CN113566739A - 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, wherein a theoretical spectrum library is established for a target to be detected, nominal values of a morphology parameter are set, then the theoretical spectrum library of the morphology parameter is interpolated to obtain an interpolated theoretical spectrum corresponding to the nominal values of the morphology parameter, a measured spectrum is obtained through measurement, a deviation value between the measured spectrum and the theoretical spectrum is calculated, and when the deviation value does not meet a threshold condition, the nominal values of the morphology parameter are updated until the deviation value meets the threshold condition, so that the extraction speed is improved under the condition of not influencing the extraction accuracy, 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 optical scatterometry, also called Optical Critical Dimension (OCD) measurement, can be summarized as: a beam of polarized light with a special polarization state is projected to the surface of a sample to be detected, 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 detected, and then the morphological parameters of the sample to be detected, such as the morphological parameters of the line width, the line height, the side wall angle, the depth, the period, the roughness and the like of the nanometer grating obtained in the photoetching, etching and other processes, are extracted from the polarized light.
Compared with microscopic morphology measurement means such as a scanning electron microscope and an atomic force microscope, the optical scattering measurement technology has the advantages of high speed, low cost, no contact, no damage and the like, so the optical scattering measurement technology is widely applied to the field of advanced process on-line monitoring. However, the measurement means such as a scanning electron microscope, an atomic force microscope and the like can directly obtain the micro-morphology parameters of the sample to be measured, and is a 'what you see is what you get' measurement means; on the contrary, the optical scatterometry technique only obtains a set of light intensity signals related to incident wavelength or incident angle distribution and other derived signals, such as reflectivity, ellipsometry parameters, muller matrix, etc., and a certain data analysis means is required to extract the morphological parameters of the sample to be measured from the measurement signals.
The basic principle of the data analysis method adopted in the optical scattering measurement can be summarized as follows: and searching a group of sample morphology parameter values in a reasonable floating range of the sample morphology parameters to ensure that the deviation between the corresponding theoretical spectrum and the sample measurement spectrum is minimum, and considering the group of morphology parameter values as the morphology parameters corresponding to the sample to be detected. The process of finding such a set of sample morphological parameters, also called the sample parameter extraction process to be measured, mainly includes two methods: non-linear regression methods and library matching methods.
The method comprises the steps of extracting to-be-measured feature parameters based on a nonlinear regression method, taking the deviation between a minimum theoretical spectrum and a measurement spectrum as an optimization target, starting from a nominal value of the to-be-measured feature parameters, and obtaining a series of intermediate iteration parameter points by calculating an iteration direction and an iteration step length, so that the deviation between the theoretical spectrum and the measurement spectrum continuously evolves towards the minimum until the deviation is smaller than a certain preset threshold value. The method has the advantages that when the parameter value to be measured is searched in the parameter space, the parameter value is generally searched along the gradient descending direction of the target function, the whole parameter space is not searched, and the convergence efficiency of the target function is high. The disadvantage is that each time an iteration direction and step length are determined by calculation, corresponding theoretical spectra need to be calculated for multiple sets of different morphological parameters (hereinafter, this process is referred to as a forward modeling process). Because the forward modeling process in the optical scattering measurement relates to the construction and solution of a complex partial differential equation, the calculation efficiency is low, and the extraction efficiency of the to-be-detected morphology parameters based on the nonlinear regression algorithm is difficult to meet the requirement of online real-time monitoring in actual production and application.
The implementation process of the library matching method is divided into an off-line stage and an on-line stage. In an off-line stage, firstly determining the floating range of the morphological parameters to be measured of the sample, then performing discretization, calculating the 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 needs to be calculated, and the theoretical spectrum with the minimum 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 the off-line stage, compared with the nonlinear regression algorithm, the calculation efficiency of the library matching on-line stage is greatly improved, and the method is also a main means actually used for on-line monitoring at present. However, the traditional library matching method only searches on the existing spectrum in the library, and the obtained measurement result always falls on the discrete grid point used for building the library, so the accuracy of the measurement result is always limited by the discrete step length of the grid.
Disclosure of Invention
The invention provides a library matching method, a library matching system, a server and a storage medium for optical scattering, which aim to solve the technical problem that the processing speed and the processing accuracy cannot be compatible in the prior art.
The invention solves the technical problem and provides a library matching method for optical scattering, which comprises the following steps:
s1, determining a floating interval of the feature parameter of the target to be detected, performing discretization processing on the feature parameter by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in the floating interval of the morphology parameters;
s4, interpolating the theoretical spectrum library by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value between the interpolated 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 morphology parameter of the target to be detected;
s52, when the deviation value is larger than or equal to the preset deviation threshold value,
acquiring an adjacent value x + delta h of the nominal value x and a theoretical spectrum f (x + delta h) corresponding to the adjacent value x + delta h, wherein a slight offset delta h is formed between the adjacent value x + delta h and the nominal value x;
obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x;
and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
Preferably, in step S4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, specifically including:
finding a grid point x' among the plurality of discrete grid points that is closest to the nominal value x;
taking the closest grid point x' as a central point, screening out a plurality of grid points in the discrete step range to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectra corresponding to the discrete grid points in the interpolation point set, and calculating an interpolated theoretical spectrum f (x) corresponding to the nominal value x.
Preferably, said slight offset Δ h is within 10% of said nominal value x.
Preferably, in step S52, the step of obtaining the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the adjacent value x + Δ h
The method specifically comprises the following steps:
finding a grid point x ' that is closest to the nominal value x 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 interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediately adjacent value x + Δ h at the grid point x' where the nominal value x is closest to obtain a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Wherein x is [ x ]1,…xi,…xm]T，x′＝[x′1,…x′i，…x′m]T，h＝[h1，…hi，…hm]T，Δh＝[Δh1，…Δhi,…Δhm]TM is the number of the morphology parameters, subscript i represents the serial number of the ith morphology parameter in the morphology parameters, and i is more than or equal to 1 and less than or equal to m.
Preferably, in the step S52, the step of determining the gradient is based on
Calculating the iteration step size of the nominal value x, including the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method
And calculating the iteration step size.
Preferably, in step S52, the updating the nominal value x of the profile parameter by the iteration step includes updating the nominal value x by the sum of the existing assignment of the profile parameter and the iteration step.
Preferably, the spectral library comprises reflectivity and/or transmittance and/or ellipsometric parameters and/or mueller matrix signals.
The present invention also proposes a library matching system for optical scattering, comprising:
the spectrum establishing unit is used for determining a floating interval of the morphology parameters of the target to be detected, performing discretization processing on the morphology parameters by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization 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, the interpolation step including: assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in a floating interval of the morphology parameters; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x;
a parameter matching unit for performing a parameter matching step, the parameter matching step including: calculating a deviation value of the interpolated theoretical spectrum f (x) and the measured spectrum, and comparing the deviation value with a preset deviation value; when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphology parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, acquiring an adjacent value x + Δ h of the nominal value x and a theoretical spectrum f (x + Δ h) corresponding to the adjacent value x + Δ h, wherein a slight deviation Δ h is formed between the adjacent value x + Δ h and the nominal value x; obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x; and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
The present invention also proposes a library matching server for optical scattering, comprising: a memory, a processor and a library matching program for optical scattering stored on the memory and executable on the processor, the library matching program for optical scattering when executed by the processor implementing the steps of the library matching method for optical scattering as described above.
The present 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 method comprises the steps of establishing a theoretical spectrum library aiming at a target to be measured, then interpolating according to the theoretical spectrum library to obtain an interpolation theoretical spectrum f (x) corresponding to a nominal value x of the morphology parameter, measuring to obtain a measured spectrum, calculating a deviation value of the measured spectrum and the interpolation theoretical spectrum f (x), and calculating the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x when the deviation value does not meet a threshold value condition
The nominal value x of the morphology parameter is updated, then the theoretical spectrum library is interpolated again until the deviation value of the measured spectrum and the interpolated theoretical spectrum f (x) corresponding to the nominal value x meets the condition, so that the extraction speed is improved under the condition of not influencing the extraction accuracy, the technical problems of low extraction speed and low extraction accuracy in the prior art are solved, the calculation power is saved, the processing speed and the extraction accuracy are improved, and the user experience is improved.
Drawings
FIG. 1 is a schematic diagram of a server architecture of a hardware operating environment according to an embodiment of the library matching method for optical scattering of the present invention;
FIG. 2 is a schematic flow chart of a library matching method for optical scattering according to the present invention;
FIG. 3 is a schematic flow chart of the method for library matching of optical scattering according to the present invention for obtaining an interpolated theoretical spectrum;
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 this invention are described below in conjunction with specific embodiments, the examples given are intended to illustrate the invention 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 operating 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 a communication bus 1002 is used to enable connective communication between these components. The user interface 1003 may comprise a Display screen (Display), and the optional user interface 1003 may also comprise 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 non-volatile memory (e.g., a magnetic disk memory). The memory 1005 may alternatively be a storage server separate from the processor 1001.
Those skilled in the art will appreciate that the architecture shown in FIG. 1 does not constitute a limitation on the servers, and may include more or fewer components than those shown, or some components in combination, or a different arrangement of components.
As shown in fig. 1, a memory 1005, which is a kind of computer storage medium, may include therein an operating system, a network communication module, a user interface module, and a library matching program for optical scattering.
In the network device shown in fig. 1, the network interface 1004 is mainly used for connecting to a backend server and performing data communication with the backend server; the user interface 1003 is mainly used for connecting peripheral equipment; the network device invokes, via the processor 1001, a library matching routine for optical scattering stored in the memory 1005, and performs the following operations:
s1, determining a floating interval of the feature parameter of the target to be detected, performing discretization processing on the feature parameter by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in the floating interval of the morphology parameters;
s4, interpolating the theoretical spectrum library by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value between the interpolated 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 morphology parameter of the target to be detected;
s52, when the deviation value is larger than or equal to the preset deviation threshold value,
acquiring an adjacent value x + delta h of the nominal value x and a theoretical spectrum f (x + delta h) corresponding to the adjacent value x + delta h, wherein a slight offset delta h is formed between the adjacent value x + delta h and the nominal value x;
obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x;
and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
Further, in step S4, interpolating 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' among the plurality of discrete grid points that is closest to the nominal value x;
taking the closest grid point x' as a central point, screening out a plurality of grid points in the discrete step range to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectra corresponding to the discrete grid points in the interpolation point set, and calculating an interpolated theoretical spectrum f (x) corresponding to the nominal value x.
Further, the slight offset Δ h is within 10% of the nominal value x, and further, the slight offset Δ h 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 + Δ h) corresponding to the adjacent value x + Δ h
The method specifically comprises the following steps:
finding a grid point x ' that is closest to the nominal value x 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 interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediately adjacent value x + Δ h at the grid point x' where the nominal value x is closest to obtain a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Wherein x is [ x ]1,…xi,…xm]T，x′＝[x′1,…x′i，…x′m]T，h＝[h1，…hi，…hm]T，Δh＝[Δh1,…Δhi,…Δhm]TM is the number of the morphology parameters, subscript i represents the serial number of ith morphology parameter in the morphology parameters, and i is more than or equal to 1 and less than or equal to m; for the gradient of the spectrum at the nominal value x of each shape parameter
The calculations were performed separately.
The interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h are subjected to second-order taylor expansion, respectively:
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, it is not necessary to determine the position of the grid point
And
theoretical spectra stored in the library can be used directly for calculation,
is the gradient of the spectrum at x',
is the second derivative of the spectrum at x',
where Δ s represents a discrete step of a parameter when a spectral library is built, and Δ s ═ Δ s1,…Δsi,…Δsm]T. Since x ', x' + Δ s, x '+ 2 Δ s are grid points in the spectrum library, the corresponding theoretical spectra f (x'), f (x '+ Δ s), f (x' +2 Δ s) are stored in the spectrum library, and need not be recalculated. Thus, the gradient of the spectrum at the nominal value x
Can be obtained quickly.
According to the gradient definition of the interpolation theoretical spectrum f (x) at the nominal value x, the traditional nonlinear regression method needs to recalculate the theoretical spectrum and then calculate the gradient thereof
Since theoretical spectral calculations are typically very time consuming, conventional non-linear regression methods are slow. The method disclosed by the invention can realize the gradient of the spectrum at the nominal value x by using the theoretical spectrum stored in the spectrum library
Fast approximation calculation of (2).
Using said gradient
A parameter iteration step size may be calculated. Different non-linear regression methods (e.g. gradient descent, gauss-newton)Law, levenberg-marquardt method) the calculation formula of the iteration step size is slightly different, for example, in levenberg-marquardt method, the iteration step size Δ x is:
wherein, y ═ f (x) represents the interpolated theoretical spectrum corresponding to the nominal value x; y is an actual measured spectrum; λ is an adjustable constant; i is an identity matrix;
and m represents the dimension of x, namely the number of the morphological parameters.
Further, in the step S52, the step of calculating the iteration step of the nominal value x based on the gradient includes using a gradient of an interpolated theoretical spectrum f (x) corresponding to the nominal value x by using the levenberg-marquardt method
And calculating the iteration step size.
Further, the spectral library comprises reflectivity and/or transmittance and/or ellipsometric parameters and/or mueller matrix signals.
In the embodiment, a theoretical spectrum library is established for a target to be detected, an interpolation theoretical spectrum f (x) corresponding to the morphology parameter nominal value x is obtained through interpolation according to the theoretical spectrum library, a measurement spectrum is obtained through measurement, so that a deviation value between the measurement spectrum and the interpolation theoretical spectrum f (x) is calculated, when the deviation value is greater than or equal to a threshold value, the morphology parameter nominal value x is updated until the deviation value is less than the threshold value, and at the moment, the deviation value is less than the nominal value x corresponding to the threshold value as a matching result, so that the technical effect of improving the extraction speed without influencing the extraction accuracy is realized, the technical problems of low extraction speed and low extraction accuracy in the prior art are solved, the calculation power 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 proposed.
The library matching method for optical scattering described with reference to fig. 2 includes the steps of:
s1, determining a floating interval of the feature parameter of the target to be detected, performing discretization processing on the feature parameter by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization 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 according to the process conditions, for example, the numerical ranges including the line width, line height, sidewall angle, depth, period, roughness characteristic parameters, etc. of the grating structure, performing discretization processing on the numerical ranges according to the preset step length to obtain a plurality of discrete grid points, then calculating the theoretical spectrum corresponding to each discrete grid point, and storing the discrete grid points and their respective corresponding theoretical spectra in the spectrum library.
S2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in the floating interval of the morphology parameters;
s4, interpolating the theoretical spectrum library by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value between the interpolated 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 interpolated 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 morphology parameter of the target to be detected;
s52, when the deviation value is larger than or equal to the preset deviation threshold value,
acquiring an adjacent value x + delta h of the nominal value x and a theoretical spectrum f (x + delta h) corresponding to the adjacent value x + delta h, wherein a slight offset delta h is formed between the adjacent value x + delta h and the nominal value x;
obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x;
and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
It is worth emphasizing that when the deviation value is smaller than the preset deviation threshold value, the precision is judged to meet the requirement at the moment, and therefore the nominal value x is directly used as the feature parameter extraction value of the target structure to be detected.
In the embodiment, the extraction speed is improved under the condition of not influencing the extraction accuracy by establishing the theoretical spectrum library for the target to be detected, interpolating the theoretical spectrum library according to the morphological parameter to obtain the interpolation theoretical spectrum f (x) corresponding to the nominal value x of the morphological parameter, calculating the deviation value between the measured spectrum and the interpolation theoretical spectrum f (x) by measuring the obtained measured spectrum, updating the morphological parameter and taking the obtained result as the matching result, so that the technical problems of low extraction speed or low extraction accuracy in the prior art are solved, the calculation power is saved, the processing speed is improved, and the user experience is improved.
Referring to fig. 3, in step S4, interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, specifically including:
first, a grid point x 'closest to the nominal value x is found in the plurality of discrete grid points [ x'1,x′2,…x′i,…x′m]TThe distance may be the euclidean distance between two points;
secondly, taking x' as a central point, screening out grid points in a plurality of discrete step ranges 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 spectrum. The interpolation method may be polynomial interpolation, lagrange interpolation, B-spline interpolation, or the like. And finally, by using the constructed spectrum interpolation function, the theoretical spectrum y corresponding to the x can be obtained through rapid numerical calculation.
It is easy to understand that, in this embodiment, the nominal value x of the topographic parameter of the sample to be measured is denoted as x ═ x1,x2,…,xm]TAnd m represents the number of the parameters to be detected, and the nominal value x provides a starting point for a search path of the nonlinear regression method in the spectrum library. Using a predetermined step deltaiAnd (i is 1,2, …, m) discretizing the parameter floating ranges respectively to obtain discrete grid points. Then, a theoretical spectrum y corresponding to each discrete grid point is simulated and calculated by using a Method such as Rigorous Coupled-Wave Analysis (Rigorous Coupled-Wave Analysis), Finite Element (Finite Element Method), Boundary Element (Boundary Element Method) and the like.
If the measured spectrum is Y, the deviation value is epsilon, and the deviation value epsilon is the root mean square error between the theoretical spectrum Y and the measured spectrum Y:
wherein, yjAnd YjRespectively representing the jth element of the theoretical spectrum Y and the measured spectrum Y, N representing the number of elements contained in a spectrum, ωjThe weighting is typically determined by the optical scatterometry system.
It will be readily appreciated that the deviation epsilon may be calculated in other suitable ways and is used herein only to illustrate the principles of the invention and not to limit it. Then, comparing the deviation epsilon of the theoretical spectrum and the measured spectrum with the preset deviation threshold tol, and if epsilon is less than tol, finishing parameter extraction; if epsilon is larger than or equal to tol, the nominal value x needs to be updated by 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 + Δ h) corresponding to the adjacent value x + Δ h
The method specifically comprises the following steps:
finding a grid point x ' that is closest to the nominal value x 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 interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediately adjacent value x + Δ h at the grid point x' where the nominal value x is closest to obtain a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Wherein x is [ x ]1,…xi,…xm]T，x′＝[x′1,…x′i,…x′m]T，h＝[h1,…hi,…hm]T，Δh＝[Δh1,…Δhi，…Δhm]TM is the number of the morphology parameters, subscript i represents the serial number of the ith morphology parameter in the morphology parameters, and i is more than or equal to 1 and less than or equal to m.
Specifically, in the step S52, the step of determining the gradient is based on the gradient
Calculating the iteration step size of the nominal value x, including the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method
And calculating the iteration step size.
Specifically, in step S52, the updating the nominal value x of the profile parameter by the iteration step includes updating the nominal value x by the sum of the existing assignment of the profile parameter and the iteration step.
In particular, the spectral library comprises signals of reflectivity and/or transmittance and/or ellipsometric parameters and/or mueller matrices.
In the embodiment, the spectral library is interpolated by disclosing a specific calculation method, and the processing speed is further increased by disclosing a specific gradient calculation method, so that the calculation resources are saved, the resource utilization efficiency is improved, and the user experience is improved.
Referring to fig. 4, the present invention also proposes a library matching system for optical scattering,
the library matching system for optical scattering comprises:
the spectrum establishing unit 10 is configured to determine a floating interval of a morphological parameter of a target to be measured, perform discretization on the morphological parameter by a set discretization step length to obtain a plurality of discretization grid points, and perform simulation calculation on a theoretical spectrum corresponding to each discretization grid point to establish a theoretical spectrum library;
the spectrum measuring unit 20 is used for measuring the target to be measured to obtain a measured spectrum;
an interpolation calculation unit 30 for performing an interpolation step, the interpolation step including: assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in a floating interval of the morphology parameters; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolated 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 a deviation value of the interpolated theoretical spectrum f (x) and the measured spectrum, and comparing the deviation value with a preset deviation value; when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphology parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, acquiring an adjacent value x + Δ h of the nominal value x and a theoretical spectrum f (x + Δ h) corresponding to the adjacent value x + Δ h, wherein a slight deviation Δ h is formed between the adjacent value x + Δ h and the nominal value x; obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x; and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
Since the system adopts all the technical solutions of all the embodiments, all the beneficial effects brought by the technical solutions of the embodiments are achieved above, and are not described in detail herein.
The present invention also proposes a library matching server for optical scattering, comprising: the server adopts all technical solutions of all the embodiments, so that all the beneficial effects brought by the technical solutions of the embodiments are achieved, and the details are not repeated herein.
The present invention further provides a readable storage medium, where a library matching program for optical scattering is stored, and when the library matching program for optical scattering is executed by a processor, the library matching method for optical scattering is implemented.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A library matching method for optical scattering, characterized in that it comprises the steps of:
s1, determining a floating interval of the feature parameter of the target to be detected, performing discretization processing on the feature parameter by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization grid point to establish a theoretical spectrum library;
s2, measuring the target to be measured to obtain a measurement spectrum;
s3, assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in the floating interval of the morphology parameters;
s4, interpolating the theoretical spectrum library by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, and calculating a deviation value between the interpolated 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 morphology parameter of the target to be detected;
s52, when the deviation value is larger than or equal to the preset deviation threshold value,
acquiring an adjacent value x + delta h of the nominal value x and a theoretical spectrum f (x + delta h) corresponding to the adjacent value x + delta h, wherein a slight offset delta h is formed between the adjacent value x + delta h and the nominal value x;
obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x;
and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
2. The library matching method for optical scattering according to claim 1, wherein in step S4, interpolating the theoretical spectrum library by the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x, specifically comprises:
finding a grid point x' among the plurality of discrete grid points that is closest to the nominal value x;
taking the closest grid point x' as a central point, screening out a plurality of grid points in the discrete step range to form an interpolation point set; and constructing a spectrum interpolation function according to the theoretical spectra corresponding to the discrete grid points in the interpolation point set, and calculating an interpolated 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 slight offset Δ h 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 + Δ h) corresponding to the adjacent value x + Δ h
The method specifically comprises the following steps:
finding a grid point x ' that is closest to the nominal value x 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 interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the adjacent value x + Δ h at a grid point x' closest to the nominal value x, and calculating the gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x
Wherein x is [ x ]1，...xi，...xm]T，x′＝[x′1，...x′i，...x′m]T，h＝[h1，...hi，...hm]T，Δh＝[Δh1，...Δhi，...Δhm]TM is the number of the morphology parameters, subscript i represents the serial number of the ith morphology parameter in the morphology parameters, and 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,in the step S52, the step of determining the gradient is based on
Calculating the iteration step size of the nominal value x, including the gradient of the interpolation theoretical spectrum f (x) corresponding to the nominal value x by adopting a Levenberg-Marquardt method
And calculating the iteration step size.
6. The library matching method for optical scattering of claim 1, wherein the step S52, updating the nominal value x of the topographical parameter with the iteration step size, specifically comprises updating the nominal value x with a sum of the existing assignment of the topographical parameter and the iteration step size.
7. Library matching method for optical scattering according to claim 1, wherein the spectral library comprises signals of reflectivity and/or transmittance and/or ellipsometric parameters and/or mueller matrices.
8. A library matching system for optical scattering,
the library matching system for optical scattering comprises:
the spectrum establishing unit is used for determining a floating interval of the morphology parameters of the target to be detected, performing discretization processing on the morphology parameters by a set discretization step length to obtain a plurality of discretization grid points, and performing simulation calculation on a theoretical spectrum corresponding to each discretization 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, the interpolation step including: assigning values to the morphology parameters of the object to be detected and recording the values as nominal values x, wherein the nominal values x are in a floating interval of the morphology parameters; interpolating the theoretical spectrum library by using the nominal value x to obtain an interpolated theoretical spectrum f (x) corresponding to the nominal value x;
a parameter matching unit for performing a parameter matching step, the parameter matching step including: calculating a deviation value of the interpolated theoretical spectrum f (x) and the measured spectrum, and comparing the deviation value with a preset deviation value; when the deviation value is smaller than the preset deviation threshold value, taking the nominal value x as an extraction value of the morphology parameter of the target to be detected; when the deviation value is greater than or equal to the preset deviation threshold value, acquiring an adjacent value x + Δ h of the nominal value x and a theoretical spectrum f (x + Δ h) corresponding to the adjacent value x + Δ h, wherein a slight deviation Δ h is formed between the adjacent value x + Δ h and the nominal value x; obtaining a gradient of the interpolated theoretical spectrum f (x) corresponding to the nominal value x based on the interpolated theoretical spectrum f (x) corresponding to the nominal value x and the theoretical spectrum f (x + Δ h) corresponding to the immediate value x + Δ h
Based on the gradient
Calculating an iteration step size of the nominal value x; and updating the nominal value x of the morphology 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 extraction value of the morphology parameter of the target to be detected.
9. A server, characterized in that the server comprises: 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, characterized in that the readable storage medium has stored thereon a library matching program for optical scattering, 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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