CN113566739B - Library matching method, system, server and storage medium for optical scattering - Google Patents
Library matching method, system, server and storage medium for optical scattering Download PDFInfo
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Abstract
The invention relates to a library matching method, a system, a server and a readable storage medium for optical scattering, which are characterized in that a theoretical spectrum library is established for a target to be detected, nominal values of morphology parameters are set, then the theoretical spectrum library of morphology parameters is interpolated to obtain an interpolation theoretical spectrum corresponding to the nominal values of morphology parameters, a measured spectrum is obtained through measurement, and when the deviation value of the measured spectrum and the theoretical spectrum does not meet a threshold condition, the nominal values of morphology parameters are updated until the deviation value meets the threshold condition, so that the extraction speed is improved under the condition that the extraction accuracy is not influenced, and the technical problems of low extraction speed and low extraction accuracy in the prior art are solved.
Description
Technical Field
The present invention relates to the field of optical scattering technologies, and in particular, to a library matching method, system, server, and storage medium for optical scattering.
Background
The basic principle of the optical scatterometry method, also known as optical critical dimension (optical critical dimension, OCD) measurement method, can be summarized as: a beam of polarized light with a special polarization state is projected to the surface of a sample to be measured, the change of the polarization state of the polarized light before and after reflection is obtained by measuring the reflected light of the sample to be measured, and then the morphological parameters of the sample to be measured, such as the linewidth, the line height, the side wall angle, the depth, the period, the roughness and the like of the obtained nano grating in the processes of photoetching, etching and the like, are extracted from the polarized light.
Compared with microscopic morphology measuring means such as a scanning electron microscope, an atomic force microscope and the like, the optical scattering measuring technology has the advantages of high speed, low cost, no contact, no damage and the like, and therefore, the method is widely applied to the field of online monitoring of the prior process. However, the microscopic morphological parameters of the sample to be measured can be directly obtained by the measuring means such as a scanning electron microscope, an atomic force microscope and the like, so that the measuring means is a 'what you see is what you get'; in contrast, the optical scattering measurement technology only obtains a group of light intensity signals related to incident wavelength or incident angle distribution and other derivative signals, such as reflectivity, ellipsometry parameters, mueller matrix and the like, and the morphological parameters of the sample to be measured can be extracted from the measurement signals through a certain data analysis means.
The basic principle of the data analysis method adopted in the optical scattering measurement can be summarized as follows: searching a group of sample morphology parameter values in a reasonable floating range of the sample morphology parameters, so that the deviation between the corresponding theoretical spectrum and the sample measured spectrum is minimum, and the group of morphology parameter values are regarded as the morphology parameters corresponding to the sample to be measured. The process of searching for such a set of sample morphology parameters, also referred to as a sample to-be-measured parameter extraction process, is implemented mainly by two methods: nonlinear regression methods and library matching methods.
And extracting the to-be-detected morphology parameters based on a nonlinear regression method, taking the deviation between the minimized theoretical spectrum and the measured spectrum as an optimization target, and starting from the nominal value of the to-be-detected morphology parameters, obtaining a series of intermediate iteration parameter points by calculating the iteration direction and the iteration step length, so that the deviation between the theoretical spectrum and the measured spectrum is continuously evolved towards the minimized state until the deviation is smaller than a certain preset threshold value. The method has the advantages that the method generally searches along the gradient descending direction of the objective function when searching the parameter value to be detected in the parameter space, rather than searching the whole parameter space, and the convergence efficiency of the objective function is higher. The disadvantage is that each time an iteration direction and step size are determined by calculation, a corresponding theoretical spectrum needs to be calculated for a plurality of sets of different morphological parameters (hereinafter this process is referred to as a forward modeling process). Because the forward modeling process in the optical scatterometry involves the construction and the solution of a complex partial differential equation, the calculation efficiency is lower, and the extraction efficiency of the morphological parameters to be detected based on a nonlinear regression algorithm is difficult to meet the requirement of online real-time monitoring in the actual production and application.
The implementation process of the library matching method is divided into an offline stage and an online stage. In the off-line stage, firstly, determining the floating range of the morphological parameters to be detected of the sample, then, performing discretization, calculating a theoretical spectrum corresponding to the discrete grid parameter points, and constructing a theoretical spectrum library. In the on-line stage, only the deviation between the measured spectrum and the theoretical spectrum in the library is calculated, and the theoretical spectrum with the smallest deviation is selected from the calculated deviation, and the corresponding morphological parameter is the final measurement result of the parameter to be measured. Because the time-consuming library building process is completed in an off-line stage, compared with a nonlinear regression algorithm, the calculation efficiency of the library matching in an on-line stage is greatly improved, and the method is a main means for on-line monitoring practically at present. However, the conventional library matching method only searches on the existing spectrum in the library, and the obtained measurement result always falls on the discrete grid points used for library construction, so that the accuracy of the measurement result is always limited by the grid discrete step size.
Disclosure of Invention
The invention provides a library matching method, a system, a server and a storage medium for optical scattering, which are used for solving the technical problem that the processing speed and the processing accuracy cannot be achieved in the prior art.
The present invention solves the above technical problems, and provides a library matching method for optical scattering, which includes the following steps:
s1, determining a floating interval of a morphology parameter of a target to be measured, performing discretization on the morphology parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning a value to the morphological parameter of the target to be measured and marking the value as a nominal value x, wherein the nominal value x is in a floating interval of the morphological parameter;
s4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value of the interpolation theoretical spectrum f (x) and the measured spectrum;
s5, comparing the deviation value with a preset deviation value;
s51, when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphological parameter of the target to be detected;
s52, when the deviation value is greater than or equal to the preset deviation threshold value,
acquiring an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h, wherein the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h;
based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x;
and updating the nominal value x of the morphological parameter by the iteration step length, and repeating the steps S4-S5 until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
Preferably, in the step S4, the interpolating the theoretical spectrum library with the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, specifically includes:
finding a grid point x' closest to the nominal value x among the plurality of discrete grid points;
screening out grid points in a plurality of discrete step ranges by taking the nearest grid point x' as a center point to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectrum corresponding to the discrete grid points in the interpolation point set, and calculating an interpolation theoretical spectrum f (x) corresponding to the nominal value x.
Preferably, the small offset Δh is within 10% of the nominal value x.
Preferably, in the step S52, the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x is obtained based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh
The method specifically comprises the following steps:
finding a grid point x ' closest to the nominal value x among the plurality of discrete grid points, wherein x=x ' +h, and h is a distance difference between x and x ';
performing second-order Taylor expansion on the interpolation theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the close adjacent value x+Δh at grid points x' with the nearest nominal value x, and calculating to obtain the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x
Wherein x= [ x ] 1 ,…x i ,…x m ] T ，x′＝[x′ 1 ,…x′ i ，…x′ m ] T ，h＝[h 1 ，…h i ，…h m ] T ，Δh＝[Δh 1 ，…Δh i ,…Δh m ] T M is the number of the morphology parameters, and the subscript i represents the sequence number of the ith morphology parameter in the morphology parameters, i is more than or equal to 1 and less than or equal to m.
Preferably, in the step S52, the gradient is based on
Calculating the overlap of the nominal values xSubstitution step length comprising the step of adopting a gradient of an interpolation theory spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method
And calculating the iteration step length.
Preferably, in the step S52, the updating the nominal value x of the morphology parameter with the iteration step includes updating the nominal value x with a sum of an existing assignment of the morphology parameter and the iteration step.
Preferably, the spectral library comprises signals of reflectivity and/or transmissivity and/or ellipsometry parameters and/or mueller matrices.
The invention also proposes a library matching system for optical scattering, comprising:
the spectrum establishment unit is used for determining a floating interval of the morphological parameter of the target to be detected, performing discretization on the morphological parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
the spectrum measuring unit is used for measuring the target to be measured to obtain a measured spectrum;
an interpolation calculation unit configured to perform an interpolation step including: assigning a nominal value x to the morphological parameter of the target to be measured, wherein the nominal value x is in a floating interval of the morphological parameter; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x;
a parameter matching unit, configured to perform a parameter matching step, where the parameter matching step includes: calculating the deviation value of the interpolation theory spectrum f (x) and the measurement spectrum, and comparing the deviation value with a preset deviation value; when the deviation value is smaller than the preset deviation threshold value, the nominal value x is used as an extraction value of the morphological parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, obtaining the tightness of the nominal value xA neighboring value x+Δh and a theoretical spectrum f (x+Δh) corresponding to the neighboring value x+Δh, wherein the neighboring value x+Δh and the nominal value x differ by a small offset Δh; based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x; updating the nominal value x of the morphological parameter by the iteration step length, and repeating the interpolation step and the parameter matching step until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
The invention also proposes a library matching server for optical scattering, comprising: the system comprises a memory, a processor and a library matching program for optical scattering stored on the memory and executable on the processor, wherein the library matching program for optical scattering realizes the steps of the library matching method for optical scattering.
The invention also proposes a readable storage medium having stored thereon a library matching program for optical scattering, which when executed by a processor implements the steps of the library matching method for optical scattering as described above.
The invention establishes a theoretical spectrum library aiming at a target to be detected, then interpolates according to the theoretical spectrum library to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x of the morphological parameter, calculates the deviation value of the measurement spectrum and the interpolation theoretical spectrum f (x) by measuring the obtained measurement spectrum, and calculates the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x when the deviation value does not meet the threshold condition
Updating the nominal value x of the morphological parameter, and then interpolating the theoretical spectrum library again until the deviation value of the interpolated theoretical spectrum f (x) corresponding to the measured spectrum and the nominal value x meets the condition, thereby improving the extraction speed without affecting the extraction accuracy, solving the technical problems of low extraction speed and low extraction accuracy in the prior art, saving calculation force, improving the processing speed and the extraction accuracy, and improving the user experience.
Drawings
FIG. 1 is a schematic diagram of a server architecture of a hardware operating environment involved in an embodiment of a library matching method for optical scattering of the present invention;
FIG. 2 is a flow chart of a library matching method for optical scattering according to the present invention;
FIG. 3 is a schematic flow chart of obtaining interpolation theory spectra in the library matching method for optical scattering according to the present invention;
FIG. 4 is a functional block diagram of a library matching system for optical scattering according to the present invention.
Detailed Description
The principles and features of the present invention are described below in connection with specific embodiments, examples of which are provided for illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, fig. 1 is a schematic diagram of a server structure of a hardware running environment according to an embodiment of the present invention.
As shown in fig. 1, the server may include: a processor 1001, such as a CPU, a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Wherein the communication bus 1002 is used to enable connected communication between these components. The user interface 1003 may include a Display (Display), and the optional user interface 1003 may also include a standard wired interface, a wireless interface. The network interface 1004 may optionally include a standard wired interface, a wireless interface (e.g., WI-FI interface). The memory 1005 may be a high-speed RAM memory or a stable memory (non-volatile memory), such as a disk memory. The memory 1005 may also optionally be a storage server separate from the aforementioned processor 1001.
Those skilled in the art will appreciate that the architecture shown in fig. 1 is not limiting of the server and may include more or fewer components than shown, or may combine certain components, or a different arrangement of components.
As shown in fig. 1, an operating system, a network communication module, a user interface module, and a library matching program for optical scattering may be included in a memory 1005 as one type of computer storage medium.
In the network device shown in fig. 1, the network interface 1004 is mainly used for connecting to a background server, and performing data communication with the background server; the user interface 1003 is mainly used for connecting peripherals; the network device invokes, via the processor 1001, a library matching program for optical scattering stored in the memory 1005 and performs the following operations:
s1, determining a floating interval of a morphology parameter of a target to be measured, performing discretization on the morphology parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning a value to the morphological parameter of the target to be measured and marking the value as a nominal value x, wherein the nominal value x is in a floating interval of the morphological parameter;
s4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value of the interpolation theoretical spectrum f (x) and the measured spectrum;
s5, comparing the deviation value with a preset deviation value;
s51, when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphological parameter of the target to be detected;
s52, when the deviation value is greater than or equal to the preset deviation threshold value,
acquiring an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h, wherein the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h;
based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x;
and updating the nominal value x of the morphological parameter by the iteration step length, and repeating the steps S4-S5 until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
Further, in the step S4, the interpolation is performed on the theoretical spectrum library by using the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, which specifically includes:
finding a grid point x' closest to the nominal value x among the plurality of discrete grid points;
screening out grid points in a plurality of discrete step ranges by taking the nearest grid point x' as a center point to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectrum corresponding to the discrete grid points in the interpolation point set, and calculating an interpolation theoretical spectrum f (x) corresponding to the nominal value x.
Further, the minute offset amount Δh is within 10% of the nominal value x, and still further, the minute offset amount Δh is within 5% of the nominal value x.
Further, in the step S52, the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x is obtained based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh
The method specifically comprises the following steps:
a grid point x ' closest to the nominal value x is found among the plurality of discrete grid points, and x=x ' +h, h being the distance difference between x and x '.
Performing second-order Taylor expansion on the interpolation theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the close adjacent value x+Δh at grid points x' with the nearest nominal value x, and calculating to obtain the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x
Wherein x= [ x ] 1 ,…x i ,…x m ] T ，x′＝[x′ 1 ,…x′ i ，…x′ m ] T ，h＝[h 1 ，…h i ，…h m ] T ，Δh＝[Δh 1 ,…Δh i ,…Δh m ] T M is the number of the morphology parameters, and subscript i represents the sequence number of the ith morphology parameter in the morphology parameters, i is more than or equal to 1 and less than or equal to m; for each nominal value x of the topographical parameter, the gradient of the spectrum
And respectively performing calculation.
The second-order taylor expansion is performed on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, and the second-order taylor expansion is performed respectively by:
from the above formula, the gradient of the spectrum at the nominal value x
The approximation is:
since x' is a grid point in the spectral library
And->
The theoretical spectral calculations stored in the library can be directly used,/-Can be calculated>
Is the gradient of the spectrum at x'>
Is the second derivative of the spectrum at x',
wherein Δs represents the discrete step size of the parameters when the spectral library is built, Δs= [ Δs ] 1 ,…Δs i ,…Δs m ] T . Since x ', x' +Δs, x '+2Δs are grid points in the spectral library, their corresponding theoretical spectra f (x'), f (x '+Δs), f (x' +2Δs) are all stored in the spectral library without requiring a recalculation. Thus, the gradient of the spectrum at the nominal value x
Can be obtained rapidly.
According to the gradient definition of the interpolation theory spectrum f (x) at the nominal value x, the theory spectrum needs to be recalculated in the traditional nonlinear regression method, and the gradient is recalculated
Since theoretical spectral calculations are typically very time consuming, traditional nonlinear regression methods are slow. The method disclosed by the invention can realize the gradient of the spectrum at the nominal value x by utilizing the theoretical spectrum stored in the spectrum library>
Is a fast approximation calculation of (c).
By using the gradient
The parameter iteration step may be calculated. The calculation formulas of the iteration step sizes in different nonlinear regression methods (such as gradient descent method, gaussian-Newton method and Levenberg-Marquardt method) are slightly different, for example, in Levenberg-Marquardt method, the iteration step size Δx is:
wherein y=f (x) represents an interpolation theoretical spectrum corresponding to the nominal value x; y is the actual measured spectrum; lambda is an adjustable constant; i is an identity matrix;
m represents the dimension of x, i.e. the number of topographical parameters.
Further, in the step S52, the calculating the iteration step of the nominal value x based on the gradient includes using a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x according to the levenberg-marquardt method
Calculation stationThe iteration step length.
Further, the spectral library comprises reflectivity and/or transmissivity and/or ellipsometry parameters and/or signals of a mueller matrix.
According to the embodiment, a theoretical spectrum library is established for a target to be detected, then an interpolation theoretical spectrum f (x) corresponding to the nominal value x of the morphology parameter is obtained through interpolation according to the theoretical spectrum library, the deviation value of the measured spectrum and the interpolation theoretical spectrum f (x) is calculated through measurement of the obtained measured spectrum, when the deviation value is larger than or equal to a threshold value, the nominal value x of the morphology parameter is updated until the deviation value is smaller than the threshold value, and at the moment, the nominal value x corresponding to the deviation value smaller than the threshold value is taken as a matching result, so that the technical effect of improving the extraction speed under the condition that the extraction accuracy is not affected is achieved, the technical problems of low extraction speed and low extraction accuracy in the prior art are solved, the calculation force is saved, the processing speed and the extraction accuracy are improved, and the user experience is improved.
Based on the above hardware structure, an embodiment of the library matching method for optical scattering of the present invention is presented.
The library matching method for optical scattering described with reference to fig. 2 comprises the steps of:
s1, determining a floating interval of a morphology parameter of a target to be measured, performing discretization on the morphology parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
it is easy to understand that the establishment of the theoretical spectrum requires determining the morphological parameters of the sample to be measured, such as a numerical range including the line width, the line height, the sidewall angle, the depth, the period, the roughness characteristic parameters, and the like of the grating structure, performing discretization processing on the numerical range according to a preset step length, thereby obtaining a plurality of discrete grid points, calculating the theoretical spectrum corresponding to each discrete grid point, and storing the discrete grid points and the theoretical spectra corresponding to each discrete grid point in a spectrum library.
S2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning a value to the morphological parameter of the target to be measured and marking the value as a nominal value x, wherein the nominal value x is in a floating interval of the morphological parameter;
s4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value of the interpolation theoretical spectrum f (x) and the measured spectrum;
it should be noted that, since the nominal value x is not necessarily on the parameter discrete grid, the interpolation theoretical spectrum f (x) corresponding to the nominal value x needs to be obtained by interpolation using the existing data in the spectrum library.
S5, comparing the deviation value with a preset deviation value;
s51, when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphological parameter of the target to be detected;
s52, when the deviation value is greater than or equal to the preset deviation threshold value,
acquiring an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h, wherein the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h;
based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x;
and updating the nominal value x of the morphological parameter by the iteration step length, and repeating the steps S4-S5 until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
It is worth emphasizing that when the deviation value is smaller than the preset deviation threshold, the accuracy meets the requirement at the moment, so that the nominal value x is directly used as the morphological parameter extraction value of the target structure to be detected.
According to the embodiment, a theoretical spectrum library is established for a target to be detected, then an interpolation theoretical spectrum f (x) corresponding to the nominal value x of the morphological parameter is obtained through interpolation according to the theoretical spectrum library of the morphological parameter, the deviation value of the measured spectrum and the interpolation theoretical spectrum f (x) is calculated through measurement of the obtained measured spectrum, the morphological parameter is updated and is used as a matching result, the extraction speed is improved under the condition that the extraction accuracy is not affected, the technical problems of low extraction speed or low extraction accuracy in the prior art are solved, the calculation force is saved, the processing speed is improved, and the user experience is improved.
Referring to fig. 3, in the step S4, the theoretical spectrum library is interpolated by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, which specifically includes:
first, a grid point x ' = [ x ' closest to the nominal value x is found among the plurality of discrete grid points ' 1 ,x′ 2 ,…x′ i ,…x′ m ] T The distance may be the Euclidean distance between two points;
and secondly, screening out grid points in a plurality of discrete step ranges by taking x' as a central point to form an interpolation point set. And then constructing a spectrum interpolation function according to the discrete grid points in the interpolation point set and the corresponding theoretical spectrums. The interpolation method can be polynomial interpolation, lagrange interpolation, B-spline interpolation and the like. And finally, utilizing the constructed spectrum interpolation function, and obtaining a theoretical spectrum y corresponding to x through rapid numerical calculation.
It is easy to understand that, in this embodiment, the nominal value x of the morphology parameter of the sample to be measured is denoted as x= [ x ] 1 ,x 2 ,…,x m ] T Wherein m represents the number of parameters to be measured, nominal valuex provides a starting point for a search path in the spectral library by the nonlinear regression method. By means of a preset step delta i (i=1, 2, …, m) discretizing the floating ranges of the parameters, respectively, to obtain discrete grid points. Then, by using methods such as strict Coupled Wave Analysis (Rigorous Coupled-Wave Analysis), finite element (Finite Element Method), boundary element (Boundary Element Method), etc., the theoretical spectrum y corresponding to each discrete grid point is calculated in a simulation manner.
If the measured spectrum is Y, the deviation value epsilon is the root mean square error between the theoretical spectrum Y and the measured spectrum Y:
wherein y is j And Y j The j-th element of the theoretical spectrum Y and the measured spectrum Y are respectively represented, N represents the number of elements contained in one spectrum, omega j The weights are represented and are typically determined by an optical scatterometry system.
It will be readily appreciated that the deviation epsilon may be calculated in other suitable ways and are presented herein for purposes of illustration only and not limitation. Then, comparing the deviation epsilon of the theoretical spectrum and the measured spectrum with a preset deviation threshold tol, and if epsilon is smaller than tol, completing parameter extraction; if ε is greater than or equal to tol, then the nominal value x needs to be updated using a nonlinear regression method.
Specifically, in the step S52, the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x is obtained based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh
The method specifically comprises the following steps:
finding a grid point x ' closest to the nominal value x among the plurality of discrete grid points, wherein x=x ' +h, and h is a distance difference between x and x ';
for the name at grid point x' where the nominal value x is nearestPerforming second-order Taylor expansion on the interpolation theoretical spectrum f (x) corresponding to the nominal value x and the interpolation theoretical spectrum f (x+Δh) corresponding to the close-proximity value x+Δh, and calculating to obtain the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x
Wherein x= [ x ] 1 ,…x i ,…x m ] T ，x′＝[x′ 1 ,…x′ i ,…x′ m ] T ，h＝[h 1 ,…h i ,…h m ] T ，Δh＝[Δh 1 ,…Δh i ，…Δh m ] T M is the number of the morphology parameters, and the subscript i represents the sequence number of the ith morphology parameter in the morphology parameters, i is more than or equal to 1 and less than or equal to m.
Specifically, in the step S52, the gradient is based on
Calculating the iteration step length of the nominal value x, including adopting a gradient of an interpolation theoretical spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method
And calculating the iteration step length.
Specifically, in the step S52, the updating the nominal value x of the morphology parameter with the iteration step includes updating the nominal value x with a sum of the existing assignment of the morphology parameter and the iteration step.
In particular, the spectral library comprises reflectivity and/or transmissivity and/or ellipsometric parameters and/or signals of a mueller matrix.
According to the embodiment, the spectrum library is interpolated by disclosing a specific calculation method, and the processing speed is further improved, the calculation resources are saved, the resource utilization efficiency is improved, and the user experience is improved by disclosing a specific gradient calculation method.
Referring to fig. 4, the present invention also proposes a library matching system for optical scattering,
the library matching system for optical scattering includes:
the spectrum establishment unit 10 is configured to determine a floating interval of a topography parameter of a target to be measured, perform discretization processing on the topography parameter with a set discrete step size to obtain a plurality of discrete grid points, and calculate a theoretical spectrum corresponding to each discrete grid point in a simulation manner to establish a theoretical spectrum library;
a spectrum measuring unit 20, configured to measure the target to be measured, so as to obtain a measured spectrum;
an interpolation calculation unit 30 for performing an interpolation step including: assigning a nominal value x to the morphological parameter of the target to be measured, wherein the nominal value x is in a floating interval of the morphological parameter; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x;
a parameter matching unit 40, configured to perform a parameter matching step, where the parameter matching step includes: calculating the deviation value of the interpolation theory spectrum f (x) and the measurement spectrum, and comparing the deviation value with a preset deviation value; when the deviation value is smaller than the preset deviation threshold value, the nominal value x is used as an extraction value of the morphological parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h are obtained, and the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h; based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient->
Calculating the iteration step length of the nominal value x; updating the nominal value x of the morphological parameter by the iteration step length, and repeating the interpolation step and the parameter matching step until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
Because the system adopts all the technical schemes of all the embodiments, the system has all the beneficial effects brought by the technical schemes of the embodiments and is not described in detail herein.
The invention also proposes a library matching server for optical scattering, comprising: the server adopts all the technical schemes of all the embodiments, so that all the beneficial effects brought by the technical schemes of the embodiments are not repeated herein.
The invention also provides a readable storage medium, on which a library matching program for optical scattering is stored, which when executed by a processor implements the library matching method for optical scattering as described above, and because the storage medium adopts all the technical solutions of all the embodiments, all the beneficial effects brought by the technical solutions of the embodiments are not described in detail herein.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A library matching method for optical scattering, characterized in that the library matching method for optical scattering comprises the steps of:
s1, determining a floating interval of a morphology parameter of a target to be measured, performing discretization on the morphology parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning a value to the morphological parameter of the target to be measured and marking the value as a nominal value x, wherein the nominal value x is in a floating interval of the morphological parameter;
s4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value of the interpolation theoretical spectrum f (x) and the measured spectrum;
s5, comparing the deviation value with a preset deviation threshold value;
s51, when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphological parameter of the target to be detected;
s52, when the deviation value is greater than or equal to the preset deviation threshold value,
acquiring an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h, wherein the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h;
based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x;
and updating the nominal value x of the morphological parameter by the iteration step length, and repeating the steps S4-S5 until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
2. The library matching method for optical scattering according to claim 1, wherein in the step S4, the theoretical spectrum library is interpolated with the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, and the method specifically comprises:
finding a grid point x' closest to the nominal value x among the plurality of discrete grid points;
screening out grid points in a plurality of discrete step ranges by taking the nearest grid point x' as a center point to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectrum corresponding to the discrete grid points in the interpolation point set, and calculating an interpolation theoretical spectrum f (x) corresponding to the nominal value x.
3. Library matching method for optical scattering according to claim 1, characterized in that the small offset Δh is within 10% of the nominal value x.
4. The library matching method for optical scattering according to claim 1, wherein in the step S52, the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x is obtained based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh
The method specifically comprises the following steps:
finding a grid point x ' closest to the nominal value x among the plurality of discrete grid points, wherein x=x ' +h, and h is a distance difference between x and x ';
performing second-order Taylor expansion on the interpolation theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh at a grid point x' closest to the nominal value x, and calculating to obtain the nominal valueGradient of interpolation theory spectrum f (x) corresponding to x
Wherein x= [ x ] 1 ，...x i ，...x m ]T，x′＝[x′ 1 ，...x′ i ，...x′ m ] T ，h＝[h 1 ，...h i ，...h m ] T ，Δh＝[Δh 1 ，...Δh i ，...Δh m ] T M is the number of the morphology parameters, and the subscript i represents the sequence number of the ith morphology parameter in the morphology parameters, i is more than or equal to 1 and less than or equal to m.
5. The library matching method for optical scattering according to claim 1, wherein in said step S52, said gradient-based
Calculating the iteration step length of the nominal value x, wherein the iteration step length comprises the gradient of the interpolation theory spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method>
And calculating the iteration step length.
6. Library matching method for optical scattering according to claim 1, characterized in that in step S52 the updating of the nominal value x of the topographical parameter with the iteration step comprises in particular updating the nominal value x with the sum of the existing assignment of the topographical parameter and the iteration step.
7. Library matching method for optical scattering according to claim 1, characterized in that the spectral library comprises reflectivity and/or transmissivity and/or ellipsometric parameters and/or signals of a mueller matrix.
8. A library matching system for optical scattering, characterized in that,
the library matching system for optical scattering includes:
the spectrum establishment unit is used for determining a floating interval of the morphological parameter of the target to be detected, performing discretization on the morphological parameter with a set discrete step length to obtain a plurality of discrete grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discrete grid point to establish a theoretical spectrum library;
the spectrum measuring unit is used for measuring the target to be measured to obtain a measured spectrum;
an interpolation calculation unit configured to perform an interpolation step including: assigning a nominal value x to the morphological parameter of the target to be measured, wherein the nominal value x is in a floating interval of the morphological parameter; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolation theoretical spectrum f (x) corresponding to the nominal value x;
a parameter matching unit, configured to perform a parameter matching step, where the parameter matching step includes: calculating a deviation value of the interpolation theory spectrum f (x) and the measurement spectrum, and comparing the deviation value with a preset deviation threshold; when the deviation value is smaller than the preset deviation threshold value, the nominal value x is used as an extraction value of the morphological parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, an immediately adjacent value x+delta h of the nominal value x and a theoretical spectrum f (x+delta h) corresponding to the immediately adjacent value x+delta h are obtained, and the immediately adjacent value x+delta h and the nominal value x differ by a small offset delta h; based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x+Δh) corresponding to the immediately adjacent value x+Δh, obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Based on the gradient
Calculating the iteration step length of the nominal value x; updating the nominal value x of the morphological parameter by the iteration step length, and repeating the interpolation step and the parameter matching step until the deviation value is smaller than a preset deviation threshold value so as to obtain the extracted value of the morphological parameter of the target to be detected.
9. A server, the server comprising: a memory, a processor and a library matching program stored on the memory and executable on the processor for optical scattering, which when executed by the processor implements the library matching method for optical scattering of any one of claims 1 to 7.
10. A readable storage medium, wherein a library matching program for optical scattering is stored on the readable storage medium, which when executed by a processor implements the library matching method for optical scattering according to any one of claims 1 to 7.
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