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.
We present the design, analysis, and real-time implementation of a distributed computation particle filter on a graphic processing unit (GPU) architecture that is especially suited for fast real-time control applications. The proposed filter architecture is composed of a number of local subfilters that can share limited information among each other via an arbitrarily chosen abstract connected communication topology. We develop a detailed implementation procedure for GPU architectures focusing on distributed resampling as a crucial step in our approach, and describe alternative methods in the literature. We analyze the role of the most important parameters such as the number of exchanged particles and the effect of the particle exchange topology. The significant speedup and increase in performance obtained with our framework with respect to both available GPU solutions and standard sequential CPU methods enable particle filter implementations in fast real-time feedback control systems. This is illustrated via experimental and simulation results using a real-time visual servoing problem of a robotic arm capable of running in closed loop with an update rate of 100 Hz, while performing particle filter calculations that involve over one million particles.