Device and method for joint interpolation and prediction of properties

Abstract

According to one aspect of the present disclosure, a method for predicting properties associated with a product unit is provided. The method may include: obtaining a plurality of data sets, wherein each of the plurality of data sets includes data associated with a spatial distribution of a parameter across the product unit; representing each of the plurality of data sets as a multidimensional object; obtaining a convolutional neural network model trained using previously obtained multidimensional objects and properties of previous product units; and applying the convolutional neural network model to a plurality of multidimensional objects representing the plurality of data sets to predict properties associated with the product unit.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European application 19154587.0 filed on January 30, 2019 and European application 19164072.1 filed on March 20, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to a method and apparatus for predicting properties associated with a product unit. In particular, the present invention relates to predicting properties based on multiple multidimensional data sets using a convolutional neural network. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern onto a substrate. For example, a lithographic apparatus may be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as a "design layout" or "design") at a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (e.g., a wafer).

[0005] Low-k 1 Photolithography can be used to process features smaller than the classical resolution limit of the lithographic apparatus. In such processes, the resolution formula can be expressed as CD=k1×λ / NA, where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the "critical dimension" (usually the smallest feature size printed, but in this case, half pitch) and k1 is an empirical resolution factor. In general, the smaller the k1, the more difficult it is to reproduce a pattern on a substrate that is similar in shape and size to that planned by the circuit designer in order to achieve specific electrical functions and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. For example, these include but are not limited to optimizing the numerical aperture (NA), customizing the illumination scheme, using a phase-shifting patterning device, various optimizations of the design layout, such as optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). Alternatively, one or more tight control loops for controlling the stability of the lithographic apparatus can be used to improve the reproduction of the pattern at low k1.

[0006] In order to improve the performance of a lithographic apparatus, metrology data from a pattern projected onto a substrate by the lithographic apparatus may be used. The metrology data may, for example, be used to adjust one or more patterning parameters of the lithographic apparatus in order to improve the reproduction of an actual pattern according to the pattern design. For example, the metrology data may be used to predict properties of a pattern on a substrate.

[0007] Different lithography measurements may have different spatial layouts. For example, different measurements may have been measured at different locations across the substrate, or may have been measured at different resolutions on the substrate. It is possible to predict the properties of the pattern based on multiple measurements. Current methods of combining these different measurements have involved converting them to a target spatial layout, so that different measurements can be combined in the same spatial layout. However, using the converted data for property prediction may have an adverse effect on the quality of the prediction. The present invention relates to improving the quality of the prediction, and avoiding the step of converting the measurement data to a target layout. Summary of the invention

[0008] The present invention provides a method for predicting properties associated with a product unit; a lithographic device for executing the method; an option for controlling the lithographic device according to the method; a computer program, the computer program comprising instructions for executing the method; and a carrier containing the computer program according to the foregoing.

[0009] According to one aspect of the present disclosure, a method for predicting properties associated with a product unit is provided. The method may include: obtaining a plurality of data sets, wherein each of the plurality of data sets includes data associated with a spatial distribution of a parameter across the product unit; representing each of the plurality of data sets as a multidimensional object; obtaining a convolutional neural network model trained using previously obtained multidimensional objects and properties of previous product units; and applying the convolutional neural network model to a plurality of multidimensional objects representing the plurality of data sets to predict properties associated with the product unit.

[0010] Optionally, the convolutional neural network model may include multiple parts, including an input part, a merging part and an output part.

[0011] Optionally, the input portion may include a plurality of partitions, each partition being configured to receive a multidimensional object from the plurality of multidimensional objects. The method may further include inputting each multidimensional object from the multidimensional objects into a corresponding partition, wherein each partition determines an input portion output for the corresponding multidimensional object.

[0012] Optionally, each part comprises at least one convolution operation.

[0013] Optionally, the method may include inputting the plurality of input portion outputs into the merging portion to determine a merging portion output.

[0014] Optionally, the first multidimensional object and the second multidimensional object among the multiple multidimensional objects have different layouts from each other, and the input part transforms the different layouts so that the input part output corresponding to the first multidimensional object among the multiple multidimensional objects and the second multidimensional object among the multiple multidimensional objects has a common layout.

[0015] Optionally, the method may also include: in the input part, applying one or more first filters to a first multidimensional object among a plurality of multidimensional objects; and in the input part, applying one or more second filters to a second multidimensional object among a plurality of multidimensional objects; wherein the application of the one or more first filters and the application of the one or more second filters are configured to determine a common layout of the input part output corresponding to the first multidimensional object and the second multidimensional object among the plurality of multidimensional objects.

[0016] Optionally, different layouts may include different sizes.

[0017] Optionally, the input portion output may include multiple potential representations of the same size.

[0018] Optionally, the first multi-dimensional object and the second multi-dimensional object of the plurality of multi-dimensional objects may have different layouts from each other. The input part outputs corresponding to the first multi-dimensional object and the second multi-dimensional object may have a common layout.

[0019] Optionally, the method may further include: in an input portion, applying one or more first filters to a first multidimensional object of the plurality of multidimensional objects; and applying one or more second filters to a second multidimensional object of the plurality of multidimensional objects. The size of the one or more first filters and the size of the one or more second filters may be set to determine a common layout of the input portion output corresponding to the first multidimensional object and the second multidimensional object of the plurality of multidimensional objects.

[0020] Optionally, the method may also include inputting the merged part output into the output part to determine the model output of the convolutional neural network model.

[0021] Optionally, each section may comprise multiple layers.

[0022] Optionally, at least one layer of the plurality of layers may be a pooling layer.

[0023] Optionally, the method may further include: obtaining training data associated with the product unit; and training the convolutional neural network model based on the obtained training data to predict data features included in one or more features of the multidimensional object. The data features may be related to a predefined structure included in the training data.

[0024] Optionally, the training data may include one or more properties of an apparatus used to pattern the product unit.

[0025] Alternatively, the data in the data set may be metrological data associated with the spatial distribution of data points across the product unit.

[0026] Optionally, the plurality of data sets may include one or more of: alignment data of the product unit; levelling data of the product unit; and overlapping fingerprint data of a device used to pattern the product unit.

[0027] Alternatively, the property to be predicted may be the spatial distribution of a target parameter across the product unit.

[0028] Optionally, the target parameter may be overlap.

[0029] Optionally, the property may include a classification of the product unit.

[0030] Optionally, one of the plurality of data sets may have a different resolution than at least another of the plurality of data sets.

[0031] Optionally, the data associated with the spatial distribution may include a plurality of data points corresponding to a plurality of locations on the product unit. The plurality of locations of a first data set in the plurality of data sets may be different from the plurality of locations of a second data set in the plurality of data sets.

[0032] Optionally, the method may further include obtaining background data corresponding to the multiple data sets. The method may further include providing the background data to the convolutional neural network model.

[0033] Optionally, the method may further include training the convolutional neural network to predict an object structure contained in the features of the multi-dimensional object, wherein the object structure is related to a predefined structure contained in the background data.

[0034] Optionally, applying the convolutional neural network model to multiple multi-dimensional objects can determine a model output, wherein the model output can include a property or a classification.

[0035] Optionally, applying the convolutional neural network model to a plurality of multi-dimensional objects may determine a model output, wherein the method may further comprise predicting the property by performing one or more processing steps on the model output.

[0036] Optionally, the classification is a classification label, which identifies one or more of the following items: a group of product units according to the properties of the product units; a binary indicator representing the position of the data within a predetermined classification.

[0037] Optionally, the method may further comprise providing the predicted property to a lithographic apparatus to determine one or more set points for the apparatus.

[0038] Alternatively, the property associated with a product unit may be a property of a pattern formed using a lithographic apparatus on the product unit.

[0039] Alternatively, the product unit may be a semiconductor substrate. Obtaining a plurality of data sets may include obtaining metrology data from processed semiconductor substrates.

[0040] According to another aspect of the present disclosure, there is provided a lithographic apparatus comprising a processor configured to predict a property according to the method described herein above.

[0041] Optionally, the lithographic apparatus may be further configured to determine one or more set points of the lithographic apparatus based on the predicted property.

[0042] According to another aspect of the present disclosure, there is provided a recipe for controlling a lithographic apparatus, the recipe comprising one or more set points of control parameters associated with the property predicted according to the above method.

[0043] Optionally, the control parameter may be associated with controlling an overlay error of the lithographic apparatus.

[0044] According to another aspect of the present disclosure, a computer program is provided. The computer program includes instructions that, when executed on at least one processor, cause the at least one processor to perform the steps of the above method.

[0045] According to another aspect of the present disclosure, a carrier containing the above-mentioned computer program is provided, wherein the carrier may be one of an electronic signal, an optical signal, a radio signal, or a non-transitory computer-readable storage medium. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0047] Figure 1 depicts a schematic overview of a lithographic apparatus;

[0048] Figure 2 depicts a schematic overview of a lithography unit;

[0049] Figure 3 A schematic diagram depicting overall lithography, showing the collaborative work between the three key technologies used to optimize semiconductor manufacturing;

[0050] Figure 4 Depicting a flow chart of a method according to an embodiment of the present invention;

[0051] Figure 5 A schematic diagram depicting the structure of a convolutional network model;

[0052] Figure 6 depicts an example convolution filter applied to a matrix; and

[0053] Figure 7 Schematic diagram depicting the structure of a convolutional network model using input measurement data. DETAILED DESCRIPTION

[0054] In this document, the terms "radiation" and "beam" are used to include all types of electromagnetic radiation, including UV radiation (e.g., having a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5-100 nm).

[0055] The terms "reticle", "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam, which corresponds to the pattern to be created in a target portion of the substrate. The term "light valve" may also be used in this context. In addition to classical masks (transmissive or reflective masks, binary masks, phase-shift masks, hybrid masks, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0056] Figure 1A lithographic apparatus LA is schematically depicted. The lithographic apparatus LA comprises an illumination system (also referred to as illuminator) IL configured to condition a radiation beam B (e.g. UV radiation, DUV radiation or EUV radiation), a mask support (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a second positioner PW configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g. wafer stage) WT configured to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support according to certain parameters, and a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0057] In operation, the illumination system IL receives a radiation beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof, for directing, shaping and / or controlling the radiation. The illuminator IL may be used to cause the radiation beam B to have a desired spatial and angular intensity distribution in its cross-section at the plane of the graphics device MA.

[0058] The term "projection system" PS as used herein should be broadly interpreted as including various types of projection systems, including refractive, reflective, refractive-reflective, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as applicable to the exposure radiation used, and / or other factors, such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0059] The lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system PS and the substrate W, which is also known as immersion lithography. More information on immersion techniques is given in US6952253, which is incorporated herein by reference.

[0060] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as a "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel and / or steps for preparing a substrate W for subsequent exposure may be performed on a substrate W on one of the substrate supports WT while another substrate W on the other substrate support WT is being used to expose a pattern on the other substrate W.

[0061] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measurement platform. The measurement platform is arranged to hold sensors and / or cleaning means. The sensors may be arranged to measure properties of the projection system PS or properties of the radiation beam B. The measurement platform may hold a plurality of sensors. The cleaning means may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of the system for providing immersion liquid. The measurement platform may be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0062] In operation, a radiation beam B is incident on a patterning device (e.g. a mask MA) held on a mask support MT and is patterned by a pattern (design layout) present on the patterning device MA. After having passed through the mask MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position measurement system IF, the substrate support WT can be accurately moved, for example, in order to position different target portions C in a focused and aligned position in the path of the radiation beam B. Similarly, a first positioner PM and possibly another position sensor ( Figure 1 The patterning device MA (not explicitly depicted in the figure) can be used to accurately position the patterning device MA relative to the path of the radiation beam B. The patterning device MA and the substrate W can be aligned using the mask alignment marks M1, M2 and the substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 as shown occupy dedicated target portions, they can be located in the space between target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are called scribe line alignment marks.

[0063] like Figure 2As shown, the lithography apparatus LA may form part of a lithography cell LC (sometimes also referred to as a lithocell or (lithography) cluster), which typically also includes equipment for performing pre-exposure and post-exposure processes on a substrate W. Conventionally, these equipment include a spin coater SC for depositing a resist layer, a developer DE for exposing the resist, a chill plate CH and a bake plate BK, for example for regulating the temperature of the substrate W, for example for regulating solvents in the resist layer. A substrate transport device or robot RO picks up substrates W from an input port I / O1, an output port I / O2, moves these substrates between different process equipment, and transfers the substrates W to a feed station LB of the lithography apparatus LA. The equipment in the lithography cell, which is also generally referred to as a coating and developing system (track), is typically under the control of a coating and developing system control unit or track control unit TCU, which itself may be controlled by a management control system SCS, which may also control the lithography apparatus LA, for example via a lithography control unit LACU.

[0064] In order for substrates W exposed by lithographic apparatus LA to be correctly and consistently exposed, it is desirable to inspect the substrates to measure properties of the patterned structures, such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. For this purpose, inspection tools (not shown) may be included in lithography cell LC. If an error is detected, for example, adjustments may be made to the exposure of subsequent substrates or other processing steps to be performed on substrate W, particularly if the inspection is performed before other substrates W of the same batch or lot are yet to be exposed or processed.

[0065] An inspection apparatus (i.e. inspection tool), which may also be referred to as a metrology apparatus, is used to determine properties of a substrate W, in particular how properties vary from one substrate W to another, or how properties associated with different layers of the same substrate W vary from layer to layer. The inspection apparatus may alternatively be configured to identify defects on the substrate W, and may for example be part of a lithography cell LC, or may be integrated into a lithography apparatus LA, or may even be a separate device. The inspection apparatus may measure properties on a latent image (the image in the resist layer after exposure), a semi-latent image (the image in the resist layer after a post-exposure bake step PEB), or a developed resist image (where exposed or unexposed portions of the resist have been removed), or even on an etched image (after a pattern transfer step such as etching).

[0066] Typically, the patterning process in the lithographic apparatus LA is one of the most critical steps in the process, which requires a high accuracy in the sizing and placement of structures on the substrate W. In order to ensure this high accuracy, Figure 3As schematically depicted in FIG, three systems can be combined in a so-called "holistic" control environment. One of the systems is the lithography apparatus LA, which is (in practice) connected to a metrology tool MT (a second system) and to a computer system CL (a third system). The key to such an "holistic" environment is to optimize the synergy between these three systems to enhance the overall process window and provide a tight control loop to ensure that the patterning performed by the lithography apparatus LA remains within the process window. The process window defines a range of process parameters (e.g., dose, focus, overlap) within which a particular manufacturing process produces a defined result (e.g., a functional semiconductor device), and process parameters in the lithography process or the patterning process are generally allowed to vary within the defined result.

[0067] The computer system CL can use (part of) the design layout to be patterned to predict which resolution enhancement technology to use, and perform computational lithography simulations and calculations to determine which mask layouts and lithography equipment settings achieve the maximum overall process window (in Figure 3 Typically, the resolution enhancement technique is arranged to match the patterning possibilities of the lithographic apparatus LA. The computer system CL may also be used to detect where within the process window the lithographic apparatus LA is currently operating (e.g. using input from a metrology tool MT) to predict whether there are defects (e.g. due to suboptimal processing) Figure 3 ), as depicted by the arrow pointing to “0” in the second scale SC2.

[0068] The metrology tool MT may provide input to the computer system CL for accurate simulation and prediction, and may provide feedback to the lithography apparatus LA to identify possible drifts, for example in the calibration or calibration state of the lithography apparatus LA (in Figure 3 ) as depicted by multiple arrows in the third scale SC3.

[0069] An example of a property (which may also be referred to as a parameter) measured by the measurement tool MT is alignment AL, overlap OVL, and leveling LVL data related to a pattern on a substrate W. Different measurement equipment can be used to measure different parameters. For different measurement parameters, the measurement data obtained may be different. For example, compared with overlap OVL and leveling LVL measurements, alignment AL measurements may be sparse. Factors determining the measurement density may include, for example, the time required to obtain the measurement, and the availability of measurement marks on the substrate W on which the measurement can be performed for the parameter. In order to predict a property or control a property by machine calibration, the measurement data of the property can be used. For example, in order to calibrate the lithography device LA for improved overlap OVL data in a pattern projected onto the substrate W, overlap OVL measurement data from a previous pattern can be used. However, it may also be possible to obtain information related to a property (such as overlap OVL) from other measurement parameters (such as alignment AL measurements and / or leveling LVL measurements).

[0070] In order to predict a property based on a number of different measurements, the data from the different measurements must be combined. If the measurements have different spatial layouts, that is, measurements are made at different locations across the substrate W, one possible way to combine the data is to convert each measurement into a target layout. The combination may be based on a target layout, where the same spatial distribution of data is provided for each measured parameter. Converting the measurement layout to the target layout may involve interpolating the data, for example, a sparse measurement layout used for alignment may be interpolated into a dense layout using known techniques. The interpolated target layout data may then be used to predict the property.

[0071] There are many problems with using interpolated data for prediction. Interpolated data is an estimate of the actual measured data and may include uncertainties that are not represented in the interpolated data. Not incorporating uncertainties into the resulting prediction model for the property may adversely affect the prediction performance. Interpolated data may misreport or ignore some of the actual measured data of the parameter, which may reduce the quality of the resulting prediction. In addition, interpolated data may be wrong, such as when very sparse data is interpolated into a very dense layout, or when considering problems with measured data (such as measured data that cannot accurately represent parameters across the substrate W caused by deformed measurement marks).

[0072] Described herein are methods and apparatus that allow overcoming the above-mentioned problems by providing an alternative to separating the interpolation and prediction steps and by efficiently performing interpolation and prediction jointly.

[0073] The method may be implemented using a convolutional neural network, which may be referred to as a convolutional neural network model (ConvNet). The ConvNet may be used to predict properties of a product unit. The product unit may be a substrate, such as a semiconductor wafer, comprising one or more patterns or features disposed thereon. The one or more patterns or features may be provided by a method comprising at least one lithographic imaging technique using a lithographic apparatus.

[0074] As described herein, measurement data of a substrate patterned in a lithographic manner can be provided to a ConvNet. Convolutional neural networks are a class of deep learning algorithms that can be used for image and pattern recognition. Convolutional neural networks can be used to process data with a grid-like topology, such as a wafer map representing the spatial distribution of parameter values ​​across a wafer. ConvNet may include an input layer, an output layer, and may include one or more additional layers, which may be referred to as hidden layers. ConvNet applies at least one convolution operation to the input, or a potential representation based on the input. An image can be provided as an input to a ConvNet, and the ConvNet can be configured to provide an output based on the input through training. The output can be a classification, that is, placing the input in one of a plurality of possible categories. For example, a ConvNet can classify an input as falling within a performance boundary or falling outside a performance boundary. Alternatively or additionally, a ConvNet can provide a continuous output, that is, the output can be a continuous quantity, such as a prediction of a property of the pattern and / or substrate W (such as, for example, a parameter value).

[0075] In the methods described herein, metrology data of a lithographically patterned substrate may be provided as the input to a ConvNet that may process the data like an image in order to discover correlations between different metrology points on the substrate. Providing the metrology data for different measured properties may allow input data (e.g., substrate images) to be processed without the need for interpolation, as the spatial distribution may represent the relationship between sparse and dense data.

[0076] The measurement of a parameter on a product unit may be represented as an image of the product unit and provided as an input to a ConvNet. The ConvNet may receive multiple images as input. The image provided as input may be a two-dimensional image representing the spatial distribution of the parameter across the product unit, wherein the spatial distribution may be the spatial distribution of the obtained measurement data. The measurement data related to the measured parameter may be referred to as a measurement data set. The measurement data set may include multiple data subsets across the spatial distribution of the product unit. For example, alignment data may have been obtained in a first subset representing alignment in the X direction and a second subset representing alignment in the Y direction. Thus, the first direction and the second direction may be perpendicular to each other. Alternatively, the first direction and the second direction may be non-perpendicular and non-parallel. Overlap data of the product unit may also be provided across the product unit in the form of two subsets in the first direction and the second direction. Leveling data including a representation of the spatial distribution of the height of the product unit may include a single channel. The spatial distribution of multiple subsets of the data set may be represented in a multidimensional object. The multidimensional object may be separated into multiple sub-images, each of which represents the spatial distribution of a subset of the measurement data set. Subsets, and sub-images of subsets, may be referred to as channels.

[0077] Described herein is a method for predicting properties associated with a product unit, wherein the method includes obtaining a plurality of data sets 102. Each of the plurality of data sets may include data associated with a spatial distribution of a parameter across the product unit. Each of the plurality of data sets may be represented as a multi-dimensional object. The method also includes obtaining a convolutional neural network 104 (ConvNet), wherein the network has been trained using previously obtained multi-dimensional objects and properties of previous product units. The trained ConvNet is applied 106 to a plurality of multi-dimensional objects to predict 108 properties associated with the product unit, wherein each multi-dimensional object represents a corresponding one of the plurality of data sets.

[0078] As described herein, measurement data may be used to refer to measurement data, such as one measurement result, a set of related measurement results, a collection of unrelated measurement results, etc. The term measurement data set may be used to refer to measurement data related to a measured parameter, such as an alignment data set. A data set may be used to refer to a set of data that may be represented as a multi-dimensional object. A data set may be a measurement data set, but need not be limited thereto, and may also include calculated or estimated data, and / or a combination of measurement data and non-measurement data.

[0079] The one or more data sets mentioned above may be measurement data sets. The measurement data sets may include measurement data associated with the spatial distribution of data points across the product unit. The data sets may be based on measurement data, but may have been processed, such as normalizing the measurement data, adjusting the units of the measurement data, or removing any data errors from the measurement data.

[0080] The plurality of data sets may include one or more of alignment AL data of the product unit, leveling LVL data of the product unit, and overlapping OVL fingerprint data of the device used to pattern the product unit. The overlapping fingerprint data may be understood as overlapping caused by performance characteristics of the device that is specific to one or more devices.

[0081] The data sets and / or the measurement data may have different resolutions, depending on the type of data set and the speed at which the data can be collected. The plurality of data sets may have the same or different resolutions. One of the plurality of data sets may have a different resolution than at least one other of the plurality of data sets. In certain implementations, all of the data sets may have different resolutions. Resolution may be understood as the number of data points provided across a product unit. In an example embodiment, the alignment AL data set may have a first resolution that is lower than a second resolution of the leveling LVL data set, such as Figure 5 As illustrated. Data sets with different resolutions can be represented as multidimensional objects of the same size, wherein the data set with the lower resolution can include more null values, i.e., values ​​without data values, than the data set with the higher resolution. Alternatively, the data set with the higher resolution can be represented as a larger multidimensional object than the multidimensional object representing the data set with the lower resolution.

[0082] The datasets provided to the ConvNet may have different resolutions. An advantage of providing the ConvNet with multiple datasets having different resolutions is that the different datasets do not require an interpolation step before they can be used in a process for predicting properties associated with a product unit. The ConvNet may receive a dataset in the form of a multidimensional object, wherein representing the dataset as a multidimensional object does not require interpolation. One or more datasets may have a different size than other datasets, and therefore, multiple multidimensional objects of different sizes may be provided to the ConvNet. As described above, this is advantageous because the interpolation step that may otherwise be required may reduce information loss within the data, which would reduce the quality of the prediction of the property.

[0083] The data associated with the spatial distribution across the product unit may include a plurality of data points corresponding to a plurality of locations on the product unit. The locations of the data points of a first data set in the plurality of data sets may be different from the locations of the data points of a second data set in the plurality of data sets. Thus, it is possible that two data sets have the same resolution but different sets of locations. The spatial distribution of the data sets may be used to include both the resolution and the location of the data sets. This information is captured in the representation of the data sets as a multidimensional object.

[0084] The property to be predicted according to the method may be a spatial distribution of a target parameter across the product unit. The target parameter may be an overlap on the product unit, or may be any other parameter useful in determining production-related characteristics of the product unit. Alternatively, or in addition, the property comprises a classification of the product unit. An example classification to be performed by a convolutional neural network comprises grouping the product units according to a property (e.g., yield or overlap). The output of the ConvNet may be a classification label representing a group ID. Another example classification is to provide a binary output (0 / 1, yes / no, true / false) to the ConvNet as a response to a binary question. For example, the ConvNet may determine whether an overlap parameter (e.g., magnification) is within a predetermined threshold and / or target value. The classification label output by the ConvNet may also, for example, assign the product unit to one or more groups based on the overlap property of the product unit. As an example, the classification label may determine whether a product unit "yes" or "no" has an acceptable overlap error. This is similar in some respects to conventional ConvNet classification that can be used to identify the class of an image (such as, for example, dog or cat) and assign a class label (such as, for example, "cat" or "no cat").

[0085] Figure 5 The structure of a convolutional neural network suitable for predicting properties of a product unit is described. The properties of the product unit may be related to parameters of the product unit and / or may include a classification label for the product unit. Figure 5 The image shows a plurality of layers L 1 To L nConvNet. An input IN in the form of a multidimensional object is provided to the ConvNet, each multidimensional object having a spatial distribution of data points corresponding to measurement data. The multidimensional objects can be called images in the sense that they are processed by the ConvNet in a manner similar to optical images, and therefore the multidimensional data can also represent measurement data in the form of optical images. The multidimensional object can include a single image, or it can alternatively include multiple sub-images. The sub-images can be called channels associated with the ConvNet. In the case where the multidimensional object includes a single image, this image can be called a channel associated with the ConvNet.

[0086] Figure 5 The ConvNet depicted in FIG. 1 includes multiple layers, labeled L 1 To L n , where n is a positive integer. The ConvNet may include a layer L called the input part 1 To L i-1 The ConvNet may also include a layer L called a merging part. i To L j-1 The ConvNet may also include a second part called the output part consisting of layer L j To L n The output part includes layer L k , in the L k The background data CTXD can be added to the ConvNet at the layer. The final layer L of the ConvNet n The output of provides output OUT. In the ConvNet, each layer receives a layer input and processes the layer input to produce a layer output. Except for the final layer L n The layer output outside can be called a potential representation, because the output will not usually be provided or used outside the ConvNet. The potential representation output by the layer is provided as input to the next layer in the ConvNet. The potential representation may, for example, include one or more two-dimensional objects. The input part of the ConvNet provides multiple separate potential representations SLT as output for each layer. The merging part and the output part provide a merged potential representation MLT as output.

[0087] As mentioned above about Figure 5As mentioned, the ConvNet may include an input portion, a merging portion, and an output portion. The portions may be placed in series in the order listed above. An advantage of performing the analysis for a portion of the separated multidimensional objects and another portion of the merging data is that the ConvNet may analyze the features of each multidimensional object individually, as well as the effects that may be found based on the combination of the data and the relationships between the data. The ConvNet is capable of receiving input data and predicting properties without the need for interpolation of the input data.

[0088] The merging process of the ConvNet is not affected by the interpolation problems described above. However, the ConvNet can perform implicit interpolation by combining data related to different data sets as part of the merged part. Therefore, a potential advantage of a ConvNet can be that this implicit interpolation considers the properties of the combination of multiple data sets as part of the implicit interpolation, rather than processing the data set independently of other data sets. This can improve the quality of the resulting prediction because the ConvNet can estimate the properties based on consideration of the data within the data set and the relationship between the data sets. When interpolation is performed as a separate calculation prior to the estimation process, the interpolation is based on one data set without considering other data sets, which can lead to the problems of interpolating data described in the above paragraphs. Using a ConvNet allows these problems to be overcome.

[0089] In the input part, multidimensional objects can be processed separately. One advantage of this is that the data layout of one multidimensional object does not have to match the data layout of another multidimensional object, nor does it have to be considered related to the data layout of another multidimensional object. As part of the input part, the data layout for different multidimensional objects can be processed so that each multidimensional object has an SLT with a common layout, which is provided to the merging part as input. Processing different multidimensional objects as a common layout enables the combination of different multidimensional objects in the merging part. Therefore, the processing performed by the ConvNet during the input layer and before the merging part converts the multidimensional objects into a common layout, thereby eliminating the need to interpolate the measurement data separately. When the input part output provides a potential representation of the same size as the input to the merging part, the same filter can be applied to all potential representations, and the representations can therefore be merged.

[0090] The input portion may receive a ConvNet input IN as a partial input. The input portion may generate an input portion output. The input portion output may include multiple discrete potential representations. The input portion may process the input IN to determine potential representations of the same size. The input portion output may include multiple potential representations, each of which has the same size. The input portion output may be provided as input to the merging portion. The merging portion may generate a merged portion output. The merged portion output may include a merged potential representation. The merged portion output may be provided as input to the output portion to generate an output. The output of the portion may be provided as an output OUT of the ConvNet. It is possible to perform one or more processing operations on the output OUT of the ConvNet before providing the output externally (e.g., to a user or device).

[0091] In the input part of the ConvNet, each multidimensional object representing a data set can be processed separately. In order to achieve the discrete processing of the multidimensional objects, the input part may include multiple partitions. The multiple partitions may be parallel partitions. Each partition may be configured to receive one of the multidimensional objects. Each partition may be provided with a different data set, which may include measurement data that has been acquired from the product unit being analyzed.

[0092] Each of the plurality of multidimensional objects may be input to a corresponding partition of the input portion, respectively. Each partition may determine a separate potential representation for each layer of the input portion. Each separate potential representation may be based on a different one of the multidimensional objects. Each partition may determine an input portion output based on a corresponding one of the multidimensional objects received. As an example, the ConvNet may include three parallel partitions: a first partition may provide an input with aligned data, a second partition may provide an input with overlapping data, and a third partition may provide an input with leveled data. The ConvNet may determine three potential representations in each layer of the input portion, i.e., one potential representation for each partition and the corresponding input data set.

[0093] The merging part can receive the input part outputs provided by the partitions of the input part, and merge them so that they can be processed in a combined manner. The merging part can combine all the input part outputs to produce a merged part output. The merged part output can be based on each multidimensional object, thereby merging the multiple data sets. The merged part output can be provided as input to the output part of the ConvNet. The output part can determine the output of the ConvNet, and the output of the ConvNet can also be referred to as a model output. For example, the output of the ConvNet can include a measurement map of the estimated characteristics of the product unit, and the measurement data is provided as input to the product unit.

[0094] One or more of the input portion, the merged portion, and the output portion may include multiple layers. In some instances, each portion includes multiple layers. If a portion includes multiple layers, one of the portions may be a pooling layer. Pooling layers will be described in more detail below.

[0095] The input portion includes a plurality of partitions, wherein the number of partitions may be determined by the number of multidimensional objects input into the ConvNet. The number of partitions may be equal to the number of multidimensional objects provided as input. The input portion may include a plurality of layers. Each layer may include the same number of partitions. There may be a corresponding partition in each layer of the input portion. Each partition of a layer may determine a separate latent representation SLT. The separate representation of a partition may be provided as input to a corresponding partition of a next layer of the input portion. The final layer (L i-1 ) The multiple discrete potential representations SLT outputted may be the input part output.

[0096] Each of the plurality of partitions of the input portion of the ConvNet may include at least one convolution operation. The convolution operation may be performed in the same layer for each partition. A layer in which a convolution operation is performed may be referred to as a convolution layer. The convolution layer in the input portion may perform a convolution operation on each partition, that is, a convolution operation is performed in the same one or more layers for each partition. The convolution layer will be described in more detail below.

[0097] The merging part may receive the input part output and process them together in a first layer of the merging part. The output of the first layer of the merging part may be a merged latent representation MLT. The merging part may include a plurality of layers, wherein each layer after the first layer of the merging part receives a merged latent representation MLT and outputs a merged latent representation MLT. The final layer (L j-1) The merged potential representation outputted by may be the merged portion output. The merged portion may include one or more convolutional layers.

[0098] The merged portion output may be received by a first layer of an output portion of the ConvNet. The output portion may include a plurality of layers. The output portion may include one or more convolutional layers. The output portion may have a plurality of layers, except for the final layer L. n Each layer except for the above receives as input the merged latent representation MLT and determines as output the merged latent representation MLT to be provided to the next layer as input. In one layer of the output part, additional data may be input to the ConvNet, referred to as background data. This data may be provided in a format other than the multidimensional object of the input IN. The background data CTXD may be, for example, a scalar or a vector and may represent a characteristic or property of the product unit, but it is not in the form of an image.

[0099] Background data may be related to product units and / or processes that affect product units. For example, the background data CXTD may include product unit type, product unit ID. The background data CXTD may also include data related to equipment (e.g., lithography equipment LA) that affects the product unit, such as equipment ID, equipment parameters. The background data CXTD may also include measurement data related to the process performed by the equipment for patterning the product unit, such as the temperature, pressure, time / date input data obtained. The background data may be represented in binary form, such as a bit indicating whether a specific product feature (e.g., a chuck) is used. The background data may include one or more integer values, for example, representing exposure time or other processing variables. The background data may contain data that is not present in the input data. As described herein, background data CXTD may be added at the output portion of the ConvNet. Background data may be cascaded and added to the ConvNet in a vector manner. A vector may be added by combining it with the output of a layer in the ConvNet and processed by the remaining layers of the ConvNet. For example, the background variables may be added in the output portion as part of the feedforward portion of the ConvNet.

[0100] The background data may hold some information that is not present in the distribution data and may aid in prediction. For example, each device and chuck may have a unique fingerprint that affects the multidimensional data. For example, knowing that the wafer was exposed to a specific device or chuck may help the model better capture parameters of interest, such as overlap. The background data may be associated with a predefined structure present on a patterned substrate, for example, as a result of using a specific chuck or device for patterning the substrate. The background data may result in a segmentation of the feature space for the multidimensional object processed by the ConvNet, wherein the segmentation takes into account the content of the background data. For example, a product unit patterned using a first chuck may have different properties than a product unit patterned using a second chuck. The ConvNet may be trained to predict the object structure on a product unit corresponding to the predefined structure based on the provided background data.

[0101] A multidimensional object may include a collection of one or more channels. The channels may be associated with the same data set, but may represent different subcategories, or subsets, of the data. For example, a multidimensional object may be a color image and may include three channels for red, green, and blue information. In another example, a multidimensional object may represent data in an n-dimensional space and may include n channels, one for each of the n dimensions. For example, alignment data may be represented in a two-dimensional space (n=2) for alignment in the X and Y directions, wherein the multidimensional object includes two channels, showing the spatial distribution of alignments in the X and Y directions, respectively. A multidimensional object may include a collection of matrices, wherein the matrices represent channels. The channels may be two-dimensional matrices. The elements in the channel matrix may be scalar values. ConvNet may be configured to receive input in a predetermined format. For example, ConvNet may be able to receive a multidimensional object in the form of one or more channels. The potential representation generated by the layer in the ConvNet may have a format similar to the input. Each layer in the ConvNet may be configured to receive one or more input channels and provide one or more output channels that form a potential representation output by the layer. The latent representation may include one or more channels. The channels of the latent representation may be a two-dimensional matrix. The number of input channels to a layer may be different from the number of output channels to a layer.

[0102] A convolutional layer may perform a convolution operation on the input of the layer. Figure 6 An example convolution operation using a filter F on a matrix M is shown. In this example, the matrix M may represent the input channels. Figure 6As shown, the sum of the products of a portion of the matrix M and the elements of the filter F can be provided as the elements of the output channel of the convolution operation. The filter F can slide on the matrix to determine multiple elements of the output channel. Factors contributing to the size of the output channel include: the size of the filter F, the size of the matrix M, and the step size (stride) of the filter sliding on the matrix M. These factors can be set as part of the configuration of the ConvNet. For example, in Figure 6 In , the stride of the filter F in both dimensions of the matrix M is one element, resulting in a 2 by 2 output matrix.

[0103] By selecting a filter size for each matrix in the input part, the output of each partition entering the merged part can be made to have the same size. The size of the output of the layer can also be determined by one or more other hyperparameters of the convolution operation, such as the stride of the filter F, or the padding added to the matrix (for example, rows and / or columns of zeros added to the matrix). For each multidimensional object input to the ConvNet, the filter F size and other hyperparameters can be set so that the output of the input part for each partition is a potential representation of size K, where K is the same for each partition. Multiple filters can be applied to multidimensional objects and / or their potential representations at multiple layers in the ConvNet. The size K of the input part output can be determined by the size of the multiple layers and / or other hyperparameters.

[0104] In this way, the input layer can take input data in the form of multi-dimensional objects of different sizes, and use the correct choice of filters and hyperparameters to convert the data into latent representations of the same size, which can be merged. Thus, when the input chip map has a different size / layout, then the filter size (and other hyperparameters of the convolution operation, such as padding and stride) changes so that the output size of the input portion for all input data is the same size.

[0105] In a convolutional layer, at least one filter is applied to each input channel. A filter may be applied to the input to determine an output channel. If there are multiple input channels, the same filter may be applied to each of the one or more input channels, or different filters may be applied to different input channels. The output channel may include the sum of the results of the convolution of the filter with different input channels. The sum may be a weighted sum. In order to obtain multiple output channels, different filters may process the same one or more input channels. For example, using a layer with one input channel, a first filter may be applied to the input channel to obtain a first output channel. A second filter may be applied to the input channel to obtain a second output channel independent of the first output channel.

[0106] The ConvNet may include a nonlinear layer for adding nonlinearity to the output of the layer. The nonlinear layer may be placed as a layer immediately following the convolutional layer. Using a nonlinear layer may improve the learning performance of the ConvNet. The nonlinear layer may, for example, be a rectified linear unit for removing negative values ​​from the output channel. Other example nonlinear layers include a sigmoid function layer and a hyperbolic tangent function layer.

[0107] The ConvNet may include a pooling layer. The pooling layer may be inserted after the convolution layer of the ConvNet. For example, the ConvNet may include a convolution layer, followed by a correction layer, followed by a pooling layer. The convolution layer, the correction layer, and the pooling layer may be layers that are immediately consecutive. The pooling layer may be used to reduce the size of the channel. The size of the channel may be defined by the number of elements in the channel. The pooling layer may, for example, achieve a reduction in channel size by dividing the input channel into discrete parts, each of which includes multiple elements of the input channel. The pooling layer may then determine an output for each discrete part, wherein the number of elements output for each discrete part is less than the number of elements in the part. As a result, the output channel is less than the input channel. The determination of the output for each part may be performed by applying a function to a part. Example functions may include calculating an average, selecting the highest value in a part (max pooling), selecting the lowest value in a part, and the like. The advantage of using a pooling layer is that it may reduce the amount of data processed within the ConvNet.

[0108] The input portion may include at least one convolutional layer. The input portion may, for example, include one or more convolutional layers. One or both of the merging portion and the output portion may also include convolutional layers. Any convolutional layer in the ConvNet may be followed by one or both of a nonlinear layer and a pooling layer. An advantage of including multiple convolutional layers in a ConvNet is that it may provide a hierarchical approach in which subsequent layers learn features of the input. The first convolutional layer may identify more significant features of the channel, such as edges or gradients within the channel. Later convolutional layers may analyze more abstract features of the channel.

[0109] The ConvNet may include layers other than convolutional layers, nonlinear layers, or pooling layers. The ConvNet may include one or more feed-forward layers. The ConvNet may include one or more fully connected layers or partially connected layers of weights and biases. For example, where the output of the ConvNet includes a classification label, the output portion of the ConvNet may include one or more feed-forward layers. The feed-forward layer may take the output of the previous layer and multiply it by a weight matrix. The output of the feed-forward layer may be a single matrix. Background data (e.g., identification data of the lithography equipment LA and / or the measurement tool MT) may be added to the feed-forward layer.

[0110] The previous paragraphs of this specification provide various options for including or excluding different layers in the ConvNet. It will be understood that the choice of which layers to use will be application specific, and that a working model will require some optimization to provide the desired results from the output. Thus, a particular ConvNet may or may not include one or more non-linear layers or pooling layers, and these non-linear layers or pooling layers may be present in different parts of the ConvNet.

[0111] Applying the ConvNet to multiple multidimensional objects can determine a model output. The model output can include predicted properties. In some cases, one or more processing steps can be performed on the model output. The one or more processing steps can be used to determine the predicted properties from the model output. The predicted properties associated with the product unit can be properties of a pattern formed on the product unit using the lithography device LA. For example, among other things, the predicted properties can relate to the overlap or alignment of features on a substrate for a specific processing method or device. The predicted properties can be provided to the lithography device LA to determine one or more set points of the lithography device LA. A processing step for determining one or more set points of the lithography device LA based at least in part on the predicted properties can be performed by one or two lithography devices in the lithography device LA on a computer system CL. The product unit can be a semiconductor substrate. Acquiring multiple data sets can include acquiring measurement data from the processed semiconductor substrate.

[0112] In order to provide a desired output whose properties can be predicted, a ConvNet is trained using known data. Training the ConvNet may include obtaining training data associated with the product unit, for example, a plurality of processed substrates for which properties (i.e., desired outputs of the ConvNet, such as overlap) have been established using other methods. Thus, the ConvNet may be trained based on the obtained training data to predict properties of the product unit, such as parameters related to the product unit (e.g., alignment, overlap, and / or leveling) and / or classification of the product unit. The parameters may be data features contained within a multidimensional object to be provided to the ConvNet. The data features may be associated with predefined data features contained within the training data, such as a pattern applied to the product unit. The data features may be related to parameters of interest, for example, overlap, alignment, and / or leveling data of a pattern applied to the product unit.

[0113] In one example, a ConvNet is trained using a training dataset of 1800 product units using the settings and processing methods of interest. 80% of the training data is used to train the ConvNet, and 20% of the training data is used to test the trained ConvNet. Once the ConvNet has been trained and tested, it can be used to determine outputs for data other than the training data, such as outputs on product units that the model has not seen (such as those that may be produced during a manufacturing run or as part of a calibration effort).

[0114] In some examples, it may be necessary to periodically retrain the model. This is particularly true if the process and / or equipment used to produce the product unit changes or is modified over time. Retraining may need to be performed using new training data obtained from the modified process or equipment.

[0115] The training data may include input data to be provided to the ConvNet, for example in the form of a plurality of data sets represented as multi-dimensional objects. The training data may include one or more properties of a device for patterning a product unit whose properties are to be measured. The predefined structure in the training data may include measurement data related to the input data. The measurement data may represent parameters estimated by the ConvNet.

[0116] Figure 7 The figure shows the application of a ConvNet to data related to a lithographic pattern of a substrate in order to predict a property of the substrate. The property may be the spatial distribution of overlap across the substrate. The predicted overlap distribution may be used, for example, to adjust the recipe parameters for subsequent patterning exposures in order to improve the pattern quality. Overlap may be difficult to measure because the measurement is very time consuming and requires marks on the substrate in order to make the measurement. Therefore, Figure 7 An advantage of the illustrated ConvNet may be that less or no overlap measure is used to obtain the overlap property.

[0117] like Figure 7 As shown, alignment data AL, leveling data LVL, and overlap fingerprint data OVL for a product unit can be provided to the ConvNet as an input IN data set. The alignment data and leveling data can be measurement data obtained from the product unit. The overlap fingerprint data may include averaged overlap data of a device that patterns the product unit. Alignment data and overlap data can be provided for two directions (X direction and Y direction). The alignment data for each direction can be represented as a two-dimensional matrix, which represents a channel. The two dimensions can correspond to two separate measurements of alignment in the corresponding X and Y directions. These directions can be perpendicular, or any other two non-parallel directions. The data set is represented as a multidimensional object. Specifically, the alignment and overlap multidimensional objects each include two two-dimensional matrices (forming 2 channels of a multidimensional object), a first channel for the X direction (AL x , OVL x ), and a second channel for the Y direction (Al y , OVL y ). The leveling multidimensional object consists of the spatial distribution of height profiles across the product unit and is represented by a single two-dimensional matrix (LVL z) is represented. The three multidimensional objects may have different sizes and / or spatial layouts. 1 To L i-1 In L, the alignment, overlap, and leveling channels are processed separately. Each layer can provide two potential representation channels as output. 1 To L i-1 At layer L, three partitions map different data sets to the same object layout. The input part output may, for example, include six two-dimensional matrices of the same size. i In , the 6 2D matrices are merged to create a latent representation based on a combination of aligned AL, overlapped OVL and leveled LVL data. Applying an additional layer L i+1 To L n To process the merged product unit pattern data. Layer L n The output OUT comprises data which can be used to predict the spatial distribution of the overlapping OVL on the product unit.

[0118] although Figure 7 represents a combination of overlap fingerprint OVL, alignment AL, and leveling LVL data provided to the ConvNet as input IN, but other combinations of input data sets may also be used according to the present disclosure, including subsets of overlap OVL, alignment AL, and leveling LVL, and / or other parameters. Example applications of ConvNets for predicting properties associated with product units include using sparse alignment data and dense leveling data to predict dense alignment data; using alignment data, leveling data, and overlap data to predict the yield of dies on a substrate; and using overlap data and alignment data to assign multiple groups to substrates based on the overlap and / or yield of the substrates.

[0119] The method described herein can be used to determine and / or update one or more control parameters and / or options for controlling a lithographic apparatus LA. The one or more parameters and / or options can be associated with properties predicted according to the method described herein. The options can include multiple set points for control parameters associated with properties associated with a product unit predicted according to the above method. The control parameters can be associated with the control of the overlay error of exposure by the lithographic apparatus LA. The multiple set points can be provided as measurement mappings. The multiple set points can be provided as coefficients of a high-order model describing positioning errors across a substrate. The options can be used to calibrate the lithographic apparatus LA. The calibration based on the options can be performed periodically. The calibration of the lithographic apparatus LA can include calibration of one or both of the coordinate systems of a substrate positioning system and a substrate measurement system within the lithographic apparatus.

[0120] The method described herein may be provided in the form of instructions contained in a computer program. The computer program may be executed on at least one processor to perform the steps of the method. The method may be performed by a computer system CL or a lithographic apparatus LA. The computer system CL or the lithographic apparatus LA comprises a processor, or may comprise a plurality of processors. The processor may be configured to predict properties according to the method described herein. The processor may be connected to a carrier, which may be included in the computer system CL or in another device (e.g., a measurement tool MT) connected to the computer system CL. The carrier may be one of an electronic signal, an optical signal, a radio signal, or a non-temporary computer-readable storage medium (e.g., a memory). The carrier comprises instructions that, when executed on a processor, cause the processor to control the device to perform any of the methods described above.

[0121] Further aspects of the invention are disclosed in the following list of numbered aspects:

[0122] 1. A method for predicting a property associated with a product unit, the method comprising:

[0123] obtaining a plurality of data sets, wherein each of the plurality of data sets includes data associated with a spatial distribution of a parameter across the product unit;

[0124] representing each of the plurality of data sets as a multidimensional object;

[0125] Obtaining a convolutional neural network model trained using properties of a previously obtained multidimensional object and a previous product unit;

[0126] A convolutional neural network model is applied to a plurality of multi-dimensional objects representing the plurality of data sets to predict properties associated with the product units.

[0127] 2. The method according to aspect 1, wherein the convolutional neural network model comprises a plurality of parts, the plurality of parts comprising an input part, a merging part and an output part.

[0128] 3. A method according to clause 2, wherein each part comprises at least one convolution operation.

[0129] 4. A method according to any one of aspects 2 or 3, wherein the input part includes multiple partitions, each partition is configured to receive a multidimensional object among the multiple multidimensional objects, and the method also includes inputting each multidimensional object among the multidimensional objects into a corresponding partition respectively, wherein each partition determines the input part output for the corresponding multidimensional object.

[0130] 5. The method according to aspect 4, further comprising inputting the plurality of input part outputs into the merging part to determine a merging part output.

[0131] 6. A method according to aspect 5, wherein a first multidimensional object and a second multidimensional object among the multiple multidimensional objects have different layouts from each other, and the input part transforms the different layouts so that the input part output corresponding to the first multidimensional object among the multiple multidimensional objects and the second multidimensional object among the multiple multidimensional objects has a common layout.

[0132] 7. The model according to aspect 6, wherein the method comprises:

[0133] In the input portion, one or more first filters are applied to a first multidimensional object of the plurality of multidimensional objects, and

[0134] applying, in the input portion, one or more second filters to a second multidimensional object of the plurality of multidimensional objects;

[0135] Wherein, the application of the one or more first filters and the application of the one or more second filters are arranged to determine a common layout of the input portion outputs corresponding to the first multi-dimensional object and the second multi-dimensional object of the plurality of multi-dimensional objects.

[0136] 8. A method according to aspect 6 or 7, wherein the different layouts include different sizes.

[0137] 9. A method according to aspect 8, wherein the input portion output comprises multiple potential representations having the same size.

[0138] 10. The method according to any one of aspects 5 to 9 further includes inputting the merged part output into the output part to determine the model output of the convolutional neural network model.

[0139] 11. A method according to any one of aspects 2 to 10, wherein each portion comprises a plurality of layers.

[0140] 12. A method according to clause 11, wherein at least one layer of the plurality of layers is a pooling layer.

[0141] 13. The method according to any of the preceding aspects, further comprising:

[0142] obtaining training data associated with the product unit; and

[0143] Training the convolutional neural network model based on the obtained training data to predict parameter-related data features within the multidimensional object;

[0144] Wherein, the data feature is related to a predefined data feature included in the training data.

[0145] 14. A method according to clause 13, wherein the training data comprises one or more properties of an apparatus used to pattern the product unit.

[0146] 15. A method according to any preceding aspect, wherein the data in the data set is metrological data associated with a spatial distribution of data points across the product unit.

[0147] 16. The method according to any preceding aspect, wherein the plurality of data sets comprises one or more of the following items:

[0148] alignment data of the product unit;

[0149] Leveling data of the product unit; and

[0150] Overlay fingerprint data of a device used to pattern the product unit.

[0151] 17. A method according to any preceding aspect, wherein the property to be predicted is the spatial distribution of a target parameter across the product unit.

[0152] 18. A method according to aspect 17, wherein the target parameter is overlap.

[0153] 19. A method according to any preceding aspect, wherein one of the plurality of data sets has a different resolution than at least another of the plurality of data sets.

[0154] 20. A method according to any of the preceding aspects, wherein the data associated with the spatial distribution includes a plurality of data points corresponding to a plurality of locations on the product unit, wherein the plurality of locations of a first data set in the plurality of data sets are different from the plurality of locations of a second data set in the plurality of data sets.

[0155] 21. The method according to any of the preceding aspects, further comprising:

[0156] obtaining background data corresponding to the plurality of data sets; and

[0157] The background data is provided to the convolutional neural network model.

[0158] 22. The method according to aspect 21, further comprising:

[0159] The convolutional neural network is trained to predict object structures contained within features of the plurality of multi-dimensional objects, wherein the object structures are related to predefined structures contained within the background data.

[0160] 23. A method according to any of the preceding aspects, wherein the convolutional neural network model is applied to the multiple multi-dimensional objects to determine a model output, wherein the model output includes a property or a classification.

[0161] 24. A method according to any one of aspects 1 to 23, wherein the method further comprises predicting the property by performing one or more processing steps on the model output.

[0162] 25. A method according to any one of aspects 23 and 24, wherein the classification is a classification label, which identifies one or more of the following items: a group of product units according to the properties of the product units; a binary indicator representing the location of the data within a predetermined classification.

[0163] 26. A method according to any preceding aspect, further comprising providing the property to a lithographic apparatus to determine one or more set points for the apparatus.

[0164] 27. A method according to any preceding clause, wherein the property associated with a product unit is a property of a pattern formed using a lithographic apparatus on the product unit.

[0165] 28. The method of any preceding aspect, wherein the product unit is a semiconductor substrate, and obtaining a plurality of data sets comprises obtaining metrology data from processed semiconductor substrates.

[0166] 29. A lithographic apparatus comprising:

[0167] A processor configured to predict a property according to the method of any one of aspects 1 to 28.

[0168] 30. The lithographic apparatus of clause 29, wherein the lithographic apparatus is further configured to determine one or more set points of the lithographic apparatus based on the property.

[0169] 31. A recipe for controlling a lithographic apparatus comprising one or more set points for control parameters associated with a property predicted according to a method according to any one of clauses 1 to 28.

[0170] 32. An option according to clause 31, wherein the control parameter is associated with controlling an overlay error of the lithographic apparatus.

[0171] 33. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to perform the steps of the method according to any one of aspects 1 to 28.

[0172] 34. A carrier embodying the computer program according to clause 33, wherein the carrier is one of an electronic signal, an optical signal, a radio signal, or a non-transitory computer-readable storage medium.

[0173] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0174] Although embodiments of the present invention may be specifically mentioned herein in the context of a lithographic apparatus, embodiments of the present invention may be used in other apparatuses. Embodiments of the present invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or a mask (or other pattern forming device). These apparatuses are generally referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0175] Although specific reference may have been made above to the use of embodiments of the present invention in the context of optical lithography, it will be appreciated that the present invention is not limited to optical lithography and may be used in other applications, such as imprint lithography, where the context permits.

[0176] Although specific embodiments of the present invention have been described above, it should be understood that the present invention may be practiced in other ways different from those described. The above description is intended to be illustrative rather than restrictive. Therefore, it will be understood by those skilled in the art that the present invention may be modified without departing from the scope of the claims set forth below.

Claims

1. A method for predicting a property associated with a substrate, the method comprising: obtaining a plurality of data sets, wherein each of the plurality of data sets comprises data associated with a spatial distribution of a parameter across the substrate; representing each of the plurality of data sets as a multidimensional object; Obtaining a convolutional neural network model trained using properties of a previously obtained multidimensional object and a previously obtained substrate; applying the convolutional neural network model to a plurality of multi-dimensional objects representing the plurality of data sets to predict properties associated with the substrate, The convolutional neural network model includes multiple parts, including an input part, a merging part and an output part; and in the input part, the multidimensional objects are processed separately from each other and converted into a common layout before the merging part.

2. The method according to claim 1, wherein the input portion comprises a plurality of partitions, each partition being configured to receive a multidimensional object among the plurality of multidimensional objects, the method further comprising inputting each multidimensional object among the multidimensional objects into a corresponding partition, wherein, Each partition determines the output portion of the input for the corresponding multidimensional object. 3 . The method of claim 2 , further comprising inputting the plurality of input portion outputs into the merging portion to determine a merging portion output.

4. The method according to claim 3, wherein: The first multidimensional object and the second multidimensional object among the multiple multidimensional objects have different layouts from each other, and the input part transforms the different layouts so that the input part output corresponding to the first multidimensional object among the multiple multidimensional objects and the second multidimensional object among the multiple multidimensional objects has a common layout.

5. The method according to claim 4, wherein the method comprises: applying, in the input portion, one or more first filters to a first multidimensional object of the plurality of multidimensional objects, and applying, in the input portion, one or more second filters to a second multi-dimensional object of the plurality of multi-dimensional objects; Wherein, the application of the one or more first filters and the application of the one or more second filters are arranged to determine the common layout of the input portion outputs corresponding to the first multi-dimensional object and the second multi-dimensional object of the plurality of multi-dimensional objects.

6. The method according to claim 1, further comprising: obtaining training data associated with the substrate; and Training the convolutional neural network model based on the obtained training data to predict data features related to the parameters within the multidimensional object; Wherein, the data feature is related to a predefined data feature included in the training data.

7. The method of claim 1, wherein the plurality of data sets comprises one or more of the following: alignment data of the substrate; Leveling data of the substrate; and Overlay fingerprint data of an apparatus for patterning the substrate. The method of claim 1 , wherein the property to be predicted is the spatial distribution of a target parameter across the substrate. The method of claim 8 , wherein the target parameter is overlap.

10. The method of claim 1, wherein one of the plurality of data sets has a different resolution than at least another of the plurality of data sets.

11. The method according to claim 1, further comprising: obtaining background data corresponding to the plurality of data sets; and The background data is provided to the convolutional neural network model.

12. The method according to claim 11, further comprising: The convolutional neural network is trained to predict object structures contained within features of the plurality of multi-dimensional objects, wherein the object structures are related to predefined structures contained within the background data.

13. The method of claim 1, wherein application of the convolutional neural network model to the plurality of multidimensional objects determines a model output, wherein the model output comprises the property or classification.

14. The method of claim 13, wherein the classification is a classification label that identifies one or more of: a group of substrates according to properties of the substrate; a binary indicator representing a location of the data within a predetermined classification.

15. A computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to perform the following steps: Get multiple data sets, where Each of the plurality of data sets includes data associated with a spatial distribution of a parameter across a substrate; representing each of the plurality of data sets as a multidimensional object; Obtaining a convolutional neural network model trained using properties of a previously obtained multidimensional object and a previously obtained substrate; applying the convolutional neural network model to a plurality of multi-dimensional objects representing the plurality of data sets to predict properties associated with the substrate, The convolutional neural network model includes multiple parts, including an input part, a merging part and an output part; and in the input part, the multidimensional objects are processed separately from each other and converted into a common layout before the merging part.

16. The computer program according to claim 15, wherein the input portion comprises a plurality of partitions, each partition being configured to receive one of the plurality of multidimensional objects, the computer program further comprising instructions for executing the step of inputting each of the multidimensional objects into a corresponding one of the partitions, wherein: Each partition determines the output portion of the input for the corresponding multidimensional object.

17. The computer program of claim 15, further comprising instructions for performing the following steps: obtaining background data corresponding to the plurality of data sets; and The background data is provided to the convolutional neural network model.

18. The computer program of claim 17, further comprising instructions configured to train the convolutional neural network to predict object structures contained within features of the plurality of multi-dimensional objects, wherein the object structures are related to predefined structures contained within the context data.

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