Post-exposure bake (PEB) consists of neutralization, diffusion, and catalysis steps, and are modeled by partial differential equations (PDEs). Commercial PEB simulation relies on numerical methods to explicitly solve PDEs in both spatial and temporal domains, and is very time consuming. A machine learning model has been applied to quickly predict the final inhibitor distribution with initial acid distribution as a model input. The accuracy, however, is not good enough; for different PEB condition comprising baking time and temperature, the model should be trained again, which is another limitation. A recurrent neural network (RNN) is proposed for fast PEB simulation. The network is constructed around convolutional long short-term memory (convLSTM), which is a popular RNN for spatio-temporal prediction. Key inputs of convLSTM include the encoded values of acid and quencher distributions as well as their multiplication; acid and quencher distributions on next time step are obtained after the outputs of convLSTM pass through decoders. Once acid distribution is derived at time instance of interest, inhibitor distribution is extracted directly from its PDE. To accelerate RNN prediction, operations are skipped and the distribution at the next time step is simply copied from the one at the current time step if PEB reaction does not occur. Experiments have shown that the runtime of PEB simulation is reduced by 88.1% with smaller total PDE loss by 35.3%, compared to commercial tool.
Process variation band (PVB) is important for a number of lithography applications such as yield estimation, hotspot detection, and so on. It is derived through multiple lithography simulations of a mask pattern while optical settings such as dose and focus are varied. Quick estimation of PVB has been studied. A simple approach assumes optical settings for innermost and outermost PVB contour; it requires only two simulations, but the assumption of such optical settings does not always hold. We postulate that two sets of good custom kernels exist; one set for lithography simulation to extract outermost PVB contour, and the other for innermost PVB contour. Since lithography simulation can be mapped to a convolutional neural network (CNN) with kernels corresponding to convolution filters, each set can be obtained by training corresponding CNN with a number of sample reference contours. Our experiments indicate that the average intersection over union (IoU) between reference- and predictedPVBs reaches 97% with 0 PBVs having IoU smaller than 50%. This can be compared to the state-of-art of PVB prediction using conditional generative adversarial networks (cGANs), where average IoU is only 89% with 12 PBVs having IoU smaller than 50%.
Model-based optical proximity correction (MB-OPC) consists of fragmentation which is decomposed into segments and iterative simulations and corrections with a feedback system. Mask bias for each segment is iteratively corrected by heuristic rule-based PID control. Although mask pattern is various, the same PID parameters are adopted. We apply reinforcement learning (RL) as a PID parameters predictor. Pattern-aware adaptive PID control through RL has the benefit of EPE convergence. RL model receives layout features and PFT values as its inputs. The reward of RL model is designed for minimizing EPE from the current mask.
Diversity of known hotspot patterns is important for hotspot detection and correction. Deliberate synthesis of hotspot patterns can improve such diversity. Machine learning generative network is a popular tool for image synthesis, but it should be trained with known hotspots anyway. We propose U-net hotspot generator. A key is to train the generator with CNN hotspot probability model, i.e. the generator is trained such that output is a variant of input image with high hotspot probability. The method allows any patterns, even coldspots, to be provided to the generator, which then yields their hotspot variants. Efficiency of hotspot generator is demonstrated through experiments.
MB-OPC contains a fragmentation step, in which each polygon edge is divided into a number of segments. Simple empirical rules dictate how the edges should be divided. Fragmentation strongly affects MB-OPC in its quality and runtime since OPC correction is performed segment by segment. Refragmentation using random forest classifier (RFC) is proposed. A segment and its surroundings are modeled using a number of features, which drive RFC to decide whether a segment should be further divided or not. It complements rule-based fragmentation in that small number of critical segments, which are not short enough and cause longer MB-OPC iterations, are quickly identified. When refragmentation is applied in standard rule-based fragmentation and MB-OPC flow, maximum EPE is reduced substantially (from 3.8nm to 2.4nm) with very marginal increase in the number of segments (7k to 7,093), yet OPC iterations are reduced (10 down to 8).
While technology is being developed, design rules undergo a number of revisions. An initial lithography model built with test patterns before the revisions inherently become inaccurate for the revised patterns. Preparing a new test layout and updating a lithography model every time design rules are revised is not practical, and cannot be a solution. We prepare some synthetic patterns in addition to initial test patterns. Synthetic patterns originate from popular test pattern generator (TPG), while projected design rule changes are taken into account. A challenge is to sort out the synthetic patterns which are really necessary in building a generic lithography model when they are used together with test patterns. Each pattern, either synthetic or test, is identified in image parameter set (IPS) space. For each test pattern in IPS space, two concentric spheres are drawn; outer one indicating the region where revised versions of test pattern may exist, and inner one indicating the region which is well covered by test pattern alone. Synthetic patterns that reside in the region bounded by the two spheres are kept, while the others are dropped. Clustering is now performed on test patterns and synthetic patterns separately, and representative pattern is drawn from each cluster. When a set of representative patterns are used to build a lithography model in 10nm memory devices, it achieves 43.5% lower CD root mean square error (RMSE) for revised design layout compared with only using a set of initial test patterns.
Fast computation of process variation band (PVB) is critical for several lithography applications such as yield estimation, hotspot detection, mask optimization, and etc. Conventionally, PVB is computed by lithography simulation that is very slow and can only be applied for a small part of a chip. These small parts of a chip are identified through a pattern matching process, where unseen patterns are often missed. We explore conditional generative adversarial networks (cGANs), a couple of machine learning models, for predicting PVB with high speed and sufficient accuracy. In our proposed method, we divide a full-chip into several small clips and then predict PVB for a small region of interest at the center of each clip. Experiments show that our proposed method can successfully predict PVB for more than 98% of the patterns with an average accuracy, and speedup of 86%, and 500 times, respectively, compared to the rigorous lithography simulation.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.