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.
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).
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