Anti-reflective coating thickness measurement method and system based on dual-path infrared reflection method

Abstract

The present application relates to the field of coating thickness measurement technology, and specifically to a method and system for measuring the thickness of an anti-reflective coating based on a dual-path infrared reflection method. The method comprises: obtaining, at each moment, a reflection signal from a measurement light path beam incident on the surface of a coating of a sample to be measured and a reflection signal from a reference light path beam incident on the surface of a coating of a standard sample; inverting the thickness measurement value of the coating of the sample to be measured at each moment; collecting reflectance spectrum data of an exposed substrate in real time; obtaining the spectral characteristic value and degree of variation at each moment; obtaining the predicted thickness measurement error at the next moment at each moment, obtaining a substrate compensation factor at each moment, and evaluating whether to re-invert and recalculate the thickness measurement value at each moment; if necessary, constructing an objective function at each moment and optimizing the parameters of the Fresnel model for the inverted thickness measurement value at each moment; and inverting and recalculating the thickness measurement value of the coating of the sample to be measured at each moment. The present application aims to improve the stability and accuracy of anti-reflective coating thickness measurement.

Description

Technical Field

[0001] The present application relates to the technical field of coating thickness measurement, and in particular to a method and system for measuring the thickness of an anti-reflective coating based on a dual-light-path infrared reflection method. Background Art

[0002] In the field of precision optical manufacturing, precise control of the thickness of anti-reflective coatings is crucial to the optical performance of devices. Currently, a dual-path infrared reflectometry method is commonly used to measure coating thickness. This method simultaneously constructs a measurement path and a reference path. The measurement path detects the reflected signal from the coating by incident infrared light at the Brewster angle, while the reference path monitors the reflected signal from a stable reference surface in real time. By dynamically comparing the two signals and applying a differential algorithm, common-mode noise such as temperature changes is directly offset, achieving high-precision, non-destructive analysis of coating thickness.

[0003] However, when using the dual-path infrared reflection method to measure the thickness of the anti-reflection coating, if the coating substrate is a multi-layer heterogeneous material, such as a semiconductor stack or a flexible display substrate, its infrared optical constants are easily affected by the process temperature, doping concentration or stress state, resulting in unexpected drift, resulting in asynchronous distortion of the reflection signal in the measurement optical path and the reflection signal in the reference optical path. Although common-mode noise can be suppressed at this time, it is impossible to distinguish the effects of coating thickness changes and substrate optical parameter drift on the reflection signal, resulting in deviations in the thickness measurement results. The existing technology mainly addresses the above problem by constructing a Fresnel model based on pre-stored substrate optical parameters. However, the pre-stored substrate optical parameters are difficult to cover the continuous gradual changes of the substrate optical parameters in actual production, resulting in the failure of the Fresnel model inversion result, affecting the measurement accuracy of the anti-reflection coating thickness. Summary of the Invention

[0004] In view of the above, it is necessary to provide an anti-reflection coating thickness measurement method and system based on the dual-path infrared reflection method, which improves the stability and accuracy of the anti-reflection coating thickness measurement compared with the traditional anti-reflection coating thickness measurement method based on the dual-path infrared reflection method:

[0005] In a first aspect, an embodiment of the present application provides a method for measuring the thickness of an anti-reflective coating based on a dual-path infrared reflection method, the method comprising the following steps:

[0006] Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each time, and obtain a dual-path differential signal; at each time, use the pre-built Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured;

[0007] Performing principal component analysis on all reflectance spectrum data before each moment to obtain principal components, obtaining spectral characteristic values ​​at each moment by comparing the reflectance spectrum data at each moment with the principal components, and combining the peak position shift factor and peak height change factor obtained at each moment through the change of all reflectance spectrum data before each moment to obtain the degree of change at each moment;

[0008] Obtaining the thickness measurement error of the thickness measurement value at each moment compared to the preset target thickness, obtaining the predicted thickness measurement error at the next moment based on all the thickness measurement errors and variations before each moment, and obtaining the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment as the difference between the dual-path differential signal and the pre-acquired ideal dual-path differential signal changes in time series;

[0009] The substrate compensation factor is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, the substrate compensation factor and the dual-optical path differential signal are combined with the refractive index and extinction coefficient of the substrate to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function is used to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

[0010] In one embodiment, the process of obtaining the spectral characteristic value is:

[0011] The reflection spectrum matrix of each moment is constructed by the reflection spectrum data of all moments before each moment, where the row index of the reflection spectrum matrix is ​​time and the column index is wavelength; the principal component analysis algorithm is used to obtain the first preset number of principal components of the reflection spectrum matrix of each moment, and the score value of the reflection spectrum data of each moment in the direction of each principal component is obtained. The spectral characteristic value is the 2 norm of the vector composed of the preset number of score values ​​at each moment.

[0012] In one embodiment, the peak shift factor is obtained by:

[0013] Obtain the peak position and peak height of each characteristic peak in the reflectance spectrum data at each moment; record the characteristic peak with the largest peak height in the reflectance spectrum data at each moment as the key characteristic peak; calculate the difference in the peak position of the key characteristic peak between each moment and the previous moment; and use the average of the differences between all moments before each moment and the previous moment as the peak position shift factor for each moment.

[0014] In one embodiment, the process of obtaining the peak height variation factor is:

[0015] Calculate the difference in peak height of the key characteristic peak between each moment and the previous moment; and take the average of the difference between all moments before each moment and the previous moment as the peak position shift factor of each moment.

[0016] In one embodiment, the degree of change is the product of the peak position shift factor, the peak height change factor and the spectral characteristic value at each moment.

[0017] In one embodiment, obtaining the predicted thickness measurement error at the next moment of each moment includes:

[0018] Arrange the thickness measurement errors and changes at all moments before each moment in time sequence to form a thickness measurement error sequence and a change sequence at each moment;

[0019] For each moment, the change sequence is used as the independent variable and the thickness measurement error sequence is used as the dependent variable. Combined with the polynomial regression model, the multivariate fitting equation at each moment is obtained, and the predicted thickness measurement error at the next moment is obtained through the multivariate fitting equation at each moment.

[0020] In one embodiment, the process of obtaining the substrate compensation factor is as follows:

[0021] Calculate the difference between the dual-path differential signal at each moment and the pre-collected ideal dual-path differential signal at each wavelength, calculate the product value of the difference at each wavelength and the weight coefficient output by the preset Gaussian weight function, and use the sum of the product values ​​at all wavelengths at each moment as the key difference feature value at each moment; arrange the key difference feature values ​​of all moments before each moment in time sequence to form a key difference sequence at each moment;

[0022] Perform a univariate linear regression on the change sequence and key difference sequence at each moment, taking the change sequence as the independent variable and the key difference sequence as the dependent variable, and obtain the regression slope at each moment;

[0023] The substrate compensation factor is a normalized value of the product of the absolute value of the regression slope and the predicted thickness measurement error.

[0024] In one embodiment, the method for evaluating whether it is necessary to re-invert and calculate the thickness measurement value at each moment is as follows: if the substrate compensation factor at each moment is less than a preset compensation threshold, it is not necessary to re-invert and calculate the thickness measurement value at each moment; otherwise, it is necessary to re-invert and calculate the thickness measurement value at each moment.

[0025] In one embodiment, the objective function is expressed as:

[0026] Where, Represents the objective function at the i-th moment; Min[ ] represents the minimum value operation; represents the base compensation factor at the i-th moment; R( ) represents the 2-norm operation; represents the dual optical path differential signal at the i-th moment; When solving the objective function using the LM nonlinear optimization algorithm, the model differential signal is calculated by combining the real-time refractive index and real-time extinction coefficient of the substrate with the Fresnel reflection formula; Indicates the difference between the real-time refractive index of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Indicates the difference between the real-time extinction coefficient of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Indicates the preset weight coefficient.

[0027] In a second aspect, an embodiment of the present application further provides an anti-reflective coating thickness measurement system based on a dual-path infrared reflection method, wherein the system includes:

[0028] Miniature infrared spectrum probe: used to emit infrared light in real time and collect reflectance spectrum data of the exposed substrate;

[0029] Signal processing unit: Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each moment, and obtain a dual-path differential signal; At each moment, use the pre-built Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured;

[0030] Performing principal component analysis on all reflectance spectrum data before each moment to obtain principal components, obtaining spectral characteristic values ​​at each moment by comparing the reflectance spectrum data at each moment with the principal components, and combining the peak position shift factor and peak height change factor obtained at each moment through the change of all reflectance spectrum data before each moment to obtain the degree of change at each moment;

[0031] Obtaining the thickness measurement error of the thickness measurement value at each moment compared to the preset target thickness, obtaining the predicted thickness measurement error at the next moment based on all the thickness measurement errors and variations before each moment, and obtaining the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment as the difference between the dual-path differential signal and the pre-acquired ideal dual-path differential signal changes in time series;

[0032] The substrate compensation factor is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, the substrate compensation factor and the dual-optical path differential signal are combined with the refractive index and extinction coefficient of the substrate to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function is used to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

[0033] This application has at least the following beneficial effects:

[0034] This application addresses the problem of gradual changes in infrared optical constants caused by temperature and stress drift on heterogeneous substrates. Principal component analysis can be used to extract the main variation patterns from a large amount of reflectance spectrum data. Spectral eigenvalues ​​can be calculated to quantify the overall deviation of substrate spectral data from the central data state, effectively reflecting the overall drift of substrate optical parameters. Peak position shift factors and peak height variation factors can be calculated to accurately capture positional and intensity changes in characteristic peaks, thereby characterizing specific changes in substrate microstructure. Calculation of the degree of variation can comprehensively reflect the synergistic effect of substrate optical parameter drift and local microscopic perturbations, facilitating subsequent evaluation of whether re-inversion calculation of coating thickness is necessary.

[0035] Furthermore, by using the thickness measurement error and variation at historical moments to predict the thickness measurement error at the next moment, the possible deviation trend and degree of the coating thickness measurement results can be predicted in advance. At the same time, the linear correlation strength between the difference between the real-time dual-path differential signal and the ideal dual-path differential signal compared to the variation is combined to dynamically generate a compensation factor, eliminating random noise interference, which is conducive to accurately quantifying the degree of compensation for the substrate optical constants.

[0036] Furthermore, when the coating thickness needs to be re-inverted and calculated, the parameters of the Fresnel model can be dynamically adjusted by introducing a substrate compensation factor and a dual-optical path differential signal, and combining the refractive index and extinction coefficient of the substrate to construct an objective function. This allows the Fresnel model to more accurately reflect the substrate situation, effectively separate the distortion signal introduced by substrate drift from the true coating thickness change signal, and eliminate the systematic deviation caused by non-common mode distortion, thereby improving the adaptability of the Fresnel model to substrate drift and the inversion accuracy, and improving the stability and accuracy of the anti-reflection coating thickness measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions and advantages of the embodiments of the present application or the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0038] Figure 1 A flowchart of a method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to an embodiment of the present application;

[0039] Figure 2 Schematic diagram of the process for obtaining the substrate compensation factor. DETAILED DESCRIPTION

[0040] In the description of the embodiments of this application, words such as "exemplary," "or," and "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "or," and "for example" is intended to present the relevant concepts in a concrete manner.

[0041] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application relates. The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. It should be understood that, unless otherwise indicated, " / " represents or.

[0042] It should also be noted that the terms "first" and "second" in this application are used to distinguish similar objects, rather than to describe a specific order or sequence.

[0043] The specific scheme of the anti-reflective coating thickness measurement method and system based on the dual-path infrared reflection method provided by the present application is described in detail below with reference to the accompanying drawings.

[0044] See also Figure 1 , which shows a flowchart of a method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method provided by an embodiment of the present application, the method comprising the following steps:

[0045] Step 1: Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each moment to obtain a dual-path differential signal; at each moment, use the pre-constructed Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured; and collect the reflection spectrum data of the exposed substrate in real time.

[0046] The infrared light emitted by the infrared light source is divided into two beams, and the measurement detector is used to collect in real time the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured at the Brewster angle, and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at the Brewster angle.

[0047] A miniature infrared spectrum probe is installed on the exposed substrate surface adjacent to the coating area of ​​the sample to be tested, which is used to emit infrared light in real time and collect the reflection spectrum data of the substrate to monitor the fluctuation of the optical parameters of the substrate.

[0048] In this embodiment, the acquisition frequency of the miniature infrared spectrum probe and the measurement detector is 100 Hz. The acquisition frequency is preset manually and can be set by the implementer. This application does not impose any special restrictions.

[0049] The difference between the reflected signal of the measurement light path beam and the reflected signal of the reference light path beam at each wavelength at each moment is calculated, and the difference values ​​at all wavelengths at each moment are arranged in ascending order of wavelength to form the dual-path differential signal at each moment.

[0050] The refractive index and extinction coefficient of a bare substrate standard sample are collected and calibrated offline using an ellipsometer. The measurement results are stored and used to pre-build a Fresnel model. It is important to note that the refractive index and extinction coefficient data for the substrate are pre-stored and not measured in real time.

[0051] The thickness of the sample coating at each moment is measured by inversion calculation using the pre-built Fresnel model based on the reflected signal of the measurement light path beam at each moment. The difference between the thickness measurement value at each moment and the preset target thickness is calculated to obtain the thickness measurement error. In this embodiment, the preset target thickness is 60 nanometers. The preset target thickness value is manually preset and can be set by the implementer according to actual conditions.

[0052] Normalize the collected reflectance spectrum data, the data in the dual-path differential signal, and the calculated thickness measurement error to eliminate the impact of dimension. Taking the collected reflectance spectrum data as an example, the following steps are performed: the maximum value of all collected reflectance spectrum data is statistically calculated, and the ratio of each reflectance spectrum data to the maximum value is calculated to achieve normalization of the reflectance spectrum data.

[0053] The thickness measurement errors of all moments before each moment are arranged in time sequence to form a thickness measurement error sequence at each moment.

[0054] The reflection spectrum matrix of each moment is constructed by the reflection spectrum data of all moments before each moment. Specifically, one row in the reflection spectrum matrix is ​​the reflection spectrum data of all wavelengths at one moment, and one column is the reflection spectrum data of all moments at one wavelength.

[0055] At the same time, according to the method for obtaining dual-path differential signals, an ideal dual-path differential signal is obtained, specifically: the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured when calculating the dual-path differential signal is replaced by the reflection signal of the measurement light path beam incident on the surface of the bare substrate standard sample, and the reflection signal of the reference light path beam incident on the coating surface of the standard sample is replaced by the reflection signal of the reference light path beam incident on the surface of the bare substrate standard sample.

[0056] Step 2: Perform principal component analysis on all the reflection spectrum data before each moment to obtain the principal component. By comparing the reflection spectrum data at each moment with the principal component, the spectral characteristic value at each moment is obtained. Combined with the changes in all the reflection spectrum data before each moment, the peak position shift factor and peak height change factor at each moment are obtained to obtain the degree of change at each moment.

[0057] When measuring the thickness of an antireflection coating using the dual-path infrared reflectometry method, if the substrate is composed of a multilayer heterogeneous material, its infrared optical constants are susceptible to unexpected drift due to dynamic changes in process temperature, doping concentration, or stress state. This drift causes asynchronous distortion between the reflected signal from the measurement path and the reflected signal from the reference path, resulting in systematic deviations in the coating thickness measurements derived from the Fresnel model inversion.

[0058] Based on the above analysis, for each moment, the reflectance spectrum matrix is ​​used as input and the principal component analysis algorithm is used. Since the first three principal components have fully covered the main variation modes of the base spectrum, and in order to avoid noise interference caused by selecting too many principal components, in this embodiment, the first three principal components are selected, and the score values ​​of the reflectance spectrum data at each moment in the three principal component directions are output. The score values ​​of the reflectance spectrum data at each moment in the three principal component directions are combined into a three-dimensional vector, and the 2-norm of the three-dimensional vector is used as the spectral characteristic value at each moment. Since the drift of the base optical parameters will inevitably leave characteristic patterns that can be captured by the principal components on the overall morphology of its spectrum, the spectral characteristic value at each moment quantifies the overall deviation direction and degree of deviation of the base spectrum morphology at each moment relative to the data center state. Among them, the principal component analysis algorithm is a well-known technology and will not be described in detail in this application. The specific meaning of the data center state is: select a bare substrate standard sample with stable optical parameters, measure the standard sample's reflectance spectrum data a preset number of times, compile the reflectance spectrum data obtained from these multiple measurements into a reflectance spectrum matrix, perform principal component analysis on the reflectance spectrum matrix and extract the first three principal components. The mean of the scores of the preset number of reflectance spectrum data in each principal component direction is used to form a point. This point is the data center state. In this embodiment, the preset number is 10, but the preset number can be set manually based on actual conditions.

[0059] Furthermore, since spectral features, such as peak position and intensity, are extremely sensitive to changes in the physicochemical state of the substrate, the Lorentz fitting algorithm is used to obtain the peak position and peak height of each characteristic peak in the reflectance spectrum data at each moment, and the characteristic peak with the largest peak height is recorded as the key characteristic peak. The difference in peak position and peak height of the key characteristic peak between each moment and the previous moment are calculated, and the mean of the difference between all moments before each moment and the previous moment is used as the peak position shift factor at each moment; the mean of the difference between all moments before each moment and the previous moment is used as the peak height change factor at each moment. Since the essence of the drift of the optical parameters of the substrate is the change of its microscopic properties, it must be directly reflected in the parameters of the key characteristic peaks. Therefore, the calculated peak position shift factor and peak height change factor can characterize the specific changes in the substrate microstructure. Among them, the Lorentz fitting algorithm is a well-known technology and will not be repeated in this application.

[0060] In this embodiment, the difference in peak positions is the absolute value of the difference between the peak positions, and the difference in peak heights is the absolute value of the difference between the peak heights.

[0061] Furthermore, the degree of change at each moment is obtained through the spectral characteristic value, peak position shift factor, and peak height change factor at each moment. The expression is:

[0062] Where, represents the degree of change at the i-th moment; represents the spectral characteristic value at the i-th moment; represents the peak position shift factor at the i-th moment; Represents the peak height change factor at the i-th moment.

[0063] It should be noted that the spectral eigenvalue quantifies the overall direction and degree of deviation of the substrate spectral morphology from the central state at the i-th moment, capturing the overall spectral variation pattern and reflecting the overall drift of the substrate optical constants. A larger spectral eigenvalue indicates a more severe deviation of the substrate state from the reference state and a higher risk of substrate fluctuation. The peak shift factor characterizes the local position change of the key characteristic peak, and the peak height variation factor characterizes the instantaneous change in the intensity of the key characteristic peak. The product of the peak shift factor and the peak height variation factor represents the synergistic strength of local perturbations in the substrate microstructure. A larger value indicates a higher risk of infrared optical constant destabilization, which in turn exacerbates the coating thickness inversion error. The degree of variation represents the comprehensive risk of substrate optical parameter drift. A larger value indicates a more significant global spectral morphological distortion caused by changes in substrate processing conditions.

[0064] Step 3: Obtain the predicted thickness measurement error at the next moment based on all thickness measurement errors and variations before each moment, and obtain the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment with the time series change of the difference between the dual-path differential signal and the pre-collected ideal dual-path differential signal.

[0065] When measuring the thickness of antireflective coatings using the dual-path infrared reflectometry method, unpredictable dynamic drift in the substrate's optical parameters can cause distortion in the reflected signal from the measurement path. This makes it impossible to distinguish between the true coating thickness change and the distortion introduced by the substrate's optical parameter drift, leading to systematic deviations in the thickness results derived from the fixed Fresnel model.

[0066] Arrange the change degrees of all moments before each moment in chronological order to form a change sequence for each moment.

[0067] The change sequence and thickness measurement error sequence at each moment are used as input, the change sequence is used as the independent variable, and the thickness measurement error sequence is used as the dependent variable. A polynomial regression model is used. During the training phase, the polynomial regression model learns the mapping relationship between the degree of change and the thickness measurement error, outputs a multivariate fitting equation, and predicts the thickness measurement error at the next moment. This allows, without compensation, to predict the degree and direction of the thickness inversion result's deviation from the true value based on the basement fluctuation state at each moment, reflecting the theoretically expected deviation from the thickness measurement caused by basement fluctuation. When obtaining the multivariate fitting equation, the first 70% of the historical data is used as the training set, and the last 30% is used as the test set. The training process of the polynomial regression model is well known in the art and will not be described in detail in this application.

[0068] Furthermore, the difference between the dual-path differential signal at each moment and the ideal dual-path differential signal at each wavelength is calculated, and the central wavelength is used as , half-height width is A Gaussian weighting function is used to calculate the product of the difference at each wavelength and the weight coefficient output by the Gaussian weighting function. The sum of the product values ​​at all wavelengths at each moment is used as the key difference eigenvalue at each moment. The key difference eigenvalues ​​of all moments before each moment are arranged in time sequence to form a key difference sequence at each moment to quantify the overall distortion. The reason for using the Gaussian weighting function is that when calculating the difference between the dual-path differential signal and the ideal dual-path differential signal, considering that different wavelengths may contribute differently to the overall distortion, the Gaussian weighting function can weight the differences of different wavelengths, so that the difference within a specific wavelength range has a greater impact on the overall distortion, while the difference of other wavelengths has a relatively smaller impact on the overall distortion, thereby more accurately reflecting the overall distortion between the dual-path differential signal and the ideal dual-path differential signal.

[0069] Furthermore, a linear regression was performed on the change sequence and key difference sequence at each moment, with the change sequence as the independent variable and the key difference sequence as the dependent variable, to obtain the regression slope. The regression slope characterizes the linear sensitivity of the key difference characteristic value to the change degree. The larger the absolute value of the regression slope, the stronger the correlation between the distortion mode detected in the dual-path differential signal at each moment and the background fluctuation, indicating that the background drift is more likely to have caused unsuppressible non-common-mode interference.

[0070] Based on the above analysis, the substrate compensation factor at each moment is obtained through the regression slope at each moment and the predicted thickness measurement error at the next moment. The expression is:

[0071] Where, represents the base compensation factor at the i-th moment; norm() represents the normalization function; represents the predicted thickness measurement error at the next moment after the i-th moment; represents the regression slope at the i-th moment; Indicates the absolute value operation.

[0072] In this embodiment, the hyperbolic tangent function is used to obtain The normalized value of the hyperbolic tangent function is a well-known technology and will not be described in detail in this application.

[0073] It should be noted that the substrate compensation factor quantifies the comprehensive compensation amount of the thickness measurement error caused by the drift of the substrate optical parameters, integrating the prediction error and the correlation strength. When the substrate undergoes temperature or stress drift during the process, its infrared spectrum morphology distortion will asynchronously distort the measurement optical path signal. The larger the substrate compensation factor, the greater the compensation required during measurement. The schematic diagram of the substrate compensation factor acquisition process is shown in the figure. Figure 2 shown.

[0074] Step 4: Use the substrate compensation factor to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, use the substrate compensation factor and the dual-path differential signal, combined with the refractive index and extinction coefficient of the substrate, to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; use the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

[0075] Because the infrared optical parameters of antireflection coating substrates are susceptible to dynamic and continuous drift due to factors such as process temperature, doping gradients, or stress states, this drift results in asynchronous, non-common-mode correlation distortion between the reflected signals of the measurement and reference beams. When substrate drift occurs, the Fresnel model constructed using pre-stored substrate optical parameters can misinterpret this distortion as a change in coating thickness, resulting in systematic thickness measurement deviations that are difficult to eliminate using conventional differential analysis.

[0076] Therefore, it is necessary to design dynamic compensation and thickness calculation strategies based on the substrate compensation factor. The substrate compensation factor quantitatively characterizes the degree of distortion risk caused by the substrate fluctuation at each moment to the original thickness measurement result and the required compensation amount. Therefore, the substrate compensation factor at each moment is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment. Specifically: if the substrate compensation factor at each moment is less than the preset compensation threshold, it means that the substrate is relatively stable and there is no need to re-invert and calculate the thickness measurement value at each moment; when the substrate compensation factor at each moment is greater than or equal to the preset compensation threshold, it means that there is significant fluctuation in the substrate and the distortion risk is high, and the thickness measurement value at each moment needs to be re-inverted and calculated.

[0077] In this embodiment, the value of the preset compensation threshold is 0.3. The value of the preset compensation threshold is preset manually and the implementer can set it according to actual conditions. This application does not impose any special restrictions.

[0078] If it is necessary to recalculate the thickness measurement value at each moment, the objective function at each moment is constructed by combining the substrate compensation factor and the dual-path differential signal at each moment with the substrate's refractive index and extinction coefficient. This is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment. Specifically, the objective function at each moment is: the substrate's refractive index and extinction coefficient. The expression of the objective function at each moment is:

[0079] Where, Represents the objective function at the i-th moment; Min[ ] represents the minimum value operation; represents the base compensation factor at the i-th moment; R( ) represents the 2-norm operation; represents the dual optical path differential signal at the i-th moment; When solving the objective function using the LM nonlinear optimization algorithm, the model differential signal is calculated by combining the real-time refractive index and real-time extinction coefficient of the substrate with the Fresnel reflection formula; Indicates the difference between the real-time refractive index of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Indicates the difference between the real-time extinction coefficient of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Represents the preset weight coefficient. is the data fitting term, is a parameter prior constraint item, the preset value of the refractive index of the substrate is the pre-stored value in step 1, and the preset value of the extinction coefficient of the substrate is the pre-stored value in step 1.

[0080] In this embodiment, the value of the preset weight coefficient is 0.3. The value of the preset weight coefficient is preset manually and the implementer can set it according to actual conditions. This application does not impose any special restrictions.

[0081] It should be noted that: The larger it is, the more serious the substrate fluctuation distortion is, and a higher fitting weight is given to the data fitting term, forcing the inversion process to adjust the refractive index and extinction coefficient to better explain the reflection signal of the measurement light path beam at the i-th moment, thereby separating the influence of substrate drift. It is used to dynamically adjust the relative weight balance between the data fitting term and the parameter prior constraint term in the objective function. The larger the value, the stronger the weight of the data fitting term. and The process makes it more likely that and Interprets distortion in the reflected signal of the measurement path beam, effectively distinguishing and compensating for substrate drift; The smaller the value, the lower the weight of the data fitting term. and In the process, it is more inclined to trust the pre-stored values ​​of the substrate optical parameters.

[0082] By using the LM nonlinear optimization algorithm (Levenberg-Marquardt algorithm) to solve the objective function, the optimized and , by utilizing the optimized and The Fresnel model constructed is used to inversely calculate the thickness measurement value of the coating of the sample to be measured at each time. The process of solving the objective function by the LM nonlinear optimization algorithm is a well-known technology and will not be described in detail in this application.

[0083] Based on the same inventive concept as the above method, the embodiment of the present application further provides an anti-reflective coating thickness measurement system based on a dual-path infrared reflection method, comprising:

[0084] Infrared light source: used to emit infrared light in a wide spectrum or specific band;

[0085] Beam splitter: used to split the infrared light output by the infrared light source into two beams;

[0086] Measuring arm optical assembly: including lenses and reflectors, used to guide the light beam to accurately impinge on the coating surface of the sample to be measured and the coating surface of the standard sample at the Brewster angle;

[0087] Measuring detector: used to collect in real time the reflection signal of the measuring light path beam incident on the coating surface of the sample to be measured at the Brewster angle, and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at the Brewster angle;

[0088] Miniature infrared spectrum probe: installed on the exposed substrate surface adjacent to the coating area of ​​the sample to be tested, used to emit infrared light in real time and collect the reflected spectrum data of the substrate;

[0089] Signal processing unit: Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each moment, and obtain a dual-path differential signal; At each moment, use the pre-built Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured;

[0090] Performing principal component analysis on all reflectance spectrum data before each moment to obtain principal components, obtaining spectral characteristic values ​​at each moment by comparing the reflectance spectrum data at each moment with the principal components, and combining the peak position shift factor and peak height change factor obtained at each moment through the change of all reflectance spectrum data before each moment to obtain the degree of change at each moment;

[0091] Obtaining the thickness measurement error of the thickness measurement value at each moment compared to the preset target thickness, obtaining the predicted thickness measurement error at the next moment based on all the thickness measurement errors and variations before each moment, and obtaining the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment as the difference between the dual-path differential signal and the pre-acquired ideal dual-path differential signal changes in time series;

[0092] The substrate compensation factor is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, the substrate compensation factor and the dual-optical path differential signal are combined with the refractive index and extinction coefficient of the substrate to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function is used to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

[0093] In summary, the present application addresses the problem of gradual changes in infrared optical constants caused by temperature and stress drift on heterogeneous substrates. Principal component analysis can be used to extract the main variation patterns from a large amount of reflectance spectrum data. Spectral eigenvalues ​​can be calculated to quantify the overall degree of deviation of the substrate spectral data from the central state, effectively reflecting the overall drift of the substrate optical parameters. Peak position shift factors and peak height variation factors can be calculated to accurately capture positional and intensity changes in characteristic peaks, thereby characterizing specific changes in the substrate microstructure. Calculation of the degree of variation can comprehensively reflect the synergistic effect of substrate optical parameter drift and local microscopic perturbations, facilitating subsequent evaluation of whether re-inversion calculation of the coating thickness is necessary.

[0094] Furthermore, by using the thickness measurement error and variation at historical moments to predict the thickness measurement error at the next moment, the possible deviation trend and degree of the coating thickness measurement results can be predicted in advance. At the same time, the linear correlation strength between the difference between the real-time dual-path differential signal and the ideal dual-path differential signal compared to the variation is combined to dynamically generate a compensation factor, eliminating random noise interference, which is conducive to accurately quantifying the degree of compensation for the substrate optical constants.

[0095] Furthermore, when the coating thickness needs to be re-inverted and calculated, the parameters of the Fresnel model can be dynamically adjusted by introducing a substrate compensation factor and a dual-optical path differential signal, and combining the refractive index and extinction coefficient of the substrate to construct an objective function. This allows the Fresnel model to more accurately reflect the substrate situation, effectively separate the distortion signal introduced by substrate drift from the true coating thickness change signal, and eliminate the systematic deviation caused by non-common mode distortion, thereby improving the adaptability of the Fresnel model to substrate drift and the inversion accuracy, and improving the stability and accuracy of the anti-reflection coating thickness measurement.

[0096] The flowcharts and block diagrams in the accompanying drawings show the possible implementation architectures, functions and operations of the systems, methods and computer program products according to the embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, program segment or part of the code, and the module, program segment or part of the code contains one or more executable instructions for implementing the specified logical functions. In some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, or they can sometimes be executed in the opposite order, which can depend on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different boxes can also occur in an order different from that disclosed in the description, and sometimes there is no specific order between different operations or steps. For example, two consecutive operations or steps can actually be executed substantially in parallel, or they can sometimes be executed in the opposite order, which can depend on the functions involved. Each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented by a dedicated hardware-based system that performs the specified function or action, or may be implemented by a combination of dedicated hardware and computer instructions.

[0097] It is obvious to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and that the present application can be implemented in other specific forms without departing from the basic characteristics of the present application. Therefore, from all perspectives, the above embodiments of the present application should be regarded as exemplary and non-restrictive.

Claims

1. Anti-reflection coating thickness measurement method based on dual-path infrared reflection method, characterized in that: The method comprises the following steps: Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each time, and obtain a dual-path differential signal; at each time, use the pre-built Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured; and collect the reflection spectrum data of the exposed substrate in real time; Performing principal component analysis on all reflectance spectrum data before each moment to obtain principal components, obtaining spectral characteristic values ​​at each moment by comparing the reflectance spectrum data at each moment with the principal components, and combining the peak position shift factor and peak height change factor obtained at each moment through the change of all reflectance spectrum data before each moment to obtain the degree of change at each moment; Obtaining the thickness measurement error of the thickness measurement value at each moment compared to the preset target thickness, obtaining the predicted thickness measurement error at the next moment based on all the thickness measurement errors and variations before each moment, and obtaining the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment as the difference between the dual-path differential signal and the pre-acquired ideal dual-path differential signal changes in time series; The substrate compensation factor is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, the substrate compensation factor and the dual-optical path differential signal are combined with the refractive index and extinction coefficient of the substrate to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function is used to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

2. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 1, wherein: The process of obtaining the spectral characteristic value is as follows: The reflection spectrum matrix of each moment is constructed by the reflection spectrum data of all moments before each moment, where the row index of the reflection spectrum matrix is ​​time and the column index is wavelength; the principal component analysis algorithm is used to obtain the first preset number of principal components of the reflection spectrum matrix of each moment, and the score value of the reflection spectrum data of each moment in the direction of each principal component is obtained. The spectral characteristic value is the 2 norm of the vector composed of the preset number of score values ​​at each moment.

3. The method for measuring thickness of anti-reflective coating based on dual-path infrared reflection method according to claim 1, characterized in that: The process of obtaining the peak shift factor is as follows: Obtain the peak position and peak height of each characteristic peak in the reflectance spectrum data at each moment; record the characteristic peak with the largest peak height in the reflectance spectrum data at each moment as the key characteristic peak; calculate the difference in the peak position of the key characteristic peak between each moment and the previous moment; and use the average of the differences between all moments before each moment and the previous moment as the peak position shift factor for each moment.

4. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 3, wherein: The process of obtaining the peak height variation factor is as follows: Calculate the difference in peak height of the key characteristic peak between each moment and the previous moment; and take the average of the difference between all moments before each moment and the previous moment as the peak position shift factor of each moment.

5. The method for measuring thickness of anti-reflective coating based on dual-path infrared reflection method according to claim 1, characterized in that: The degree of change is the product of the peak position shift factor, the peak height change factor and the spectral characteristic value at each moment.

6. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 1, wherein: The obtaining of the predicted thickness measurement error at the next moment at each moment includes: Arrange the thickness measurement errors and changes at all moments before each moment in time sequence to form a thickness measurement error sequence and a change sequence at each moment; For each moment, the change sequence is used as the independent variable and the thickness measurement error sequence is used as the dependent variable. Combined with the polynomial regression model, the multivariate fitting equation at each moment is obtained, and the predicted thickness measurement error at the next moment is obtained through the multivariate fitting equation at each moment.

7. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 1, wherein: The process of obtaining the substrate compensation factor is as follows: Calculate the difference between the dual-path differential signal at each moment and the pre-collected ideal dual-path differential signal at each wavelength, calculate the product value of the difference at each wavelength and the weight coefficient output by the preset Gaussian weight function, and use the sum of the product values ​​at all wavelengths at each moment as the key difference feature value at each moment; arrange the key difference feature values ​​of all moments before each moment in time sequence to form a key difference sequence at each moment; Perform a univariate linear regression on the change sequence and key difference sequence at each moment, taking the change sequence as the independent variable and the key difference sequence as the dependent variable, and obtain the regression slope at each moment; The substrate compensation factor is a normalized value of the product of the absolute value of the regression slope and the predicted thickness measurement error.

8. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 1, wherein: The method for evaluating whether it is necessary to re-invert and calculate the thickness measurement value at each moment is as follows: if the substrate compensation factor at each moment is less than a preset compensation threshold, it is not necessary to re-invert and calculate the thickness measurement value at each moment; otherwise, it is necessary to re-invert and calculate the thickness measurement value at each moment.

9. The method for measuring thickness of an anti-reflective coating based on a dual-path infrared reflection method according to claim 1, wherein: The expression of the objective function is: Where, Represents the objective function at the i-th moment; Min[ ] represents the minimum value operation; represents the base compensation factor at the i-th moment; R( ) represents the 2-norm operation; represents the dual optical path differential signal at the i-th moment; When solving the objective function using the LM nonlinear optimization algorithm, the model differential signal is calculated by combining the real-time refractive index and real-time extinction coefficient of the substrate with the Fresnel reflection formula; Indicates the difference between the real-time refractive index of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Indicates the difference between the real-time extinction coefficient of the substrate and its preset value when solving the objective function using the LM nonlinear optimization algorithm; Indicates the preset weight coefficient.

10. An anti-reflection coating thickness measurement system based on a dual-path infrared reflection method, applying the anti-reflection coating thickness measurement method based on a dual-path infrared reflection method in claim 1, characterized in that: The system contains: Miniature infrared spectrum probe: used to emit infrared light in real time and collect reflectance spectrum data of the exposed substrate; Signal processing unit: Obtain the difference between the reflection signal of the measurement light path beam incident on the coating surface of the sample to be measured and the reflection signal of the reference light path beam incident on the coating surface of the standard sample at each moment, and obtain a dual-path differential signal; At each moment, use the pre-built Fresnel model to invert the reflection signal of the measurement light path beam to obtain the thickness measurement value of the coating of the sample to be measured; Performing principal component analysis on all reflectance spectrum data before each moment to obtain principal components, obtaining spectral characteristic values ​​at each moment by comparing the reflectance spectrum data at each moment with the principal components, and combining the peak position shift factor and peak height change factor obtained at each moment through the change of all reflectance spectrum data before each moment to obtain the degree of change at each moment; Obtaining the thickness measurement error of the thickness measurement value at each moment compared to the preset target thickness, obtaining the predicted thickness measurement error at the next moment based on all the thickness measurement errors and variations before each moment, and obtaining the substrate compensation factor at each moment by combining the degree of change of all the variations before each moment as the difference between the dual-path differential signal and the pre-acquired ideal dual-path differential signal changes in time series; The substrate compensation factor is used to evaluate whether it is necessary to re-invert and calculate the thickness measurement value at each moment; if necessary, the substrate compensation factor and the dual-optical path differential signal are combined with the refractive index and extinction coefficient of the substrate to construct an objective function at each moment, which is used to optimize the parameters of the Fresnel model for inverting the thickness measurement value at each moment, specifically: the refractive index and extinction coefficient of the substrate; the Fresnel model constructed using the refractive index and extinction coefficient of the substrate obtained by solving the objective function is used to invert and calculate the thickness measurement value of the coating of the sample to be measured at each moment.

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