A coating element quality stability evaluation method based on statistical process control

Abstract

The application relates to the field of optical element manufacturing, and discloses a coating element quality stability evaluation method based on statistical process control, which comprises the following steps: establishing an analysis database by testing the characteristics and performance parameters of optical elements; introducing a single-variable micro-disturbance calculation parameter sensitivity coefficient and generating a sensitivity matrix; calling a prior distribution and combining current batch sample data, using a conjugate prior updating rule to calculate a posterior parameter to generate a control limit for data monitoring; calculating a process capability index, a batch drift amount and a controlled proportion, combining a sensitivity matrix weight to calculate a comprehensive index, and dividing a quality consistency grade; comparing assembled actual measurement performance with design indexes, and according to a comparison result, tightening the control limit or correcting the weight and storing the same in a knowledge base. Through the application, dynamic updating of the control limit and multi-dimensional parameter fusion evaluation are realized, and a self-adaptive closed-loop feedback correction mechanism of terminal actual measurement to a previous monitoring standard is constructed.

Description

Technical Field

[0001] This invention relates to the field of optical component manufacturing, specifically to a method for evaluating the quality stability of coated components based on statistical process control. Background Technology

[0002] Coated components are an important part of optical systems, and their multilayered film structure makes the manufacturing process susceptible to interference from environmental and process parameter fluctuations. To ensure batch product quality, industrial production typically employs statistical process control methods to sample and monitor characteristic parameters and optical performance parameters during production.

[0003] Most existing statistical process control methods rely on static, fixed control limits. In multi-batch continuous production, equipment status and basic operating conditions drift slightly over time. Fixed control boundaries cannot be adaptively adjusted using historical process data, making it difficult to adapt to dynamically changing production environments and easily leading to inaccurate early warnings for anomalies caused by fluctuations in operating conditions. Meanwhile, the quality of coated components involves physical characteristic parameters such as film stress and surface roughness, as well as optical performance parameters such as reflectivity and wavefront distortion. Existing evaluation models often judge these parameters independently, failing to fully consider the varying sensitivity of fluctuations in different characteristic parameters to the final optical performance. This fragmented approach to parameter evaluation makes it difficult for the final evaluation results to accurately reflect the overall quality consistency of the entire batch of components.

[0004] Furthermore, current quality control processes typically stop at the component manufacturing stage. Even after final system assembly, coated components that pass factory quality inspections sometimes exhibit optical performance deviations from design expectations. The lack of an effective data link between manufacturing monitoring standards and actual assembly performance prevents the control boundaries and evaluation weights of preceding production processes from being adjusted in reverse based on the actual application performance. This monitoring model, lacking closed-loop feedback, limits the continuous optimization of coating process standards and further improvement in quality yield. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for evaluating the quality stability of coated components based on statistical process control. This method solves the problems in existing coating component quality evaluation, such as the inability of fixed control limit settings to adapt to dynamic production, the difficulty of accurately reflecting the impact of parameter fluctuations on the final optical performance by a single evaluation index, and the lack of an effective feedback and adaptive correction mechanism between manufacturing monitoring standards and actual assembly performance.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for evaluating the quality stability of coated components based on statistical process control, comprising: Test the characteristic parameters and performance parameters of the same system coated optical elements, and establish a basic database for optical analysis when the stability of the characteristic parameters and performance parameters reaches a set threshold. The performance change of the test sample under univariate small perturbation is introduced, the sensitivity coefficient of the candidate feature parameter is calculated, key quality characteristics are screened and a sensitivity matrix is ​​generated; The prior distribution characteristics of key quality properties are determined by retrieving the basic database of optical analysis. The posterior distribution parameters are calculated by combining the current batch sample data and using the conjugate prior update rule. Control limits are generated based on the posterior distribution parameters to monitor the current batch sample data. Calculate the process capability index, inter-batch drift, and controlled proportion of the key quality characteristics of the current batch; combine the weights obtained by normalizing the sensitivity matrix to calculate the batch quality consistency index; and classify the quality consistency level. The measured performance of the coated components after assembly is obtained and compared with the design specifications. Based on the comparison results, the control limits are tightened or the weights are adjusted and stored in the knowledge base for the next batch of production.

[0007] Furthermore, testing the characteristic and performance parameters of the same system-coated optical elements involves dividing the light-transmitting area of ​​the optical elements into micro-regions and collecting characteristic and performance parameters at different locations. Characteristic parameters include film stress, surface defect density, and surface roughness; performance parameters include absorptivity, reflectivity, center wavelength of the reflection band, wavefront distortion, and uniformity. When non-compliant parameters exist that do not reach the set threshold, the spatial difference distribution data and batch difference fluctuation data of the non-compliant parameters are extracted, the causes of the differences are traced, and feedback is provided to the manufacturing process.

[0008] When introducing the performance change of the test sample under univariate small perturbation, calculating the sensitivity coefficient of candidate feature parameters, screening key quality characteristics and generating a sensitivity matrix, the maximum value of the sensitivity coefficient corresponding to each candidate feature parameter is extracted. All candidate feature parameters are sorted in descending order according to the value of the maximum value. A set number of parameters in the top column of the sorted list are selected as key quality characteristics. The sensitivity coefficients corresponding to the selected key quality characteristics are used to construct a sensitivity matrix for weight allocation in subsequent steps.

[0009] Furthermore, the prior distribution characteristics of key quality characteristics are determined by retrieving the basic database of optical analysis. The posterior distribution parameters are calculated by combining the current batch sample data and using the conjugate prior update rule. This includes: setting the prior mean of the key quality characteristics to follow a normal distribution and the prior variance to follow an inverse gamma distribution; calculating the sample mean and sample variance of the current batch sample data; and using the conjugate prior update rule to fuse the normal distribution and the inverse gamma distribution with the sample mean and sample variance to derive the posterior mean and posterior variance.

[0010] Based on the posterior distribution parameters, control limits are generated to monitor the current batch of sample data. This includes: calculating the upper and lower control limits by combining the preset control width coefficient and the posterior standard deviation obtained by taking the square root of the posterior mean and posterior variance; comparing the newly collected test data points of the current batch with the upper and lower control limits; and triggering an abnormal state when the value of the newly collected test data points of the current batch is greater than the upper control limit or less than the lower control limit, or when the newly collected test data points of the current batch show a non-random pattern of a unidirectional continuous upward trend in the time series.

[0011] Calculate the process capability index, inter-batch drift, and controlled proportion of the key quality characteristics of the current batch, including: calculating multiple process capability indices based on the set upper and lower specification limits, the current batch mean, and the current batch standard deviation, and extracting the minimum value among them; extracting the absolute value of the difference between the current batch mean and the historical batch mean as the inter-batch drift; and calculating the proportion of data points in the current batch that are under control to the total number of test points as the controlled proportion.

[0012] The batch quality consistency index is calculated by combining the weights obtained from the normalization of the sensitivity matrix, and the quality consistency levels are divided. This includes: normalizing the sensitivity matrix to obtain the first weight, second weight, and third weight, and setting the upper limit of tolerance drift; multiplying the first weight by the minimum value of the process capability index, multiplying the second weight by a constant minus the difference between the inter-batch drift amount and the upper limit of tolerance drift, and multiplying the third weight by the controlled proportion. The sum of the three multiplication results is used to obtain the comprehensive batch quality consistency index; the comprehensive batch quality consistency index is compared with the classification boundary threshold to classify the product quality of the current batch into Grade A, which represents exemption from inspection; Grade B, which represents qualification; and Grade C, which represents deterioration.

[0013] Furthermore, the measured performance of the assembled coated components is obtained and compared with the design specifications. Based on the comparison results, the control limits are tightened or the weights are adjusted and stored in the knowledge base for the next batch of production. This includes: when the measured performance is better than the design specifications, the ratio of the design specifications to the measured performance is extracted to generate an adjustment coefficient. The current control limit is multiplied by the adjustment coefficient to generate a narrowed new control limit, which is then stored in the knowledge base for monitoring boundaries in the next batch of production. When measured performance deteriorates, the distribution sequence of key process parameters and measured performance is extracted by retrospectively analyzing historical process control data. The Pearson correlation coefficient between the key process parameters and measured performance is calculated. The sum of the constant and the Pearson correlation coefficient is multiplied back to the original parameter weights to obtain new parameter weights. All new parameter weights are normalized and then stored in the knowledge base.

[0014] After testing the characteristic and performance parameters of the coated optical elements in the same system, the process also includes: establishing a test coordinate system for the antireflective coating elements in the deep ultraviolet band and setting a matrix as the test area; testing the micro-absorption coefficient of each matrix point; calculating the statistical mean and fluctuation range of the micro-absorption coefficient of each matrix point; quantifying the spatial stability by subtracting the difference between the fluctuation range and the statistical mean using a constant; and when the spatial stability is lower than the preset standard, using X-ray photoelectron spectroscopy to characterize the abnormal micro-areas of the test elements and extracting the characteristic peaks of carbon and oxygen elements to investigate the contamination mechanism.

[0015] This invention provides a method for evaluating the quality stability of coated components based on statistical process control. It has the following beneficial effects: 1. This invention determines prior distribution characteristics by retrieving a basic optical analysis database and generates control limits by calculating posterior distribution parameters using conjugate prior update rules combined with current batch sample data. This design overcomes the limitations of using fixed control limits in traditional statistical process control, enabling dynamic adjustment of monitoring boundaries based on the fusion results of historical prior data and current batch measured data, thus improving the accuracy of coating element quality monitoring under fluctuating operating conditions.

[0016] 2. This invention extracts the minimum value of the process capability index, the inter-batch drift, and the controlled proportion, and combines them with the weights obtained from the sensitivity matrix normalization for weighted summation to calculate the comprehensive batch quality consistency index. This multi-index fusion calculation method transforms the absolute qualification judgment of a single parameter into a comprehensive quantitative evaluation, and uses the sensitivity matrix to reflect the degree of influence of different characteristic parameters on actual optical performance, making the final quality consistency level more objective.

[0017] 3. This invention compares the measured performance of the assembled coated components with the design specifications. When the performance exceeds the design specifications, the ratio is extracted to generate an adjustment coefficient to tighten the control limits. When performance deteriorates, the Pearson correlation coefficient is used to correct the parameter weights. This mechanism establishes a feedback adjustment channel between the end application and the preceding manufacturing process, enabling the control boundaries and evaluation weights to adaptively iterate based on the actual assembly results, thereby continuously optimizing the production control benchmark for the next batch of products. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for evaluating the quality stability of coated components based on statistical process control, according to an embodiment of the present invention. Figure 2 This is a diagram showing the test results of surface contamination in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] See attached document Figure 1 This invention provides a method for evaluating the quality stability of coated components based on statistical process control, comprising the following steps: S10. Establish a basic optical analysis database based on homogeneous coated optical elements. Test the characteristic and performance data of different locations in the micro-area of ​​a certain number of homogeneous coated optical elements, with the test locations covering a predetermined proportion of the light-transmitting area of ​​the elements. Extracted characteristic and performance parameters include film stress, absorptivity, surface defect density, surface roughness, reflectivity, center wavelength of the reflection band, wavefront distortion, and uniformity. Analyze the stability and variability of the characteristic and performance data. When the stability of a specific parameter reaches a set threshold, establish a basic optical analysis database. When a specific parameter does not reach the set threshold, analyze the spatial and batch differences of that parameter, investigate the causes of the differences, and provide feedback for improvement to the process. S20, Key Quality Characteristic Screening Based on Optical Sensitivity Matrix. The characteristic parameters of the coated element are used as input variables, and optical performance indicators are used as output variables. Samples with approximately univariate small perturbations are selected from the candidate characteristic parameter set, and the optical performance indicators of the corresponding samples are tested. The performance changes caused by the univariate perturbation are analyzed, and the sensitivity coefficient of each candidate characteristic parameter is calculated. The maximum sensitivity of each candidate characteristic parameter to each optical performance indicator is extracted, and the parameters are sorted in descending order according to the maximum sensitivity value. A set number of parameters are selected as key quality characteristics of the coated element, and the sensitivity matrix is ​​output for weight allocation in subsequent steps. S30, Adaptive control limit generation based on Bayesian inference. It determines the prior distribution characteristics of key quality features using a basic optical analysis database, collects sample data of the current batch of coated elements, and calculates the batch sample mean and variance. It then calculates the posterior distribution parameters using a conjugate prior update rule. Based on the set control width coefficient and the posterior distribution parameters, it generates dynamic upper and lower control limits. In subsequent processing, new data points are compared with the dynamic control limits; an alarm is triggered when a new data point exceeds the control limits or a non-random pattern occurs. S40, Batch Quality Consistency Index Calculation and Classification. The process capability index is calculated by obtaining the tolerance allocation values ​​of the optical path system. The difference between the current batch average and the historical batch average is extracted to calculate the inter-batch drift. The controlled points in the test data are counted to calculate the controlled proportion. The sensitivity matrix is ​​normalized to obtain the weights of each sub-item. The batch quality consistency index is calculated by combining the process capability index, inter-batch drift, and controlled proportion with their corresponding weights. Based on the batch quality consistency index, batch quality consistency is classified into preset levels. S50, a closed-loop feedback correction mechanism for process performance. It acquires the measured performance of the assembled coated components and compares it with the design specifications. When the measured performance exceeds the design specifications, the control limits are automatically tightened according to the ratio between the measured performance and the design specifications. When specific performance degradation occurs, historical test data is reviewed, and the Pearson correlation coefficient between each key quality characteristic and the overall machine's measured performance is calculated. This correlation coefficient is then used to update the weights of the corresponding parameters. The corrected control limits and updated weights are stored in the knowledge base for use in the next batch of production.

[0021] In this embodiment, the basic data collection and stability assessment process specifically includes the following steps: S101, Test the characteristic parameters and performance parameters of samples of coated optical elements of the same system. As a preferred method, the process of obtaining initial data needs to control the consistency of the samples, selecting no less than 30 coated optical elements of the same system as test samples. The aforementioned coated optical elements of the same system refer to elements that use the same film system design, the same substrate material, and are produced under the same machine process parameters. The light-transmitting area of ​​the coated optical element is divided into micro-areas. Those skilled in the art can use a matrix grid division method with equal intervals to select different positions within the micro-area for data collection to ensure the spatial representativeness and dispersion of the test data. The distribution range of the test positions is set to cover no less than 60% of the light-transmitting area of ​​the element.

[0022] The extracted parameters encompass characteristic parameters representing physical properties and optical performance parameters representing imaging quality, specifically including film stress, absorptivity, surface defect density, surface roughness, reflectivity, center wavelength of the reflection band, wavefront distortion, and uniformity. For the specific measurement process of various physical and optical parameters of the coated element, those skilled in the art can use conventional methods such as interferometer measurement of surface accuracy or dark-field microscopy to inspect surface defects. The specific equipment selection and testing principles are well-known technologies in the field and will not be elaborated here. Through multi-micro-area and multi-parameter sampling tests, an initial data set for characterizing the state of the coated element is obtained.

[0023] S102, analyze the stability and variability of various parameters in the initial dataset. Summarize the acquired test data, calculate the spatial distribution of each parameter in the micro-area and the numerical fluctuations between different test samples, thereby quantifying the consistency of the data. In specific engineering implementations, the above stability can be characterized by calculating the proportion of data points within the set tolerance range to the total number of test data points. Combined with the historical yield baseline of the manufacturing process or the tolerance tolerance allocated to the optical path system, a reference threshold for parameter stability evaluation is set. In this embodiment, the judgment threshold for surface defect density is set to 80%, and the judgment thresholds for other parameters such as film stress, absorptivity, surface roughness, reflectivity, center wavelength of the reflection band, wavefront distortion, and uniformity are uniformly set to 90%. The calculated actual stability test results are compared with the set reference thresholds.

[0024] S103. Based on the judgment results, establish a basic optical analysis database or perform process feedback. When the stability result of the surface defect density reaches or exceeds 80%, and the stability results of all other parameters reach or exceed 90%, the currently acquired test sample data can be considered to meet the requirements of preliminary process control. The compliant characteristic parameters and performance parameters are archived to establish a basic optical analysis database, which provides data support for subsequent quality characteristic screening and control limit generation in the system.

[0025] When any parameter fails to reach the set threshold, the spatial difference distribution data of the corresponding parameter in different micro-regions is extracted, and the batch difference fluctuation data of the parameter between different test samples is also extracted to trace the causes of spatial and batch differences in the parameter. The causes of the differences and corresponding data are fed back to the coating process manufacturing stage to guide the manufacturing stage to carry out improvement operations such as pollution source tracing or process parameter optimization. To avoid the system falling into an algorithm loop of repeated feedback execution due to continuous abnormalities in the manufacturing process, when the number of feedback improvements for the same parameter reaches the system's set retry limit, if the data of subsequent produced coating element samples still does not meet the set stability threshold, a system abnormality alarm is triggered and the database establishment process is terminated, prompting manual intervention to check the equipment status.

[0026] The screening process for key quality characteristics based on the optical sensitivity matrix includes the following steps: S201, Construct a mapping model between physical parameters and optical performance. In this embodiment, to establish a quantitative mapping relationship from film physical parameters to optical performance, the characteristic parameters of the coated elements in the basic optical analysis database are used as input variables, and the optical performance indicators are used as output variables. As a preferred approach, the candidate characteristic parameter set composed of the input variables is denoted as... Its specific characteristics are as follows ,in The total number of candidate feature parameters; the set contains several candidate feature parameters. Candidate feature parameters include process variables characterizing the physical state of the film, such as film stress and surface defect density. Output variables include performance variables that determine the imaging quality of the lithography machine, such as the center wavelength of the reflection band, wavefront distortion residual, and dimensional uniformity.

[0027] S202, perform univariate small perturbation analysis to obtain the performance change. Select corresponding coated element samples from the candidate feature parameter set. For each candidate feature parameter... Select samples from the sample library that have approximately univariate small perturbations The samples. Considering that naturally extracted samples in actual industrial production are unlikely to have only absolutely single variable fluctuations, in order to avoid the evaluation process being interrupted due to the inability to match qualified samples, those skilled in the art can simultaneously prepare dedicated process test films, or obtain corresponding sample data by applying virtual parameter perturbations through optical simulation software.

[0028] The processed sample exhibits slight numerical fluctuations in a specific target characteristic parameter, while its other characteristic parameters remain consistent within the allowable error range. Optical performance data of this sample is obtained through testing and compared with benchmark data in the basic optical analysis database to extract the performance variation caused by the univariate perturbation of this characteristic parameter. For the testing and numerical extraction of optical performance index data, those skilled in the art can use conventional equipment such as interferometers or spectrometers to obtain the data. The specific hardware operation and comparison principles are well-known technologies in this field and will not be elaborated here.

[0029] S203, calculate the sensitivity coefficients of characteristic parameters and screen key quality characteristics. Based on the acquired small perturbation amounts. With performance change The sensitivity coefficient of the candidate feature parameters of the coated element is calculated using the following formula: ; In the formula, Indicates the sensitivity coefficient; Indicates the amount of performance change; This represents a small perturbation. Indicates the index of the corresponding candidate feature parameter; This indicates the serial number of the corresponding optical performance index.

[0030] After calculating the sensitivity coefficients for each parameter, the maximum sensitivity of each candidate feature parameter to all corresponding optical performance indicators is extracted, and its mathematical expression is as follows: ; In the formula, This indicates that the sensitivity coefficient is maximized across multiple optical performance metrics.

[0031] Based on the specific value of the maximum sensitivity corresponding to each candidate feature parameter, all candidate feature parameters are sorted in descending order. The system then extracts a predetermined number of the top-ranked parameters. The parameters are considered key quality characteristics of the coating element. In this embodiment, the set quantity... The sensitivity coefficients can be preset by the evaluation system based on actual monitoring needs, or dynamically selected based on whether the maximum sensitivity exceeds the environmental noise tolerance threshold of the optical path system, combined with the numerical results sorted in descending order. The sensitivity coefficients corresponding to the selected key quality characteristics are then used to construct a sensitivity matrix, denoted as... : ; In the formula, This represents the sensitivity matrix. The generated sensitivity matrix is ​​output and saved, and used in subsequent evaluation steps to calculate the weight allocation of each quality characteristic. By introducing a sensitivity matrix evaluation mechanism, the system can effectively filter redundant parameters with negligible impact on optical performance in most operating scenarios, monitoring only the core process variables that determine the quality of the optical path.

[0032] The adaptive control limit dynamic generation process based on Bayesian inference specifically includes the following steps: S301. In small-batch production scenarios where the sample size of a single batch of products is less than 20, directly establishing statistical monitoring limits based on a small number of current batch samples often carries the risk of excessive bandwidth or unstable limits. To address this issue, this embodiment introduces a Bayesian inference method, utilizing a trade-off mechanism between historical experience data and the current small sample size for dynamic calculation. The evaluation system retrieves the established optical analysis database, extracts test data of key quality characteristics from historical controlled batches, and calculates the statistical mean and statistical variance of the corresponding historical data, using this as the basis for constructing the prior distribution characteristics of the parameters.

[0033] As a preferred approach, the system assumes that the mean of key quality characteristics follows a normal distribution, and the corresponding variance follows an inverse gamma distribution. The assumed normal distribution model is denoted as... , in the formula, This represents the prior mean; Let represent the prior variance. The defined inverse gamma distribution model is denoted as . , in the formula, Indicates shape parameters; Indicates the scale parameter.

[0034] S302, During the processing of the current batch of components, the system synchronously collects a sample size of... The test data, specifically the sequence, is denoted as... For the collected sample sequences, calculate the sample mean of the current batch. With sample variance Based on Bayesian theory, the system utilizes a conjugate prior update rule to fuse a prior distribution model based on historical data with the measured sample data of the current batch, thereby deriving the updated posterior distribution parameters. The specific formula for calculating the posterior mean is as follows: ; In the formula, This represents the posterior mean; Indicates sample size; This represents the sample mean; Indicates the sample variance; This represents the prior mean; This represents the prior variance.

[0035] The corresponding approximate formula for calculating the posterior variance is as follows: ; In the formula, This represents the posterior variance. In practical engineering calculations and deployments, the evaluation system can use the mathematical principles of conjugate distributions to accurately calculate the posterior distribution parameters. The specific mathematical process for deriving the accurate parameters of the conjugate distribution can be implemented by those skilled in the art based on standard Bayesian statistical inference theory; this is a well-known technique in the field and will not be elaborated upon here.

[0036] S303, after acquiring the various posterior distribution parameters, the system generates an adaptive monitoring boundary for the current batch by combining it with preset control width coefficients. To match the statistical confidence level standards commonly used in industry, the control width coefficients... The value is set to 3, corresponding to a 99% confidence level. Based on this, dynamic upper and lower control limits are generated, calculated using the following formula: ; ; In the formula, Indicates the upper control limit; Indicates the lower control limit; This indicates the control width coefficient; This represents the posterior standard deviation, which is obtained by taking the square root of the posterior variance. This represents the posterior mean.

[0037] During subsequent continuous manufacturing processes, the system receives new test data points and compares them with the adaptive monitoring boundaries. An abnormal state is triggered when the value of a new data point exceeds the upper control limit or falls below the lower control limit. Simultaneously, the system analyzes the distribution characteristics of the test data over time, triggering an anomaly alarm mechanism when a preset non-random pattern is detected. This non-random pattern can be set based on conventional control chart anomaly criteria, such as the appearance of six consecutive data points exhibiting a unidirectional, continuously rising trend.

[0038] Upon alarm triggering, the system outputs an intercept command to the production control terminal, prompting operators to check equipment status or calibration parameters. Considering the possibility of missing historical data during the new product introduction phase, which could prevent the extraction of valid prior parameters, the system incorporates bypass logic. When sufficient historical prior data is not retrieved, the evaluation system temporarily degrades to accumulating basic data using conventional statistical process control methods until the historical sample size meets the prior modeling conditions, thus avoiding interruptions in the calculation process.

[0039] The process for calculating and quantifying the batch quality consistency index includes the following steps: S401, calculate the process capability index, batch-to-batch drift, and data control ratio. In this embodiment, during the manufacturing process, in addition to monitoring the controlled state of individual parameters, the overall batch quality consistency is crucial to the final imaging stability of the lithography machine. Therefore, a multi-dimensional comprehensive evaluation index needs to be introduced. The evaluation system extracts the optical performance and physical characteristic data of the current batch of components to construct the basic indicators for quality assessment. Based on the system tolerance allocation of the optical path, upper and lower specification limits are set, and combined with the statistical mean and standard deviation of the current batch data, the process capability index of each key parameter is calculated. The calculation formula is as follows: ; In the formula, Indicates process capability index; Indicates the upper specification limit; Indicates the lower specification limit; This represents the average value of the current batch. Indicates the standard deviation of the current batch; This indicates a minimum value operation. After obtaining the process capability index for multiple parameters, based on the conservative evaluation principle dominated by the worst-performing parameter, the system extracts the minimum value and denotes it as... Participate in subsequent calculations.

[0040] To assess consistency fluctuations between batches, the system calculates the batch drift relative to historical controlled states, using the following formula: ; In the formula, Indicates the amount of drift between batches; This represents the average value of the current batch. This represents the historical batch average. To establish a drift tolerance evaluation benchmark, the system sets an upper limit for drift tolerance based on product specification tolerances, denoted as . To avoid computational anomalies such as the denominator being zero during subsequent division operations, the specific value of this tolerance drift upper limit is strictly limited to a real number greater than zero.

[0041] At the same time, the system counts the number of data points in the current batch that are under control, divides this number by the total number of test points to obtain the control ratio, which is denoted as . .

[0042] S402, determine the indicator weights and calculate the comprehensive index of batch quality consistency. The evaluation system retrieves the sensitivity matrix generated in the previous steps and normalizes the sensitivity coefficients within it. In this embodiment, the normalization process specifically uses the ratio of the maximum sensitivity value of a single parameter to the sum of the maximum sensitivity values ​​of all parameters in the sensitivity matrix. Through the normalization operation, the system converts the sensitivity matrix into weight parameters corresponding to each evaluation indicator, specifically including the first weight. Second weight and the third weight Furthermore, the sum of the values ​​of the above three weight parameters is set to equal 1. Based on the basic indicators and corresponding weights obtained above, the system constructs a calculation model for the batch quality consistency index, with the specific formula as follows: ; In the formula, Indicates the batch quality consistency index; Indicates the first weight; This represents the minimum value of the process capability index; Indicates the second weight; Indicates the amount of drift between batches; Indicates the upper limit of the tolerance drift; Indicates the third weight; This indicates the controlled proportion. As a preferred method, when the actual inter-batch drift exceeds the tolerance drift limit, causing the calculated term within the parentheses in the formula to have a negative value, the system uses a truncation mechanism to force it to zero, thereby preventing the final weighted composite index from being distorted due to excessive penalties.

[0043] S403, Perform batch quality consistency quantification and grading. After obtaining the batch quality consistency index, the evaluation system automatically compares the calculated value with preset grading boundary thresholds. Based on the comparison results, the product quality of the current batch is divided into three preset levels. When the batch quality consistency index is greater than or equal to 0.9, the current batch is determined to be Grade A, indicating excellent product quality and eligible for release as an inspection-free batch. When the index is greater than or equal to 0.7 and strictly less than 0.9, the current batch is determined to be Grade B, indicating acceptable product quality. When the index is less than 0.7, the current batch is determined to be Grade C, indicating severe consistency degradation. For batches determined to be Grade C, the system triggers an intervention response process, prompting the manufacturing end to rework the components in that batch, or to downgrade their use if the secondary standards are met. Through the above quantification and grading operations, standardized evaluation of performance consistency within and between batches is achieved.

[0044] The process for closed-loop feedback correction of process and performance includes the following steps: S501, Obtain the measured performance of the coated components after assembly and perform a comparison. In this embodiment, the evaluation system establishes a data communication channel between the manufacturing end and the application end. After the current batch of coated components is assembled into the lithography machine system and completes the overall machine testing, the system obtains the measured performance corresponding to that batch of components, denoted as... As a preferred method, the measured performance obtained covers core indicators affecting the overall imaging quality, such as actual aberrations and uniformity. The system extracts the pre-entered design parameters corresponding to this component, denoted as... The measured performance was compared and analyzed with the design specifications.

[0045] S502, tightening control limits based on performance positive optimization results. When the measured performance is better than the design specifications, it indicates that the actual manufacturing process of the current batch has reached a more optimal optical performance convergence state. To solidify this optimized state, the evaluation system triggers the calculation logic for automatically tightening the control limits. Considering the differences in the dimensions and evaluation directions of different optical performance indicators, for example, transmittance is an evaluation indicator where a larger value is better, while aberration is an evaluation indicator where a smaller value is better.

[0046] To ensure the mathematical correctness of the control limit tightening logic and avoid logical loopholes where different indicator judgment directions lead to abnormally relaxed new control limits, the performance indicators defined here are constructed based on a "larger is better" model. If the evaluation object belongs to a "smaller is better" model, the system automatically extracts its reciprocal and substitutes it into subsequent calculations. Based on this, the system generates an adjustment coefficient using the proportional relationship between design indicators and measured performance. The specific calculation formula is as follows: ; In the formula, Indicates the new control limits; Indicates the original control limits; Indicates design specifications; This represents the measured performance. To ensure the stability of engineering calculations, the specific values ​​of the measured performance mentioned above are limited to real numbers greater than zero. Through this adjustment mechanism, the system can adaptively narrow the monitoring boundaries of subsequent production, prompting process standards to converge towards a more stringent high-performance range.

[0047] S503 performs historical backtracking and weight updates based on performance degradation characteristics. In actual industrial operation, simple forward tightening cannot cover all process fluctuation scenarios. When specific performance degradation phenomena occur in the measured data, such as abnormal patterns like excessive trilobal aberration, the system initiates a reverse diagnostic process. The evaluation system backtracks the historical statistical process control data corresponding to this batch, extracting the distribution sequence of each key process parameter and the measured performance of the entire machine. The system calculates the Pearson correlation coefficient between each key process parameter and the overall machine performance, denoted as... The specific calculation process of the Pearson correlation coefficient can be described by those skilled in the art using conventional statistical methods for calculating the quotient of covariance and standard deviation, which are well-known techniques in the field and will not be elaborated upon here.

[0048] After obtaining the Pearson correlation coefficient, the evaluation system dynamically adjusts the weight of the corresponding parameter in the batch quality consistency index based on this coefficient. The calculation formula is as follows: ; In the formula, Indicates the weight of the new parameter; Indicates the original parameter weights; This represents the Pearson correlation coefficient. By introducing this modified formula, the system can quantify the impact of a single parameter on overall performance degradation. For specific process parameters that exhibit a strong positive correlation with performance degradation, their correlation coefficients tend to be positive. Based on this, the system automatically amplifies the monitoring weight of this parameter in the comprehensive evaluation, achieving precise control over sensitive parameters that lead to degradation. To ensure the mathematical completeness of the overall evaluation system and avoid distortion of subsequent evaluation indices, the system performs a normalization operation on all evaluation weights simultaneously after updating individual weights, maintaining the basic condition that the total weight sum is 1.

[0049] S504 establishes a global closed-loop mechanism for process evaluation and performance data. The system stores the newly calculated control limits and updated parameter weights obtained in the above steps into a knowledge base. When executing the production and evaluation tasks of the next batch of coated optical components of the same system, the evaluation system directly calls the updated data in this knowledge base as the operating benchmark. Through the feedback chain of data acquisition, comparison, correction, and distribution, a complete data closed-loop system is established. This closed-loop mechanism breaks down the physical barrier between manufacturing-end data and application-end data, enabling coating process standards to continuously iterate based on feedback from real optical path performance, thus promoting the continuous convergence of the process state towards better optical performance.

[0050] See attached document Figure 2 This invention provides a method for evaluating the quality stability of coated components based on statistical process control, and includes the following steps for testing and failure mechanism diagnosis analysis in specific application scenarios: S601, Select the target element and set the micro-area test matrix. In this embodiment, the evaluation system uses an antireflection coating element in the deep ultraviolet band as the specific test object. To comprehensively obtain the physical and optical state within the light-transmitting area of ​​the element, a test coordinate system is established on the surface of the antireflection coating element, and a 2×2 matrix with a 2mm interval is set as the test area. The test points set by this matrix basically cover the core light-transmitting area of ​​the element. Subsequently, the system controls the test equipment to sequentially perform characteristic parameter and performance data acquisition operations on each matrix point. As a preferred method, the micro-area absorption coefficient is extracted as the evaluation index in this test. Specifically, the absorption coefficients of the four points are measured to be 0.138, 0.147, 0.092, and 0.102, respectively. The specific measurement process of micro-area optical parameters such as the absorption coefficient can be obtained by those skilled in the art using conventional spectral analysis test equipment, which is a well-known technology in the field and will not be described in detail here.

[0051] S602, Calculate micro-area data stability and perform anomaly detection. After obtaining the micro-area distribution data, its spatial uniformity needs to be quantitatively evaluated. The system calculates the statistical mean and fluctuation range of the absorption coefficients at the four matrix points, and derives the actual spatial stability of the current micro-area data based on the ratio distribution of the range and the mean. The specific derivation model is to directly quantify the percentage of spatial stability by calculating the difference between the constant 1 and the quotient of the range and the mean (i.e., the calculation formula is: 1 - range / mean). To establish an evaluation benchmark, the system extracts the parameter stability threshold from the pre-entered optical analysis basic database. This threshold is usually set to 90% based on the optical characteristics benchmark of historical good products. The calculated actual spatial stability value is compared and analyzed with this preset threshold. Through comparison, it is found that the fluctuation range of the absorption coefficients in the four micro-areas of the current component deviates from the normal tolerance limit, resulting in its actual spatial distribution stability being lower than the set 90% standard. Based on this deviation result, the evaluation system generates a parameter anomaly signal for this batch of components and automatically triggers the subsequent failure mechanism diagnosis process.

[0052] S603, Perform surface composition analysis and process closed-loop traceability. For the deep ultraviolet antireflection film element that triggered the abnormal signal, the system calls the material characterization equipment to perform microscopic material analysis on its surface. In this embodiment, X-ray photoelectron spectroscopy is used to characterize the composition of the abnormal micro-regions of the test element. Combined with Figure 2 As shown, the horizontal axis of the energy spectrum test result graph represents the binding energy, with the unit being electron volts (eV); the vertical axis represents the photoelectron count rate (c / s, i.e., counts per second). Figure 2 The “Atomic%” label in the upper left corner indicates the atomic percentage of each element in the test micro-region.

[0053] By analyzing the characteristic peak positions and quantitative data in the energy dispersive spectroscopy (EDS) spectrum, in addition to detecting conventional spectral peaks belonging to the background materials of optical components, such as fluorine (corresponding to peaks such as F1s in the spectrum, with an atomic percentage of 21.5%) and calcium (corresponding to peaks such as Ca2p in the spectrum, with an atomic percentage of 16.1%), significant carbon (corresponding to peaks such as C1s in the spectrum) and oxygen (corresponding to peaks such as O1s in the spectrum) characteristics were also identified on the component surface. Furthermore, the quantitative results showed that the atomic percentage of carbon was as high as 45.0%, and the atomic percentage of oxygen was 14.7%. Their peak intensities and elemental proportions significantly exceeded the background baseline under normal process conditions, indicating the presence of unexpected carbon and oxygen deposition on the component surface.

[0054] Based on the material composition identification results, the system deduced that the failure mechanism of the abnormal degradation of the absorption coefficient in this micro-area was highly correlated with carbon and oxygen contamination on the component surface. Further matching of this contamination mechanism with a process failure mode library revealed that the physical cause of carbon and oxygen deposition was likely contact with organic contaminants during the manufacturing process, or prolonged exposure in the production environment without the use of protective measures such as vacuum isolation or nitrogen protection. After completing the failure attribution, the evaluation system generated a diagnostic report containing specific troubleshooting recommendations. This conclusion was fed back to the upstream process in manufacturing to perform contamination source tracing, and simultaneously fed back to the warehouse management stage, prompting relevant operators to check and correct storage protection conditions. Through these steps, a complete quality closed loop was constructed, from performance anomaly identification and microscopic mechanism diagnosis to production process optimization.

Claims

1. A method for evaluating the quality stability of coated components based on statistical process control, characterized in that, include: Test the characteristic parameters and performance parameters of the same system coated optical elements, and establish a basic database for optical analysis when the stability of the characteristic parameters and performance parameters reaches a set threshold. The in-system coated optical element is an antireflection coating element in the deep ultraviolet band. After testing the characteristic parameters and performance parameters of the in-system coated optical element, a test coordinate system is established for the deep ultraviolet antireflection coating element and a matrix is ​​set as the test area; the micro-area absorption coefficient of each matrix point is tested; the statistical mean and fluctuation range of the micro-area absorption coefficient of each matrix point are calculated. Spatial stability is quantified by subtracting the difference between the fluctuation range and the quotient of the statistical mean from a constant. When the spatial stability is lower than the preset standard, X-ray photoelectron spectroscopy is used to characterize the abnormal micro-regions of the antireflection membrane element in the deep ultraviolet band, and the characteristic peak positions of carbon and oxygen elements are extracted to investigate the pollution mechanism. The performance change of the test sample under univariate small perturbation is introduced, the sensitivity coefficient of the candidate feature parameter is calculated, key quality characteristics are screened and a sensitivity matrix is ​​generated; The prior distribution characteristics of the key quality characteristics are determined by retrieving the basic optical analysis database, and the posterior distribution parameters are calculated by combining the current batch sample data and using the conjugate prior update rule. Control limits are generated based on the posterior distribution parameters to monitor the current batch sample data. Calculate the process capability index, inter-batch drift, and controlled proportion of the key quality characteristics of the current batch; calculate the batch quality consistency index by combining the weights obtained by normalizing the sensitivity matrix; and classify the quality consistency level. The measured performance of the coated element after assembly is obtained and compared with the design specifications. When the measured performance is better than the design specifications, the ratio of the design specifications to the measured performance is extracted to generate an adjustment coefficient. The current control limit is multiplied by the adjustment coefficient to generate a new, narrowed control limit. When the measured performance deteriorates, the historical process control data is retrospectively analyzed to extract the distribution sequence of key process parameters and the measured performance. The Pearson correlation coefficient between the key process parameters and the measured performance is calculated. The sum of the constant and the Pearson correlation coefficient is multiplied by the original parameter weights to obtain new parameter weights. Normalization is performed on all the new parameter weights. The new control limits or the normalized new parameter weights are stored in the knowledge base for the next batch of production.

2. The method for evaluating the quality stability of coated components based on statistical process control according to claim 1, characterized in that, The characteristic parameters and performance parameters of the tested homogeneous coated optical elements are used to establish a basic optical analysis database when the stability of the characteristic parameters and performance parameters reaches a set threshold. This database includes: The light-transmitting area of ​​the same system of coated optical elements is divided into micro-regions, and characteristic parameters and performance parameters are collected at different locations; The characteristic parameters include film stress, surface defect density, and surface roughness; The performance parameters include absorptivity, reflectivity, center wavelength of the reflection band, wavefront distortion, and uniformity. When there are substandard parameters that do not reach the set threshold, the spatial difference distribution data and batch difference fluctuation data of the substandard parameters are extracted, the cause of the difference is traced, and feedback is given to the manufacturing process.

3. The method for evaluating the quality stability of coated components based on statistical process control according to claim 1, characterized in that, The process of introducing the performance change of the test sample under univariate small perturbation, calculating the sensitivity coefficient of candidate feature parameters, screening key quality characteristics, and generating a sensitivity matrix includes: Extract the maximum value of the sensitivity coefficient corresponding to each of the candidate feature parameters; Sort all the candidate feature parameters in descending order according to the value of the maximum value; A set number of parameters from the top of the sorted list are selected as the key quality characteristics, and the sensitivity coefficients corresponding to the selected key quality characteristics are used to construct the sensitivity matrix for weight allocation in subsequent steps.

4. The method for evaluating the quality stability of coated elements based on statistical process control according to claim 1, characterized in that, The process of retrieving the basic optical analysis database to determine the prior distribution characteristics of the key quality characteristics, and calculating the posterior distribution parameters by combining the current batch sample data and using the conjugate prior update rule, includes: The prior mean of the key quality characteristics is assumed to follow a normal distribution, and the prior variance of the key quality characteristics is assumed to follow an inverse gamma distribution. Calculate the sample mean and sample variance of the current batch of sample data; The normal distribution and the inverse gamma distribution are fused with the sample mean and the sample variance using the conjugate prior update rule to derive the posterior mean and posterior variance.

5. The method for evaluating the quality stability of coated elements based on statistical process control according to claim 4, characterized in that, The step of generating control limits based on the posterior distribution parameters to monitor the current batch of sample data includes: The upper control limit and the lower control limit are calculated by combining the preset control width coefficient and the posterior standard deviation obtained by taking the square root of the posterior mean and the posterior variance, respectively. The newly collected test data points of the current batch are compared with the upper control limit and the lower control limit; An abnormal state is triggered when the value of the newly collected current batch test data point is greater than the upper control limit or less than the lower control limit, or when the newly collected current batch test data point exhibits a non-random pattern of a unidirectional continuous upward trend in the time series.

6. The method for evaluating the quality stability of coated elements based on statistical process control according to claim 1, characterized in that, The calculation of the process capability index, batch-to-batch drift, and controlled proportion of the key quality characteristics for the current batch includes: Based on the set upper and lower specification limits, as well as the mean and standard deviation of the current batch, multiple process capability indices are calculated and the minimum value is extracted for subsequent calculations. The absolute value of the difference between the current batch mean and the historical batch mean is extracted as the inter-batch drift. The controlled ratio is defined as the proportion of data points in the current batch that are under control to the total number of test points.

7. The method for evaluating the quality stability of coated elements based on statistical process control according to claim 6, characterized in that, The batch quality consistency index is calculated by combining the weights obtained from the normalization of the sensitivity matrix, and the quality consistency levels are divided, including: The sensitivity matrix is ​​normalized to obtain the first weight, the second weight, and the third weight, and an upper limit for tolerance drift is set. The batch quality consistency index is obtained by multiplying the first weight by the minimum value of the process capability index, multiplying the second weight by a constant minus the difference between the inter-batch drift amount and the quotient of the tolerance drift limit, and multiplying the third weight by the controlled proportion. The batch quality consistency index is compared with the grading boundary threshold to classify the product quality of the current batch into Grade A, which indicates exemption from inspection; Grade B, which indicates qualification; and Grade C, which indicates deterioration.

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