Implementation and measurement method of thick film sample pre-fitting algorithm

Abstract

The invention relates to the field of thick film measurement, and discloses an implementation measurement method of a thick film sample pre-fitting algorithm, comprising the following steps: step 1, establishing a model for a specific sample; step 2, inputting a film thickness value di, calculating ellipsometric angles psi and delta in a central wavelength range, and converting data into signals with 1 / lambda ([mu] m-1) as coordinates; 3, solving an average period Di at the central wavelength, and inputting different film thickness values di for multiple times to obtain a corresponding relation between the average period T and the thickness d; and 4, analyzing measurement data, and finding a thickness approximate value. According to the method, the pre-fitting time is compressed to be within 0.5 s, on one hand, when the relation between the film thickness and the distance between the adjacent extreme points of the signal is established and measurement data is analyzed, the extreme points are searched and data statistics is carried out by adopting an efficient algorithm, and the calculation time is shortened;

Description

Technical Field

[0001] The present invention relates to the technical field of thick film measurement, in particular to a method for realizing a thick film sample pre-fitting algorithm. Background Art

[0002] In fields such as materials science and electronic engineering, accurate measurement of thick film samples is crucial for understanding material properties, optimizing production processes, and ensuring product quality. However, traditional methods for measuring thick film samples have many limitations and are in urgent need of improvement. In terms of measurement accuracy, traditional measurement methods often fail to meet the growing demand for high precision. For example, common caliper measurements, limited by their mechanical structure and manual reading errors, typically only achieve millimeter-level accuracy. For thick film samples, especially those with thicknesses on the micron or even nanometer scale, caliper measurements are simply unable to accurately obtain thickness information, let alone detect the microstructure and properties within the film.

[0003] After searching, the patent publication number is CN201811602778.4, which discloses a method for measuring the initial value of film thickness suitable for spectroscopic ellipsometer, including setting detection parameters, using ellipsometer to measure and obtain the Stokes parameters of the sample film; decomposing the S spectrum from the Stokes parameters and performing noise reduction processing on it; screening out the zero value points in the S spectrum and obtaining the corresponding wavelengths, and calculating the initial value of the sample film thickness based on the zero value points of the S spectrum and their corresponding wavelengths. The technical solution of the present invention addresses the problem of inaccurate initial value measurement of thin films in the prior art. By detecting the Stokes parameters of the ellipsometer measurement to obtain the spectrum zero point, the zero point is used to accurately estimate the initial value of the film thickness. However, when using this method to measure the film thickness, there are problems such as long pre-fitting time and low fitting efficiency. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention provides a measurement method for realizing a pre-fitting algorithm for thick film samples, which solves the problems of long pre-fitting time and low fitting efficiency.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: A method for implementing a pre-fitting algorithm for thick film samples, comprising the following steps: Step 1: Build a model for specific samples; Step 2: Enter the film thickness value d i Calculate the ellipsometric angles psi and delta within the central wavelength range and convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 3: Calculate the average period D at the center wavelength i , by inputting different film thickness values d multiple times i, and obtain the corresponding relationship between the average period T and thickness d; Step 4: Analyze the measurement data and find the approximate thickness value; Step 5: Input the approximate thickness value D obtained by pre-fitting and perform fitting.

[0006] Preferably, the calculation of the ellipsoidal angles psi and delta within the central wavelength range includes the following: Step 1, calculate the characteristic matrix of the film layer; Step 2: Calculate the amplitude reflection coefficient of the film system; Step 3, calculating the ellipsoidal angle according to the ellipsoidal angle definition; Step 4: Convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 5: Calculate the average period D at the center wavelength i ; Step 6: Repeat steps 2 to 5 to calculate the period corresponding to different thickness values and find the average period D i The corresponding relationship with thickness d.

[0007] Preferably, in the calculation of the ellipsoidal angles psi and delta within the central wavelength range, the characteristic matrix of the film layer is calculated according to the following formula: Where η is the effective optical admittance, which is equal to η in p-light and s-light respectively. p and η S .

[0008] Preferably, in the calculation of the ellipsoidal angles psi and delta within the central wavelength range, the amplitude reflection coefficient of the film system is calculated according to the following formula: Preferably, in the calculation of the ellipsoidal angles psi and delta within the central wavelength range, the ellipsoidal angle is calculated according to the following formula: The present invention provides a method for implementing a pre-fitting algorithm for thick film samples. It has the following beneficial effects: 1. The present invention compresses the pre-fitting time to less than 0.5s. On the one hand, when establishing the relationship between the film thickness and the spacing between adjacent extreme points of the signal and analyzing the measurement data, an efficient algorithm is used to find the extreme points and perform data statistics, thereby reducing the calculation time. On the other hand, the approximate thickness value obtained by pre-fitting is used as the initial value to narrow the search range of the fitting algorithm and accelerate the fitting convergence speed. At the same time, the parallel computing power of modern computers is fully utilized to optimize data processing and calculations, completing a large number of calculations in a short time, meeting the needs of fast measurement, and greatly improving the overall measurement efficiency. 2. This invention establishes a multilayer film optical model based on thin film optical theory, comprehensively considering factors such as thin film optical constants, film thickness, and incident angle, to accurately calculate the propagation characteristics of light in the film. When calculating the ellipsometric angle, the derivation process from the characteristic matrix to the amplitude reflection coefficient and then to the ellipsometric angle fully exploits the inherent connection between film thickness and optical properties. This ensures that the obtained ellipsometric angle contains rich film information, laying the foundation for subsequent accurate measurement of film thickness. Compared with traditional measurement methods, it can more accurately reflect the true thickness and characteristics of the film. 3. The present invention establishes a model to find the relationship between film thickness and signal, analyzes the measurement data to determine the approximate thickness value, and then accurately describes the data through data fitting, forming a complete and orderly measurement process. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 This is one of the flow charts of the method of the present invention; Figure 2 is the photoresist ellipsometric curve of the present invention; Figure 3 This is the period-thick film relationship curve of the present invention. DETAILED DESCRIPTION

[0010] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0011] Please see the attached Figure 1-3 The embodiment of the present invention provides a method for implementing a pre-fitting algorithm for thick film samples, comprising the following steps: Step 1: Build a model for specific samples; Step 2: Enter the film thickness value d i Calculate the ellipsometric angles psi and delta within the central wavelength range and convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 3: Calculate the average period D at the center wavelength i , by inputting different film thickness values d multiple times i , and obtain the corresponding relationship between the average period T and thickness d; Step 4: Analyze the measurement data and find the approximate thickness value; Step 5: Input the approximate thickness value D obtained by pre-fitting and perform fitting.

[0012] Calculation of ellipsometric angles psi and delta within the central wavelength range includes the following: Step 1, calculate the characteristic matrix of the film layer; Step 2: Calculate the amplitude reflection coefficient of the film system; Step 3, calculating the ellipsoidal angle according to the ellipsoidal angle definition; Step 4: Convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 5: Calculate the average period D at the center wavelength i ; Step 6: Repeat steps 2 to 5 to calculate the period corresponding to different thickness values and find the average period D i The corresponding relationship with thickness d.

[0013] When calculating the ellipsometric angles psi and delta within the central wavelength range, the characteristic matrix of the film layer is calculated according to the following formula: Where η is the effective optical admittance, which is equal to η in p-light and s-light respectively. p and η S .

[0014] When calculating the ellipsoidal angles psi and delta within the central wavelength range, the amplitude reflection coefficient of the film system is calculated according to the following formula: In calculating the ellipsometric angles psi and delta within the central wavelength range, the ellipsometric angle is calculated according to the following formula: The technical solution of the present invention includes the following contents: Find the relationship between the film thickness and the distance between adjacent extreme points of the signal: Establish a model: For Si-SiO2 samples, a multilayer optical model is established based on thin film optical theory. When light propagates in different media (air, SiO2 film, Si substrate), reflection and refraction will occur. According to Maxwell's equations and boundary conditions, the transfer matrix method is derived to describe the behavior of light in the multilayer film structure. In this model, the optical constants of the film (such as refractive index, extinction coefficient), film thickness and incident angle factors jointly determine the propagation characteristics of light in it.

[0015] Calculate the ellipsoid angle: When the film thickness value d is input i Finally, the characteristic matrix of the film layer is calculated through the model.

[0016] The characteristic matrix of the film layer is calculated according to the following formula: Where η is the effective optical admittance, which is equal to η in p-light and s-light respectively. p and η S .

[0017] The characteristic matrix reflects the phase change and polarization change of light propagating once in the film layer. Then, the amplitude reflection coefficient of the film system is calculated based on the characteristic matrix: This involves the reflection and transmission of different polarized light (s-polarized light and p-polarized light) at the interface of each layer. Based on the definition of ellipsometric angle, that is, the change in polarization state before and after reflection of polarized light, the ellipsometric angles psi and delta within the central wavelength range are calculated: These two ellipsometric angles contain information about film thickness and optical constants.

[0018] Data conversion and period calculation: The calculated ellipsometric data is converted into 1 / λ(μm -1 ) as the coordinates. This is because in some optical analyses, using the wave number (1 / λ) as a variable can more clearly show the signal characteristics. At the center wavelength, the signal will show periodic changes. This is due to the interference effect of light in the film layer. By finding the extreme points of the signal, the distance between adjacent extreme points can be determined. The average period D is obtained by taking the average of multiple measurements. i Different film thicknesses will lead to different interference of light in the film layer, thus causing the signal period to change. By inputting different film thickness values d multiple times i , we can reveal the intrinsic relationship between the average period T and the thickness d, which is essentially determined by the interference of light and the optical properties of the film; analyze the measurement data and find the approximate value of the thickness: Measurement and data conversion: Perform actual measurement on the sample to obtain ellipsometric data at different wavelengths. These data reflect the current optical state of the sample, and then convert the measured data into 1 / λ (μm -1 ) is the coordinate signal, which is consistent with the data format used when establishing the relationship previously, making it easier to perform subsequent analysis.

[0019] Average period calculation: At the center wavelength, the propagation characteristics of light of different wavelengths in the film layer are slightly different, resulting in slight differences in the signal period at different wavelengths. Therefore, when calculating the average period D, it is necessary to comprehensively consider the spacing between extreme points within a certain range near the center wavelength. By statistical averaging, an average period that can represent the overall characteristics is obtained.

[0020] Determine the approximate thickness value: Based on the previously established correspondence between the average period T and thickness d, which is equivalent to a known functional relationship, the average period D obtained by the current measurement is substituted into this relationship and, through mathematical calculation, the corresponding approximate thickness value can be solved. This is based on the previously discovered intrinsic relationship between film thickness and signal period, and can achieve reverse deduction from signal characteristics to film thickness; Data fitting: Input the approximate thickness value: Use the approximate thickness value D obtained by pre-fitting as the initial parameter. This is because this value already contains preliminary information about the sample thickness, which can provide a good starting point for subsequent precise fitting and reduce the search space and calculation amount of fitting.

[0021] Fitting process: Select an appropriate fitting function to fit the measured data. For example, polynomial fitting is used. The principle is to construct a polynomial function that approximates the measured data points as closely as possible. During the fitting process, the coefficients of the polynomial are determined by minimizing an error function (such as the mean square error). The mean square error measures the degree of discrepancy between the calculated value of the fitting function and the actual measured value. By continuously adjusting the coefficients to minimize this discrepancy, a fitting curve that best matches the measured data is obtained. This method enables more accurate description and analysis of the sample's thickness and related optical properties. This method reduces the pre-fitting time to less than 0.5 seconds, primarily due to the following advantages: First, during the relationship establishment and data analysis process, an efficient algorithm is used to find extreme points and perform data statistics, reducing computation time. Second, the approximate thickness value obtained from the pre-fitting is used as the initial value, significantly narrowing the search range of the fitting algorithm and accelerating convergence. Third, throughout the entire process, data processing and computation are optimized, fully utilizing the parallel computing capabilities of modern computers, greatly improving fitting efficiency.

[0022] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for implementing a pre-fitting algorithm for thick film samples, characterized in that: The following steps are involved: Step 1: Build a model for specific samples; Step 2: Enter the film thickness value d i Calculate the ellipsometric angles psi and delta within the central wavelength range and convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 3: Calculate the average period D at the center wavelength i , by inputting different film thickness values d multiple times i , and obtain the corresponding relationship between the average period T and thickness d; Step 4: Analyze the measurement data and find the approximate thickness value; Step 5: Input the approximate thickness value D obtained by pre-fitting and perform fitting.

2. The method for realizing the pre-fitting algorithm of thick film samples according to claim 1, characterized in that: The calculation of the ellipsometric angles psi and delta within the central wavelength range includes the following: Step 1, calculate the characteristic matrix of the film layer; Step 2: Calculate the amplitude reflection coefficient of the film system; Step 3, calculating the ellipsoidal angle according to the ellipsoidal angle definition; Step 4: Convert the data into 1 / λ(μm -1 ) is a signal of coordinates; Step 5: Calculate the average period D at the center wavelength i ; Step 6: Repeat steps 2 to 5 to calculate the period corresponding to different thickness values and find the average period D i The corresponding relationship with thickness d.

3. The method for realizing the pre-fitting algorithm of thick film samples according to claim 2, characterized in that: In the calculation of the ellipsoid angles psi and delta within the central wavelength range, the characteristic matrix of the film layer is calculated according to the following formula: Where η is the effective optical admittance, which is equal to η in p-light and S-light respectively. p and η s ; 4. The method for realizing the pre-fitting algorithm of thick film samples according to claim 2, characterized in that: In the calculation of the ellipsoid angle psi and delta within the central wavelength range, the amplitude reflection coefficient of the film system is calculated according to the following formula:

5. The method for realizing the pre-fitting algorithm of thick film samples according to claim 2, characterized in that: In the calculation of the ellipsoidal angles psi and delta within the central wavelength range, the ellipsoidal angle is calculated according to the following formula:

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