A method for measuring the thickness of a mid-infrared low-absorption material in optical scatterometry

Abstract

The application provides a thickness measurement method of an infrared low-absorption material in optical scattering measurement, a complete method for obtaining the full-waveband refractive index of the infrared low-absorption material is designed by configuring each step in advance. Meanwhile, since the refractive index may be fine-tuned during actual sample measurement, the material needs to be expressed by a vibrator model which can be adjusted and can express the refractive index in the full waveband, therefore, a mapping from the refractive index to the vibrator model OSC is trained by a machine learning method based on a neural network, then the OSC model is directly obtained from the refractive index of the infrared low-absorption material through the mapping, and finally a complete method for quickly replacing the refractive index of the infrared low-absorption material by the vibrator model is formed, which solves the time-consuming problem of manual step-by-step adjustment and the complexity of manual fitting configuration and manual derivation adjustment from the refractive index to the OSC model.

Description

Technical Field

[0001] This invention relates to the fields of optics and semiconductor materials, and more specifically, to a method for measuring the thickness of infrared low-absorption materials in optical scattering measurements. Background Technology

[0002] In the semiconductor industry, the measurement and extraction of thickness of semiconductor nanofilm materials plays a crucial role in improving product quality and yield in manufacturing. Optical scattering measurement, compared to traditional atomic microscopy, scanning electron microscopy, and transmission electron microscopy, offers advantages such as speed, low cost, non-contact, non-destructive testing, and ease of integration, thus gaining widespread application in advanced process monitoring and manufacturing. However, optical scattering measurement is not a "what you see is what you get" method; it requires extracting the parameters of the target structure from the measured spectrum, essentially making it a model-based measurement method. For thin film measurement, extracting the thickness of infrared low-absorption materials first requires determining their refractive index. Current methods often involve manual, step-by-step trial and error, which is slow, tedious, and prone to inaccuracies due to the numerous and time-consuming steps, leading to unsatisfactory final results. Furthermore, to create a complete morphological structure for batch measurement of material thickness, the refractive index of the infrared low-absorption material layer needs to be replaced with an OSC model, currently derived and adjusted manually step-by-step, a complex, time-consuming, and error-prone process. Summary of the Invention

[0003] This invention addresses the technical problems existing in the prior art by providing a method for measuring the thickness of infrared low-absorption materials in optical scattering measurements, comprising:

[0004] Step 1: Establish the original morphological structure, replace the infrared low-absorption material with the refractive index to be extracted in the original morphological structure with the Cauchy model, and extract the material parameters of the Cauchy model based on uniform spotting and the LM nonlinear regression fitting method in a wide band to obtain the first morphological structure.

[0005] Step 2: In the wide band, perform LM nonlinear regression fitting based on the B-spline model to match the refractive index of the Cauchy model and obtain the material parameters of the B-spline model.

[0006] Step 3: Based on the B-spline model, replace the Cauchy model in the first morphological structure to obtain the second morphological structure. Gradually expand from the wide band to the full band. Based on the LM nonlinear regression fitting method, perform multiple regression fittings to update the material parameters of the B-spline model in the second morphological structure to obtain the third morphological structure.

[0007] Step 4: In the entire wavelength range, multiple sets of OSC material parameters and corresponding refractive index sets are obtained by uniformly scattering points, and a mapping from refractive index to OSC material parameters is trained by a neural network machine learning method.

[0008] Step 5: Use the B-spline model in the third morphology structure to derive the full-band refractive index, use the full-band refractive index to obtain the OSC material parameters through the mapping in step 4, and then replace the Cauchy model in the first morphology structure with the OSC model to obtain the fourth morphology structure.

[0009] Step 6: For the same type of infrared low-absorption material sample to be tested, the thickness of the infrared low-absorption material to be extracted is obtained in one step by using the fourth morphology structure and the LM nonlinear regression algorithm in the whole band, while relaxing the OSC part parameters and thickness parameters.

[0010] This invention provides a method for measuring the thickness of infrared low-absorption materials in optical scattering measurements. By pre-configuring the morphology, band variation scheme, parameter fluctuation, and initial value finding scheme for each regression step, a complete method for obtaining the infrared low-absorption refractive index nk in one step is designed. Simultaneously, since fine-tuning of the refractive index nk may occur during actual sample measurement, a mapping from the refractive index nk to the oscillator model OSC is trained using a neural network-based machine learning method. This allows the oscillator model OSC to be directly obtained from the infrared low-absorption refractive index nk, ultimately forming a complete method for rapid substitution of the infrared low-absorption refractive index using the oscillator model. This solves the time-consuming problem of manual step-by-step adjustments, the complexity of multiple tedious manual configuration and fitting, and the complexity of manually deriving and adjusting the nk to OSC model. Attached Figure Description

[0011] Figure 1 A flowchart of a method for measuring the thickness of low-absorption infrared materials in optical scattering measurement provided by the present invention;

[0012] Figure 2 This is a schematic diagram of the morphological structure. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined with each other to form feasible technical solutions. Such combinations are not constrained by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0014] In practical optical scattering measurements, for thin film measurements, extracting the thickness of infrared low-absorption materials first requires determining their refractive index. Current methods often involve manual, step-by-step trial and error, which is not only slow and tedious, but also prone to inaccuracies at each step due to the numerous and time-consuming steps, leading to unsatisfactory final results. Furthermore, to fabricate a complete morphological structure for batch measurement of material thickness, the refractive index of the infrared low-absorption material layer needs to be replaced with an oscillator model (OSC). Currently, this is also done manually, step-by-step, which is complex, time-consuming, and prone to errors.

[0015] To obtain the refractive index of the thickness of the infrared low-absorption material more accurately and quickly, and to more easily and quickly replace it with the OSC oscillator model, this invention proposes a complete, accurate, and rapid method for measuring the thickness of infrared low-absorption materials in optical scattering measurements. (See [link to relevant documentation]). Figure 1 The method includes:

[0016] Step 1: Establish the original morphological structure, replace the infrared low-absorption material with the refractive index to be extracted in the original morphological structure with the Cauchy model, and extract the material parameters of the Cauchy model based on uniform spotting and LM nonlinear regression fitting method in a wide band to obtain the first morphological structure.

[0017] Understandably, for standard specimens, their original morphological structure can be established by referring to... Figure 2 The morphological structure includes multiple layers of materials, such as SiO2 layer, Si layer and infrared low-absorption material. The structural parameters of the infrared low-absorption material, including thickness, material parameters and refractive index, are unknown. The structural parameters of the other layers are known. Therefore, it is necessary to measure the thickness of the infrared low-absorption material. First, it is necessary to extract the refractive index of the infrared low-absorption material.

[0018] Since the structural parameters of the infrared low-absorption material are unknown, the first morphological structure is obtained by substituting the infrared low-absorption material with the Cauchy model, and the material parameters of the Cauchy model in the first morphological structure are solved.

[0019] The Cauchy model can be expressed as nk = c(A,x), which is the functional relationship between the refractive index nk and the material parameters A and thickness h of the Cauchy model. The spectral expression of the first morphology structure is y = f(c(A,x),h,x), where x represents the wavelength, (x,y) is the spectrum, A and h are the material parameters of the Cauchy model, and h is the material thickness. The first morphology structure represents the mapping relationship between the material parameters, thickness and spectrum of the Cauchy model.

[0020] Step 1, which involves extracting Cauchy model material parameters based on uniformly scattered points and using the LM nonlinear regression fitting method within a wide band to obtain the first morphological structure, includes: selecting a wide-band portion of the measurement spectrum from the full-band measurement spectrum; and using the LM nonlinear regression fitting method to solve for the Cauchy model material parameters A and material thickness h based on the wide-band portion of the measurement spectrum and the spectral expression y = f(c(A, x), h, x) of the first morphological structure.

[0021] Understandably, based on the spectral expression y = f(c(A, x), h, x) of the first morphology, a wide-band portion of the measurement spectrum is selected from the full-band measurement spectrum, and the wide-band portion of the measurement light is substituted into the spectral expression of the first morphology. The Cauchy model material parameters A and material thickness h are obtained based on the LM nonlinear regression fitting method.

[0022] Step 2: Within a wide band, perform LM nonlinear regression fitting based on the B-spline model to match the refractive index of the Cauchy model, and obtain the material parameters of the B-spline model.

[0023] Understandably, since the Cauchy model can only match the broad spectrum of the spectrum measured by this infrared low-absorption material, it cannot match the entire measurement spectrum. Therefore, the structural parameters are first solved by matching the Cauchy model in the broad spectrum. Then, the updated Cauchy model in the first morphology structure is replaced with the equivalent refractive index of the B-spline model.

[0024] As an example, the expression for the B-spline model is nk = b(M, x). In the wide band, based on the expressions for the Cauchy model nk = c(A, x), the expression for the B-spline model nk = b(M, x), and the material parameter A of the Cauchy model, the material parameter M of the B-spline model is solved in the wide band.

[0025] Understandably, in step 1, the parameters A and material thickness h of the Cauchy model are solved. In subsequent steps, the material thickness h remains unchanged, and the material parameter A is known. According to the Cauchy model nk = c(A,x), the refractive index nk can be calculated. Then, based on the refractive index nk, the material parameters of the B-spline model are calculated using the LM nonlinear regression algorithm.

[0026] Step 3: Based on the B-spline model, replace the Cauchy model in the first morphological structure to obtain the second morphological structure. Gradually expand from the wide band to the full band. Based on the LM nonlinear regression fitting method, perform multiple regression fittings to update the material parameters of the B-spline model in the second morphological structure to obtain the third morphological structure.

[0027] Understandably, the second morphological structure is obtained by replacing the Cauchy model in the first morphological structure with the B-spline model obtained in step 2. The second morphological structure is applicable to measuring material parameters in a wide band. However, when measuring material parameters, it is usually necessary to measure them in the entire band. Therefore, the second morphological structure is extended to the entire band to solve for the material parameters of the B-spline model applicable to the entire band.

[0028] As an example, step 3, based on the B-spline model replacing the Cauchy model in the first morphological structure, obtains the second morphological structure, gradually expanding from a wide band to the full band. Multiple regression fittings are performed using the LM nonlinear regression fitting method to update the material parameters of the B-spline model in the second morphological structure, resulting in the third morphological structure, including:

[0029] In the wide band, based on the B-spline model nk=b(M,x) replacing the Cauchy model nk=c(A,x) in the first morphological structure, the spectral expression of the second morphological structure is obtained as y=f(b(M,x),h,x);

[0030] Within the full-band measurement spectrum from waveL0 to waveR, a wide band from waveL to waveR is selected. WaveL is gradually extended to the left using a step size of wave_step until the left boundary of the full-band reaches waveL0. Each time the band is extended, the corresponding measurement spectrum is used to perform an LM nonlinear regression fit on M and h in y = f(b(M, x), h, x) to update the values. The next LM nonlinear regression fit uses the M and h values ​​from the previous LM nonlinear regression fit as the initial values. After the final LM nonlinear regression, the values ​​of the B-spline material parameters and thickness are M. n and h n The corresponding third morphological structure is obtained as y = f(b(M) n ,x),h n ,x), where n is the number of iterations of the LM nonlinear regression fitting, M n h represents the material parameters of the B-spline model after the last iteration. nThis represents the thickness after the last iteration.

[0031] Understandably, the selection of the wide band waveL to waveR, and the gradual expansion of waveL to the left according to the step wave_step until the left boundary of the full band waveL0, includes: within the full band waveL0 to waveR of the measured spectrum, selecting the wide band waveL to waveR, and for the wide band waveL to waveR, expanding the bands sequentially according to the step wave_step (waveL-step to waveR), (waveL-2step to waveR), ..., (waveL0 to waveR), and the expanded waveL0 to waveR is the full band.

[0032] Step 4: In the entire wavelength range, multiple sets of OSC material parameters and corresponding refractive index sets are obtained by uniformly scattering points, and a mapping from refractive index to OSC material parameters is trained using a neural network machine learning method.

[0033] Understandably, the third morphology structure is suitable for measuring the parameters of infrared low-absorption materials across the entire wavelength range, but it still has certain limitations. When using another sample of the same material, the parameter measurement using the B-spline across the entire wavelength range will result in parameter jumps and large errors. Therefore, in this invention, the B-spline needs to be replaced by a model that can describe the refractive index properties of the infrared low-absorption material across the entire wavelength range and whose parameters will not jump when the fit is left open across the entire wavelength range, namely the OSC model.

[0034] As an example, step 4 involves obtaining multiple sets of OSC material parameters and corresponding refractive index sets using a uniformly distributed point method across the entire wavelength range, and training a mapping from refractive index to OSC material parameters using a neural network machine learning method, including:

[0035] Using the OCS oscillator model, different OSC material parameters were set in the full-band waveL0~waveR by uniformly scattering points, generating a large number of data pairs of different OSC material parameters and refractive index nk as training sets.

[0036] Based on the training set, a neural network machine learning method is used to train a mapping from refractive index to OSC material parameters across the entire wavelength range.

[0037] Step 5: Use the B-spline model in the third morphology structure to derive the full-band refractive index. Use the full-band refractive index to obtain the OSC material parameters through the mapping in Step 4. Then replace the Cauchy model in the first morphology structure with the OSC model to obtain the fourth morphology structure.

[0038] Understandably, the full-band refractive index is derived based on the updated B-spline model nk = b(Mn, x) in step 3. Then, the OSC material parameters are obtained by mapping the full-band refractive index through machine learning, and the OSC model is obtained. This OSC model is then used to replace the Cauchy model in the first morphology structure to obtain the fourth morphology structure.

[0039] Step 6: For other infrared low-absorption material samples of the same type, the thickness of the infrared low-absorption material to be extracted is obtained in one step by using the fourth morphology structure and the LM nonlinear regression algorithm across the entire wavelength range, while relaxing the OSC part parameters and thickness parameters.

[0040] Understandably, by obtaining a set of full-band measurement spectra of other infrared low-absorption materials of the same type, and using the fourth morphology structure and the LM nonlinear regression algorithm, the thickness h of the infrared low-absorption material to be extracted can be obtained by relaxing some parameters of the OSC model and the thickness parameter.

[0041] This invention provides a method for measuring the thickness of infrared low-absorption materials in optical scattering measurements. By pre-configuring the morphology, band variation scheme, parameter fluctuation, and initial value finding scheme for each regression step, a complete method for obtaining the infrared low-absorption refractive index nk in one step is designed. Simultaneously, since fine-tuning of the refractive index nk may occur during actual sample measurement, a mapping from the refractive index nk to the oscillator model OSC is trained using a neural network-based machine learning method. This allows the oscillator model OSC to be directly obtained from the infrared low-absorption refractive index nk, ultimately forming a complete method for rapid substitution of the infrared low-absorption refractive index using the oscillator model. This solves the time-consuming problem of manual step-by-step adjustments, the complexity of multiple tedious manual configuration and fitting, and the complexity of manually deriving and adjusting the nk to OSC model.

[0042] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0043] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0044] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for measuring the thickness of infrared low-absorption materials in optical scattering measurements, characterized in that, include: Step 1: Establish the original morphological structure, replace the infrared low-absorption material with the refractive index to be extracted in the original morphological structure with the Cauchy model, and extract the material parameters of the Cauchy model based on uniform spotting and the LM nonlinear regression fitting method in a wide band to obtain the first morphological structure. Step 2: In the wide band, perform LM nonlinear regression fitting based on the B-spline model to match the refractive index of the Cauchy model and obtain the material parameters of the B-spline model. Step 3: Based on the B-spline model, replace the Cauchy model in the first morphological structure to obtain the second morphological structure. Gradually expand from the wide band to the full band. Based on the LM nonlinear regression fitting method, perform multiple regression fittings to update the material parameters of the B-spline model in the second morphological structure to obtain the third morphological structure. Step 4: In the entire waveband, multiple sets of OSC material parameters and corresponding refractive index sets of the oscillator model are obtained by uniformly scattering points. The mapping from refractive index to OSC material parameters of the oscillator model is trained by a neural network machine learning method. Step 5: Use the B-spline model in the third morphology structure to derive the full-band refractive index, use the full-band refractive index to obtain the OSC material parameters of the oscillator model through the mapping in step 4, and then use the OSC oscillator model to replace the Cauchy model in the first morphology structure to obtain the fourth morphology structure. Step 6: For the same type of infrared low-absorption material sample to be tested, the thickness of the infrared low-absorption material to be extracted is obtained in one step by using the fourth morphology structure and the LM nonlinear regression algorithm in the whole band, while relaxing the OSC part parameters and thickness parameters of the oscillator model.

2. The method for measuring the thickness of infrared low-absorption materials according to claim 1, characterized in that, The expression for the Cauchy model is nk=c(A,x), and the spectral expression for the first morphology structure is y=f(c(A,x),h,x), where x represents the wavelength, (x,y) is the spectrum at wavelength x, A is the material parameter of the Cauchy model, h is the material thickness, and nk is the refractive index. In step 1, the material parameters of the Cauchy model are extracted based on uniformly scattered points and the LM nonlinear regression fitting method over a wide wavelength range to obtain the first morphological structure, including: Select a wide-band portion of the measurement spectrum from the full-band measurement spectrum; Based on the measured spectrum of the wide-band portion and the spectral expression y=f(c(A,x),h,x) of the first morphology, the material parameters A and material thickness h of the Cauchy model are solved using the LM nonlinear regression fitting method.

3. The method for measuring the thickness of infrared low-absorption materials according to claim 2, characterized in that, The expression for the B-spline model is nk = b(M, x). In step 2, within a wide wavelength range, LM nonlinear regression is performed based on the B-spline model to match the refractive index of the Cauchy model, obtaining the material parameters of the B-spline model, including: Within a wide band, based on the Cauchy model expression nk=c(A,x), the B-spline model expression nk=b(M,x), and the Cauchy model material parameter A, the B-spline model material parameter M is solved within a wide band.

4. The method for measuring the thickness of infrared low-absorption materials according to claim 3, characterized in that, Step 3 involves replacing the Cauchy model in the first morphological structure with a B-spline model to obtain the second morphological structure. This process is gradually expanded from a wide band to the full band. Multiple regression fittings are performed using the LM nonlinear regression fitting method to update the material parameters of the B-spline model in the second morphological structure, resulting in the third morphological structure, including: In the wide band, based on the B-spline model nk=b(M,x) replacing the Cauchy model nk=c(A,x) in the first morphological structure, the spectral expression of the second morphological structure is y=f(b(M,x),h,x); Within the full-band measurement spectrum (waveL0~waveR), a wide band (waveL~waveR) is selected. WaveL is gradually extended to the left using a step size (wave_step) until the left boundary of the full-band (waveL0). Each time the band is extended, the corresponding measured spectrum is used to perform an LM nonlinear regression fit on M and h in y=f(b(M,x),h,x) to update the values. The next LM nonlinear regression fit uses the M and h values ​​from the previous LM nonlinear regression fit as the initial values. After the final LM nonlinear regression, the material parameters and thickness of the B-spline are Mn and hn, respectively, resulting in the corresponding third morphology structure y=f(b(M,x),h,x). n ,x),h n ,x), where n is the number of iterations of the LM nonlinear regression fitting, M n h represents the material parameters of the B-spline model after the last iteration. n This represents the thickness after the last iteration.

5. The method for measuring the thickness of infrared low-absorption materials according to claim 4, characterized in that, The selection of widebands waveL~waveR, and the gradual expansion of waveL to the left according to the step wave_step until the left boundary of the entire band waveL0, includes: Within the full-band waveL0~waveR of the measured spectrum, a wide band waveL~waveR is selected. For the wide band waveL~waveR, the bands are extended in sequence according to the step wave_step: (waveL-wave_step~waveR), (waveL-2wave_step~waveR), ..., (waveL0~waveR). The extended waveL0~waveR is the full-band.

6. The method for measuring the thickness of infrared low-absorption materials according to claim 4, characterized in that, Step 4 involves obtaining multiple sets of OSC material parameters and corresponding refractive index sets for the oscillator model using a uniformly distributed point method across the entire wavelength range. A neural network-based machine learning method is then used to train a mapping from refractive index to OSC material parameters, including: Using the OSC oscillator model across the entire waveband from waveL0 to waveR, different OSC material parameters were set by uniformly scattering data points, generating a large number of data pairs of different OSC material parameters and refractive index nk as a training set. Based on the training set, a neural network machine learning method is used to train a mapping from refractive index to OSC material parameters of the oscillator model across the entire wavelength range. Based on the updated B-spline model nk=b(M) n The full-band refractive index is derived by deriving x), and then the OSC material parameters of the oscillator model are obtained by mapping the full-band refractive index through machine learning.

7. The method for measuring the thickness of infrared low-absorption materials according to claim 6, characterized in that, Step 6, for other infrared low-absorption material samples of the same type, uses the fourth morphology structure and the LM nonlinear regression algorithm across the entire wavelength range to obtain the thickness of the infrared low-absorption material to be extracted in one step, while disregarding the OSC parameters and thickness parameters of the oscillator model. This includes: A set of full-band measurement spectra of the same infrared low-absorption material to be tested is obtained. Through the fourth morphology structure and the LM nonlinear regression algorithm, the thickness h of the infrared low-absorption material to be extracted is obtained with the OSC part parameters and thickness parameters of the oscillator model relaxed.

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