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Reticle modification involving model-based optical proximity correction (MB-OPC) has driven generations of advanced CMOS nodes for more than two decades and may soon be carried over by inverse lithography technology (ILT). However, the demand for computational resources for ILT reticles cannot be addressed easily but only through massive parallel computation to this date. The development of quantum computing, in particular, quantum annealing algorism (QAA) is aimed to solve optimization problems in the real world, provided that the tasks can be framed into a binary quadratic model (BQM). Moreover, QAA is potentially capable of finding the global minimum solution of an optimization problem, instead of the local minimum provided by many gradient-based approaches. As the current ILT reticles have been largely generated using gradient-based algorithms, it is of great interest to investigate the applicability of QAA for reticle optimizations. We recast the mask optimization problem into a quadratic unconstrained binary optimization (QUBO) problem by defining the Hamiltonian as the difference between the target absolute amplitude image to that of an optimized mask. The approximation is valid due to the dominated first kernel in the sum of the coherent system (SOCS) approach for the aerial image calculation. The simulations are carried out in D-wave Advantage 6 system accessed through Amazon Bracket. Due to the limited number of qubits, we restrict the reticle optimization problems to N= 25, 36, 49, and 64 variables which map to a maximal 5760 physical qubits thru Pegasus embedding. In QAA, we investigate the effects of annealing time and inter-sample correlation, as well as the pausing strategies in the annealing schedule on the probability of finding the best solution to the target mask. We also compare the problem solved by QAA followed by the classical steepest descent (SD) algorithm versus the SD algorithm only. The hybrid QAA/SD approach produces the highest probability of finding the target mask with approximately two-thirds run time reduction from the SD solver only, suggesting that QAA indeed has the potential in finding the global-minimal solution.
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