Morphological parameter measuring method

Abstract

The invention provides a morphology parameter measurement method, which comprises the following steps of: constructing a first weight vector set comprising a plurality of weight vectors for a first spectrum matching function, performing spectrum matching on a reference spectrum by using the first spectrum matching function for each weight vector in the first weight vector set, and obtaining a value of a corresponding loss function according to a matching result, and obtaining a first loss function set. Afterwards, a minimum loss function is obtained, because a matching result corresponding to the minimum loss function is more accurate, a weight vector corresponding to the minimum loss function is used as a target weight vector, a second spectrum matching function is constructed by using the target weight vector, the measurement spectrum and the theoretical spectrum, and a morphology parameter measurement value is obtained. The reference sample and the sample to be measured comprise the same periodic structure, so that the target weight vector determined by the reference spectrum of the reference sample can be used for obtaining a more matched theoretical spectrum for the measurement spectrum, and further more accurate morphology parameter measurement values of the sample to be measured can be obtained.

Description

Technical Field

[0001] This disclosure relates to the field of morphological parameter measurement technology for periodic structures, and in particular to a method for measuring morphological parameters. Background Technology

[0002] As the semiconductor industry continues to advance towards nanometer technology nodes, the linewidth of integrated circuits is constantly shrinking, and the structural design of integrated circuit devices is becoming increasingly complex. Only through strict process control can fully functional circuits and high-speed operating devices be obtained.

[0003] In current semiconductor manufacturing process control, optical critical dimension (OCD) measurement equipment is a common device with advantages such as high speed, low cost, and non-destructive operation. It can be used to measure the morphological parameters of periodic structures on samples.

[0004] In related technologies, methods for measuring morphological parameters may include two steps:

[0005] Step 1, Spectrum Acquisition Process. The optical scattering signal of the sample is acquired and processed into a measurement spectrum. The measurement spectrum includes, but is not limited to: reflectance spectrum, polarization state change spectrum, Fourier coefficient spectrum of polarization state analysis, or directly output spectrum describing the scattering process (such as NCS spectrum or Mueller spectrum).

[0006] Step 2, spectral matching process. A model of the periodic structure on the sample is established, and optimal matching is achieved between the theoretical spectrum and the measured spectrum. This model includes the morphological model of the periodic structure on the sample and incident light information. The theoretical spectrum corresponds to known theoretical values ​​of morphological parameters, which in turn correspond to the aforementioned morphological model. Therefore, the theoretical morphological parameter values ​​corresponding to the matched theoretical spectrum can be used as the measured morphological parameter values ​​of the sample.

[0007] In existing technologies, a spectral matching function is established to match the theoretical spectrum with the measured spectrum. The calculation result of the spectral matching function directly determines the accuracy of the measured morphological parameters of the sample. Therefore, how to construct a spectral matching function to improve the accuracy of morphological parameter measurements is a problem that the industry needs to consider.

[0008] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] In view of the problems in the prior art, the purpose of this disclosure is to provide a method for measuring morphological parameters to overcome the difficulties of the prior art and improve the accuracy of morphological parameter measurement values.

[0010] This disclosure provides a method for measuring morphological parameters, which includes:

[0011] The measurement spectrum of the periodic structure on the test sample and the reference spectrum and corresponding morphological parameter reference values ​​of the periodic structure on the reference sample are obtained. The test sample and the reference sample are similar samples with the same periodic structure, and the reference spectrum and the measurement spectrum include the same number of spectral elements, wherein the number is at least one.

[0012] A weight vector is constructed based on the weights corresponding to each of the spectral elements. A first spectral matching function is constructed using the weight vector, the reference spectrum, and the theoretical spectrum. Weight values ​​are assigned to the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set. The theoretical spectrum is a theoretical spectrum about the periodic structure obtained based on a spectral calculation algorithm.

[0013] Iterate through each weight vector in the first weight vector set, use the first spectral matching function to obtain the theoretical spectrum that matches the reference spectrum the most, and use it as the reference theoretical spectrum corresponding to the weight vector. Calculate the value of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter, obtain the first loss function set corresponding to the first weight vector set, obtain the minimum loss function based on the first loss function set, and use the weight vector corresponding to the minimum loss function as the target weight vector.

[0014] A second spectral matching function is constructed based on the target weight vector, the measured spectrum, and the theoretical spectrum. The theoretical spectrum that matches the measured spectrum with the highest degree of matching is obtained using the second spectral matching function as the target theoretical spectrum. The theoretical morphological parameters corresponding to the target theoretical spectrum are used as the measured values ​​of the morphological parameters of the periodic structure.

[0015] Optionally, configuring weight values ​​for the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set, includes:

[0016] For each weight in the weight vector, a corresponding preset weight value range is obtained, and multiple random values ​​are taken in each weight value range. Multiple different weight vectors are constructed using the multiple random values ​​of each weight to form a first weight vector set.

[0017] Optionally, the step of obtaining a corresponding preset weight value range for each weight in the weight vector, and performing multiple random value selections within each preset weight value range, and constructing multiple distinct weight vectors using the multiple random values ​​of each weight, includes:

[0018] For each of the M weights in the weight vector, take a corresponding M preset weight value range, where M is the number of spectral elements;

[0019] Perform the following random selection steps at least M+1 times to obtain M+1 distinct weight vectors:

[0020] A value is randomly selected from the range of each weight value to obtain M values, and a weight vector is formed based on the M values.

[0021] Optionally, obtaining the minimum loss function based on the first set of loss functions includes:

[0022] Set the baseline value of the evaluation function to zero;

[0023] Calculate the average weight vector for the first weight vector set, and based on the average weight vector, reuse the first spectral matching function to obtain the corresponding reference theoretical spectrum, and obtain the value of the loss function corresponding to the corresponding reference theoretical spectrum as the average loss function;

[0024] The current value of the evaluation function relative to the average loss function of the first loss function set is obtained as the current value of the evaluation function. The absolute value of the difference between the current value of the evaluation function and the baseline value of the evaluation function is obtained. The absolute value of the difference is compared with a preset threshold, and the baseline value of the evaluation function is updated to the current value of the evaluation function. The preset threshold is a positive number.

[0025] When the absolute value of the difference is not greater than a preset threshold, the minimum loss function among the current first loss functions is obtained based on the current first loss function set.

[0026] Optionally, calculating the average weight vector for the first weight vector set includes:

[0027] The values ​​of the loss functions in the first set of loss functions are sorted by size, and the average weight vector is calculated for each weight vector corresponding to the value of each loss function other than the largest loss function.

[0028] Optionally, the evaluation function may take the form of a function of mean square error, root mean square error, or mean absolute error.

[0029] Optionally, obtaining the minimum loss function based on the first set of loss functions further includes:

[0030] When the absolute value of the difference is greater than the preset threshold, the weight vector corresponding to the maximum loss function in the current first loss function set is adjusted to obtain an adjusted weight vector. The weight vector corresponding to the maximum loss function in the current first weight vector set is replaced by the adjusted weight vector to form the current first weight vector set. Based on the adjusted weight vector, the first spectral matching function is reused to obtain the corresponding reference theoretical spectrum, and the value of the loss function corresponding to the corresponding reference theoretical spectrum is obtained as the adjusted loss function. The maximum loss function in the current first loss function set is replaced by the adjusted loss function. Based on the replaced first loss function set as the current first loss function set, the process of calculating the average weight vector on the first weight vector set is returned until the absolute value of the difference is not greater than the preset threshold.

[0031] Optionally, adjusting the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector includes:

[0032] Based on the step size, the average weight vector, and the weight vector corresponding to the maximum loss function, a weight vector function with the step size as the independent variable is established. Multiple different preset step size values ​​are substituted into the weight vector function to calculate multiple different candidate weight vectors, and the weight value of each weight in each candidate weight vector is located within the range of the corresponding weight value. A second weight vector set is obtained based on the multiple candidate weight vectors.

[0033] Based on the second weight vector set, the first spectral matching function is reused to obtain the theoretical spectrum that matches the reference spectrum the most closely as the reference theoretical spectrum, so as to obtain the second loss function set corresponding to the second weight vector set.

[0034] Based on the comparison between the minimum value of the loss function in the second loss function set and the maximum loss function, it is determined whether to make the adjustment. If the minimum value of the loss function in the second loss function set is less than the maximum loss function, the determination result is yes, and the weight vector corresponding to the maximum loss function is adjusted to the weight vector corresponding to the minimum value of the loss function to obtain the adjusted weight vector.

[0035] Optionally, adjusting the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector further includes:

[0036] If the minimum value of the loss function is not less than the maximum loss function, the result is negative, and the minimum value of the loss function is taken as the minimum loss function.

[0037] Optionally, based on the library matching method and the first spectral matching function or based on the regression method and the first spectral matching function, the theoretical spectrum that matches the reference spectrum with the highest degree is obtained as the reference theoretical spectrum; based on the library matching method and the second spectral matching function or based on the regression method and the second spectral matching function, the theoretical spectrum that matches the measured spectrum with the highest degree is obtained as the target theoretical spectrum.

[0038] The calculation of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter includes:

[0039] The value of the loss function is calculated based on the root mean square error, root mean square error, or mean absolute error of the morphology parameters corresponding to the reference theoretical spectrum and the reference values ​​of the morphology parameters corresponding to the reference spectrum.

[0040] The morphological parameter measurement method disclosed herein has the following advantages:

[0041] This disclosure proposes a method for measuring morphological parameters. First, a first weight vector set containing multiple weight vectors is constructed for a first spectral matching function. Then, for each weight vector in the first weight vector set, the first spectral matching function is used to perform an actual spectral matching operation on the reference spectrum, and the value of the corresponding loss function is obtained based on the matching result, thus obtaining a first loss function set containing the values ​​of multiple loss functions. Next, the minimum loss function is obtained, because the matching result corresponding to the minimum loss function is more accurate, so its corresponding weight vector is used as the target weight vector. A second spectral matching function is constructed using the target weight vector, the measured spectrum, and the theoretical spectrum to obtain the measured morphological parameter values. Since the reference sample and the sample to be tested are similar samples including the same periodic structure, further using the target weight vector determined by the reference spectrum of the reference sample to match the measured spectrum can also obtain a more matching theoretical spectrum (called the target theoretical spectrum), thereby enabling more accurate morphological parameter measurements for the sample to be tested. Attached Figure Description

[0042] Other features, objects, and advantages of this disclosure will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0043] Figure 1 A flowchart illustrating the morphological parameter measurement method provided in the embodiments of this disclosure is shown.

[0044] Figure 2 A schematic cross-sectional view of a sample to be tested, illustrating one embodiment, is shown.

[0045] Figure 3 exhibit Figure 1One of the schematic diagrams showing the range of weight values ​​in the topographic parameter measurement method.

[0046] Figure 4 exhibit Figure 1 The second schematic diagram shows the range of weight values ​​in the topographic parameter measurement method.

[0047] Figure 5 Shown Figure 3 The diagram shows the range of values ​​shown.

[0048] Figure 6 Shown Figure 4 The diagram shows the range of values ​​shown.

[0049] Figure 7 exhibit Figure 1 A flowchart of an alternative implementation of the topographic parameter measurement method shown.

[0050] Figure 8 exhibit Figure 1 A flowchart of an alternative implementation of the topographic parameter measurement method shown.

[0051] Figure 9 exhibit Figure 1 The diagram illustrates the principle of obtaining candidate weight vectors by discretely selecting points in the topographic parameter measurement method. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this disclosure clearer, the disclosure will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this disclosure, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0053] The accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware forwarding modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0054] Furthermore, the process shown in the accompanying drawings is merely illustrative and does not necessarily include all steps. For example, some steps can be broken down, some steps can be combined or partially combined, and the actual execution order may change depending on the actual situation.

[0055] In related technologies, the spectral matching function is often characterized by the mean square error (MSE) between the theoretical spectrum and the measured spectrum. Since the MSE is always a non-negative number, usually positive but can also be 0, a smaller MSE value indicates a higher degree of matching between the theoretical and measured spectra. When the MSE value is at its minimum, the theoretical spectrum with the highest degree of matching with the measured spectrum has been obtained.

[0056] Specifically, the spectral matching function is expressed using the mean square error between the theoretical spectrum and the measured spectrum as follows:

[0057]

[0058] in, The vector representation of the topographic parameters to be measured can be called the topographic parameter vector, λ. j Characterizing the j-th wavelength, S i Characterizing the i-th theoretical spectral element, Let M represent the i-th measured spectral element, M represent the number of spectral elements, and N represent the number of wavelengths.

[0059] For the aforementioned spectral matching function, some related techniques assign a weight of 1 to each spectral element without considering whether the weight values ​​for each spectral element are reasonable, resulting in inaccurate matching results and consequently inaccurate measurements of morphological parameters.

[0060] This disclosure proposes an improved method for measuring morphological parameters. First, the target weight value corresponding to each spectral element in the spectral matching function is determined. Then, the spectral matching function based on the target weight value is used to perform spectral matching to obtain the measured value of the morphological parameters, thereby improving the accuracy of the measured value of the morphological parameters.

[0061] The steps of the morphology parameter measurement method provided in the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings.

[0062] Figure 1 A flowchart illustrating the morphology parameter measurement method provided in the embodiments of this disclosure is shown, such as... Figure 1 As shown, the method for measuring morphological parameters includes, but is not limited to, the following steps:

[0063] Step 110: Obtain the measurement spectrum of the periodic structure on the test sample, and the reference spectrum and corresponding morphological parameter reference values ​​of the periodic structure on the reference sample, wherein the test sample and the reference sample are similar samples including the same periodic structure, and the reference spectrum and the measurement spectrum include the same number of spectral elements, wherein the number is at least one.

[0064] Step 120: Construct a weight vector based on the weights corresponding to each spectral element; construct a first spectral matching function using the weight vector, the reference spectrum, and the theoretical spectrum; assign weight values ​​to the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set; wherein the theoretical spectrum is a theoretical spectrum about the periodic structure obtained based on a spectral calculation algorithm.

[0065] Step 130: Traverse each weight vector in the first weight vector set, use the first spectral matching function to obtain the theoretical spectrum with the highest matching degree with the reference spectrum as the reference theoretical spectrum corresponding to the weight vector, calculate the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter, obtain the first loss function set corresponding to the first weight vector set, obtain the minimum loss function based on the first loss function set, and use the weight vector corresponding to the minimum loss function as the target weight vector;

[0066] Step 140: Construct a second spectral matching function based on the target weight vector, the measured spectrum, and the theoretical spectrum. Use the second spectral matching function to obtain the theoretical spectrum that matches the measured spectrum the most as the target theoretical spectrum. Use the theoretical morphology parameters corresponding to the target theoretical spectrum as the measured values ​​of the morphology parameters of the periodic structure.

[0067] In this embodiment, the measured values ​​of the morphological parameters are the measured values ​​of the morphological parameters to be measured. The measured values ​​of the morphological parameters can also be represented in vector form, which will not be elaborated here.

[0068] This disclosure proposes a method for measuring morphological parameters. First, a first weight vector set containing multiple weight vectors is constructed for a first spectral matching function. Then, for each weight vector in the first weight vector set, the first spectral matching function is used to perform a spectral matching operation on the reference spectrum, and the value of the corresponding loss function is obtained based on the matching result, thus obtaining a first loss function set containing the values ​​of multiple loss functions. Next, the minimum loss function is obtained, because the matching result corresponding to the minimum loss function is more accurate, so its corresponding weight vector is used as the target weight vector. A second spectral matching function is constructed using the target weight vector, the measured spectrum, and the theoretical spectrum to obtain the measured morphological parameter values. Since the reference sample and the sample to be tested are similar samples including the same periodic structure, the target weight vector determined using the reference spectrum of the reference sample can also obtain a more matching theoretical spectrum (called the target theoretical spectrum) for the measured spectrum, thereby obtaining more accurate morphological parameter measurements for the sample to be tested.

[0069] The following describes specific implementation methods. Figure 1The steps in the method for measuring the topographic parameters shown will be explained in detail below.

[0070] In this embodiment of the disclosure, when performing step 110, the optical scattering signal of the periodic structure is acquired using a spectrometer in the OCD measurement device and further processed into a measurement spectrum.

[0071] For example, the type of spectrum is determined based on the type of spectrometer (e.g., an ellipsometry or a reflectance spectrometer). Measured spectra include, but are not limited to, reflectance spectra, spectra of polarization state changes, spectra of Fourier coefficients from polarization state analysis, or spectra that directly describe the scattering process, such as NCS spectra or Mueller spectra.

[0072] For example, such as Figure 2 As shown, the sample to be tested 2 includes a substrate 21 and a periodic structure 22 thereon. The periodic structure 22 is a device structure fabricated on the substrate 21, which is arranged periodically, for example, as an array.

[0073] In this embodiment, the morphological parameters to be measured are used to describe the aforementioned periodic structure 22, and the number of such parameters is at least one. For example... Figure 2 As shown, the model of the periodic structure 22 is trapezoidal, so its morphological parameters to be measured can be the lower base W. bottom Top bottom W top The height H, the lower base (also called the length), and the upper base (also called the width) can be represented as a vector of morphological parameters. Recorded as v1,…,v K It is the morphological parameter to be measured, K≥1.

[0074] here Figure 2 As an example, in the corresponding implementation, the topographic parameters to be measured can be specifically determined by the user, such as line width or sidewall angle. Those skilled in the art can select the topographic parameters to be measured according to actual needs, and no limitation is made here.

[0075] In this embodiment, the reference sample and the sample to be tested are of the same type. For example, the sample to be tested is a wafer, and the reference sample is a wafer of the same type. The sample to be tested can also be a photomask, and the reference sample is a photomask of the same type. In the semiconductor field, the sample can be a wafer or a photomask, both of which can include a periodic structure and a substrate. Those skilled in the art often refer to periodic structures as grating structures, such as photoresist grating structures. Furthermore, the reference sample and the sample to be tested have the same periodic structure, and the reference spectrum and the measured spectrum include the same number of spectral elements. This increases the usability of the target weight vector selected based on the reference spectrum to the measured spectrum. The acquisition method for the reference spectrum can be referenced from the measured spectrum, and will not be elaborated further here.

[0076] Among them, the morphological parameters corresponding to the reference spectrum of the reference sample are known values ​​and are considered to be standard reference values, which are used for subsequent calculation of the loss function.

[0077] In this embodiment of the disclosure, the reference spectrum can be G reference spectra obtained from G (i.e., at least one) reference points on a reference sample (such as a reference wafer). Correspondingly, there are G sets of morphology parameter reference values. Each set of morphology parameter reference values ​​can be represented as a morphology parameter reference vector. These G morphology parameter reference vectors can be denoted as... Where G is greater than or equal to 1. In one embodiment, G reference spectra can be acquired using an OCD measuring device; the morphological parameter reference vectors corresponding to these reference points can be obtained using a scanning electron microscope, or the same OCD measuring device can be used to acquire these morphological parameter reference vectors.

[0078] In this embodiment, the spectral type of the measured spectrum is related to the selected spectrometer, while the number of spectral elements is related to the spectral type. For example, if the OCD measurement device includes a single-rotation ellipsometer for measuring NCS spectra or a double-rotation ellipsometer for measuring Mueller spectra, the NCS spectrum contains three spectral elements: N, C, and S; the Mueller spectrum contains 16 spectral elements S1 to S2. 16 In the corresponding implementation, appropriate OCD measurement equipment and the corresponding spectral type of the measurement spectrum can be selected according to actual needs, and no limitation is made here.

[0079] In this embodiment of the disclosure, the theoretical spectrum is the theoretical spectrum of the periodic structure obtained based on a spectral calculation algorithm, wherein the spectral calculation algorithm can be a rigorous coupled wave analysis (RCWA) algorithm or a finite difference time domain (FDTD) algorithm.

[0080] In this embodiment of the disclosure, as can be seen from step 120, the weight vector includes the weights corresponding to each spectral element, which can be characterized as follows: Where M is the number of spectral elements, w1, w2, ..., w M Each spectral element is characterized by a corresponding weight, and a corresponding weight value is assigned to it. In this embodiment, the weight w2 is merely an example and is not intended to limit the number of spectral elements M to ≥ 2. In this embodiment, M ≥ 1.

[0081] In this embodiment of the disclosure, in step 120, a first spectral matching function is constructed using the weight vector, the reference spectrum, and the theoretical spectrum. The first spectral matching function is characterized as follows:

[0082] λ j S represents the j-th wavelength. i Represents the i-th theoretical spectrum, Let w represent the i-th measured spectrum, N represent the number of wavelengths, 1≤j≤N, 1≤i≤M, and w i This represents the weight of the i-th spectral element.

[0083] In this embodiment of the disclosure, multiple different weight vectors are obtained by assigning weight values ​​to the weights in the weight vectors, forming a first weight vector set. The different weight vectors refer to the fact that, in any two weight vectors, at least one set of corresponding weights has different weight values. For example, in a weight vector, weight w... i The weight value and the same weight w in another weight vector i If the weight values ​​are different, then the two weight vectors can be identified as different weight vectors.

[0084] In one implementation, weight values ​​are assigned to the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set, including:

[0085] For each weight in the weight vector, a corresponding preset weight value range is obtained (wherein, the weight value range can also be called the weight value range or the weight value range), and multiple random values ​​are taken in each weight value range respectively. Multiple different weight vectors are constructed using multiple random values ​​of each weight to form a first weight vector set.

[0086] Using a preset weight value range narrows the range of random values, thereby increasing the usability of random values ​​and improving the efficiency of morphological parameter measurement. Since the number of weights is the same as the number of spectral elements, when there are multiple spectral elements, there are also multiple weights. In this case, the preset weight value ranges for any two weights (e.g., weight w1 and weight w2) can be the same or different. Furthermore, the preset weight value range is an empirical value and can be set based on historical data; it is not limited here.

[0087] In the optional approach, each weight is randomly selected multiple times, and then these weights can be combined in any way to obtain different weight vectors. This implementation does not limit the combination method, as long as multiple different weight vectors can be obtained.

[0088] This disclosure provides an exemplary combination approach.

[0089] Initialization is performed; specifically, the number of iterations is initialized to q = 1, and the M+1 weight vectors are initialized to M+1 distinct weight vectors, i.e. These different weight vectors can be called the initial weight vectors, using... This is an illustration, where 1 ≤ c ≤ M+1. The following explains how to obtain M+1 different weight vectors.

[0090] First, the preset range of values ​​for the weight of the i-th spectral element (i.e., the preset range of weight values) is expressed as [lb i ,ub i ], lb and ub are abbreviations for lower boundary and upper boundary, respectively. For example, lb i The value range is 0 to 3, ub i The value range is 3 to 10 lb i <ub i .

[0091] Next, [lb] i ,ub i The range is divided into M+1 subdivided value ranges, specifically:

[0092] Then, a value is randomly selected from each subdivision range, and the randomly selected value from the c-th subdivision range is denoted as w. rd,c,i Assign the weight value to the i-th spectral element of the c-th weight vector, and iterate through the weights of all spectral elements of the c-th weight vector to obtain an initial weight vector, denoted as: By performing the value selection more than M+1 times, M+1 weight vectors can be obtained. These weight vectors are usually different. If there are identical weight vectors, the value selection is performed again for one of the identical weight vectors to obtain different weight vectors, resulting in a total of M+1 distinct weight vectors.

[0093] The following will take M=2 as an example, that is, the weight vector has the weights of 2 spectral elements, to explain how to obtain 3 different weight vectors.

[0094] The weight w1 of the first spectral element takes values ​​in the range [lb1, ub1]. Dividing [lb1, ub1] into three sub-ranges, the values ​​are as follows: Characterized as Figure 3 The range of values ​​and the sub-range of values ​​are shown.

[0095] The weight w2 of the second spectral element takes values ​​in the range [lb2, ub2]. Dividing [lb2, ub2] into three sub-ranges, the values ​​are as follows: Characterized as Figure 4 The range of values ​​and the sub-range of values ​​are shown.

[0096] Combination Figure 5 As shown, in A random value is selected and denoted as w. rd,1,1 ,exist A random value is selected and denoted as w. rd,2,1 ,exist A random value is selected and denoted as w. rd,3,1 ;

[0097] Combination Figure 6 As shown, in A random value is selected and denoted as w. rd,1,2 ,exist A random value is selected and denoted as w. rd,2,2 ,exist A random value is selected and denoted as w. rd,3,2 .

[0098] Step 3

[0099] Based on the above initialization process, three different weight vectors are obtained: weight vector and It can be used as the first weight vector set.

[0100] The above implementation method uses M=2 as an example to obtain three different weight vectors. In this implementation method, the dimension of the weight vector is equal to the number of spectral elements, such as an M-dimensional vector. Therefore, based on the concept of a polyhedron, an M-dimensional polyhedron is constructed with M+1 vertices, that is, M+1 weight vectors are constructed during initialization.

[0101] The above implementation subdivides the preset weight value range corresponding to the spectral elements and then randomly selects values. This results in a more uniform distribution of the initialized weight vector compared to a scheme where values ​​are randomly selected directly without subdivision within the preset weight value range, leading to a faster acquisition of the target weight vector. For example, the subdivision of the preset weight value range is equal division.

[0102] In an optional implementation, the weights may not be subdivided or may be divided equally as an example. For each weight, M+1 random values ​​are taken within the entire preset weight value range.

[0103] Therefore, obtaining a corresponding preset weight value range for each weight in the weight vector, and performing multiple random value selections within each preset weight value range, and constructing multiple distinct weight vectors using the multiple random values ​​of each weight, may include:

[0104] For each of the M weights in the weight vector, take a corresponding M preset weight value range, where M is the number of spectral elements;

[0105] Perform the following random selection steps at least M+1 times to obtain M+1 distinct weight vectors:

[0106] A value is randomly selected from each of the preset weight values ​​to obtain M values, and a weight vector is formed based on the M values.

[0107] In some implementations, performing M+1 random value selection steps yields M+1 weight vectors, and these weight vectors are all different. In other implementations, performing M+1 random value selection steps yields M+1 weight vectors, and some of these weight vectors have the same weight vector, so it is necessary to continue performing random value selection steps until M+1 different weight vectors are obtained.

[0108] In this disclosure embodiment, exemplarily, the first weight vector set as described above (exemplarily, including weight vectors) is used. and ), combined with the first spectral matching function ρ(w1,w2,…,w) as described above M ), specifically, execution step 130:

[0109] Using the above G reference spectra and theoretical spectra as input, traverse each weight vector in the first weight vector set, and apply the first spectral matching function ρ(w1,w2,…,w) respectively. M Using either a library matching algorithm or a regression algorithm, the theoretical spectra with the highest matching degree are obtained by matching each of the G reference spectra. This determines the corresponding G reference theoretical spectra and their theoretical values ​​for morphological parameters. The theoretical values ​​of the morphological parameters corresponding to each reference theoretical spectrum are represented as vectors, resulting in a total of G vectors, denoted as . Furthermore, due to the difference between the theoretical values ​​of the morphology parameters and the weight vector Related, so these vectors can be denoted as

[0110] Based on the aforementioned reference theoretical spectrum and its corresponding theoretical values ​​of morphological parameters, respectively Reference values ​​of morphological parameters Calculate the loss function The value of represents the mean square error (MSE) between the theoretical value and the reference value of the morphological parameter, reflecting the measurement accuracy of the theoretical value of the morphological parameter;

[0111] By calculating the loss function The value of the first weight vector set is used to obtain the first loss function set corresponding to the first weight vector set mentioned above. Based on the current first loss function set, the minimum loss function is obtained to minimize the loss function and obtain the target weight vector. Used as target weights for each spectral element.

[0112] In this embodiment of the disclosure, combined with Figure 7 As shown, obtaining the minimum loss function based on the first set of loss functions specifically includes the following steps:

[0113] Step 700: Set the baseline value of the evaluation function to zero;

[0114] Step 710: Calculate the average weight vector for the first weight vector set, and based on the average weight vector, reuse the first spectral matching function to obtain the corresponding reference theoretical spectrum, and obtain the value of the loss function corresponding to the corresponding reference theoretical spectrum as the average loss function;

[0115] Step 720: Obtain the value of the evaluation function of the first loss function set relative to the average loss function as the current value of the evaluation function, obtain the absolute value of the difference between the current value of the evaluation function and the baseline value of the evaluation function, compare the absolute value of the difference with a preset threshold, and update the baseline value of the evaluation function to the current value of the evaluation function, wherein the preset threshold is a positive number;

[0116] Step 730: When the absolute value of the difference is not greater than a preset threshold, obtain the minimum loss function among the current first loss functions based on the current first loss function set.

[0117] This implementation combines the evaluation function to evaluate the first set of loss functions. When the absolute value of the difference between the current value of the evaluation function and the benchmark value of the evaluation function is not greater than a preset threshold, it indicates that a more accurate measurement value of the morphological parameters can be obtained based on the weight vector corresponding to the minimum loss function in the current first set of loss functions.

[0118] In one specific implementation, in conjunction with the specific content of step 120 above, when the q-th iteration obtains the q-th first weight vector set, the weight vectors in the q-th first weight vector set are traversed, and the calculation is performed. It is the c-th weight vector in the first weight vector set obtained in the q-th iteration before sorting, according to each The values ​​are then used to reorder the M+1 weight vectors in the first weight vector set from smallest to largest, and the sorted weight vectors are obtained as follows: in It is the first weight vector, and its corresponding loss function value is the smallest. It is the second weight vector, and its corresponding loss function value is the largest. It is the c-th weight vector after sorting in the q-th iteration.

[0119] Next, the average weight vector of the q-th iteration is calculated. Optionally, the weight vector used in calculating the average weight vector does not include the second weight vector mentioned above; instead, the average weight vector of the sorted first M weight vectors is calculated. Based on this average weight vector, the first spectral matching function is used to obtain the average loss function.

[0120] Since the weight vector in the first spectral matching function is an unassigned weight vector, meaning that all weights in this weight vector are variables, using the first spectral matching function based on the average weight vector to obtain the corresponding reference theoretical spectrum and obtaining the value of the loss function corresponding to the reference theoretical spectrum means: substituting the average weight vector into the weight vector in the first spectral matching function, obtaining the theoretical spectrum with the highest matching degree with the reference spectrum based on the replaced first spectral matching function as the reference theoretical spectrum corresponding to the weight vector (which is the average weight vector at this time), and calculating the value of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter. This value of the loss function is called the average loss function.

[0121] Finally, convergence testing is performed. The evaluation function used for convergence testing can be in the form of a function of mean square error, root mean square error, or mean absolute error. For example, using the root mean square error function, it can be specifically expressed as:

[0122]

[0123] In this process, for the first loss function set obtained in the q-th iteration, the evaluation function as described above is used to calculate the value of the evaluation function in the q-th iteration, which is called the current value of the evaluation function. Since q is 1 at this time, the absolute value of the difference between the current value of the evaluation function in the 1st iteration and the baseline value of the evaluation function is calculated. The absolute value of the difference is compared with the preset threshold ε, and the baseline value of the evaluation function is updated to the current value of the evaluation function. The purpose is to ensure that as the number of iterations increases (the number of iterations q will gradually increase in subsequent implementations), the absolute value of the difference is calculated using the values ​​of the evaluation functions after two adjacent iterations. This will not be elaborated further here. In addition, the preset threshold ε is a positive number less than 1, for example, 10. -6 If convergence is achieved, the iteration stops, and the target weight vector is output.

[0124] In the above implementation, the calculation of the average weight vector for the first weight vector set specifically includes the following steps:

[0125] The values ​​of the loss functions in the first loss function set are sorted by size, and the average weight vector is calculated for each weight vector corresponding to the value of each loss function other than the largest loss function.

[0126] In the above implementation, the second weight vector corresponding to the maximum loss function is removed when calculating the average weight vector because the maximum loss function indicates that the measurement error of the theoretical value of the topography parameter based on the second weight vector is relatively large. This improves the accuracy of the evaluation function, resulting in a more accurate target weight vector, and thus increases the accuracy of the theoretical value of the topography parameter.

[0127] In an optional approach, the weight vector corresponding to the maximum loss function can also be included when calculating the average weight vector.

[0128] In this disclosure, reference continues to be made to Figure 7 Step 740, as shown, which involves obtaining the minimum loss function based on the first loss function set, further includes:

[0129] When the absolute value of the difference is greater than the preset threshold, the weight vector corresponding to the maximum loss function in the current first loss function set is adjusted to obtain an adjusted weight vector. The weight vector corresponding to the maximum loss function in the current first weight vector set is replaced by the adjusted weight vector to form the current first weight vector set. Based on the adjusted weight vector, the first spectral matching function is reused to obtain the corresponding reference theoretical spectrum, and the value of the loss function corresponding to the corresponding reference theoretical spectrum is obtained as the adjusted loss function. The maximum loss function in the current first loss function set is replaced by the adjusted loss function. Based on the replaced first loss function set as the current first loss function set, the process of calculating the average weight vector on the first weight vector set is returned until the absolute value of the difference is not greater than the preset threshold.

[0130] In this embodiment of the disclosure, based on Figure 8 As shown, adjusting the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector includes the following steps:

[0131] Step 810: Based on the step size, the average weight vector, and the weight vector corresponding to the maximum loss function, establish a weight vector function with the step size as the independent variable. Substitute multiple preset different step size values ​​into the weight vector function to calculate multiple different candidate weight vectors, and ensure that the weight value of each weight in each candidate weight vector is within the range of the corresponding preset weight value. Based on the multiple candidate weight vectors, obtain a second weight vector set.

[0132] Step 820: Based on the second weight vector set, the first spectral matching function is used again to obtain the theoretical spectrum that matches the reference spectrum the most as the reference theoretical spectrum, so as to obtain the second loss function set corresponding to the second weight vector set;

[0133] Step 830: Based on the comparison between the minimum value of the loss function in the second loss function set and the maximum loss function, determine whether to perform the adjustment. If the minimum value of the loss function in the second loss function set is less than the maximum loss function, the determination result is yes, and the weight vector corresponding to the maximum loss function is adjusted to the weight vector corresponding to the minimum value of the loss function to obtain the adjusted weight vector.

[0134] Using the above implementation method, multiple different candidate weight vectors are obtained by discretely taking values ​​of the weight vector in the high-dimensional space. Specifically, discrete points on the straight line in the high-dimensional space corresponding to the weight vector corresponding to the maximum loss function and the average weight vector are used as multiple different candidate weight vectors. The minimum value of the loss function corresponding to each candidate weight vector and the corresponding weight vector are obtained. The judgment is then performed. When the judgment result is yes, the weight vector corresponding to the maximum loss function is replaced with the weight vector corresponding to the minimum value of the loss function corresponding to each weight vector. In this implementation method, the value of the evaluation function can be converged by continuously replacing the weight vector corresponding to the maximum loss function, that is, the loss function reaches the minimum value.

[0135] For example, for Figure 8 The specific implementation of the candidate weight vector used in the algorithm is explained below:

[0136] Get A vector representing the minimum endpoints of the preset weight values ​​for each spectral element. A vector representing the endpoints of the maximum values ​​of the preset weight values ​​corresponding to each spectral element;

[0137] Calculate the first weight vector function To obtain at least one candidate weight vector, m = 1, 2, ..., N m Δ1 can be called the first step length, 0 < Δ1 < 1, N m yes The number of, Δ1N m ≤0.5, for example Δ1=0.5, N m =1, The distance from the average weight vector is the second weight vector. The distance from the average weight vector is Δ1m times. From the formula, we can derive: direction and The opposite direction;

[0138] Calculate the second weight vector function To obtain at least one candidate weight vector, p = 1, 2, ..., N p Δ2 can be called the second step size, 0 < Δ2 < 1, Np yes The number of, Δ2N p ≥2, exemplary Δ2=0.5, N p =4, The distance from the average weight vector is the second weight vector. The distance from the average weight vector is Δ2p times. From the formula, we can derive: direction and They are in the same direction.

[0139] In one implementation, with M=2, meaning the weight vector has weights with 2 spectral elements, then, combining the above-mentioned sorting of weight vectors, the corresponding weight vector in the first weight vector set is:

[0140] Take Δ1=0.5, N m =1, Δ2=0.5, N p For example, =4

[0141]

[0142] Then, such as Figure 9 As shown, the discrete points obtained in the high-dimensional space are:

[0143] In order to be in Discrete points on the left, in The discrete points on the right are respectively

[0144] In one implementation, the second weight vector set can be constructed directly using the discrete points mentioned above, and steps 820 and 830 can be executed.

[0145] In another embodiment, the minimum endpoint of the preset weight value range corresponding to the weights of each spectral element can be further incorporated. and the endpoint of the maximum value Construct a second set of weight vectors.

[0146] Specifically, steps 820 to 830 are performed to calculate... Get The minimum value in the range is denoted as min. if Then use the minimum value corresponding to replace The remaining weight vectors remain unchanged, i.e. Here, u = 1, 2, ..., M, and then q = q + 1, which increases the number of iterations. Continue to execute the relevant content in step 740. Specifically, return the content of the current first weight vector set based on the adjusted weight vector and replace the weight vector corresponding to the maximum loss function. This will not be elaborated further here.

[0147] like Figure 8 Step 840, as shown, adjusts the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector. It further includes: if the minimum value of the loss function is not less than the maximum loss function, then the result is negative, and the minimum value of the loss function is taken as the minimum loss function. That is, as in the example above, the iteration stops, and the target weight vector is output.

[0148] In this embodiment of the disclosure, when performing step 130, since the values ​​of the loss functions may be the same, the first set of loss functions may contain one or more minimum loss functions. If the first set of loss functions contains multiple minimum loss functions, then the weight vector corresponding to one of the minimum loss functions is randomly selected as the target weight vector.

[0149] In an optional embodiment of this disclosure, the first spectral matching function can be a mean square error function, a root mean square error function, or a mean absolute error function, and the second spectral matching function can also be a mean square error function, a root mean square error function, or a mean absolute error function. The first and second spectral matching functions have the same functional form, for example, both being mean square error functions, so that the target weight vector obtained based on the first spectral matching function can be applied to the second spectral matching function, thereby obtaining more accurate morphological parameter measurements.

[0150] In an optional embodiment of this disclosure, during execution Figure 1 In step 130, the theoretical spectrum that best matches the reference spectrum is obtained as the reference theoretical spectrum, based on either the library matching method and the first spectral matching function or the regression method and the first spectral matching function.

[0151] In an optional embodiment of this disclosure, during execution Figure 1 In step 140, the theoretical spectrum that best matches the measured spectrum is obtained as the target theoretical spectrum, based on either the library matching method and the second spectral matching function or the regression method and the second spectral matching function.

[0152] In an optional embodiment of this disclosure, calculating the value of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter includes:

[0153] The value of the loss function is calculated based on the root mean square error, root mean square error, or mean absolute error of the morphology parameters corresponding to the reference theoretical spectrum and the reference values ​​of the morphology parameters corresponding to the reference spectrum.

[0154] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "platform."

[0155] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of this disclosure and should not be construed as limiting the specific implementation of this disclosure to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of this disclosure, and all such modifications and substitutions should be considered within the scope of protection of this disclosure.

Claims

1. A method for measuring morphological parameters, characterized in that, include: The measurement spectrum of the periodic structure on the test sample and the reference spectrum and corresponding morphological parameter reference values ​​of the periodic structure on the reference sample are obtained. The test sample and the reference sample are similar samples with the same periodic structure, and the reference spectrum and the measurement spectrum include the same number of spectral elements, wherein the number is at least one. A weight vector is constructed based on the weights corresponding to each spectral element. A first spectral matching function is constructed using the weight vector, the reference spectrum, and the theoretical spectrum. Weight values ​​are assigned to the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set. The theoretical spectrum is a theoretical spectrum about the periodic structure obtained based on a spectral calculation algorithm. Iterate through each weight vector in the first weight vector set, use the first spectral matching function to obtain the theoretical spectrum that matches the reference spectrum the most, and use it as the reference theoretical spectrum corresponding to the weight vector. Calculate the value of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter, obtain the first loss function set corresponding to the first weight vector set, obtain the minimum loss function based on the first loss function set, and use the weight vector corresponding to the minimum loss function as the target weight vector. A second spectral matching function is constructed based on the target weight vector, the measured spectrum, and the theoretical spectrum. The theoretical spectrum that matches the measured spectrum with the highest degree of matching is obtained using the second spectral matching function as the target theoretical spectrum. The theoretical morphological parameters corresponding to the target theoretical spectrum are used as the measured values ​​of the morphological parameters of the periodic structure.

2. The method for measuring morphological parameters according to claim 1, characterized in that, The step of assigning weight values ​​to the weights in the weight vector to obtain multiple different weight vectors, forming a first weight vector set, includes: For each weight in the weight vector, a corresponding preset weight value range is obtained, and multiple random values ​​are taken in each weight value range. Multiple different weight vectors are constructed using the multiple random values ​​of each weight to form a first weight vector set.

3. The method for measuring morphological parameters according to claim 2, characterized in that, The step of obtaining a preset weight value range for each weight in the weight vector, and performing multiple random value selections within each preset weight value range, and constructing multiple distinct weight vectors using the multiple random values ​​of each weight, includes: For each of the M weights in the weight vector, take a corresponding M preset weight value range, where M is the number of spectral elements; Perform the following random selection steps at least M+1 times to obtain M+1 distinct weight vectors: A value is randomly selected from the range of each weight value to obtain M values, and a weight vector is formed based on the M values.

4. The method for measuring morphological parameters according to claim 2 or 3, characterized in that, The step of obtaining the minimum loss function based on the first set of loss functions includes: Set the baseline value of the evaluation function to zero; Calculate the average weight vector for the first weight vector set, and based on the average weight vector, reuse the first spectral matching function to obtain the corresponding reference theoretical spectrum, and obtain the value of the loss function corresponding to the reference theoretical spectrum as the average loss function. The current value of the evaluation function relative to the average loss function of the first loss function set is obtained as the current value of the evaluation function. The absolute value of the difference between the current value of the evaluation function and the baseline value of the evaluation function is obtained. The absolute value of the difference is compared with a preset threshold, and the baseline value of the evaluation function is updated to the current value of the evaluation function. The preset threshold is a positive number. When the absolute value of the difference is not greater than a preset threshold, the minimum loss function among the current first loss functions is obtained based on the current first loss function set.

5. The method for measuring morphological parameters according to claim 4, characterized in that, The step of calculating the average weight vector for the first weight vector set includes: The values ​​of the loss functions in the first set of loss functions are sorted by size, and the average weight vector is calculated for each weight vector corresponding to the value of each loss function other than the largest loss function.

6. The method for measuring morphological parameters according to claim 4, characterized in that, The evaluation function takes the form of a function of mean square error, root mean square error, or mean absolute error.

7. The method for measuring morphological parameters according to claim 4, characterized in that, The step of obtaining the minimum loss function based on the first loss function set further includes: When the absolute value of the difference is greater than the preset threshold, the weight vector corresponding to the maximum loss function in the current first loss function set is adjusted to obtain an adjusted weight vector. The weight vector corresponding to the maximum loss function in the current first weight vector set is replaced by the adjusted weight vector to form the current first weight vector set. Based on the adjusted weight vector, the first spectral matching function is reused to obtain the corresponding reference theoretical spectrum, and the value of the loss function corresponding to the corresponding reference theoretical spectrum is obtained as the adjusted loss function. The maximum loss function in the current first loss function set is replaced by the adjusted loss function. Based on the replaced first loss function set as the current first loss function set, the process of calculating the average weight vector on the first weight vector set is returned until the absolute value of the difference is not greater than the preset threshold.

8. The method for measuring morphological parameters according to claim 7, characterized in that, The step of adjusting the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector includes: Based on the step size, the average weight vector, and the weight vector corresponding to the maximum loss function, a weight vector function with the step size as the independent variable is established. Multiple different preset step size values ​​are substituted into the weight vector function to calculate multiple different candidate weight vectors, and the weight value of each weight in each candidate weight vector is located within the range of the corresponding weight value. A second weight vector set is obtained based on the multiple candidate weight vectors. Based on the second weight vector set, the first spectral matching function is reused to obtain the theoretical spectrum that matches the reference spectrum the most closely as the reference theoretical spectrum, so as to obtain the second loss function set corresponding to the second weight vector set. Based on the comparison between the minimum value of the loss function in the second loss function set and the maximum loss function, it is determined whether to make the adjustment. If the minimum value of the loss function in the second loss function set is less than the maximum loss function, the determination result is yes, and the weight vector corresponding to the maximum loss function is adjusted to the weight vector corresponding to the minimum value of the loss function to obtain the adjusted weight vector.

9. The method for measuring morphological parameters according to claim 8, characterized in that, The step of adjusting the weight vector corresponding to the maximum loss function in the current first loss function set to obtain the adjusted weight vector further includes: If the minimum value of the loss function is not less than the maximum loss function, the result is negative, and the minimum value of the loss function is taken as the minimum loss function.

10. The method for measuring morphological parameters according to claim 1, characterized in that, Based on the library matching method and the first spectral matching function or based on the regression method and the first spectral matching function, the theoretical spectrum that matches the reference spectrum the most is obtained as the reference theoretical spectrum; Based on the library matching method and the second spectral matching function, or based on the regression method and the second spectral matching function, the theoretical spectrum that best matches the measured spectrum is obtained as the target theoretical spectrum; The calculation of the loss function based on the theoretical value of the morphology parameter corresponding to the reference theoretical spectrum and the reference value of the morphology parameter includes: The value of the loss function is calculated based on the root mean square error, root mean square error, or mean absolute error of the morphology parameters corresponding to the reference theoretical spectrum and the reference values ​​of the morphology parameters corresponding to the reference spectrum.

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