The directed assembly of block copolymers is a promising approach to extend lithographic processes and fabricate devices with critical dimensions below 10 nm. However, morphologies produced through spontaneous self-assembly usually lack the long-range order which is desirable for applications. The use of patterned substrates, either chemically or topographically, are two proposed solutions to enforce long-range order. We use Monte Carlo simulations of a coarse-grained model to study those strategies and identify under which conditions a defect-free assembly is obtained. The cases of standing cylinders and lamellae are both considered.

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