CN114396881A - Method and device for fast Fourier transform fitting in spectral measurement and analysis - Google Patents
Method and device for fast Fourier transform fitting in spectral measurement and analysis Download PDFInfo
- Publication number
- CN114396881A CN114396881A CN202111479092.2A CN202111479092A CN114396881A CN 114396881 A CN114396881 A CN 114396881A CN 202111479092 A CN202111479092 A CN 202111479092A CN 114396881 A CN114396881 A CN 114396881A
- Authority
- CN
- China
- Prior art keywords
- spectrum
- fitting
- data
- product
- spectrum data
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 230000003595 spectral effect Effects 0.000 title claims abstract description 60
- 238000000034 method Methods 0.000 title claims abstract description 56
- 238000004458 analytical method Methods 0.000 title claims abstract description 20
- 238000005259 measurement Methods 0.000 title claims abstract description 18
- 238000001228 spectrum Methods 0.000 claims abstract description 129
- 239000000463 material Substances 0.000 claims abstract description 24
- 238000007781 pre-processing Methods 0.000 claims abstract description 16
- 238000000572 ellipsometry Methods 0.000 claims description 8
- 230000006870 function Effects 0.000 claims description 8
- 238000003860 storage Methods 0.000 claims description 8
- 238000002834 transmittance Methods 0.000 claims description 5
- 238000011478 gradient descent method Methods 0.000 claims description 3
- 230000001502 supplementing effect Effects 0.000 claims description 2
- 230000008901 benefit Effects 0.000 abstract description 3
- 238000010586 diagram Methods 0.000 description 14
- 238000004590 computer program Methods 0.000 description 11
- 230000008569 process Effects 0.000 description 10
- 238000002310 reflectometry Methods 0.000 description 9
- 238000004422 calculation algorithm Methods 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 5
- 238000009826 distribution Methods 0.000 description 5
- 238000012986 modification Methods 0.000 description 5
- 230000004048 modification Effects 0.000 description 5
- 230000003287 optical effect Effects 0.000 description 4
- 239000002356 single layer Substances 0.000 description 3
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 2
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000010287 polarization Effects 0.000 description 2
- 238000000985 reflectance spectrum Methods 0.000 description 2
- 239000004065 semiconductor Substances 0.000 description 2
- 229910052710 silicon Inorganic materials 0.000 description 2
- 239000010703 silicon Substances 0.000 description 2
- 239000000758 substrate Substances 0.000 description 2
- 230000004075 alteration Effects 0.000 description 1
- 238000007405 data analysis Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 239000010410 layer Substances 0.000 description 1
- 235000012239 silicon dioxide Nutrition 0.000 description 1
- 239000000377 silicon dioxide Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/01—Arrangements or apparatus for facilitating the optical investigation
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/55—Specular reflectivity
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/01—Arrangements or apparatus for facilitating the optical investigation
- G01N2021/0106—General arrangement of respective parts
- G01N2021/0112—Apparatus in one mechanical, optical or electronic block
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- General Health & Medical Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- Life Sciences & Earth Sciences (AREA)
- Health & Medical Sciences (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Spectroscopy & Molecular Physics (AREA)
- Investigating Or Analysing Materials By Optical Means (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
The invention relates to a method and a device for fast Fourier transform fitting in spectral measurement and analysis, which comprises the steps of obtaining spectral data of a product to be detected and preprocessing the spectral data; then, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data; and finally, according to the material of the product to be measured and the estimated parameter range, acquiring a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, wherein the parameter corresponding to the optimal fitting solution is the parameter corresponding to the product to be measured. The invention utilizes the advantage that the frequency spectrum MSE has higher tolerance to the initial value, and uses the frequency spectrum to fit the parameters so as to reduce the requirement on the initial value.
Description
Technical Field
The invention relates to the technical field of data analysis of precise optical measuring instruments, in particular to a method and a device for fast Fourier transform fitting in spectral measurement and analysis.
Background
The film measurement is generally applied to the fields of semiconductor industry, biological medicine industry and the like, and the main purpose of the measurement is to obtain the information such as the thickness, the optical constant and the like of the film. In the semiconductor manufacturing industry, faster measurement speed and accurate measurement result are often required, and reflectivity, ellipsometry and the like are currently common nondestructive measurement means.
The reflectivity, transmittance, ellipsometry parameters, etc. are generally obtained by a film thickness meter, an ellipsometer, etc. The reflectivity and the transmittance are the ratio of the light intensity reflected and transmitted from the surface of the sample to the incident light intensity; the ellipsometry principle is that a non-polarized light source is used to generate polarized light through a polarization state generator, when the light is incident on the surface of a sample, the reflected light changes in polarization state, and an analyzer is used to detect the ellipsometry spectrum of the sample.
After obtaining the spectral data of the sample, certain analysis and calculation means are usually adopted to obtain information such as the thickness and optical constants of the sample.
The commonly used analysis means is to obtain the initial value of the parameter to be solved through a certain algorithm, and then obtain the parameter which is best matched with the spectrum as the final result by using a spectrum fitting method. The common method for obtaining the initial value is to establish a spectrum library according to the parameter grid and then search the closest as the initial value; or in some cases by analytical methods, FFT methods, etc.
The spectral fitting method is highly dependent on the initial values, and if the initial value given by the initial value algorithm has a large deviation (for example, for Si, the deviation is 50 nm), the fitting method will obtain a wrong result. Except for some special cases, the initial value algorithm is a method for searching a library by using a library building method in most cases, and the library building process can be slow, especially for the case of thick films and complex models. And often the results of the library search deviate far from the final correct value, where conventional spectral fitting is subject to error.
Disclosure of Invention
The invention provides a method and a device for fast Fourier transform fitting in spectral measurement and analysis, aiming at the technical problems in the prior art.
As a first aspect of the present invention, the present invention provides a method of fast fourier transform fitting in spectral measurement analysis, comprising the steps of:
s1, acquiring the spectral data of the product to be detected, and preprocessing the spectral data;
s2, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
s3, according to the material of the product to be measured and the estimated parameter range, obtaining a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining the parameter corresponding to the optimal fitting solution which is the parameter corresponding to the product to be measured.
Further, the spectral data includes: ellipsometry, reflectance, transmittance.
Further, the pretreatment comprises: removing drift, expanding interpolation, windowing and supplementing 0 before and after so as to lead the length of the spectral data to accord with 2nIn the form of (1).
Further, the fitting method adopted in step S3 includes: gradient descent method, Newton method, Levenberg-Marquardt (LM) method.
Further, the objective function fitted in step S3 is:
wherein, ViIs a first frequency spectrum numberAccording to the value of the ith point, Vi' is a value of an ith point in the second spectrum data corresponding to the ith point in the first spectrum data, and N is the number of points in the first spectrum data.
Further, if all the frequency spectrums of the first frequency spectrum data are selected for fitting, N represents the number of data points of the whole frequency spectrum; and if part of the frequency spectrum in the first frequency spectrum data is selected for fitting, finding out the position of the point with the highest peak value in the first frequency spectrum, taking all points in the range of 1 to 3 times of the peak height around the point with the highest peak value to participate in the fitting, wherein N is the number of all the points participating in the fitting.
Further, the spectrum database at least comprises the following three items of data: the method comprises the following steps of material name, material parameters and corresponding spectrum data, wherein the material parameters comprise material thickness.
As a second aspect of the present invention, the present invention provides an apparatus for fast fourier transform fitting in spectral measurement analysis, comprising:
the preprocessing module is used for acquiring spectral data of a product to be detected and preprocessing the spectral data;
the FFT module is used for carrying out Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
and the fitting module is used for acquiring a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database according to the material of the product to be measured and the estimated parameter range, fitting the first spectrum data with initial values corresponding to the plurality of second spectrum data in sequence, and fitting the parameter corresponding to the optimal solution, namely the parameter corresponding to the product to be measured to be solved.
As a third aspect of the present invention, the present invention provides an electronic apparatus comprising:
a memory for storing a computer software program;
a processor for reading and executing the computer software program to further implement the method for fitting fast fourier transform in spectral measurement analysis according to the first aspect of the present invention.
As a fourth aspect of the invention, the invention provides a non-transitory computer readable storage medium having stored therein a computer software program for implementing a method of fast fourier transform fitting in spectral measurement analysis according to the first aspect of the invention.
The method utilizes the advantage that the frequency spectrum MSE has higher tolerance on the initial value, and uses the frequency spectrum to fit the parameters so as to reduce the requirement on the initial value; even when the model is particularly complex, the thickness is particularly thick, and the error is particularly large, the parameters obtained by this method can be further used as initial values for spectrum fitting.
Drawings
FIG. 1 is a schematic flow chart of a method provided by an embodiment of the present invention;
FIG. 2 is a diagram of a normal spectral MSE distribution;
FIG. 3 is a diagram of the MSE distribution of the FFT spectrum;
FIG. 4 is a graph of a single layer model reflectance spectrum distribution in an embodiment of the present invention;
FIG. 5 is a graph of a single layer model reflectivity spectrum distribution according to an embodiment of the present invention;
FIG. 6 is a schematic structural diagram of an apparatus according to an embodiment of the present invention;
fig. 7 is a schematic structural diagram of an electronic device according to an embodiment of the present invention;
fig. 8 is a schematic structural diagram of a non-transitory computer-readable storage medium according to an embodiment of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, an embodiment of the present invention provides a method for fitting a fast fourier transform in a spectral measurement analysis, including the following steps:
and S1, acquiring the spectrum data of the product to be detected, and preprocessing the spectrum data. The spectral data includes ellipsometric spectra, reflectance spectra, transmittance spectra, and the like. Wherein, the ellipsometry spectrum can select any one of NCS, psi delta or complex reflectance rho to represent. The preprocessing of the spectrum comprises deshifting, extended interpolation and additionWindow and front and back 0 compensation to make data length in accordance with 2nIn the form of (1).
And S2, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data.
The obtained first spectrum data can be only reserved in the first half part or can be reserved in the whole part after being processed in the next step. Meanwhile, the first spectrum data can be obtained by using Discrete Fourier Transform (DFT) to replace Fast Fourier Transform (FFT).
S3, according to the material of the product to be measured and the estimated parameter range, obtaining a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining the parameter corresponding to the optimal fitting solution which is the parameter corresponding to the product to be measured.
The frequency spectrum database at least comprises the following three items of data: material name, material parameters and their corresponding spectral data. For example, for silicon Si, different material thicknesses correspond to different spectral data. The known material and thickness of the product to be tested can be used for obtaining the frequency spectrum data thereof by searching the database, and the material and frequency spectrum data of the product to be tested can also be used for deducing the material thickness.
In the fitting process, the adopted objective function is as follows:
wherein, ViIs the value of the ith point in the first spectral data, Vi' is a value of an ith point in the second spectrum data corresponding to the ith point in the first spectrum data, and N is the number of points in the first spectrum data.
If all the frequency spectrums of the first frequency spectrum data are selected for fitting, N represents the number of data points of the whole frequency spectrum; and if part of the frequency spectrum in the first frequency spectrum data is selected for fitting, finding out the position of the point with the highest peak value in the first frequency spectrum, taking all points in the range of 1 to 3 times of the peak height around the point with the highest peak value to participate in the fitting, wherein N is the number of all the points participating in the fitting.
The fitting method comprises the following steps: gradient descent method, Newton method, Levenberg-Marquardt (LM) method.
Based on the difficulty of ellipsometry analysis in the background technology, the invention provides a method for fitting fast Fourier transform in spectrum measurement and analysis, which utilizes the advantage of higher tolerance of spectrum MSE to an initial value and uses spectrum to fit parameters so as to reduce the requirement on the initial value; even when the model is particularly complex, the thickness is particularly thick, and the error is particularly large, the parameters obtained by this method can be further used as initial values for spectrum fitting.
Taking a single-layer model reflectivity as an example, the model substrate is silicon Si, a silicon dioxide film is attached on the model substrate, the thickness is 9000nm, the vertical incidence is achieved, the bandwidth (bandwidth) is 3nm, the reflectivity spectrum is shown in fig. 4, the frequency spectrum is shown in fig. 5, fig. 5 shows only a part of the frequency spectrum in the peak range, a part of points near the peak position need to determine whether the peak is the peak represented by the material of the fitted layer according to the known approximate range of the thickness, and then a part of points need to be selected, and the number N of points can be from 1 to 3 times the peak height in principle. Fitting is carried out by fitting 6 points before and after the peak, including the peak, and 13 points in total, and the same range is used for the spectrum obtained by forward calculation in the fitting process.
Obtaining the reflectivity of the sample, then preprocessing the reflectivity spectrum, such as methods of de-drifting, extended interpolation, windowing and the like, and performing fast Fourier transform on the processed reflectivity spectrum to obtain the frequency spectrum of the sample, wherein only the first half of the frequency spectrum is reserved.
And (3) constructing a theoretical model of the sample, and determining parameters needing fitting and initial values. For clarity of illustration and illustration only the thickness parameters are fitted here. The initial value can be obtained by a method of establishing a library and searching the library, wherein the FFT frequency spectrum is used for establishing the library, and compared with the method of establishing the library by a spectrum, the FFT frequency spectrum can be used for establishing the library in a smaller scale and at a higher speed.
And fitting by using the obtained initial value, wherein the fitted objective function is as follows:
in the fitting process, the forward process is to calculate a theoretical spectrum according to an initial value and a model, then perform FFT on the theoretical spectrum by using the same preprocessing means to obtain a spectrum, and use the same spectrum range (note that the spectrum range is determined in the FFT spectrum of the actually measured spectrum) to participate in the fitting.
The fitting process is actually a process of finding a global minimum point based on a given initial value. The position of the global optimum is not known in the fitting, but for the sake of clear description of the problem, the distribution of the MSE is drawn by a large calculation amount, the point with the lowest MSE is the global optimum, and is the target of the fitting, as shown in fig. 2 and 3, in fig. 2, there is one global optimum at 9000nm, and there are 7 local optima, that is, the positions of the other 7 valleys; there is only one valley 9000 in FIG. 3, i.e., global optimum.
Fig. 2 shows a spectrum MSE used, and if the initial value given in the fitting process deviates far from the 9000 position, for example 8500, the fitting converges to a valley at about 8300 position, but cannot jump to the 9000 position, and in fact, only the initial value between 8900 and 9100 converges to 9000. While fig. 3 uses the frequency spectrum MSE, even if the initial value is given to 8500 or even 8000, it can converge to the position of 9000, since this is the nearest valley and is also the global optimum solution. That is, the fitting algorithm can only find the nearest valley, and cannot jump.
The convergence region of fig. 2 is 200nm (8900-9100 nm), while the convergence region of fig. 3 is about 2000nm, which is enlarged by 10 times, so that the initial value requirement is lower during the fitting process, and the calculation amount of the library building and other initial value algorithms is smaller, thereby saving more calculation time.
As shown in fig. 6, an embodiment of the present invention provides an apparatus for fast fourier transform fitting in spectral measurement analysis, including:
the preprocessing module is used for acquiring spectral data of a product to be detected and preprocessing the spectral data;
the FFT module is used for carrying out Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
and the fitting module is used for acquiring a plurality of second spectrum data corresponding to the product to be detected in the estimated parameter range from the spectrum database according to the material of the product to be detected and the estimated parameter range, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining a parameter corresponding to the optimal fitting solution, namely the parameter corresponding to the product to be detected.
Referring to fig. 7, fig. 7 is a schematic view of an embodiment of an electronic device according to an embodiment of the invention. As shown in fig. 7, an embodiment of the present invention provides an electronic device, which includes a memory 510, a processor 520, and a computer program 511 stored in the memory 520 and executable on the processor 520, wherein the processor 520 executes the computer program 511 to implement the following steps:
s1, acquiring the spectral data of the product to be detected, and preprocessing the spectral data;
s2, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
s3, according to the material of the product to be measured and the estimated parameter range, obtaining a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining the parameter corresponding to the optimal fitting solution which is the parameter corresponding to the product to be measured.
Referring to fig. 8, fig. 8 is a schematic diagram illustrating an embodiment of a computer-readable storage medium according to the present invention. As shown in fig. 8, the present embodiment provides a computer-readable storage medium 600 having a computer program 611 stored thereon, the computer program 611, when executed by a processor, implementing the steps of:
s1, acquiring the spectral data of the product to be detected, and preprocessing the spectral data;
s2, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
s3, according to the material of the product to be measured and the estimated parameter range, obtaining a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining the parameter corresponding to the optimal fitting solution which is the parameter corresponding to the product to be measured.
It should be noted that, in the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to relevant descriptions of other embodiments for parts that are not described in detail in a certain embodiment.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (10)
1. A method for fast Fourier transform fitting in spectral measurement analysis is characterized by comprising the following steps:
s1, acquiring the spectral data of the product to be detected, and preprocessing the spectral data;
s2, performing Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
s3, according to the material of the product to be measured and the estimated parameter range, obtaining a plurality of second spectrum data corresponding to the product to be measured in the estimated parameter range from the spectrum database, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining the parameter corresponding to the optimal fitting solution which is the parameter corresponding to the product to be measured.
2. The method of claim 1, wherein the spectral data comprises: ellipsometry, reflectance, transmittance.
3. The method of claim 1, wherein the pre-processing comprises: removing drift, expanding interpolation, windowing and supplementing 0 before and after so as to lead the length of the spectral data to accord with 2nIn the form of (1).
4. The method according to claim 1, wherein the fitting method adopted in step S3 includes: gradient descent method, Newton method, Levenberg-Marquardt (LM) method.
5. The method of claim 1, wherein the objective function fitted in step S3 is:
wherein, ViIs the value of the ith point in the first spectral data, Vi' is a value of an ith point in the second spectrum data corresponding to the ith point in the first spectrum data, and N is the number of points in the first spectrum data.
6. The method of claim 5, wherein if all spectra of the first spectral data are selected for fitting, then N represents the number of data points for the entire spectrum; and if part of the frequency spectrum in the first frequency spectrum data is selected for fitting, finding out the position of the point with the highest peak value in the first frequency spectrum, taking all points in the range of 1 to 3 times of the peak height around the point with the highest peak value to participate in the fitting, wherein N is the number of all the points participating in the fitting.
7. The method of claim 1, wherein the spectrum database comprises at least the following three items of data: the method comprises the following steps of material name, material parameters and corresponding spectrum data, wherein the material parameters comprise material thickness.
8. An apparatus for fast fourier transform fitting in spectrometric analysis, comprising:
the preprocessing module is used for acquiring spectral data of a product to be detected and preprocessing the spectral data;
the FFT module is used for carrying out Fast Fourier Transform (FFT) on the preprocessed spectral data to obtain first spectral data;
and the fitting module is used for acquiring a plurality of second spectrum data corresponding to the product to be detected in the estimated parameter range from the spectrum database according to the material of the product to be detected and the estimated parameter range, comparing the first spectrum data with the plurality of second spectrum data, fitting an initial value corresponding to one second spectrum data which is closest to the first spectrum data, and obtaining a parameter corresponding to the optimal fitting solution, namely the parameter corresponding to the product to be detected.
9. An electronic device, comprising:
a memory for storing a computer software program;
a processor for reading and executing the computer software program to perform a method of fast fourier transform fitting in a spectrometric analysis of any one of claims 1-7.
10. A non-transitory computer readable storage medium having stored therein a computer software program for implementing the method of fast fourier transform fitting in a spectrometric analysis of any one of claims 1-7.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111479092.2A CN114396881A (en) | 2021-12-06 | 2021-12-06 | Method and device for fast Fourier transform fitting in spectral measurement and analysis |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111479092.2A CN114396881A (en) | 2021-12-06 | 2021-12-06 | Method and device for fast Fourier transform fitting in spectral measurement and analysis |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN114396881A true CN114396881A (en) | 2022-04-26 |
Family
ID=81225865
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111479092.2A Pending CN114396881A (en) | 2021-12-06 | 2021-12-06 | Method and device for fast Fourier transform fitting in spectral measurement and analysis |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114396881A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116660176A (en) * | 2023-06-09 | 2023-08-29 | 无锡迅杰光远科技有限公司 | Fourier spectrum automatic baseline correction method, device and storage medium |
| CN119028476A (en) * | 2024-10-29 | 2024-11-26 | 杭州泽天春来科技股份有限公司 | Data processing method, system and readable medium for Fourier infrared gas analyzer |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2001349705A (en) * | 2000-06-06 | 2001-12-21 | Fuji Photo Optical Co Ltd | Error correction method in frequency analysis using wavelength scanning laser interferometer |
| CN1732372A (en) * | 2002-10-28 | 2006-02-08 | 特维特程序控制技术有限公司 | Method and apparatus for thickness decomposition of complicated layer structures |
| CN101458214A (en) * | 2008-12-15 | 2009-06-17 | 浙江大学 | Organic polymer solution concentration detecting method |
| CN103398732A (en) * | 2013-08-08 | 2013-11-20 | 天津大学 | Low-coherence interferometric demodulation method based on spectrum nonlinear effect dispersion compensation |
| CN111998783A (en) * | 2020-07-13 | 2020-11-27 | 北京工业大学 | Reflective THz time-domain spectral thickness measurement method based on evolutionary optimization algorithm |
| CN112304895A (en) * | 2020-11-19 | 2021-02-02 | 西北工业大学 | Method for determining complex dielectric function of semiconductor material |
| CN112629421A (en) * | 2020-12-31 | 2021-04-09 | 武汉颐光科技有限公司 | Film thickness measuring method based on fast Fourier transform |
| CN113075754A (en) * | 2021-04-01 | 2021-07-06 | 南京红露麟激光雷达科技有限公司 | Method and device for acquiring raindrop spectrum based on coherent Doppler laser radar |
| CN113281268A (en) * | 2021-05-31 | 2021-08-20 | 华中科技大学 | Data analysis method and system for rotating polarization device spectrum ellipsometer |
-
2021
- 2021-12-06 CN CN202111479092.2A patent/CN114396881A/en active Pending
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2001349705A (en) * | 2000-06-06 | 2001-12-21 | Fuji Photo Optical Co Ltd | Error correction method in frequency analysis using wavelength scanning laser interferometer |
| CN1732372A (en) * | 2002-10-28 | 2006-02-08 | 特维特程序控制技术有限公司 | Method and apparatus for thickness decomposition of complicated layer structures |
| CN101458214A (en) * | 2008-12-15 | 2009-06-17 | 浙江大学 | Organic polymer solution concentration detecting method |
| CN103398732A (en) * | 2013-08-08 | 2013-11-20 | 天津大学 | Low-coherence interferometric demodulation method based on spectrum nonlinear effect dispersion compensation |
| CN111998783A (en) * | 2020-07-13 | 2020-11-27 | 北京工业大学 | Reflective THz time-domain spectral thickness measurement method based on evolutionary optimization algorithm |
| CN112304895A (en) * | 2020-11-19 | 2021-02-02 | 西北工业大学 | Method for determining complex dielectric function of semiconductor material |
| CN112629421A (en) * | 2020-12-31 | 2021-04-09 | 武汉颐光科技有限公司 | Film thickness measuring method based on fast Fourier transform |
| CN113075754A (en) * | 2021-04-01 | 2021-07-06 | 南京红露麟激光雷达科技有限公司 | Method and device for acquiring raindrop spectrum based on coherent Doppler laser radar |
| CN113281268A (en) * | 2021-05-31 | 2021-08-20 | 华中科技大学 | Data analysis method and system for rotating polarization device spectrum ellipsometer |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116660176A (en) * | 2023-06-09 | 2023-08-29 | 无锡迅杰光远科技有限公司 | Fourier spectrum automatic baseline correction method, device and storage medium |
| CN119028476A (en) * | 2024-10-29 | 2024-11-26 | 杭州泽天春来科技股份有限公司 | Data processing method, system and readable medium for Fourier infrared gas analyzer |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| KR102431942B1 (en) | Detection and measurement of dimensions of asymmetric structures | |
| CN102620665B (en) | Use the method and apparatus that white light scanning interferometry carries out film thickness measurement | |
| EP3298460B1 (en) | Optical metrology using differential fitting | |
| WO2021237949A1 (en) | Critical-dimension measurement method and system based on dispersion relation of momentum space | |
| US9874527B2 (en) | Removing process-variation-related inaccuracies from scatterometry measurements | |
| EP2539668B1 (en) | Method for measurng in patterned structures | |
| CN114396881A (en) | Method and device for fast Fourier transform fitting in spectral measurement and analysis | |
| US20040080761A1 (en) | Method and apparatus for thickness decomposition of complicated layer structures | |
| US11520321B2 (en) | Measurement recipe optimization based on probabilistic domain knowledge and physical realization | |
| WO2016154352A1 (en) | Model-based single parameter measurement | |
| CN111121653B (en) | Single-layer film critical thickness estimation value calculation method | |
| JP2011027461A (en) | Method of measuring pattern shape, method of manufacturing semiconductor device, and process control system | |
| US20220114438A1 (en) | Dynamic Control Of Machine Learning Based Measurement Recipe Optimization | |
| CN112345464B (en) | Ellipsometer optimization calibration method | |
| US7103142B1 (en) | Material analysis using multiple X-ray reflectometry models | |
| CN112629421B (en) | Film thickness measuring method based on fast Fourier transform | |
| CN112880574B (en) | Film thickness measuring method | |
| US9347872B1 (en) | Meta-model based measurement refinement | |
| CN109470154A (en) | Value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers | |
| US11530913B2 (en) | Methods and systems for determining quality of semiconductor measurements | |
| CN115579304B (en) | Wafer detection method and device, computer equipment and readable storage medium | |
| CN112345463A (en) | Ellipsometer-based method for measuring parameters of sample to be measured | |
| US8170838B2 (en) | Simulating two-dimensional periodic patterns using compressed fourier space | |
| CN114384017A (en) | Spectroscopic matching calibration method based on ellipsometer | |
| US20240186191A1 (en) | Measurements Of Semiconductor Structures Based On Spectral Differences At Different Process Steps |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20220426 |