CN111879236A - Method for determining parameters of sample to be measured from theoretical spectrum library and measuring equipment - Google Patents

Method for determining parameters of sample to be measured from theoretical spectrum library and measuring equipment Download PDF

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CN111879236A
CN111879236A CN202010671891.9A CN202010671891A CN111879236A CN 111879236 A CN111879236 A CN 111879236A CN 202010671891 A CN202010671891 A CN 202010671891A CN 111879236 A CN111879236 A CN 111879236A
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CN111879236B (en
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张晓雷
叶星辰
张厚道
施耀明
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Shanghai Precision Measurement Semiconductor Technology Inc
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    • 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
    • G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • 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
    • G01B11/03—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness by measuring coordinates of points
    • 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
    • G01B11/0608—Height gauges
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Abstract

The invention provides a device for determining the shape parameters of a sample to be measured and measuring based on spectrum library matching, which comprises a theoretical spectrum library constructed according to a structural model of the sample to be measured, a measured spectrum obtained, and an initial approximate optimal matching spectrum and an initial approximate optimal matching parameter vector of the measured spectrum determined from the theoretical spectrum library; acquiring at least three sampling points of each parameter to be measured, and the mean square error of a theoretical spectrum and a measured spectrum corresponding to each sampling point; and performing parabolic fitting on a distribution curve of mean square errors of the theoretical spectrum and the measured spectrum corresponding to at least three sampling points of each parameter to be measured relative to the parameter values corresponding to the sampling points, so as to obtain a global optimal matching value of each parameter to be measured. By the method, the matching precision between the measured spectrum and the theoretical spectrum is obviously improved, and the problem of inaccurate interpolation caused by the traditional method when coupling exists between the morphological parameters is solved.

Description

Method for determining parameters of sample to be measured from theoretical spectrum library and measuring equipment
Technical Field
The invention relates to the technical field of semiconductor detection equipment, in particular to a method for determining parameters of a sample to be detected from a theoretical spectrum library based on an OCD (optical proximity detector) measurement technology and measurement equipment.
Background
As the semiconductor manufacturing industry develops, the size of semiconductor devices is continuously reduced, the device structure design is increasingly complex, and more stringent control requirements are imposed on the semiconductor manufacturing process, so that wafer measurement or inspection needs to be performed after many process steps of the semiconductor manufacturing process to obtain higher yield. An optical critical-Dimension (OCD) measurement technique is a commonly used critical Dimension measurement technique in semiconductor manufacturing processes.
The basic working principle of the OCD measuring technology is as follows: the method comprises the steps of establishing a theoretical spectrum library corresponding to a sample morphology model, searching a specific theoretical spectrum from the library to realize the optimal matching with a measurement spectrum obtained by OCD measurement equipment, and determining the morphology parameters of the sample. Although the distribution characteristics of the medium cannot be directly deduced through the measurement spectrum, a model can be established and parameterized based on the distribution of the scattering medium, and then a theoretical spectrum library of the model corresponding to different parameter values is calculated by using a numerical calculation method, namely, the light scattering when the measurement spectrum is acquired by the OCD measuring equipment is subjected to simulation calculation. And finding out specific parameters corresponding to the theoretical spectrum which is optimally matched with the measured spectrum from the theoretical spectrum library, wherein the specific parameters are used as morphological parameters for representing the structural characteristics of the sample.
In the existing OCD measurement technology, the Error scale between the theoretical spectrum and the measured spectrum usually adopts Mean Squared Error (MSE) or Goodness of Fit (Goodness of Fit). Taking the mean square error as an example, we express it as a function of the parameter to be measured,
Figure BDA0002582589310000011
here, (x)1,…,xN) Representation of the drawing to be testedN parameters to be measured, S (x), of the sample morphology structure1,…,xN；λk) Representing the wavelength λ of the light emitted by the set of morphological parameterskFrom the calculated theoretical spectral value, LS (lambda)k) For the measured spectrum value at the wavelength point, the number K of the wavelength points should be greater than the number N of the parameters to be measured. Clearly, the MSE is not negative, and a MSE closer to 0 indicates that the theoretical spectrum is closer to the measured spectrum. Obtaining profile parameters by library matching, i.e. finding a set of globally optimal profile parameters
Figure BDA0002582589310000021
So that the MSE takes a global minimum in the parameter space, i.e.
Figure BDA0002582589310000022
In the process of establishing the theoretical spectrum library, discretization processing must be performed on the structural parameters of the to-be-detected sample morphology model, that is, the theoretical spectrum library obtained based on the structural parameters with discontinuous changes cannot include the theoretical spectrum corresponding to all values in the value range of each parameter. Therefore, the structural parameters (hereinafter referred to as initial approximate optimal matching structural parameters) corresponding to the theoretical spectrum (hereinafter referred to as initial approximate optimal matching theoretical spectrum) with the minimum MSE of the measured spectrum searched and obtained from the discretized spectrum library deviate from the real values of the structural parameters of the sample to a certain extent, and cannot be directly output as a measurement result, otherwise, the accuracy and the repeatability of OCD measurement are seriously influenced. The key to solving this match bias problem is to correct the results using the spectral and structural parameter information of the initial near-best match point at neighboring grid points in the spectral library. Because the spectrum is usually smooth along with the change of the morphology parameters, near the initial approximate optimal matching point, the mean square error MSE is continuous and smooth relative to the high-dimensional hypersurface formed by the morphology parameters, and the global minimum value of the hypersurface can be found in the region, and the corresponding coordinates are the optimal matching parameters which are finally required to be obtained.
In the existing OCD measurement technology, correction after library matching usually assumes that all parameters are mutually independent, then a plurality of sampling points are selected near an initial approximate optimal matching point along the coordinate axis of each parameter, the mean square error of a theoretical spectrum and a measured spectrum corresponding to the sampling points is calculated, the mean square error in each parameter dimension is fitted into a quadratic curve along with the parameter value distribution, the minimum value of the quadratic curve is found, and the global optimal matching value of the parameters to be measured is determined one by one. However, in many samples to be measured, the plurality of morphological parameters of the samples to be measured are not independent but have strong coupling; for example, the MSE between the theoretical spectrum and the measured spectrum is sensitive to changes in the combination of several topographical parameters, but the contribution of each of these parameters to the spectral change is difficult to determine, which corresponds to the MSE distribution appearing as a non-orthogonal hypersurface near the near-optimal match point (see fig. 1). At this time, if a conventional method is adopted, that is, each parameter dimension is corrected independently, a sampling point selected only along a certain parameter coordinate axis (i.e., the coordinate axis where the profile parameter HT is located in fig. 1 or the coordinate axis where the profile parameter MCD is located) near an initial approximate optimal matching point may deviate from the bottom area of the hypersurface, or information included in MSE curve change in a single parameter dimension is insufficient, which makes a subsequent MSE curve fitting method unreasonable or even ineffective, and finally results in insufficient measurement accuracy of the profile parameter.
Aiming at the technical problem, the method improves the selection strategy of the sampling point so as to more accurately obtain the morphological parameters of the sample.
Disclosure of Invention
The invention aims to disclose a method and measuring equipment for determining parameters of a sample to be measured from a theoretical spectrum library, which are used for overcoming various defects in the prior art, in particular for obtaining a theoretical spectrum closer to a measured spectrum of the sample to be measured and further obtaining more accurate global optimal matching parameters of the sample to be measured, and also discloses measuring equipment for optical critical dimensions.
In order to achieve the first object, the present invention provides a method for determining a parameter of a sample to be measured from a theoretical spectral library, comprising the following steps:
s1, constructing a theoretical spectrum library according to a structural model of a sample to be measured, wherein the structural model of the sample to be measured comprises at least two parameters to be measured, values of each parameter to be measured are combined to form a plurality of parameter vectors to be measured, discrete grid points and theoretical spectra are obtained based on the parameter vectors to be measured, the discrete grid points and the theoretical spectra are in one-to-one correspondence with one another, and the theoretical spectrum library comprises the parameter vectors to be measured, the discrete grid points and the theoretical spectra;
s2, obtaining a measured spectrum, and determining an initial approximate optimal matching spectrum and an initial approximate optimal matching parameter vector of the measured spectrum from a theoretical spectrum library;
s3, acquiring at least three sampling points of each parameter to be measured, and the mean square error of the theoretical spectrum and the measured spectrum corresponding to each sampling point, wherein the sampling points comprise grid points corresponding to an initial approximate optimal matching spectrum and re-matched sampling points of each parameter to be measured acquired based on an initial approximate optimal matching parameter vector;
s4, parabolic fitting is carried out on the mean square error of the theoretical spectrum and the measured spectrum corresponding to at least three sampling points of each parameter to be measured relative to the distribution curve of the parameter value corresponding to each sampling point, and the global optimal matching value of each parameter to be measured is obtained.
As a further improvement of the present invention, the step S1 of obtaining discrete grid points and theoretical spectra based on the parameter vector to be measured includes: and respectively carrying out discretization processing on each parameter to be measured according to the value range of each parameter to be measured and the library building step length preset by each parameter to be measured, forming discrete grid points by parameter vectors to be measured formed by the value combination of each parameter to be measured, and acquiring the theoretical spectrum corresponding to each parameter vector to be measured through the RCWA algorithm.
As a further improvement of the present invention, the step S2 specifically includes: obtaining a measured spectrum, performing library matching on the measured spectrum and a theoretical spectrum library, obtaining a mean square error between the measured spectrum and the theoretical spectrum, and determining the theoretical spectrum with the minimum mean square error between the measured spectrum and the theoretical spectrum library as an initial approximate optimal matching spectrum of the measured spectrum, wherein a parameter vector corresponding to the initial approximate optimal matching spectrum is an initial approximate optimal matching parameter vector of the measured spectrum.
As a further improvement of the present invention, the sampling point of the re-matching of each parameter to be measured obtained based on the initial approximate best matching parameter vector in step S3 includes:
acquiring adjacent grid points of the initial approximate optimal matching parameter vector on the corresponding coordinate axis of each parameter to be measured;
respectively taking adjacent grid points on the corresponding coordinate axis of each parameter to be measured as reference points, fixing the value of the parameter to be measured of the adjacent grid points on the corresponding coordinate axis, floating the rest parameters to be measured by the respective library building step length of the rest parameters to be measured, obtaining a plurality of sampling parameter vectors of each parameter to be measured, and obtaining theoretical spectrums corresponding to the sampling parameter vectors from the theoretical spectrum library to form a sub-spectrum library of each parameter to be measured;
and respectively re-matching the theoretical spectrum in the sub-spectrum library of each parameter to be measured with the measured spectrum, and determining a parameter vector to be measured corresponding to the theoretical spectrum with the minimum mean square error value between the theoretical spectrum and the measured spectrum from the sub-spectrum library as a re-matched sampling point of the corresponding parameter to be measured.
As a further improvement of the present invention, the adjacent grid points are at least two adjacent grid points having a library step length of an integer multiple of the corresponding selected parameter to be measured along the increasing and/or decreasing direction of the selected parameter to be measured;
the at least two neighboring grid points include a first neighboring grid point and a second neighboring grid point.
As a further improvement of the invention, the number of the sub-spectrum libraries of each parameter to be measured is at least two, including a first sub-spectrum library and a second sub-spectrum library;
the first sub-spectral library is acquired based on the first neighboring grid point and the second sub-spectral library is acquired based on the second neighboring grid point.
As a further improvement of the invention, the number of the re-matched sampling points of each parameter to be measured is at least two, including a re-matched first sampling point and a re-matched second sampling point;
the first sampling point which is matched again is obtained based on the first sub-spectrum library, and the second sampling point which is matched again is obtained based on the second sub-spectrum library;
as a further improvement of the present invention, in step S4, parabolic fitting is performed on a distribution curve of the mean square error of the theoretical spectrum and the measured spectrum corresponding to each of the at least three sampling points of each parameter to be measured with respect to the value of the parameter to be measured corresponding to the sampling point based on a parabolic equation disclosed by the following formula:
MSE(xN)＝aN(xN)2+bNxN+cN；
wherein x isNRepresenting any of said parameters to be measured, MSE (x)N) The mean square error of the theoretical spectrum and the measured spectrum corresponding to the sampling point of the parameter to be measured is represented as aN，bN，cNThree characteristic parameters of a fitted parabolic equation corresponding to said parameter to be measured, aN>0。
As a further improvement of the present invention, the step S4 further includes:
solving three characteristic parameters a of a fitting parabolic equation of each parameter to be measured by adopting the numerical values of the parameter to be measured corresponding to the three sampling points of each parameter to be measured and the mean square error value corresponding to each sampling pointN，bN，cN；
Three characteristic parameters a of the fitting parabolic equation based on each parameter to be measuredN，bN，cNDetermining the global optimum matching value of each parameter to be measured as
Figure BDA0002582589310000051
Based on the same invention idea, the invention also discloses a measuring device of the optical key dimension, which uses the method for determining the parameters of the sample to be measured from the theoretical spectral library created by any one of the above inventions and outputs the global optimal matching value of each parameter to be measured.
Compared with the prior art, the invention has the beneficial effects that:
in the method for determining the parameters of the sample to be measured from the theoretical spectrum library and the measuring equipment based on the method, at least three sampling points of each parameter to be measured are obtained based on an initial approximate optimal matching spectrum and an initial approximate optimal matching parameter, and the mean square error of a theoretical spectrum corresponding to each sampling point and a measured spectrum is obtained, wherein the at least three sampling points comprise grid points corresponding to the initial approximate optimal matching spectrum and sampling points which are matched again; and then parabolic fitting is carried out on the mean square error of the theoretical spectrum and the measured spectrum corresponding to at least three sampling points of each parameter to be measured relative to the distribution curve of the corresponding parameter value to be measured of the sampling points so as to determine the global optimal matching parameter of each parameter to be measured. The sampling points of the parameters to be measured, which are obtained through the re-matching, are closer to the bottom of the MSE hypersurface, and the MSE values of the sampling points are smoother relative to an MSE curve formed by the corresponding parameters to be measured and are suitable for fitting by using a quadratic curve, so that the goodness of fit is improved compared with the prior art. The global optimum matching parameter of each parameter to be measured, which is fitted by at least three sampling points of each parameter to be measured, is more accurate, namely, the matching precision between the measured spectrum and the theoretical spectrum is greatly improved, so that the accuracy of obtaining parameter information of a sample is improved, and the fitting effect of a hyper-curved surface which takes the Mean Square Error (MSE) of the measured spectrum and the theoretical spectrum library as non-orthogonality is remarkably improved, so that the method is favorable for accurately detecting the micro-surface structure of the semiconductor device.
Drawings
FIG. 1 is a schematic diagram of a scenario in which the Mean Square Error (MSE) of a sample measured spectrum and a theoretical spectrum library is a non-orthogonal hypersurface;
FIG. 2 is a schematic diagram of a topographical model and topographical parameters of a sample;
FIG. 3 is an overall flow chart of a method of determining a parameter of a sample to be measured from a theoretical spectral library;
FIG. 4 is a diagram illustrating the construction of candidate parameter sets according to the present invention, wherein G2Global best match parameter vector, G, obtained for this patent fitting1The global optimal matching parameter vector is obtained by fitting in the prior art;
FIG. 5 is a fitting parabolic graph obtained by performing a parabolic fitting process on a morphological parameter HT according to the method for determining a parameter of a sample to be measured from a theoretical spectral library disclosed herein;
fig. 6 is a fitting parabolic graph obtained by performing a parabolic fitting process on the morphological parameter MCD according to the method for determining the parameter of the sample to be measured from the theoretical spectral library disclosed in the present invention.
Detailed Description
The present invention is described in detail with reference to the embodiments shown in the drawings, but it should be understood that these embodiments are not intended to limit the present invention, and those skilled in the art should understand that functional, methodological, or structural equivalents or substitutions made by these embodiments are within the scope of the present invention.
Term "Topography parameters"in the present application, the parameters of Critical Dimension (CD) features such as line width, sidewall angle (SWA), height/depth, etc., of a two-dimensional or three-dimensional sample of a semiconductor or integrated circuit or other semiconductor or integrated circuit having a microscopic surface structure (e.g., two-dimensional polysilicon gate etch (PO), isolation trench (STI), isolation layer (Spacer), double exposure (double patterning) or three-dimensional VIA (VIA), fin field effect transistor (FinFET), flash memory (NAND), etc.) at various process stages such as post-development inspection (ADI), post-etch inspection (AEI), etc. Term "Sample to be tested"and term"Sample (I)"has the technical meaning of equivalent.
The first embodiment is as follows:
referring to fig. 1 to 6, an embodiment of a method for determining a parameter of a sample to be measured from a theoretical spectral library (hereinafter referred to as "method") according to the present invention is disclosed.
In this example, the measured spectrum is actually measured on the surface of the sample by an OCD measuring device based on the method disclosed in this example, and the theoretical spectrum library is calculated by using a Rigorous Coupled Wave Analysis (RCWA) algorithm. The model of the structure to be measured for theoretical spectrum library creation is shown in fig. 2, and a grating formed on a Substrate (Substrate) of a semiconductor device has two morphological parameters, namely, a middle line width (MCD) and a Height (HT).
The method disclosed in this embodiment is exemplified by the two profile parameters MCD and HT. Other topography parameters such as bottom line width, top line width, sidewall angle (SWA), trench depth, etc. may also be included in the actual measurement process. And then matching the theoretical spectrum and the measured spectrum in the theoretical spectrum library by calculating the Mean Square Error (MSE) of the theoretical spectrum and the measured spectrum. A smaller MSE value indicates that the two spectra are more similar, and if the MSE is 0, it indicates that the two spectra are identical.
Referring to fig. 3, the method disclosed in this embodiment includes the following steps S1 to S4. It should be noted that the descriptions such as step S1 and step S2 in the application do not constitute a strict definition of the order of some or all of the steps, and all the steps may be combined and described based on the same order.
Step S1, a theoretical spectrum library is constructed according to a structural model of a sample to be measured, the structural model of the sample to be measured comprises at least two parameters to be measured, values of each parameter to be measured are combined to form a plurality of parameter vectors to be measured, discrete grid points and theoretical spectra are obtained based on the parameter vectors to be measured, the discrete grid points and the theoretical spectra are in one-to-one correspondence with one another, and the theoretical spectrum library comprises the parameter vectors to be measured, the discrete grid points and the theoretical spectra. .
Specifically, a structural morphology model of the sample to be detected is established according to the morphology and the structure of the sample, and the structural model of the sample to be detected comprises corresponding structural parameters. Illustratively, the sample to be measured has N parameters to be measured, N is more than or equal to 2, and the sample to be measured at least comprises a first parameter x to be measured1And a second parameter x to be measured2Using the parameter vector X to be measured as (X)1,x2,…，xN)，xi(i ═ 1, 2.., N) represents the structural model of the sample to be testedThe value of each parameter to be measured is combined to form a plurality of parameter vectors to be measured, and the value range of each parameter to be measured can be determined by the process conditions. Further, acquiring discrete grid points and a theoretical spectrum based on the parameter vector to be measured includes: according to the value range of each parameter to be measured, discretization processing is carried out on each parameter to be measured according to the library building step length preset by each parameter to be measured, a parameter vector to be measured formed by the value combination of each parameter to be measured forms a discrete grid point, and a theoretical spectrum corresponding to each parameter vector to be measured is obtained through an RCWA algorithm. Each discrete grid point represents a parameter vector to be measured and has a theoretical spectrum corresponding to the parameter vector to be measured, namely the parameter vector to be measured, the discrete grid points and the theoretical spectrum are in one-to-one correspondence with each other. The preset library building step size of each parameter to be measured can be adjusted according to requirements, and the plurality of discrete grid points are in an N-dimensional curved surface form. Therefore, the construction of a theoretical spectrum library is completed according to the structural model of the sample to be detected, and the theoretical spectrum library comprises the parameter vector to be detected, the discrete grid points and the theoretical spectrum which are in one-to-one correspondence with each other.
Referring to fig. 1, fig. 2 and fig. 4, in this embodiment, the sample to be measured has 2 parameters to be measured: first parameter x to be measured1And a second parameter x to be measured2The parameter vector S to be measured can be (x)1，x2) A structural model representing the sample to be measured, specifically, the morphological parameter HT is the first parameter x to be measured1The feature parameter MCD is a second parameter x to be measured2. Wherein, the value range of the morphology parameter HT is from 20nm to 40nm, 6 points are taken at equal step length, and then the library establishing step length delta x of the morphology parameter HT1Is 4 nm; the value range of the appearance parameter MCD is from 20nm to 40nm, 6 points are taken at equal step length, and then the library establishing step length delta x of the appearance parameter MCD is obtained2And 4nm, combining all values of the morphology parameter HT and the morphology parameter MCD to form 36 parameter vectors to be measured to form 36 discrete grid points in a theoretical spectrum library, wherein each discrete grid point corresponds to one parameter vector to be measured, the discrete grid points are in a two-dimensional plane form, and meanwhile, a corresponding theoretical spectrum can be obtained based on each parameter vector to be measured. It is to be noted thatIn this embodiment, the first parameter x to be measured1Step length of building a library and a second parameter x to be measured2The preset library building step lengths can be equal or unequal, and the preset library building step lengths can be smaller than or equal to the nanometer level.
And step S2, obtaining the measured spectrum, and determining the initial approximate optimal matching spectrum and the initial approximate optimal matching parameter vector of the measured spectrum from the theoretical spectrum library.
The step S2 specifically includes: the method comprises the steps of obtaining an actual measured spectrum of a sample by using OCD measuring equipment, carrying out library matching on the measured spectrum and a theoretical spectrum library, obtaining a mean square error between the measured spectrum and the theoretical spectrum, determining the theoretical spectrum with the minimum Mean Square Error (MSE) between the measured spectrum and the theoretical spectrum library as an initial approximate optimal matching spectrum of the measured spectrum, and determining a parameter vector X' to be measured corresponding to the initial approximate optimal matching spectrum as an initial approximate optimal matching parameter vector of the measured spectrum. For ease of distinction, the best match parameter vector X' is represented as:
Figure BDA0002582589310000091
Figure BDA0002582589310000092
the grid points corresponding to the approximate best matching parameter vector X' can also be obtained for the specific values of the corresponding parameters.
In this embodiment, according to a constructed theoretical spectrum library, Mean Square Errors (MSEs) between theoretical spectra and measured spectra corresponding to 36 discrete grid points in the theoretical spectrum library are respectively calculated, and the theoretical spectra with the minimum mean square error between the theoretical spectrum library and the measured spectra are obtained by comparison and correspond to grid points a (28,32), a parameter vector to be measured corresponding to the grid points a (28,32) is an initial approximate optimal matching parameter of the measured spectra, and an MSE value between the theoretical spectra and the measured spectra corresponding to the grid points a (28,32) is 1.0009.
Step S3, at least three sampling points of each parameter to be measured are obtained, and the mean square error of the theoretical spectrum and the measured spectrum corresponding to each sampling point is obtained, wherein the sampling points comprise grid points corresponding to the initial approximate optimal matching spectrum and re-matched sampling points of each parameter to be measured, which are obtained based on the initial approximate optimal matching parameter vector.
Specifically, the obtaining of at least three sampling points of each parameter to be measured includes taking a grid point corresponding to the initial approximate optimal matching spectrum as one of the sampling points of each parameter to be measured, and obtaining a re-matched sampling point of each parameter to be measured based on the initial approximate optimal matching parameter vector. The method comprises the following steps of obtaining a re-matched sampling point of each parameter to be measured based on an initial approximate optimal matching parameter vector, wherein the re-matched sampling point comprises the following steps:
s311, obtaining adjacent grid points of the initial approximate optimal matching parameter vector on the corresponding coordinate axis of each parameter to be measured. The adjacent grid points are at least two adjacent grid points which have integer times of corresponding library step length of the selected parameter to be measured along the increasing and/or decreasing direction of the selected parameter to be measured, and the at least two adjacent grid points comprise a first adjacent grid point and a second adjacent grid point. S312, with the adjacent grid point on the corresponding coordinate axis of each parameter to be measured as a reference point, fixing the value of the parameter to be measured of the adjacent grid point on the corresponding coordinate axis, floating the rest parameters to be measured by the respective library building step length of the rest parameters to be measured, obtaining a plurality of sampling parameter vectors of each parameter to be measured, and obtaining the theoretical spectrum corresponding to each sampling parameter vector from the theoretical spectrum library to form a sub-spectrum library of each parameter to be measured. The number of the sub-spectrum libraries of each parameter to be measured is at least two, and the sub-spectrum libraries comprise a first sub-spectrum library and a second sub-spectrum library, wherein the first sub-spectrum library is acquired based on the first adjacent grid point, and the second sub-spectrum library is acquired based on the second adjacent grid point.
And S313, respectively re-matching the theoretical spectrum in the sub-spectrum library of each parameter to be measured with the measured spectrum, and determining the parameter vector to be measured corresponding to the theoretical spectrum with the minimum mean square error value between the theoretical spectrum and the measured spectrum from the sub-spectrum library as a re-matched sampling point of the corresponding parameter to be measured. The number of the re-matched sampling points of each parameter to be detected is at least two, the number of the re-matched sampling points comprises a re-matched first sampling point and a re-matched second sampling point, the re-matched first sampling point is obtained based on the first sub-spectrum library, and the re-matched second sampling point is obtained based on the second sub-spectrum library.
Preferably, the first and second re-matched sampling points are located on one side or both sides of a grid point (a grid point) corresponding to the initial approximate best-matching spectrum. In the present embodiment, the first and second re-matched sampling points are located on two sides of the grid point (a grid point) corresponding to the initial near-best-matching spectrum. It should be noted that the first re-matched sampling point and the second re-matched sampling point may also be located at one side of the grid point (a grid point) corresponding to the initial approximate optimal matching spectrum, as long as parabolic fitting can be performed on the distribution curve of the MSE values corresponding to the three sampling points relative to the corresponding parameter values to be measured according to the grid point corresponding to the initial approximate optimal matching spectrum, the first re-matched sampling point of each parameter to be measured, and the second re-matched sampling point.
In particular, to find the first parameter x to be measured1For example, the first and second re-matched sample points comprise: using the first parameter x to be measured1X of position1The coordinate axis is a reference coordinate axis, and the grid point corresponding to the initial approximate optimal matching parameter vector X' is selected to be in X1N (n represents an integer different from 0) times the adjacent grid points of the library step length on the coordinate axis, and optionally, taking n as 1, namely
Figure BDA0002582589310000111
The first neighboring grid point (shifted one binning step in the increasing direction) as the initial approximate best match parameter vector X', where Δ X1Represents a first parameter x to be measured1Step length of building a library. Taking the first adjacent grid point as a reference point, and fixing the first parameter x to be measured of the first adjacent grid point1Value of (2)
Figure BDA0002582589310000112
Using the rest to be testedNumber x2,…,xNThe multiples of the respectively set library building step length are taken as the reference, and the rest parameters x to be measured are floated2,…,xNObtaining the parameter values in the respective value ranges to obtain a first parameter x to be measured1And obtaining theoretical spectra corresponding to the sampling parameter vectors from a theoretical spectrum library to form a first parameter x to be measured1The first sub-spectrum library is used for re-matching the measured spectrum based on the first sub-spectrum library, namely determining the theoretical spectrum of the minimum value of MSE between the measured spectrum and the first sub-spectrum library and the corresponding parameter vector X to be measured1' as the first parameter x to be measured1The first sampling point of the re-matching, note
Figure BDA0002582589310000113
Similarly, n is selected to be-1, and the grid point corresponding to the initial best matching parameter vector X' can be obtained in the first parameter X to be measured1X of position1Second adjacent grid point on coordinate axis
Figure BDA0002582589310000114
Taking a second adjacent grid point (moving one library establishing step length along the decreasing direction) as a reference point, fixing a first parameter to be measured of the second adjacent grid point, floating the rest parameters to be measured by the library establishing step lengths of the rest parameters to be measured, and acquiring a first parameter x to be measured from the original theoretical spectrum library1The first parameter x to be measured is obtained based on the second sub-spectrum library1The second sample point of (a) to be re-matched. Thereby, by changing the first parameter x to be measured1Step length delta x of building a library1Can be along the parameter x1Finding out a plurality of adjacent grid points of the initial approximate optimal matching parameter X' by the coordinate axes, thereby further acquiring the first parameter X to be measured1The plurality of re-matched sample points.
It should be noted that the adjacent grid points are grid points obtained along the increasing and/or decreasing direction of the selected topographic parameter, n is an integer greater than 0 (for example, n is 1,2, 3) representing the increasing direction of the parameter, and n is smaller than the increasing direction of the parameterAn integer of 0 (e.g., n-1, -2, -3) represents the decreasing direction of the parameter. Based on this, the same method as above is performed for each of the other parameters to be measured, and a parameter vector X ═ (X) to be measured can be obtained1,x2,…，xN) Each parameter x inNThe theoretical spectra corresponding to the at least 3 sampling points and each sampling point are respectively recorded as the mean square error of the theoretical spectra corresponding to the at least 3 sampling points and the measured spectrum
Figure BDA0002582589310000121
Wherein g isN，hNIs an integer which is not 0, but can not exceed the maximum range of the multiple of the library establishing step length of each parameter to be measured in the theoretical spectrum library.
In the prior art, a first adjacent grid point and a second adjacent grid point of an initial approximate optimal matching parameter vector on a corresponding coordinate axis where each parameter to be measured is located are directly used as a first sampling point and a second sampling point of the corresponding parameter to be measured, and no matching process is performed. Obviously, the prior art does not consider the possible coupling relationship among the parameters to be measured, and the sampling points selected along the coordinate axis of the single parameter often deviate from the bottom area of the MSE hypersurface, i.e. the MSE curve based on the sampling points can not be described by a quadratic curve. From another perspective, near the near-optimal matching point, when the coupling between the parameters to be measured dominates the MSE change, the information contained by the MSE curves over the dimensions of the individual parameters is insufficient, and the correction of the result by fitting these curves is limited or even erroneous. When an MSE curve is fitted and sampling points of each parameter to be measured are selected, a plurality of sampling parameter vectors of each parameter to be measured are obtained by obtaining adjacent grid points of initial approximate optimal matching parameter vectors on corresponding coordinate axes of each parameter to be measured, taking the adjacent grid points as reference points, fixing the value of the parameter to be measured of the adjacent grid points on the corresponding coordinate axes and floating the rest parameters by respective library building step lengths of the rest parameters to be measured, theoretical spectra corresponding to the sampling parameter vectors are obtained from the theoretical spectrum library to form a sub-spectrum library of each parameter to be measured, the theoretical spectra and the measured spectra in the corresponding sub-spectrum library are matched once again, grid points corresponding to the theoretical spectra with the minimum MSE value between the measured spectra are determined from the sub-spectrum library to serve as re-matched sampling points of the corresponding parameter to be measured, the sampling point of each parameter to be measured is closer to the bottom of the MSE hypersurface, the MSE value of the sampling point is smoother relative to the MSE curve formed by the corresponding parameter to be measured, and the sampling point is suitable for fitting by using a quadratic curve, so that the goodness of fit is improved. That is, obtaining the sampling point of each parameter to be measured by re-matching is more reasonable and reliable than performing MSE curve fitting by using the adjacent grid point of the initial approximate optimal matching parameter as the sampling point of each parameter to be measured in the prior art, so that the MSE curve fitting is performed based on the sampling points, and the obtained global optimal matching parameter is more accurate.
Referring to fig. 2 and 4, in this embodiment, the sample to be measured has 2 parameters to be measured: the feature parameter HT and the feature parameter MCD have 36 discrete grid points in a theoretical spectrum library established based on the two parameters to be measured, and have 36 theoretical spectra correspondingly. It is calculated that the initial near-best-match morphological parameter obtained in the theoretical spectral library is point a (28,32), i.e. the initial near-best-match parameter vector X ═ (28,32), which corresponds to a MSE value between the theoretical spectrum and the measured spectrum of 1.0009. Acquiring sampling points of the morphological parameter HT comprises the following steps: and taking the HT coordinate axis where the morphology parameter HT is located as a reference coordinate axis, selecting an adjacent grid point A1(32, 32) of 1 time of library building step length of the initial approximate optimal matching parameter vector A on the HT coordinate axis as a first adjacent grid point (along the increasing direction of the morphology parameter HT) of the initial approximate optimal matching parameter vector A. And taking the first adjacent grid point A1 as a reference point, fixing the parameter value 32 of the morphology parameter HT, floating the parameter value of the morphology parameter MCD in the value range, obtaining a plurality of sampling parameter vectors of the morphology parameter HT, and obtaining a corresponding theoretical spectrum from a theoretical spectrum library based on each sampling parameter vector, thereby obtaining a first sub-spectrum library of the morphology parameter HT.
From the first plurality of sub-spectral libraries, a theoretical spectrum and its corresponding parameter vector F, F ═ of the minimum value of MSE between the measured spectra are determined (32, 28))，MSE(HTF＝32)＝1.0009,HTFRepresents the HT values at grid points F, which are the first sample points for the re-matching of the topographical parameter HT. Similarly, a left-adjacent grid point a2(20, 32) of the initial approximate best matching parameter vector a (28,32) on the HT coordinate axis is selected, and it should be noted that, without loss of generality, the feature parameter HT of a2 is a change amount of the library step length (i.e. along the decreasing direction of the feature parameter HT) based on minus 2 times of the feature parameter HT in the initial approximate best matching parameter vector, and is used as a second adjacent grid point of the initial approximate best matching parameter vector a, and the second parameter x to be measured is floated by fixing the parameter value 20 of the feature parameter HT with the second adjacent grid point as a reference point2Namely, the parameter value of the morphology parameter MCD in the value range, a plurality of sampling parameter vectors are obtained, and the theoretical spectrum corresponding to each sampling parameter vector is obtained from the theoretical spectrum library, so that the second sub-spectrum library of the morphology parameter HT is obtained.
From the second sub-spectral library, the theoretical spectrum and its corresponding parameter vector H, H ═ 20, 36, MSE (HT) for the minimum value of MSE between the measured spectra are determinedH＝20)＝1.0068,HTHRepresents the HT values at grid point H, which is the second sample point of the re-match of the topographical parameter HT. Since the initial approximate best match parameter vector is also a sampling point, the morphological parameter HT is obtained by at least three sampling points H, F, A, MSE (HT)H)，MSE(HTF)，MSE(HTA) The mean square error values between the theoretical spectrum and the measured spectrum respectively corresponding to the sampling points H, F and A are respectively.
Similarly, by transforming the variable with different times and step lengths, a plurality of adjacent grid points of the initial approximate optimal matching parameter X' can be found along the HT coordinate axis, so as to further obtain the first parameter X to be measured1I.e. a plurality of sampling points of the topographical parameter HT, and each having a corresponding theoretical spectrum. According to the method, the second parameter x to be measured can be obtained in the same way2Namely at least 3 sampling points of the topographic parameter MCD and the theoretical spectrum corresponding to each sampling point. It should be noted that the sampling points of each parameter to be measured are determined not to be in execution sequence.
Step S4, parabolic fitting is carried out on the mean square error of the theoretical spectrum and the measured spectrum corresponding to at least three sampling points of each parameter to be measured relative to the distribution curve of the parameter value corresponding to each sampling point, and the global optimal matching value of each parameter to be measured is obtained.
Any sampling point corresponding to each parameter to be measured has a corresponding theoretical spectrum, the Mean Square Error (MSE) of the theoretical spectrum and the measured spectrum corresponding to all the sampling points of each parameter to be measured is subjected to parabolic fitting relative to the distribution curve of the parameter value corresponding to the corresponding sampling point, so that the mathematical relationship of the mean square error of the theoretical spectrum and the measured spectrum corresponding to each parameter relative to the specific parameter value is obtained, and further the minimum MSE in the parabola and the corresponding parameter value can be determined according to the parameter values corresponding to the at least 3 sampling points and the corresponding mean square error value, namely the global optimal matching value of the corresponding parameter to be measured is obtained.
And in the same way, traversing all sampling points corresponding to the rest of the feature parameters to perform the parabolic fitting to obtain the global optimal matching values of all the parameters to be measured, recording the parameter vector consisting of the global optimal matching values of all the parameters to be measured as a global optimal matching parameter vector, wherein the number of times of the parabolic fitting is equal to the number of the selected feature parameters. The more sampling points the parabolic fit, the more accurate the fitting result. In order to reduce the amount of calculation, in this embodiment, three sampling points are obtained for each parameter to be measured to perform parabolic fitting.
Specifically, each parameter x to be measuredNThe mean square error MSE (x) of the theoretical spectrum and the measured spectrum corresponding to each of the three sampling pointsN) The distribution curve of the parameter values corresponding to the sampling points is subjected to parabolic fitting based on a parabolic equation disclosed by the following equation (2),
MSE(xN)＝aN(xN)2+bNxN+cNformula (2);
in the formula (2), aN，bN，cNFor any parameter x to be measuredNOf corresponding fitted parabolic equationsThree characteristic parameters, here requiring aN>0 to ensure that the parabola can take a minimum value.
Further, each parameter x to be measured is adoptedNThe three sampling points correspond to the parameter values to be measured
Figure BDA0002582589310000151
And the mean square error value corresponding to each sampling point
Figure BDA0002582589310000152
Figure BDA0002582589310000153
Solving each parameter x to be measuredNThree characteristic parameters a of the above fitting parabolic equationN，bN，cN. Wherein, gN，hNIs an integer which is not 0 and does not exceed the maximum range of the multiple of the library establishing step length of each parameter to be measured in the theoretical spectrum library.
Illustratively, in this embodiment, g is chosenN＝-1，hNAs 1, three characteristic parameters a of the parabolic equation shown in the formula (2) are solved by the equation set shown in the following formula (3)N,bN,cN：
Figure BDA0002582589310000154
Based on this, each parameter x to be measured can be determinedNIn the range of the variation of the numerical value thereof,
Figure BDA0002582589310000155
when the spectrum is measured, the mean square error between the corresponding theoretical spectrum and the measured spectrum is the minimum,
Figure BDA0002582589310000161
namely, each parameter x to be measured of the sample to be measuredNThe global best match value.
Referring to fig. 5 and 6, in the present embodiment, the first parameter x to be measured is respectively measured1(i.e., topographical parameters)HT) and a second parameter x to be determined2The theoretical spectra corresponding to the respective sampling points of (i.e. the morphological parameter MCD) are parabolic fitted to the mean square error distribution of the measured spectrum. Firstly, substituting the parameter values corresponding to at least 3 sampling points of the morphology parameter HT and the corresponding Mean Square Error (MSE) values into equation (3), so as to obtain the following equation set (4):
Figure BDA0002582589310000162
based on the equation set shown in equation (4) above, it can be calculated: a is1＝6.19e-05，b1＝-3.71e-03，c11.06, i.e. obtaining a global best match value for the profile parameter HT
Figure BDA0002582589310000163
By adopting the same method and combining with the method shown in FIG. 6, the global optimum matching value MCD of the morphology parameter MCD can be obtained2，MCD 230. The above global best match value HT2And global best match value MCD2Forming a global best match parameter vector G2(30，30)。
As shown in FIG. 4, to verify the accuracy of the global best match value, the method is based on the result of HT2And MCD2Composed global best match parameter vector G2(30, 30) obtaining a parameter vector G2Corresponding theoretical spectrum, and calculating the mean square error MSE (G) of the theoretical spectrum and the measured spectrum2(30，30))＝1。
In the prior art, the first parameter x to be measured1Namely, a plurality of sampling points of the morphology parameter HT are points A, A1 and A5, and the mean square error of the theoretical spectrum and the measured spectrum corresponding to the three sampling points is MSE (HT)A＝28)＝1.0009，MSE(HTA1＝32)＝1.0045，MSE(HTA524, 1.0095, the second parameter x to be measured2Namely, a plurality of sampling points of the morphology parameter MCD are points A, A3 and A4, and the mean square error of the theoretical spectrum and the measured spectrum corresponding to the three sampling points is MSE (MCD)A＝32)＝1.0009，MSE(MCDA3＝36)＝1.02197，MSE(MCDA4＝28)＝1.0095。
The global optimal matching numerical value of the morphological parameters HT and MCD which are fitted by adopting a parabola for sampling point sets in the prior art is HT1＝27.18nm，MCD131.16nm, corresponding global best match value HT1And global best match value MCD1Forming corresponding global best match parameter vectors G1(27.18, 31.16) which corresponds to a mean square error of the theoretical spectrum with the measured spectrum of MSE (G)1(27.18, 31.16)) ═ 1.0008. Therefore, the mean square error value of the theoretical spectrum and the measured spectrum corresponding to the global optimal matching parameter vector of the sample to be measured determined by the method disclosed by the embodiment is smaller than the mean square error value of the theoretical spectrum and the measured spectrum which are optimally matched and calculated by the traditional fitting method. It should be noted that, the number of times of parabolic fitting performed by the method disclosed in this embodiment based on the parabolic equation is equal to the number of parameters to be measured included in the structural model of the sample to be measured. When the structural model of the sample to be measured is defined by the feature parameter HT, the feature parameter MCD, and the feature parameter sidewall angle (SWA), it is necessary to perform the parabolic fitting 3 times.
The method disclosed by the embodiment has technical advantages for the hypersurface in which the mean square error MSE of the measured spectrum and the theoretical spectrum library is non-orthogonal, and the global optimal matching parameter vector of the sample to be measured is obtained through fitting. The method comprises the steps of obtaining adjacent grid points of initial approximate optimal matching parameter vectors on corresponding coordinate axes of each parameter to be measured, fixing the numerical values of the parameter to be measured of the adjacent grid points on the corresponding coordinate axes by taking the adjacent grid points as reference points, floating other parameters by using respective library building step lengths of the other parameters to be measured, obtaining a plurality of sampling parameter vectors of each parameter to be measured, obtaining theoretical spectra corresponding to the sampling parameter vectors from the theoretical spectrum library to form a sub-spectrum library of each parameter to be measured, matching theoretical spectra and measured spectra in the corresponding sub-spectrum library once again, determining grid points corresponding to the theoretical spectra with minimum MSE (mean Square error) values between the measured spectra from the sub-spectrum library as re-matched sampling points of the corresponding parameters to be measured, and enabling the obtained sampling points of each parameter to be measured to be closer to the bottom of the MSE hyper-curved surface, the MSE values of the sampling points are smoother relative to an MSE curve formed by corresponding parameters to be measured and are suitable for fitting by using a quadratic curve, so that the goodness of fit is improved, namely the MSE curve fitting is performed on the sampling points of each parameter to be measured, which are acquired based on the method, and the obtained global optimal matching parameters are more accurate.
Example two:
based on the method disclosed in the first embodiment and based on the same inventive concept, the present embodiment also discloses an apparatus for measuring an optical critical dimension, which is characterized in that the method for determining a morphological parameter of a sample to be measured from a theoretical spectral library disclosed in the first embodiment is used, and a global optimal matching value of each parameter to be measured is output. Please refer to the first embodiment for a specific technical solution of the method in this embodiment, which is not described herein again.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (10)

1. A method for determining parameters of a sample to be measured from a theoretical spectral library is characterized by comprising the following steps:
s1, constructing a theoretical spectrum library according to a structural model of a sample to be measured, wherein the structural model of the sample to be measured comprises at least two parameters to be measured, values of each parameter to be measured are combined to form a plurality of parameter vectors to be measured, discrete grid points and theoretical spectra are obtained based on the parameter vectors to be measured, the discrete grid points and the theoretical spectra are in one-to-one correspondence with one another, and the theoretical spectrum library comprises the parameter vectors to be measured, the discrete grid points and the theoretical spectra;
s2, obtaining a measured spectrum, and determining an initial approximate optimal matching spectrum and an initial approximate optimal matching parameter vector of the measured spectrum from a theoretical spectrum library;
s3, acquiring at least three sampling points of each parameter to be measured, and the mean square error of the theoretical spectrum and the measured spectrum corresponding to each sampling point, wherein the sampling points comprise grid points corresponding to an initial approximate optimal matching spectrum and re-matched sampling points of each parameter to be measured acquired based on an initial approximate optimal matching parameter vector;
s4, parabolic fitting is carried out on the mean square error of the theoretical spectrum and the measured spectrum corresponding to at least three sampling points of each parameter to be measured relative to the distribution curve of the parameter value corresponding to each sampling point, and the global optimal matching value of each parameter to be measured is obtained.
2. The method as claimed in claim 1, wherein the step S1 of obtaining discrete grid points and theoretical spectra based on the parameter vector to be measured includes: and respectively carrying out discretization processing on each parameter to be measured according to the value range of each parameter to be measured and the library building step length preset by each parameter to be measured, forming discrete grid points by parameter vectors to be measured formed by the value combination of each parameter to be measured, and acquiring the theoretical spectrum corresponding to each parameter vector to be measured through the RCWA algorithm.
3. The method according to claim 1, wherein the step S2 specifically includes: obtaining a measured spectrum, performing library matching on the measured spectrum and a theoretical spectrum library, obtaining a mean square error between the measured spectrum and the theoretical spectrum, and determining the theoretical spectrum with the minimum mean square error between the measured spectrum and the theoretical spectrum library as an initial approximate optimal matching spectrum of the measured spectrum, wherein a parameter vector corresponding to the initial approximate optimal matching spectrum is an initial approximate optimal matching parameter vector of the measured spectrum.
4. The method according to claim 1, wherein the sampling points of the re-matching of each parameter to be measured obtained based on the initial approximate best matching parameter vector in step S3 include:
acquiring adjacent grid points of the initial approximate optimal matching parameter vector on the corresponding coordinate axis of each parameter to be measured;
respectively taking adjacent grid points on the corresponding coordinate axis of each parameter to be measured as reference points, fixing the value of the parameter to be measured of the adjacent grid points on the corresponding coordinate axis, floating the rest parameters to be measured by the respective library building step length of the rest parameters to be measured, obtaining a plurality of sampling parameter vectors of each parameter to be measured, and obtaining theoretical spectrums corresponding to the sampling parameter vectors from the theoretical spectrum library to form a sub-spectrum library of each parameter to be measured;
and respectively re-matching the theoretical spectrum in the sub-spectrum library of each parameter to be measured with the measured spectrum, and determining a parameter vector to be measured corresponding to the theoretical spectrum with the minimum mean square error value between the theoretical spectrum and the measured spectrum from the sub-spectrum library as a re-matched sampling point of the corresponding parameter to be measured.
5. The method according to claim 4, characterized in that said adjacent grid points are at least two adjacent grid points having a library step size of an integer multiple of the respective selected parameter under test in the direction of increasing and/or decreasing of the selected parameter under test;
the at least two neighboring grid points include a first neighboring grid point and a second neighboring grid point.
6. The method of claim 5,
the number of the sub-spectrum libraries of each parameter to be measured is at least two, and the sub-spectrum libraries comprise a first sub-spectrum library and a second sub-spectrum library;
the first sub-spectral library is acquired based on the first neighboring grid point and the second sub-spectral library is acquired based on the second neighboring grid point.
7. The method according to claim 6, wherein the number of the re-matched sampling points of each parameter to be measured is at least two, including a re-matched first sampling point and a re-matched second sampling point;
the first sampling point which is matched again is obtained based on the first sub-spectrum library, and the second sampling point which is matched again is obtained based on the second sub-spectrum library;
and the first and second re-matched sampling points are positioned on one side or two sides of the grid point corresponding to the initial approximate optimal matching spectrum.
8. The method according to any one of claims 1 to 7, wherein in step S4, a parabolic fitting is performed on a distribution curve of mean square error of a theoretical spectrum and a measured spectrum corresponding to each of at least three sampling points of each parameter to be measured with respect to a parameter value to be measured corresponding to the sampling point based on a parabolic equation disclosed by the following formula:
MSE(xN)＝aN(xN)2+bNxN+cN；
wherein x isNRepresenting any of said parameters to be measured, MSE (x)N) Representing the respective parameter to be measuredMean square error of the theoretical spectrum and the measured spectrum corresponding to the sampling points, aN，bN，cNThree characteristic parameters of a fitted parabolic equation corresponding to said parameter to be measured, aN>0。
9. The method according to claim 8, wherein the step S4 further comprises:
solving three characteristic parameters a of a fitting parabolic equation of each parameter to be measured by adopting the numerical values of the parameter to be measured corresponding to the three sampling points of each parameter to be measured and the mean square error value corresponding to each sampling pointN，bN，cN；
Three characteristic parameters a of the fitting parabolic equation based on each parameter to be measuredN，bN，cNDetermining the global optimum matching value of each parameter to be measured as
Figure FDA0002582589300000031
10. An optical critical dimension measurement device, characterized in that it uses the method of determining the parameters of the sample to be measured from the theoretical spectral library as claimed in any of claims 1 to 9 and outputs the global best match value for each parameter to be measured.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113566739A (en) * 2021-08-23 2021-10-29 上海精测半导体技术有限公司 Library matching method, system, server and storage medium for optical scattering
WO2022156578A1 (en) * 2021-01-20 2022-07-28 睿励科学仪器（上海）有限公司 Method and apparatus for acquiring sample parameter information
WO2022213740A1 (en) * 2021-04-08 2022-10-13 睿励科学仪器（上海）有限公司 Method and apparatus for comparing spectra

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20020038196A1 (en) * 2000-08-10 2002-03-28 Johnson Kenneth C. Database interpolation method for optical measurement of diffractive microstructures
CN102798342A (en) * 2012-08-02 2012-11-28 华中科技大学 Fitting error interpolation based library matching method for optical scattering measurement
CN105444666A (en) * 2014-05-29 2016-03-30 睿励科学仪器（上海）有限公司 Method and device for measuring OCD (optical critical dimension)

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20020038196A1 (en) * 2000-08-10 2002-03-28 Johnson Kenneth C. Database interpolation method for optical measurement of diffractive microstructures
CN102798342A (en) * 2012-08-02 2012-11-28 华中科技大学 Fitting error interpolation based library matching method for optical scattering measurement
CN105444666A (en) * 2014-05-29 2016-03-30 睿励科学仪器（上海）有限公司 Method and device for measuring OCD (optical critical dimension)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2022156578A1 (en) * 2021-01-20 2022-07-28 睿励科学仪器（上海）有限公司 Method and apparatus for acquiring sample parameter information
WO2022213740A1 (en) * 2021-04-08 2022-10-13 睿励科学仪器（上海）有限公司 Method and apparatus for comparing spectra
CN113566739A (en) * 2021-08-23 2021-10-29 上海精测半导体技术有限公司 Library matching method, system, server and storage medium for optical scattering
CN113566739B (en) * 2021-08-23 2023-06-13 上海精测半导体技术有限公司 Library matching method, system, server and storage medium for optical scattering

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