Method and device for evaluating statistically distributed measured values ​​in inspecting components of a lithographic process

Abstract

The present invention relates to a method (900) for evaluating statistically distributed measurement values ​​(100, 300, 350) in an element (810) for inspecting a lithography process, comprising the following steps: (a) using a plurality of parameters (730) in a trained machine learning model (700), wherein the parameters (730) characterize a state of a measurement environment (880) during a time period associated with the measurement of the measurement values ​​(100, 300, 350); and (b) executing the trained machine learning model (700) in order to evaluate the measurement values ​​(100, 300, 350).

Description

[0001] This application claims the priority of German patent application DE 10 2018 211099.9 filed on July 5, 2018, the entire contents of which are incorporated herein by reference as part of the present disclosure. 1. Technical Field

[0002] The present invention relates to a method and a device for improving the measurement accuracy of a measuring device used in the field of the semiconductor industry. In particular, the present invention relates to a method and a device for evaluating statistically distributed measurement values ​​in inspecting components of a lithography process. 2. Background technology

[0003] Due to the increasing integration density in the semiconductor industry, photolithography masks have to image smaller and smaller structures on the wafer. The increasing miniaturization of structures on the wafer and therefore on the pattern-bearing elements used for wafer exposure, such as photolithography masks or templates for nanoimprint lithography, has a profound impact on the inspection, metrology and verification of pattern-bearing elements. Contemporary measurement devices or tools for monitoring and repairing photolithography masks, templates and / or wafers during the process of producing photolithography masks, templates and / or wafers are very complex in order to take into account the extremely stringent requirements constituted by accuracy in the semiconductor industry.

[0004] Examples of such measurement devices, such as for processes for producing lithography masks, photomasks and / or just masks, are inspection tools for detecting defects present on photomasks, metrology tools for measuring critical dimensions (CD) and positioning errors of patterned elements (e.g., WLCD tools or tools), verification tools to determine whether a mask defect is visible on the wafer (e.g. AIMS TM tools), mask repair tools (such as a tool) and phase measurement tool.

[0005] In new approaches, attempts are currently being made to address many challenges in the quality assessment of photomasks with the aid of machine learning (ML) models. As examples, the following documents should be cited for this process: WO 2017 / 087653A1, WO 2017 / 117 568A1, WO 2017 / 120 253A1, WO 2017 / 123 555A1, WO 2017 / 123 561A1, WO 2017 / 117 573A1, WO 2017 / 123 555A1 and WO 2017 / 205 537A1.

[0006] Patent specification DE 10 2007 924 B4 describes a method for automatically detecting incorrect measurements by means of a quality factor after the measurement of the quality factor. The detected incorrect measurement is rejected and replaced by a new measurement that satisfies the quality factor.

[0007] Establishing a measured quality factor for a high precision measurement device such as mentioned above is a complex process, as the relationship between the quality factor and the associated measurement for a high precision complex tool is generally unknown.

[0008] The present invention therefore solves the problem of specifying a device and a method which increase the measurement accuracy of a measuring device and which at least partially avoid the disadvantages described above. 3. Summary of the invention

[0009] According to an aspect of the invention, the problem is solved by a method as described below and an apparatus as described below. In one embodiment, a method for evaluating statistically distributed measurement values ​​in an element of an inspection lithography process comprises the following steps: (a) using a plurality of parameters in a trained machine learning model, wherein the parameters characterize the state of the measurement environment during a time period allocated for the measurement of the measurement values; and (b) executing the trained machine learning model in order to evaluate the measurement values.

[0010] The method according to the invention makes it possible to automatically indicate how a planned or recorded measurement value is or will be located in its statistical distribution before, during or after the measurement based on parameters characterizing the measurement environment. The significance of the measurement value can thus already be evaluated before, during or just after the measurement of the measurement value. By initiating appropriate countermeasures, the method according to the invention thus makes it possible to significantly improve the measurement accuracy of high-precision complex measuring devices.

[0011] The method according to the invention can detect any unknown relationships between the measurement data and the parameters characterizing the measurement environment and use them for evaluating the measured values. This is a key advantage of the method described here, because in the case of very precise and complex measuring devices, the causal relationships between the measurement data and the parameters characterizing the measurement environment are generally unknown.

[0012] Ideally, the measured values ​​and the parameters characterizing the measurement environment should be measured at the same "point in time". In a practical measuring device, the measurement of the measured values ​​does not occur at a point in time, but within a time interval. This means that a time period is allocated to the measurement or recording of the measured values ​​or the measurement or recording of the measured values ​​is related to the time period. The characterizing parameters should characterize the measurement environment within the time period allocated to the measurement. However, this does not mean that the measurement must be performed within the relevant time period for each characterizing parameter. Characterizing parameters that are subject to rapid changes should be measured once or even multiple times within the time period allocated to the planned measurement. In contrast, for characterizing parameters that are only subject to slow drift, it may be sufficient to perform measurements in a time interval larger than the time period allocated to the planned measurement.

[0013] The measured values ​​may be evaluated based on a quality criterion. The quality criterion may include at least one element from the following group: a threshold value on an expected value assigned to a statistical distribution of the measured values, an assignment of one of a plurality of ranges predefined by the statistical distribution of the measured values, and a deviation of the measured values ​​from an expected value of the statistical distribution.

[0014] The quality criterion may classify the measured values. The classification of the measured values ​​may be binary, i.e. the measured values ​​meet or do not meet the requirements. The binary classification of the measured values ​​may be implemented based on a threshold. However, the classification may also include the assignment of multiple categories of measured values, i.e. the measured values ​​may, for example, meet the quality criterion very well or well or may not meet the quality criterion. In addition, the quality criterion may define a quality parameter in the form of a continuous function. The quality parameter may be normalized or may not be normalized.

[0015] The aim of the method according to the invention is to enable a prediction about the relative repetition accuracy of a measurement.

[0016] The measured values ​​can be evaluated before the planned measurement and the method according to the invention can also comprise the step of not performing the planned measurement of the measured values ​​if a quality criterion is not met in the time period allocated for the planned measurement of the measured values.

[0017] An important advantage of the method described in the present application is that, already before the measurement is carried out, at the planned point in time of the measurement, it can be determined whether the measurement environment is in a state that is favorable for carrying out the measurement. Thus, it becomes possible to increase the measurement accuracy of the device and at the same time only slightly increase the measurement complexity, but even without initially generating measurement values ​​that are subsequently rejected.

[0018] The method defined above further comprises the step of postponing the planned measurement until a quality criterion is met in the time period allocated for the planned measurement of the measured values.

[0019] For efficiency reasons, it is more advantageous to only perform usable measurements rather than subsequently identifying unusable measurements, rejecting them and replacing them with new measurements.

[0020] The measured value can be evaluated after it has been measured, and the method according to the invention further comprises the step of rejecting the measured value if a quality criterion is not met in the time period allocated to the planned measurement of the measured value.

[0021] The method presented in this application can also be implemented such that first a measurement is performed and then the recorded measured values ​​are analyzed or evaluated.

[0022] The trained machine learning model can track the measurements or data records of the measuring device and constantly monitor (i.e. measure) all basic characterization parameters. The characterization parameters are provided as input data to the trained machine learning model and the trained model predicts the value or value of the quality criterion. The statement of the trained model can then be used to initiate or postpone the measurement of the measured value. The output of the quality criterion by the machine learning model can have the following effect: the measuring device rejects the last recorded measurement value and performs a re- or repeated measurement.

[0023] The method according to the invention may further comprise the step of generating a confidence statement about the measured value. The confidence statement may be transmitted together with the measured value of the measuring device.

[0024] The confidence statement reflects how the ML model evaluates its output data in terms of reliability. As an example, a measurement value evaluated as an outlier with a confidence statement of 95% will lead to the rejection of the measurement value. In contrast, an evaluation that the measurement value meets the quality criterion to the extent of 51% will lead to maintaining or re-measuring the measurement value, depending on the application. The method according to the invention can predict both a statement about whether a quality criterion is met or not met and a confidence statement about the quality criterion. However, the confidence statement can also be determined subsequently and externally to the machine learning model based on its output data.

[0025] Features of elements of a lithography process may include pattern elements of a photomask or wafer, and / or alignment marks of a photomask or wafer.

[0026] The confidence statement of the measured value depends, for example, on the type of illumination of the feature on which the measurement is based. This means that the measurement of pattern elements and / or alignment marks of the photomask in reflection (i.e. using reflected light) or transmission (i.e. using transmitted light) affects the confidence statement of the measured pattern elements and / or the measured alignment marks.

[0027] Furthermore, the confidence statement of the measured value may be independent of the illumination intensity and / or the measurement position on the element of the lithographic process.

[0028] Additionally, the method according to the invention may comprise the step of generating a warning and / or error message by the measuring device as a result of the confidence statement of one or more measured values. Thus, the ML model may indicate that it cannot reliably assess the situation. A human expert may intervene in the process as a result of the warning and / or error message output.

[0029] The method according to the invention comprises the following step: stopping the measuring device due to a confidence statement of one or more measured values. By terminating the recording of further measured data by the measuring device, the generation of worthless measured values ​​can be avoided.

[0030] The characterization parameters may include two or more elements from the following group: temperature of the measurement environment, pressure of the measurement environment, air humidity of the measurement environment, refractive index of the measurement environment, focusing position of a device for measuring the measurement value, wavelength of the optical system of the device, exposure intensity of the optical system of the device, exposure setting of the optical system of the device, coherence of the optical system of the device, detector setting of the device, setting of one or more interferometers of the device, setting of one or more attenuation systems of the device, and setting of one or more drivers of the device.

[0031] Parameters characterizing the measurement environment include both the environmental conditions at the measurement location or in the immediate vicinity of the measurement location and the settings of the measuring device that implements the measurement.

[0032] Characterizing parameters may include the temporal development of their values.

[0033] Characterizing parameters can include not only measured values ​​or values ​​in the time range assigned to the measurement, but also the recent development of their values ​​can be introduced into the method as explained above. Considering the time development of the values ​​of the characterizing parameters can contribute to the improved evaluation of existing measured values ​​and / or measured values ​​to be measured.

[0034] The measured value may include a plurality of measurement records. The plurality of measurement records may include at least one changed characterizing parameter.

[0035] The measurement value may include repeatedly measuring, for example, the position of a pattern element and / or a critical dimension (CD) at a specified position of a lithography mask. The measurement data or measurement records of the progressive measurements may then be combined to form a measurement value or measurement point. The time range associated with or assigned to the measurement when the measurement value includes multiple measurement records is typically significantly larger than the time range assigned to or associated with the measurement value when the measurement value is based on a single measurement.

[0036] Repeated measurements can be carried out under substantially identical conditions, i.e. in the case where one of the parameters characterizing the measurement environment is not intentionally changed. However, one or more of the characterizing parameters can also be changed in a defined manner for the individual measurement records. As an example, the exposure setting, the focus setting, and / or the coherence of the exposure of the position of the photomask can be set individually for the individual measurement records.

[0037] A plurality of measurement records may comprise measuring a focal stack. Furthermore, the confidence statement of the measurement value of the focal stack may be independent of the number of records of the focal stack.

[0038] At least one of the characteristic parameters can include at least one characteristic variable of its static distribution during a plurality of measurement recordings of measured values.

[0039] If recording the measured values ​​as described above includes repeatedly measuring the variable, the characterizing parameter is subject to statistical fluctuations in the time period in which the measurement recording is performed. Instead of determining the characterizing parameter only for the main time points in the time period of the measurement recording, the characterizing parameter can also be measured repeatedly, for example periodically, in the time interval and the statistical distribution of the measured values ​​can be determined in the time interval. As a result, the accuracy of the characterizing parameter can be increased.

[0040] The machine learning model may include at least one element from the following group: kernel density estimator, statistical model, decision tree, linear model, time-varying model, nearest neighbor classification and k nearest neighbor algorithm, and nonlinear expansion with nonlinear feature transformation.

[0041] Kernel density estimators (referred to as: KDE) enable continuous estimation of unknown probability distributions based on random samples. Kernel density estimators may include, for example, Gaussian, Cauchy, Picard or Epanechnikov kernels, where kernel parameters, such as bandwidth, included in the machine learning model may be assigned or estimated for all input parameters individually or jointly. In general, any similar function that imports the input parameters present into a valid kernel function may be used.

[0042] The statistical model may include at least one mixture distribution. The mixture distribution may include elements from the following group: Gaussian mixture distribution (GMM, Gaussian mixture model), multivariate normal distribution and categorical mixture distribution. The appropriate number of mixture distributions depends on the data present and can be optimized with the aid of a validation data set.

[0043] A decision tree (DT) may include at least one element from the following group: a conventional decision tree (DT), a randomized decision tree (RDT) and a decision forest (DF) and a random variant of the latter (RDF). In RDT and RDF, the degree or "level" of randomization may vary. For each node, all possible decisions or only a random selection of possible decisions may be presented in training. For each leaf of the decision tree, all training examples presented until then or only a subset of the training examples may be used.

[0044] The linear model may include at least one element from the following group: Latent Dirichlet Allocation (LDA), Support Vector Machine (SVM), Logistic Regression, Least Squares (Least Squares Estimation), Lasso Regression, Ridge Regression, and Perceptron. Advantageous application of linear models requires normalization of input data and training data.

[0045] The machine learning model may include a nonlinear extension of an SVM in the form of a kernel support vector machine. In addition, the machine learning model may include a nonlinear extension of a Gaussian mixture distribution in the form of a Gaussian process regression. In addition, the machine learning model may include a deep neural network (DNN).

[0046] The time varying model may include at least one element from the following group: a recurrent neural network and a hidden Markov model. In an alternative exemplary embodiment, the time varying model may be simulated by the time invariant model using earlier measured parameters available as input data to the time invariant model.

[0047] Time-varying or time-dependent machine learning models make it possible to take into account the temporal distribution of parameters characterizing the measurement environment.

[0048] In a recurrent neural network (RNN), the output of a layer is incorporated into the same layer with additional inputs at a subsequent point in time. A preferred embodiment of an RMM is an LSTM (Long Short Term Memory) network.

[0049] In addition, the machine learning model may include two or more different types of machine learning models from the group specified above. A machine learning model that uses a combination or group of multiple different types of models or multiple learning algorithms can generally achieve better results than an ML model based on a single type of model or a single learning algorithm. The calculation of the results of many different types of models typically takes longer than the evaluation of a single type of ML model. However, in return, the results corresponding to an ML model with one type of ML model or one learning algorithm can already be achieved with a smaller calculation depth.

[0050] The predictions of different components of the combination can contribute to the prediction of the machine learning model in an equally weighted manner. The predictions of different types of ML models can contribute to the prediction of the machine learning model in a weighted manner.

[0051] A group of machine learning models including different types of ML models may be gradually built up in a training phase by equipping each type of model newly added to the group with training data that the previous type of model in the group could not predict or could only predict poorly.

[0052] With the aid of automated machine learning (automated machine learning or AutoML), a machine learning model of two or more different ML model types may be selected.

[0053] Hyperparameters of machine learning models and / or different ML model types of machine learning types can likewise be optimized with the aid of automated machine learning.Hyperparameters of machine learning models are model parameters defined before the start of the training phase of the machine learning model.

[0054] A training parameter set for training a machine learning model may include a data pair: a characterization parameter of the i-th measurement value and a quality criterion of the i-th measurement value.

[0055] The training data set used to train the machine learning model includes data pairs: characterization parameters of the i-th measurement value at the j-th position of the component in the lithography process, and quality criteria of the i-th measurement value at the j-th position of the component in the lithography process.

[0056] As already explained above, the quality criterion may comprise the fulfillment of a threshold condition for the measured value, the assignment of the measured value to one of a plurality of ranges or categories or the value of a continuous function.

[0057] Furthermore, the method according to the invention comprises the step of adapting the trained machine learning model to modifications of the measuring device performing the measurements.

[0058] After maintaining and / or replacing parts of the measuring device, the trained machine learning model can be adapted to the modified measuring device through a relearning process using a new or second training data set.

[0059] Furthermore, the method according to the invention may comprise the step of adapting the trained machine learning model to a location-specific installation of the measuring device.

[0060] The trained model can be adapted to the position-specific installation of the measuring device with the aid of the second training data set. The complexity of the adaptation process or relearning process depends on the implementation of the selection of the machine learning model. As an example, for the adaptation process, it may also be necessary to have the training data of the first training data set in storage and make them available for the relearning process. Furthermore, the complexity or computational complexity depends on the implementation of the selection of the machine learning model.

[0061] A computer program may comprise instructions which, when executed by a computer system, cause the computer system to perform the method steps of any one of the methods described above.

[0062] In one embodiment, an apparatus for evaluating statistically distributed measurements in an element inspecting a lithography process comprises: (a) a component for using a plurality of parameters in a trained machine learning model, wherein the parameters characterize a state of a measurement environment during a time period allocated for measurement of the measurement values; and (b) a component for executing the trained machine learning model to evaluate the measurement values.

[0063] The device according to the invention may further comprise means for performing measurements.

[0064] The means for performing the measurements may comprise a source for generating a particle beam and a detector for detecting particles from an element of a lithographic process.

[0065] The particle beam may include at least one element selected from the following group: a photon beam, an electron beam, an ion beam, an atomic beam and a molecular beam, and / or the detector may include at least one element selected from the following group: a photomultiplier tube, a photodiode, an avalanche photodiode, a CCD camera and an X-ray detector.

[0066] The device according to the invention may also comprise means for determining a characterizing parameter and / or means for changing a characterizing parameter.

[0067] Furthermore, the device according to the invention can comprise means for postponing a planned measurement and / or means for rejecting a measured value.

[0068] The element of the lithography process may include at least one element from the following group: a lithography mask, a template for nanoimprint lithography, and a wafer. 4. Description of the drawings

[0069] The following detailed description describes presently preferred exemplary embodiments of the present invention with reference to the accompanying drawings, in which:

[0070] Figure 1 An exemplary statistical distribution of measured values ​​at a location on a component of a lithography process is shown;

[0071] Figure 2 Presents about Figure 1 a histogram of the distribution of the measured values ​​shown;

[0072] Figure 3 shows the results after introducing a threshold condition for identifying outliers in the measured values. Figure 1 Statistical distribution diagram of

[0073] Figure 4 The figure shows the results after removing the measurement outliers that do not meet the threshold condition. Figure 3 Histogram of ;

[0074] Figure 5 Shows the Figure 1 The set of characteristic parameters of the distribution of the measured values ​​illustrated in Figure 5 Marked in Figure 3 Measurement outliers identified in ;

[0075] Figure 6 Schematically illustrates the training process of a machine learning model;

[0076] Figure 7 Schematically illustrates the execution of a machine learning model;

[0077] Figure 8 Some components of the measuring device are schematically presented; and

[0078] Fig. 9 A flow chart of a method for evaluating statistically distributed measurements in inspecting components of a lithography process is shown. 5. Specific implementation methods

[0079] The currently preferred embodiments of the method according to the invention and the device according to the invention are explained in more detail below based on the evaluation of the measured values ​​of a lithography mask. The method according to the invention and the device according to the invention can be used to evaluate all types of transmissive and reflective photomasks. In addition, the method according to the invention and the device according to the invention can also be used to evaluate the measured values ​​derived from templates and / or wafers for nanoimprint lithography. However, the method according to the invention and the device according to the invention are not limited to elements applied to lithography processes. Instead, they can generally be used to evaluate the measured values ​​of high-precision measuring devices that generate a large amount of measurement data, so that a machine learning model can be trained by this large amount of measurement data.

[0080] Figure 1 An example of a statistical distribution of measurement values ​​100 at a specified location of a photolithography mask is shown. In detail, Figure 1 1000 repetitions of the measurement of the measurement point 100 at the j-th position of the photomask are presented, i.e. N=1000. As an example, 200 measurement positions may be distributed over the photomask, i.e. M=200. The M measurement points may be distributed over the photolithography mask in a regular grid. However, it is more advantageous to distribute the M measurement points between pattern elements and / or alignment marks of the photomask. Figure 1 In the illustrated example, M measurement points distributed over the photomask are measured continuously. After all M measurement points have been measured once, the process is repeated N times. Thus, Figure 1 The abscissa in represents the time development of the measured value of the lithography mask at the j-th position during the measurement process.

[0081] Figure 1 The ordinate in the graph presents the measured value 100s at the jth position. j (i) As the expected value or mean of a statistical distribution j >The difference. Figure 1 In the example shown in FIG, the following apply: 1≤i≤N=1000 and 1≤j≤M=200. In addition, the measurement value 100s j (i) Presented as expected or average value j >Normalized to standard deviation σ=s j (i)- j >, that is, s j,N (i)=(s j (i)- j >) / σ.

[0082] ​​​​ Figure 2 is shown from the measured values ​​of 100s j (i) or j,N (i) The histogram derived from the statistical distribution of Figure 2 A 3σ value of 3σ = 3 is derived in , ie the interval of the statistical distribution in which 99.73% of all measured values ​​100 are in the normal distribution.

[0083] Figure 3 Again, it shows Figure 1 , which has a dashed line 380 depicting a normalized deviation of ±2σ. The dashed line 380 implements the measured value 100s j (i) or j,N (i) Threshold conditions. Measurement values ​​100 of the statistical distribution that are within the ±2σ interval are considered usable measurements 300, and measurement values ​​100 that are outside the ±2σ interval are considered rejected outliers 350. In one process, in the case of a normal distribution, 95.45% of all measurements 100 are classified as "good" and 4.55% of the measurements that are outside the dashed line are classified as "bad". Figure 3 In the illustrated example, out of 1000 measured values ​​100, 49 measured values ​​350 are outside the ±2σ range or interval.

[0084] Figure 4 Presented Figure 1 Medium measurement value 100s j (i) Histogram of the statistical distribution of 300 measurements within the range of ±2σ. 300 measurements j (i) or i,N (i) The maximum measurement error is obtained by eliminating the outlier 350 Figure 1 The 3σ=3 in the equation is reduced to Figure 3 3σ=2 in this equation.

[0085] Figures 1 to 4 The diagram shows that after the measurement it is always possible to decide on the basis of a statistical analysis of all the measured values ​​100 that the recorded measured values ​​100s j (i) which are outliers 350 in the statistical distribution of (i) and thus optimize the evaluation of the measurement and thus the accuracy of the measuring device. The advantage of the method described in the present application is that it makes it possible to decide whether a planned measurement will produce a "good" measurement value 300 (i.e. a usable measurement value 300) or a "bad" measurement value 350 (i.e. an outlier 350) before or during the execution of the planned measurement. As a result, the measurement accuracy of the measuring device can be increased considerably without perceptibly impairing the throughput of the measuring device.

[0086] Figure 5 The characteristic parameter P j (i) is a set of Figure 1 The measured values ​​s shown in the figure j (i) Statistical distribution of Figure 5 The characteristic parameter P j (i) An example of a possible temporal profile. j (i) in the set with Figure 3 In a similar way, it is marked by a "square" Figure 5 The outlier value in is 350.

[0087] If you can Figure 5 Collected, in the measurement value s j (i) or j,N (i) All parameters P that characterize the measurement environment j (i) are equipped with a label or annotation "good" (i.e., within the ±2σ interval) or "poor" (i.e., outside this range). Figure 4 The threshold condition for separating "good" and "bad" measured values ​​in the example can be selected so that only a few measured values ​​are to be characterized as outliers. As a result, the measurement accuracy of the measuring device is only slightly improved; in return, the duration for performing measurements by the device is only slightly increased. However, it is also possible to define a quality criterion such that the measurement accuracy of the measuring device can be significantly increased. This improvement is achieved by measuring the measured values ​​s j (i) is achieved at the expense of the measurement duration.

[0088] In addition to Figures 1 to 5 In addition to the threshold conditions (i.e., binary classification) shown in the figure, quality criteria can also include multi-category classification ( Figure 3 In addition, the quality criterion can be in the form of a continuous function ( Figure 3 Advantageously, the machine learning model and the quality criteria are adapted to the problem to be solved.

[0089] Figure 6 The diagram 690 in FIG. 1 schematically illustrates the training of a machine learning model 600 or ML model 600. Before the ML model 600 can predict the position of a measurement point 100, 300, 350 within its statistical distribution based on the parameters characterizing the measurement environment, the ML model 600 must be trained using a large data set or training data set for this purpose. The training data is generated by using a measurement device to perform a long measurement sequence of the same type. As an example, a registration tool (e.g. ) is used to repeatedly measure a photomask or a wafer in the same way n times, wherein n must be selected to be such that the relevant characterizing parameters of the measuring device change significantly during the measuring process. Furthermore, the measuring environment can change and thus the characterizing parameters can be systematically changed during the recording of the training data in order to generate a database that is as representative as possible for the purpose of training.

[0090] The training data set includes characterization parameters 630 for training and quality criteria 640 associated with the characterization parameters 630 for training. The training data is provided to the training ML model 600 at the input layer 610. The quality criteria 640 indicates the classification of the characterization parameters 630 for training, i.e., in the simplest case indicating whether the characterization parameters 630 for training meet the threshold condition 380. During the training phase, the training or learning ML model 600 generates predictions 650 of the quality criteria 640 from the training characterization parameters 630 and the associated quality criteria 640. The predicted quality criteria 650 are compared with the quality criteria 640 assigned to the measurement. This is done in the training phase. Figure 6 6 is illustrated by a double-headed arrow 660. The trained ML model 600 provides a quality criterion 650 of the prediction at its output layer 620.

[0091] Depending on the ML model 600 chosen, there are various methods for adapting the parameters of the ML model 600 during the training phase. As an example, the iterative technique “stochastic gradient descent” has been established for DNNs (Deep Neural Networks), which typically have a large number of parameters. In this case, the training data are repeatedly “submitted” to the learning ML model 600, i.e. the latter uses its current set of parameters to calculate a prediction 650 of the quality criterion 640 from the feature parameters 630 used for training. A comparison as discussed above is then carried out. If a deviation occurs between the prediction 650 of the quality criterion 640 and the actual value of the quality criterion 640, the parameters of the learning ML model 600 are adapted. The training phase ends once a local optimum is reached, i.e. the deviation of the predicted quality criterion 650 from the actual quality criterion 640 no longer changes, or the predefined time budget of the training cycle of learning or training the ML model 600 has been exhausted.

[0092] For most linear machine learning models, there are closed computational specifications for the optimal assignment of model parameters, i.e., the determination of the model parameters of these models is not based on iterative approximations. For example, to determine the model parameters of a decision tree, various partitioning criteria can be selected, such as the gain of information. In addition, the decision tree can also be subsequently pruned, for example to a maximum depth and / or a maximum diversity per leaf. Expectation-maximization methods or algorithms are often used for mixture models, such as Gaussian mixture models. For nearest neighbor models as well as for Parzen density estimation and kernel regression, the model parameters do not have to be estimated, but rather hyperparameters of the kernel parameters are optimized.

[0093] Characterization parameters 630 for training may be derived from an optical measurement device, such as Figure 8 The measuring device 800 to be discussed in the context of . However, the methods described in this application can also be used for any measuring device that generally uses a particle beam to image an element of a lithography process. In particular, the methods explained here can be used for a scanning electron microscope and / or a measuring device that uses an ion beam to image a photomask or a wafer.

[0094] Figure 7 The diagram 700 in FIG. 1 schematically illustrates the execution of a trained ML model 700 that transforms characterization parameters 730 measured by a measuring device and quality criteria 740 assigned to the characterization parameters 730 into predicted quality criteria 750 for measured values ​​100, 300, 350 of a measurement planned using the measuring device. The trained ML model 700 is provided with the assigned values ​​of the characterization parameters 730 and the quality criteria 740 via an input layer 710. The trained machine learning model 700 generates at an output layer 720 a prediction of the quality criteria 750 for the measured values ​​100, 300, 350 of the measurement planned using the measuring device.

[0095] The ML model 700 may include one of the models described in Section 3. Advantageously, a model adapted to the problem to be solved is selected from a large number of available general ML models. Furthermore, advantageously, the selected general ML model 700 is adapted to the problem to be solved and to the required prediction accuracy of the quality criterion 750. The ML model 700 may be adapted, for example, by adapting the complexity of the kernel function of the ML model 700. In the case of an ML model with an encoder-decoder architecture, this may also be performed, for example, by correspondingly selecting a number of layers in the ML model. For an ML model 700 implemented in the form of a hybrid form as described above, for example, the number of leaves in the RDT or the number of trees in the RDF may be adapted to the problem to be solved.

[0096] Figure 8 A cross-sectional view through a schematic diagram of an apparatus 800 or measuring apparatus 800 is shown, which can be used to measure the critical dimensions of the pattern elements of the structure or pattern elements of the photomask and / or wafer, the position errors of the pattern elements of the mask and / or wafer and / or the overlay errors (i.e. the CD (critical dimension) of the pattern elements thereof) when aligning the masks of the mask stack. A photolithography mask 810 or more generally an element 810 of a photolithography process is held by a high precision measurement stage 805 or stage 805. At Figure 8In the example illustrated in , the photomask 810 is a reflective mask, for example a mask for the extreme ultraviolet (EUV) wavelength range. However, the measuring device 800 can also measure a transmissive photomask 810. The measuring stage 805 is actively controlled by the positioning unit 815 in all six degrees of freedom and Figure 8 In the example illustrated in FIG. 8 , the measuring stage 805 is only a movable part of the measuring device 800. The position of the measuring stage 805 in the plane of the photomask 810 (hereinafter referred to as the xy plane) is detected by one or more interferometers 820, for example by one or more laser interferometers. In addition, the interferometer 820 can be used to determine the position of the measuring stage 805 in the z direction ( Figure 8 (not shown in the figure).

[0097] An excimer laser that generates light in the DUV (deep ultraviolet) wavelength range (for example, an ArF (argon fluoride) laser that emits at a wavelength in the range of 193 nm) is used as the light source 825 in the measuring device 800. Figure 8 In the example illustrated in FIG. 8 , the numerical aperture (NA) of the lens 830 is 0.6. However, a lens 830 having a larger NA may be used in the measuring device 800 in order to improve the resolution capability of the measuring device 800. By moving the measuring stage 805 in the vertical direction or z direction, the laser radiation of the light source 825 is focused onto the surface of the mask 810. The front side of the mask 810 (which is the side of the mask 810 facing the lens 830) has a pattern element, which is Figure 8 Not shown in the figure.

[0098] A CCD (charge coupled device) sensor 835 forms a spatially resolved detector of the measuring device 800. The CCD sensor 835 measures the light reflected locally by the mask 810. Typically, the CCD sensor 835 comprises a two-dimensional pixel arrangement or pixel array, for example 1000×1000 pixels. The CCD sensor 835 sends its measurement signal to a signal processing unit 840, which calculates an image from the signal detected by the CCD sensor 835. An exposure system 827 having a light source 825 and a lens 830 as essential components, and the detector 835 form an optical system 885 of the measuring device 800.

[0099] The computer system 850 may display the image calculated by the signal processing unit 840 and / or may store the measured data as raw data and / or image data in the non-volatile memory 855. For the sake of clarity, the display of the computer system 850 is shown in FIG. Figure 8The machine learning model 600 and / or the trained ML model 700 may be stored in a memory 855 of the computer system 850. In addition, the assigned values ​​of the characterization parameters 630 and the quality criteria 640 used for training may be stored in the memory 855. The computer system 850 includes one or more processors 860 that train the ML model 600 and / or execute the trained ML model 700. The processor(s) may be implemented in the form of one or more powerful GPUs (graphics processing units).

[0100] The optimization unit 860 of the computer system 850 causes the signal processing unit 840 to carry out or postpone the planned measurement of the measured values ​​100 , 300 , 350 by means of the optical system 885 of the measuring device 800 .

[0101] Finally, the analysis unit 865 can analyze the measured values ​​of the measuring device 800 and determine characteristic variables of the statistical distribution of the measured values. In addition, the analysis unit 865 of the computer system 850 can classify the planned measured values ​​and the measured values ​​that have been measured.

[0102] The computer system 850 may be implemented as discrete units, such as Figure 8 However, the computer system 850 and / or the signal processing unit 840 may also be integrated ( Figure 8 ) into the measuring device 800.

[0103] The computer system 850 may monitor and / or control the measurement unit 815 , the one or more interferometers 820 , the light source 825 , the lens 830 , the CCD sensor 835 , the signal processing unit 840 , the analysis unit 865 , and the optimization unit 860 of the measurement stage 805 .

[0104] The surface of the photolithography mask 810 may be slightly tilted. In addition, the mask 810 is slightly bent due to its inherent weight, resulting in a change in the optimal focusing condition. Therefore, the measurement device 800 has an autofocus (AF) system 870 (based on a tilted grid) Figure 8 (not shown). The tilted reflector 875 and the partially transmissive reflector 880 direct the laser beam onto the lens 830. In addition, Figure 8 The exemplary measurement apparatus 800 in illustrative embodiment includes an optical assist system 890 for substantially aligning a lens 830 with a pattern element of a photomask 810 .

[0105] If mask 810 is a transparent mask, light source 825 is directed onto photomask 810 from below through a second lens, and lens 830 collects laser radiation that leaves the surface of photomask 810 ( Figure 8 not shown).

[0106] In addition, the measuring device 800 includes measuring, for example, in a measuring environment 880 ( Figure 8 Sensors for measuring pressure, temperature and / or air humidity (not shown).

[0107] final, Fig. 9 A flow chart 900 of a method for evaluating statistically distributed measured values ​​100, 300, 350 in inspecting an element 810 of a lithography process is shown. In step 910, the method starts. In a first step 920, a plurality of parameters 730 characterizing the state of the measurement environment 880 in the time period allocated to the measurement of the measured values ​​100, 300, 350 are used in the trained machine learning model 700. Then, a second step 930 involves executing the trained machine learning model 700 in order to evaluate the measured values ​​100, 300, 350. Finally, in step 940, the method ends.

Claims

1. A method (900) for evaluating statistically distributed measured values ​​(100, 300, 350) in inspecting a component (810) of a lithography process, comprising the following steps: a. using a plurality of characterization parameters (730) in a trained machine learning model (700), wherein the characterization parameters (730) characterize the state of the measurement environment (880) during a time period allocated to the measurement of the measurement values ​​(100, 300, 350); and b. executing the trained machine learning model (700) to evaluate the measurements (100, 300, 350); Obtaining a trained machine learning model (700) by training the machine learning model (600) using a training data set; The training data set includes characterization parameters (630) for training and quality criteria (640) associated with the characterization parameters (630) for training.

2. The method (900) of claim 1, wherein: The measured values ​​(100, 300, 350) are evaluated based on a quality criterion (740) assigned to the characterization parameter (730).

3. The method (900) of claim 2, wherein: The quality criterion (740) assigned to the characterization parameter (730) comprises at least one element from the following group: a threshold value (380) regarding an expected value assigned to a statistical distribution of the measured values ​​(100, 300, 350), an assignment to one of a plurality of ranges predefined for the statistical distribution of the measured values ​​(100, 300, 350), and a deviation of the measured values ​​(100, 300, 350) from an expected value of the statistical distribution.

4. The method (900) according to claim 3, wherein: The measured values ​​(100, 300, 350) are evaluated before the planned measurement, and the method further comprises the following step: if the quality criterion (740) assigned to the characterization parameter (730) is not met in the time period assigned to the planned measurement of the measured values ​​(100, 300, 350), the planned measurement of the measured values ​​(100, 300, 350) is not performed.

5. The method (900) according to claim 4, further comprising the steps of: The planned measurement is postponed until the quality criterion (740) assigned to the characterization parameter (730) is met in the time period assigned to the planned measurement of the measured values ​​(100, 300, 350).

6. The method (900) according to any one of claims 2 to 4, wherein: The measured values ​​(100, 300, 350) are evaluated after they have been measured, and the method further comprises the step of rejecting the measured values ​​(100, 300, 350) if the quality criterion (740) assigned to the characterization parameter (730) is not met during a time period assigned to the planned measurement of the measured values ​​(100, 300, 350).

7. The method (900) according to any one of the preceding claims 2-4, further comprising the following steps: A confidence statement is generated regarding the measured values ​​(100, 300, 350).

8. The method (900) according to any one of the preceding claims 2-4, wherein: The characterization parameters (730) include two or more elements from the following group: the temperature of the measurement environment (880), the pressure of the measurement environment (880), the air humidity of the measurement environment (880), the refractive index of the measurement environment (880), the focus position of the device (800) for measuring the measurement value (100, 300, 350), the wavelength of the optical system (885) of the device (800), the exposure intensity of the optical system (885) of the device (800); the exposure setting of the optical system (885) of the device (800), the coherence of the optical system (885) of the device (800), the detector setting of the device (800), the setting of one or more interferometers (820) of the device (800), the setting of one or more attenuation systems of the device (800) and the setting of one or more drivers of the device (800).

9. The method (900) according to any one of the preceding claims 2-4, wherein: The characterizing parameter (730) includes the temporal development of its value.

10. The method (900) according to any one of the preceding claims 2-4, wherein: The measured values ​​(100, 300, 350) include a plurality of measurement records.

11. The method (900) of claim 10, wherein: The plurality of measurement records includes at least one changed characterization parameter (730).

12. The method (900) of claim 11, wherein: At least one of the characterizing parameters (730) comprises at least one characteristic variable of its static distribution during a plurality of measurement recordings of the measured values ​​(100, 300, 350).

13. The method (900) according to any one of the preceding claims 2-4, wherein: The machine learning model (600) includes at least one element from the following group: kernel density estimator, statistical model, decision tree, linear model, time-invariant model, nearest neighbor classification and k nearest neighbor algorithm, and nonlinear extensions thereof with nonlinear feature transformation.

14. The method (900) of claim 13, wherein: The machine learning model (600) includes two or more different types of models from the group of machine learning models.

15. The method (900) according to any one of the preceding claims 2 to 4, wherein: The training data set used to train the machine learning model (600) includes data pairs: characterization parameters (630) of the i-th measurement value (100, 300, 350) at the j-th position of the element (810) of the lithography process, and quality criteria (640) of the i-th measurement value (100, 300, 350) at the j-th position of the element (810) of the lithography process.

16. A computer program product comprising instructions which, when executed by a computer system, cause the computer system to perform the method steps of any one of claims 1 to 15.

17. An apparatus (800) for evaluating statistically distributed measured values ​​(100, 300, 350) in inspecting a component (810) of a lithography process, comprising: a. A component for using a plurality of characterization parameters (730) in a trained machine learning model (700), wherein the characterization parameters (730) characterize the state of a measurement environment (880) during a time period assigned to the measurement of the measurement values ​​(100, 300, 350); and b. executing said trained machine learning model (700) to evaluate said measured values ​​(100, 300, 350); Obtaining a trained machine learning model (700) by training the machine learning model (600) using a training data set; The training data set includes characterization parameters (630) for training and quality criteria (640) associated with the characterization parameters (630) for training.

18. The apparatus (800) of claim 17, further comprising: means for performing said measurements.

19. The device (800) according to claim 18, wherein: The means for performing the measurement comprises a source (825) for generating a particle beam and a detector (835) for detecting particles from an element (810) of the lithographic process.

20. The device (800) according to any one of claims 17 to 19, further comprising: Means for determining the characterizing parameter (730) and / or means for changing the characterizing parameter (730).

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