Film thickness atomic-scale solving method based on parameter backtracking modeling

Abstract

The invention provides a thin film thickness atomic-scale solving method based on parameter backtracking modeling, and belongs to the technical field of thin film thickness measurement. Comprising the following steps: collecting actual reflection spectrum data of a to-be-detected film; constructing a reflection spectrum theoretical model containing a thin film material optical constant and a to-be-solved thickness; setting a solving threshold value according to a to-be-measured film thickness solving precision requirement; determining an optical constant of the thin film material to be measured, inputting a thickness estimation value to the reflection spectrum theoretical model, and generating a theoretical reflection spectrum corresponding to the optical constant and the thickness estimation value; and determining the thickness of the to-be-measured film by comparing the mean square error and iterative optimization of the actual reflection spectrum data and the theoretical reflection spectrum through the local spectrum. Through reverse parameter traceability and closed-loop feedback optimization, atomic-scale precision film thickness measurement can be realized only through local spectral data, the solving efficiency is high, the anti-interference performance is high, and the method is suitable for industrial detection scenes needing atomic-scale precision control, such as optical device manufacturing, optical coating and semiconductor manufacturing.

Description

Technical Field

[0001] The present invention relates to the technical field of film thickness measurement, and in particular to a method for atomic-level solution of film thickness based on parameter inverse simulation. Background Art

[0002] In fields such as semiconductor manufacturing and optical device fabrication, accurate measurement of thin film thickness is critical to ensuring product performance. Traditional thin film thickness measurement methods, such as contact thickness measurement, are prone to damage to the film surface. While some non-contact measurement methods, such as laser thickness measurement, avoid contact damage, in practice, external factors such as machine vibration and environmental noise can significantly interfere with the measurement results, resulting in unstable measurement accuracy and difficulty meeting the requirements of atomic-level precision measurement.

[0003] Currently, thin film thickness measurement technology based on the principle of spectral interferometry has been applied to a certain extent. Spectral interferometry uses the phase difference of interference fringes or the spectrum of nanometer-level light wavelengths to correlate film thickness with optical path difference. Compared to the mechanical errors of contact measurement or the diffraction limit of optical microscopes, the accuracy of spectral interferometry is determined by wavelength stability and spectrometer resolution. It can break through the physical limitations of traditional methods and achieve theoretical accuracy at the atomic level. However, it is usually based on a series of complex forward mathematical deduction processes based on measured spectral data. The fast Fourier transform method is often used to solve the film thickness. This method has a strong dependence on the various parameters of the initial data. When faced with complex environmental interference such as machine vibration and environmental noise, the actual accuracy and stability of the film thickness solution will be greatly affected.

[0004] In addition, the existing thin film thickness measurement technology based on spectral interference mainly adopts forward mathematical deduction methods, such as the fast Fourier transform method, which calculates the film thickness through the reflection spectrum period and amplitude data. The disadvantage is that, since the reflection spectrum is usually a non-uniform oscillation period, the measured data needs to be adjusted in a series of ways to transform it into a uniform period when solving. At the same time, interference such as machine vibration and environmental noise will cause the measured reflection spectrum to produce local period offset or amplitude distortion. These errors are directly transmitted to the calculation results, greatly affecting the accuracy of the film thickness solution. The film thickness solution accuracy is usually at the micron level, which is difficult to meet the requirements of atomic-level solution accuracy. Secondly, the existing film thickness solution method needs to process full-band spectral data, which has high computational complexity and low solution efficiency, making it difficult to adapt to the fast dynamic measurement needs of industrial scenarios.

[0005] Therefore, there is an urgent need for a thin film thickness calculation method that can achieve atomic-level precision and high stability under complex working conditions. Summary of the Invention

[0006] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide an atomic-level solution method for thin film thickness based on parameter inverse tracing and closed-loop feedback optimization. Through inverse parameter tracing and closed-loop feedback optimization, atomic-level precision thin film thickness measurement can be achieved with only local spectral data. The solution has high efficiency and strong anti-interference ability, and is suitable for industrial detection scenarios that require atomic-level precision control, such as optical device manufacturing, optical coating, and semiconductor manufacturing.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation includes the following steps:

[0009] S1, collecting actual reflection spectrum data of the film to be tested;

[0010] S2. Construct a theoretical model of reflectance spectrum including the optical constants of the thin film material and the thickness to be determined;

[0011] S3. Setting a solution threshold according to the accuracy requirement of the film thickness to be measured;

[0012] S4, determining the optical constants of the thin film material to be measured and inputting the thickness estimation value into the reflection spectrum theoretical model to generate a theoretical reflection spectrum corresponding to the optical constants and the thickness estimation value;

[0013] S5. Determine the thickness of the film to be measured by comparing the mean square error of the actual reflection spectrum data and the theoretical reflection spectrum and performing iterative optimization through local spectral comparison.

[0014] Preferably, in S1, the actual reflection spectrum data of the film to be tested is collected by an optical detection device and recorded as I r , the optical detection equipment includes but is not limited to a spectrometer.

[0015] Preferably, in S2, the reflectance spectrum theoretical model is established based on the film structure, substrate material and film material of the film to be measured, and includes three variables: refractive index N, extinction coefficient K and thickness d to be determined.

[0016] Preferably, in S2, after the thin film material to be measured is determined, the refractive index N and the extinction coefficient K are fixed values, and the thickness d to be determined is the only parameter to be solved.

[0017] Preferably, in S3, the solution threshold is an adjustable parameter, denoted as ε, so that the film thickness solution accuracy covers the atomic level to the millimeter level.

[0018] Preferably, in S4, the input thickness estimation value is an initial setting value, and the optical constant is determined by the material properties of the thin film to be measured.

[0019] Preferably, in S4, the determined refractive index N, extinction coefficient K and thickness estimation value are input into the reflection spectrum theoretical model to generate a theoretical reflection spectrum I t .

[0020] Preferably, in S5, the following steps are specifically included:

[0021] Select actual reflectance spectrum data I r The finite period spectrum in the middle region is similar to the theoretical reflection spectrum I t Compare the spectra of a finite number of cycles at the same position and calculate the mean square error between the two. The formula is:

[0022] (I r -I t ) 2 ≤ε;

[0023] If the mean square error is not greater than the set solution threshold, the current thickness estimate is determined to be the true thickness of the film to be measured and the final film thickness is output.

[0024] Preferably, in S5, the method further includes:

[0025] If the mean square error is greater than the set solution threshold, the parameter optimization mechanism is triggered, and the thickness estimation value is iteratively optimized using the parameter optimization algorithm according to the result of the mean square error and S4 to S5 are repeated until the mean square error is no greater than the set solution threshold, and the final film thickness is output. The parameter optimization algorithm includes but is not limited to the gradient descent method or the gradient ascent method.

[0026] Preferably, a parameter traceability closed-loop feedback system is formed during the iterative optimization process, and only the actual reflectance spectrum data I r Finite-period spectra in the middle region, without processing full-band data.

[0027] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0028] (1) The present invention transforms the film thickness solution into the matching problem between theoretical spectrum and actual spectrum through the reverse parameter tracing mechanism, avoiding the periodic homogenization error of traditional forward deduction and achieving atomic-level precision measurement.

[0029] (2) The present invention selects finite data of a finite number of complete cycles in the middle region of the actual reflection spectrum for parameter inverse reconstruction, without the need to process full-band spectral information, which greatly reduces the computational complexity, improves the solution efficiency, and meets the real-time dynamic measurement needs of industrial scenarios.

[0030] (3) The present invention utilizes a closed-loop feedback optimization system, combined with a gradient descent or gradient ascent method to dynamically optimize the film thickness value. By gradually iteratively approximating the true thickness of the film, the error transmission caused by external interference such as machine vibration and environmental noise is dynamically suppressed, thereby significantly improving the measurement stability and solving the problem of poor anti-interference performance of the prior art.

[0031] (4) The present invention adjusts the accuracy level of film thickness solution by adjusting the judgment threshold and controls the convergence condition by setting the mean square error threshold. The accuracy of film thickness solution can cover the entire range from atomic level to millimeter level, and has a wide range of applications. At the same time, it adopts a non-contact measurement method, which does not require contact with the sample or complex pretreatment, thus avoiding damage to the film surface. It is suitable for precision industrial detection scenarios such as optical device manufacturing, semiconductors, and optical coatings. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0033] Figure 1 A flowchart of a method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to the present invention is provided;

[0034] Figure 2 This is a schematic diagram of a method for atomic-level solution of film thickness based on parameter inverse simulation according to the present invention. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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.

[0036] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] The present invention provides an atomic-level solution method for film thickness based on parameter inverse simulation, which uses inverse parameter tracing to obtain film thickness parameters. By establishing a theoretical model of reflectance spectrum based on three variables: the optical constants of the film material (refractive index N, extinction coefficient K) and the film thickness d, the refractive index N and extinction coefficient K of the material can be determined after the film material is determined. In this case, the film thickness d is the only parameter variable to be determined in the model. Therefore, by adjusting the film thickness parameter d in the model, the theoretical reflectance spectrum I can be controlled. t According to the film thickness measurement accuracy requirement, the fitting matching threshold ε is set and the generated theoretical reflection spectrum I t Compared with the actual collected reflectance spectrum I r Compare them, when the mean square error (I t -I r ) 2 When the current thickness d is less than the preset threshold ε, it is determined that the current thickness d is the true value of the film thickness. If the accuracy requirement is not met, the parameter optimization mechanism is triggered to recalculate the film thickness d, forming a parameter traceability closed-loop feedback system. This method only requires the selection of the reflection spectrum I r The parameter inverse simulation of a limited number of periodic spectra in the intermediate region does not require the full spectrum information, greatly improving the efficiency of film thickness determination. At the same time, the closed-loop feedback optimization mechanism effectively avoids the influence of high-frequency or random errors such as machine vibration and environmental noise on the forward solution of the reflectance spectrum, breaking through the accuracy limitations of forward deduction, achieving atomic-level precision measurement of film thickness, and improving the stability of the measurement system. Ultimately, this method achieves highly efficient, high-precision, automated, and non-destructive film thickness detection, which is particularly suitable for industrial inspection scenarios requiring atomic-level precision control, such as optical device manufacturing, optical coating, and semiconductor manufacturing.

[0038] Specifically, such as Figure 1 and Figure 2 As shown, the present invention provides a method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation, comprising the following steps:

[0039] S1, collecting actual reflection spectrum data of the film to be tested;

[0040] S2. Construct a theoretical model of reflectance spectrum including the optical constants of the thin film material and the thickness to be determined;

[0041] S3. Setting a solution threshold according to the accuracy requirement of the film thickness to be measured;

[0042] S4, determining the optical constants of the thin film material to be measured and inputting the thickness estimation value into the reflection spectrum theoretical model to generate a theoretical reflection spectrum corresponding to the optical constants and the thickness estimation value;

[0043] S5. Determine the thickness of the film to be measured by comparing the mean square error of the actual reflection spectrum data and the theoretical reflection spectrum and performing iterative optimization through local spectral comparison.

[0044] Furthermore, in S1, the actual reflection spectrum data of the film to be tested is collected by an optical detection device, for example, by a spectrometer, and is recorded as I r In S2, the theoretical model for reflectance spectroscopy is established based on the film structure, substrate material, and film material of the film to be measured. It contains three variables: the refractive index N, the extinction coefficient K, and the thickness d to be determined. Once the film material to be measured is determined, the refractive index N and the extinction coefficient K are fixed values, and the thickness d to be determined is the only parameter to be solved.

[0045] In S3, the solution threshold is an adjustable parameter, denoted as ε, which enables the film thickness solution accuracy to cover the atomic level to the millimeter level.

[0046] In S4, the input thickness estimation value is an initial setting value, and the optical constant is determined by the material properties of the film to be measured. The determined refractive index N, extinction coefficient K and thickness estimation value are input into the reflection spectrum theoretical model to generate a theoretical reflection spectrum I t .

[0047] In S5, it specifically includes:

[0048] Select actual reflectance spectrum data I r The finite period spectrum in the middle region is similar to the theoretical reflection spectrum I t Compare the spectra of a finite number of cycles at the same position and calculate the mean square error between the two. The formula is:

[0049] (I r -I t ) 2 ≤ε;

[0050] If the mean square error is not greater than the set solution threshold, the current thickness estimate is determined to be the true thickness of the film to be measured and the final film thickness is output. r 3 to 5 complete cycles in the middle region, and the theoretical reflection spectrum I t Spectra of 3 to 5 cycles at the same position are compared.

[0051] If the mean square error is greater than the set solution threshold, the parameter optimization mechanism is triggered, and the parameter optimization algorithm is used to iteratively optimize the thickness estimation value according to the result of the mean square error and repeat S4 to S5 until the mean square error is no greater than the set solution threshold, and the final film thickness is output. Among them, the parameter optimization algorithm in the above content can be selected from but not limited to the gradient descent method or the gradient ascent method. The iterative optimization process forms a parameter traceability closed-loop feedback system, which only needs to use the actual reflectance spectrum data I r Finite-period spectra in the middle region, without processing full-band data.

[0052] Based on the above process, through reverse parameter tracing, the thickness solution is converted into a matching problem between the theoretical spectrum and the actual spectrum. Only local spectral data is required to complete high-precision calculations. Combined with a closed-loop feedback mechanism to suppress noise interference, the film thickness measurement with atomic-level precision is finally achieved, thereby solving the problem of insufficient accuracy of film thickness solution in the existing technology due to the forward deduction relying on full-band data and poor anti-interference ability.

[0053] In addition, since the traditional method relies on full spectrum data and is easily affected by noise, the present invention effectively filters out high-frequency random noise such as vibration and environmental disturbance through local spectrum matching and closed-loop optimization, thereby improving measurement stability. At the same time, compared with the forward solution method, the use of finite period data in the present invention reduces the amount of calculation, has high solution efficiency, and can meet the real-time dynamic measurement needs of industrial scenarios. In addition, the present invention can achieve full coverage of film thickness solution accuracy from atomic level to millimeter level by controlling the solution threshold according to actual use needs, which is superior to the micron-level solution accuracy and fixed solution accuracy level of existing solution methods, and has stronger applicability and practicality. Therefore, the film thickness solution method of the present invention does not require contact with the sample or complex pretreatment, has high solution efficiency, and can achieve solution accuracy up to the atomic level. It is suitable for precision manufacturing scenarios such as optical device processing, semiconductors, optical coatings, and is compatible with a variety of thin film materials and various types of film layer structures.

[0054] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for calculating the thickness of thin films at the atomic level based on parameter inverse simulation, characterized in that: The following steps are involved: S1, collecting actual reflection spectrum data of the film to be tested; S2. Construct a theoretical model of reflectance spectrum including the optical constants of the thin film material and the thickness to be determined; S3. Setting a solution threshold according to the accuracy requirement of the film thickness to be measured; S4, determining the optical constants of the thin film material to be measured and inputting the thickness estimation value into the reflection spectrum theoretical model to generate a theoretical reflection spectrum corresponding to the optical constants and the thickness estimation value; S5. Determine the thickness of the film to be measured by comparing the mean square error of the actual reflection spectrum data and the theoretical reflection spectrum and performing iterative optimization through local spectral comparison.

2. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 1, characterized in that: In S1, the actual reflection spectrum data of the film to be tested is collected by optical detection equipment and recorded as I r , the optical detection equipment includes but is not limited to a spectrometer.

3. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 1, characterized in that: In S2, the reflectance spectrum theoretical model is established based on the film structure, substrate material and film material of the film to be measured, and includes three variables: refractive index N, extinction coefficient K and thickness d to be determined.

4. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 3, characterized in that: In S2, when the thin film material to be measured is determined, the refractive index N and the extinction coefficient K are fixed values, and the thickness d to be determined is the only parameter to be solved.

5. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 1, characterized in that: In S3, the solution threshold is an adjustable parameter, denoted as ε, which enables the film thickness solution accuracy to cover the atomic level to the millimeter level.

6. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 1, characterized in that: In S4, the input estimated thickness value is an initial setting value, and the optical constant is determined by the material properties of the film to be measured.

7. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 6, characterized in that: In S4, the determined refractive index N, extinction coefficient K and thickness estimation value are input into the reflection spectrum theoretical model to generate a theoretical reflection spectrum I t .

8. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 1, characterized in that: In S5, it specifically includes: Select actual reflectance spectrum data I r The finite period spectrum in the middle region is similar to the theoretical reflection spectrum I t Compare the spectra of a finite number of cycles at the same position and calculate the mean square error between the two. The formula is: (I r -I t ) 2 ≤ε; If the mean square error is not greater than the set solution threshold, the current thickness estimate is determined to be the true thickness of the film to be measured and the final film thickness is output.

9. The method for calculating the thickness of a thin film at the atomic level based on parameter inverse simulation according to claim 8, characterized in that: In S5, also included: If the mean square error is greater than the set solution threshold, the parameter optimization mechanism is triggered, and the thickness estimation value is iteratively optimized using the parameter optimization algorithm according to the result of the mean square error and S4 to S5 are repeated until the mean square error is no greater than the set solution threshold, and the final film thickness is output. The parameter optimization algorithm includes but is not limited to the gradient descent method or the gradient ascent method.

10. The method for atomic-level solution of film thickness based on parameter inverse simulation according to claim 1, characterized in that: The iterative optimization process forms a parameter traceability closed-loop feedback system, which only requires the use of actual reflectance spectrum data I r Finite-period spectra in the middle region, without processing full-band data.

Images