Inverse Lithography Technique Research Articles

L2O-ILT: Learning to Optimize Inverse Lithography Techniques

L2O-ILT: Learning to Optimize Inverse Lithography Techniques

A self-training end-to-end mask optimization framework based on semantic segmentation network

As the process advances and the minimum linewidth gets closer to the physical limit, inverse lithography technique (ILT) is widely used for optical proximity correction (OPC). However, the computational overhead of the ILT method is high, and the printability of the mask is poor. In response to these limitations, we proposed ERFNet-ILT, a self-training method for an end-to-end learning framework for generating optimized masks directly from layout patterns, which introduces a feature fusion module at the end of the encoder and uses dilated convolution to expand the receptive field, thereby extracting layout pattern information such as edges, vertices and corners of the layout pattern from the feature map. The framework has shorter model building time and higher mask printability. Compared with the state-of-the-art methods, experimental quantitative results show that the proposed framework achieves 2.5 % squared L2 error and 7.9 % process variation band reduction within a comparable mask correction time.

DevelSet: Deep Neural Level Set for Instant Mask Optimization

As one of the key techniques for resolution enhancement technologies (RETs), optical proximity correction (OPC) suffers from prohibitive computational costs as feature sizes continue to shrink. Inverse lithography techniques (ILT) treat the mask optimization process as an inverse imaging problem, yielding high-quality curvilinear masks. However, ILT methods often fall short of printability and manufacturability due to their time-consuming procedures and excessive computational overhead. In this paper, we propose DevelSet, a potent metal layer OPC engine that replaces discrete pixel-based masks with implicit level set-based representations. With a GPU-accelerated lithography simulator, DevelSet achieves end-to-end mask optimization using a neural network to provide quasi-optimized level set initialization and further evolution with a CUDA-based mask optimizer for fast convergence. The backbone of DevelSet-Net is a transformer-based multi-branch neural network that offers a parameter selector to eliminate the need for manual parameter initialization. Experimental results demonstrate that the DevelSet framework outperforms state-of-the-art approaches in terms of printability while achieving fast runtime performance (around 1 second). We expect this enhanced level set technique, coupled with a CUDA/DNN accelerated joint optimization paradigm, to have a substantial impact on industrial mask optimization solutions.

Fast inverse lithography approach based on a model-driven graph convolutional network.

Inverse lithography technique (ILT) is a leading-edge method to improve the image fidelity of an advanced optical lithography system by performing pixel-wise optimization on the transmission function of photomask. However, traditional ILTs are computationally intensive, which limits their application in high volume manufacturing of integrated circuits. This paper proposes a model-driven graph convolutional network (MGCN) framework combined with the dense concentric circular sampling (DCCS) method to effectively improve computational efficiency and imaging fidelity of current ILTs. Firstly, the DCCS template is used to extract the geometric features from the layout pattern of integrated circuits, which are then input into a GCN-based encoder to predict the optimized mask pattern of the ILT. Then, a model-driven decoder based on the lithography imaging process is developed to retrieve the print image of the predicted ILT mask. By means of the cooperation between the encoder and decoder, an unsupervised training strategy is proposed to avoid the time-consuming labelling process of the training samples. With the help of the parallel computing under GPU framework, the well-trained encoder can make a fast prediction of ILT mask with high-fidelity image results. The results demonstrate the state-of-the-art performance of the proposed MGCN approach compared to some other comparative ILT methods.

Generation of inverse assist features using generative adversarial networks

Adding the assist feature in the optical proximity correction (OPC) procedure is crucial for improving the process window. The rule-based assist feature placement is very fast; however, the resultant process window still requires improvement. The model-based assist feature placement presents a better process window, but its iterative nature makes it extremely time-consuming. The assist features (AFs) that are optimized by using the inverse lithography technique perform best in terms of lithographic metrics such as the Depth of Focus, Mask Error Enhancement Factor, and Normalized Image Log Slope; these features can be added to the objective function. However, the inverse lithography technique is a pixel-level correction method, which is even more time-consuming. Consequently, it is typically used to provide guidance for rule-based AF placement. In this study, we design novel generative adversarial networks (GANs) that can generate AFs to increase the speed of assist feature placement while maintaining relatively high lithographic performance using inverse lithography techniques. The results demonstrate that the proposed generative adversarial network methods are three orders of magnitude faster than the inverse lithography techniques. Additionally, they exhibit lower edge placement errors and process variation bands when compared to the inverse lithography techniques.

Global Source Optimisation Based on Adaptive Nonlinear Particle Swarm Optimisation Algorithm for Inverse Lithography

Source optimisation (SO) is an approved approach to improve the imaging quality in inverse lithography techniques. It is critical to apply an optimisation approach with high convergence efficiency and minimum errors in pixel-based SO. To improve the convergence efficiency of the pixel-based SO, a route of particle swarm optimiser (PSO) combined with the adaptive nonlinear control strategy (ANCS) is proposed in this study. As a global optimisation algorithm, ANCS-PSO has the attributes of breaking away from the local optimum by adjusting the particle learning factor adaptively. In addition, the nonlinear control approach can broaden the search range and speed up the convergence of the iteration operation. The proposed approach also is compared with the linear decreasing inertia weight strategy and the simulated annealing strategy. The performance verification simulation displays the validity of PSO-ANCS and its potentials in SO with high convergence efficiency and optimisation capacity, by comparing the linear decreasing inertia weight strategy and the simulated annealing strategy.

Nonlinear compressive inverse lithography aided by low-rank regularization.

Photolithography is at the core of the semiconductor industry that is used to fabricate microscale and nanoscale integrated circuits. Inverse lithography is a technique extensively used to compensate for lithography patterning distortions. It refers to methods that pre-distort the photomask patterns such that their projection, through the photolithography system, results in a pattern that is as close as possible to the intended original. However, most inverse lithography technique (ILT) methods suffer from large computational complexity. This paper develops a nonlinear compressive sensing framework for ILT that effectively improves the computational efficiency and image fidelity, while at the same time controlling the mask complexity. Based on a nonlinear lithography imaging model, the compressive ILT is formulated as an inverse optimization problem aimed at reducing the patterning error, and enforcing the sparsity and low rank properties of the mask pattern. A downsampling strategy is adopted to reduce the dimensionality of the cost function, thus alleviating the computational burden. Sparsity and low-rank regularizations are then used to constrain the solution space and reduce the mask complexity. The split Bregman algorithm is used to solve for the inverse optimization problem. The superiority of the proposed method is verified by a set of simulations and comparison to traditional ILT algorithms.

GAN-OPC: Mask Optimization With Lithography-Guided Generative Adversarial Nets

Mask optimization has been a critical problem in the VLSI design flow due to the mismatch between the lithography system and the continuously shrinking feature sizes. Optical proximity correction (OPC) is one of the prevailing resolution enhancement techniques (RETs) that can significantly improve mask printability. However, in advanced technology nodes, the mask optimization process consumes more and more computational resources. In this article, we develop a generative adversarial network (GAN) model to achieve better mask optimization performance. We first develop an OPC-oriented GAN flow that can learn target-mask mapping from the improved architecture and objectives, which leads to satisfactory mask optimization results. To facilitate the training process and ensure better convergence, we propose a pretraining scheme that jointly trains the neural network with inverse lithography technique (ILT). We also propose an enhanced generator design with a U-Net architecture and a subpixel super-resolution structure that promise a better convergence and a better mask quality, respectively. At convergence, the generative network is able to create quasi-optimal masks for given target circuit patterns and fewer normal OPC steps are required to generate high quality masks. The experimental results show that our flow can facilitate the mask optimization process as well as ensure a better printability.

Efficient optical proximity correction based on semi-implicit additive operator splitting

Inverse lithography techniques (ILT) have been extensively used by the semiconductor industry to compensate for the inherent image distortions in optical lithography. However, the iterative ILT optimization procedure requires rather prohibitive time steps leading to poor efficiency with explicit time discretization. In this paper, a semi-implicit time discretization scheme is applied, enabling stable computation of mask synthesis with large time steps. Additive operator splittering (AOS) is implemented with respect to coordinate axes, reducing mask synthesis to consecutive one-dimensional updates represented by tridiagonal linear equations, which is solved efficiently by the Thomas algorithm. Simulation results merit the superiority of the proposed semi-implicit approach with improved convergence performance.

Model-driven convolution neural network for inverse lithography.

Optical lithography is a fundamental process to fabricate integrated circuits, which are the basic fabric of the information age. Due to image distortions inherent in optical lithography, inverse lithography techniques (ILT) are extensively used by the semiconductor industry to improve lithography image resolution and fidelity in semiconductor fabrication. As the density of integrated circuits increases, computational complexity has become a central challenge in ILT methods. This paper develops a new and powerful framework of a model-driven convolution neural network (MCNN) to obtain the approximate guess of the ILT solutions, which can be used as the input of the following ILT optimization with much fewer iterations as compared with conventional ILT algorithms. The combined approach to use the proposed MCNN together with the gradient-based method can improve the speed of ILT optimization algorithms up to an order of magnitude and further improve the imaging performance of coherent optical lithography systems. This paper, to the best of our knowledge, is the first to exploit a state-of-the-art MCNN to solve the ILT problem and provide considerable performance advantages. The imaging model of optical lithography is utilized to establish a neural network architecture and an unsupervised training strategy. The neural network architecture and the initial network parameters are derived by unfolding and truncating the model-based iterative ILT optimization procedure. Then, a model-based decoder is proposed to enable the unsupervised training of the neural network, which averts the time-consuming labelling process in training data. This work opens a new window for MCNN techniques to effectively improve the computational efficiency and imaging performance of conventional ILT algorithms. Some impressive good simulation results are provided to verify the superiority of the proposed MCNN approach.

Sparse nonlinear inverse imaging for shot count reduction in inverse lithography.

Inverse lithography technique (ILT) is significant to reduce the feature size of ArF optical lithography due to its strong ability to overcome the optical proximity effect. A critical issue for inverse lithography is the complex curvilinear patterns produced, which are very costly to write due to the large number of shots needed with the current variable shape beam (VSB) writers. In this paper, we devise an inverse lithography method to reduce the shot count by incorporating a model-based fracturing (MBF) in the optimization. The MBF is formulated as a sparse nonlinear inverse imaging problem based on representing the mask as a linear combination of shots followed by a threshold function. The problem is approached with a Gauss-Newton algorithm, which is adapted to promote sparsity of the solution, corresponding to the reduction of the shot count. Simulations of inverse lithography are performed on several test cases, and results demonstrate reduced shot count of the resulting mask.

Optical proximity correction using holographic imaging technique

In this work, the preliminary results of the holographic imaging technique (HIT) as a resolution enhancement technique (RET) hybrid inverse lithography technique (ILT) optical proximity correction mask correction is presented. The proposed technique is based on the illumination system and free space propagation of the mask. First, an in-line hologram (Gabor hologram) is generated by computing the target pattern diffraction pattern. Second, the computed hologram is synthesized as pattern contours to form a mask for a conventional optical system. In this study, a simple HIT corrected mask is validated with compact lithographic exposure system mathematical model for demonstrating the preliminary validity of the proposed method. Future plans to validate HIT for the most aggressive process nodes are proposed. The proposed technique has not been exercised against conventional ILT or other RET techniques, and does not contain analysis of resolution improvement achievable with those techniques.

Fast convolution method and its application in mask optimization for intensity calculation using basis expansion.

Finer grid representation is required for a more accurate description of mask patterns in inverse lithography techniques, thus resulting in a large-size mask representation and heavy computational cost. To mitigate the computation problem caused by intensive convolutions in mask optimization, a new method called convolution using basis expansion (CBE) is discussed in this paper. Matrices defined in fine grid are projected on coarse gird under a base matrix set. The new matrices formed by the expansion coefficients are used to perform convolution on the coarse grid. The convolution on fine grid can be approximated by the sum of a few convolutions on coarse grid following an interpolation procedure. The CBE is verified by random matrix convolutions and intensity calculation in lithography simulation. Results show that the use of the CBE method results in similar image quality with significant running speed enhancement compared with traditional convolution method.

Influence of ZnO nanowire array morphology on field emission characteristics

In this work the growth and field emission properties of vertically aligned and spatially ordered and unordered ZnO nanowires are studied. Spatially ordered nanowire arrays of controlled array density are synthesized by both chemical bath deposition and vapour phase transport using an inverse nanosphere lithography technique, while spatially unordered arrays are synthesized by vapour phase transport without lithography. The field emission characteristics of arrays with 0.5, 1.0, and 1.5 μm inter-wire distances, as well as unordered arrays, are examined, revealing that, within the range of values examined, field emission properties are mainly determined by variations in nanowire height, and show no correlation with nanowire array density. Related to this, we find that a significant variation in nanowire height in an array also leads to a reduction in catastrophic damage observed on samples during field emission because arrays with highly uniform heights are found to suffer significant arcing damage. We discuss these results in light of recent computational studies of comparable nanostructure arrays and find strong qualitative agreement between our results and the computational predictions. Hence the results presented in this work should be useful in informing the design of ZnO nanowire arrays in order to optimize their field emission characteristics generally.

Inverse e-beam lithography on photomask for computational lithography

Computational lithography, e.g., inverse lithography technique (ILT) and source mask optimization, is considered necessary for the “extremely low k1” lithography process of sub-20 nm device node. The ideal design of a curvilinear mask for computational lithography requires many changes during photomask fabrication. These range from preparation of the mask data to measurement and inspection. The manufacturability of a photomask for computational lithography is linked to predictable and manageable quality of patterning. Here, we have proposed the use of “inverse e-beam lithography” on photomask for computational lithography, which overcomes the patterning accuracy limits of conventional e-beam lithography. Furthermore, the preferred target design for ILT, a new verification method, and the accuracy required for the mask model are also discussed; with consideration of acceptable writing time (<24 h ) and computing power.

Line Search‐Based Inverse Lithography Technique for Mask Design

As feature size is much smaller than the wavelength of illumination source of lithography equipments, resolution enhancement technology (RET) has been increasingly relied upon to minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this paper, we investigate the problem of pixelated binary mask design in a partially coherent imaging system. Similar to previous approaches, the mask design problem is formulated as a nonlinear program and is solved by gradient‐based search. Our contributions are four novel techniques to achieve significantly better image quality. First, to transform the original bound‐constrained formulation to an unconstrained optimization problem, we propose a new noncyclic transformation of mask variables to replace the wellknown cyclic one. As our transformation is monotonic, it enables a better control in flipping pixels. Second, based on this new transformation, we propose a highly efficient line search‐based heuristic technique to solve the resulting unconstrained optimization. Third, to simplify the optimization, instead of using discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Forth, we introduce a jump technique in order to jump out of local minimum and continue the search.

Mask Synthesis for Aerial Image Fidelity in Optical Lithography Using a Coarse-Grid-Approximation Level-Set Approach

Inverse lithography technique, which treats mask synthesis as an inverse problem, has been considered as a strong contender to deal with the 45 nm technology node and beyond. But one problem exists in present pixel based mask synthesis algorithms: to describe mask patterns more accurately and to obtain better image quality, usually need finer grid representation, which results in extremely intensive computations. In this paper, a new method is proposed to mitigate this issue based on level-set method. This method utilizes the coarse-grid-approximation (CGA), which means the mask pattern defined on the fine grids is approximated using a new mask defined on coarse grids. The mask optimization is then performed on coarse girds and the final result is acquired by extracting mask patterns from coarse grids to fine grids. This method is demonstrated using a periodic array of contact holes pattern. Comparing with a gradient based algorithm and the traditional level-set algorithm, this method can provide almost the same image quality, but with over 100X running speed enhancement.

Source and Mask Co-Optimization Using a Gradient Based Method in Optical Lithography

With the technology node entering 45nm and below and the delay of the EUV lithography, the resolution enhancement techniques (RET) has been considered indispensable to extend the life time of conventional 193nm lithography. Traditional RETs, for example, optical proximity correction (OPC), phase-shifting mask (PSM), inverse lithography technique (ILT) and so on, use a fixed source thus limiting the degrees of freedom during the mask pattern optimization. To overcome the restriction, recently, source and mask co-optimization (SMO) has been proposed as a strong contender in RET. However, SMO is very computationally intensive. To mitigate the issue, we adopt a method which has demonstrated in good effectivity and efficiency in illumination source optimization. Based on the gray-level pixel based source representation, the gradient of the cost function is calculated to guide optimization to improve the wafer image fidelity and depth of focus (DOF). Moreover, the similar method has been used in mask optimization to form a complete SMO algorithm. The SMO algorithm is demonstrated using two mask patterns with critical dimension (CD) of 45nm, including a periodic array of contact holes and a tri-bar pattern. Both the results showed high image quality have been achieved using our SMO algorithm.

ILT Approach for Compensating 3-D Mask Effects

As mask features scale to smaller dimensions, the so-called “3-D mask effects” which have mostly been neglected before, become important. This paper properly models the 3-D thick mask effects, and then analyses the object-based inverse lithography technique using a simulated annealing algorithm to determine the mask shapes that produce the desired on-wafer results. Evaluations against rigorous simulations show that the synthesized masks provide good image fidelity up to 0.94, and this approach gives improved accuracy and faster results than existing methods.