Method for measuring parameter values of an optical measuring process, and corresponding metrology system

Abstract

The invention relates to a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns, comprising: acquiring an imaging dataset (22) of the object using the optical metrology system; providing a prior probability distribution (32) for the at least one parameter of the optical measuring process, and providing a likelihood function (40) that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset (22) of the object; measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution (46) of the at least one parameter. The invention also relates to a corresponding optical metrology system.

Description

[0001] 19.11.2025 h - se

[0002] - 1 -

[0003] Method for measuring parameter values of an optical measuring process, and corresponding metrology system

[0004] Related Applications

[0005] This application claims benefit of German patent application No. 10 2024 134360.5 filed on November 21st, 2024, which is hereby incorporated by reference in its entirety.

[0006] Field of the Invention

[0007] The invention relates to a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns. The method and corresponding system can be utilized for quantitative metrology, defect detection, process monitoring, or defect review of integrated circuits within photolithography masks, reticles or wafers.

[0008] Background of the Invention

[0009] Manufacturing of objects comprising integrated circuit patterns, in particular of photolithography masks, reticles or wafers, is a complex task due to the decreasing size of the structures forming the circuit patterns. Manufacturing of wafers comprising semiconductor structures requires a complex sequence of deposition and removal of physical substances at nano-scale resolutions. Producing the small structure dimensions imaged onto the wafer requires photolithographic masks or templates for nanoimprint photolithography.

[0010] On account of the tiny structure sizes of the circuit pattern elements of photolithography masks and the complex production process of semiconductor structures, it is not possible to exclude errors during their production. Therefore, extracting measurements such as displacements of structures of integrated circuit patterns, critical dimensions or inter- and intra-structure distances is important to monitor the manufacturing process of objects comprising integrated circuit patterns.

[0011] Metrology systems measure positions of structures in objects comprising integrated circuit patterns by analyzing an acquired optical imaging dataset of the object. To obtain informative measurements, a very high precision is required. However, edge positions cannot always be directly estimated from the acquired imaging dataset of the object due to a low-pass filtering effect of the numerical aperture and due to optical proximity effects that lead to edge displacements in the imaging dataset. In addition, aberrations and further error sources reduce the measurement precision.

[0012] To alleviate the aforementioned problems, DE 10 2011 078999 A1 discloses an approach for measuring parameters of a photolithography mask. The approach repeatedly simulates an aerial imaging dataset from a design of the photolithography mask for a set of parameters comprising mask displacement parameters and metrology system parameters. The parameters are optimized until the simulated aerial imaging dataset is sufficiently similar to an acquired aerial imaging dataset of the photolithography mask. However, deriving parameters of the underlying photolithography mask from a noisy aerial imaging dataset is an inverse problem which is difficult to solve and can lead to large measurement errors.

[0013] It is, therefore, an objective of the invention to improve the accuracy of the measured parameter values.

[0014] The objectives are achieved by the invention specified in the independent claims. Advantageous embodiments and further developments of the invention are specified in the dependent claims.

[0015] Summary of the invention

[0016] Embodiments of the invention concern methods and systems for measuring parameter values of at least one parameter of an optical measuring process that involves an object comprising integrated circuit patterns.

[0017] A first embodiment of the invention involves a method for measuring parameter values of at least one parameter (e.g., of at least one optical metrology parameter) of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns. The method comprises: acquiring an imaging dataset of the object comprising integrated circuit patterns using the optical metrology system; providing a prior probability distribution for the at least one parameter of the optical measuring process, and providing a likelihood function that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset of the object; and measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution of the at least one parameter comprising the prior probability distribution for the at least one parameter of the optical measuring process and the likelihood function. The statistical properties of the posterior probability distribution of the at least one parameter comprising the prior probability distribution for the at least one parameter of the optical measuring process and the likelihood function can be estimated using Bayesian inference.

[0018] Bayesian inference allows for the integration of prior knowledge of the at least one parameter in the form of a prior probability distribution when estimating parameter values. For example, highly unlikely or impossible parameter values are prevented using corresponding prior probability distributions within a statistically sound framework. In this way, the accuracy of the measured parameter values of the optical measuring process is improved.

[0019] An integrated circuit pattern can, for example, comprise semiconductor structures. An object comprising integrated circuit patterns can refer, for example, to a photolithography mask, a reticle or a wafer. In a photolithography mask or reticle the integrated circuit patterns can refer to mask structures used to generate semiconductor patterns in a wafer during the photolithography process. In a wafer the integrated circuit patterns can refer to semiconductor structures, which are imprinted on the wafer during the photolithography process.

[0020] An optical metrology system refers to a system that comprises an image acquisition system for acquiring an imaging dataset of the object. The imaging dataset is analyzed to measure properties of the object by the optical metrology system. Properties of the object can, for example, comprise the type of integrated circuit patterns in the object (lines and spaces, holes or logical, etc.), material properties of the object (refractive indices, electric permittivities, magnetic permeabilities, etc.), dimensions of the object (layer thicknesses, structure dimensions), locations of structures in the object, displacements of structures or of the whole object, further properties of the object (critical dimensions, linewidths, corner-rounding, side-wall-angles, etching angles, undercuts, etc.). According to an embodiment of the invention, the likelihood function evaluates the likelihood of a deviation between the acquired imaging dataset of the object from a simulated imaging dataset of the object, and the simulated imaging dataset of the object simulates the optical measuring process for the object comprising integrated circuit patterns and the parameter values of the at least one parameter of the optical measuring process. In order to compute the likelihood of the acquired imaging dataset given at least one parameter value (hypothesis), an imaging dataset is simulated from the at least one parameter value, and the simulated imaging dataset is compared to the acquired imaging dataset.

[0021] The simulated imaging dataset may be computed from a physical forward model of the optical metrology process.

[0022] The simulated imaging dataset of the object can, for example, be simulated using a design of the object comprising integrated circuit patterns. In this way, accurate simulations and, thus, meaningful likelihood functions can be established, and accurate parameter values can be estimated.

[0023] According to an example, the likelihood function evaluates the likelihood of the deviation of the acquired imaging dataset of the object from the simulated imaging dataset of the object using a noise model. By considering realistic noise models, e.g., a shot noise model, to describe the deviation of the acquired imaging dataset from the simulated imaging dataset, the accuracy of the estimated parameter values is improved. A noise model can comprise one, two or more noise models, e.g., a dominant shot noise model and a small part of a Gaussian noise model. The noise model can be estimated from an acquired imaging dataset to obtain a realistic estimate of the noise model, e.g., from the acquired imaging dataset itself, or it can be calibrated before using another acquired imaging dataset.

[0024] In an example, the likelihood function incorporates a noise model comprising shot noise.

[0025] In an embodiment, the likelihood function comprises the application of a trained machine learning model. Thus, the likelihood function does not have to be defined but is automatically derived from training data. In this way, the accuracy of the likelihood predictions is increased as it is directly learned from sample data, and the user effort is reduced. In addition, the machine learning model is able to capture underlying knowledge about the likelihood function from the sample data that is not visible for a user.

[0026] In an example, the likelihood function comprises the application of a trained machine learning model that uses the acquired imaging dataset of the object and the simulated imaging dataset of the object or their difference as input and computes a likelihood of the parameter values of the at least one parameter as output. Thus, the machine learning model derives the likelihood from the acquired imaging dataset and the simulated imaging dataset.

[0027] In another example, the trained machine learning model uses the acquired imaging dataset of the object and the parameter values of the at least one parameter as input and computes a likelihood of the parameter values of the at least one parameter as output. Thus, the machine learning model directly derives the likelihood from the parameter values and the acquired imaging dataset without prior simulation of imaging datasets. Since this model is trained end-to-end it can reach a higher accuracy of the likelihood predictions. However, as the learning task is more complex the machine learning model may be more complex and require more time for training.

[0028] In an example, the trained machine learning model is configured to evaluate a likelihood function of the physical parameter.

[0029] The term “parameter” refers to a quantitative physical variable of the optical measuring process describing (i) a property of the object comprising integrated circuit patterns (e.g., critical dimension, overlay, height, displacement, rotation, orientation, etc.) or (ii) a physical or operational property of the optical metrology system (e.g., focus offset, illumination parameter, exposure, numerical aperture, aberration term, wavelength, coherence, field distortion, etc.). In an example, the at least one parameter is from the group comprising parameters of the object comprising integrated circuit patterns, parameters of the optical metrology system. In a preferred embodiment, at least one parameter is a parameter of the object comprising integrated circuit patterns.

[0030] Instead of measuring parameters globally from the acquired imaging dataset, parameters can also be measured locally from a section of the acquired imaging dataset. For example, displacements or critical dimensions. According to an example, the acquired imaging dataset is, thus, subdivided into regions, a prior probability distribution and a likelihood function is defined within each region, and at least one parameter value of a parameter of the optical measuring process is measured from each region by estimating statistical properties of a posterior probability distribution comprising the prior probability distribution and the likelihood function within the region. In this case, the prior probability distribution within one or more regions can be defined with respect to a measured parameter value or with respect to a posterior probability distribution of a parameter within another region. In case of displacement parameters, for example, the prior probability distribution within one region can be defined with respect to an already measured parameter in another region, e.g., in the neighboring region, in order to increase the accuracy of the measured parameter values and to reduce the computation time.

[0031] In an example, the at least one parameter comprises a displacement of the object comprising integrated circuit patterns or of a section of the object comprising integrated circuit patterns with respect to a nominal position or a critical dimension of the integrated circuit patterns of the object.

[0032] According to an aspect of the invention, the optical measuring process comprises two or more parameters that are assumed to be independent, and the prior probability distribution of the two or more parameters is indicated by marginal probability distributions of the two or more parameters. In this way, the indication of a prior probability distribution as well as the sampling from the prior probability distribution is simplified and requires less computation time.

[0033] In an example, the posterior probability distribution is approximated using a Markov Chain Monte Carlo approach comprising iteratively: randomly drawing parameter values for the at least one parameter of the optical measuring process from a probability distribution; evaluating the likelihood function for the drawn parameter values; depending on the evaluated likelihood of the drawn parameter values, preserving the drawn parameters as a sample of the posterior probability distribution or discarding the drawn parameters. In this way, even for unknown posterior probability distributions, statistical properties can be derived quickly and accurately. In a preferred embodiment of the invention, the posterior probability distribution is approximated using a Laplace approximation that fits a Gaussian distribution with a mean equal to the maximum a posteriori estimate of the posterior probability distribution and a precision equal to the observed Fisher information. Using a Laplace approximation reduces the computation time by a large factor and is still sufficiently accurate for diverse types of integrated circuit patterns.

[0034] In an example, the at least one parameter consists of a displacement of the object comprising integrated circuit patterns or of a section of the object comprising integrated circuit patterns with respect to a nominal position, the likelihood function evaluates the likelihood of a deviation between the acquired imaging dataset of the object from a simulated imaging dataset of the object, the simulated imaging dataset of the object is only computed in the first iteration, and further simulated imaging datasets of the object for further displacement parameters are computed by applying a phaseterm in the frequency domain. By computing only a single simulated imaging dataset and using a phase term in the frequency space instead, the computation time of the method is strongly reduced.

[0035] According to an aspect, the method further comprises estimating a credibility interval for the at least one parameter of the optical measuring process from the approximated posterior probability distribution. From the credibility interval, information about the uncertainty of a parameter estimate can be derived and measures can be taken to improve and / or repeat the measurement.

[0036] In an example the method, further comprises deriving an uncertainty estimate for the measured parameter values of the at least one parameter value from the approximated posterior probability distribution, e.g., by deriving a credibility interval or from the size of the credibility interval. From the uncertainty estimate, information about the uncertainty of a parameter estimate can be derived and measures can be taken to improve and / or repeat the measurement.

[0037] In a preferred embodiment, the method further comprises, in response to the uncertainty estimate for the measured parameter values exceeding a threshold or falling below a threshold, modifying parameters of the optical metrology system. In this way, the optical metrology system can be automatically re-calibrated, the accuracy of the measured parameters is improved, or resources and computation time are reduced. The modified parameters of the optical metrology system can be, for example, from the group comprising exposure time, laser intensity, field of view. Any of these parameters can be modified to improve the accuracy of the measured parameters or to reduce the required resourced or computation time.

[0038] The method can further comprise, in response to the uncertainty estimate for the measured parameter values exceeding a threshold, repeating the optical measuring process. In this way, the accuracy of the measured parameters is improved.

[0039] The method can further comprise detecting defects in the object comprising integrated circuit patterns using the measured parameter values.

[0040] According to an embodiment of the invention, an optical metrology system for measuring properties of an object comprising integrated circuit patterns comprises: an image acquisition system for acquiring an imaging dataset of the object comprising integrated circuit patterns; one or more processing devices; and one or more machine- readable hardware storage devices comprising instructions that are executable by the one or more processing devices to perform operations comprising a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns according to any of the embodiments, examples or aspects of the invention described above.

[0041] The invention described by examples and embodiments is not limited to the embodiments and examples but can be implemented by those skilled in the art by various combinations or modifications thereof.

[0042] Brief Description of the Drawings

[0043] Fig. 1 shows a schematical layout of an optical metrology system for objects comprising integrated circuit patterns;

[0044] Fig. 2 illustrates an exemplary transmission-based image acquisition system, e.g., a deep ultraviolet (DUV) image acquisition system, for transmission-based photolithography masks; Fig. 3 illustrates an exemplary reflection-based image acquisition system, e.g., an extreme ultra-violet light (EUV) image acquisition system, for reflection-based photolithography masks;

[0045] Fig. 4 shows an imaging dataset of an object comprising integrated circuit patterns with fuzzy edges that makes measurements inaccurate;

[0046] Fig. 5 illustrates a flowchart of a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns;

[0047] Fig. 6 exemplarily illustrates the steps of the method for measuring parameter values of at least one parameter of an optical measuring process, here for measuring a two-dimensional displacement of a structure in a photolithography mask;

[0048] Fig. 7 shows a comparison of MCMC-based marginal probability distributions and Laplace-based marginal probability distributions for estimating displacement parameters sxand sy;

[0049] Fig. 8 shows four different imaging datasets for estimating displacement parameters:

[0050] Fig. 9 shows Laplace approximations of posterior probability distributions for displacement parameters for the four different imaging datasets in Fig. 8 with different uncertainty;

[0051] Fig. 10 shows a corner plot and marginals of the posterior probability distribution for correlated displacement parameters for design D4 in Fig. 8;

[0052] Fig. 11 illustrates a machine learning model that is part of a likelihood function and that maps a difference imaging dataset to a likelihood;

[0053] Fig. 12 illustrates a machine learning model that is part of a likelihood function and that maps an imaging dataset and parameter values to a likelihood. Fig. 13 illustrates a flowchart of a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns, further comprising re-calibrating parameters of the optical metrology system and / or repeating the measurement;

[0054] Fig. 14 compares a histogram over displacement errors of a standard registration method to a histogram of displacement errors of the method according to the invention;

[0055] Fig. 15 shows locally varying parameter values in the form of local displacements;

[0056] Fig. 16 illustrates ambiguities in the likelihood function due to periodic integrated circuit patterns that can be resolved using a prior probability distribution;

[0057] Fig. 17a-d) illustrates a fast method for obtaining displaced simulated imaging datasets by using a phase-term in the frequency domain; and

[0058] Fig. 18 shows a system for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns.

[0059] Detailed Description

[0060] In the following, advantageous exemplary embodiments of the invention are described and schematically shown in the figures. Throughout the figures and the description, same reference numbers are used to describe same features or components. Dashed lines indicate optional features.

[0061] Fig. 1 shows a schematical layout of an image acquisition system 10 in an optical metrology system for measuring properties of objects comprising integrated circuit patterns, e.g., for a photolithography mask, reticle or wafer. A beam column 2, e.g. a SEM column, emits electron beam 8, e.g., at an accelerating electron voltage of 200 eV to 1 keV. The electron beam 8 is incident upon the object 4. The object is located on a stage 7 that can be moved. A sensor 6 detects secondary and backscattered electrons 9 and provides an imaging dataset of the surface of the object 4. The image acquisition system 10 can, for example, be a scanning electron microscope. From the imaging dataset parameter values of parameters of the optical measuring process that involves the optical metrology system and the object 4 can be derived. Preferably, the at least one parameter comprises parameters of the photolithography mask. The at least one parameter can also comprise parameters of the optical metrology system.

[0062] In case the object comprising integrated circuit patterns is a photolithography mask, the optical measuring process for measuring properties of the photolithography mask can use a variety of image acquisition systems depending on the type of the photolithography mask, e.g., transmission-based image acquisition systems as illustrated in Fig. 2 or reflection-based image acquisition systems such as EUV systems as illustrated in Fig. 3. The image acquisition system can generate an aerial imaging dataset of the photolithography mask that is used to measure parameter values of at least one parameter of the optical measuring process that involves the optical metrology system and the photolithography mask. Preferably, the at least one parameter comprises parameters of the photolithography mask. The at least one parameter can also comprise parameters of the optical metrology system.

[0063] Fig. 2 illustrates an exemplary transmission-based image acquisition system 10’ for acquiring aerial images of objects, e.g., a DUV system. Major components are a light source 12, which may be a deep-ultraviolet (DUV) excimer laser source, imaging optics which, for example, define the partial coherence and which may include optics that shape radiation from the light source 12, a photolithography mask 14, illumination optics 16 that illuminate the photolithography mask 14 and projection optics 17 that project an imaging dataset of the photolithography mask design onto a wafer plane 18. An adjustable filter or aperture at the pupil plane of the projection optics 17 may restrict the range of beam angles that impinge on the wafer plane 18, where the largest possible angle defines the numerical aperture of the projection optics NA = nsin(Qmax), wherein n is the refractive index of the media between the substrate and the last element of the projection optics 17, and emaxis the largest angle of the beam exiting from the projection optics 17 that can still impinge on the wafer plane 18. The radiation distribution at the wafer plane 18 is imaged by an image sensor 20 of a camera to generate an aerial image. The image acquisition system 10’ can, for example, be equipped with a staring array sensor or a line-scanning sensor or a time-delayed integration (TDI) sensor.

[0064] Illumination optics 16 may include optical components for shaping, reducing and / or projecting radiation from the light source 12 before the radiation passes the photolithography mask 14. Projection optics 17 may include optical components for shaping, reducing and / or projecting the radiation after the radiation passes the photolithography mask 14. The illumination optics 16 exclude the light source 12, the projection optics exclude the photolithography mask 14.

[0065] Illumination optics 16 and projection optics 17 may comprise various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. Illumination optics 16 and projection optics 17 may also include components operating according to any of these design types for directing, shaping or controlling the projection beam of radiation, collectively or singularly.

[0066] Fig. 3 illustrates an exemplary reflection-based image acquisition system 10” for acquiring aerial images of objects, e.g., an extreme ultraviolet light (EUV) system. Major components are a light source 12, which may be a laser plasma light source, illumination optics 16 which, for example, define the partial coherence and which may include optics that shape radiation from the light source 12, a photolithography mask 14, and projection optics 17 that project an imaging dataset of the photolithography mask onto a wafer plane 18. An adjustable filter or aperture at the pupil plane of the projection optics 17 may restrict the range of beam angles that impinge on the wafer plane 18, where the largest possible angle defines the numerical aperture of the projection optics NA = n sin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics 17, and emaxis the largest angle of the beam exiting from the projection optics 17 that can still impinge on the wafer plane 18. The radiation distribution at the wafer plane 18 is imaged by an image sensor 20 of a camera to generate an aerial imaging dataset. The image acquisition system 10” can, for example, be equipped with a staring array sensor or a line-scanning sensor or a time-delayed integration (TDI) sensor. In the present document, the terms "illumination", “radiation” or “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 3-100 nm).

[0067] An image acquisition system 10’, 10” such as the ones shown in Fig. 2 and 3, can be used to generate an aerial imaging dataset of an object comprising integrated circuit patterns. The aerial imaging dataset can be acquired by the image acquisition system 10, 10’, 10” using light of an actinic wavelength. Using light of an actinic wavelength for metrology means that the light used for metrology is of the same wavelength as the light used during the photolithography process.

[0068] Optical metrology systems acquire imaging datasets (e.g., SEM imaging datasets or aerial imaging datasets) of objects comprising integrated circuit patterns using an image acquisition system. The imaging datasets are used by the optical metrology system to measure properties of the integrated circuit patterns and / or of the optical metrology system.

[0069] Due to the small size of the structures in the integrated circuits a high accuracy of the measurements and the imaging dataset is required. Because of low-pass filtering effects, optical proximity effects, aberrations and further imaging errors structure dimensions and positions cannot be estimated with high accuracy from the generated imaging dataset. Fig. 4 shows an imaging dataset 22, in particular an aerial image of a section of a photolithography mask, comprising edges 24 that do not allow to measure structure dimensions or edge positions with sufficient accuracy.

[0070] To alleviate these issues, a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns as illustrated in Fig. 5 can be used. The method 26 comprises the following steps: acquiring an imaging dataset of the object comprising integrated circuit patterns using the optical metrology system in a step M 1 ; providing a prior probability distribution for the at least one parameter of the optical measuring process, and providing a likelihood function that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset of the object in a step M2; and measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution of the at least one parameter comprising the prior probability distribution for the at least one parameter of the optical measuring process and the likelihood function, e.g., using Bayesian inference in a step M3.

[0071] Bayesian inference is a method of statistical inference in which Bayes theorem is used to estimate a posterior probability of parameters by defining a prior probability distribution over the parameters and a likelihood function to estimate the likelihood of a given parameter hypothesis. Let H indicate a hypothesis (a set of parameter values for the parameters of the optical measuring process) and let E indicate the evidence (the acquired imaging dataset). Then Bayes rule reads

[0072] Instead of defining the posterior probability distribution P(H|E) which is usually unknown, a prior probability distribution P(W) over the at least one parameter is defined together with a likelihood function that measures the likelihood P(E\H) for obtaining the acquired imaging dataset in case of the hypothesis. P(E) is constant and can be ignored during optimization. Statistical properties of the posterior probability distribution can be estimated from the posterior probability distribution in different ways, for example by optimization (MAP estimate), by estimating moments (mean, variance), or by deriving credibility intervals or further uncertainty estimates from the posterior probability distribution. Since the posterior probability distribution is often not available, it can be approximated, for example by sampling from the posterior probability distribution or by fitting a function to the posterior probability distribution.

[0073] To obtain parameter values for the at least one parameter of the optical measuring process, the posterior probability distribution can be optimized by deriving a maximum a posteriori (MAP) estimate, e.g., by using numerical methods such as gradient based optimization (Newton’s method, conjugate gradient method, etc.). The required derivatives can be computed numerically.

[0074] To obtain further statistical properties, an estimate of the full posterior probability distribution can be of use. In case the analytical form of the posterior probability distribution is unknown, the posterior probability distribution can be approximated using sam- pling methods such as Markov Chain Monte Carlo (MCMC), or a Laplace approximation. MCMC generates samples from the posterior probability distribution, whereas the Laplace approximation generates a local Gaussian fit to the posterior probability distribution for known MAP and Hessian. In order to obtain an uncertainty estimate for the measured parameter values of the at least one parameter value from the estimated posterior distribution, a credibility interval can be computed.

[0075] In an example, the at least one parameter is from the group comprising parameters of the object comprising integrated circuit patterns, parameters of the optical metrology system. A parameter of an object or system describes a property of the object or system. Parameters of the object comprising integrated circuit patterns comprise, for example, properties of the object, e.g., the type of integrated circuit patterns in the object (lines and spaces, holes or logical, etc.), material properties of the object (refractive indices, electric permittivities, magnetic permeabilities, etc.), dimensions of the object (layer thicknesses, structure dimensions), locations of structures in the object, displacements of structures or of the whole object, further properties of the object (critical dimensions, linewidths, corner-rounding, side-wall-angles, etching angles, undercuts, etc.). Parameters of the optical metrology system comprise, for example, illumination parameters, a numerical aperture, an imaging scale, a defocus, an exposure time, a wavelength, a partial coherence of the illumination, aberrations, pupil apodizations, a field uniformity, etc. Thus, the method can be used to measure parameters of properties of the object comprising integrated circuit patterns and / or parameters of the optical metrology system. In this way, the optical metrology system can be continuously calibrated.

[0076] Fig. 6 exemplarily illustrates the steps of the method for measuring parameter values of at least one parameter of an optical measuring process, here for measuring a two- dimensional displacement of a structure in an object, here in a photolithography mask. In addition, optical parameters of the optical metrology system can be estimated, e.g., a defocus, a numerical aperture or an illumination setting. The displacement is measured with respect to a nominal position of the structure. The nominal position can, for example, be indicated using a reference image of the object, prior knowledge, or a user input. During image acquisition 28 the optical metrology system as illustrated, for example, in Fig. 1 to 3 above, acquires an imaging dataset 22 of the object comprising integrated circuit patterns, e.g., an aerial image. The imaging dataset 22 can comprise one or more images of one or more portions of the object comprising integrated circuit patterns or of the whole object. According to the techniques described herein, various imaging modalities may be used to acquire the imaging dataset. Imaging datasets can comprise single-channel images or multi-channel images, e.g., focus stacks. For instance, it is possible that the imaging dataset includes 2-D images. It is possible to employ a multi beam scanning electron microscope (mSEM). mSEM employs multiple beams to acquire contemporaneously images in multiple fields of view. Thereby, a large imaging dataset is acquired within a short duration of time. Other examples for imaging datasets including 2D images relate to imaging modalities such as optical imaging, phase-contrast imaging, x-ray imaging, etc. It is also possible that the imaging dataset is a volumetric 3-D dataset, which can be processed slice-by-slice or as a three-dimensional volume. Here, a crossbeam imaging system including a focused- ion beam (FIB) source, an atomic force microscope (AFM) or a scanning electron microscope (SEM) could be used. Furthermore, magnetic resonance (MR) images, ultrasound images or computed tomography (CT) images could be used. Multimodal imaging datasets may be used, e.g., a combination of x-ray imaging and SEM. The imaging dataset can, additionally or alternatively, comprise aerial images. An aerial image shows the radiation intensity distribution at substrate level. It can be used to simulate the radiation intensity distribution generated by a photolithography mask during the photolithography process. The system used to acquire an aerial image can, for example, be equipped with a staring array sensor or a line-scanning sensor or a time-delayed integration (TDI) sensor.

[0077] During parameter sampling 30, a joint prior probability distribution 32 over the at least one parameter is provided. In case of two or more parameters, the parameters can be assumed as independent from one another. In this case, separate marginal prior probability distributions can be used for each parameter. Each marginal prior probability distribution can be represented by a probability density function as shown in Fig. 6. Fig. 6 indicates three separate marginal prior probability density functions 34 of the joint prior probability distribution 32 for three parameters (two-dimensional displacement and one optical parameter) whose parameter values are to be estimated by the method. The marginal probability density functions can be measured in experiments, or they can be defined by a user, e.g., a Gaussian or a uniform distribution. The prior probability distribution for the two-dimensional displacement of the structure in the object is a Gaussian with mean 0. The prior probability distribution for the additional optical parameter is a uniform distribution over the interval [-0.3; 0.3], In case no prior knowledge is available for a parameter, a uniform distribution over a sufficiently large interval can be assumed.

[0078] During parameter sampling 30 samples are drawn from the prior probability distribution 32. In this case, a parameter value for each of the three parameters is drawn independently from the corresponding marginal probability density function.

[0079] During likelihood evaluation 40, the likelihood of the samples parameters is evaluated. According to the example illustrated in Fig. 6, the likelihood function evaluates the likelihood of a deviation between the acquired imaging dataset 22 of the object from a simulated imaging dataset 36 of the object, wherein the simulated imaging dataset 36 of the object simulates the optical measuring process for the object comprising integrated circuit patterns and the parameter values of the at least one parameter of the optical measuring process.

[0080] A simulation method can be used to generate simulated imaging datasets 36 of the object, e.g., aerial images of the photolithography mask.

[0081] For example, for simulating aerial images, there are rigorous simulation methods such as finite difference time domain (FDTD) or rigorous coupled wave analysis (RCWA) that are known to a person skilled in the art. Since they require long computation times, fast approximations such as the thin element approximation (TEA) can be used. The thin element approximation (TEA) assumes that the thickness of the structures on the photolithography mask is very small compared to the wavelength, and that the widths of the structures on the photolithography mask are very large compared to the wavelength. However, as photolithographic processes use radiation of shorter and shorter wavelengths, these assumptions do not hold anymore, and mask 3D effects must be taken into account. To obtain fast and accurate results, simulation methods that are based on physical models but still do not rely on the thin mask assumption can be used, e.g., the one disclosed in WO 2024 141484 A1 or in DE 102022 135019 A1. Alternatively, simulation methods using a trained neural network can be used for simulating an aerial image, e.g., from a design of the object comprising integrated circuit patterns. Alternatively, classical methods such as Gaussian Processes or polynomial approximations can be used for simulating an aerial image. If one only focusses on alignment / registration parameters, only a single forward simulation is required as the subpixel shift can be done in post-processing by using sine-interpolation (Fourier shifts) which is exact for a Nyquist-sampled simulated noise-free reference image.

[0082] The simulated imaging dataset 36 can be simulated from an underlying design of the object. In case the object is a photolithography mask or reticle, the simulated imaging dataset 36 can be simulated from a design of the photolithography mask. In case the object is a wafer, the simulated imaging dataset 36 can be simulated from a design of the photolithography mask that was used to print the wafer. Apart from a design, any other model of the object can be used for the simulation.

[0083] A design of a photolithography mask refers to a representation of the photolithography mask or a section thereof. The design can, for example, comprise a computer readable file, such as a CAD file or a GDS file, or a technical drawing, a set of polygons representing the structures of the photolithography mask or a section thereof. A design of a photolithography mask can comprise parameters describing the location of structures in the photolithography mask, e.g., the location of absorber structures or layers in a multilayer. A design of a photolithography mask can comprise parameters describing the shape of structures in the photolithography mask, e.g., the shape of the absorber structures such as side wall angles or corner rounding, etc. A design of a photolithography mask can comprise descriptions of the structures within the photolithography mask, e.g., in the form of curves, contours, polygons, Splines, NURBS, Bezier curves, etc. A design of a photolithography mask can comprise material information, e.g., complex refractive indices of materials contained in the photolithography mask, electric permittivities, magnetic permeabilities, or derived representations. A design of a photolithography mask can comprise parameters describing dimensions of structures in the photolithography mask, e.g., the thicknesses of the layers in the multilayer of an EUV mask or the thickness of absorber layers, or the dimension of the absorber structures. A design of a photolithography mask can comprise an image, e.g., a 2D image or a 3D image (e.g., a volume of voxels or a number of 2D slices of a volume), that represents properties of the photolithography mask. The image can contain one, two or more channels. The image can comprise image elements, e.g., pixels or voxels. A design can refer to the design of a complete photolithography mask, or it can refer to the design of a section of the photolithography mask. In a preferred example, the simulated imaging dataset 36 of the object 4, in this case a photolithography mask, is simulated using a method that simulates the propagation of incident electromagnetic waves within a first section of the photolithography mask comprising multiple structures using a forward Helmholtz equation and in a second section of the photolithography mask (e.g., in a multilayer of the photolithography mask) analytically or numerically. A corresponding method is, for example, described in WO 2024 141484 A1 or in DE 102022 135019. In this way, a large speed-up of the method is achieved, which is beneficial to compensate for longer computation times of Bayesian methods, in order to make the method applicable for industrial applications that often require real-time or near real-time methods.

[0084] In a preferred example, the simulated imaging dataset 36 of the object 4 is simulated using machine learning model that is trained to map a design of the object 4, in particular of a photolithography mask, to a simulated imaging dataset 36. Using transfer learning, for example, the accuracy of the simulated imaging dataset 36 can be improved. To this end, training data can be used that comprises measured imaging dataset 36 for designs in order to better adapt the simulated imaging dataset 36 to acquired imaging datasets.

[0085] The simulation of the simulated imaging dataset 36 is carried out using parameters of the optical measuring process. The parameters comprise parameters of the photolithography mask and, optionally, of the optical metrology system used to generate the imaging dataset. However, due to noise in the acquired imaging dataset 22, the simulated imaging dataset 36 always deviates from the acquired imaging dataset 22.

[0086] To increase the accuracy of the measured parameter values, the likelihood function can take into account a noise model for the deviations between the imaging dataset 22 and the simulated imaging dataset 36. Thus, the likelihood function can evaluate the likelihood of the deviation of the acquired imaging dataset 22 of the object from the simulated imaging dataset 36 of the object using a noise model. For optical metrology systems for objects comprising integrated circuit patterns shot noise is a common source of noise. Shot noise is not identically distributed (non-i.i.d.). An identical noise distribution implies that the noise is invariant to signal intensity. This is not the case for shot noise in aerial images, since it depends on photon counts and, thus, on the pixel intensity. Therefore, it is beneficial to use a noise model that comprises a shot noise model, e.g., a Poisson distribution, for formulating the likelihood function.

[0087] Let indicate the two-dimensional displacement of the structure in the object in x and y direction, let further Irefindicate the simulated (reference) imaging dataset 36, Imeasthe acquired (measured) imaging dataset 22 and i the pixel index within the imaging datasets, then the likelihood function under a Poisson distributed shot noise model can be written as follows:

[0088] Alternatively, the likelihood function under an independent and identically distributed Gaussian read-out noise model could be written as follows:

[0089] In general, any arbitrary combination of noise models is feasible, taking into account, for example, complex sensor behavior or pre-processing steps, which could, potentially, even lead to spatially varying and correlated noise distributions.

[0090] In Fig. 6, a logarithm of a likelihood function (log likelihood function 42) for a two- dimensional displacement sx, syis shown. Instead of defining the noise model, e.g., as a Poisson or Gaussian distribution, the noise model can also be estimated from the acquired imaging dataset 22 of the object, e.g., by estimating the variance of the intensity within homogeneous regions.

[0091] The posterior probability distribution can be approximated using a MCMC method comprising: randomly drawing parameter values for the at least one parameter of the optical measuring process from a probability distribution (parameter sampling 30); evaluating the likelihood function for the drawn parameter values (likelihood function evaluation 40); depending on the evaluated likelihood of the drawn parameter values, preserving the drawn parameters as a sample of the posterior probability distribution or discarding the drawn parameters. The parameter values for the at least one parameter of the optical measuring process can, for example, be drawn from the prior probability distribution 32. Alternatively, the parameter values for the at least one parameter of the optical measuring process can, for example, be drawn from a proposal probability distribution of a new proposed parameter given the previously drawn parameter. In this case, the drawn parameters are preserved as a sample of the posterior probability distribution depending on the evaluated likelihood of the drawn parameter values and the prior probability distribution 32.

[0092] To generate samples from the posterior probability distribution, the steps of parameter sampling 30 and likelihood function evaluation 40 are iterated 44. Various MCMC methods are known such as Metropolis Hastings sampling or Gibb’s sampling. According to an exemplary sampling strategy, each randomly sampled parameter values from the prior probability distribution are evaluated using the likelihood function. For example, an acceptance interval within the interval [0,1] is generated from the value of the likelihood function. The higher the likelihood function value the larger the acceptance interval within [0,1], Then a random value is drawn from a uniform distribution over the interval [0,1], and the randomly sampled parameter values are accepted as a sample of the posterior probability distribution in case the random value lies within the acceptance interval. Otherwise, the randomly sampled parameter values are rejected as samples of the posterior probability distribution. In this way, an approximated posterior probability distribution 46 is obtained. Fig. 6 shows the approximated posterior probability distribution 46 for the displacement sxof the structure in x-di recti on.

[0093] From the approximated posterior probability distribution 46, results 48 of the parameter estimation can be obtained, e.g., a credibility interval 50 for the at least one parameter. A moment of the posterior probability distribution or a MAP estimate 52 can also be obtained from the approximated posterior probability distribution 46. A MAP estimate 52 can, for example, be obtained by evaluating the approximated posterior probability distribution 46 for each drawn sample and selecting the one with the highest probability. Alternatively, numerical methods such as gradient based optimization (Newton’s method, conjugate gradient method, etc.) can be used to obtain a MAP estimate 52. The required derivatives can be computed numerically. In Fig. 6, a MAP estimate 52 of the displacement of the structure in the object is computed from the approximated posterior probability distribution 46. In addition, 90% credibility intervals for the displacement in x and y direction are computed from the approximated posterior probability distribution 46 using the marginal probability distributions 54 over sx and sy. For the displacement in x-direction sxthe MAP estimate is 4.07 and the credibility interval is [4.07 - 0.23; 4.07 + 0.22], For the displacement in y-direction sythe MAP estimate is 2.10 and the credibility interval is [2.10 - 0.22; 2.10 + 0.23],

[0094] MCMC methods require a large amount of forward simulations to approximate the posterior probability distribution, which is time-consuming. To reduce the computation time, the posterior probability distribution can be approximated using a Laplace approximation that provides an analytical expression of the posterior probability distribution by fitting a Gaussian distribution with a mean equal to the maximum a posteriori estimate of the posterior probability distribution and a precision equal to the observed Fisher information. The MAP estimate can be obtained, e.g., by standard gradient based optimization, and it has to be computed anyway to obtain the estimated parameter values for the at least one parameter of the optical measuring process. Hence, the computational overhead is reduced to computation of the Hessian matrix, which can be efficiently obtained, e.g., by automatic differentiation. Fig. 7 shows a comparison of MCMC-based marginal probability distributions 53 and Laplace-based marginal probability distributions 55 for estimating displacement parameters sxand sy.

[0095] Despite its simplicity, it has been ascertained by the inventors that the Laplace approximation is, surprisingly, a suitable approximation for various types of integrated circuit patterns and complex noise models. At the same time, it provides a speed-up of, for example, more than 1 .000. The suitability of the Laplace approximation for various designs is, for example, illustrated in Fig. 8 to 10. Fig. 8 shows four different designs of sections of photolithography masks: D1 , D2, D3 and D4. For each of these designs a two-dimensional displacement is estimated using the method described above. The posterior probability distribution is approximated using the Laplace approximation yielding the results in Fig. 9 for the four designs. It is noted that an increased edge length of the structure in the design reduces the uncertainty of the posterior probability distribution. The approximated posterior probability distribution of design D2 is, for example, more spread out (meaning higher uncertainty) than the one of design D3. It is also noted, that correlations between parameters can be identified using the method described above, see, for example, the corner plot in Fig. 10 for design D4. Alternative to MCMC or a Laplace approximation, other methods can be used for Bayesian inference. For example, stochastic variational inference (SVI) could be used. This approximation is computationally more expensive than the Laplace approximation, but it allows to approximate non-Gaussian distributions. Stochastic variational inference approximates the true posterior by searching the space of variational distributions to find one that is most similar to the true posterior according to some measure of distance or divergence, e.g., the Kullback Leibler divergence. Alternatively, for low-dimensional parameter optimization problems, one could use numerical quadrature schemes to compute statistical moments of the posterior probability distribution.

[0096] In any of the above-mentioned optimization approaches, derivative information can be efficiently employed, which can be computed using an automatic-differentiable simulator, in particular, by using Hamiltonian MC in case of MCMC methods or stochastic gradient descent in case of SVI.

[0097] In case the simulation model does not capture all relevant physical effects or error sources, the method can be extended by fitting an additional model discrepancy term as outlined, for example, in the article “Bayesian calibration of computer models”, by M. Kennedy, A. O’Hagan, in the Journal of the Royal Statistical Society, Statistical Methodology, Series B, 2002.

[0098] Instead of defining a noise model or any other likelihood function, the likelihood function can comprise the application of a trained machine learning model. The machine learning model can, for example, derive the likelihood from a comparison of the acquired imaging dataset and the simulated imaging dataset. Alternatively, the likelihood can be directly computed from the acquired imaging dataset and the sampled parameter values for the at least one parameter of the optical measuring process.

[0099] According to an example of the invention illustrated in Fig. 11 , the likelihood function 40 comprises using a trained machine learning model 56 that uses the acquired imaging dataset 22 of the object and the simulated imaging dataset 36 of the object as input and computes a likelihood of the parameter values of the at least one parameter as output. Alternatively, a difference imaging dataset 62 of the acquired imaging dataset 22 and the simulated imaging dataset 36 can be used as input 66 to the machine learning model 56. The machine learning model 56 can, for example, be configured as a convolutional neural network (CNN) as shown in Fig. 11.

[0100] The CNN illustrated in Fig. 11 serves as likelihood function 40 that estimates the likelihood of a simulated imaging dataset 36 given an acquired imaging dataset 22. The difference imaging dataset 62 is used as input 66. The input 66 is processed by several convolution and max-pooling layers 58 followed by two fully connected layers 60. Finally, the CNN returns the value of the likelihood function 40 as output.

[0101] An exemplary training of this CNN can be carried out as follows: the training data comprises 100,000 crops of size 512 x 512 of difference imaging datasets 62 of imaging datasets 22 and simulated imaging datasets 36 containing various integrated circuit patterns such as lines and spaces, holes, pin dots or logic patterns, and a desired likelihood value, e.g., from the interval [0,1], For optimization, AdamW is used for 100 epochs with a batch size of 32, a learning rate of 5e-4 with a decay of 0.98 in each epoch. A cross-entropy loss is used as loss function. The CNN contains a single channel input 66 (the difference imaging dataset 62). Alternatively, the imaging dataset 22 of the object and the simulated imaging dataset 36 of the object could be used as input 66. The output of the CNN is a single likelihood value.

[0102] In another example illustrated in Fig. 12, the trained machine learning model 56’ does not use the simulated imaging dataset 36 or a difference imaging dataset 62 as input 66. Instead, the trained machine learning model 56’ directly uses the acquired imaging dataset 22 and the sampled parameter values 64 of the at least one parameter of the optical measuring process as input 66. In this way, the machine learning model 56’ generates its own simulation of the imaging dataset 22 that may be more accurate, since the machine learning model 56’ is trained end-to-end and from training data. In this case, the likelihood function 40 comprises a trained machine learning model 56’ that uses the acquired imaging dataset 22 of the object and the parameter values 64 of the at least one parameter as input 66 and computes a likelihood 40 of the parameter values of the at least one parameter as output. The training of this machine learning model can be carried out as described in the previous paragraph with different training data comprising acquired imaging datasets, parameter values and desired likelihood values. From the approximated posterior probability distribution, uncertainty measures for measuring the uncertainty of the estimated parameter values can be generated. To this end, the method can further comprise deriving an uncertainty estimate for the measured parameter values of the at least one parameter value from the approximated posterior probability distribution.

[0103] An uncertainty estimate can comprise a credibility interval. A credibility interval can, for example, be established in case of a Gaussian posterior probability distribution by using a mean value and a multiple of an estimate of the standard deviation, e.g., [p - 3o; n + 3o], For MCMC methods, a credibility interval can be established by finding the interval around a MAP estimate that contains a certain percentage, e.g., 97%, of the samples drawn from the approximated posterior probability distribution.

[0104] An uncertainty estimate can comprise an estimated variance. The variance can be estimated from samples of the posterior probability distribution or from a closed form of the posterior probability distribution if available. An uncertainty estimate can be obtained from the size of a credibility interval for the at least one parameter of the optical measuring process. The larger the credibility interval for a parameter is, the more uncertain is the estimated parameter value.

[0105] As illustrated in Fig. 13, in response to the uncertainty estimate for the measured parameter values exceeding a threshold or falling below a threshold, the method 26’ can further comprise modifying parameters of the optical metrology system. In case the uncertainty estimate exceeds a threshold, the method can further comprise repeating the optical measuring process. The steps M1 to M3 are identical to the method 26 described above. In a step M4, an uncertainty estimate is derived from the posterior probability distribution, e.g., from the size of a credibility interval. If the uncertainty estimate does not exceed a threshold (normal uncertainty 82), the measurement is reliable and the parameter values and, optionally, uncertainty estimates, are returned as a result 48 of the method. If the uncertainty estimate, however, exceeds a threshold (high uncertainty 84), the reliability of the measurement is low. In this case, in a step M6, parameters of the optical metrology system can be modified, e.g., re-calibrated.

[0106] The modified parameters of the optical metrology system can, for example, be from the group comprising exposure time, laser intensity, field of view. By increasing the exposure time or the laser intensity, imaging datasets of higher quality can be acquired. By modifying the field of view, the contents of the imaging dataset is modified, which can reduce the uncertainty of the measurement, e.g., by resolving ambiguities.

[0107] The parameters of the optical metrology system can be modified by a user, e.g., upon receiving a warning of high uncertainty estimates, or the parameters can be modified automatically upon receiving one or more parameter estimates of high uncertainty. In this way, the optical metrology system is automatically re-calibrated depending on the uncertainty in the measured parameters. Rules can be defined for automatically modifying parameters of the optical metrology system, e.g., a certain number of high uncertainty measurements in a row have to be fulfilled before a parameter modification is carried out. For automatically modifying the parameters, tables can be established by a user that indicate the desired parameter change depending on different uncertainty estimates.

[0108] Alternatively or in addition, the optical measuring process can be repeated in a step M5 - either after modifying the parameters of the optical metrology system or with the same parameters of the optical metrology system.

[0109] In case of very low uncertainty estimates (low uncertainty 86) that fall below a threshold, parameters of the optical metrology system can also be modified to save image acquisition and computation time as well as resources. For example, the exposure time or the laser intensity or the field of view can be reduced, while still obtaining measurements of sufficiently low uncertainty.

[0110] In this way, the parameters of the optical metrology system can be modified to obtain measurements of low uncertainty at a minimum expanse of resources and computation time.

[0111] Fig. 14 shows a comparison of registration errors for images with shot noise using a standard registration method that implicitly assumes independent and identically distributed (i.i.d) noise on the left, and using the method described above that can handle non-i.i.d. noise on the right. The standard registration errors 68 were obtained using a cross-correlation method. The MAP registration errors 70 were obtained using Bayes inference and uniform prior probability distributions for the parameters (non- informative priors), that is without making any prior assumptions on the parameters. Even without using any prior knowledge, the mean registration error is reduced by more than 40% from 0.36 nm for the standard registration method to 0.26 nm for the MAP registration method.

[0112] Instead of globally measuring parameter values from an imaging dataset of the object, parameter values can be measured locally, for example in case the parameters describe local properties of the object, for example within a limited section of the object. Such locally defined parameter values can be measured by subdividing the acquired imaging dataset into regions and measuring parameters from these regions. Within each region of the imaging dataset, a prior probability distribution and a likelihood function is defined, and at least one parameter value of a parameter of the optical measuring process is measured from each region by estimating statistical properties of a posterior probability distribution comprising the prior probability distribution and the likelihood function within the region. The regions can be overlapping, or they can represent a partitioning of the imaging dataset. The prior probability distributions and / or the likelihood functions can be identical for different regions, or they can differ for different regions.

[0113] Fig. 15 illustrates, for example, the measuring process for measuring displacements 72 of different structures of the integrated circuit patterns in an object. Each displacement 72 is measured locally from overlapping regions of the imaging dataset. According to an aspect of the invention, the prior probability distribution within one or more regions is defined with respect to a measured parameter value of a parameter within another region or with respect to a posterior probability distribution of at least one parameter within another region. In different regions of the object, there are often correlations between neighboring regions, e.g., due to large-scale thermal-mechanical deformations of the object or due to electron beam optical effects. For example, neighboring structures in neighboring regions often have the same or similar displacements. Therefore, the prior probability distribution within one region can be defined with respect to the displacement measured within another, e.g., a neighboring, region. For example, the prior probability distribution can be Gaussian with mean equal to the MAP estimate of the neighboring region, thereby assuming similar displacements. In this way, the information from the previous measurement could be incorporated into the prior distribution for the displacement parameters of the next measurement. Fig. 16 illustrates the use of the prior probability distribution for regularization of ambiguous parameter optimization problems. On the left-hand side, a periodic design 74 is shown that contains periodic lines. Such periodic designs frequently occur in objects comprising integrated circuit patterns. Measuring displacement parameters for such structures is difficult, since multiple displacements are equally likely. Therefore, the likelihood function 40 on the right-hand side has lots of modes, and the measured parameters would be influenced by very little noise variations, e.g., due to line edge roughness. In such cases, the use of prior probability distributions can serve for regularization of the parameter optimization problem. For example, a prior probability distribution that favors small displacements would lead to a unique mode of the posterior probability distribution and, thus, efficiently regularize the problem - without requiring heuristics or pre-defined constraints.

[0114] During each MCMC iteration, a simulated imaging dataset is generated, and the likelihood function evaluates the likelihood of a deviation between the acquired imaging dataset and the simulated imaging dataset. In a special case, the at least one parameter of the optical measuring process only consists of displacement parameters. According to an aspect of the invention, in this case, Bayesian inference using MCMC requires only a single simulation of a simulated imaging dataset for evaluating the likelihood function - provided the following assumptions are fulfilled: a) the imaging datasets are Nyquist sampled, meaning that the pixel distance is smaller or equal to the Nyquist sampling rate defined by the imaging pupil of the optical metrology system, b) the noise is the dominant error source, c) the parameters of the optical metrology system are sufficiently well calibrated and do not have to be optimized. In this case, the simulated imaging dataset is noise-free and can, hence, be (sub-pixel) shifted without any approximation errors (apart from boundary effects). Then, instead of iteratively computing the simulated imaging dataset, the simulated imaging dataset of the object is only computed in the first iteration of the MCMC method, e.g., for the nominal position. Further simulated imaging datasets of the object for further displacement parameters in further iterations are computed by using sine-interpolation or applying a phase-term in the frequency domain. In this way, only a single simulation is required that leads to a large speed-up of the method.

[0115] Fig. 17 a) to d) illustrate this special case. Fig. 17 a) shows a simulated nominal imaging dataset 36. The simulation of a single imaging dataset is sufficient to generate shifted simulated imaging datasets for any two-dimensional displacement instead of re-simulating each of the imaging datasets for shifted designs. The displaced simulated imaging dataset is obtained by applying a phase term in frequency space. Fig. 17 b) shows a simulated shifted imaging dataset 76 after re-simulation of the shifted design. Fig. 17 c) shows a shifted simulated nominal imaging dataset 78 obtained by applying a phase-term in the frequency domain. In this way, the simulated imaging datasets 36 can be generated at very low computation times for various displacements. Fig. 17 d) shows the difference 80 between the simulated shifted imaging dataset 76 and the shifted simulated nominal imaging dataset 78, which is 0 up to numerical precision errors. Thus, the accuracy is preserved.

[0116] The method can further comprise detecting defects in the object comprising integrated circuit patterns using the measured parameter values. Rules or thresholds can, for example, be defined to identify defects from measured parameters. For example, a threshold can be defined for a critical dimension, and upon exceeding the threshold a defect can be identified. In another example, a maximum allowed displacement can be defined for structures in the object, and, upon, exceeding the threshold, a defect can be identified.

[0117] Fig. 18 schematically illustrates an optical metrology system 88 for measuring properties of an object 90 comprising integrated circuit patterns. The optical metrology system 88 includes an image acquisition system 10, 10’, 10” as described above with respect to Fig. 1 to 3 for acquiring imaging datasets 22 of the object 4, e.g., aerial images of photolithography masks or SEM images of photolithography masks or wafers. The image acquisition system 10, 10’, 10” for obtaining an imaging dataset 22 of the object 4 comprising integrated circuit patterns can comprise a charged particle beam device, for example, a Helium ion microscope, a cross-beam device including FIB and SEM, an atomic force microscope or any charged particle imaging device, or an aerial image acquisition system. The image acquisition system 10, 10’, 10” for obtaining an imaging dataset 22 of the object 4 comprising integrated circuit patterns can provide an imaging dataset 22 to the data analysis device 90. The data analysis device 90 includes one or more processors 92, e.g., implemented as a CPU, GPU or TPU. The one or more processors 92 can receive the imaging dataset 22 via an interface 96. The one or more processors 92 can load program code from a machine- readable hardware-storage device 94, e.g., program code for executing a method 26 for measuring at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns according to an embodiment of the invention as described above. The one or more processors 92 can execute the program code. The optical metrology system 88 optionally comprises a database for loading and / or saving data, e.g., machine learning models, thresholds, rule tables, etc. The optical metrology system 88 optionally comprises a user interface, e.g., for modifying parameters of the optical metrology system for re-calibration.

[0118] Reference throughout this specification to “an embodiment” or “an example” or “an aspect” means that a particular feature, structure or characteristic described in connection with the embodiment, example or aspect is included in at least one embodiment, example or aspect. Thus, appearances of the phrases “according to an embodiment”, “according to an example” or “according to an aspect” in various places throughout this specification are not necessarily all referring to the same embodiment, example or aspect, but may. Furthermore, the particular features or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0119] Furthermore, while some embodiments, examples or aspects described herein include some but not other features included in other embodiments, examples or aspects combinations of features of different embodiments, examples or aspects are meant to be within the scope of the claims, and form different embodiments, as would be understood by those skilled in the art.

[0120] Embodiments, examples or aspects of the invention are described by the following clauses:

[0121] 1. A method 26 for measuring parameter values of at least one parameter (e.g., of at least one optical metrology parameter) of an optical measuring process that uses an optical metrology system 88 for measuring properties of an object 4 comprising integrated circuit patterns, the method comprising:

[0122] - Acquiring an imaging dataset 22 of the object 4 comprising integrated circuit patterns using the optical metrology system 88;

[0123] Providing a prior probability distribution 32 for the at least one parameter of the optical measuring process, and providing a likelihood function 40 that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset 22 of the object 4;

[0124] Measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution 46 of the at least one parameter (e.g., of the at least one optical metrology parameter) comprising the prior probability distribution 32 for the at least one parameter of the optical measuring process and the likelihood function 40.

[0125] 2. The method of clause 1 , wherein the likelihood function 40 evaluates the likelihood of a deviation between the acquired imaging dataset 22 of the object 4 from a simulated imaging dataset 36 of the object 4, and wherein the simulated imaging dataset 36 of the object 4 simulates the optical measuring process for the object 4 comprising integrated circuit patterns and the parameter values of the at least one parameter of the optical measuring process.

[0126] 3. The method of clause 2, wherein the simulated imaging dataset 36 of the object 4 is simulated using a design 38 of the object 4 comprising integrated circuit patterns.

[0127] 4. The method of clause 2 or 3, wherein the likelihood function 40 evaluates the likelihood of the deviation of the acquired imaging dataset 22 of the object 4 from the simulated imaging dataset 36 of the object 4 using a noise model.

[0128] 5. The method of clause 4, wherein the noise model comprises a shot noise model.

[0129] 6. The method of clause 4 or 5, wherein the noise model is estimated from an acquired imaging dataset 22 of the object 4.

[0130] 7. The method of any one of the preceding clauses, wherein the likelihood function 40 comprises the application of a trained machine learning model 56, 56’.

[0131] 8. The method of any one of clauses 2 to 6, wherein the likelihood function 40 comprises the application of a trained machine learning model 56 that uses the acquired imaging dataset 22 of the object 4 and the simulated imaging dataset 36 of the object 4 or their difference 62 as input 66 and computes a likelihood of the parameter values of the at least one parameter as output.

[0132] 9. The method of clause 7, wherein the trained machine learning model 56’ uses the acquired imaging dataset 22 of the object 4 and the parameter values of the at least one parameter as input 66 and computes a likelihood of the parameter values of the at least one parameter as output.

[0133] 10. The method of any one of the preceding clauses, wherein the at least one parameter is from the group comprising parameters of the object 4 comprising integrated circuit patterns and parameters of the optical metrology system 88.

[0134] 11 . The method of any one of the preceding clauses, wherein the acquired imaging dataset 22 is subdivided into regions, wherein a prior probability distribution 32 and a likelihood function40 is defined within each region, and wherein at least one parameter value of a parameter of the optical measuring process is measured from each region by estimating statistical properties of a posterior probability distribution 46 comprising the prior probability distribution 32 and the likelihood function 40 within the region.

[0135] 12. The method of clause 11 , wherein the prior probability distribution within one or more regions is defined with respect to a measured parameter value or with respect to a posterior probability distribution of a parameter within another region.

[0136] 13. The method of any one of the preceding clauses, wherein the at least one parameter comprises a displacement 72 of the object 4 comprising integrated circuit patterns or of a section of the object 4 comprising integrated circuit patterns with respect to a nominal position.

[0137] 14. The method of any one of the preceding clauses, wherein the at least one parameter comprises a critical dimension of the integrated circuit patterns of the object 4.

[0138] 15. The method of any one of the preceding clauses, wherein the optical measuring process comprises two or more parameters that are assumed to be independent, and wherein the prior probability distribution 32 of the two or more parameters is indicated by marginal probability distributions 54 of the two or more parameters. The method of any one of the preceding clauses, wherein the posterior probability distribution 46 is approximated using a Markov Chain Monte Carlo approach comprising iteratively: randomly drawing parameter values for the at least one parameter of the optical measuring process from a probability distribution; evaluating the likelihood function 40 for the drawn parameter values; depending on the evaluated likelihood of the drawn parameter values, preserving the drawn parameters as a sample of the posterior probability distribution 46 or discarding the drawn parameters. The method of any one of the preceding clauses, wherein the posterior probability distribution 46 is approximated using a Laplace approximation that fits a Gaussian distribution with a mean equal to the maximum a posteriori estimate 52 of the posterior probability distribution 46 and a precision equal to the observed Fisher information. The method of clause 16, wherein the at least one parameter consists of a displacement 72 of the object 4 comprising integrated circuit patterns or of a section of the object 4 comprising integrated circuit patterns with respect to a nominal position, wherein the likelihood function 40 evaluates the likelihood of a deviation between the acquired imaging dataset 22 of the object 4 from a simulated imaging dataset 36 of the object 4, wherein the simulated imaging dataset 36 of the object 4 is only computed in the first iteration, and wherein further simulated imaging datasets 36 of the object 4 for further displacement parameters are computed by applying a phase-term in the frequency domain. The method of any one of the preceding clauses, further comprising estimating a credibility interval 50 for the at least one parameter of the optical measuring process from the approximated posterior probability distribution 46. The method of any one of the preceding clauses, further comprising deriving an uncertainty estimate for the measured parameter values of the at least one parameter value from the approximated posterior probability distribution 46. 21 . The method of clause 20, wherein the uncertainty estimate comprises the size of a credibility interval 50 for the at least one parameter of the optical measuring process.

[0139] 22. The method of clause 20 or 21 , further comprising, in response to the uncertainty estimate for the measured parameter values exceeding a threshold or falling below a threshold, modifying parameters of the optical metrology system 88.

[0140] 23. The method of clause 22, wherein the modified parameters of the optical metrology system 88 are from the group comprising exposure time, laser intensity, field of view.

[0141] 24. The method of any one of clauses 20 to 23, further comprising, in response to the uncertainty estimate for the measured parameter values exceeding a threshold repeating the optical measuring process.

[0142] 25. The method of any one of the preceding clauses, further comprising detecting defects in the object 4 comprising integrated circuit patterns using the measured parameter values.

[0143] 26. The method of any one of the preceding clauses, wherein the object 4 comprising integrated circuit patterns is a photolithography mask or a wafer.

[0144] 27. An optical metrology system 88 for measuring properties of an object 4 comprising integrated circuit patterns, the optical metrology system comprising: an image acquisition system 10, 10’, 10” for acquiring an imaging dataset 22 of the object 4 comprising integrated circuit patterns; one or more processing devices 92; and one or more machine-readable hardware storage devices 94 comprising instructions that are executable by the one or more processing devices 92 to perform operations comprising a method 26, 26’ of any one of the preceding clauses.

[0145] In summary, the invention relates to a method for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system for measuring properties of an object comprising integrated circuit patterns, comprising: acquiring an imaging dataset of the object using the optical metrology system; providing a prior probability distribution for the at least one parameter of the optical measuring process, and providing a likelihood function that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset of the object; measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution of the at least one parameter. The invention also relates to a corresponding optical metrology system.

[0146] Reference number list

[0147] 2 beam column

[0148] 4 Object

[0149] 6 Sensor

[0150] 7 Stage

[0151] 8 Electron beam

[0152] 9 Secondary and backscattered electrons

[0153] 10, 10’, 10” Image acquisition system

[0154] 12 Light source

[0155] 14 Photolithography mask

[0156] 16 Illumination optics

[0157] 17 Projection optics

[0158] 18 Wafer plane

[0159] 19 Projection section

[0160] 20 Image sensor

[0161] 22 Imaging dataset

[0162] 24 Edge

[0163] 26, 26’ Method

[0164] 28 Image acquisition

[0165] 30 Parameter sampling

[0166] 32 Prior probability distribution

[0167] 34 Marginal probability density function

[0168] 36 Simulated imaging dataset

[0169] 38 Design

[0170] 40 Likelihood function

[0171] 42 Log likelihood function

[0172] 44 Iteration

[0173] 46 Posterior probability distribution

[0174] 48 Result

[0175] 50 Credible interval

[0176] 52 MAP estimate

[0177] 53 MCMC-based marginal probability distribution

[0178] 54 Marginal probability distribution

[0179] 55 Laplace-based marginal probability distribution

[0180] 56, 56’ Machine learning model Convolution and max-pooling layer

[0181] Fully connected layer

[0182] Difference imaging dataset

[0183] Parameter values

[0184] Input

[0185] Standard registration error

[0186] MAP registration error

[0187] Displacement

[0188] Periodic design

[0189] Simulated shifted imaging dataset

[0190] Shifted simulated imaging dataset

[0191] Difference

[0192] Normal uncertainty

[0193] High uncertainty

[0194] Low uncertainty

[0195] Optical metrology system

[0196] Data analysis device

[0197] Processing device

[0198] Hardware storage device

[0199] Interface

Claims

- 38 -Claims1. A method (26) for measuring parameter values of at least one parameter of an optical measuring process that uses an optical metrology system (88) for measuring properties of an object (4) comprising integrated circuit patterns, the method comprising:- Acquiring an imaging dataset (22) of the object (4) comprising integrated circuit patterns using the optical metrology system (88);Providing a prior probability distribution (32) for the at least one parameter of the optical measuring process, and providing a likelihood function (40) that evaluates the likelihood of parameter values of the at least one parameter using the acquired imaging dataset (22) of the object (4);Measuring parameter values of the at least one parameter of the optical measuring process by estimating statistical properties of a posterior probability distribution (46) of the at least one parameter comprising the prior probability distribution (32) for the at least one parameter of the optical measuring process and the likelihood function (40).

2. The method of claim 1 , wherein the likelihood function (40) evaluates the likelihood of a deviation between the acquired imaging dataset (22) of the object (4) from a simulated imaging dataset (36) of the object (4), and wherein the simulated imaging dataset (36) of the object (4) simulates the optical measuring process for the object (4) comprising integrated circuit patterns and the parameter values of the at least one parameter of the optical measuring process.

3. The method of claim 2, wherein the simulated imaging dataset (36) of the object (4) is simulated using a design (38) of the object (4) comprising integrated circuit patterns.

4. The method of claim 2 or 3, wherein the likelihood function (40) evaluates the likelihood of the deviation of the acquired imaging dataset (22) of the object (4) from the simulated imaging dataset (36) of the object (4) using a noise model.

5. The method of claim 4, wherein the noise model comprises a shot noise model.- 39 -6. The method of claim 4 or 5, wherein the noise model is estimated from an acquired imaging dataset (22) of the object (4).

7. The method of any one of the preceding claims, wherein the likelihood function (40) comprises the application of a trained machine learning model (56, 56’).

8. The method of claim 7, wherein the trained machine learning model is configured to compute a likelihood function comprising a probability density over the at least one parameter.

9. The method of any one of claims 2 to 8, wherein the likelihood function (40) comprises the application of a trained machine learning model (56) configured to use the acquired imaging dataset (22) of the object (4) and the simulated imaging dataset (36) of the object (4) or their difference (62) as input (66) and to compute a likelihood of the parameter values of the at least one parameter as output.

10. The method of claim 7 or 8, wherein the trained machine learning model (56’) uses the acquired imaging dataset (22) of the object (4) and the parameter values of the at least one parameter as input (66) and computes a likelihood of the parameter values of the at least one parameter as output.11 . The method of any one of the preceding claims, wherein the at least one parameter is from the group comprising parameters of the object (4) comprising integrated circuit patterns and parameters of the optical metrology system (88).

12. The method of any one of the preceding claims, wherein the acquired imaging dataset (22) is subdivided into regions, wherein a prior probability distribution (32) and a likelihood function(40) is defined within each region, and wherein at least one parameter value of a parameter of the optical measuring process is measured from each region by estimating statistical properties of a posterior probability distribution (46) comprising the prior probability distribution (32) and the likelihood function (40) within the region.

13. The method of claim 12, wherein the prior probability distribution within one or more regions is defined with respect to a measured parameter value or with respect to a posterior probability distribution of a parameter within another region.- 40 -14. The method of any one of the preceding claims, wherein the at least one parameter comprises a displacement (72) of the object (4) comprising integrated circuit patterns or of a section of the object (4) comprising integrated circuit patterns with respect to a nominal position.

15. The method of any one of the preceding claims, wherein the at least one parameter comprises a critical dimension of the integrated circuit patterns of the object (4).

16. The method of any one of the preceding claims, wherein the optical measuring process comprises two or more parameters that are assumed to be independent, and wherein the prior probability distribution (32) of the two or more parameters is indicated by marginal probability distributions (54) of the two or more parameters.

17. The method of any one of the preceding claims, wherein the posterior probability distribution (46) is approximated using a Markov Chain Monte Carlo approach comprising iteratively: randomly drawing parameter values for the at least one parameter of the optical measuring process from a probability distribution; evaluating the likelihood function (40) for the drawn parameter values; depending on the evaluated likelihood of the drawn parameter values, preserving the drawn parameters as a sample of the posterior probability distribution (46) or discarding the drawn parameters.

18. The method of any one of the preceding claims, wherein the posterior probability distribution (46) is approximated using a Laplace approximation that fits a Gaussian distribution with a mean equal to the maximum a posteriori estimate (52) of the posterior probability distribution (46) and a precision equal to the observed Fisher information.

19. The method of any one of the preceding claims, wherein the at least one parameter consists of a displacement (72) of the object (4) comprising integrated circuit patterns or of a section of the object (4) comprising integrated circuit patterns with respect to a nominal position, wherein the likelihood function (40) evaluates the likelihood of a deviation between the acquired imaging dataset (22) of the object (4) from a simulated imaging dataset (36) of the object (4), wherein the simulated imaging dataset (36) of the object (4) is only computed in the first iteration, andwherein further simulated imaging datasets (36) of the object (4) for further displacement parameters are computed by applying a phase-term in the frequency domain.

20. The method of any one of the preceding claims, further comprising estimating a credibility interval (50) for the at least one parameter of the optical measuring process from the approximated posterior probability distribution (46).

21. The method of any one of the preceding claims, further comprising deriving an uncertainty estimate for the measured parameter values of the at least one parameter value from the approximated posterior probability distribution (46).

22. The method of claim 21 , wherein the uncertainty estimate comprises the size of a credibility interval (50) for the at least one parameter of the optical measuring process.

23. The method of claim 21 or 22, further comprising, in response to the uncertainty estimate for the measured parameter values exceeding a threshold or falling below a threshold, modifying parameters of the optical metrology system (88).

24. The method of claim 23, wherein the modified parameters of the optical metrology system (88) are from the group comprising exposure time, laser intensity, field of view.

25. The method of any one of claims 21 to 24, further comprising, in response to the uncertainty estimate for the measured parameter values exceeding a threshold repeating the optical measuring process.

26. The method of any one of the preceding claims, further comprising detecting defects in the object (4) comprising integrated circuit patterns using the measured parameter values.

27. The method of any one of the preceding claims, wherein the object (4) comprising integrated circuit patterns is a photolithography mask or a wafer.

28. The method of any one of the preceding claims, wherein the at least one parameter comprises at least one optical metrology parameter.

29. An optical metrology system (88) for measuring properties of an object (4) comprising integrated circuit patterns, the optical metrology system comprising: an image acquisition system (10, 10’, 10”) for acquiring an imaging dataset (22) of the object (4) comprising integrated circuit patterns; one or more processing devices (92); and one or more machine-readable hardware storage devices (94) comprising instructions that are executable by the one or more processing devices (92) to perform operations comprising a method (26, 26’) of any one of the preceding claims.

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