Large scale complex lithography using machine learning models

Abstract

Embodiments of the present disclosure relate to large scale complex lithography using machine learning models. A computational lithography process uses a machine learning model. A first spatial image resulting from a lithography mask is computed using a two-dimensional model of the lithography mask. This first spatial image is applied to a first machine learning model which infers a second spatial image. The first machine learning model is trained using a training set comprising spatial images computed using a more accurate three-dimensional model of the lithography mask. The two-dimensional model is faster to compute than the three-dimensional model, but it is less accurate. The first machine learning model mitigates this inaccuracy.

Description

[0001] Related applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 194,801, filed May 28, 2021, entitled "Large-scale computational lithography using machine learning models". All the subject matter of the foregoing is incorporated herein by reference in its entirety. Technical Field

[0003] This invention generally relates to computational lithography. More specifically, this disclosure relates to computational lithography using machine learning models. Background Technology

[0004] One step in semiconductor wafer fabrication involves photolithography. In a typical photolithography process, a light source generates light, which is collected and guided by a collection / irradiation optics to illuminate a photomask. A projection optics relays the pattern generated by the illuminated mask onto the wafer. The resulting light distribution (called a spatial image) exposes the resist on the wafer according to the illumination pattern of the spatial image. The patterned photoresist is then developed and the resulting photoresist structure is used in processes for fabricating structures on the wafer.

[0005] Because photomasks are complex and expensive to manufacture, simulations are used to design them and to design the entire photolithography process. These computer simulations are called computational lithography. A typical computational lithography workflow is based on physical models. It can involve rigorously solving Maxwell's equations in three dimensions, solving the differential equations that control the reaction-diffusion process, and solving other mathematical models of the underlying physical processes. The end result can be a prediction of the three-dimensional (3D) resist profile. However, implementing this conventional computational lithography workflow can be computationally expensive. Summary of the Invention

[0006] In some aspects, computational lithography uses machine learning models instead of computationally expensive physical models. First, a two-dimensional model of the lithographic mask is used to compute a spatial image generated by the mask. This first spatial image is applied to a first machine learning model, which infers a second spatial image. The first machine learning model is trained using a training set that includes spatial images computed using a more accurate three-dimensional model of the lithographic mask. The two-dimensional model is computationally faster than the three-dimensional model, but it is less accurate. The first machine learning model mitigates this inaccuracy.

[0007] In other aspects, an exposure model is applied to a second-space image to generate an acidic latent image. This acidic latent image is then applied to a second machine learning model, which infers the resist profile from it. The exposure model is a simplified model that is computationally fast but less accurate than desired, and the second machine learning model mitigates this inaccuracy.

[0008] Other aspects include components, devices, systems, improvements, methods, processes, applications, computer-readable media, and other technologies related to any of the above. Attached Figure Description

[0009] This disclosure will be more fully understood from the following detailed description and the accompanying drawings illustrating embodiments of the present disclosure. The drawings are provided to give knowledge and understanding of embodiments of the present disclosure and are not intended to limit the scope of the disclosure to these specific embodiments. Furthermore, the drawings are not necessarily drawn to scale.

[0010] Figure 1 This is a flowchart of the computational lithography process according to an embodiment of the present invention.

[0011] Figure 2A and Figure 2B An example architecture of a machine learning model according to an embodiment of this disclosure is shown.

[0012] Figure 3A and Figure 3B This is a flowchart of training a machine learning model according to an embodiment of the present disclosure.

[0013] Figure 4 It is a weighted graph of the cost function according to an embodiment of the present disclosure.

[0014] Figure 5 Flowcharts depicting various processes used during the design and manufacture of integrated circuits according to some embodiments of the present invention are described.

[0015] Figure 6 A diagram depicts an example computer system in which embodiments of the present disclosure may be operated. Detailed Implementation

[0016] Various aspects of this disclosure relate to large-scale computational lithography using machine learning models. Instead of performing computationally expensive simulations based on mathematical models of the underlying physical processes, machine learning models are trained to infer desired results and then used in the computational lithography process to augment faster but less accurate simulation models. This accelerates the overall simulation while maintaining sufficient accuracy.

[0017] Traditional computational lithography workflows begin by simulating a spatial image generated from a topographical (3D) description of the photomask. This uses a computationally expensive process of solving Maxwell's equations in 3D to calculate the electric field behind the photomask given an incident electric field on it. From this, the intensity distribution within the photoresist layer is calculated. This is then used to calculate the acid latent image, taking into account the exposure dose. In the next step, the reaction diffusion process during post-exposure baking and possible mechanical deformation processes is calculated. This is another computationally expensive process. The resulting information is used to obtain the development rate for simulating the formation of the lithographic pattern within the photoresist. Simulation of the development process is also computationally expensive.

[0018] While the total throughput based on physical models can be mathematically accurate, it is computationally expensive. This limits its application. For example, it may be too expensive to actually run these simulations on mask areas larger than approximately 10µm × 10µm. Running these simulations multiple times may also be too slow when iterating the design of lithographic masks. The computationally expensive throughput also requires more computational resources, including more memory, more processing power, and more communication bandwidth. This also increases the cost.

[0019] In one aspect, computationally expensive models are replaced by faster-running trained machine learning models. For example, instead of using a 3D model of a lithographic mask and then rigorously solving Maxwell's equations in 3D to predict the spatial image generated by the mask, a faster 2D model coupled with a machine learning model trained to infer the differences between the 2D and 3D mask models can be used. The 2D mask model simulates faster, and the machine learning model reduces accuracy loss. Supervised learning can be used to train the machine learning model, where the training set includes spatial images computed using the 2D model and corresponding spatial images computed using the 3D model.

[0020] A similar approach can be used to simulate the resist profile generated by a given acidic latent image. Instead of using computationally expensive models based on reaction-diffusion processes during post-exposure baking, possible mechanical deformation, and resist development, a machine learning model is used. A simple exposure model can be used to calculate the acidic latent image from a spatial image, and then the machine learning model infers the resist profile from the acidic latent image. Supervised learning can also be used, training the machine learning model based on training samples calculated using more complex models.

[0021] Using machine learning models in this way can lead to faster runtimes for computational lithography simulations while maintaining sufficient accuracy. This can accelerate design time and reduce costs. It enables computational lithography to be used in situations that were previously infeasible, such as when the mask area is too large or too many simulations are required. The use of machine learning models can also reduce the computational resources required: less memory, less processing power, and less communication bandwidth.

[0022] Figure 1 This is a flowchart of a computational lithography process according to an embodiment of the present disclosure. Figure 1 The left side shows the lithography system 120, and Figure 1 The right side illustrates the computational lithography flow used to simulate this system. In the lithography system 120, a light source (not shown) generates a light distribution (irradiation field 122) incident on a lithographic mask 124 having a specific mask topology. Light from the irradiation field 122 propagates through the lithographic mask 124, resulting in a light distribution referred to as the near field. This light is imaged by projection optics 126 onto a resist 128 on a substrate 130 (e.g., a semiconductor wafer). The light distribution irradiating the resist 128 is referred to as the spatial image. The spatial image exposure results in resist processes (e.g., including exposure, post-exposure baking (PEB), and development) that shape (contour) the resist 128.

[0023] Figure 1 The right side illustrates the computational lithography flow for predicting the resist profile 116 from the lithographic mask description 100. The two-dimensional (2D) mask model 102 uses the lithographic mask description 100 as input and predicts the resulting spatial image 104, which will be referred to as a two-dimensional mask model (2DMM) spatial image because it is based on a two-dimensional model of the lithographic mask 124. The model that generates the 2DMM spatial image may include a model for irradiating the mask, a thin mask model, and an imaging model for projecting the light field from the mask onto the resist location.

[0024] Thin mask model 102 models the lithographic mask as a thin sheet, where each point on the sheet affects the phase and amplitude of the incident illumination, but ignores other effects caused by the mask's thickness. As a result, the thin mask model can be computed relatively quickly. This contrasts with a full three-dimensional mask model, where three-dimensional topological effects during mask diffraction are also considered, for example, to predict behaviors such as critical size (CD), pattern shift, guide tilt, and optimal focus shift. In a rigorous three-dimensional mask model, the mask diffraction process is governed by Maxwell's equations and is typically solved in three dimensions using a rigorous electromagnetic field (EMF) solver applied to the three-dimensional description of the lithographic mask.

[0025] The effect of the projection optics 126 can be modeled using either the Abbe imaging model or the Hopkins imaging model. For applications such as full-chip optical proximity correction (OPC) or inverse lithography (ILT), the Hopkins imaging model combined with singular value decomposition (SVD) can be used to improve computational efficiency.

[0026] Two-dimensional mask model 102 is computed faster than three-dimensional mask model, but it largely ignores the effects of the three-dimensional topology of the mask. These effects are taken into account by the first machine learning model 106, as described in more detail below. The 2DMM spatial image 104 is applied to the first machine learning model 106, which infers a spatial image 108 that mitigates the inaccuracies caused by ignoring the effects of the three-dimensional mask.

[0027] For example, spatial images 104 and 108 can be represented by two-dimensional slices of the spatial images at different z-heights. The first machine learning model 106 can consider the interactions between the different slices, which can be ignored by the two-dimensional mask model. For convenience, spatial image 108 will be referred to as a three-dimensional mask model (3DMM) spatial image because it takes into account three-dimensional masking effects, even though it is not directly generated by applying a three-dimensional mask model such as Maxwell's equations. The 3DMM spatial image 108 considers the three-dimensional topology of the lithographic mask, but the computational cost required for a full three-dimensional simulation based on Maxwell's equations is avoided by using the first machine learning model 106.

[0028] exist Figure 1 In this process, spatial images 104 and 108 are normalized relative to the exposure dose. The exposure dose is a measure of the amount of energy used to expose the resist. Because they are normalized, spatial images 104 and 108 are dose-independent and do not need to be recalculated with dose changes. The actual dose 109 is applied to the 3DMM spatial image 108 using exposure model 110. This results in an acid latent image 112. Then, a second machine learning model 114 infers the three-dimensional resist profile 116 corresponding to the acid latent image 112. In a more rigorous conventional approach, the reaction-diffusion process during post-exposure baking and possible mechanical deformation processes is calculated. The resulting information is used to obtain the development rate for simulating the formation of photolithographic patterns within the photoresist. The development process is modeled, including the resist shrinkage effect. In some cases, these more complex models can solve partial differential equations to describe these resist processes. Here, the second machine learning model 114 replaces these more computationally expensive models.

[0029] Figure 1One advantage of the computational lithography process described herein is that the three-dimensional information and effects of the mask, the intensity distribution, and the concentration of relevant chemicals in the resist are considered by the first machine learning model 106 and the second machine learning model 114 to generate a three-dimensional resist profile 116. This can lead to more accurate predictions because the properties of any mask (intensity, concentration, etc.) at one z-height or the resist can influence the properties at another z-height.

[0030] In some implementations, all simulation results 104, 108, 112, and 116 are three-dimensional. Spatial images 104 and 108 represent the intensity distribution throughout the entire volume, also describing the acid latent image, and the resist profile is a description of the three-dimensional shape of the resist. These three-dimensional quantities can be represented as a set of two-dimensional slices at different heights. In some cases, all four of these quantities have the same number of slices at the same z-height.

[0031] Figure 1 Another feature of the computational lithography process described herein is that it can be applied to different exposure doses 109 without switching or retraining the first machine learning model 106 and the second machine learning model 114. The same machine learning models can be used for different dose conditions, for example, by normalizing them relative to the dose or by training them for different dose conditions. Furthermore, the first machine learning model 106 and the second machine learning model 114 preferably do not use the dose as input, such that the dose is used only by the exposure model 110.

[0032] Figure 2A and Figure 2B Example architectures of the first machine learning model 106 and the second machine learning model 114 are shown. Figure 2A As shown, two machine learning models 106 and 114 form a dual U-net structure. The first machine learning model 106 is one U-net, and the second machine learning model 114 is another U-net. The arrangement of these two U-net structures is such that the output from the first machine learning model 106 becomes the input to the second machine learning model 114 via the exposure model 110.

[0033] Figure 2BThis is a diagram of the first U-net machine learning model 106. The U-net structure includes a contraction path 240 and a dilation path 260. The contraction path 240 includes a series of convolutional stages 242 linked together by a downsampling stage 244. The convolutional stages 242 perform convolutions and can also apply nonlinear functions. If the input to the convolutional stage 242 has dimensions M x M x J, where the image size is M x M with J channels, then the output of the stage typically has dimensions N x M x K, where N ≈ M and K > J. Within the convolutional stages 242, the image size remains approximately the same, but the number of channels increases as more features are developed. The downsampling stage 244 reduces the resolution of the image size. For example, if the input to the downsampling stage 244 has size M x M x J, then the output can have size (M / 2) x (M / 2) x J. Different downsampling techniques can be used. One example is blurring, followed by max pooling. This has the advantage of improving the model relative to shifting in the input. Physically, a shift in the input will result in a corresponding shift in the output, so machine learning models should also exhibit that behavior. Fuzzy pooling exhibits this behavior, while other types of downsampling do not.

[0034] The dilation path 260 reverses the size change of the contraction path 240. The convolutional stage 242 has a corresponding stage 262 that can be implemented in different ways. For example, stage 262 may include two operations: convolution and a concatenation of the convolution's output with skip connection 250. As another example, stage 262 could be a transposed convolution. The downsampling stage 244 has a corresponding upsampling stage 264.

[0035] Since the output of the U-net model is not only classes or labels, but also images, which in most cases have a similar size to the input, upsampling in the dilation path 260 is used to recover resolution and information from the feature map. Different methods can be used: interpolation, such as bilinear, bicubic and nearest neighbor, non-pooling, and transposed convolution. This specific example uses bilinear interpolation.

[0036] Skip connection 250 to pass data from contraction path 240 to expansion path 260. In this way, features generated at each stage 242 of contraction path 240 can be collected along expansion path 260.

[0037] In some implementations, the input to the first U-net 106 is a 2DMM spatial image 104 represented as an MxMxJ array, where the j-index represents an MxM slice of the spatial image at different z-heights. The output of the first U-net 106 is a 3DMM spatial image 108, which also has a size of MxMxJ. The two spatial images 104 and 108 are sampled at the same (x, y, z) spatial location.

[0038] exist Figure 2AIn the equation, exposure model 110 is given by a single equation:

[0039] Acidic latent image = 1 - exp(-C*D*(3DMM spatial image)) (1)

[0040] Where C is a parameter and D is the exposure dose 109. The 2DMM spatial image 104 and the 3DMM spatial image 108 are normalized relative to the dose, and the exposure dose 109 is then considered as Equation 1. Therefore, the first machine learning model 106 can be used for different dose values, because Equation 1 defines a one-to-one mapping between the 3DMM spatial image and the acid latent image. Each sample in the MxMxJ samples of the 3DMM spatial image 108 is transformed into a corresponding sample of the acid latent image 112. The resulting acid latent image 112 also has a size MxMxJ sampled at the same (x, y, z) spatial location.

[0041] The second U-net machine learning model 114 has a similar structure to the first U-net 106, with corresponding contraction paths 270, expansion paths 290, and cross links 280. The input is an MxMxJ acidic latent image 112, and the output is a resist profile 116. The resist profile 116 can also be represented by an MxMxJ array. Each of the J slices defines the contour (edge) of the resist at that z-height. The contour can be represented by a signed distance value function. The value of the function at each (x, y) sampling point has a magnitude and a sign. The magnitude is the distance from the sample point to the nearest resist profile, and the sign indicates whether the sample point is located inside or outside the nearest resist profile (i.e., inside or outside the three-dimensional resist structure).

[0042] In the example in Figure 2, the first machine learning model 106 and the second machine learning model 114 are supervised deep learning models. Supervised deep learning models are trained using a training set with known input-output pairs. The output of each pair can be referred to as the ground truth or the target. Two machine learning models, 106 and 114, can be trained separately.

[0043] Figure 3A and Figure 3B These are flowcharts illustrating the training of a first machine learning model 106 and a second machine learning model 114 according to embodiments of the present disclosure. These figures show the generation of the training set and the training of the first machine learning model 106 and the second machine learning model 114. This is done for convenience. It does not mean that these steps must occur simultaneously. For example, the training set can be generated separately and then used to train the machine learning model at a later time.

[0044] like Figure 3AAs shown, the first machine learning model 106 receives a 2DMM spatial image 104 as input. This is computed by applying a two-dimensional mask model 102 to the design of the lithographic mask 100. The output of the first machine learning model 106 is a 3DMM spatial image 108. For the training set, a ground truth 3DMM spatial image 308 is computed using a three-dimensional mask model 302. This can be a physical simulation model, such as a rigorous solution to Maxwell's equations. The training set of the first machine learning model 106 then includes input / output pairs of (a) the 2DMM spatial image 104 computed using the two-dimensional model of the lithographic mask and (b) the corresponding ground truth 3DMM spatial image 308 computed using the three-dimensional model 302 of the lithographic mask. For convenience, the spatial images 104 and 308 in the training set can be referred to as the training spatial images. The output 3DMM spatial image 108 inferred by the first machine learning model 106 is compared with the ground truth spatial image 308 in the training set, and the first machine learning model 106 is trained based on this comparison.

[0045] 2DMM spatial images offer advantages because they are continuous and constrained in the frequency domain, thus potentially without information loss when represented on a pixel grid. 2DMM spatial images also include information about defocus and other aberrations. Therefore, a first machine learning model 106 can be trained to account for these, rather than requiring different machine learning models for different amounts of defocus or aberrations.

[0046] Figure 3B A similar method is shown for the second machine learning model 114. This second machine learning model 114 receives an acidic latent image 112 as input. The acidic latent image 112 can be generated from a spatial image, for example, by applying Equation 1. The output of the second machine learning model 114 is a resist profile 116, represented, for example, as a signed distance value. Based on explicitly tracking the profile, the signed distance value has advantages over the descriptive one. Compared to a binary cost function, it allows for a smoother cost function and makes it easier to give weights based on the profile, as in... Figure 4 As described in [the document]. For the training set, a physical model 314 for resist exposure and development is used to determine the ground truth resist profile 316. The training set for the second machine learning model 114 includes input / output pairs of (a) the acid latent image 112 and (b) the corresponding ground truth resist profile 316. The resist profile 116 inferred by the second machine learning model 114 is compared with the ground truth resist profile 316 in the training set, and the second machine learning model 114 is trained based on this comparison 317.

[0047] An exposure model 110 may also be included for training purposes. In this case, a 3DMM spatial image can be used as input. Parameters for the exposure model, such as C in Equation 1, can be adjusted by training a second machine learning model 114.

[0048] In some embodiments, the first machine learning model 106 and the second machine learning model 114 use multiple slices (e.g., 3-7 slices) at different z-heights. This captures three-dimensional information about the resist profile 116, such as the sidewall angles of the resist profile. It also increases the accuracy of the inference model. As an example, for the case of three z-heights, the first machine learning model 106 throughout the process takes three slices of a 2DMM spatial image as input and three slices of a 3DMM spatial image as output. Then, the second stages 110-114 use the three 3DMM spatial images output from the first machine learning model 106 as input and use the three slices of the photoresist profile 116 as targets. This improves the overall model accuracy compared to training using only one slice, because the interactions between slices can be taken more directly into account.

[0049] Training steps 309 and 317 for the two machine learning models use a cost function. This cost function can be weighted based on the ground truth outputs from the training set. For the first U-net106, the ground truth aerial image 308 can be used as the weights. This will assign greater weights to regions with higher light intensity.

[0050] For the second U-net 114, the weight W can be given by the following equation.

[0051] W = exp(-α·SD) 2 (2) Where SD = signed distance value, and α = constant. This assigns more weight to points closer to the contour. The constant value α in Equation 2 determines the width of the region surrounding the contour in which the weight is greater. A larger α value means the weight W decreases more quickly.

[0052] An example of this weighting relationship is shown in Figure 4 In the diagram, the x-axis represents the position, and the y-axis represents the weight value W at that position. In this example, the profile is located at the position marked by the dashed line 410. For example, the resist feature could be a line with edges at both positions 410. The weight W has a maximum value of 1 at these positions because the signed distance value is 0. The weight W decreases as the position moves away from the profile position 410.

[0053] During training, the entire model utilizes 2DMM and 3DMM spatial images along with a signed distance function, as it trains two separate machine learning models. The 2DMM and 3DMM spatial images are input / output pairs for one machine learning model, and the 3DMM spatial image and signed distance function for the resist profile are input / output pairs for the other machine learning model. During inference, the entire process can predict the signed distance function by taking only the 2DMM spatial image as input. The 2DMM spatial image is sufficient because the 3D effect is learned and overridden by the deep learning model. The overall runtime is reduced because the computation of the 2DMM spatial image is faster. In addition to the 2DMM spatial image, the overall model also takes dose values ​​as input, which are then used internally to create a latent image without adding additional computational load.

[0054] The above method has been tested with different datasets from different sources. The results show that the model delivers the advantage of simulating large areas. Table 1 below shows a runtime comparison between the rigorous 3D model (e.g., the S-lithography HPL model) and the current deep learning model shown in Figure 2.

[0055] Table 1 compares the runtime of a 300µm×300µm region between a rigorous 3D model and a deep learning model using 800 cores.

[0056]

[0057] As shown in Table 1, deep learning models have a significantly faster turnaround time (TAT) than rigorous 3D models. For a 1mm × 1mm region with the same number of cores (800), a TAT of 1.8 days (43h14m) is achieved, whereas with rigorous 3D models, large areas typically require too long a TAT to be feasible. The TAT figures shown in Table 1 are measured for a fully rigorous large-scale lithography rule-check process (in this example, Proteus lithography rule-check or PLRC) that includes PLRC runtime. Therefore, the TAT (time required to simulate resist profiles) of pure simulation obtained using deep learning methods is much higher.

[0058] The method described above accelerates the simulation of 3D photoresist profiles by using 2DMM spatial images as input, while incorporating the computationally time-consuming aspect into the machine learning model. This allows for the simulation of larger areas within a reasonable timeframe. Rigorous 3D models are typically limited to smaller areas of approximately 10µm × 10µm without partitioning, while the method described in this paper can be feasible for areas of 100µm × 100µm, 1mm × 10mm, or even larger. Even larger areas can be partitioned into tiles, where each tile is simulated to generate a corresponding tile of the 3D resist profile. These tiles are then assembled to generate the 3D resist profile over the entire area. Simulations of different tiles can be performed in parallel.

[0059] Furthermore, this also significantly reduces training time because training is performed only once for different dose / defocus conditions within a single model. In the example above, a rigorous S-lithography printing model was used to create the training dataset. Therefore, the deep learning model learns different effects and captures them in the predicted output. This method also has the advantage of reducing memory usage during simulation. It addresses the memory issues faced during simulations over large areas.

[0060] The computational lithography process described above can be used for various applications. For example, it can be used to predict resist profiles. If the predicted resist profile does not match the desired profile, this can be used to correct various aspects of the lithography system: source design, photomask design, etc. Once the photomask and lithography system are designed, the computational lithography process can be used to verify the correctness of the design.

[0061] Figure 5 An exemplary set of processes 500 is illustrated during the design, verification, and manufacturing of an article of art, such as an integrated circuit, for converting and verifying design data and instructions representing the integrated circuit. Each of these processes can be constructed and implemented as multiple modules or operations. The term "EDA" stands for "Electronic Design Automation." These steps begin with the creation of a product concept 510 using information provided by the designer, which is then converted into information to create an article of art using a set of EDA processes 512. When the design is complete, it is tape-out 534, where tape-out refers to the original pattern (e.g., geometric pattern) of the integrated circuit being sent to a manufacturing apparatus to create a mask set, which is then used to manufacture the integrated circuit. After tape-out, semiconductor dies are fabricated 536, and packaging and assembly processes 538 are performed to produce a finished integrated circuit 540.

[0062] Specifications for circuits or electronic structures can range from low-level transistor material placement to high-level description languages. High levels of abstraction can be used to design circuits and systems using hardware description languages ​​(“HDLs”) such as VHDL, Verilog, SystemVerilog, SystemC, MyHDL, or OpenVera. HDL descriptions can be translated into logic-level register-transfer-level (“RTL”) descriptions, gate-level descriptions, placement-level descriptions, or mask-level descriptions. Each lower level of abstraction, which is a less abstract description, adds more useful details to the design description; for example, more details for modules include descriptions. Lower levels of abstraction, which are less abstract descriptions, can be computer-generated, exported from design libraries, or created by another design automation process. An example of a specification language used to specify a lower level of abstraction with more detailed descriptions is SPICE, used for detailed descriptions of circuits with many analog components. The description at each level of abstraction is enabled to be used by the corresponding tools at that layer (e.g., formal verification tools). The design process can use... Figure 5 The sequence described herein. A process that can be described by an EDA product (or tool).

[0063] During system design phase 514, the functionality of the integrated circuit to be manufactured is specified. The design can be optimized for desired characteristics such as power consumption, performance, area (physical and / or lines of code), and cost reduction. At this stage, the design can be divided into different types of modules or components.

[0064] During logic design and functional verification 516, modules or components in a circuit are specified in one or more description languages, and the functional accuracy of that specification is checked. For example, components of a circuit can be verified to generate outputs that conform to the requirements of the specifications of the circuit or system being designed. Functional verification can use simulators and other programs, such as test bench generators, static HDL checkers, and formal verifiers. In some embodiments, a special system of components referred to as a “simulator” or “prototype system” is used to accelerate functional verification.

[0065] During synthesis and design 518 for testing, HDL code is converted into a netlist. In some embodiments, the netlist may be a graph structure, where edges of the graph structure represent components of the circuit, and nodes of the graph structure represent how the components are interconnected. Both HDL code and netlist are hierarchical artifacts that can be used by EDA products to verify whether the integrated circuit functions according to a specified design during manufacturing. The netlist can be optimized for a target semiconductor manufacturing technology. Additionally, the completed integrated circuit can be tested to verify that it meets specifications.

[0066] During netlist verification (520), the consistency between the netlist and timing constraints, as well as the correspondence between the netlist and HDL code, are checked. During design planning (522), the overall layout of the integrated circuit is constructed and analyzed for timing and top-level routing.

[0067] During layout or physical implementation 524, physical placement (positioning of circuit components such as transistors or capacitors) and wiring (connecting circuit components through multiple conductors) are performed, and cells can be selected from a library to implement a specific logic function. As used herein, the term "cell" can specify a set of transistors, other components, and interconnections that provide Boolean logic functions (e.g., AND, OR, NOT, XOR) or storage functions (such as flip-flops or latches). As used herein, a circuit "block" can refer to two or more cells. Both cells and circuit blocks can be referred to as modules or components and are implemented as physical structures and in simulations. Parameters, such as size, are specified for the selected cells (based on "standard cells"), and these parameters are made accessible in a database for use in EDA products.

[0068] During the analysis and extraction phase 526, circuit functionality is verified at the layout level, allowing for finer-grained layout design. During physical verification 528, the layout design is checked to ensure that manufacturing constraints are correct, such as DRC constraints, electrical constraints, and lithographic constraints, and to ensure that circuit functionality conforms to the HDL design specifications. During resolution enhancement 530, the geometry of the layout is transformed to improve the fabrication method of the circuit design.

[0069] During the tape-out process, data is created for the production of a photomask (after which photolithographic enhancement is applied, if appropriate). During mask data preparation 532, the "tape-out" data is used to generate a photomask, which is used to produce the finished integrated circuit.

[0070] Computer systems (such as) Figure 6 The storage subsystem of the computer system 600 can be used to store programs and data structures used by some or all of the EDA products described herein, as well as units for developing libraries and products for physical and logical designs for using libraries.

[0071] Figure 6 An example machine of computer system 600 is shown, within which a set of instructions can be executed to cause the machine to perform any or one of the methods discussed herein. In alternative implementations, the machine may be connected (e.g., networked) to other machines in a LAN, intranet, extranet, and / or the Internet. The machine may operate as a server or client machine in a client-server network environment, as a peer-to-peer (or distributed) network environment, or as a server or client machine in a cloud computing infrastructure or environment.

[0072] A machine can be a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a cellular phone, a network device, a server, a network router, a switch or bridge, or any machine capable of executing a set of instructions (sequentially or otherwise) to perform the actions to be taken by the specified machine. Furthermore, although a single machine is shown, the term "machine" should also be understood to include any collection of machines that individually or jointly execute a set (or more) of instructions to perform any or more of the methods discussed herein.

[0073] Example computer system 600 includes a processing device 602, a main memory 604 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM), static memory 606 (e.g., flash memory, static random access memory (SRAM), etc.), and a data storage device 618, which communicate with each other via a bus 630.

[0074] Processing device 602 represents one or more processors, such as microprocessors, central processing units, etc. More specifically, the processing device may be a Complex Instruction Set Computing (CISC) microprocessor, a Reduced Instruction Set Computing (RISC) microprocessor, a Very Long Instruction Word (VLIW) microprocessor, or a processor that implements other instruction sets, or a processor that implements combinations of instruction sets. Processing device 602 may also be one or more special-purpose processing devices, such as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), network processors, etc. Processing device 602 may be configured to execute instructions 626 for performing the operations and steps described herein.

[0075] The computer system 600 may also include a network interface device 608 for communication via a network 620. The computer system 600 may also include a video display unit 610 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 612 (e.g., a keyboard), a cursor control device 614 (e.g., a mouse), a graphics processing unit 622, a signal generation device 616 (e.g., a speaker), a video processing unit 628, and an audio processing unit 632.

[0076] Data storage device 618 may include machine-readable storage medium 624 (also referred to as non-transitory computer-readable medium) on which one or more sets of instructions 626 or software embodying any one or more of the methods or functions described herein are stored. The instructions 626 may also reside wholly or at least partially in main memory 604 and / or processing device 602 during execution by computer system 600, which also constitute machine-readable storage media.

[0077] In some implementations, instruction 626 includes instructions for implementing functions corresponding to this disclosure. Although machine-readable storage medium 624 is shown as a single medium in the example implementations, the term "machine-readable storage medium" should be understood to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) storing one or more sets of instructions. The term "machine-readable storage medium" should also be understood to include any medium capable of storing or encoding a set of instructions for execution by a machine and causing the machine and processing device 602 to perform any one or more methods of the methods of this disclosure. The term "machine-readable storage medium" should therefore be understood to include, but is not limited to, solid-state memory, optical media, and magnetic media.

[0078] Some parts of the foregoing detailed description have been presented based on the algorithms and symbolic representations of operations on data bits within computer memory. These algorithmic descriptions and representations are the most efficient way for those skilled in the art of data processing to communicate the essence of their work to others skilled in the art. An algorithm can be a sequence of operations that leads to a desired result. These operations are operations that require physical manipulation of physical quantities. Such quantities can take the form of electrical or magnetic signals that can be stored, combined, compared, and otherwise manipulated. Such signals can be referred to as bits, values, elements, symbols, characters, items, numbers, etc.

[0079] However, it should be remembered that all these and similar terms are associated with appropriate physical quantities and are merely convenient notations applied to those quantities. Unless otherwise stated, it is apparent from this disclosure that, throughout the specification, certain terms refer to the actions and processes of a computer system or similar electronic computing device that manipulate and convert data, represented as physical (electronic) quantities within the registers and memories of the computer system, into other data, similarly represented as physical quantities within the computer system's memory or registers or other such information storage devices.

[0080] This disclosure also relates to means for performing the operations described herein. Such means may be specifically constructed for the intended purpose, or may include a computer selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a computer-readable storage medium, such as, but not limited to, any type of disk including floppy disks, optical disks, CD-ROMs and magneto-optical disks, read-only memory (ROM), random access memory (RAM), EPROM, EEPROM, magnetic cards or optical cards, or any type of medium suitable for storing electronic instructions, each coupled to a computer system bus.

[0081] The algorithms and displays presented herein are not substantially related to any particular computer or other device. Various other systems may be used in conjunction with the programs taught herein, or it may be demonstrated that it is convenient to construct more specialized devices to perform the methods. Furthermore, this disclosure is not described with reference to any particular programming language. It will be understood that various programming languages ​​may be used to implement the teachings of this disclosure as described herein.

[0082] This disclosure may be provided as a computer program product or software, which may include a machine-readable medium storing instructions that can be used to program a computer system (or other electronic device) to perform processes according to this disclosure. Machine-readable media include any mechanism for storing information in a machine-readable (e.g., computer-readable) form. For example, machine-readable (e.g., computer-readable) media include machine-readable (e.g., computer-readable) storage media, such as read-only memory (“ROM”), random access memory (“RAM”), disk storage media, optical storage media, flash memory devices, etc.

[0083] In the foregoing disclosure, implementations of this disclosure have been described with reference to specific example implementations. It will be apparent that various modifications can be made to these implementations without departing from the broader spirit and scope of the embodiments of this disclosure as set forth in the appended claims. Where elements are referred to in the singular in this disclosure, more than one element may be depicted in the drawings, and the same elements are labeled with the same numerals. Therefore, this disclosure and the drawings should be considered illustrative rather than restrictive.

Claims

1. A method comprising: Receive the first spatial image predicted by the two-dimensional model of the photolithographic mask; as well as A first machine learning model is applied by a first processor to infer a second spatial image from a first spatial image, wherein the first machine learning model receives the first spatial image as input and infers the second spatial image as output, the first machine learning model is trained using a training set including (a) samples of the first spatial image and (b) ground truth values ​​of the corresponding second spatial image predicted by a 3D model of a lithographic mask, and the 3D model of the lithographic mask uses a 3D description of the lithographic mask.

2. The method according to claim 1, further comprising: The exposure model is applied to the second-space image to generate an acidic latent image; as well as A second machine learning model is applied by a second processor to infer the resist profile from the acid latent image.

3. The method of claim 2, wherein each of the first spatial image, the second spatial image, the acid latent image, and the resist profile is three-dimensional.

4. The method of claim 3, wherein each of the first spatial image, the second spatial image, the acid latent image, and the resist profile comprises a set of two-dimensional slices at different heights, and each set has the same number of slices at the same height.

5. The method of claim 2, wherein the second spatial image is a normalized image independent of the exposure dose, and applying the exposure model includes applying the exposure dose to the normalized second spatial image.

6. The method of claim 2, wherein neither the first machine learning model nor the second machine learning model uses exposure dose as input.

7. The method of claim 2, wherein the resist profile is represented by a signed distance value function, wherein, The magnitude of the signed distance value function at a point is the distance from the point to the nearest contour of the resist profile, and the sign of the signed distance value function indicates whether the point is inside or outside the nearest contour.

8. The method of claim 1, wherein the two-dimensional model of the photomask models each point of the photomask as influencing the phase and amplitude of light incident on the photomask.

9. A system comprising: Memory, storing instructions; as well as A processor, coupled to the memory, executes the instructions, which, when executed, cause the processor to perform the following operations: Access a first training set comprising: (a) samples of a first spatial image predicted by a two-dimensional model of the photomask; and (b) ground truth values ​​of a corresponding second spatial image predicted by a three-dimensional model of the photomask, wherein the three-dimensional model of the photomask uses a three-dimensional description of the photomask; and The computational lithography model is trained using the first training set, wherein the computational lithography model uses the lithography mask to simulate the lithography process, the computational lithography model includes a first machine learning model that infers a second spatial image from the first spatial image, the first machine learning model receiving the first spatial image as input and inferring the second spatial image as output, and training the computational lithography model includes training the first machine learning model based on a comparison of (x) the inferred second spatial image output by the first machine learning model and (y) the ground truth value of the second spatial image from the first training set.

10. The system according to claim 9, wherein: The computational lithography model also includes an exposure model for generating an acid latent image from a 3DMM spatial image, and a second machine learning model for inferring the resist profile from the acid latent image; and Training the computational lithography model also includes training the second machine learning model using a second training set, which includes (a) an acid latent image and (b) the corresponding ground truth resist profile.

11. The system of claim 10, wherein training at least one of the machine learning models uses a weighted cost function having weights as a function of the output in the training set.

12. The system of claim 10, wherein the first training set and the second training set comprise inputs and corresponding outputs generated using different exposure doses and different defocusing conditions.

13. The system of claim 10, wherein parameterizing the exposure model and training the computational lithography model includes adjusting the parameters of the exposure model by incorporating one of the machine learning models used in training the machine learning model.

14. The system of claim 9, wherein the underlying ground truth 3DMM spatial image is computed using a three-dimensional rigorous Maxwell equation model of the photolithographic mask.

15. A non-transitory computer-readable medium comprising stored instructions, which, when executed by a processor, cause the processor to perform the following operations: Design of receiving photolithography masks; The design of the photolithographic mask is divided into blocks; For each patch, a computational lithography model is applied, which uses the lithographic mask to simulate the patch's contribution to the lithography process; The computational lithography model mentioned above includes: A first machine learning model infers a second spatial image from a first spatial image, the first spatial image being predicted by a two-dimensional model of the tiles; wherein the first machine learning model receives the first spatial image as input and infers the second spatial image as output, and the first machine learning model is trained using a training set comprising (a) samples of the first spatial image and (b) ground truth values ​​of the corresponding second spatial image predicted by a three-dimensional model of a lithographic mask, and the three-dimensional model of the lithographic mask using a three-dimensional description of the lithographic mask; An exposure model for generating an acidic latent image from the second spatial image; and A second machine learning model infers the resist profile from the acid latent image; Assemble the resist profile for the block; and Design based on the assembled resist contouring lithography process.

16. The non-transitory computer-readable medium of claim 15, wherein the first machine learning model and the second machine learning model comprise a dual U-net structure.

17. The non-transitory computer-readable medium of claim 15, wherein the tile has an area at least 10 × 10 times larger than the area that can be modeled using a rigorous three-dimensional electromagnetic model of the tile.

18. The non-transitory computer-readable medium of claim 15, wherein the tile has an area of ​​at least 100 μm × 100 μm.

19. The non-transitory computer-readable medium of claim 15, wherein the first machine learning model and the second machine learning model each comprise a supervised deep learning model.

20. The non-transitory computer-readable medium of claim 15, wherein adjusting the design of the photolithography process includes modifying the design of the photomask based on the resist profile of the assembly.

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