Model-based Optical Proximity Correction Research Articles

Neural-ILT 2.0: Migrating ILT to Domain-Specific and Multitask-Enabled Neural Network

Optical proximity correction (OPC) in modern design closures has become extremely expensive and challenging. Conventional model-based OPC encounters performance degradation and large process variation, while aggressive approach, such as inverse lithography technology (ILT), suffers from large computational overhead for both mask optimization and mask writing processes. In this article, we developed Neural-ILT, an end-to-end learning-based OPC framework, which literally conducts mask prediction and ILT correction for a given layout in a single neural network, with the objectives of: 1) mask printability enhancement; 2) mask complexity optimization; and 3) flow acceleration. A domain-specific model pretraining recipe, which introduces the domain knowledge of lithography system, is proposed to help Neural-ILT achieving faster and better convergence. Quantitative results show that compared to the state-of-the-art (SOTA) learning-based OPC solutions and conventional OPC flows, Neural-ILT can achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$15\times $ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$30\times $ </tex-math></inline-formula> turnaround time (TAT) speedup and the best mask printability with relatively lower mask complexity. Based on the developed infrastructure, we further investigated the feasibility of handling multiple mask optimization tasks for different datasets within a common Neural-ILT platform. We believe this work could bridge well-developed deep learning toolkits to GPU-based high-performance lithographic computations to achieve groundbreaking performance boosting on various computational lithography-related tasks.

I-line photolithographic metalenses enabled by distributed optical proximity correction with a deep-learning model.

High pattern fidelity is paramount to the performance of metalenses and metasurfaces, but is difficult to achieve using economic photolithography technologies due to low resolutions and limited process windows of diverse subwavelength structures. These hurdles can be overcome by photomask sizing or reshaping, also known as optical proximity correction (OPC). However, the lithographic simulators critical to model-based OPC require precise calibration and have not yet been specifically developed for metasurface patterning. Here, we demonstrate an accurate lithographic model based on Hopkin's image formulation and fully convolutional networks (FCN) to control the critical dimension (CD) patterning of a near-infrared (NIR) metalens through a distributed OPC flow using i-line photolithography. The lithographic model achieves an average ΔCD/CD = 1.69% due to process variations. The model-based OPC successfully produces the 260 nm CD in a metalens layout, which corresponds to a lithographic constant k1 of 0.46 and is primarily limited by the resolution of the photoresist. Consequently, our fabricated NIR metalens with a diameter of 1.5 mm and numerical aperture (NA) of 0.45 achieves a measured focusing efficiency of 64%, which is close to the calculated value of 69% and among the highest reported values using i-line photolithography.

Neural Network Classifier-Based OPC With Imbalanced Training Data

Machine learning-guided optical proximity correction, called ML-OPC in this paper, has recently been proposed to alleviate long runtime of model-based OPC. ML-OPC using regression methods has been presented but with limited prediction accuracy. We propose neural network classifier-based OPC (NNC-OPC), in which a neural network classifier serves as a mask bias model. A few techniques are applied to enhance basic NNC-OPC: parameterization of layout segments using polar Fourier transform signals, dimensionality reduction through weighted principal component analysis, and sampling of training layout segments. Training segments are typically imbalanced over the range of mask biases, which may cause large prediction error for segments that appear less frequently. This is resolved by three techniques: 1) synthetic data generation; 2) class reorganization; and 3) an adaptive learning rate. Experiments with NNC-OPC with all techniques applied indicate that prediction error of mask bias and training time are reduced by 29% and 80%, respectively, compared to state-of-the-art ML-OPC with regression methods.

PV-Aware Analog Sizing for Robust Analog Layout Retargeting with Optical Proximity Correction

For analog integrated circuits (ICs) in nanometer technology nodes, process variation (PV) induced by lithography may not only cause serious wafer pattern distortion, but also result in device mismatch, which can readily ruin circuit performance. Although the conventional optical proximity correction (OPC) operations can effectively improve the wafer image fidelity, an analog circuit without robust device sizes is still highly vulnerable to such a mismatch effect. In this article, a PV-aware sizing-inclusive analog layout retargeting framework, which encloses an efficient hybrid OPC scheme for yield enhancement, is proposed. The device sizes are tuned during the layout retargeting process by using a deterministic circuit-sizing algorithm considering PV conditions. Our hybrid OPC method combines global rule-based OPC with local model-based OPC functions to boost the wafer image quality improvement but without degrading the computational efficiency. The experimental results show that our proposed framework can achieve the best wafer image quality and circuit performance preservation compared to any other alternative approaches.

Analog Layout Retargeting With Process-Variation-Aware Hybrid OPC

For high-quality analog layout retargeting, in this brief we propose a hybrid optical proximity correction (OPC) methodology, which features special handling against geometry manufacturing deviation caused by process variation (PV). Based on the unique nature of analog layouts, accuracy limitation of the rule-based OPC (RB-OPC) is compensated by geometry preprocessing operations in our proposed layout retargeting flow, and is further shrunk by a local model-based OPC postprocessing operation without incurring any chip area increment. An innovative RB PV-band correction scheme is developed to preserve analog circuit performance against possible PV. The experiments show that our analog layout retargeting flow integrated with the proposed PV-aware hybrid OPC can achieve much higher efficiency with even lower mask complexity and edge placement error compared to alternative methods.

Prediction of biases for optical proximity correction through partial coherent identification

Most approaches to model-based optical proximity correction (OPC) use an iterative algorithm to determine the optimum mask. Each iteration requires at least one simulation, which is the most time-consuming part of model-based OPC. As the layout becomes more complicated and the process conditions are driven to the physical limit, the required number of iterations increases dramatically. To overcome this problem, we propose a method to predict the OPC bias of layout segments with a single-hidden-layer neural network. The segments are characterized by length and based on intensities at the corresponding control points, and these features are used as input to the network, which is trained with an extreme learning machine. We obtain a best-error root mean square of 1.29 nm from training and test experiments for layout clips sampled from a random contact layer of a logic device. In addition, we reduced the iterations by 27.0% by initializing the biases in the trained network before performing the main iterations of the OPC algorithm.

Optical proximity correction with hierarchical Bayes model

Optical proximity correction (OPC) is one of the most important techniques in today’s optical lithography-based manufacturing process. Although the most widely used model-based OPC is expected to achieve highly accurate correction, it is also known to be extremely time-consuming. This paper proposes a regression model for OPC using a hierarchical Bayes model (HBM). The goal of the regression model is to reduce the number of iterations in model-based OPC. Our approach utilizes a Bayes inference technique to learn the optimal parameters from given data. All parameters are estimated by the Markov Chain Monte Carlo method. Experimental results show that utilizing HBM can achieve a better solution than other conventional models, e.g., linear regression-based model, or nonlinear regression-based model. In addition, our regression results can be used as the starting point of conventional model-based OPC, through which we are able to overcome the runtime bottleneck.

Forming Freeform Source Shapes by Utilizing Particle Swarm Optimization to Enhance Resolution in Extreme UV Nanolithography

This paper investigated pixel-based source shape optimization to enhance the resolution in a projection extreme UV (EUV) lithography system. The particle swarm optimization method was proposed to optimize the source shapes. The layout patterns of the masks were corrected using model-based optical proximity correction. The optimal source shape in an EUV lithography system was verified using numerical calculations, through which the aerial image of two types of mask pattern exposure was determined. The two types of mask patterns were a logic line/space (L/S) pattern with a critical dimension (CD) of 16 nm and a SRAM contact hole (CH) pattern with a CD of 45 nm. Two significant metrics were used to evaluate the modified source performance: the latent image intensity and process window. Results from the numerical calculations showed that for L/S target patterns, using the optimal source produced a latent image error of 13.02% after exposure that was superior to that of traditional off-axis source exposure. The latent image intensity of the mask between the lines and the gaps differed substantially, corner rounding situations had effectively improved, and no bridges were observed. Concerning CH target patterns, using the optimal source produced a latent image error of 0.04% after exposure that was also superior to that of traditional sources. The latent image intensity between the holes and the gaps also differed significantly, and the latent image intensity distribution at the four corners of the CH had straight angles. Because the source shapes calculated in this study comprised pixel-based sources, the controllable microelectromechanical system mirror array chip was used to match each mirror to each pixel source, and the calculated source shapes were successfully projected.

An Investigation on OPC Model Coverage to Improve CD Uniformity

Model-based Optical Proximity Correction (model-based OPC) has become a necessity for state of the art IC fabrication at advanced node technology. It needs one “reliable” OPC model for successful application of model-based OPC. Namely, the reliable OPC model needs to have much wider coverage and high accuracy to characterize the physical processes that take place during the photoresist exposure and development. One of the key factors for reliability of OPC model is model coverage which depends strongly on test pattern samples for model calibration. In this paper, two sets of test structures were selected to do OPC model calibration to qualify CD uniformity of patterns in array structures at 3xnm technology node. The results show the intermediate number of features for a given pitch is necessary for wider coverage of OPC model. The model including such patterns can improve CD uniformity of array structure. One methodology to design optimal permutation and combination for test patterns is proposed.

Fast aerial image simulations for partially coherent systems by transmission cross coefficient decomposition with analytical kernels

Aerial image simulation is one of the most critical components in the model-based optical proximity correction (OPC), which has become a necessary part of resolution enhancement techniques used to improve the performance of subwavelength optical lithography. In this paper, a fast aerial image simulation method is proposed for partially coherent systems by decomposing the transmission cross coefficient (TCC) into analytical kernels. The TCC matrix is projected onto a function space whose basis is analytical circle-sampling functions (CSFs) and converted into a much smaller projected matrix. By performing singular value decomposition (SVD) to the projected matrix, its eigenvectors together with the CSFs are used to generate a set of analytical TCC kernels. The proposed method avoids directly performing SVD to the large TCC matrix, making it much more runtime efficient than the conventional SVD method. Furthermore, the grid size of the kernels can be flexibly set to any desired value in aerial image simulations, which is not realizable with the conventional SVD method. The comparison of aerial image intensity errors and edge placement errors calculated by the proposed method and the conventional SVD method has confirmed the validity of the proposed method. An OPC example is also provided to further demonstrate its efficiency.

Fast aerial image simulations using one basis mask pattern for optical proximity correction

Aerial image simulation is one of the key parts in the model-based optical proximity correction (OPC) technique, which has become a must have process to improve lithography performance with ever-decreasing feature sizes. In this paper, a fast aerial image simulation approach is proposed by using one basis mask pattern to generate a lookup table, where the convolutions of the basis pattern with the partially coherent kernels are precalculated and stored. A rectilinear polygon mask pattern used in integrated circuit layouts can be decomposed into several shifted basis patterns. Its convolutions with kernels for use in aerial image calculation can then be quickly obtained from the precalculated lookup table by applying the translation-invariant property of two-dimensional convolution. Simulations conducted by using the proposed approach have demonstrated that this approach yields a superior quality in the fields of aerial image calculation and OPC optimization, due to the advantage of dramatically decreasing the storage requirement. It is fully expected that this approach will be simple to implement and will provide a useful practical means for OPC systems.

Non-delta-chrome optical proximity correction methodology for process models with three-dimensional mask effects

As integrated circuit design dimensions continue to shrink, previously ignored three-dimensional (3-D) mask effects have become significant for the accurate prediction and correction of proximity effects. Optical proximity correction (OPC) process models must consequently take into account 3-D mask effects. The state-of-the-art model-based OPC methodology, which is called delta-chrome OPC (DCOPC), needs the repeated computation of the mask perturbation to facilitate its convergence. The increasing complexity of OPC process models challenges this DCOPC methodology because each computation of the mask perturbation becomes prohibitively expensive. In this study, a new model-based OPC methodology, which is called non-delta-chrome OPC (non-DCOPC), is proposed without introducing any mask perturbations. It only requires image intensity information to achieve convergence using classical control techniques, and its effectiveness is demonstrated, showing that the run time with and without considering 3-D mask effects can be significantly improved. In addition, the correction accuracy of the DCOPC and non-DCOPC methodologies without considering 3-D mask effects is quite comparable. However, the correction accuracy considering 3-D mask effects can be slightly improved by the non-DCOPC methodology.

Erratum to: A sparse matrix model-based optical proximity correction algorithm with model-based mapping between segments and control sites

Optical proximity correction (OPC) is a key step in modern integrated circuit (IC) manufacturing. The quality of model-based OPC (MB-OPC) is directly determined by segment offsets after OPC processing. However, in conventional MB-OPC, the intensity of a control site is adjusted only by the movement of its corresponding segment; this scheme is no longer accurate enough as the lithography process advances. On the other hand, matrix MB-OPC is too time-consuming to become practical. In this paper, we propose a new sparse matrix MB-OPC algorithm with model-based mapping between segments and control sites. We put forward the concept of ‘sensitive area’. When the Jacobian matrix used in the matrix MB-OPC is evaluated, only the elements that correspond to the segments in the sensitive area of every control site need to be calculated, while the others can be set to 0. The new algorithm can effectively improve the sparsity of the Jacobian matrix, and hence reduce the computations. Both theoretical analysis and experiments show that the sparse matrix MB-OPC with model-based mapping is more accurate than conventional MB-OPC, and much faster than matrix MB-OPC while maintaining high accuracy.

A sparse matrix model-based optical proximity correction algorithm with model-based mapping between segments and control sites

A sparse matrix model-based optical proximity correction algorithm with model-based mapping between segments and control sites

Regularization in Inverse Lithography: Enhancing Manufacturability and Robustness to Process Variations

Inverse lithography, as a mask design tool, has the capability of producing unintuitive patterns with topologies much different from those obtained from either rule-based or model-based optical proximity correction (OPC). These mask patterns may have the advantage of producing circuit patterns that are otherwise very difficult to achieve; on the other hand, the mask may be too complicated that renders it impossible to manufacture, or that the cost of producing it would be astronomical. There is also good likelihood that the resulting circuit patterns may be severely affected when there are process variations, such as in focus or dose. In this work, we discuss how various regularization techniques may be employed to tackle these two problems: simplifying the mask pattern in an inverse lithography process, and incorporating robustness explicitly in the design algorithm.

Reducing the pattern redundancy in optical proximity correction modeling by analyzing the pattern linearity

In modern photolithography, optical proximity correction (OPC) has been widely adopted to improve the image fidelity of the mask on silicon wafer and, hence, improve the yield and the performance of integrated circuits. In recent years, model based optical proximity correction (MBOPC) has evolved from a nice-to-have feature to a must-have feature, especially, for the advanced nodes, 90 nm and beyond. The purpose of MBOPC is to adjust the designed pattern on the photomask to introduce mask perturbations, such that the layout printed on the wafer is as close as possible to the drawn layout. Before MBOPC is conducted on the full chip, a high quality and yet compact OPC model must be built, which simulates the photolithography process accurately. A high quality OPC model apparently relies on the quality of the empirical critical-dimension data in terms of both metrology noisiness and layout representativeness. Although more measurements on a large number of patterns will keep overall noise at lower levels and provide better input to OPC modeling, it is crucial to choose the representative patterns wisely and minimize the redundancy of gauges due to the limited metrology budget and the requirement of shortening turnaround time. In this article, the authors propose a method that checks the linear response of the optical signal on the one-dimensional (1D) patterns and selects the most representative patterns among all possible 1D structures.

Model based optical proximity correction runtime saving with multisegment solver

In modern photolithography, model based optical proximity correction (MBOPC) has evolved from a nice-to-have feature to a must-have feature and has been widely adopted to improve the process throughput. The purpose of MBOPC is to adjust the designed pattern on the photomask to introduce mask perturbations such that the layout printed on the wafer is as close as possible to the drawn layout. In regular MBOPC process, the polygons are dissected into segments and corrections are conducted segment by segment. While it is relatively easy and straightforward to find the optimal segment size for most one-dimensional features, it is hard for many two-dimensional features, especially line-end areas. By solving a few segments around line-end areas together, multisegment solver (MSS) showed a good contour match. However, this method is expensive on model calculation, as there is more than one segment size to be optimized and a large number of searching iterations is needed, which makes its runtime sensitive to the number kernels retained in OPC model. In this study, a novel method of computing the signal change in the MBOPC process with MSS is proposed by analyzing the optical kernel sensitivity to mask perturbation. The experimental results show that while the correction accuracy of the MBOPC process with a simplified model is maintained, the MBOPC runtime is reduced by 37%.

Binary mask optimization for forward lithography based on the boundary layer model in coherent systems

Recently, a set of generalized gradient-based optical proximity correction (OPC) optimization methods have been developed to solve for the forward and inverse lithography problems under the thin-mask assumption, where the mask is considered a thin 2D object. However, as the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent, and thus these effects must be taken into account in OPC optimization methods. OPC methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength regime. This paper focuses on developing model-based forward binary mask optimization methods that account for the thick-mask effects of coherent imaging systems. The boundary layer (BL) model is exploited to simplify and characterize the thick-mask effects, leading to a model-based OPC method. The BL model is simpler than other thick-mask models, treating the near field of the mask as the superposition of the interior transmission areas and the boundary layers. The advantages and limitations of the proposed algorithm are discussed, and several illustrative simulations are presented.

Kernel Count Reduction in Model Based Optical Proximity Correction Process Models

As the leading-edge photolithography is approaching rapidly closer to the theoretical optical resolution limit, model based optical proximity correction (MBOPC) has evolved from a nice-to-have feature to a must-have feature. The purpose of MBOPC is to adjust the designed pattern on the photomask to introduce mask perturbations such that the layout printed on the wafer is as close as possible to the drawn layout. Before MBOPC is performed across a full chip, a process model is calibrated based upon manufacturing process data measured from scanning electron microscope (SEM) pictures of test patterns. The process model is usually composed of two components, signal intensity and threshold, and the intersections of these two components determine the layout contours that will be printed on wafer. It is found that the accuracy of the process model is improved as more kernels are used to represent the model. However, pattern correction runtime is proportional to the number of kernels used for the model, thereby introducing a constraint to incorporate least number of kernels in the process model. In this study, a novel method of computing the signal change in the MBOPC process is proposed, which is used to maintain the correction accuracy and reduce the MBOPC runtime.

Abbe singular-value decomposition: Compact Abbe’s kernel generation for microlithography aerial image simulation using singular-value decomposition method

Abbe’s method and Hopkin’s method are among the most popular microlithography aerial image simulation methods. In particular, Hopkin’s method is generally more popular for the high speed aerial image simulation domain, and it is used in model-based optical proximity correction. This is due to a general perception that Hopkin’s method can generate more compact sets of kernels compared with Abbe’s method, due to the application of a singular-value decomposition (SVD) process to Hopkin’s large transmission cross coefficient matrix. On the other hand, the primitive Abbe’s method is very simple, since it only needs to decompose the source field into independent point sources with a two-dimensional partitioning criteria. Albeit its simplicity, compared with Hopkin’s method, in general, Abbe’s method, generates a larger set of kernels. In this article the authors propose applying SVD to the original Abbe’s kernels, the essential kernels according to their singular values. Experimental results show that the algorithm, the Abbe-SVD method, accomplishes over 68 times of both runtime and memory saving over the traditional Hopkin’s SVD method for kernel generation.