The present application claims priority to the German patent application DE to 2018 207880.7, filed on 18 May 2018, the entire content of which is herewith incorporated by reference. 1. Technical field

The present invention relates to a method and an apparatus for evaluating an unknown effect of defects of an element of a photolithography process. In particular, the present invention relates to a method and an apparatus for evaluating an unknown effect of de- fects for one or more elements of a photolithography process by applying a model of machine learning, which establishes a relationship between an image, design data asso ciated with the image and an effect of the defects arising from the image.

2. Prior art

As a consequence of the growing integration density in the semiconductor industry, photolithography masks or templates for nanoimprint lithography have to image in creasingly smaller structures on wafers. The advances in miniaturization of structures on semiconductor wafers and hence also on the photolithographic masks, photomasks or simply masks used to expose the wafers have far-reaching effects on the inspection of photolithographic masks, the metrology of photomasks and the analysis of mask de fects. Typically, a photomask is analysed by virtue of measuring an aerial image of a mask portion and comparing the latter to a reference aerial image of the mask portion. In the specialist field, this procedure is referred to as a die-to-die method. It is possible to ascertain a defect probability map, a defect map, or a defect effect map of defects of the mask portion on the basis of this comparison.

The increasing complexity of the structures on photomasks, for example amplified by the more frequent application of optical proximity corrections (OPCs), may lead to certain structures on a photomask no longer being repeated or only still being repeated infrequently (so-called single die masks). Hence, a quality assessment of such masks (e.g., a defect inspection or defect review) is no longer possible or only possible with greater outlay, i.e., after a longer search for a suitable reference position, by means of the above-described die-to-die method.

A method that can be used in such cases (but also independently thereof) is the so- called die-to-database method, in which a reference aerial image is obtained by means of an optical imaging simulation (rendering) from design data, for example from layout data. The method in which a reference image is generated from design data of a mask can be used independently of the aforementioned problem.

A reference aerial image of a mask with the aid of the simulation could previously be generated in two ways. Firstly, a reference aerial image can be calculated with the aid of an ab-initio or rigorous simulation. However, producing reference aerial images for an alysing defects and/ or for correcting defects on the basis of ab-initio simulations, which numerically solve Maxwell’s equations, is very time-consuming and therefore currently, and in the near future, hardly practical in a manufacturing environment. Secondly, use can be made of a simplified model, which assumes the mask structures to be two-dimensional and the diffracted waves to be freely propagating, which is known as“Kirchhoff model” or as“scalar imaging model”, for the purposes of generating a ref erence aerial image from design data by means of a simulation. A simulation of a refer ence aerial image on the basis of the Kirchhoff model is orders of magnitude faster than a rigorous simulation; however, it is not able to image all mask effects sufficiently accu rately. Hence, the quality of a reference aerial image produced by means of a Kirchhoff model is insufficient in many cases.

In a new, further approach, attempts are currently being made to approach numerous challenges in the quality assessment of photomasks with the aid of a machine learning (ML) model. The following documents are specified in an exemplary manner for this procedure: WO 2017 / 087653 At, WO 2017 / 117568 At, WO 2017 / 120 253 At, WO 2017 / 123 555 At, WO 2017 / 123 561 At, WO 2017 / 117573 At, WO 2017 / 123 555 At and WO 2017/ 205537 At. As explained above, the production of a reference aerial image for a photolithographic mask can be a complicated process, both by measurement and with the aid of simula tion. The present invention is therefore based on the object of specifying a method and an apparatus that at least partly avoid the above-described disadvantages when evaluating the quality of a photolithographic mask.

3. Summary of the invention

According to one aspect of the present invention, this problem is solved by a method according to Claim 1.

A method for determining at least one unknown effect of defects of an element of a photolithography process may comprise the steps of: (a) providing a model of machine learning for a relationship between an image, design data associated with the image and at least one effect of the defects of the element of the photolithography process arising from the image; (b) training the model of machine learning using a multiplicity of images used for training purposes, design data associated with the images used for training purposes and corresponding effects of the defects; and (c) determining the at least one unknown effect of the defects by applying the trained model of machine learn ing to a measured image and the design data associated with the measured image.

A method according to the invention avoids the complicated production of a reference image for being able to assess the quality of a photolithographic mask and/ or a wafer.

Further, a method according to the invention makes the comparison of a measured im age with a reference image superfluous.

By way of example, the complicated training process of the model of machine learning or of the ML model can be carried out once for a specific mask type and a certain opti cal measuring system, which produces the aerial images. By way of example, the train ing process can be carried out at a central location, which is optimally equipped for this object. The trained ML models for different mask types can then be provided together with the optical measuring or imaging system and the design data in a manufacturing environment. By applying the trained ML model to a measured aerial image and by providing the associated design data, it is then possible to determine a previously unknown effect of the defects in a portion of the mask represented by the measured aerial image, either directly or after minimal fitting.

A model of machine learning produces knowledge from experience. A model of ma- chine learning learns from examples that are provided to the model in the form of training or learning data in a learning or training phase. Using this, internal variables of the model, for example parameters of parametric mapping, can be occupied by suita ble values in order to be able to describe relationships in the training data. As a conse quence, the ML model in the training phase as a rule does not simply learn the training data off by memorizing but identifies patterns and/ or rules in the training data. The quality of the learned relationships is typically assessed on the basis of validation data in order to assess the generalizability of the trained model to new data, i.e., data that is unknown during the training. A trained ML model can be applied to an element of a photolithography process in order to predict the potential effects of defects in an image unknown to the ML model should the associated design data be provided. After the completion of the training phase, a successfully trained ML model, i.e., a trained ML model with good generalizability is therefore able to assess data unknown to it, i.e., un known images, if the associated design data are provided. The image may comprise at least one element from the group: an image recorded by an optical measuring system, an image recorded by a scanning particle microscope, and an image recorded by a scanning probe microscope.

An optical measuring system may comprise an AIMS™, PROVE®, and/ or WLCD tool. A scanning particle microscope may comprise a scanning electron microscope (SEM) and/ or a scanning ion microscope. A scanning probe microscope may comprise an ele ment from the group: a scanning tunnelling microscope, a scanning force microscope, a magnetic force microscope, a near-field scanning optical microscope and a scanning near-field acoustic microscope.

The application of a method according to the invention is not restricted to images rec orded by an optical measurement system. Rather, a method according to the invention can be used for images that were produced by different imaging modalities. The design data may comprise at least one element from the group: layout data and computer-aided design (CAD) data. The design data can be available in the form of pixel data and/or polygons or polygonal chains. The model of machine learning may comprise a sub-symbolic system.

The knowledge, i.e., the training data and the induced rules, is explicitly represented in the case of a symbolic system. In the case of a sub-symbolic system, a calculable behav iour is taught to the model without, however, having a detailed view into the learnt so lution paths.

The model of machine learning may comprise at least one element from the group: a parametric mapping, an artificial neural network (ANN), a deep neural network (DNN), a time delay neural network, a convolutional neural network (CNN), a recurrent neural network (RNN), a long short-term memory (LSTM) network, and a generative model.

Discriminative models can produce output data from input data; generative models can produce output data from input data and can additionally reproduce the input data. The model of machine learning may comprise: (a) at least one encoder block for deter mining information-carrying features of an image and the design data associated with the image; and (b) at least one decoder block for producing at least one effect of the de fects from the determined information- carrying features. Further, the model of machine learning may comprise: (a) at least one encoder layer for determining information-canying features of an image and the design data associated with the image; and (b) at least one decoder layer for producing at least one effect of the defects from the determined information-canying features, wherein the effect of the defects shows what an overlay of the image with a reference image looks like.

The model of machine learning may comprise at least 2, preferably 10 to 1500, more preferably 15 to 1000 and most preferably 30 to 100 layers.

The layers of the model of machine learning may realize various parameterized and non-parameterized functions. Thus, an artificial neural network may comprise two or more convolutional layers and two or more deconvolutional layers. Here, the size of the convolutional filters may be selected to be larger, especially for a small number of con volutional layers, in order to be able to resort to sufficiently many data during the pro cessing. Further, the artificial neural network may comprise two or more pooling layers and two or more de-pooling layers. Moreover, a model of machine learning may con- tain two or more nonlinear activation functions for realizing complex relationships, for instance a hyperbolic tangent, a sigmoid and/or a piecewise linear function. Inde pendently thereof, a model of machine learning may contain two or more adaptive nor malization layers, for instance a batch normalization. The method according to the invention may further include the step of: fitting a num ber of layers of the model of machine learning to a predetermined or demanded accu racy of an aerial image. In particular, the method according to the invention can in clude the step of: fitting a number of encoder layers and/ or decoder layers to a prede termined accuracy of an image.

Artificial neural networks (ANN) typically consist of the linking of a plurality of layers, which consequently realize a sequential transformation of the inputs into outputs, for example. The topology of the network, i.e., the number of layers, the choice of the func tion of each layer, the parameters or model parameters of each of the layers (such as the number and the size of filter kernels), and the connections between the individual layers are selected depending on the object to be achieved. Here, it is possible for the outputs of one layer of the ANN to be provided as inputs not only to a subsequent layer.

The element of the photolithography process may comprise at least one element from the group: a photolithographic mask, a template for nanoimprint technology and a wa fer. The photolithographic mask can comprise a transmitting or reflecting mask.

A method according to the invention is not restricted to determining an arrangement of defects of a photolithographic mask. Rather, it may also be used for analysing tem- plates from the field of nanoimprint technology and wafers.

The defects may comprise at least one element from the group: placement errors of one or more pattern elements of one or more elements of the photolithography process; critical dimension errors of one or more pattern elements of the element of the photoli- thography process; and material defects of the element of the photolithography pro cess. Determining the at least one unknown effect of a defect may comprise at least one an swer to one of the following questions: Is the effect of the defect below a predetermined threshold? Is the defect visible on a wafer? Is the defect that is visible on a wafer cor- rectable?

The image recorded by the optical imaging system may comprise an aerial image and/ or the aerial image may comprise an aerial image focus stack. The same design data underlie the various aerial images of a focus stack. The precision of the prediction of the effect of defects of an element of a photolithography process can be increased by at least partial training of the ML model using an aerial image focus stack instead of an individual aerial image. The ML model required to this end is realiz able, for example, as a common model which receives either data from aerial image fo- cus stacks or individual aerial images as inputs. However, it is also possible to use two separate ML models, which are coupled via common parameter values, for example.

The training of the model of machine learning may comprise: providing the multiplicity of aerial images used for training purposes and the multiplicity of design data associ- ated with the aerial images used for training purposes as input data and providing the multiplicity of effects of the defects corresponding to the aerial images used for training purposes as comparison data for the output data of the model of machine learning.

It is a peculiarity of the present application that data from two data sources are pre- sented to the ML model in each case, both during the training phase and during the use phase, said data sources having a connection to one another.

The aerial images used for training purposes may comprise measured aerial images and/ or simulated aerial images.

It is an advantage of the method according to the invention that the aerial images re quired for training purposes need not all be measured.

The method according to the invention may further include the step of: simulating de- sign data and/ or modified design data of the element of the photolithography process for the purposes of producing simulated images. Further, the method according to the invention can include the step of: simulating design data and/ or modified design data of a photolithographic mask for the purposes of producing simulated aerial images.

A training data record should comprise images or aerial images without defects, i.e., images or aerial images that can be used as reference images and reference aerial im ages, respectively. However, additionally, a training data record should also comprise images/aerial images that have a multiplicity of the known relevant defects of an ele ment of a photolithography process or of the known relevant mask defects in the case of photomasks. Should the images/aerial images used for training purposes have been generated in part or as a whole with the aid of a simulation tool, the design data under lying the simulated images/aerial images maybe changed or modified in such a way that the simulated images/aerial images exhibit the known relevant defects of the ele ment of the photolithography process, for example the known relevant mask defects. Producing simulated images/ aerial images may comprise at least one element from the group: cariying out a rigorous simulation by numerically solving Maxwell's equations, wherein design data and/or modified design data of the element of the photolithogra phy process are used as input data, cariying out a simulation with the aid of a Kirchhoff model, wherein the design data and/ or the modified design data of the element of the photolithography process are used as input data, cariying out a particle-beam-based imaging simulation, wherein design data and/ or modified design data of the element of the photolithography process are used as input data and cariying out a scanning-probe- based imaging simulation, wherein design data and/or modified design data of the ele ment of the photolithography process are used as input data.

Training the model of machine learning may comprise determining leamable parame ters of the model of machine learning. In the case of convolutional layers, the training of the model of machine learning may comprise determining weights of the filter masks.

In the case of convolutional and deconvolutional layers, the leamable parameters are typically the weights of the filter masks of the individual convolutional layers. In order to increase the model complexity, the convolutional results of a layer are usually addi tionally transformed in nonlinear fashion. To this end, as already referred to above, the input of each neuron, ascertained by means of a discrete convolution, is converted into an output in a convolutional layer with the aid of an activation function, i.e., for instance, by the application of a sigmoid function (sig(t)=o.5-(i+ tanh(t/2)) or a recti fied linear unit (ReLU, f(x) = max(o, x)). The concatenation of a plurality of convolu tional layers, which each comprise an activation function, allows complex patterns to be learned from the provided data - both for perception objectives and for transforming between various data modalities (for example, between design data and image data).

An ML model employed in this application has the peculiarity that the latter predicts an output, specifically at least one effect of at least one defect of an element of a photoli thography process, on the basis of two input data records, specifically an image and de- sign data. In a first embodiment, the two input data records can be concatenated to form a single input. In this embodiment, the architecture of the ML model does not dif fer from conventional exemplary embodiments.

However, in a second embodiment, it is also possible for the ML model to have two sep- arate branches or input branches on the input side for the two image and design data inputs, which are combined within the ML model. This second embodiment facilitates separate processing of the two inputs in order to prepare these in targeted fashion for common processing in one or more common layers of the ML model. The two separate input branches of the ML model may have the same number of layers. However, it is currently preferred to fit the number of layers of the two input branches of the ML model to the specifics of the respective input data. Individual layers of the two separate input branches may be connected to one another.

The second embodiment of an ML model, as explained above, can be trained in various ways: The initial model parameters (I) may be chosen randomly, (II) may be adopted from an ML model that has already carried out a similar objective and/or (III) may be pre-learnt in unsupervised fashion.

Regarding (I): Should the initial numerical values of the model parameters be chosen randomly, the same random distribution or different random distributions may be cho sen for the two input branches of the ML model.

Regarding (II): Should other ML models, which have the same or a similar architecture as/to the two input branches of the ML model in training, already be used, the model parameters thereof can be used as initial model parameters for the training phase. As a result, the initial numerical values of the model parameters for the training process can be set separately for the two separate input branches of the ML model. The training process of the ML model can be simplified by the modular determination of the initial model parameters. Regarding (III): Should the two input branches of the ML model be embodied as auto encoders, i.e., the input data of the input branches can be reproduced at the output thereof, as is the case, for example, if the input branches are realized in the form of en coder-decoder architectures, the model parameters determined from the reproduction of the input data can be used as start parameters of the ML model. The model parame- ters of the two input branches trained thus are often helpful for the initialization of the entire ML model in the training phase.

The provision of corresponding effects of defects for training the model of machine learning may further comprise the step of: overlaying an image used for training pur- poses with a reference image for producing the at least one effect of the defects corre sponding to the image.

The provision of corresponding effects of defects for training the model of machine learning may further comprise the step of: determining a reference image by: imaging a substantially defect-free region of the element of the photolithography process, which has the same pattern elements as the region of the measured image, and/or simulating the design data for the region of the measured image of the element of the photolithog raphy process. The provision of corresponding effects of defects for training the model of machine learning may further comprise the step of: determining a reference aerial image by: imaging a substantially defect-free region of the photolithographic mask, which has the same pattern elements as the region of the measured aerial image, and/ or simulating the design data for the region of the measured aerial image of the photolithographic mask. Overlaying the image with the reference image may comprise: forming a difference be tween the image and the reference image. Further, overlaying the aerial image with the reference aerial image may comprise: forming a difference between the aerial image and the reference aerial image. Forming the difference may comprise at least one element from the group: determining a deviation of a critical dimension (CD), determining a contrast deviation, and deter mining a placement deviation of one or more pattern elements. Typically, a measured image, just like a reference image, is present in the form of a two- dimensional pixel arrangement. Each pixel is normally associated with a certain bit depth such that the latter can be represented as greyscale value steps. A difference im age, which illustrates the effect of defects, arises by an overlay of reference aerial image and aerial image

An effect of defects of an element of a photolithography process, for example a photo mask, can be captured in a defect effect map. A defect effect map describes effects of deviations of a measured image in relation to a reference image, as explained above. By way of example, the arrangement of the printable defects, i.e., the defects visible on a wafer on the mask or the mask portion, can then be ascertained directly from the defect effect map by predetermining one or more threshold conditions. Moreover, in addition to the predicted effects of the defect, the ML model can be trained to additionally pre dict whether a printable defect can be corrected. The training further may include the step of: comparing the at least one effect of the de fects determined by a model of machine learning in training from the image used for training purposes with the at least one effect of the defects corresponding to the image used for training purposes. The training of the model of machine learning may comprise supervised learning. Su pervised learning is described in the book "Pattern Recognition and Machine Learning" by C.M, Bishop, Springer 2006, ISBN- 10: 0-387-31073-8.

The training of the model of machine learning may comprise: (a) training the model of machine learning using a first number of simulated images, design data associated with the simulated images with corresponding effects of the defects in a first phase; and (b) training the model of machine learning using a second number of measured images, de sign data associated with the measured images with corresponding effects of the defects in a second phase, with the first phase being carried out before the second phase. The first number of simulated images can be greater than the second number of measured images. The first number of simulated images can be greater than the second number of measured images by a factor of to.

The training of the model of machine learning may further comprise the step of: run- ning through the aforementioned steps (a) and (b) at least twice.

It may be complicated to measure the large number of images, for example thousands of images, for instance aerial images, which are required for training the ML model.

The method according to the invention renders it possible to train the ML model on the basis of simulated images and associated design data in a first step. Simulated images can be produced in a large number with the aid of a simulation tool. In a second step, the ML model that was pre-trained by means of the simulated images is finally pre pared for its use with the aid of a restricted number of measured images. A computer program may comprise instructions which, when executed by a computer system, prompt the computer system to cariy out the method steps of the aspects speci fied above.

According to a further aspect of the present invention, the problem specified above is solved by an apparatus according to Claim 18.

An apparatus for determining at least one unknown effect of defects of an element of a photolithography process may comprise: (a) means for providing a model of machine learning for a relationship between an image, design data associated with the image and at least one effect of the defects arising from the image; (b) means for training the model of machine learning using a multiplicity of images used for training purposes, design data associated with the images used for training purposes and corresponding effects of the defects; and (c) means for determining the at least one unknown effect of the defects by applying the trained model of machine learning to a measured image and the design data associated with the measured image.

The apparatus may comprise an exposure system for the element of the photolithogra phy process and a magnifying lens that is embodied to image a portion of the element of the photolithography process on a photodetector. The apparatus may comprise an AIMS™ tool. 4. Description of the drawings

The following detailed description describes currently preferred exemplary embodi ments of the invention, with reference being made to the drawings, in which:

Fig. l schematically reproduces the currently frequently used workflow for as sessing the quality of an element of a photolithography process;

Fig. 2 schematically shows an example of a model of machine learning with an in put layer, an output layer and the associated input data and output data;

Fig. 3 schematically illustrates a section of a second example of a model of ma chine learning with two separate input branches;

Fig. 4 schematically shows a section of an apparatus by means of which the

method described in this application can be carried out;

Fig. 5 schematically illustrates a reference aerial image of a portion of an element of a photolithography process;

Fig. 6 schematically shows an aerial image of a portion of an element of a photoli thography process;

Fig. 7 schematically presents a portion of a defect probability map;

Fig. 8 schematically elucidates a training cycle of the training phase of a model of machine learning;

Fig. 9 schematically reproduces the workflow for assessing the quality of an ele ment of a photolithography process when a trained model is used to this end, said trained model establishing a relationship between a measured aerial image and the associated design data and thereby facilitating a pre diction of a defect distribution of an element of a photolithography process; and Fig. 10 finally illustrates a flowchart of a method for determining an unknown ar rangement of defects of an element of a photolithography process.

5. Detailed description of preferred exemplary embodiments

Currently preferred embodiments of the method according to the invention and the ap paratus according to the invention are explained in more detail below on the basis of determining an unknown effect of defects of a photolithographic mask. However, the application of the method according to the invention and of the apparatus according to the invention is not restricted to photomasks. Rather, said apparatus and method can be applied to further elements of a photolithography process, for example to a template or a mould of nanoimprint lithography, which can be used instead of a photomask. Fur ther, the method according to the invention and the apparatus according to the inven tion can be used to assess the quality of a wafer during the processing thereof. In gen- eral, the method described in this application can be used to assess the quality of ob jects whose design data are present and whose defects can be imaged.

Figure 1 schematically shows the currently preferably used workflow for assessing the quality of a photomask. A currently frequently used method for ascertaining a defect ef- feet map for a photolithographic mask provides the determination of a reference aerial image for a region of a mask to be examined in a first step. Should a mask comprise many regions or partial areas, or at least a plurality thereof, which contain the same ar rangement of pattern elements, a defect-free region of the mask can be selected to rec ord a reference aerial image. For the purposes of measuring an aerial image, and hence also for measuring a reference aerial image, use can be made, for example, of an AIM S ^’ ™ (aerial image metrology system) tool and/ or a PROVE® tool for determining place ment errors, or a WLCD for determining the critical dimension (CD).

In semiconductor and micro-systems technology, the term“CD” for critical dimension denotes a defined size in a test structure, the measurement of which allows statements to be made about the quality of the manufacturing of a process step.

Should regions or partial areas with an identical arrangement of pattern elements not repeat on a mask, or only repeat at veiy long intervals, the above-described method (the so-called die-to-die method) for determining a reference aerial image cannot be used or can only be used with greater outlay, i.e., after a relatively long search for a suitable reference position. A method that can be used in such cases (but also inde pendently thereof) for the purposes of generating a reference aerial image is the so- called die-to-database method, in which a reference aerial image is obtained by means of an optical imaging simulation (rendering) from design data, for example from layout data.

An ideal reference aerial image of a mask is calculated with the aid of an ab initio or a rigorous simulation. An ab initio simulation takes account of the optical interaction (scattering, diffraction, absorption, reflection) of the illumination radiation of the opti- cal imaging system, i.e., of the electromagnetic waves incident on the photomask, with the structures of the photomask, and the subsequent propagation of the transmitted and/ or the reflected electromagnetic fields upstream or downstream of the mask into the plane of the detector of an optical analysis system in numerically rigorous fashion on the basis of Maxwell's equations. This means that Maxwell's equations are solved in three dimensions for the respective boundary conditions by way of suitable numerical methods. This represents a particular challenge, in particular for the masks whose structures or patterns appear three-dimensional to the illumination radiation on ac count of the different materials of a photomask. A simplified model which assumes the mask structures to be two-dimensional and the diffracted waves to be freely propagating is referred to as "Kirchhoff s model" or“scalar imaging model". A simulation of a reference aerial image on the basis of the Kirchhoff model is orders of magnitude faster; however, it is not able to image all mask effects sufficiently accurately.

After determining a reference aerial image (either by simulation or by measuring a de fect-free mask portion), an aerial image of a region to be analysed of a photomask or, in general, of an element of a photolithography process is measured in a second step.

Once again, as specified above, this measurement can be implemented with the aid of one of the aforementioned tools, for example.

Thereupon, the positions of the respective pattern elements or the CD data, for exam ple, are extracted from the two images, i.e., the measured aerial image and the refer ence aerial image, in a third step. Subsequently, a defect effect map is created in a fourth step for a region to be examined or for the entire active surface of a photomask by comparing the two data records ex tracted from the two images. Here, the comparison of the two data records extracted from the two images can be implemented by forming a difference.

Finally, where necessary, the effects of the defects, for example the printable defects, can be ascertained in a portion of the mask or over the entire mask from the defect ef fect map on the basis of one or more thresholds (not illustrated in Figure t). The diagram 290 in Figure 2 schematically shows a model of machine learning 200 or an ML model 200, which illustrates a relationship between an aerial image 230, design data 240 associated with the aerial image 230 and one or more effects 250 of defects of an element of a photolithography process emerging from the aerial image 230. The ML model 200 may comprise an artificial neural network (ANN). The ANN may comprise a deep neural network. It is expedient to fit the model of machine learning 200 to the re quired prediction accuracy. By way of example, fitting of the model 200 can be imple mented by an appropriate choice of number of layers. As an alternative or in addition thereto, it is advantageous to fit the functional description of the ML model 200 to the object to be achieved, specifically the prediction of one or more effects 250 of the de- fects, or to a defect effect map 250 of a photolithographic mask.

The ML model 200 has an input layer 210. The input data 230, 240 are provided to the trained ML model 200 via the input layer 210 during operation. In the application de scribed here, the input data 230, 240 during operation are, firstly, a measured image or an aerial image 230 and, secondly, the design data 240 associated with the measured image or aerial image 230. By way of example, the design data 240 may be layout data or CAD (computer-aided design) data of a mask and may be present, for example, in the form of pixel data or, for instance, as polygons or polygonal chains. If the design data are available as polygons, it is necessary to convert the polygon chains into pixel data.

Further, the ML model 200 has an output layer 220, by means of which the trained model of machine learning 200 provides its output data 250, specifically the defect ef fect map 250, at the output. In the example illustrated in Figure 2, this is a prediction of the effect(s) 250 of one or more defects of a photolithographic mask or of a portion of a photomask. The diagram 390 of Figure 3 schematically shows a model of machine learning 300, the architecture of which is specifically fitted to the object to be achieved. The exemplary ML model 300 of Figure 3 has a first input branch 380 with six layers 310, 320, 330, 340, 350, 360, wherein the first layer 310 is configured as an input layer, by means of which the aerial image 230 is provided to the ML model 300. The layers 310 to 360 of the first input branch 380 of the ML model 300 pre-process the aerial image 230 such that the output of the first input branch 380 can be provided as an input for the first common layer 375 of the main part 370 of the ML model 300.

Further, the ML model 300 illustrated in an exemplary fashion in Figure 3 has a second input branch 385 with four layers 315, 325, 335, 345. In a manner analogous to the first input branch 380, the first layer 315 of the second input branch 385 is embodied as an input layer, which serves to provide the design data 240 to the ML model 300. The lay- ers 315 to 345 of the second input branch 385 of the ML model 300 process the design data 240 such that the output of the second input branch 385 can be provided as an in put, parallel to the input of the first input branch 380, for the first common layer 375 of the main part 370 of the ML model 300. Like the ML model 200, the ML model 300 outputs its output data 250, specifically the defect effect map 250, via the output layer 395 of the main part 370.

Before the ML model 200, 300 can be used for predictive purposes, it must be trained using a data record that is as comprehensive as possible. Figure 4 schematically shows a section through an apparatus 490 that can be used to measure aerial images 230. Further, the apparatus 490 can be used to measure aerial images, which are used as a part of a training data record for training the model 200, 300.

The apparatus 490 comprises a computer system 400, which is linked to a measuring device 420 by way of a connection 410. The connection 410 may be embodied in a wired or wireless manner. In the example illustrated in Figure 4, the measuring device 420 examines a photolithographic mask 450 by means of the interaction 430. The mask 450 can be a transmitting or a reflecting mask. The photomask 450 of Figure 4 is an example of an element 450 of a photolithography process. The measuring device 420 can be an imaging measuring device 420. By way of example, the measuring device 420 can be an AIMS™ or an AIMS™ EUV, i.e., an AIMS for the extreme ultraviolet wavelength range. Further, the measuring device 420 may comprise a PROVE® tool and/ or a WLCD tool. The measuring device 420 can be used to produce an aerial image focus stack by varying the focal plane. As a result, the measuring device 420 facilitates the measurement of an aerial image focus stack of the mask 450. In addition to an optical measuring device 420, which analyses the mask 450 and pro duces an aerial image 230 by means of a photonic interaction, the measuring device 420 may, however, also interact 330 with the mask 450 with the aid of a neutral or charged partial beam and may generate an image of the sample, i.e., the photolitho graphic mask 450, on the basis of reflected and/or transmitted neutral and/or charged particles. The measuring device 420 may comprise a scanning electron microscope, particularly if the element of the photolithography process describes a wafer (not shown in Figure 4).

However, the measuring device 420 may also comprise a scanning probe microscope, which probes a surface of the mask 450 and, as a result, produces an image of the sur face contour of the mask 450 or, more generally, of an element 450 of a photolithogra phy process (not illustrated in Figure 4). A scanning probe microscope may comprise a scanning force microscope, for example. Moreover, it is possible for the measuring de vice 420 to comprise an imaging measuring device and, additionally, a scanning probe microscope, for example. A three-dimensional image of the mask 450 can be produced on the basis of the measurement data of an imaging measuring device and of a scan ning probe microscope.

The computer system 400 controls the measuring device 420 by way of the connection 410. Further, the computer system 400 receives measurement data of the measuring device 420 by way of the connection 410. The computer system 400 of Figure 4 can produce an aerial image 230 from the measurement data of the measuring device 420. Further, in the example illustrated in Figure 4, the computer system 400 comprises the ML model 200, 300. The computer system 400 is designed to execute the trained ML model 200, 300. Further, the computer system 400 is configured so that it can carry out the training of the ML model 200, 300 described below. Graphics processors (GPU, graphical processor unit) are particularly suitable for executing models of machine learning 200, 300. It is therefore advantageous if the computer system 400 contains one or more capable graphics processors or another objective-optimized computer hardware, for instance a tensor processing unit (TPU) by Google (not illustrated in Fig ure 4). Further, the computer system 400 comprises an interface 460. The computer system 400 can receive design data 240 or layout data 240 belonging to the mask 450, which are analysed by the measuring device 420, via the interface 460. The interface 460 can be a wireless or wired communications interface to an intranet or the Internet. Further, the interface 460 may comprise a data medium drive.

The training of the ML models 200, 300 of Figures 2 and 3 is explained in exemplary fashion on the basis of Figures 5 to 8 below. The model 200, 300 can be trained with the aid of the apparatus 490 of Figure 4. However, for the purposes of cariying out the training of the ML model 200, 300, it is also possible to provide a computer system de signed specifically to this end, the input data 230, 240 and corresponding output data being provided to said computer system. Figure 5 schematically shows a plan view of a reference aerial image 500 for a portion of the photolithographic mask 450. The reference aerial image 500 illustrated in Figure 5 in an exemplary fashion presents a vertical strip structure with four strips 510, 520, 530, 540, which have a material that absorbs the actinic wavelength of the photolitho graphic mask 450. The strip structure of the reference aerial image 500 in Figure 5 has substantially no defects. Here, like at other points of the present application, the ex pression“substantially” means a measurement which has no detectable changes in rela tion to a predetermined design if use is made of measuring appliances according to the prior art for the measurement. By way of example, the reference aerial image 500 of Figure 5 can be measured by the measuring device 420 of the apparatus 490. To this end, a location on the mask 450 is selected, which comprises the strip structure 510, 520, 530, 540 reproduced in Figure 5 and which is known to be a location at which the mask 450 has no defects. However, should the mask 450 not have a defect-free strip structure 510, 520, 530, 540 in the vicinity of a region of the mask 450 to be examined or should the strip structure reproduced in the reference aerial image 500 only be present once on the photomask 450, the reference aerial image 500 is produced from the design data 240 of the mask 450, which correspond to the reference aerial image 500, with the aid of a simulation tool. As already explained above, a simulation for generating the reference aerial image 500 can be performed on the basis of a rigorous or ab initio simulation of the design data 240 by way of a numerical solution of Maxwell’s equations for the portion of the photomask 500 which is reproduced by the reference aerial image 500. Canying out a rigorous simulation supplies a highly precise reference aerial image 500; however, this is often a time-consuming process.

Depending on the accuracy required by the reference aerial image 500, it may therefore be an alternative to implement the reference aerial image 500 on the basis of a so- called“Kirchhoff model” or a“scalar imaging model”. This simulation process requires significantly less outlay in comparison with the rigorous simulation.

Figure 6 shows a measured aerial image 600 of the photomask 450 for the same por tion of the mask 450 as in Figure 5. In the example illustrated in Figure 6, the strip 520 has a defect 650 of missing absorber material. Moreover, the third strip 530 has a de fect 660 of excess absorbing material in the measured exemplary aerial image 600. The measured aerial image 600 may be part of a training data record. However, the meas ured aerial image 600 may also be input together with the associated design data 240 into the trained model 200, 300 for the purposes of predicting the effect 250 of the de fects 650, 660. Finally, a simulated aerial image of a training data record, which was generated on the basis of modified design data with the aid of a simulation tool, could have a very similar look to the measured aerial image 600.

Figure 7 presents a portion 710 of a special manifestation of a defect effect map 700. The portion 710 of the defect effect map 700 is formed by comparing the reference aer ial image 500 with the measured aerial image 600. In detail, the portion 710 of the de- feet effect map 700 can be formed by forming the difference between the reference aer ial image 500 and the measured aerial image 600. As already explained above, the dif ference image is implemented on the basis of greyscale values of the reference aerial image 500 and the measured aerial image 600. Since the difference image has a higher bit depth than the reference aerial image 500 and the measured aerial image 600, the defects 650, 660 of missing absorber material 650 and excess absorber material 660 can be distinguished in the portion 710 of the defect effect map 700. By virtue of por tions 710 of the defect effect map 700 being determined over the entire mask 450 or over all relevant regions of the mask 450, it is possible to generate a defect effect map 700 for the photolithographic mask 450 or, in general, for an element 450 of a photoli- thography process. The portion 710 of the defect effect map 700 can be incorporated into a training data record for the model 200, 300 as corresponding effect of the defects 650, 660.

A sufficient availability of consistent and representative training data is important for determining the internal model parameters of the ML model 200, 300 in a training process. Figure 8 schematically shows an example of a training cycle for the model 800. In terms of design and in respect of the functional characterization, the model 800 of Figure 8 is identical to the model 200, 300 of Figures 2 and 3. However, unlike the model 200, 300, the model 800 has not yet been trained. In the example illustrated in Figure 8, the measured aerial image 600 and the associated design data 240 are pro vided as input data of the training sequence to the input layer 210 of the model of ma chine learning 800. At its output layer 220, the model 800 in training predicts the por tion 810 of a defect effect map with the defects 850 and 860 from these input data. The portion 810 of the defect effect map is compared to the portion 710 of the defect effect map 700 of Figure 7. In Figure 8, the comparison is indicated by the double-headed ar row 870.

Depending on the selected ML model 800, there are various methods to determine the model parameters of the ML model 800 during a training phase. By way of example, the“stochastic gradient descent” iterative technique or corresponding variants have be come established for ML models 800 that are available in the form of deep neural net works. In this training method, the training data, i.e., the aerial image 830 used for training purposes, for example the measured aerial image 600 and the associated de sign data 240, are repeatedly presented to the model 800, i.e., the latter calculates the portion 810 of a defect effect map using the current model parameters and compares the calculated portion 810 to the measured portion 710 of the defect effect map 700.

The model parameters of the ML model 800 are modified in the case of deviations be tween the two portions 710 and 810. Typically, the training phase for an input data rec ord is terminated when the portion 810 has reached a (local) optimum, meaning that the deviations between the portions 710 and 810 hardly change any more over all image pairs, or after a predetermined time interval has expired or a predetermined number of training steps have been run through. Alternatively, a training process of the ML model 800 can be completed when the validation accuracy significantly increases when use is made of a separate validation data record, this being an indication for overfitting of the ML model 800. The model 800 can be trained in two steps. In a first step, aerial images 830 in the form of simulated aerial images used for training purposes can be provided together with as sociated design data 240 to the input layer 210 of the model 800. In a second step, measured aerial images 600 are subsequently presented to the model 800 as aerial im- ages 830 used for training purposes, together with the corresponding design data 240.

Before the trained ML model 200, 300 is used, the predictive power of the trained model 200, 300 can be analysed with the aid of a verification step. When verifying the trained model 200, 300, the precision of the prediction of the trained model 200, 300 is analysed on the basis of an independent validation data record.

The diagram 900 of Figure 9 shows the workflow for assessing the quality of an ele ment 450 of a photolithography process if the trained model 200, 300 is used in the process instead of a comparison of a reference aerial image 500 with a measured aerial image 600. Initially, an aerial image 600 of a photolithographic mask 450 is measured in step 910. Thereupon, the design data 240 belonging to the measured aerial image 600 are provided to the trained model of machine learning 200, 300 in step 920. The trained ML model 200, 300 directly ascertains the effect 250 of the defects 650, 660 of the aerial image 600 in step 930 on the basis of the measured aerial image 600 and the associated design data 240. The workflow reproduced in Figure 9 avoids the determina tion of a reference aerial image 500.

Finally, the flowchart 1000 of Figure 10 presents the workflow of a method for deter mining at least one unknown effect of defects 650, 660 of an element 450 of a photoli- thography process. The method begins in step 1010. In step 1020, a model of machine learning 200, 300 is provided for a relationship between an aerial image 600, design data 240 associated with the aerial image 600 and an effect of the defects 650, 660 of the element 450 of the photolithography process arising from the aerial image 600. In the next step 1030, the model of machine learning 200, 300 is trained using a multi plicity of aerial images 830 used for training purposes, design data 240 associated with the aerial images 830 used for training purposes and corresponding effects 710 of the defects 650, 660. Thereupon, in step 1040, the unknown effect of the defects 650, 660 is determined by applying the trained model 200, 300 to a measured aerial image 600 and the design data 240 associated with the measured aerial image 600. Finally, the method ends in step 1050.