Prediction and Metrics of Stochastic Photoresist Thickness Defects

Abstract

A mask pattern for a semiconductor device can be used as input to determine a photoresist thickness probability distribution using a machine learning module. For example, the machine learning module can determine a Z-height probability map, which can be used to determine and distinguish the probabilistic variation in photoresist thickness for a semiconductor device. The Z-height can be calculated at a coordinate along the X and Y directions.

Description

[Technical Field]

[0001] FIELD OF THE DISCLOSURE This disclosure relates to metrology of photoresist on semiconductor wafers. [Background technology]

[0002] [CROSS-REFERENCE TO RELATED APPLICATIONS] This application claims priority to U.S. Provisional Patent Application No. 63 / 106,356, filed October 28, 2020, the disclosure of which is incorporated herein by reference.

[0003] As the semiconductor manufacturing industry evolves, the demands on yield management, particularly metrology and inspection systems, are increasing. As critical dimensions continue to shrink, the industry is under pressure to achieve high yields and high-value production in shorter periods of time. Reducing the total time between detecting a yield problem and correcting it increases the return on investment for semiconductor manufacturers.

[0004] Lithographic projection apparatus can be used in the manufacture of integrated circuits (ICs). A patterning device (e.g., a mask) can provide a circuit pattern ("design layout") corresponding to an individual layer of the IC, which can be transferred onto a target portion (e.g., containing one or more dies) on a wafer that is covered with a radiation-sensitive photoresist layer, such as by irradiating the target portion with the circuit pattern on the patterning device. Typically, a single wafer contains multiple adjacent target portions, and the lithographic projection apparatus transfers the circuit pattern onto each target portion, one at a time. In one type of lithographic projection apparatus, the circuit pattern of the entire patterning device can be transferred onto a single target portion in a single exposure; this is commonly known as a wafer stepper. In another type of apparatus, commonly known as a step-and-scan apparatus, the projection beam scans the patterning device along a given reference direction (the "scan" direction) while the substrate is moved synchronously, either parallel to or anti-parallel to the reference direction. Different portions of the circuit pattern on the patterning device are gradually transferred onto one target portion. In general, the lithographic projection apparatus will have a magnification factor M (generally <1), so that the speed F at which the substrate is moved will be a factor M multiplied by the speed at which the patterning device is scanned by the projection beam.

[0005] Before the circuit pattern from the patterning device is transferred to the wafer, the wafer may undergo various procedures, such as priming, photoresist coating, and a soft bake. After exposure, the wafer may undergo other procedures, such as a post-exposure bake (PEB), development, a hard bake, and measurement / inspection of the transferred circuit pattern. These procedures are used to create individual layers of a device (e.g., an IC). The wafer may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, and chemical-mechanical polishing, all of which are intended to create individual layers of the device. If several layers are required for the device, the entire procedure, or a variation of it, is repeated for each layer. Ultimately, devices are present in each target portion on the wafer. The devices are then separated from one another by techniques such as dicing or sawing, and the individual devices can be mounted on carriers, connected to pins, or the like.

[0006] The patterns formed on the wafer through lithography define the functional elements of the IC, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used in the creation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007] Semiconductor manufacturing processes continue to improve, resulting in a steady increase in the amount of features per device, e.g., transistors, while continually reducing feature dimensions. Current technology allows for the fabrication of device layers using lithographic projection equipment that projects a design layout onto a substrate using illumination from an illumination source, resulting in individual feature dimensions much smaller than 100 nm, e.g., less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source).

[0008] This process, in which features having dimensions smaller than the classical resolution limit of the lithographic projection equipment are printed, is commonly referred to as low-k1 lithography, following the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation employed (currently often 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the lithographic projection equipment, CD is the critical dimension (generally the smallest feature size that will be printed), and k1 is an empirical resolution factor. Generally, the smaller k1, the more difficult it is to reproduce a pattern on the substrate that resembles the shape and dimensions defined by the circuit designer, and thus to achieve exceptional electrical functionality and performance. To overcome these difficulties, sophisticated fine-tuning processes are applied to the lithographic projection equipment and / or the design layout. Examples include, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifting patterning devices, optical proximity correction (OPC; sometimes called optical and process correction) in the design layout, or other methods commonly defined as resolution enhancement techniques (RET).

[0009] There are many methods for characterizing expected variations for printed patterns, but most of these methods are based on a top-down view of the pattern (e.g., polygons or contours that describe the pattern shape in the XY plane). These XY polygons can be extracted from top-down scanning electron microscope (SEM) images or predicted based on lithography simulations. For SEM images, experiments can be performed in which focus and dose are varied from their baseline conditions. The measured focus-exposure matrix can then be directly reviewed with a critical dimension scanning electron microscope (CDSEM) for a subset of patterns, or the wafer can be inspected and defect detection results sent to a review SEM (e.g., process window quantification (PWQ) methodology). Again, this leads to features in the XY plane and the expected variations are related to focus and dose. Performing these focus and dose curve experiments can determine how robust the lithography process will be in a manufacturing environment. For example, the experimental dose curve can be used to approximate wafer reflectivity variations and dose fluctuations due to photon shot noise, and the focus curve can be used to approximate wafer height variations (topography) found in a manufacturing environment.

[0010] The focal dose perturbation experimental method described above is not well suited to stochastic variations caused by shot noise effects, since failure events can be rare and still be detrimental to yield. This means that it may be necessary to perform a large number of experimental measurements to detect parts-per-million or parts-per-billion failure modes and be able to repair them. Because the cycle time for defect discovery affects yield improvement, a different approach is needed to increase the return on investment.

[0011] In lithography simulation, the photoresist profile shape at a given Z-height above the wafer is predicted directly, or a full 3D profile is predicted and the simulated photoresist profile is sliced ​​at a specified Z-height, resulting in a pattern polygon. Similar to the experimental procedure described above, simulations can be run at various focus and dose settings to determine robustness to variations seen in manufacturing. This simulation technique, when polygons representing a range of focus / dose conditions are superimposed for a particular pattern, is called a process variation band, or PV-band, calculation. Mask dimension variations are also typically incorporated into the PV-band calculation.

[0012] While this PV-band simulation approach can be extended to predict variability due to stochastic variations, these methods typically focus on predicting the 3-sigma variability of a normal distribution of edge positions. Edge position metrics (e.g., line width roughness, line edge roughness, or circular edge roughness) can be predicted based on various characteristics of the design (e.g., dose, image log slope). The dose sensitivity of the nominal pattern can also be used to predict the stochastic variations of the pattern. These models focus on metrics in the XY plane and their response in the XY plane. Because these models assume a normal distribution of perturbations to the nominal case, they tend to underestimate the probability of extremely rare events. Furthermore, both experimental and simulation-based approaches examine patterns defined in the XY plane and have found that they exhibit poor correlation to yield. Line edge roughness is a measure of the 3-sigma variation of the edges of line patterns and typically does not correlate with electrical yield. [Prior art documents] [Patent documents]

[0013] [Patent Document 1] International Publication No. 2019 / 162346 Summary of the Invention [Problem to be solved by the invention]

[0014] There is a long-standing need for a full-chip model that can predict the probability of rare events arising from the stochastic nature of photoresist exposure, facilitating rapid defect detection and leading to better yield control. Therefore, improved techniques for stochastic modeling of photoresists are needed. [Means for solving the problem]

[0015] In a first embodiment, a method is provided in which a mask pattern for a semiconductor device is input into a machine learning module and a photoresist thickness probability distribution for the semiconductor device is determined based on the mask pattern.

[0016] The machine learning module may be configured to run a general linear model, a neural network, a Bayesian inference, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine.

[0017] The machine learning module may be further configured to determine a probability map of photoresist thickness.

[0018] The thickness probability distribution can provide photoresist thickness information for a given coordinate along the X and Y directions.

[0019] The machine learning module may be further configured to determine local intensities for certain coordinates along the X and Y directions.

[0020] The machine learning module may be further configured to determine an image contrast, an image gradient, an image log-slope, or a normalized image log-slope for a coordinate along the X and Y directions.

[0021] The thickness probability distribution can be determined to an accuracy level of about 1 ppb.

[0022] In one example, the machine learning module includes a first model, a second model, and a third model, where the first model predicts a mask diffraction pattern given a rasterized mask image, the second model predicts an in-photoresist image given the mask diffraction pattern, and the third model predicts a photoresist thickness distribution given the in-photoresist image.

[0023] A computer program product comprising a non-transitory computer readable storage medium with a computer readable program embodied therein can be configured to perform the method of the first embodiment.

[0024] In a second embodiment, a system is provided that includes a machine learning module operable using a processor, the machine learning module configured to determine a photoresist thickness probability distribution for a semiconductor device based on a mask pattern.

[0025] The machine learning module may be configured to run a general linear model, a neural network, a Bayesian inference, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine.

[0026] The machine learning module may be further configured to determine a probability map of photoresist thickness.

[0027] The thickness probability distribution can provide photoresist thickness information for a given coordinate along the X and Y directions.

[0028] The machine learning module may be further configured to determine local intensity, image contrast, image gradient, image log-slope, or normalized image log-slope for a coordinate along the X and Y directions.

[0029] The thickness probability distribution can be determined down to about 1 ppb of photoresist.

[0030] In one example, the machine learning module includes a first model, a second model, and a third model, where the first model predicts a mask diffraction pattern given a rasterized mask image, the second model predicts an in-photoresist image given the mask diffraction pattern, and the third model predicts a photoresist thickness distribution given the in-photoresist image.

[0031] The machine learning module can be in electronic communication with an imaging system having an energy source and a detector.

[0032] For a more complete understanding of the nature and purpose of the present disclosure, reference should be made to the accompanying drawings in conjunction with the detailed description below. [Brief explanation of the drawings]

[0033] [Figure 1] 1 is a diagram of an embodiment of the present disclosure; [Figure 2] 1 is a flowchart of a method according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0034] Although certain embodiments describe the claimed subject matter, other embodiments exist within the scope of this disclosure, including embodiments that do not provide all of the benefits and features described herein. Various structural, logical, process step, and electronic changes may be made without departing from the scope of this disclosure. Accordingly, the scope of this disclosure is determined solely by reference to the appended claims.

[0035] Photolithography can exhibit defects governed by the quantum nature of light and matter. For example, quantized light is represented by photons, and chemical reactants in photoresist are represented by discrete molecules. These are often referred to as shot noise or stochastic defects. While stochastic defects can be common in EUV lithography, they can also appear at exposure wavelengths used in other lithographic processes, such as ArF immersion. "Stochastic" means that while the average behavior can be within desired specifications (e.g., photoresist width, tip-to-tip measurements of line edges, or photoresist thickness), fluctuations can also occur, causing failures in the pattern with a nonzero probability (e.g., bridging or breaking of line / space patterns). With millions of transistors in a wafer, even a very low failure probability can result in significant yield loss.

[0036] Stochastic failures are often found with inspection tools and then characterized by top-down SEM. Inspection and characterization can occur after lithography (after develop inspection (ADI)) or after subsequent etching and cleaning steps (after etch inspection (AEI) or after clean inspection (ACI)). The AEI / ACI results can be most relevant to yield, which depends on the remaining photoresist thickness at ADI.

[0037] According to embodiments of the present disclosure, these defects can be predicted using a model of local photoresist thickness, which in turn can explain the full-chip layout in relation to probabilistic failures. This can be used to predict probabilistic variations in photoresist thickness. Unlike prior art, this index determines photoresist thickness parameters at all locations, including suspected failure locations. According to embodiments of the present disclosure, photoresist thickness can be directly analyzed at all locations. Photoresist thickness is an indicator of defect rate and yield because it directly correlates to pattern transfer errors during etching. For example, if unwanted photoresist is found in a space (e.g., a space-bridging defect) and its thickness is greater than a certain threshold, the etching process will not remove the desired amount of material from the substrate in the space region. Similarly, if the photoresist is not thick enough in a line region (e.g., a line-break defect), the etching process may remove the remaining photoresist and begin to remove material from the substrate in the line region, which is undesirable. These photoresist thickness errors will cause pattern transfer errors whether or not an edge (as defined in the XY plane) is nearby.

[0038] Local photoresist thickness can be resolved using a simulator, such as PROLITH™, a physics-based simulator sold by KLA Corporation. This can be in the form of a cumulative histogram over multiple simulations or a single instance, thereby determining a probability distribution for the photoresist thickness. Physics-based models of the lithographic process can be developed using methods such as PROLITH™. Using simulators such as PROLITH™, stochastic events due to photon and chemical shot noise can be simulated. This is typically done using a Monte Carlo-type process that randomly samples a known distribution of photon absorption rates, such as a Poisson distribution. Multiple simulations can be run to generate a sample of events for a given set of lithography conditions. The simulated responses, such as line widths or contact hole diameters, can be binned into a histogram to represent their occurrence probability. These probability distributions of responses from such physics-based simulators have been found to be consistent with experimentally determined results.

[0039] A machine learning module 100 is shown in FIG. 1. The machine learning module 100 is configured to determine a photoresist thickness probability distribution for a semiconductor device based on a mask pattern. The machine learning module 100 can be configured to run a supervised machine learning model, including, but not limited to, a general linear model, a neural network, Bayesian inference, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine. A convolutional neural network can be used for image input. A Bayesian neural network can be used to determine an output probability or distribution.

[0040] The machine learning module 100 can be trained using results from a simulator. The dataset can be a collection of mask patterns, which can include approximately 2000 patterns and have a size of approximately 1 μm. According to one example, intermediate data from the simulator can be used to train the machine learning module 100. The intermediate data can be used to create three separate models that can be chained together during prediction. That is, simulations can be run with additional variations in common lithography parameters, such as exposure dose and focus settings, to generate intermediate results for training three models (e.g., Models A, B, and C).

[0041] The models used by the machine learning module 100 can determine various properties near a region of interest. For example, the inset in FIG. 1 shows an example of a photoresist line. This photoresist line has defects that could cause problems in a subsequent etching process. Various properties can be determined in the region of interest, which can be located at or near certain coordinates along the X and Y directions. Properties can also be determined from an aerial image or an in-photoresist image. The in-photoresist image is an optical image of the interior of the photoresist formed during exposure. It can be the result of an intermediate calculation and the output of one of the three models (e.g., Model B). It can be stored as light intensity at sampled X, Y, and Z locations in the simulation domain. It can then serve as starting data for subsequent chemical reactions, which can produce the actual physical shape or relief image of the photoresist after development.

[0042] FIG. 2 is a flowchart of method 200. At 201, a mask pattern for a semiconductor device is input into a machine learning module. The mask pattern can be thought of as a polygonal shape that represents the chip designer's intent. It can be stored in various types of files, such as a design file. For actual machine learning training, it can be converted into a raster format (value table) along the X and Y dimensions.

[0043] The machine learning module can be machine learning module 100 in FIG. 1. In 202, a photoresist thickness probability distribution is determined for the semiconductor device based on the mask pattern. A probability distribution is a mathematical function that gives the probability of occurrence of various levels of photoresist thickness. In practical terms, this means that the distribution is determined by inputting a few (e.g., 2-15) parameter values ​​from the model into the function. By applying maximum likelihood principles during training of model C, the model can be "taught" to generate correct parameters for the probability distribution. As in any other machine learning process, the model output (i.e., distribution) can be evaluated for correctness by comparing it to the "true" output (e.g., simulator photoresist relief) using a maximum likelihood metric.

[0044] The machine learning module can be further configured to determine a Z-height probability map, for example, at a given coordinate along the X and Y directions. The probability map is a surface representing the probability of events at each X and Y location. In one example, it is calculated using the distribution predicted by the model. The probability that the photoresist height at location X and Y is above or below a threshold can be predicted. In locations where a small photoresist thickness is expected (spaces), even a small probability of having some thickness above the threshold is indicative of a potential (bridging) defect. Conversely, in locations where a large photoresist thickness is expected (lines), the probability of having a thickness below the threshold (too small) is an indicator of a potential line-break defect. This is illustrated in the subdivision of Figure 1, where the thickness along the Z direction is not uniform. These probabilities are calculated on a dense X and Y grid that covers the entire area under test or the entire chip. The probability map can represent the Z-height and photoresist thickness of the photoresist surface.

[0045] The thickness probability distribution can provide Z-height information for a given coordinate along the X and Y directions. The thickness probability distribution can be determined to an accuracy level of approximately 1 ppb. 1 ppb is the target accuracy of 10 ppb for model useful range and accuracy. -9 It represents the probability of achieving a lower goal, say 10 -10 , 10 -11 etc. The volume of photoresist in a particular area can also be determined. Resolving photoresist thickness offers advantages over simply resolving edge placement errors, such as those typically output by optical proximity correction (OPC) and OPC verification software.

[0046] Statistical characteristics of the photoresist thickness along the Z direction (i.e., Z height) can be determined at certain coordinates along the X and Y directions. That is, the photoresist thickness along the Z direction can be determined at discrete points in the photoresist structure or along the length of the photoresist structure. If the model is divided into A, B, and C sections, steps can include predicting a mask diffraction pattern using Model A given a rasterized mask image, optionally along with other imaging parameters (e.g., chief ray angle, etc.). Then, predicting an intra-photoresist image using Model B given the mask diffraction pattern, optionally along with defocus and other imaging parameters (e.g., chief ray angle, flare, aberrations, etc.). Then, predicting photoresist thickness distribution parameters using Model C given the photoresist image, optionally along with exposure dose and other exposure and photoresist parameters. Thresholds can be used to predict the probability of under- or over-thickness of the photoresist.

[0047] The method can be used to search for lithographic defects. Z-thickness tends to be more directly related to rare lithography defects that limit yield. Areas of interest are identified as locations intended to have no photoresist (e.g., near the center of a space) or a large amount of photoresist (e.g., near the center of a line). The probability of over- or under-thickness of photoresist in those locations can be analyzed and reported. According to one example, Z-thickness can be resolved to a probability of 1 ppb, but not limited to a 1 ppb accuracy level in areas where the photoresist should be completely removed. According to another example, Z-thickness can be resolved to a probability of 1 ppb, but not limited to a 1 ppb accuracy level in areas where the full thickness of photoresist should be present. According to yet another example, Z-thickness can be resolved to a probability of 1 ppb, but not limited to a 1 ppb accuracy level in any area.

[0048] Other properties can be determined at certain coordinates along the X and Y directions and can be properties of the image in the photoresist determined prior to the Z height, including local intensity, image contrast, image gradient, image log slope, normalized image log slope, probability of location of the photoresist edge, or other properties.

[0049] The disclosed embodiments can be used to find defects in the photoresist. The disclosed embodiments can also be used to correct a mask to eliminate defects in the photoresist. That is, results from using the method can be used as a form of feedback to mask design. Process parameters (e.g., focus) during photoresist application can be modified based on results from using the method.

[0050] In FIG. 1 , the machine learning module 100 also includes an optional imaging system 101, which is in electronic communication with the machine learning module 100. The imaging system 101 includes an energy source and a detector. The energy source generates energy and directs it toward the wafer. The energy source may be, for example, a light source or an electron source. The detector is configured to detect energy reflected from the wafer to generate an image. The energy may be, for example, a light beam, an electron beam, an ion beam, or other type of particle beam. For example, an optical inspection system or SEM may provide continuous feedback to the machine learning module 100 by measuring photoresist samples on one or more wafers.

[0051] The imaging system 101, or a processor within the imaging system 101, can be configured to send images of the wafer to the machine learning module 100. The images can be used for additional training of the model run by the machine learning module 100. That is, wafers created using information from the machine learning module 100 can be used to further train or enhance the machine learning module 100. Other specimen wafers or other production wafers can also be used to further train or enhance the machine learning module 100.

[0052] The machine learning module 100 and its internal subsystems may include a personal computer system, an image computer, a mainframe computer system, a workstation, a network device, an internet device, or other device. The machine learning module 100 or its internal subsystem(s) may include any suitable processor known in the art, such as a parallel processor, to run the model. In some examples, the processor may be or include a graphics processing unit (GPU). Additionally, the subsystem(s) or the machine learning module 100 may include a platform with high-speed processing and software, whether a standalone or networked tool. The machine learning module 100 may include or be coupled to a display and user input device for selecting desired process parameters.

[0053] In certain embodiments, the various steps, functions, and / or operations of the machine learning module 100 and the subsystems therein and methods disclosed herein may be performed by one or more of electronic circuits, logic gates, multiplexers, programmable logic devices, ASICs, analog or digital controllers / switches, microcontrollers, or information processing systems. Program instructions implementing methods, such as those described herein, may be transmitted or stored on a carrier medium. The carrier medium may include a storage medium, such as a read-only memory, a random-access memory, a magnetic or optical disk, a non-volatile memory, a solid-state memory, or a magnetic tape. The carrier medium may also include a transmission medium, such as a wire, cable, or wireless transmission link. For example, the various steps described throughout this disclosure may be performed by a single processor (or computer system), or alternatively, by multiple processes (or multiple computer systems). Furthermore, the various subsystems included in the neural network module 101 may comprise one or more information processing or logic systems. Therefore, the above description should not be construed as a limitation on the present disclosure, but merely as illustrative.

[0054] Convolutional neural networks (CNNs) can be used in the machine learning module 100 according to some embodiments. CNNs are a type of feedforward artificial neural network whose connectivity patterns between neurons (i.e., pixel clusters) are inspired by the organization of animal visual cortex. Individual cortical neurons respond to stimuli in constrained spatial regions known as receptive fields. The receptive fields of different neurons overlap, tiling the visual field. The response of an individual neuron to stimuli within its receptive field can be mathematically approximated by the convolution operation.

[0055] A CNN can have multiple layers of receptive fields. These are small sets of neurons that process portions of an input image or set of images. The outputs of these sets are then tiled so that their input regions overlap, resulting in a better representation of the original image. This can be repeated for each such layer. Because of the tiling, a CNN can tolerate translation of its input image. A CNN can have neurons that form a 3D volume. CNN layers can have neurons arranged along three dimensions: width, height, and depth. Neurons in a layer are connected only to a small region, or receptive field, of the previous layer. Different types of layers, both locally connected and fully connected, can be stacked to form a CNN architecture. A CNN exploits spatially local correlations by enforcing local connectivity patterns between neurons in adjacent layers. This architecture ensures that its trained filters generate the strongest response to spatially local input patterns. By stacking many such layers, the derived nonlinear filters become increasingly global (i.e., respond to larger spatial regions of pixels). This allows the network to first generate good representations of small subsets of the input and then use these to build a representation of a larger area. In a CNN, each filter is replicated across the entire visual field. These replicated units share the same parameterization (weight vectors and biases) to form a feature map. This means that all neurons in a given convolutional layer detect the exact same features. This replication of units allows features to be detected regardless of their location within the visual field, thus establishing translation invariance.

[0056] Together, these properties enable CNNs to achieve better generalization to imaging problems. Weight sharing also helps reduce the number of free parameters to be learned, thereby lowering the memory requirements for running the network. Reducing the memory footprint allows for the training of larger, more powerful networks. CNNs can have local or global pooling layers that combine the outputs of neuron clusters. Pooling layers can also consist of various combinations of convolutional and fully connected layers, and pointwise nonlinearities can be applied at the end or after each layer. The introduction of convolutional operations targeted at small regions of the input reduces the number of free parameters and improves generalization. One of the advantages of convolutional networks is the use of shared weights in convolutional layers, which means that the same filter (weight bank) is used for each pixel in the layer. This also reduces the memory footprint and improves performance.

[0057] A CNN architecture can be formed by a stack of individual layers that transform the input volume into an output volume (e.g., one that holds class scores) through a differentiable function. A small number of individual types of layers can be used. The convolutional layer consists of a set of learnable filters (or kernels) with various parameters that have small receptive fields but extend through the full depth of the input volume. During the forward pass, each filter is convolved across the width and height of the input volume to compute dot products between the filter's entries and its input and generate a two-dimensional activation map for the filter. As a result, the network learns filters that activate when it encounters a particular type of feature at a certain spatial location in the input. The full output volume of the convolutional layer is formed by stacking the activation maps for all filters along the depth dimension. Each entry in the output volume can also be interpreted as the output of a neuron that sees a small region of the input and shares parameters with neurons in the same activation map.

[0058] When dealing with high-dimensional inputs, such as images, connecting neurons to every neuron in a preceding volume can be impractical because such network architectures do not account for the spatial structure of the data. CNNs can exploit spatially local correlations by enforcing local connectivity patterns between neurons in adjacent layers. For example, each neuron is connected to only a small region of its input volume. The extent of this connectivity is a hyperparameter, called the neuron's receptive field. The connections can be spatially local (along width and height) but can extend along the entire depth of the input volume. Such architectures ensure that the trained filters produce the strongest response to spatially local input patterns. In some embodiments, transfer learning can be used to train CNNs, generating hyperparameters for each CNN. Transfer learning involves training a CNN on a very large dataset and then using the weights of the trained CNN as a fixed feature extractor or initialization for the focus task.

[0059] For example, three hyperparameters control the size of the output volume of the convolutional layer: its depth, stride, and padding size / type. The depth of the output volume controls the number of neurons in the layer that connect to the same region of the input volume. All of these neurons learn to activate different features in the input. For example, if the first CNN layer receives a raw image as input, different neurons along the depth dimension may be activated in the presence of edges or color blobs of different orientations. The stride controls how depth columns are allocated around the spatial dimensions (width and height). When the stride is 1, new depth columns of neurons are allocated to spatial locations that are only one spatial unit apart. This leads to significant overlap of receptive fields between columns, resulting in a larger output volume. Conversely, when a larger stride is used, the receptive fields overlap less, resulting in an output volume with smaller spatial dimensions. Sometimes it is convenient to pad the input volume with zeros on its boundaries. The size of this zero padding is the third hyperparameter. Padding controls the spatial size of the output volume. In particular, it is sometimes desirable to exactly preserve the spatial size of the input volume.

[0060] According to certain embodiments, a parameter sharing scheme can be used in layers to control the number of free parameters. If a patch feature is useful for computation at one spatial location, it can also be useful for computation at another location. In other words, a single two-dimensional depth slice can be represented as a depth slice, and neurons within each depth slice can be constrained to use the same weights and biases.

[0061] Because all neurons in a single depth slice can share the same parameterization, the forward pass at each depth slice of the layer can be computed as a convolution of the input volume with the weights of that neuron. Thus, the set of weights with which the input is convolved can generally be called a filter (or kernel). The result of this convolution is an activity map, and the sets of activity maps for the individual filters can be stacked together along the depth dimension to generate the output volume.

[0062] Sometimes parameter sharing is not effective, for example, when the input images to a CNN have a unique centralized structure, where completely different features are expected to be learned at different spatial locations.

[0063] Pooling is another feature of CNNs and is a form of nonlinear downsampling. There are several nonlinear functions that can implement pooling, including max pooling. In max pooling, the input image is partitioned into a set of non-overlapping rectangles, and the maximum value of each subregion is output. Once a feature is found, its exact location is less important than its approximate location relative to other features. Pooling layers function to gradually reduce the spatial size of the representation, thereby reducing the amount of parameters and computation in the network and thus controlling overfitting. Pooling layers can be placed between successive Connie layers in a CNN architecture.

[0064] Another layer in a CNN can be a ReLU (rectified linear unit) layer, which is a layer of neurons applied with a non-saturating activation function. The ReLU layer allows for the enhancement of the nonlinear properties of the decision function and the network as a whole without affecting the receptive fields of its convolutional layers.

[0065] Then, after several convolutional and / or max-pooling layers, fully connected layers accomplish high-level inference in the neural network. Neurons in fully connected layers have full connections to all activations in the previous layer. These activations can be calculated using matrix multiplication followed by a bias offset.

[0066] According to certain embodiments, dropout techniques can be used to prevent overfitting. As used herein, dropout is a regularization technique that reduces overfitting in neural networks by preventing complex co-adaptation to training data. The term "dropout" refers to dropping out units (both hidden and visible) within a neural network. For example, at each training stage, individual nodes can be "dropped out" of the CNN with probability 1-p, or retained with probability p, leaving a reduced CNN. According to certain embodiments, incoming and outgoing edges to dropped-out nodes can also be removed. Only the reduced CNN is trained. The removed nodes can then be reinserted into the network with their original weights.

[0067] The probability that a hidden node will be retained (i.e., not dropped) during the training stage can be approximately 0.5. For input nodes, the retention probability can be higher. By avoiding training all nodes on the entire training data, dropout reduces overfitting in CNNs and improves training speed.

[0068] Training data can be input for model training (e.g., CNN training), which can be performed in any suitable manner. For example, model training can involve inputting training data to a CNN and modifying one or more parameters of the model until the model's output is the same as (or substantially the same as) external validation data. Model training can produce one or more trained models, which can be sent to model selection, which is performed using validation data. For the validation data input to the one or more trained models, the results produced by each of the one or more trained models can be compared with the validation data to determine which model is the best model. For example, the model that produces results that most closely match the validation data can be selected as the best model. Then, model evaluation of the selected model (e.g., the best model) can be performed using test data. Model evaluation can be performed in any suitable manner. The best model can also be sent to model deployment, where it can be sent to a semiconductor inspection tool for use (post-training mode).

[0069] A wide variety of CNNs can be used in the embodiments of the present disclosure. Different CNNs can be used depending on the particular scanning mode or situation. The configuration of the CNN can be varied depending on the simulator configuration, wafer, image data acquisition subsystem, or predetermined parameters.

[0070] Other models can be used in machine learning module 100. For example, a Bayesian neural network is a probabilistic graphical model that represents a set of variables and their conditional dependencies using a directed acyclic graph. A Bayesian network can take an event that has occurred and predict the likelihood that any one of several known potential causes was a contributing factor.

[0071] An additional embodiment relates to a non-transitory computer-readable medium having stored thereon program instructions executable by a processor, particularly for performing a computer-implemented method of determining process parameters as disclosed herein. The program instructions executable on a neural network module are stored within the non-transitory computer-readable medium, which may be embodied in an electronic data storage unit or other storage medium. The computer-implemented method may include any step(s) of any method(s) described herein, including method 200.

[0072] The steps of the methods may be performed as described herein. The methods may include any other step(s) that may be performed by a processor and / or computer subsystem(s) or system(s) described herein. The steps may be performed by one or more computer systems, which may be configured according to any of the embodiments described herein. In addition, the methods described above may be performed by any of the system embodiments described herein.

[0073] Although the present disclosure has been described in connection with one or more specific embodiments, it will be understood that other embodiments of the present disclosure may be made without departing from the spirit and scope of the present disclosure, which is to be construed as limited only by the appended claims and their reasonable interpretation.

Claims

1. 1. A method comprising: inputting a mask pattern for a semiconductor device into a machine learning module; and the machine learning module determines and outputs a photoresist thickness probability distribution for the semiconductor device based on the mask pattern; method.

2. 10. The method of claim 1, wherein the machine learning module is configured to run a general linear model, a neural network, a Bayesian inference, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine.

3. 10. The method of claim 1, wherein the machine learning module is further configured to determine a probability map of photoresist thickness.

4. 2. The method of claim 1, wherein the thickness probability distribution provides photoresist thickness information for a coordinate along the X and Y directions.

5. The method of claim 1 , wherein the machine learning module is further configured to determine local intensities associated with certain coordinates along the X and Y directions.

6. The method of claim 1 , wherein the machine learning module is further configured to determine image contrast for a coordinate along an X direction and a Y direction.

7. The method of claim 1 , wherein the machine learning module is further configured to determine image gradients associated with coordinates along the X and Y directions.

8. The method of claim 1 , wherein the machine learning module is further configured to determine an image log-slope for a coordinate along the X and Y directions.

9. The method of claim 1 , wherein the machine learning module is further configured to determine a normalized image log-slope for a coordinate along the X and Y directions.

10. 10. The method of claim 1, wherein the thickness probability distribution is determined to an accuracy level of about 1 ppb.

11. 2. The method of claim 1, wherein the machine learning module comprises a first model, a second model, and a third model, wherein the first model predicts a mask diffraction pattern given a rasterized mask image, the second model predicts an in-photoresist image given the mask diffraction pattern, and the third model predicts a photoresist thickness distribution given the in-photoresist image.

12. 10. A computer provided with a non-transitory computer readable storage medium having a computer readable program embodied thereon, the computer readable program configured to perform the method of claim 1.

13. 1. A system comprising: A system comprising a machine learning module operable using a processor, the machine learning module configured to determine a photoresist thickness probability distribution for a semiconductor device based on a mask pattern.

14. 14. The system of claim 13, wherein the machine learning module is configured to run a general linear model, a neural network, a Bayesian inference, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine.

15. 14. The system of claim 13, wherein the machine learning module is further configured to determine a probability map of photoresist thickness.

16. 14. The system of claim 13, wherein the thickness probability distribution provides photoresist thickness information for a coordinate along the X and Y directions.

17. 14. The system of claim 13, wherein the machine learning module is further configured to determine local intensity, image contrast, image gradient, image log-slope, or normalized image log-slope for a coordinate along an X direction and a Y direction.

18. 14. The system of claim 13, wherein the thickness probability distribution is determined down to about 1 ppb of photoresist.

19. 14. The system of claim 13, wherein the machine learning module comprises a first model, a second model, and a third model, wherein the first model predicts a mask diffraction pattern given a rasterized mask image, the second model predicts an in-photoresist image given the mask diffraction pattern, and the third model predicts a photoresist thickness distribution given the in-photoresist image.

20. 14. The system of claim 13, wherein the machine learning module is in electronic communication with an imaging system having an energy source and a detector.

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