A method for film thickness analysis

Abstract

The present invention provides a film thickness analysis method, which calculates the measured reflectivity of a sample to be measured according to the measured light intensity of the sample to be measured; matches the measured reflectivity with the theoretical reflectivity in the simulation spectral library; obtains the theoretical reflectivity corresponding to the minimum variance, and takes the film thickness value of each corresponding layer as the initial film thickness value of the sample to be measured; iteratively optimizes the initial film thickness value of the sample to be measured based on the LM nonlinear regression algorithm to solve the optimal film thickness value of the sample to be measured; calculates the correlation between the measured reflectivity and the theoretical reflectivity; if the correlation is less than the set threshold, detrends the measured reflectivity, and then rematches it in the simulation spectral library to obtain the film thickness value. The method of the present invention can efficiently and accurately simulate the optical reflection characteristics of a multi-layer thin film system by combining the measurement data of a spectrometer and simulation calculations, match with the measured data, provide accurate material and structure information, and provide important technical support for the fields of modern optics and materials science.

Description

Technical Field

[0001] The present invention relates to the field of optical scattering measurement, and more specifically, to a film thickness analysis method applicable to spectral analysis of complex multi-layer thin film systems. Background Art

[0002] In the fields of modern optics and materials science, the design and analysis of multi-layer thin film systems are of great significance. Multi-layer thin films are widely used in optical coating, semiconductor manufacturing, biosensors and other high-tech fields. The system realizes specific optical functions by controlling the reflection, transmission and absorption characteristics of light. Optical scattering measurement is an analytical technique that uses the scattering phenomenon that occurs when light interacts with matter to obtain the physical properties and structural information of a sample. When light encounters the surface of a substance or passes through a medium, scattering occurs, and the distribution, intensity and polarization state of this scattered light carry important information about the surface characteristics and internal structure of the substance.

[0003] With the development of technology, accurately measuring and simulating the optical properties of multi-layer thin film systems has become the focus of research. These systems are usually composed of multiple layers of different materials, and the thickness and refractive index of each layer of material have a significant impact on the reflection and transmission characteristics of light. Traditional calculation methods involve a large number of matrix operations and complex optical theories in calculating the optical properties of multi-layer thin film systems, with high computational complexity and low efficiency when dealing with multi-layer structures; due to the complexity of multi-layer thin film systems, traditional calculation methods have deficiencies in accuracy and are difficult to accurately simulate the optical properties of actual systems; and the existing technology is difficult to flexibly handle multi-layer thin film systems with different material and thickness combinations, lacking adaptability and scalability. Summary of the Invention

[0004] In order to overcome the deficiencies in the film thickness analysis technology in the prior art, the present invention provides a film thickness analysis method in optical scattering measurement, which well solves the problem of large error in solving parameters due to large difference in data scales.

[0005] A film thickness analysis method provided by the present invention includes:

[0006] Step S1, obtaining the measured light intensity of the sample to be measured, and calculating the measured reflectivity of the sample to be measured according to the measured light intensity;

[0007] Step S2, calculating the variance between the measured reflectivity and each theoretical reflectivity in the simulation spectral library, where the correspondence between the thickness value of each layer of the multi-layer thin film system and the theoretical reflectivity is constructed in the simulation spectral library;

[0008] Step S3, obtaining the theoretical reflectivity corresponding to the minimum variance, and taking the thickness value of each corresponding layer as the initial film thickness value of the sample to be measured;

[0009] Step S4: Iteratively optimize the initial film thickness value of the sample to be measured based on the LM non-linear regression algorithm, and solve for the optimal film thickness value of the sample to be measured;

[0010] Step S5: Calculate the correlation between the measured reflectivity and the theoretical reflectivity corresponding to the optimal film thickness value;

[0011] Step S6: If the correlation is less than the set threshold, perform detrending processing on the measured reflectivity to obtain the measured spectrum after detrending processing, and return to Step S2; if the correlation is greater than or equal to the set threshold, end the process.

[0012] A film thickness analysis method provided by the present invention calculates the measured reflectivity of a sample to be measured based on the measured light intensity of the sample to be measured; matches the measured reflectivity with the theoretical reflectivity in the simulation spectrum library; obtains the theoretical reflectivity corresponding to the minimum variance, and uses the corresponding film thickness value of each layer as the initial film thickness value of the sample to be measured; iteratively optimize the initial film thickness value of the sample to be measured based on the LM non-linear regression algorithm, and solve for the optimal film thickness value of the sample to be measured; calculate the correlation between the measured reflectivity and the theoretical reflectivity; if the correlation is less than the set threshold, perform detrending processing on the measured reflectivity, and re-match in the simulation spectrum library to obtain the film thickness value. The method of the present invention can efficiently and accurately simulate the optical reflection characteristics of a multi-layer thin film system by combining spectrometer measurement data and simulation calculations, match with the measured data, provide accurate material and structure information, and provide important technical support for the fields of modern optics and materials science. Description of the Drawings

[0013] Figure 1 It is a flowchart of a film thickness analysis method provided by the present invention;

[0014] Figure 2 It is an overall process schematic diagram of a film thickness analysis method;

[0015] Figure 3 It is a schematic diagram of the fitting reflectivity effect using LM iterative solution;

[0016] Figure 4-1 It is a schematic diagram of the fitting effect without using the detrending algorithm;

[0017] Figure 4-2 It is a schematic diagram of the fitting effect using the detrending algorithm. Detailed Embodiments

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. Additionally, the technical features in each embodiment or individual embodiment provided by the present invention can be combined with each other arbitrarily to form a feasible technical solution. Such combination is not restricted by the order of steps and / or the structural composition mode, but must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0019] To solve the problems raised in the background art, the present invention proposes a film thickness analysis method applied to optical scattering measurement. By combining the measurement data of a spectrometer and simulation calculations, this method can efficiently and accurately simulate the optical reflection characteristics of a multi-layer thin film system, match with the measured data, provide accurate material and structural information, and provide important technical support for the fields of modern optics and materials science.

[0020] See Figure 1 , which is a flowchart of a film thickness analysis method provided by the present invention. The method mainly includes:

[0021] Step S1: Obtain the measured light intensity of the sample to be measured, and calculate the measured reflectivity of the sample to be measured based on the measured light intensity.

[0022] Among them, step S1, obtaining the measured light intensity of the sample to be measured and calculating the measured reflectivity of the sample to be measured based on the measured light intensity, includes:

[0023] Collect the measured light intensity of the sample to be measured at N measurement wavelength points through a spectrometer, and calculate the corresponding measured reflectivity based on the measured light intensity at each measurement wavelength point:

[0024]

[0025] Normalize the measured reflectivity:

[0026]

[0027] Among them, I sample,i represents the measured light intensity of the sample to be measured at the i-th measurement wavelength point, I dark,i represents the measured light intensity measured at the i-th measurement wavelength point when there is no light irradiating the sample to be measured, which is used to eliminate the noise influence of the instrument itself. R std,idenotes the reflectivity of the known standard sample at the i-th measurement wavelength point, denotes the minimum measured reflectivity among all measurement wavelength points, denotes the maximum measured reflectivity among all measurement wavelength points, is the measured reflectivity at the i-th measurement wavelength point after normalization.

[0028] It can be understood that light is incident on the surface of the thin film from the air at a certain angle. When this incident light reaches the surface of the thin film, it is divided into two parts: one part is reflected back into the air, and the other part enters the thin film. When the incident light reaches the surface of the thin film, part of the light is reflected. The direction of this part of the reflected light is symmetric with the incident light, forming the first reflected ray. The light that enters the thin film propagates in the thin film and undergoes multiple reflections between the bottom surface and the top surface of the thin film. At each reflection, part of the light is transmitted into the substrate, forming transmitted rays. The transmitted light is the light that finally penetrates the thin film and enters the substrate after multiple reflections in the thin film. These rays undergo multiple reflections and interference during the process of penetrating the thin film, resulting in changes in their phase and intensity. The data such as the spectral band, incident angle, and topography measured by the spectrometer can be used to accurately describe and simulate the propagation process of this light in the multi-layer thin film system.

[0029] Thus, the spectrometer can give the measured spectral band and light intensity, that is, collect the light intensity information (referred to as the measured light intensity) at multiple measurement wavelength points (for example, N measurement wavelength points in the spectral band) of the spectrometer, and calculate the measured reflectivity at each measurement wavelength point according to the above formula for calculating the measured reflectivity, and normalize the measured reflectivity at each measurement wavelength point using the above formula for calculating the theoretical reflectivity.

[0030] Step S2, calculate the variance between the measured reflectivity and each theoretical reflectivity in the simulation spectral library, and the corresponding relationship between the thickness value of each layer of the multi-layer thin film system and the theoretical reflectivity is constructed in the simulation spectral library.

[0031] Among them, according to the input number of thin film layers and the thickness range of each layer of the thin film, multiple possible thickness values of each layer of the thin film are uniformly generated; the thickness values of each layer of the thin film are taken according to the multiple possible thickness values of each layer of the thin film to form different thin film structure combinations; for each thin film structure combination, calculate the optical theoretical reflectivity, generate the corresponding relationship between the thickness value of each layer of the multi-layer thin film system and the theoretical reflectivity, and construct the simulation spectral library.

[0032] It is understandable that according to the parameters input by the user (such as the number of thin film layers, the thickness range of each layer, etc.), the possible thickness values of each thin film layer are uniformly generated. That is, there are multiple values for the thickness of each thin film layer. Then, different thin film structures can be formed by taking different thickness values for each thin film layer. Calculate the optical theoretical reflectivity of each thin film structure, construct a simulation spectral library, and save the corresponding relationship between the thickness value (hereinafter referred to as the thickness value) of each thin film layer and the theoretical reflectivity in the simulation spectral library.

[0033] Among them, the method for calculating the theoretical reflectivity according to the thickness value of the thin film structure is as follows:

[0034] Define the possibilities of different thin film structure combinations, and calculate the optical theoretical reflectivity for each thickness combination. Define the characteristic matrix D of the k-th thin film layer of the multi-layer thin film system at each measurement wavelength point k and the phase change matrix P k . The characteristic matrix describes the behavior of light at the interface, while the phase change matrix describes the phase change of light when propagating in the layer.

[0035] Among them, for p-polarized light, the characteristic matrix D of the k-th thin film layer k,p is expressed as:

[0036]

[0037] For s-polarized light, the characteristic matrix D of the k-th thin film layer k,s is expressed as:

[0038]

[0039] The phase change matrix P k is expressed as:

[0040]

[0041] The phase change angle β k is:

[0042]

[0043] Among them, θ k is the incident angle of the k-th thin film layer, n k is the refractive index of the k-th thin film layer, d k is the thickness value of the k-th thin film layer, and λ is the measurement wavelength.

[0044] According to the characteristic matrix D k and the phase change matrix P k of each thin film layer, calculate the transmission matrix M of each thin film structure combination. The transmission matrix M of the entire multi-layer thin film structure can be expressed as the product of the characteristic matrices and phase change matrices of each layer:

[0045]

[0046] Among them, is the inverse matrix of the characteristic matrix of the first-layer thin film, is the inverse matrix of the characteristic matrix of the k-th layer thin film, and j is the number of thin film layers.

[0047] Calculate the reflection coefficient r according to the transfer matrix M:

[0048]

[0049] Among them, M 21 and M 11 are the elements of the transfer matrix M.

[0050] According to the reflection coefficients r p and r s of p-polarized light and s-polarized light, the total reflectance R (i.e., the theoretical reflectance) of each thin film structure combination is:

[0051]

[0052] Normalize the theoretical reflectance R to:

[0053]

[0054] Among them, represents the minimum theoretical reflectance among all measured wavelength points, represents the maximum theoretical reflectance among all measured wavelength points, is the normalized theoretical reflectance.

[0055] Through the above method, the theoretical reflectance of each thin film structure with different thickness values at different measured wavelength points can be calculated, and the corresponding relationship between the thickness value and the theoretical reflectance is saved in the simulation spectrum library.

[0056] Match the measured reflectance calculated in step S1 with the theoretical reflectance in the simulation spectrum library. During the matching process, the variance between the measured reflectance and each theoretical reflectance in the simulation spectrum library can be calculated, and the variance can be expressed as:

[0057]

[0058] Among them, represents the measured reflectance at the i-th measured wavelength point, represents the theoretical reflectance at the i-th measured wavelength point, and N is the number of measured wavelength points.

[0059] Step S3, obtain the theoretical reflectance corresponding to the minimum variance, and use the corresponding thickness value of each layer of thin film as the initial film thickness value of the sample to be measured.

[0060] It is understandable that according to the minimum variance, the theoretical reflectivity that is initially most similar to the measured reflectivity is determined, and the thickness corresponding to the theoretical reflectivity with the minimum variance is considered as the initial thickness value d of the sample to be measured. 0

[0061] Step S4: Based on the LM nonlinear regression algorithm, perform iterative optimization on the initial film thickness value of the sample to be measured to solve the optimal film thickness value of the sample to be measured.

[0062] It is understandable that according to the initial thickness value d obtained in the previous step 0 , use the nonlinear regression algorithm to iteratively find the optimal solution.

[0063] In the process of measuring the film thickness, combined with the single-layer film structure model, using the Levenberg-Marquardt (LM) algorithm can effectively optimize the calculation of the film thickness. The following are the detailed step descriptions and formula derivations:

[0064] First, obtain the initial film thickness value d of the sample to be measured from step S3 0 , and then calculate the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the initial film thickness value d 0 :

[0065]

[0066] where N is the number of measurement wavelength points, is the measured reflectivity at the i-th measurement wavelength point, is the initial film thickness value d 0 and is the theoretical reflectivity at the i-th measurement wavelength point corresponding to the initial film thickness value d.

[0067] Taking the minimization of the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the initial film thickness value d 0 as the optimization objective, solve for the film thickness update step δd 1 ;

[0068] Based on the film thickness update step δd 1 perform the first update on the initial film thickness value d 0 to obtain d 1 = d 0 + δd 1 , and based on the updated film thickness value d 1 , calculate the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the updated film thickness value d 1 again;

[0069] Calculate the film thickness update step δd for the second update based on the mean square error MSE after the first update 2 , and for the initial film thickness value d0 Perform the second update to obtain d 2 = d 1 + δd 2 , and continuously update the initial film thickness value until the calculated mean square error MSE is less than or equal to the set deviation threshold to obtain the optimal film thickness value.

[0070] Among them, the method for solving the film thickness update step size δd includes:

[0071] Perform a first-order Taylor expansion approximation on the theoretical reflectivity R theory (d 1 ) as:

[0072]

[0073] Among them, δd 1 represents the small increment of the film thickness value, is the partial derivative at the initial film thickness value d 0 ;

[0074] Taking the minimization of the mean square error MSE between the measured reflectivity and the theoretical reflectivity as the optimization objective, solve for δd 1 to minimize the following relationship:

[0075]

[0076] To minimize the above relationship, δd needs to satisfy the following relationship equation:

[0077]

[0078] Among them, μ > 0 is the damping factor, and ε is the variance between the measured reflectivity and the theoretical reflectivity; solve the above relationship equation to obtain the film thickness update step size δd 1 :

[0079]

[0080] For each update of the initial film thickness value d 0 , calculate the corresponding film thickness update step size δd h , and δd h represents the film thickness update step size when the initial film thickness value d 0 is updated for the nth time.

[0081] According to the film thickness value after each update, calculate the corresponding theoretical reflectivity for the updated film thickness value based on the method of calculating the theoretical reflectivity in step S2. Then calculate the mean square error MSE between the measured reflectivity and the theoretical reflectivity, and determine whether the mean square error MSE is less than the set error threshold. If it is less than, end the iterative update process and obtain the updated film thickness value at this time. If the mean square error MSE is still greater than the set error threshold, then update the film thickness value again based on the film thickness value d 1 On this basis, continuously update the film thickness value until the calculated mean square error MSE is less than the set error threshold, and obtain the film thickness value at this time, which is the optimal film thickness value of the sample to be measured. Figure 3 Fig. Figure 3 shows a schematic diagram of the fitting reflectivity effect solved by LM iteration. Among them, the red curve represents the graph of the measured reflectivity versus wavelength, and the blue curve represents the graph of the theoretical reflectivity versus wavelength. The abscissa is the wavelength, and the ordinate is the reflectivity.

[0082] Step S5, calculate the correlation between the measured reflectivity and the theoretical reflectivity corresponding to the optimal film thickness value.

[0083] It can be understood that when the thickness value of a single-layer film in the film structure is relatively large, sometimes the fitting effect is also very poor just by normalizing the measured reflectivity. In response to this situation, based on the previous algorithm steps, an automatic detrending algorithm for the measured reflectivity is added to improve the fitting effect. After calculating the measured reflectivity and the theoretical reflectivity corresponding to the optimal film thickness value in the above steps, by calculating the correlation gof between the measured reflectivity R meas and the theoretical reflectivity R theory to determine whether detrending is needed. Among them, the correlation gof between the measured reflectivity R meas and the theoretical reflectivity R theory can be calculated by the following method:

[0084] a. Calculate the mean value:

[0085] First, calculate the mean values of the measured reflectivity and the theoretical reflectivity. The formulas are as follows:

[0086]

[0087] where N represents the number of measured wavelength points, R meas,i represents the measured reflectivity at the i-th measured wavelength point, R theory,i represents the theoretical reflectivity at the i-th measured wavelength point, S meas represents the mean value of the measured reflectivity, and S theory represents the mean value of the theoretical reflectivity.

[0088] b. Centralize the measured reflectivity and the theoretical reflectivity respectively based on their mean values:

[0089] R′ meas,i = R meas,i - S meas , R′ theory,i = R theory,i - S theory ;

[0090] Wherein, R′ meas,i represents the de-centered measured reflectance at the i-th measurement wavelength point, and R′ theory,i represents the de-centered theoretical reflectance at the i-th measurement wavelength point.

[0091] c. Calculate the mean value d of the centered measured reflectance meas and the mean value d of the theoretical reflectance theory :

[0092]

[0093] d. Calculate the variance r of R' meas and the variance f of R' theory :

[0094]

[0095] e. Calculate the covariance rf between the measured reflectance and the theoretical reflectance:

[0096]

[0097] f. Calculate the correlation gof between the measured reflectance and the theoretical reflectance, and normalize it to between [0, 1]:

[0098]

[0099] Step S6, if the correlation is less than the set threshold, perform detrending on the measured reflectance to obtain the detrended measured spectrum, and return to Step S2; if the correlation is greater than or equal to the set threshold, end the process.

[0100] It is understandable that if the correlation between the measured reflectance and the theoretical reflectance is less than the set threshold, detrending needs to be performed on the measured reflectance. The method for detrending the measured reflectance is:

[0101] Based on the measured reflectances at multiple measurement wavelength points, fit the measured reflectance based on a third-order polynomial. The third-order polynomial fitting formula is:

[0102] R meas (λ) = a 3 λ 3 + a 2 λ 2 + a1 λ + a 0 ;

[0103] where a = [a 3 , a 2 , a 1 , a 0 T is the polynomial coefficient;

[0104] Based on the least squares method, a fitting objective function is established, and the objective function is to minimize the sum of the squares of the errors between the measured reflectance and the fitted measured reflectance;

[0105]

[0106] Solve the objective function to obtain a = [a 3 , a 2 , a 1 , a 0 T .

[0107] Calculate the fitted reflectance at each measured wavelength point:

[0108] R fit，i = (a 3 λ i 3 + a 2 λ i 2 + a 1 λ i + a 0 )) 2 ;

[0109] Perform detrending on the measured reflectance:

[0110] R detrend,i = R meas,i - R fit,i ;

[0111] where R detrend,i is the detrended measured reflectance at the i-th measured wavelength point, and R meas,i is the measured reflectance at the i-th measured wavelength point.

[0112] Based on the detrended measured reflectance, execute step S2, that is, perform matching in the simulation spectral library, and by executing steps S2 - S4 again, solve the optimal film thickness value of the sample to be measured.

[0113] where, Figure 4-1 is the schematic diagram of the fitting reflectance effect of the LM iterative solution without using the detrending algorithm, Figure 4-2 ​​Schematic diagram of the fitting reflectivity effect by LM iterative solution using the detrending algorithm. Among them, the red curve represents the graph of the measured reflectivity versus wavelength, and the blue curve represents the graph of the theoretical reflectivity versus wavelength. The abscissa is the wavelength, and the ordinate is the reflectivity. From Figure 4-1 and Figure 4-2 it can be seen that the fitting reflectivity effect by LM iterative solution using the detrending algorithm is significantly better.

[0114] A film thickness analysis method provided by the present invention has the following beneficial effects compared with the prior art:

[0115] (1) In optical scatterometry, due to the large difference in data scales, it often leads to relatively large errors in the solved parameters. By normalization processing, the present invention can effectively reduce the influence of data scale differences on the solution results, and improve the matching accuracy and reliability.

[0116] (2) It is difficult for traditional methods to efficiently and accurately match experimental measurement data and simulation calculation data. By constructing a simulation spectral library and combining the LM algorithm and the automatic detrending algorithm, the present invention can quickly find the simulation reflectivity most similar to the data to be measured, and achieve the precise matching of experimental data and simulation data.

[0117] It should be noted that in the above embodiments, the descriptions of the various embodiments have their own emphases. For the parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0118] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic inventive concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0119] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A film thickness analysis method, characterized in that: include: Step S1, obtaining the measured light intensity of the sample to be tested, and calculating the measured reflectivity of the sample to be tested according to the measured light intensity; Step S2, calculating the variance between the measured reflectivity and each theoretical reflectivity in a simulation spectrum library, wherein the simulation spectrum library constructs a corresponding relationship between the thickness value of each layer of a multilayer thin film system and the theoretical reflectivity; Step S3, obtaining the theoretical reflectivity corresponding to the minimum variance, and taking the corresponding thickness value of each layer of the thin film as the initial value of the film thickness of the sample to be tested; Step S4, iteratively optimizing the initial value of the film thickness of the sample to be tested based on the LM nonlinear regression algorithm to solve the optimal film thickness value of the sample to be tested; Step S5, calculating the correlation between the measured reflectivity and the theoretical reflectivity corresponding to the optimal film thickness value; Step S6, if the correlation is less than the set threshold, detrending the measured reflectance, obtaining the measured spectrum after detrending, and returning to step S2; if the correlation is greater than or equal to the set threshold, the process ends; The step S1, obtaining the measured light intensity of the sample to be tested, and calculating the measured reflectivity of the sample to be tested according to the measured light intensity, includes: The spectrometer collects the measured light intensity of the sample to be tested at N measuring wavelength points, and calculates the corresponding measured reflectivity according to the measured light intensity at each measuring wavelength point: The measured reflectance is normalized: Among them, I sample,i It represents the measured light intensity of the sample to be tested at the i-th measurement wavelength point, I dark,i It represents the measured light intensity at the i-th measurement wavelength point when there is no light irradiating the sample to be measured, R std,i represents the reflectance of a known standard sample at the i-th measurement wavelength point, Indicates the minimum measured reflectance among all measured wavelength points, Indicates the maximum measured reflectance among all measured wavelength points, The reflectance is measured at the normalized i-th measurement wavelength point.

2. The film thickness analysis method according to claim 1, characterized in that: Build a simulated spectral library, including: According to the input number of film layers and the thickness range of each film layer, multiple possible thickness values ​​of each film layer are uniformly generated; The thickness value of each film layer is determined according to the possible multiple thickness values ​​of each film layer to form different film structure combinations; For each combination of thin film structures, the theoretical optical reflectivity is calculated, the corresponding relationship between the thickness value of each layer of the multilayer thin film system and the theoretical reflectivity is generated, and a simulation spectrum library is constructed.

3. The film thickness analysis method according to claim 2, characterized in that: For each combination of film structures, the optical theoretical reflectivity is calculated, including: Define the characteristic matrix Dk and phase change matrix Pk of the kth layer of the multilayer film system at each measurement wavelength point, where for p-polarized light: For s-polarized light: Phase change matrix P k : The phase change angle βk is: Among them, θ k is the incident angle of the kth film, n k is the refractive index of the kth film layer, d k is the thickness of the kth film layer, and λ is the measurement wavelength; According to the characteristic matrix D of each film k And the phase change matrix P k , calculate the transmission matrix M of each film structure combination: in, is the inverse matrix of the characteristic matrix of the first film, is the inverse matrix of the characteristic matrix of the k-th film, j is the number of film layers; According to the transmission matrix M, the reflection coefficient r is calculated: Among them, M 21 and M 11 are the elements of the transmission matrix M; According to the reflection coefficient r of p-polarized light and s-polarized light p and r s , the theoretical reflectivity R of each film structure combination is: The theoretical reflectivity R is normalized to: in, Represents the minimum theoretical reflectivity among all measured wavelength points, Represents the maximum theoretical reflectivity among all measured wavelength points, is the normalized theoretical reflectivity; According to the thickness value of each film layer, the theoretical reflectivity at each measuring wavelength point is calculated.

4. The film thickness analysis method according to claim 1, characterized in that: The step S2, calculating the variance between the measured reflectivity and each theoretical reflectivity in the simulation spectrum library, comprises: in, represents the measured reflectance at the i-th measurement wavelength point, represents the theoretical reflectivity of the i-th measurement wavelength point, and N is the number of measurement wavelength points.

5. The film thickness analysis method according to claim 1, characterized in that: The step S4, iteratively optimizing the initial value of the film thickness of the sample to be tested based on the LM nonlinear regression algorithm to solve the optimal film thickness value of the sample to be tested, includes: Calculate the mean square error (MSE) between the measured reflectivity and the theoretical reflectivity corresponding to the initial value of the film thickness: Where N is the number of measurement wavelength points, is the measured reflectance at the ith measurement wavelength point, is the theoretical reflectivity at the i-th measurement wavelength point corresponding to the initial value of film thickness d0; Taking the minimization of the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the initial value of the film thickness d0 as the optimization goal, the film thickness update step δd1 is solved; The initial film thickness value d0 is updated for the first time based on the film thickness update step δd1 to obtain d1=d0+δd1, and based on the updated film thickness value d1, the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the updated film thickness value d1 is calculated again; The second updated film thickness update step δd2 is calculated based on the mean square error MSE after the first update, and the initial value of the film thickness d0 is updated for the second time to obtain d2 = d1 + δ d 2. The optimal film thickness value is obtained by continuously updating the initial value of the film thickness until the calculated mean square error (MSE) is less than or equal to the set deviation threshold.

6. The film thickness analysis method according to claim 5, characterized in that: The method takes minimization of the mean square error MSE between the measured reflectivity and the theoretical reflectivity corresponding to the initial value d0 of the film thickness as the optimization goal, and solves the film thickness update step δd1, including: Theoretical reflectivity R theory (d1) is approximated by the first-order Taylor expansion: Among them, δd1 represents a small increment of film thickness value, is the partial derivative at the initial value of film thickness d0; Taking the minimization of the mean square error MSE between the measured reflectivity and the theoretical reflectivity as the optimization goal, δd1 is solved to minimize the following relationship: In order to minimize the above relationship, δd needs to satisfy the following relationship equation: Among them, μ>0 is the damping factor, ε is the variance between the measured reflectivity and the theoretical reflectivity; By solving the above relationship equation, the film thickness update step δd1 is obtained: Each time the initial value of the film thickness d0 is updated, the corresponding film thickness update step δd is calculated h ,δd h Indicates the film thickness update step size when the initial film thickness value d0 is updated for the nth time.

7. The film thickness analysis method according to claim 1, characterized in that: Step S5, calculating the correlation between the measured reflectivity and the theoretical reflectivity corresponding to the optimal film thickness value, comprising: Calculate the mean of the measured reflectivity and the mean of the theoretical reflectivity corresponding to the optimal film thickness value: Where N represents the number of measurement wavelength points, R meas,i represents the measured reflectance at the i-th measurement wavelength point, R theory,i represents the theoretical reflectivity at the i-th measurement wavelength point; The measured reflectivity and theoretical reflectivity are centered based on the mean value of the measured reflectivity and the mean value of the theoretical reflectivity, respectively. The formula is as follows: R’ meas,i =R meas,i -S meas ,R’ theory,i =R theory,i -S theory ; Calculate the mean of the measured reflectivity after decentralization and the mean of the theoretical reflectivity corresponding to the optimal film thickness value: Calculate R' meas The variance r and R' theory The variance f is: Compute the covariance: Calculate the correlation gof and standardize it to [0,1]:

8. The film thickness analysis method according to claim 1, characterized in that: The step S6, if the correlation is less than a set threshold, detrending the measured reflectivity to obtain a detrended measured spectrum, comprises: According to the measured reflectance at multiple measurement wavelength points, the measured reflectance is fitted based on a third-order polynomial. The third-order polynomial fitting formula is: R meas (λ)=a3λ 3 +a2λ 2 +a1λ+a0; Where a=[a3,a2,a1,a0] T are the polynomial coefficients; Establishing a fitting objective function based on the least squares method, wherein the objective function is to minimize the sum of squares of errors between the measured reflectivity and the measured reflectivity after fitting; Solve the objective function and get a=[a3,a2,a1,a0] T ; Calculate the fitted reflectance at each measured wavelength point: R fit，i =(a3λ i 3 +a2λ i 2 +a1λ i +a0)) 2 ; Detrend the measured reflectance: R detrend,i =R meas,i -R fit,i ; Among them, R detrend,i is the measured reflectance after detrending at the ith measurement wavelength point, R meas,i is the measured reflectivity at the i-th measurement wavelength point.

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