A method for constructing a multi-parameter constrained dispersion model for optical metrology

Abstract

The present application relates to a kind of construction methods for the construction of multi-parameter constraint dispersion model for optical measurement, comprising: establishing physical optical model;Extract the external process parameters affecting physical parameters, establish the mapping relationship between external process parameters and physical parameters, and optimize physical optical model based on the mapping relationship;Sampling is carried out on external process parameters and structure parameters within the whole process window, and the corresponding theoretical optical response signal is generated in batches using physical optical model;The sampled external process parameters and theoretical optical response signal are used as the input of machine learning algorithm, and the mapping relationship between physical parameters and multiple external process parameters is used as the output, and the multi-parameter constraint dispersion model is pre-trained;Further optimize the multi-parameter constraint dispersion model by using the sampled external process parameters and the optical signal actually collected as input.The multi-parameter constraint dispersion model has good numerical stability, high robustness and compatibility with external process parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of semiconductor metrology, and in particular to a method for constructing a multi-parameter constrained dispersion model for optical metrology. BACKGROUND

[0002] Optical metrology methods such as ellipsometry and reflectometry are widely used in the field of semiconductor metrology, and are of great significance for quality monitoring, process optimization, cost control, and yield of semiconductor products. The constraints of the dielectric response of the sample material have a crucial impact on the accuracy of the measurement.

[0003] For modeling the dielectric response function of a material, existing models include the standard Cauchy model, the Lorentz model, the Tauc-Lorentz model, the Cody-Lorentz model, and the Gaussian model.

[0004] With the development of modern semiconductor technology, there is a growing demand for characterization of the optical response, dielectric properties, and related physical parameters of various new materials. To accommodate multiple dielectric response mechanisms, the generalized oscillator model integrates multiple physical oscillators (such as Lorentz, Tauc-Lorentz, Cody-Lorentz, and Gaussian) and constructs a complex dielectric function through linear superposition, thereby achieving high-precision fitting and analysis of advanced materials such as high-dielectric-constant materials, multi-element alloys, and nanocomposite films, and providing a key tool for optical thin film characterization and semiconductor device design.

[0005] The above optical dispersion models are relatively mature in form and have shown good applicability in the analysis of traditional material systems. However, in actual semiconductor manufacturing processes, these models typically only consider the intrinsic dielectric response of the material and fail to effectively incorporate external process parameters related to process conditions. These external process parameters, particularly in process-sensitive new semiconductor materials such as high-dielectric-constant materials and alloy materials, significantly affect their optical constants, making it difficult for existing optical dispersion models to meet the high-precision prediction needs of such materials.

[0006] In addition, if external process parameters are simply introduced as variables in traditional models, it often leads to a significant increase in model degrees of freedom, instability in the fitting process, and a sharp rise in computational load, reducing the robustness and practical value of the model. Therefore, there is an urgent need to develop a new optical dispersion modeling method that can accommodate external process parameters while maintaining good numerical stability. SUMMARY

[0007] To solve at least part of the above problems in the prior art, the present application provides a method for constructing a multi-parameter constrained dispersion model for optical metrology, comprising the following steps:

[0008] a physical optical model between the key parameters to be measured and the spectrum signal is preliminarily established according to the physical structure of the measurement object, and parameters of the physical optical model further include physical parameters;

[0009] external process parameters affecting the physical parameters are extracted, a mapping relationship between the external process parameters and the physical parameters is established, and the physical optical model is optimized based on the mapping relationship;

[0010] The external process parameters and the structure parameters are sampled within the full process window, and the corresponding theoretical optical response signals are batch generated by using the physical optical model;

[0011] The sampled external process parameters and the theoretical optical response signals are used as inputs of a machine learning algorithm, and the mapping relationship between the physical parameters and the plurality of external process parameters is used as output, and a multi-parameter constrained dispersion model is pre-trained;

[0012] The sampled external process parameters and the actually collected optical signals are used as inputs, and the mapping relationship between the physical parameters and the plurality of external process parameters is used as output, and the multi-parameter constrained dispersion model is further optimized.

[0013] Further, the key parameters include one or more of a film thickness, a structure size, a refractive index and an extinction coefficient;

[0014] The physical parameters include one or more of a non-key parameter film thickness, a non-key parameter structure size and a dispersion model parameter;

[0015] The structure parameters include the physical parameters and the key parameters.

[0016] Further, the type of the physical model is determined according to the physical structure of the measurement object and the key parameters to be measured, and a physical optical model between the key parameters to be measured and the spectrum signal is constructed by an empirical formula of an optical dispersion model, wherein a mapping relationship formula of the physical optical model is as follows:

[0017]

[0018] : spectrum signal, wavelength range of measurement spectrum It can be from deep ultraviolet to mid-infrared band; : film thickness; : structure size; : material complex refractive index; : function mapping relationship derived by the physical optical model.

[0019] ​Furthermore, the spectral signal measured by ellipsometry is a broadband signal with a wavelength range from deep ultraviolet to mid-infrared. Based on the optical dispersion model, the mapping relationship between the material's complex refractive index and wavelength is further constructed:

[0020] dp represents the parameters of the dispersion model;

[0021] The mapping relationship of the physical optics model is further derived as follows:

[0022] ),

[0023] : Spectral signal; CP: Key parameter to be measured; dp: Dispersion model parameter, determined according to the dispersion model used; : Film thickness, which is not a critical parameter; : Structural dimensions that are not critical parameters.

[0024] Furthermore, after extracting the external process parameters that affect the physical parameters, a mapping relationship between the external process parameters and the physical parameters of the physical optics model is constructed:

[0025] ,

[0026] : External process parameter to physical parameter mapping model; ep: External process parameter; pp: Physical parameter, including one or more of the following: film thickness (non-critical parameter), structural dimensions (non-critical parameter), and dispersion model parameters;

[0027] Based on the mapping relationship between external process parameters and the physical parameters of the physical optics model, the physical optics model is further optimized as follows:

[0028] ,

[0029] Where the external process parameter ep is used as The input parameters are used to adjust the mapping relationship between key parameters and the spectral signal signal.

[0030] Furthermore, the machine learning algorithm includes physical information-guided neural network algorithms, linear regression algorithms, support vector machine algorithms, or decision tree algorithms.

[0031] Furthermore, the machine learning algorithm is a neural network algorithm guided by physical information;

[0032] When pre-training a multi-parameter constrained dispersion model, sampled external process parameters and theoretical optical response signals are used as inputs, and the data loss function is... for:

[0033] ,

[0034] N: represents the number of samples during training, is a theoretical optical response signal, is a model reconstructed optical signal.

[0035] Further, when optimizing the multi-parameter constraint dispersion model, a composite loss function is used:

[0036] ,

[0037] wherein the physical consistency loss function is:

[0038] ,

[0039] is an actually collected optical signal, represents that in the ith iteration, the current model reconstructed optical signal is calculated to update the structure parameters by the LM algorithm, and the structure parameters are substituted into the forward transmission matrix model or the strict coupled wave analysis to obtain a new reconstructed optical signal;

[0040] represents a regularization loss, and λ1 and λ2 are balance hyperparameters in the composite loss function.

[0041] Further, the optical dispersion model includes a standard Cauchy model, a Lorentz model, a Cody-Lorentz model, a Gaussian model or a generalized oscillator model.

[0042] The present application has at least the following beneficial effects:

[0043] The construction method of the multi-parameter constraint dispersion model of the optical measurement of the present application first constructs a physical model based on the empirical formula of the traditional optical dispersion model, then establishes a function mapping relationship between the external process parameters and the physical parameters, optimizes the physical model, samples the external process parameters and the structure parameters within the whole process window, and generates corresponding theoretical optical response signals in batches by using the physical optical model, pre-trains the multi-parameter constraint dispersion model by using the theoretical optical response signals and the external process parameters, and finally further optimizes the multi-parameter constraint dispersion model by taking the sampled external process parameters and the actually collected optical signals as inputs, the present application combines the machine learning algorithm and the mature physical model describing the material optical dispersion to construct a hybrid model, which can construct a multi-parameter constraint dispersion model with good numerical stability, high robustness and compatibility with external process parameters without greatly increasing the calculation amount;

[0044] The neural network algorithm guided by physical information further fits the noise and system error in actual measurement under the premise of maintaining physical consistency. BRIEF DESCRIPTION OF DRAWINGS

[0045] To further clarify the above and other advantages and features of the present embodiments, a more particular description of embodiments of the application will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the application and are therefore not to be considered limiting of its scope. The drawings incorporate graphics for purposes of clarity and represent the same or corresponding parts of the application with the same or similar designations throughout various figures.

[0046] Figure 1 A flow chart illustrating constructing a multi-parameter constrained dispersion model for optical metrology according to one embodiment of the present application is shown. DETAILED DESCRIPTION

[0047] It should be noted that components in the drawings can be exaggerated for illustrative purposes and are not necessarily drawn to scale.

[0048] In the present application, the embodiments are merely intended to illustrate the solutions of the present application and should not be understood as limiting.

[0049] In the present application, the quantifier "one", "a" does not exclude the scenario of multiple elements, unless specifically indicated.

[0050] It should also be noted herein that, for the sake of clarity and simplicity, only a part of components or assemblies can be shown in the embodiments of the present application, but those skilled in the art can understand that, under the teaching of the present application, the required components or assemblies can be added according to the specific scene needs.

[0051] It should also be noted herein that, within the scope of the present application, the phrases "same", "equal", "equal to" and the like do not mean that the numerical values of the two are absolutely equal, but allow a certain reasonable error, that is, the phrases also cover "substantially the same", "substantially equal", "substantially equal to".

[0052] It should also be noted herein that, in the description of the present application, the orientations or positional relationships indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0053] In addition, the embodiments of the present application describe the process steps in a specific order, however, this is only for the convenience of distinguishing the steps, and is not limited to the order of the steps, and the order of the steps can be adjusted according to the adjustment of the process in different embodiments of the present application.

[0054] Optical measurement methods such as ellipsometry and reflectance spectroscopy are widely used in the field of semiconductor measurement, and are of great significance for quality monitoring, process optimization, cost control, and yield of semiconductor products. The constraints of the dielectric response of the sample material have a crucial impact on the measurement accuracy.

[0055] For modeling of material dielectric response functions, there are empirical and semi-empirical formulas based on elementary models of statistical rules. Among them, the standard Cauchy model (Cauchy0 Model) as a typical empirical formula, through the polynomial expansion form:

[0056]

[0057]

[0058] where A, B, and C are Cauchy coefficients, which are empirical parameters obtained by fitting experimental data, and have no direct microscopic physical meaning, λ represents the wavelength in vacuum, n represents the refractive index, and k represents the extinction coefficient.

[0059] The normal dispersion behavior of transparent media in the visible light band is described, although it lacks a clear physical mechanism, but because of its simple form, it is still widely used in optical design. With the establishment of classical electron theory, the Lorentz model (Lorentz Model) based on the harmonic oscillator theory, its dielectric function expression is:

[0060]

[0061] where ω0 represents the natural resonance angular frequency, corresponding to the natural frequency of electronic transition; γ is the damping coefficient, ω is the angular frequency of the incident light, is the high-frequency relative dielectric constant, ω p is the plasma angular frequency.

[0062] The Lorentz model regards electrons as damped oscillators, successfully describing the absorption and dispersion behavior near the resonance energy, and laying the theoretical foundation for a class of physical dispersion models.

[0063] The Tauc-Lorentz model combines the Tauc law with the Lorentz oscillator, and introduces the optical band gap parameter , which is suitable for characterization of amorphous semiconductor absorption edge, and the imaginary part of the dielectric function expression is:

[0064] ​​​,

[0065] E g E0is the center energy of the Lorentz oscillator, A is the intensity coefficient of the resonance term, E is the incident photon energy.

[0066] The Cody-Lorentz model, which is developed on the basis of the above model, further introduces the Urbach energy and the matrix element energy , to more accurately describe the tail state distribution and non-ideal broadening of the absorption edge. The expression of the imaginary part of the dielectric function is:

[0067] ,

[0068] G(E) is the interband transition correction term, L(E) is the Lorentz resonance term; A is the intensity coefficient of the resonance term, and E is the incident photon energy, E0is the optical band gap of the material, A is the intensity coefficient of the resonance term, is the conversion energy parameter in the Cody-Lorentz model that defines the characteristics of the interband transition start. From a physical point of view, it represents the rate of transition from band edge absorption to bulk phase absorption, and its numerical value is directly related to the structural order of the material. From the perspective of mathematical fitting or engineering application, it ensures the continuity of the first derivative of the imaginary part of the dielectric function at , eliminating the slope discontinuity that may be caused by the Tauc model and playing a smoothing correction role.

[0069] The above models can be calculated to obtain the real part of the dielectric function through the Kramers-Kroning relationship.

[0070] Another common model is the Gaussian Model, which assumes that the optical transition energy is normally distributed, and the imaginary part of the dielectric function can be expressed as:

[0071] ,

[0072] A is the intensity coefficient of the resonance term, and E is the incident photon energy, E0is the center energy of the Lorentz oscillator, and this form is suitable for handling the non-uniform broadening effect in disordered systems.

[0073] For the optical properties of non-uniform composite materials, the Bruggeman Effective Medium Approximation Model (BEMA) is commonly used:

[0074] ,

[0075] represents the effective dielectric constant, represents the intrinsic dielectric constant of the i-th component, represents the volume fraction of the i-th component. According to the intrinsic dielectric constant of each component , the volume fraction and the geometric distribution form, the overall equivalent dielectric constant of the composite material is calculated, which can also represent the same macroscopic optical response as the real composite material that the pseudo material can produce.

[0076] With the development of modern semiconductor technology, the demand for characterization of the optical response, dielectric properties and related physical parameters of various new materials has emerged. In order to consider various dielectric response mechanisms, the generalized oscillator model integrates multiple physical oscillators (such as Lorentz, Tauc-Lorentz, Cody-Lorentz, Gaussian, etc.) to construct a complex dielectric function through linear superposition:

[0077] ,

[0078] This achieves high-precision fitting and analysis of advanced materials such as high-dielectric-constant materials, multi-element alloys, and nanocomposite films, providing a key tool for optical film characterization and semiconductor device design.

[0079] The above optical dispersion model is relatively mature in form and has shown good applicability in the analysis of traditional material systems. However, in actual semiconductor manufacturing processes, such models usually only consider the intrinsic dielectric response of the material itself and fail to effectively introduce external process parameters related to process conditions, such as film thickness, deposition temperature, reaction gas ratio, annealing conditions, and precursor composition. These parameters, especially in process-sensitive new semiconductor materials such as high-dielectric-constant materials (High-k materials, such as , , ) and alloy materials (such as ), will significantly affect their optical constants (such as refractive index, extinction coefficient, etc.), thereby placing higher demands on the prediction accuracy of the model.

[0080] In addition, if the above external process parameters are simply introduced as variables in traditional models, it often leads to a significant increase in model degrees of freedom, instability in the fitting process, a sharp rise in computational load, and other problems, reducing the robustness and practical value of the model.

[0081] The present application aims at the problems of limited stability and applicability caused by introducing external process parameters as variables in the above-mentioned traditional model, and proposes a construction method of a multi-parameter constraint dispersion model for optical measurement. The method introduces a machine learning algorithm into the original model, and through algorithm iteration training, can realize nonlinear mapping from external process parameters to optical constants, which is mathematically expressed as:

[0082]

[0083]

[0084] Wherein, n is the refractive index, k is the extinction coefficient, Optical bandgap, is the angular frequency of the incident light, represents external process parameters such as temperature, precursor ratio, etc., and can also be parameters such as film thickness that affect material dispersion. Through the mapping relationship, the external process parameters can be efficiently and stably inverted and a more robust dispersion model can be constructed under the premise of ensuring the physical meaning of the model. This method significantly reduces the computational complexity of multi-parameter fitting, and improves the practicality and reliability of the model in the actual semiconductor manufacturing scene. The construction method of the multi-parameter constraint dispersion model is described in detail below.

[0085] Figure 1 A flowchart of constructing a multi-parameter constraint dispersion model for optical measurement according to an embodiment of the present application is shown.

[0086] As Figure 1 shown, a construction method of a multi-parameter constraint dispersion model for optical measurement includes the following steps:

[0087] Step 1: A physical optical model between the key parameters to be measured and the spectrum signal is preliminarily established according to the physical structure of the measurement object, and the parameters of the physical optical model also include physical parameters.

[0088] Step 2: Extract the external process parameters that affect the physical parameters, establish the mapping relationship between the external process parameters and the physical parameters, and optimize the physical optical model based on the mapping relationship.

[0089] Step 3: Sample the external process parameters and structure parameters within the full process window, and use the physical optical model to batch generate corresponding theoretical optical response signals.

[0090] Step 4: Take the sampled external process parameters and theoretical optical response signals as the input of the machine learning algorithm, and the mapping relationship between the physical parameters and the plurality of external process parameters as the output, and pre-train the multi-parameter constraint dispersion model.

[0091] Step 5, further optimize the multi-parameter constrained dispersion model with the sampled external process parameters and the actually collected optical signals as inputs. The multi-parameter constrained dispersion model has the advantages of high accuracy, high robustness, high efficiency and iteration.

[0092] Figure 1 A flow chart of constructing a multi-parameter constrained dispersion model for optical metrology according to one embodiment of the present application is shown.

[0093] Step 1, preliminarily establish a physical optical model between the key parameters to be measured and the spectral signal according to the physical structure of the metrology object, and the parameters of the physical optical model also include physical parameters. The physical parameters include the thickness of the non-key parameter film, the structure size of the non-key parameter and the dispersion model parameters, etc.

[0094] Determine the type of the physical model according to the physical structure of the metrology object and the key parameters to be measured, and construct the physical optical model between the key parameters to be measured and the spectral signal based on the empirical formula of the optical dispersion model.

[0095] The metrology model structure is the structure of the semiconductor sample actually produced in the actual process production through various process flows (such as deposition, etching, epitaxial growth, etc.). The metrology model structure includes the specific structure of the semiconductor sample and the type of optical material. The physical optical model is a model that can be used for spectral simulation by optical simulation algorithm after further analyzing the optical properties of the optical material in the metrology model structure and extracting the optical parameters of the sample.

[0096] According to the metrology model structure, the specific structure of the semiconductor sample and the type of optical material can be known, and the physical optical model can be constructed based on the type of optical material through the existing empirical formula of the optical dispersion model. The existing optical dispersion model can be a standard Cauchy model, a Lorentz model, a Tauc-Lorentz model, a Cody-Lorentz model, a generalized oscillator model, etc.

[0097] The physical optical model can be one or more of a transmission matrix model (TTM), a rigorous coupled wave analysis model (RCWA), a finite-difference time-domain model (FDTD), etc. The type of the physical optical model can be selected according to the parameters to be measured. The transmission matrix model can calculate the thickness of the optical film, the optical constant (refractive index n and extinction coefficient k). The rigorous coupled wave analysis model can be used to calculate the optical structure size, the three-dimensional topography (side wall angle, round angle, etc.). The finite-difference time-domain model can be used to calculate the complete process of the evolution of the electromagnetic field in time and space when the light interacts with any complex three-dimensional structure, so as to obtain all the optical response and field distribution information.

[0098] In practical applications, one or more of the transfer matrix model, the rigorous coupled-wave analysis model, and the finite-difference time-domain model can be selected to construct the physical-optics model according to the characteristics (such as whether periodic, structural complexity) of the structure of the sample to be measured and the efficiency requirements.

[0099] The optical dispersion model (standard Cauchy model, Lorentz model, Tauc-Lorentz model, etc.) and the physical-optics model (transfer matrix model, rigorous coupled-wave analysis model, etc.) are in a hierarchical complementary relationship, the former is the quantitative basis for material properties, and the latter is a calculation tool for the interaction of light and structure, and the combination of the two constitutes the core physical-optics model of indirect optical measurement (such as ellipsometric spectroscopy).

[0100] When using an ellipsometer or other indirect measurement technology for optical measurement, a physical-optics model (such as the commonly used transfer matrix model in optical thin film measurement and the rigorous coupled-wave analysis model in optical structure size) between the key parameters to be measured and the spectral signal can be constructed by a series of optical simulation algorithms. The mapping relationship formula of the physical-optics model is as follows:

[0101]

[0102] Spectrum signal, wavelength range of the measured spectrum It can be from deep ultraviolet to mid-infrared band, and according to the ellipsometer architecture, a multi-channel composite spectral signal can also be obtained; Film thickness; Structure size; Material complex refractive index; Function mapping relationship derived by the physical-optics model; the mapping relationship is calculated according to the actual analysis scene by the transfer matrix model or the rigorous coupled-wave analysis model.

[0103] According to the constructed physical-optics model, the spectral signal is fitted and calculated, and the key parameters can be obtained. In semiconductor optical measurement applications, the key parameters (CP) measured by ellipsometric spectroscopy mainly include one or more of film thickness, structure size, refractive index, and extinction coefficient. Since ellipsometric spectroscopy is a wide-band signal measurement from deep ultraviolet to mid-infrared, according to a series of optical dispersion models, the mapping relationship between the material complex refractive index and the wavelength can be further constructed:

[0104] dp represents the dispersion model parameter;

[0105] Therefore, for a wide-band signal, the mapping relationship of the physical-optics model can be further derived as:

[0106] )​

[0107] : Spectral signal (Broadband spectral signal), which can include ellipsometric spectral signal intensity or reflectance spectral signal intensity; CP: Key parameter to be measured; dp: Dispersion model parameter, determined according to the dispersion model used, for example, if the standard Cauchy model is used, the dispersion model parameter will be the Cauchy coefficient 、 、 、 、 、 ; : Film thickness of non-key parameter; : Structure size of non-key parameter; Non-key parameter refers to a model parameter that is not the focus of monitoring in the current measurement station in the process flow. Only a part of the film thickness, structure size, refractive index and extinction coefficient will be defined as a key parameter in the current measurement station.

[0108] The structure size can be a line width or a diameter of a hole, etc. For different structures, the structure size is different. For example, for an interconnection line, the structure size is a line width; for a via, the structure size is a diameter of a hole.

[0109] The mapping relationship above is calculated according to the actual analysis scene by a transfer matrix model or a rigorous coupled wave analysis model, etc.

[0110] Step 2, extract external process parameters affecting physical parameters, establish a mapping relationship between external process parameters and physical parameters, and optimize the physical optical model based on the mapping relationship.

[0111] According to the physical simulation, the spectral signal of the measured sample is affected by a series of key parameters to be measured and a series of non-key parameters (non-measured parameters), and the key parameters and the non-key parameters can include film thickness, structure size, dispersion model parameter, etc. When the physical optical model performs fitting calculation on the spectral signal to obtain the key parameters, the problem of processing part of the non-key parameters is faced. In the process flow of the actual production of the measured sample, the change of the external process parameter can affect part of the non-key parameters. If this part of the non-key parameters is selected as the fitting strategy, the model cannot correctly reflect the influence of the change of the external process parameter on the parameters, so that the model can only be applied to some specific external process parameters, the model is under-fitting, and the robustness is significantly reduced; if this part of the non-key parameters is selected as the fitting strategy, the model complexity is excessively increased, leading to over-fitting, and reducing the accuracy of the measurement of the key parameters.

[0112] ​To solve the influence of external process parameters on the robustness and accuracy of the physical optical model, the external process parameters affecting the model are extracted, and the mapping relationship between the external process parameters and the physical parameters of the physical optical model is further constructed:

[0113] ,

[0114] : external process parameters to physical parameter mapping model; ep: external process parameters, such as temperature, time, exposure dose, exposure focal length, etc., and also can be thickness, size, etc. related to material optical dispersion strength; pp: physical parameters, which can be one or more of non-critical parameter film thickness, non-critical parameter structure size, and dispersion model parameter;

[0115] Based on the mapping relationship between the external process parameters and the physical parameters, the physical optical model of the spectral signal fitting can be further optimized as:

[0116] ,

[0117] In this model, the external process parameters ep can be used as input parameters, so as to adjust the mapping relationship between the key parameters CP and the spectral signal signal, so that the model can be applicable to sample model fitting under different external process parameters, and the accuracy of the mapping model of the key parameters CP and the spectral signal signal is improved.

[0118] Step 3: Sampling external process parameters and structure parameters within the full process window, and generating corresponding theoretical optical response signals in batches by using the physical optical model.

[0119] Grid or Latin hypercube sampling is performed on the external process parameters and structure parameters within the full process window, and the corresponding theoretical optical response signals are generated in batches by using the established physical optical model. This data serves as a physical prior knowledge base for subsequent machine learning models.

[0120] The full process window described in the present application refers to the fluctuation range allowed near the design nominal value of the key process parameters in the process of manufacturing semiconductor or precision optical elements. Sampling within this window can ensure that the generated training data covers all normal process fluctuations that may occur in actual production, thereby making the finally trained model robust. Typical process window parameters include but are not limited to: etching process parameters, deposition / plating process parameters, lithography process parameters, and material process parameters. In specific implementation, the full process window is determined by the design rules and tolerances of the specific process. The present application generates a high-fidelity data set that can fully reflect the process variability by performing systematic sampling in this multi-dimensional parameter space, which is a key prerequisite for subsequent machine learning models to learn and generalize to actual production environment.

[0121] In the present application, the structural parameters specifically refer to the quantifiable geometric and material characteristic parameters of the micro-nano structure to be measured. These parameters are the direct input of the physical optical model (such as TTM or RCWA), and the changes thereof will directly affect the output optical response signal. The structural parameters mainly include geometric size parameters (film thickness, line width, groove depth, diameter, height, etc.), material optical constant parameters (refractive index, extinction coefficient, etc.), and topography parameters (bottom corner radius, top roughness, trapezoidal cross-section upper and lower base width, etc.). The present application samples these structural parameters within their process window, drives batch simulation of the physical optical model, and thereby establishes an accurate mapping relationship from the structural space to the optical signal space, serving as the training basis for machine learning. The structural parameters include physical parameters and key parameters.

[0122] Step 4: Pre-training the multi-parameter constrained dispersion model using the sampled external process parameters and theoretical optical response signals as the input of the machine learning algorithm, and the mapping relationship between the physical parameters and the plurality of external process parameters as the output. For a determined physical optical model and optical material, the dispersion model parameters are known.

[0123] The multi-parameter constrained dispersion model is a machine learning model constructed by fusing physical prior knowledge (such as physical equations and simulation data) for quickly replacing physical simulation. Its core features are physical constraints and proxy (substitute simulation).

[0124] The machine learning algorithm can be a physics information guided neural network algorithm, a linear regression algorithm, a support vector machine algorithm, a decision tree algorithm, etc. The physics information guided neural network is a main and advanced technical approach for constructing such a physically constrained proxy model. It specifically refers to directly embedding the physical laws (such as optical transmission equations) into the neural network in the form of hard constraints (such as modifying the network structure) or soft constraints (such as adding the physical equation residuals to the loss function), thereby guiding the training and prediction thereof. It is preferred to use the physics information guided neural network as the specific architecture for implementing the physically constrained proxy model, because it can realize a deeper fusion of physical laws and data-driven. In addition, the proxy model can also be constructed in other ways, for example, training a general neural network using physical simulation data, and the physical constraints are embodied in the training data itself rather than in the network. In the present application, the physics information guided neural network algorithm is preferred, and the loss function introduced below is the loss function corresponding to the physics information guided neural network algorithm.

[0125] The purpose of pre-training the multi-parameter constrained dispersion model is to preliminarily learn the physical mapping law from the optical signal to the structural parameter.

[0126] When pre-training the multi-parameter constrained dispersion model, only the data loss function is used :

[0127] ,

[0128] N represents the number of samples during training, i.e., the number of samples used to calculate the loss at one time; is the theoretical optical response signal, is the optical signal reconstructed by the model.

[0129] Moreover, in order to stabilize the training and let the model focus on learning the basic mapping from the spectrum to the parameters first, sometimes a restrictive strategy is adopted. For example, only part of the layers of the neural network (such as the last regression output layer) may be trained, while the parameters of the backbone feature extraction layer are temporarily “frozen” (fixed) and not updated.

[0130] Step 5: The sampled external process parameters and the actually collected optical signals are used as inputs to further optimize the multi-parameter constrained dispersion model. The multi-parameter constrained dispersion model has the advantages of high accuracy, high robustness, high efficiency and iteration. When optimizing the multi-parameter constrained dispersion model, the output is still the mapping relationship between the physical parameters and the external process parameters.

[0131] In order to ensure that the output of the multi-parameter constrained dispersion model strictly obeys the physical law, the following composite loss function is adopted:

[0132] ,

[0133] Among them, the data loss function :

[0134] ,

[0135] is the theoretical optical response signal, is the optical signal reconstructed by the model, and N represents the number of samples during training;

[0136] Physical consistency loss function:

[0137] ,

[0138] is the actually collected optical signal, indicates that in the i th iteration, the optical signal reconstructed by the current model is calculated to update the structure parameters by the LM algorithm, and the structure parameters are substituted into the forward transmission matrix model (TTM) or the rigorous coupled wave analysis model (RCWA) to obtain a new reconstructed optical signal.

[0139] The physical consistency loss function forces the dispersion model parameters output by the neural network to reconstruct the spectrum under the forward rigorous optical engine, which must be highly consistent with the measured spectrum.

[0140] LM, Levenberg-Marquardt algorithm, is an efficient and robust iterative optimization algorithm designed for solving nonlinear least squares problems. In this dynamic iteration process, the input is the reconstructed optical signal of the current training model, and the output is the structural parameters obtained by the regression algorithm. Forward optical simulation engine based on transfer matrix or rigorous coupled wave analysis method (FDTD can also be replaced).

[0141] Closed-loop logic of physical consistency loss: the calculation of this loss constitutes a key closed loop: measured spectrum→ → predicted structural parameters→ forward engine → reconstructed optical signal. The final penalty is the difference between the reconstructed optical signal and the original measured spectrum. The core purpose is to embed the forward physical law as a hard constraint in training, ensuring that the network-predicted parameters not only have small data fitting errors, but also pass the self-consistency test of physical principles, thereby outputting physically credible results.

[0142] Regularization loss : L2 regularization of network weights to prevent overfitting.

[0143] λ1, λ2 are balance hyperparameters (i.e. weight coefficients) in the compound loss function, used to accurately adjust the relative importance of different constraint terms in the total optimization objective. λ1 controls the strength of the physical consistency loss, increasing λ1 will force the model to predict more strictly adhere to the physical law. λ2 controls the strength of the regularization loss, increasing λ2 will enhance the penalty of model complexity, which helps to prevent overfitting.

[0144] The optimization objective of the trainable weight parameters of the neural network is to minimize the total loss weighted by λ1 and λ2 . The values of λ1 and λ2 themselves are set before training begins, and the optimal value is usually determined on the validation set through standard machine learning processes such as cross-validation. Its role is to guide the neural network to find the best balance point between data fitting, physical compliance, and model simplicity. When pre-training the multi-parameter constrained dispersion model, only the data loss function is used, and λ1 and λ2 are 0.

[0145] In order to adapt the neural network to the measured data comprehensively, all the previously frozen network layer parameters need to be "unfrozen" to make them all trainable. Then, under the condition that all network parameters can be freely updated, the loss function The joint fine-tuning is performed by a composite loss function. The purpose of this operation is to ensure that the network can make more fine adjustments to its overall representation ability under the guidance of physical constraints based on the basic knowledge learned by pre-training, so as to better model the complex factors such as noise and system error specific in the measured data, and realize the best migration from the “simulation domain” to the “measured domain”.

[0146] While some embodiments of the application have been described above, it is understood that they have been presented by way of example only. Numerous variations, changes, and substitutions will occur to those skilled in the art without departing from the scope of the application. It is therefore intended that the appended claims cover all such variations as fall within the scope of the application.

Claims

1. A method for constructing a multi-parameter constrained dispersion model for optical metrology, characterized in that, The method comprises the following steps: According to the physical structure of the measurement object, a preliminary physical optical model between the key parameters to be measured and the spectrum signal is established, and the parameters of the physical optical model also include physical parameters; the type of the physical model is determined according to the physical structure of the measurement object and the key parameters to be measured, and the physical optical model between the key parameters to be measured and the spectrum signal is constructed through an empirical formula of an optical dispersion model, wherein the mapping relationship formula of the physical optical model is as follows: )， : spectral signal, wavelength range of the measured spectrum : from deep ultraviolet to mid-infrared wavelength band : film thickness : structure size : material complex refractive index : function mapping relationship derived by physical optical model External process parameters affecting the physical parameters are extracted, a mapping relationship between the external process parameters and the physical parameters is established, and the physical optical model is optimized based on the mapping relationship; The external process parameters and the structure parameters are sampled within the whole process window, and the corresponding theoretical optical response signals are batch generated by using the physical optical model; The sampled external process parameters and the theoretical optical response signals are used as inputs of a machine learning algorithm, and the mapping relationship between the physical parameters and the multiple external process parameters is used as an output, so as to pre-train a multi-parameter constraint dispersion model; The sampled external process parameters and the actually collected optical signals are used as inputs, and the mapping relationship between the physical parameters and the multiple external process parameters is used as an output, so as to further optimize the multi-parameter constraint dispersion model; The machine learning algorithm is a physical information guided neural network algorithm; When pre-training the multi-parameter constrained dispersion model, the sampled external process parameters and the theoretical optical response signals are used as inputs, and a data loss function is: ， N: represents the number of samples at training time, is the theoretical optical response signal, is the optical signal reconstructed by the model. When the multi-parameter constraint dispersion model is optimized, a composite loss function is used: ， The physical consistency loss function is as follows: ， for the actually acquired optical signals, represents that in the i-th iteration, the optical signal reconstructed by the current model is used to calculate the updated structural parameters by the LM algorithm, and the structural parameters are substituted into the forward transmission matrix model or the rigorous coupled wave analysis to obtain a new reconstructed optical signal; represents the regularization loss, and λ1, λ2are the balancing hyperparameters in the compound loss function.

2. The method for constructing a multiparameter constrained dispersion model for optical metrology according to claim 1, wherein, The key parameters include one or more of a film thickness, a structure size, a refractive index and an extinction coefficient; The physical parameters include one or more of a non-key parameter film thickness, a non-key parameter structure size and a dispersion model parameter; The structure parameters include the physical parameters and the key parameters.

3. The method for constructing a multiparameter constrained dispersion model for optical metrology according to claim 1, wherein, The spectrum signal of the ellipsometric spectrum measurement is a wideband signal in a wavelength range from deep ultraviolet to mid-infrared, and a mapping relationship between a material complex refractive index and a wavelength is further constructed according to the optical dispersion model: dp represents a dispersion model parameter; The mapping relationship of the physical optical model is further derived as follows: )， : spectral signal; CP: key parameter to be measured; dp: dispersion model parameter, determined according to the dispersion model used; : film thickness of non-key parameters; : structure size of non-key parameters.

4. The method for constructing a multiparameter constrained dispersion model for optical metrology according to claim 3, wherein, After the external process parameters affecting the physical parameters are extracted, a mapping relationship between the external process parameters and the physical parameters of the physical optical model is further constructed: ， : external process parameter to physical parameter mapping model; ep: external process parameter; pp: physical parameters, including one or more of a non-key parameter film thickness, a non-key parameter structure size and a dispersion model parameter; According to the mapping relationship between the external process parameters and the physical parameters of the physical optical model, the physical optical model is further optimized as follows: ， where the external process parameters ep are input parameters for adjusting the mapping of the key parameters and the spectral signal signal.

5. The method for constructing a multiparameter constrained dispersion model for optical metrology according to claim 1, wherein, The machine learning algorithm includes a physical information guided neural network algorithm, a linear regression algorithm, a support vector machine algorithm or a decision tree algorithm.

6. The method for constructing a multiparameter constrained dispersion model for optical metrology according to claim 1, wherein, The optical dispersion model includes a standard Cauchy model, a Lorentz model, a Cody-Lorentz model, a Gaussian model or a generalized oscillator model.

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