Extreme Ultraviolet (EUV) photolithography is seen as the key enabler for increasing transistor density in the next decade. In EUV lithography, 13.5 nm EUV light is illuminated through a reticle, holding a pattern to be printed, onto a silicon wafer. This process is performed about 100 times per wafer, at a rate of over a hundred wafers an hour. During this process, a certain percentage of the light energy is converted into heat in the wafer. In turn, this heat causes the wafer to deform which increases the overlay error, and as a result, reduces the manufacturing yield. To alleviate this, we propose a firm real-time control system that uses a wafer heat feed-forward model to compensate for the wafer deformation. The model calculates the expected wafer deformation, and then, compensates for that by adjusting the light projection and or the wafer movement. However, the model computational demands are very high. As a result, it needs to be executed on dedicated HW that can perform computations quickly. To this end, we deploy Graphics Processing Units (GPUs) to accelerate the calculations. In order to fit the computations within the required time budgets, we combine in a novel manner multiple techniques, such as compression and mixed-precision arithmetic, with recent advancements in GPUs to build a GPU-based real-time control system. A proof-of-concept implementation using NVIDIA P100 GPUs is able to deliver decompression throughput of 33 GB s and a sustained 198 GFLOP s per GPU for mixed-precision dense matrix-vector multiplication.
In the present work, fault detection in industrial automation processes is investigated. A fault detection method for observable process variables is extended for application cases, where the observations of process variables are noisy. The principle of this method consists in building a probability distribution model and evaluating the likelihood of observations under that model. The probability distribution model is based on a hybrid automaton which takes into account several system modes, i.e. phases with continuous system behaviour. Transitions between the modes are attributed to discrete control events such as on off signals. The discrete event system composed of system modes and transitions is modeled as finite state machine. Continuous process behaviour in the particular system modes is modeled with stochastic state space models, which incorporate neural networks. Fault detection is accomplished by evaluation of the underlying probability distribution model with a particle filter. In doing so both the hybrid system model and a linear observation model for noisy observations are taken into account. Experimental results show superior fault detection performance compared to the baseline method for observable process variables. The runtime of the proposed fault detection method has been significantly reduced by parallel implementation on a GPU.