, its coupling strength value was 92.14, which is greater than the coupling strength judgment threshold of 70. Therefore, this location pair was selected as the target analysis object. This comparison process was repeated for all identified location pairs related to the capacitor detection structure, and all location pairs with coupling strength values ​​greater than 70 were compiled to establish a list of target analysis location pairs.

[0073] The boundary offset calculation submodule calls the target analysis part pair and extracts the displacement change curve of the corresponding part from the structural response dataset. For each part of the MEMS device, it calculates the maximum coordinate change value along the direction axis perpendicular to the capacitor detection surface as the capacitor gap change value. It also calculates the boundary offset direction angle based on the angle between the displacement vector in the direction and the normal vector of the packaging front boundary to obtain the boundary offset quantization value.

[0074] The target analysis part pair list established by the target part filtering submodule is invoked. Taking the pair (sensitive beam center, active capacitor plate center) as an example, the displacement change curve of the measurement point at the center of the active capacitor plate is extracted from the structural response dataset. This curve records the displacement trajectory of the center of the active capacitor plate in 3D space throughout the entire manufacturing process. The normal vector of the capacitor detection surface is in the positive z-axis direction. To calculate the capacitor gap change, it is necessary to traverse all data points in the displacement change curve of the center of the active capacitor plate and focus only on the change of its z-axis coordinate. By comparing the z-axis coordinate values ​​at all time points, the maximum value is found. For example, at 30 seconds, the z-axis coordinate change value reaches its maximum, which is 15 nanometers. This maximum coordinate change value of 15 nanometers is defined as the capacitor gap change. Subsequently, based on the displacement vector of the measurement point at the moment of maximum displacement, the boundary offset direction angle is calculated. At 30 seconds, the displacement vector is (1.5, 2.0, 15.0) nanometers. The normal vector of the capacitor plate boundary before encapsulation is in the positive z-axis direction, and its vector representation is (0, 0, 1). The angle between the displacement vector and the normal vector is the boundary offset direction angle. This angle is calculated using the standard vector angle formula:

[0075] ;

[0076] in, : Represents the final calculated boundary offset direction angle, in degrees (°). It quantifies the deviation angle between the actual surface normal of the active capacitor plate and its ideal normal during design after the process is completed. : Represents the displacement vector of the measured point at the moment of maximum displacement. It is a three-dimensional vector pointing from the origin to the endpoint of the displacement at that moment, and its component form is: The unit is nanometers. In this example, based on the displacement change curve, the displacement vector of the center of the moving capacitor plate at the 30th second is (1.5, 2.0, 15.0) nanometers. : Represents the boundary normal vector in the ideal state before packaging. It defines the standard orientation of the capacitor plate surface and is a standard unit vector. In this embodiment, the capacitor sensing surface is parallel to the xy plane, and its normal is along the positive z-axis direction, so this vector is (0, 0, 1). : This represents the dot product (inner product) operator between two vectors, and its result is a scalar. : Represents the Euclidean norm (or modulus) operator for vectors, used to calculate the length of a vector in three-dimensional space.

[0077] 1. Parameter assignment: .

[0078] 2. Calculate the vector dot product: .

[0079] 3. Calculate the vector magnitude: , , .

[0080] 4. Substitute into the formula to calculate the included angle: .

[0081] The boundary offset direction angle was found to be 9.59 degrees. The three data points—location identifier (center of the active capacitor plate), capacitor gap change (15 nm), and boundary offset direction angle (9.59 degrees)—were integrated to obtain the quantized boundary offset value for that location. For all locations in the target analysis location list, the operations of extracting displacement curves, calculating gap change, and direction angle were repeated to obtain the quantized boundary offset value for each target location.

[0082] The variable parameter construction submodule extracts the capacitance gap change and boundary offset direction angle of each part of the MEMS device based on the boundary offset quantization value, and associates them with the change time period in the process to construct a boundary change parameter set.

[0083] Based on the boundary offset quantization value calculated by the boundary offset calculation submodule for each target part, key information is extracted. Taking the center of the moving capacitor plate as an example, the change in capacitor gap is extracted, which is 15 nanometers; the boundary offset direction angle is extracted, which is 9.59 degrees. Simultaneously, the time period of these changes needs to be correlated. From the displacement change curve, it can be found that the maximum displacement of 15 nanometers occurs at the 30th second of the isothermal phase. Therefore, these three pieces of information—the change in capacitor gap of 15 nanometers, the boundary offset direction angle of 9.59 degrees, and the time point of the change at the 30th second—are correlated. This extraction and correlation operation is repeated for the boundary offset quantization values ​​of all target parts. For example, for the center of the fixed capacitor plate, the extracted data might be a change in capacitor gap of -2 nanometers (indicating movement in the opposite direction), a boundary offset direction angle of 2.1 degrees, and a change time point of the 55th second. These parameter sets extracted from all parts are integrated to finally construct a complete dataset, namely the boundary change parameter set. This parameter set details the critical structural parts that significantly affect the accuracy of capacitance detection during the manufacturing process, including the magnitude of their boundary displacement, the angle of deviation, and the time point at which this occurs.

[0084] Please see Figure 5 The model building module includes:

[0085] The geometric relationship definition submodule obtains the original structural dimensions and boundary conditions of each part of the MEMS device, sets a three-dimensional coordinate reference system, and combines the displacement data of each part of the MEMS device in the structural response dataset to define the initial geometric shape and mutual position of each part of the MEMS device and establish the initial geometric relationship parameters.

[0086] First, the original, ideal structural dimensions and boundary conditions of each structural component are obtained from the MEMS device design files. This data includes the length, width, and thickness of the sensitive beam, the area of ​​the capacitor plates, and the initial spacing. For example, the initial spacing between the movable and fixed capacitor plates is designed to be 500 nanometers. Next, a reference frame is established in a 3D Cartesian coordinate system, with the geometric center of the device placed at the origin. Then, combining the displacement data of each component of the MEMS device recorded in the structural response dataset at the start of the process (i.e., time 0), the initial geometry and relative positions of each component before the simulation begin are defined. Although the displacement at time 0 is theoretically zero, this step aims to establish a unified data structure that links the design dimensions with subsequent displacement data. For example, the initial geometry of the movable capacitor plate is determined by its design dimensions, and its initial position in the reference frame is determined by its coordinates relative to the origin. These geometric and positional information for all components are integrated to establish initial geometric relationship parameters.

[0087] The boundary condition setting submodule, based on the initial geometric relationship parameters, calls the capacitance gap change and boundary offset direction angle from the boundary change parameter set to set the initial value and change range of the electrode spacing, and determines the stress loading boundary based on the stress input value in the structural response dataset to obtain the model boundary constraint conditions;

[0088] Specifically, the initial value and variation range of the electrode spacing are set by taking the electrode spacing recorded in the original structural dimensions as the initial value, and combining the capacitance gap change and boundary offset direction angle in the boundary change parameter set to calculate the maximum and minimum offset of the electrode spacing during the process, and defining the numerical range between the maximum and minimum offset as the variation range.

[0089] Specifically, determining the stress loading boundary based on the stress input value in the structural response dataset involves extracting the stress input values ​​of all parts from the structural response dataset, identifying and locating structural parts whose stress input values ​​exceed a preset stress threshold, and setting the geometric surface of the structural parts as the stress loading boundary.

[0090] The initial geometric relationship parameters are established based on the geometric relationship definition submodule, and the capacitance gap change and boundary offset direction angle from the boundary change parameter set are called. First, the initial value and range of the electrode spacing are set. The electrode spacing of 500 nm recorded in the original structural dimensions is used as the initial value. Combining the capacitance gap change of 15 nm for the moving capacitor plate and the capacitance gap change of -2 nm for the fixed capacitor plate in the boundary change parameter set, the maximum and minimum offsets of the electrode spacing during the process are calculated. The maximum offset occurs when the two plates move towards each other most violently, and its value is the sum of the absolute values ​​of their displacements, i.e., 15 nm plus 2 nm, which equals 17 nm. The minimum offset occurs when the two plates move away from each other most violently, and its value is also 17 nm. Therefore, the range of electrode spacing is defined as the numerical range from (500 minus 17) nm to (500 plus 17) nm, i.e., 483 nm to 517 nm. Next, the stress loading boundary is determined based on the stress input value in the structural response dataset. The stress input values ​​for all parts throughout the entire manufacturing process were extracted from the dataset, and structural parts with stress values ​​exceeding a preset stress threshold were identified. The preset stress threshold was set based on the yield strength of the silicon material used in the device. The yield strength of silicon is approximately 150 MPa; considering a 30% safety margin, the preset stress threshold was set to 105 MPa. The rationality of this threshold was verified through nanoindentation experiments and cyclic loading experiments, showing that plastic deformation of the material is negligible when the stress is below 105 MPa. In the structural response dataset, the maximum stress value at the support arm reached 110 MPa, exceeding the preset stress threshold. Therefore, the geometric surface of the support arm was set as the stress loading boundary. The previously set electrode spacing variation range was integrated with the determined stress loading boundary to obtain the model boundary constraints.

[0091] The simulation model building submodule integrates the geometric relationships, electrode spacing, and stress input paths of each part of the MEMS device based on the initial geometric relationship parameters and model boundary constraints, covering all structural parts of the MEMS device, and constructs the initial simulation model of the MEMS device in the process stage.

[0092] The initial geometric parameters obtained from the geometric relationship definition submodule and the model boundary constraints obtained from the boundary condition setting submodule are integrated. The geometric relationships of each part, such as the connection method between the sensitive beam and the support arm, and the fixing relationship between the support arm and the substrate, are defined. The initial value of the electrode spacing of 500 nm and its variation range of 483 to 517 nm are applied as variable constraints between the movable and fixed capacitor plates. The stress input path, i.e., the previously defined support arm surface, is defined as the force loading interface of the model. By integrating this geometric information, boundary constraints, and loading path, and ensuring that the model covers all structural parts of the MEMS device, including all sensitive structures, support structures, and packaging cavities, an initial simulation model of the MEMS device in the manufacturing process is constructed.

[0093] Please see Figure 6 The instruction generation module includes:

[0094] The boundary parameter correction submodule calls the original structural boundary values ​​of each part of the MEMS device in the initial simulation model and the capacitance gap change and boundary offset direction angle in the boundary change parameter set to correct the electrode gap value, and performs directional replacement on the corresponding boundary coordinates according to the boundary offset direction angle to establish the corrected boundary parameters.

[0095] The original structural boundary values ​​of each part of the MEMS device recorded in the initial simulation model are retrieved, combined with the capacitance gap change and boundary offset direction angle from the boundary change parameter set. Taking the movable capacitor plate as an example, its original structural boundary values ​​define its initial position and geometry in the model. The capacitance gap change of the movable capacitor plate is obtained from the boundary change parameter set, with a value of 15 nanometers and a direction in the positive z-axis. Simultaneously, its boundary offset direction angle is obtained, with a value of 9.59 degrees. First, the electrode gap value is corrected. The original electrode gap is 500 nanometers; due to the 15-nanometer displacement of the movable capacitor plate, the gap decreases, and the corrected electrode gap value is 500 minus 15 equals 485 nanometers. Next, based on the boundary offset direction angle of 9.59 degrees, the coordinates of the corresponding boundary of the movable capacitor plate are directionally replaced. This means that the boundary normal, originally along the pure z-axis direction, now needs to be rotated by 9.59 degrees. The specific operation involves adjusting the z-coordinate values ​​of all grid nodes constituting the surface of the active capacitor plate, while simultaneously fine-tuning their x and y coordinate values ​​according to the rotation angle, thereby tilting the entire boundary in 3D space. This correction process is repeated for all affected boundaries, ultimately establishing a complete set of corrected boundary parameters that reflect the process effects.

[0096] The stress loading adjustment submodule re-plans the stress application sequence during the packaging stage based on the corrected boundary parameters, calculates the loading duration for each part of the MEMS device, and generates stress loading sequence parameters.

[0097] Based on the corrected boundary parameters established by the boundary parameter correction submodule, the stress application sequence during the encapsulation stage was replanned. In the initial model, the stress application sequence was uniform and synchronous. However, the corrected boundary parameters showed that the support arm was the main high-stress area, while the active capacitor plate experienced significant boundary offset. Therefore, the stress application sequence was replanned, changing the original synchronous application of pressure across the entire encapsulation boundary to a step-by-step application. First, 70% of the total pressure was applied to the area far from the support arm and capacitor structure. Second, while maintaining the pressure from the first step, the remaining pressure was slowly applied to the area closer to the support arm. Simultaneously, the loading duration for each location was calculated. Since the stress value at the support arm exceeded a preset threshold, the loading duration for this location needed to be extended to slow down the rate of stress concentration. The original total loading time was 10 seconds; now, it was adjusted so that the loading time for non-critical areas was shortened to 5 seconds, while the loading duration for the support arm area was extended to 15 seconds, thus lengthening the total loading time window. This replanning generated new stress loading sequence parameters, which defined in detail the location, order, magnitude, and duration of pressure application.

[0098] The control instruction integration submodule calculates the detection window position, width, and scanning cycle required for monitoring the capacitance detection structure based on the corrected boundary parameters, and constructs a feedback control instruction set.

[0099] Based on the corrected boundary parameters established by the boundary parameter correction submodule, the various control parameters required for online monitoring of the capacitance detection structure are calculated. First, the position of the detection window is calculated. Since the corrected electrode gap becomes 485 nm and the boundary tilts by 9.59 degrees, the response curve of the capacitance value with displacement also changes accordingly. Based on the new response curve, a new capacitance value range that most sensitively reflects displacement changes is calculated; the center point of this range is the new detection window position. Next, the width of the detection window is calculated. Considering the uncertainty caused by the boundary offset, the window width needs to be appropriately widened to capture all possible functional changes. The original window width was 5% of the design center value of the capacitance; now, based on the boundary offset direction angle of 9.59 degrees, the width is increased to 8%. Finally, the scanning cycle is calculated. Since the stress loading sequence is adjusted, the stress change rate slows down, so the scanning cycle (i.e., sampling frequency) for monitoring capacitance changes can be reduced from 1000 times per second to 800 times per second. The calculated detection window position, width, and scanning cycle are integrated to construct a set of digital instructions, i.e., a feedback control instruction set.

[0100] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A simulation and feedback control system for MEMS device manufacturing process errors, characterized in that, The system includes: The response data acquisition module collects displacement and stress change data of each part of the MEMS device under process temperature changes and packaging stress, analyzes the corresponding relationships, and constructs a structural response dataset. The coupling relationship analysis module determines the consistency of the direction of stress transmission from one part to other parts based on the displacement-stress correspondence data of each part of the MEMS device in the structural response dataset, calculates the coupling strength value between the parts with consistent directions, and constructs a stress transmission strength parameter group. The variable parameter extraction module, based on the stress transmission intensity parameter group, filters the MEMS device parts connected to the capacitance detection structure, and calculates the boundary offset based on the displacement change of each part of the MEMS device connected to the capacitance detection structure, based on the centering of the filtered MEMS device parts, and constructs a boundary change parameter set. The model building module constructs an initial simulation model of the MEMS device during the manufacturing process based on the structural response dataset and the boundary change parameter set. The instruction generation module calls the initial simulation model and the boundary change parameter set, adjusts the stress loading and detection window settings of each part of the MEMS device during the MEMS device packaging stage, and generates a feedback control instruction set.

2. The MEMS device manufacturing process error simulation and feedback control system according to claim 1, characterized in that, The structural response dataset includes displacement change curves, stress change sequences, and time synchronization labels. The stress transfer strength parameter set specifically includes coupling strength value distribution, direction consistency identifier, and location mapping index. The boundary change parameter set includes capacitor gap change, boundary offset direction angle, and change time period. The initial simulation model includes three-dimensional structural coordinates, stress loading boundary conditions, and electrode spacing definition. The feedback control instruction set specifically includes stress loading adjustment value, loading time period setting value, and detection window boundary coordinates.

3. The MEMS device manufacturing process error simulation and feedback control system according to claim 1, characterized in that, The response data acquisition module includes: The real-time data acquisition submodule sets measurement points for each part of the MEMS device, including the sensitive beam, support arm, capacitor plate, electrode edge and packaging cavity wall. During the entire process of process heating, isothermal, cooling and sealing, it collects the displacement change value and corresponding stress change value of each measurement point under the action of process temperature and packaging stress in real time, and obtains the multi-point displacement stress time sequence. The dynamic trajectory construction submodule calls the multi-point displacement-stress time sequence, calculates the rate of change and direction vector between the recorded values ​​at each time point along the time axis for the displacement and stress data sequence of each measurement point, and fits them to form a continuous stress change curve and a continuous displacement change curve, thereby establishing the dynamic response trajectory of the structural part. The response relationship mapping submodule separates the stress change curve and displacement change curve of each part of the MEMS device from the dynamic response trajectory of the structural parts. It extracts the peak value and valley value of the stress change curve and the maximum and minimum offset points of the displacement change curve, calculates the correspondence and numerical difference of the two sets of feature points in the time dimension, and establishes a structural response dataset.

4. The MEMS device manufacturing process error simulation and feedback control system according to claim 3, characterized in that, The coupling relationship analysis module includes: The orientation consistency determination submodule calls the stress change data of each part of the MEMS device in the structural response dataset in the same time period, calculates the angle between the stress vectors of any two parts, compares the angle with the orientation consistency determination threshold, filters all part pairs with stress vector angles less than the orientation consistency determination threshold, and establishes a list of orientation consistent part pairs. The coupling strength calculation submodule extracts the stress change rate of the corresponding parts in the list of parts with consistent orientation, calculates the ratio of stress change rate of each pair of parts, filters out parts pairs with stress change rate ratio less than the rate consistency judgment threshold, integrates the orientation angle and rate ratio of the filtered parts pairs to calculate the coupling strength value, and obtains the coupling strength between parts. The stress transfer strength construction submodule summarizes the coupling strength between all the parts, classifies and arranges them according to the identifier of the part pair, and constructs a stress transfer strength parameter group.

5. The MEMS device manufacturing process error simulation and feedback control system according to claim 4, characterized in that, For calculating the coupling strength value The formula used is: ； in, The basic value representing the coupling strength, The weighting coefficient represents the angle between directions. This represents the actual angle between the stress vectors of the two analyzed parts. This indicates the threshold for determining directional consistency. Indicates the penalty factor for the included direction angle. The weighting coefficients representing the rate ratios This represents the ratio of the magnitudes of the rate of stress change at two locations. This indicates the threshold for determining rate consistency.

6. The MEMS device manufacturing process error simulation and feedback control system according to claim 4, characterized in that, The variable parameter extraction module includes: The target part selection submodule calls the stress transfer strength parameter group to identify part pairs that have a mechanical connection with the capacitance detection structure, extracts the coupling strength value of the part pairs with mechanical connection and compares it with the coupling strength judgment threshold, selects part pairs with coupling strength values ​​greater than the coupling strength judgment threshold as target analysis objects, and establishes target analysis part pairs; The boundary offset calculation submodule calls the target analysis part pair and extracts the displacement change curve of the corresponding part from the structural response dataset. For each part of the MEMS device, it calculates the maximum coordinate change value along the direction axis perpendicular to the capacitor detection surface as the capacitor gap change, and calculates the boundary offset direction angle based on the angle between the displacement vector in the direction and the normal vector of the packaging front boundary to obtain the boundary offset quantization value. The variable parameter construction submodule extracts the capacitance gap change and boundary offset direction angle of each part of the MEMS device based on the boundary offset quantization value, and associates them with the change time period in the process to construct a boundary change parameter set.

7. The MEMS device process error simulation and feedback control system according to claim 6, characterized in that, The model building module includes: The geometric relationship definition submodule obtains the original structural dimensions and boundary conditions of each part of the MEMS device, sets a three-dimensional coordinate reference system, and combines the displacement data of each part of the MEMS device in the structural response dataset to define the initial geometric shape and mutual position of each part of the MEMS device and establish initial geometric relationship parameters. The boundary condition setting submodule, based on the initial geometric relationship parameters, calls the capacitance gap change and boundary offset direction angle from the boundary change parameter set to set the initial value and change range of the electrode spacing, and determines the stress loading boundary based on the stress input value in the structural response dataset to obtain the model boundary constraint conditions; The simulation model building submodule integrates the geometric relationships, electrode spacing, and stress input paths of each part of the MEMS device based on the initial geometric relationship parameters and the model boundary constraints, covering all structural parts of the MEMS device, and constructs the initial simulation model of the MEMS device in the process stage.

8. The MEMS device process error simulation and feedback control system according to claim 7, characterized in that, Specifically, the initial value and variation range of the electrode spacing are set by taking the electrode spacing recorded in the original structural dimensions as the initial value, and combining the capacitance gap change and the boundary offset direction angle in the boundary change parameter set to calculate the maximum and minimum offset of the electrode spacing during the manufacturing process, and defining the numerical interval between the maximum and minimum offset as the variation range.

9. The MEMS device manufacturing process error simulation and feedback control system according to claim 7, characterized in that, The step of determining the stress loading boundary based on the stress input value in the structural response dataset specifically involves extracting the stress input values ​​of all parts from the structural response dataset, identifying and locating structural parts whose stress input values ​​exceed a preset stress threshold, and setting the geometric surface of the structural parts as the stress loading boundary.

10. The MEMS device manufacturing process error simulation and feedback control system according to claim 7, characterized in that, The instruction generation module includes: The boundary parameter correction submodule calls the original structural boundary values ​​of each part of the MEMS device in the initial simulation model and the capacitance gap change and boundary offset direction angle in the boundary change parameter set to correct the electrode gap value, and performs directional replacement on the corresponding boundary coordinates according to the boundary offset direction angle to establish the corrected boundary parameters. The stress loading adjustment submodule re-plans the stress application sequence during the packaging stage based on the corrected boundary parameters, calculates the loading duration for each part of the MEMS device, and generates stress loading sequence parameters. The control instruction integration submodule calculates the detection window position, width, and scanning cycle required for monitoring the capacitance detection structure based on the corrected boundary parameters, and constructs a feedback control instruction set.

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