Prediction and Measurement of Random Photoresist Thickness Defects

Abstract

A machine learning module can be used to determine the probability distribution of photoresist thickness by using a mask pattern of a semiconductor device as input. For example, the machine learning module can determine a probability map of the Z-height. This can be used to determine the random variation in the photoresist thickness of the semiconductor device. The Z-height can be calculated at coordinates in both the X and Y directions.

Description

[0001] Cross-reference of related applications

[0002] This application claims priority to provisional patent application No. 63 / 106,356, filed October 28, 2020, the disclosure of which is hereby incorporated by reference. Technical Field

[0003] This disclosure relates to the metering of photoresist on semiconductor wafers. Background Technology

[0004] The evolution of the semiconductor manufacturing industry places higher demands on yield management, and especially on metrology and inspection systems. Critical dimensions continue to shrink, and the industry needs to reduce the time spent achieving high-yield, high-value production. Minimizing the total time from detecting a yield problem to resolving it maximizes the return on investment for semiconductor manufacturers.

[0005] Photolithography projection equipment can be used in the fabrication of integrated circuits (ICs). In this case, a patterning apparatus (e.g., a mask) provides a circuit pattern (“design layout”) corresponding to individual layers of the IC, and this circuit pattern can be transferred to target portions (e.g., including one or more dies) on a wafer coated with a radiation-sensitive photoresist layer, for example, by radiating the target portion through the circuit pattern on the patterning apparatus. Generally, a single wafer contains multiple adjacent target portions, and the circuit pattern is sequentially transferred to the multiple adjacent target portions one at a time by the photolithography projection equipment. In one type of photolithography projection equipment, the circuit pattern on the entire patterning apparatus is transferred to a target portion in a single exposure, which is commonly referred to as a wafer stepper. In an alternative apparatus, commonly referred to as a stepping and scanning apparatus, the projection beam scans across the patterning apparatus in a given reference direction (“scanning” direction) while simultaneously moving the substrate parallel or antiparallel to this reference direction. Different portions of the circuit pattern on the patterning apparatus can be progressively transferred to a target portion. Since photolithography projection equipment generally has a magnification factor M (usually <1), the speed F of moving the substrate will be a factor of M times the speed of the projection beam scanning patterning device.

[0006] Before the circuit pattern is transferred from the patterning device to the wafer, the wafer may undergo various processes, such as primer coating, photoresist coating, and soft baking. After exposure, the wafer may undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. These processes are used to fabricate individual layers of a device (e.g., an IC). The wafer may then undergo various processes to form all the individual layers of the desired device, such as etching, ion implantation (doping), metallization, oxidation, and chemical mechanical polishing. If several layers are required in the device, the entire process or its variations are repeated for each layer. Ultimately, the device will exist in each target portion of the wafer. These devices are then separated from each other using techniques such as dicing or sawing, and individual devices can be mounted on carriers, connected to pins, etc.

[0007] The patterns formed on a wafer via photolithography define the functional components of an IC, such as microprocessors and memory chips. Similar photolithography techniques are also used in the fabrication of flat panel displays, microelectromechanical systems (MEMS), or other devices.

[0008] As semiconductor manufacturing processes continue to advance, the size of functional components has been continuously reduced while the number of functional components (e.g., transistors) per device has been steadily increasing. In the latest technology, layers of the device are manufactured using photolithography projection equipment, which projects a design layout onto a substrate using illumination from a light source, thereby producing individual functional components with dimensions well below 100 nm (which can be less than half the wavelength of radiation from the light source (e.g., a 193 nm light source)).

[0009] According to the resolution formula CD = k1 × λ / NA, this process, in which features are printed with dimensions smaller than the classical resolution limit of a photolithography projection device, is generally referred to as low-k1 lithography, where λ is the wavelength of the radiation used (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the photolithography projection device, CD is the critical size (typically the minimum printed feature size), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it is to reproduce patterns on a substrate that resemble the shape and size planned by the circuit designer to achieve specific electrical functionalities and performance. To overcome these difficulties, complex fine-tuning steps are applied to the photolithography projection device and / or design layout. These include (but are not limited to) optimization of NA and optical coherence settings, custom illumination schemes, the use of phase-shift patterning devices, 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).

[0010] Many methods exist for characterizing the expected variations in a printed pattern, but many of these methods are based on a top-down view of the pattern (e.g., polygons or contours describing the pattern shape in the XY plane). These XY polygons can be extracted from top-down scanning electron microscopy (SEM) images or predicted from lithography simulations. For the SEM images, experiments can be performed where the focus and dose vary from their nominal conditions. Then, for a subset of the pattern, a critical-size scanning electron microscope (CDSEM) is used to directly re-examine the measured focus-exposure matrix or inspect the wafer, and detected defects are sent to the re-examined SEM (e.g., process window qualification (PWQ) metrology). Again, this results in features in the XY plane, and the expected variations are related to focus and dose. Focus and dose profiling experiments are performed to determine how robust the lithography process will be in the manufacturing environment. For example, experimental dose profiling is used to approximate variations in wafer reflectivity or dose fluctuations attributed to photon shot noise. Focus profiling is used to approximate variations in wafer height (morphology) as seen in the manufacturing environment.

[0011] The focus-dose perturbation experimental method described above is not very suitable for random variations caused by shot noise effects, because failure events can be rare but still detrimental to yield. This means that a large number of experimental measurements may need to be performed to detect failure modes that are one in a million or one in a billion that can then be repaired. The cycle time for defect discovery affects yield improvement, thus requiring an alternative approach to maximize return on investment.

[0012] In photolithography simulation, the shape of the photoresist profile is predicted directly at a fixed Z-height above the wafer, or a complete 3D profile is predicted and then cut at a specified Z-height, resulting in patterned polygons. Similar to the experimental procedures described above, simulations can be performed under various focus and dose settings to determine robustness to variations observed in manufacturing. When a series of polygons for a specific pattern are superimposed, this simulation method is referred to as the calculation of the process variation band or PV band. Variations in mask size are also commonly included in the PV band calculation.

[0013] Simulation methods for scalable PV strips can predict variability attributable to random variations, but these methods typically focus on predicting the 3σ variability of a normally distributed edge location. Edge location metrics (e.g., linewidth roughness, line edge roughness, or round edge roughness) can be predicted from different design characteristics (e.g., dose, image log slope). The metrological sensitivity of the nominal pattern can also be used to predict random variations in the pattern. These models focus on metrics in the XY plane and responses within the XY plane. Because these models assume that perturbations to the nominal case are normally distributed, they may underestimate the probability of extremely rare events. Finally, both experimental and simulation-based methods examine patterns defined in the XY plane that have been shown to have poor correlations with yield. Line edge roughness (a measure of the 3σ variation of the edge of the line pattern) is generally not related to the electric field.

[0014] There has long been a need for a full-chip model capable of predicting the probability of rare events arising from the stochastic nature of photoresist exposure and facilitating rapid defect detection for better yield control. Therefore, an improved technique for modeling the stochasticity of photoresist is required. Summary of the Invention

[0015] A method is provided in a first embodiment. The method includes inputting a mask pattern of a semiconductor device into a machine learning module, and determining a probability distribution of photoresist thickness of the semiconductor device based on the mask pattern.

[0016] The machine learning module can be configured to operate general linear models, neural networks, Bayesian inference, Bayesian neural networks, deep neural networks, convolutional neural networks, or support vector machines.

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

[0018] The thickness probability distribution can provide photoresist thickness information in the X and Y directions.

[0019] The machine learning module can be further configured to determine the local intensity of the coordinates in the X and Y directions.

[0020] The machine learning module can be further configured to determine image contrast, image gradient, image log slope, or normalized image log slope in the X and Y directions.

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

[0022] In this example, the machine learning module includes a first model, a second model, and a third model. The first model predicts a mask diffraction pattern based on a rasterized mask image. The second model predicts an image in the photoresist based on the mask diffraction pattern. The third model predicts the photoresist thickness distribution based on the image in the photoresist.

[0023] A computer program product includes a computer-readable program having therein embodied a method configurable to perform the method of the first embodiment.

[0024] A second embodiment provides a system. The system includes a processor-operable machine learning module. The machine learning module is configured to determine a probability distribution of photoresist thickness in a semiconductor device based on a mask pattern.

[0025] The machine learning module can be configured to operate general linear models, neural networks, Bayesian inference, Bayesian neural networks, deep neural networks, convolutional neural networks, or support vector machines.

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

[0027] The thickness probability distribution can provide photoresist thickness information in the X and Y directions.

[0028] The machine learning module can be further configured to determine the local intensity, image contrast, image gradient, image log slope, or normalized image log slope of the coordinates in the X and Y directions.

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

[0030] In this example, the machine learning module includes a first model, a second model, and a third model. The first model predicts a mask diffraction pattern based on a rasterized mask image. The second model predicts an image in the photoresist based on the mask diffraction pattern. The third model predicts the photoresist thickness distribution based on the image in the photoresist.

[0031] The machine learning module can communicate electronically with an imaging system that includes an energy source and a detector. Attached Figure Description

[0032] For a more complete understanding of the nature and objectives of this disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, wherein:

[0033] Figure 1 The drawings are based on embodiments of this disclosure; and

[0034] Figure 2 This is a flowchart of the method according to this disclosure. Detailed Implementation

[0035] While the claimed subject matter will be described with reference to specific embodiments, other embodiments (including those that do not provide all the benefits and features set forth herein) are also within the scope of this disclosure. Various structural, logical, procedural, and electronic changes may be made without departing from the scope of this disclosure. Therefore, the scope of this disclosure is defined only by reference to the appended claims.

[0036] Photolithography can exhibit defects driven by the quantization properties of light and materials. For example, light is quantized into photons, and the chemical reactants in the photoresist are discrete molecules. These are often referred to as shot noise defects or random defects. These random defects can be common to EUV lithography but can also occur at exposure wavelengths used in other lithography processes, such as ArF immersion. “Randomness” means that the average behavior can simultaneously exhibit fluctuations (e.g., bridging or breaking of line / space patterns) within the desired specification (e.g., photoresist width, tip-to-tip measurement of line ends, or photoresist thickness) that cause the pattern to fail with a non-zero probability. Given that a wafer contains billions of transistors, even a very small probability of failure can lead to a large yield loss.

[0037] Random failures are typically detected using inspection tools and then characterized by top-down SEM. Inspection and characterization can occur after photolithography (post-development inspection (ADI)) or after subsequent etching or cleaning steps (post-etching inspection (AEI) or post-cleaning inspection (ACI)). AEI / ACI results are most relevant to yield and depend on the remaining photoresist thickness at the ADI.

[0038] The embodiments disclosed herein can use a model of localized photoresist thickness to predict these defects, enabling the complete chip layout to be characterized for random failures. This can be used to predict random variations in photoresist thickness. Unlike prior art, this metric determines photoresist thickness parameters at all locations (including locations where failures may occur). The embodiments disclosed herein can directly analyze photoresist thickness at all locations. Due to the direct correlation between photoresist thickness and pattern transfer errors during etching, photoresist thickness is an indicator of defect rate and yield. For example, if unwanted photoresist is found in a space (e.g., a space bridge defect) and its thickness exceeds a certain threshold, the etching process will be unable to remove material from the substrate in the space region as needed. Similarly, if the photoresist is not thick enough in a line region (e.g., a broken line defect), the etching process may remove the remaining photoresist and begin removing material from the substrate in the line region, which is undesirable. These photoresist thickness errors will cause pattern transfer errors regardless of whether edges (as defined in the XY plane) are nearby.

[0039] Localized photoresist thickness can be characterized using simulators such as PROLITH, a physics-based simulator sold by KLA Corporation. This can be presented as a cumulative histogram over a single example or many simulations to determine the probability distribution associated with the photoresist thickness. Physics-based models of lithography processes can be developed using methods similar to PROLITH. Simulators like PROLITH can be used to simulate random events, attributable to photon and chemical shot noise. This is typically performed using a Monte Carlo-type process that randomly samples known distributions (e.g., a Poisson distribution for photon absorptivity). Multiple simulations can be performed to generate samples of events for a given set of lithography conditions. The simulated responses (e.g., line width or aperture diameter) can be stratified into histograms to represent the probability of occurrence. These probability distributions of responses from such physics-based simulators have been shown to agree with experimentally determined results.

[0040] exist Figure 1 The image illustrates a machine learning module 100. The machine learning module 100 is configured to determine the probability distribution of photoresist thickness in a semiconductor device based on a mask pattern. The machine learning module 100 can be configured to operate a supervised machine learning model, which includes (but is not limited to) general linear models, neural networks, Bayesian inference, Bayesian neural networks, deep neural networks, convolutional neural networks, or support vector machines. Convolutional neural networks can be used for image input. Bayesian neural networks can be used to determine probabilities or distributions as output.

[0041] The machine learning module 100 can be trained using results from the simulator. The dataset can be a collection containing approximately 2000 mask patterns, each approximately 1 μm in size. In this example, intermediate data from the simulator can be used to train the machine learning module 100. This intermediate data can be used to create three separate models that can be linked during prediction. Therefore, simulations can be run with additional variations of common lithography parameters (such as exposure dose and focus settings) to produce intermediate results for training three models (e.g., models A, B, and C).

[0042] The model used by the machine learning module 100 can determine various properties near the region of interest. For example, Figure 1The illustrations contain exemplary photoresist lines. These lines contain defects that can cause problems during subsequent etching steps. Various properties can be determined at or around a region of interest, which may be located at or around coordinates in the X and Y directions. Properties can also be determined in aerial images or images within the photoresist. An image within the photoresist is an optical image of the interior of the photoresist formed during exposure; it can be the result of intermediate calculations and the output of one of three models (e.g., model B). It can be stored as the light intensity at sampled X, Y, and Z locations in a simulation domain. It can serve as initial data for subsequent chemical reactions that produce an embossed image or the actual physical shape of the photoresist after development.

[0043] Figure 2 This is a flowchart of method 200. In 201, a mask pattern of the semiconductor device is input into the machine learning module. The mask pattern can be viewed as a polygonal shape representing the chip designer's intent. It can be stored in various file types (e.g., design files). For actual machine learning training, it can be converted into a raster format (value table) in the X and Y dimensions.

[0044] The machine learning module can provide Figure 1 The machine learning module 100. In 202, a probability distribution of photoresist thickness in a semiconductor device is determined based on a mask pattern. The probability distribution is a mathematical function that gives the probability of different levels of photoresist thickness occurring. In practice, it means that the model output enters a function that defines the distribution with several values ​​of parameters (e.g., a count between 2 and 15). During model C training, the maximum likelihood principle can be applied to “teach” the model to produce the correct parameters for the probability distribution. Just as in any other machine learning process, the correctness of the model output (i.e., the distribution) can be evaluated by comparing it to the “true” output (e.g., a simulator photoresist relief) using a likelihood metric.

[0045] The machine learning module can be further configured to determine a probability map of the Z-height at coordinates, for example, in the X and Y directions. A probability map is a surface representing the probability of an event at each XY location. In this example, it is calculated using a distribution predicted by the model. The probability of the photoresist height at location X,Y being higher or lower than a threshold can be predicted. In locations (spaces) where low photoresist thickness is expected, even a low probability of having a thickness above the threshold is a sign of a potential (bridge-type) defect. Conversely, in locations (lines) where high photoresist thickness is expected, a probability of having a thickness below the threshold (too low) is an indication of a potential break-line defect. Figure 1 The subset illustrates that the thickness is non-uniform in the Z direction. These probabilities are calculated on a dense grid in the X, Y directions covering the entire area under test or the entire chip. The probability map can represent the Z-height of the photoresist surface and the photoresist thickness.

[0046] The thickness probability distribution provides Z-height information for the coordinates in the X and Y directions. The thickness probability distribution can be determined to an accuracy level of approximately 1 ppb. 1 ppb represents a probability of 10^-9, which is the target for the model's usability and accuracy. The target can be reduced to even lower levels, such as 10^-10, 10^-11, etc. The volume of photoresist in a specific region can also be determined. Characterizing the photoresist thickness offers advantages over simply characterizing edge placement errors (such as those typically output by optical proximity correction (OPC) and OPC verification software).

[0047] The statistical properties of the photoresist thickness (i.e., Z-height) in the Z-direction at coordinates in the X and Y directions can be determined. Therefore, the photoresist thickness in the Z-direction at discrete points on the photoresist structure or along the length of the photoresist structure can be determined. If the model is partitioned into parts A, B, and C, the steps may include using model A to predict the mask diffraction pattern based on the rasterized mask image and optionally using other imaging parameters (e.g., principal ray angle, etc.). Next, using model B, based on the mask diffraction pattern, optionally using defocus and other imaging parameters (e.g., principal ray angle, flare, aberration, etc.), the image in the photoresist can be predicted. Next, using model C, based on the image in the photoresist, optionally using exposure dose and other exposure and photoresist parameters, the photoresist thickness distribution parameters can be predicted. Using a threshold, the probability that the photoresist thickness is too low or too high can be predicted.

[0048] This method can be used to search for lithographic defects. Z-direction thickness tends to be more directly related to infrequent lithographic defects that limit yield. Regions of interest can be identified as locations where there is no intended photoresist (e.g., near the center of space) or a large amount of photoresist (e.g., near the center of a line). The probability that the photoresist thickness is too high or too low at these locations can be analyzed and reported. In one example, in a region where the photoresist should be completely removed, the Z-direction thickness can be characterized as a probability of approximately 1 ppb, but not limited to an accuracy level of 1 ppb. In another example, in a region where the full thickness of photoresist should be present, the Z-direction thickness can be characterized as a probability of approximately 1 ppb, but not limited to an accuracy level of 1 ppb. In yet another example, in any arbitrary region, the Z-direction thickness can be characterized as a probability of approximately 1 ppb, but not limited to an accuracy level of 1 ppb.

[0049] Other properties at coordinates in the X and Y directions can be determined, which may be properties of the image in the photoresist determined before the Z height. These properties include local intensity, image contrast, image gradient, image logarithmic slope, normalized image logarithmic slope, probability of the location of photoresist edges, or other properties.

[0050] The embodiments disclosed herein can be used to locate defects in photoresist. The embodiments disclosed herein can also be used to correct masks to avoid defects in photoresist. Therefore, the results of using the method can be used as a form of feedback for mask design. Process parameters (e.g., focus) during photoresist application can be modified based on the results of using this method.

[0051] exist Figure 1 In this embodiment, the machine learning module 100 also includes an optional imaging system 101 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 directed to the wafer. The energy source can be, for example, a light source or an electronic source. The detector is configured to detect energy reflected from the wafer to generate an image. The energy can be, for example, a light beam, an electron beam, an ion beam, or another type of particle beam. For example, an optical inspection system or SEM can provide continuous feedback to the machine learning module 100 by measuring photoresist samples on one or more wafers.

[0052] Imaging system 101 or its processor can be configured to transmit images of the wafer to machine learning module 100. The images can be used for additional training of the model operated by machine learning module 100. Therefore, wafers produced using information from machine learning module 100 can be used to further teach or enhance machine learning module 100. Other sample wafers or other production wafers can also be used to further teach or enhance machine learning module 100.

[0053] Machine learning module 100 and its subsystems may include personal computer systems, graphics computers, mainframe computer systems, workstations, network devices, Internet devices, or other devices. Machine learning module 100 or its subsystems may also include any suitable processor known in the art (e.g., a parallel processor). This processor can be used to operate the model. In this example, the processor may be or may include a graphics processing unit (GPU). Additionally, the subsystem or machine learning module 100 may include a platform with high-speed processing and software (as a standalone tool or a networked tool). Machine learning module 100 may include or be coupled to a display and user input device to select desired process parameters.

[0054] In some embodiments, the various steps, functions, and / or operations of the machine learning module 100 and its subsystems, as well as the methods disclosed herein, are implemented by one or more of the following: electronic circuits, logic gates, multiplexers, programmable logic devices, ASICs, analog or digital controllers / switches, microcontrollers, or computing systems. Program instructions for implementing methods such as those described herein may be transmitted via or stored on a carrier medium. The carrier medium may include storage media, such as read-only memory, random access memory, magnetic disks or optical disks, non-volatile memory, solid-state memory, magnetic tape, and the like. The carrier medium may include transmission media, such as wires, cables, or wireless transmission links. For example, the various steps described throughout this disclosure may be implemented by a single processor (or computer system) or alternatively by multiple processes (or multiple computer systems). Furthermore, the different subsystems of the neural network module 101 may comprise one or more computing or logic systems. Therefore, the foregoing description should not be construed as limiting the scope of this disclosure but is merely illustrative.

[0055] In this embodiment, a convolutional neural network (CNN) may be used in the machine learning module 100. A CNN is a type of feedforward artificial neural network in which the connectivity patterns between its neurons (i.e., pixel clusters) are inspired by the animal visual cortex. Individual cortical neurons respond to stimuli in a confined spatial region called a receptive field. The receptive fields of different neurons partially overlap, causing them to tile the visual field. The response of an individual neuron to stimuli within its receptive field can be mathematically approximated by a convolution operation.

[0056] CNNs can comprise multiple receptive fields. These are small sets of neurons that process portions of the input image. The outputs of these sets are then tiled so that their input regions overlap to obtain a better representation of the original image. This can be repeated for each such layer. Tiling allows the CNN to tolerate translations of the input image. CNNs can have a 3D volume of neurons. CNN layers can have neurons arranged in three dimensions: width, height, and depth. Neurons within a layer are connected only to a small region of the layer preceding them; this small region is called the receptive field. Dissimilar types of layers (both locally and fully connected) are stacked to form the CNN architecture. CNNs utilize spatial local correlations by reinforcing patterns of local connectivity between neurons in neighboring layers. The architecture ensures that learned filters produce the strongest response to spatially local input patterns. Stacking many such layers results in nonlinear filters that become increasingly global (i.e., responding to larger regions of pixel space). This allows the network to first produce a good representation of a small portion of the input and then assemble a representation of a larger region from it. In a CNN, each filter is replicated across the entire field of view. These replicated units share the same parameterization (weight vectors and biases) and form a feature map. This means that all neurons in a given convolutional layer detect exactly the same features. This replication of units allows features to be detected regardless of their position in the field of view, thus constituting the property of translation invariance.

[0057] These properties together allow CNNs to better generalize imaging problems. Weight sharing also helps by reducing the number of learned free parameters, thus reducing the memory requirements for running the network. Reduced memory footprint allows for the training of larger, more powerful networks. CNNs can contain local or global pooling layers that combine the outputs of clusters of neurons. Pooling layers can also consist of various combinations of convolutional and fully connected layers, where pointwise nonlinearity is applied at the end or after each layer. Introducing convolutional operations on small regions of the input reduces the number of free parameters and improves generalization. One advantage of convolutional networks is the use of shared weights in convolutional layers, meaning the same filters (weight library) are used for every pixel in the layer. This also reduces memory footprint and improves performance.

[0058] A CNN architecture can be formed by stacking dissimilar layers that transform the input volume into an output volume (e.g., preserving class scores) via a differentiable function. Several dissimilar types of layers can be used. A convolutional layer has various parameters consisting of a set of learnable filters (or kernels) with small receptive fields but extending through the full depth of the input volume. During forward passes, each filter is convolved across the width and height of the input volume, thereby computing the dot product between the filter entry and the input and producing a two-dimensional activation map of the filter. Thus, the network learns filters that activate when they see a specific type of feature at a spatial location in the input. By stacking the activation maps of all filters along the depth dimension, the full output volume of the convolutional layer is formed. Each entry in the output volume can also be interpreted as the output of a neuron that views a small region in the input and shares parameters with neurons in the same activation map.

[0059] When processing high-dimensional inputs such as images, connecting neurons to all neurons in a previous volume can be impractical because this network architecture does not consider the spatial structure of the data. CNNs can leverage spatial local correlations by reinforcing patterns of local connectivity between neurons in neighboring layers. For example, each neuron connects only to a small region of the input volume. The degree of this connectivity is a hyperparameter called the neuron's receptive field. Connections can be spatially local (along width and height) but can extend along the entire depth of the input volume. This architecture ensures that learned filters produce the strongest response to spatially local input patterns. In one embodiment, training a CNN involves using transfer learning to generate the hyperparameters for each CNN. Transfer learning may involve training the CNN on a very large dataset and then using the trained CNN weights as initialization or fixed feature extractors for the task of interest.

[0060] For example, three hyperparameters control the size of the output volume of a convolutional layer: 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 these neurons will learn to activate different features in the input. For example, if the first CNN layer takes the original image as input, then different neurons along the depth dimension can be activated in the presence of various oriented edges or color spots. The stride controls how the depth columns are distributed around the spatial dimensions (width and height). When the stride is one, new neuron depth columns are assigned to spatial locations separated by only one spatial unit. This results in heavily overlapping receptive fields between columns and also a large output volume. Conversely, if a higher stride is used, the receptive fields will overlap less, and the resulting output volume will have a smaller spatial size. Sometimes, it is convenient to use zero-padding on the boundaries of the input volume. The size of this zero-padding is the third hyperparameter. Padding provides control over the spatial size of the output volume. Specifically, sometimes it is desirable to precisely preserve the spatial size of the input volume.

[0061] In some embodiments, a parameter sharing scheme can be used in layers to control the number of free parameters. If a tile feature can be computed at one spatial location, it can also be computed at different locations. In other words, when a single 2D depth slice is represented as a depth slice, neurons in each depth slice can be restricted to using the same weights and biases.

[0062] Since all neurons in a single depth slice can share the same parameterization, the forward pass in each depth slice of a layer can be computed as a convolution of the neuron's weights with the input volume. Therefore, the weighted array is often referred to as a filter (or kernel), which is convolved with the input. The result of this convolution is an activation map, and the activation maps of each different filter are stacked together along the depth dimension to produce the output volume.

[0063] Sometimes, for example, when the input image to a CNN has a particular centered structure in which completely different features are expected to be learned at different spatial locations, parameter sharing may be ineffective.

[0064] Pooling is another feature of CNNs, and it is a form of non-linear downsampling. Several non-linear functions exist for performing pooling, with max pooling being one. Max pooling partitions the input image into a set of non-overlapping rectangles and outputs the maximum value for each such sub-region. Once a feature is found, its precise location may not be as important as its approximate location relative to other features. The function of pooling layers is to progressively reduce the size of the representation space, thereby reducing the number of parameters and computation in the network, and thus controlling overfitting. Pooling layers can be positioned between consecutive cone layers in a CNN architecture.

[0065] Another layer in a CNN can be a ReLU (Rectified Linear Unit) layer. This is a layer of neurons that applies a non-saturating activation function. ReLU layers can increase the non-linearity of the decision function and the overall network without affecting the receptive field of the convolutional layers.

[0066] Finally, after several convolutional and / or max-pooling layers, higher-order inference in the neural network is performed via fully connected layers. Neurons in fully connected layers have complete connections to all activations in previous layers. These activations can be computed using matrix multiplication followed by bias offsets.

[0067] In some embodiments, dropout techniques can be used to prevent overfitting. As mentioned herein, dropout is a regularization technique used to reduce overfitting in neural networks by preventing complex co-adaptation to training data. The term "dropout" refers to discarding units (both hidden and visible) from a neural network. For example, at each training phase, individual nodes may be "dropped" from a CNN with probability 1-p or retained with probability p, such that the simplified CNN is preserved. In some embodiments, incoming and outgoing edges to the dropped nodes may also be removed. Only the simplified CNN is trained. The removed nodes can then be reinserted into the network with their original weights.

[0068] During training, the probability that a hidden node will be retained (i.e., not dropped) can be approximately 0.5. For input nodes, the retention probability can be higher. By avoiding training all nodes on all training data, dropping nodes reduces overfitting in CNNs and improves training speed.

[0069] Training data can be input into model training (e.g., CNN training), which can be performed in any suitable manner. For example, model training may involve inputting training data into a CNN and modifying one or more parameters of the model until the model's output is the same (or substantially the same) as external validation data. Model training may produce one or more trained models, which can then be sent to model selection, performed using validation data. The results produced by each of the one or more trained models for the validation data input into 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 the result that most closely matches the validation data can be selected as the best model. Test data can then be used for model evaluation of the selected model (e.g., the best model). 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 testing tool for use (post-training mode).

[0070] Many different types of CNNs can be used in the embodiments of this disclosure. Different CNNs can be used based on certain scanning patterns or conditions. The configuration of the CNN can be changed based on simulator configuration, chip, image data acquisition subsystem, or predetermined parameters.

[0071] Other models can be used in the 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 via a directed acyclic graph. Bayesian networks can employ the likelihood of an event occurring and predicting that any of several possible known causes is a contributing factor.

[0072] Additional embodiments relate to a non-transitory computer-readable medium storing program instructions that can be executed by a processor to perform a computer-implemented method for determining process parameters, as disclosed herein. Electronic data storage units or other storage media may contain a non-transitory computer-readable medium containing program instructions executable on a neural network module. The computer-implemented method may include any step of any method described herein (including method 200).

[0073] Each step of the method can be performed as described herein. The method may also include any other steps that can be performed by the processor and / or computer subsystem or system described herein. The steps may be performed by one or more computer systems, which may be configured according to any embodiment described herein. Furthermore, the method described above can be performed by any system embodiment described herein.

[0074] While this disclosure has been described with respect to one or more specific embodiments, it should be understood that other embodiments of this disclosure may be made without departing from its scope. Therefore, this disclosure is to be considered limited only by the appended claims and their reasonable interpretation.

Claims

1. A method comprising: A mask pattern of a semiconductor device is input into a machine learning module, wherein the mask pattern is a design file containing a polygonal shape of a mask; and Based on the mask pattern, the machine learning module is used to determine the photoresist thickness probability distribution of the semiconductor device, wherein the machine learning module includes a first model, a second model, and a third model, wherein the first model predicts the mask diffraction pattern based on the rasterized mask image, wherein the second model predicts the image in the photoresist based on the mask diffraction pattern, and wherein the third model predicts the photoresist thickness distribution based on the image in the photoresist.

2. The method of claim 1, wherein the machine learning module is configured to operate 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.

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

4. The method according to claim 1, wherein the thickness probability distribution provides photoresist thickness information in the X and Y directions.

5. The method of claim 4, wherein the machine learning module is further configured to determine the local intensity of coordinates in the X direction and the Y direction.

6. The method of claim 4, wherein the machine learning module is further configured to determine image contrast in the X direction and the Y direction.

7. The method of claim 4, wherein the machine learning module is further configured to determine the image gradients of the coordinates in the X direction and the Y direction.

8. The method of claim 4, wherein the machine learning module is further configured to determine the image log slope of the coordinates in the X direction and the Y direction.

9. The method of claim 4, wherein the machine learning module is further configured to determine the normalized image log slope of the coordinates in the X direction and the Y direction.

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

11. The method of claim 1, further comprising training the machine learning module, wherein, The training includes: Intermediate data is generated from the simulator using a set of mask patterns; and The intermediate data is used to train the machine learning module.

12. A computer program product comprising a non-transitory computer-readable storage medium having a computer-readable program embodied therein, the computer-readable program being configured to perform the method according to claim 1.

13. A system comprising: A machine learning module is configured to operate using a processor that communicates electronically with an imaging system, the imaging system including an energy source and a detector, wherein the machine learning module is configured to determine a probability distribution of photoresist thickness in a semiconductor device based on a mask pattern, wherein the mask pattern is a design document containing a polygonal shape of a mask, wherein the machine learning module includes a first model, a second model, and a third model, wherein the first model predicts a mask diffraction pattern based on a rasterized mask image, wherein the second model predicts an image in the photoresist based on the mask diffraction pattern, and wherein the third model predicts a photoresist thickness distribution based on the image in the photoresist.

14. The system of claim 13, wherein the machine learning module is configured to operate 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.

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

16. The system of claim 13, wherein the thickness probability distribution provides photoresist thickness information in the X and Y directions.

17. The system of claim 16, wherein the machine learning module is further configured to determine local intensity, image contrast, image gradient, image log slope, or normalized image log slope of coordinates in the X and Y directions.

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

19. The system of claim 13, wherein the machine learning module is trained using intermediate data from a simulator, wherein the intermediate data is generated from a set of mask patterns.

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