Understanding defects in DSA: calculation of free energies of block copolymer DSA systems via thermodynamic integration of a mesoscale block-copolymer model

Directed self-assembly (DSA) of block copolymers (BCPs) is a promising method for producing the sub-20nm features required for future semiconductor device scaling, but many questions still surround the issue of defect levels in DSA processes. Knowledge of the free energy associated with a defect is critical to estimating the limiting equilibrium defect density that may be achievable in such a process. In this work, a coarse grained molecular dynamics (MD) model is used to study the free energy of a dislocation pair defect via thermodynamic integration. MD models with realistic potentials allow for more accurate simulations of the inherent polymer behavior without the need to guess modes of molecular movement and without oversimplifying atomic interactions. The free energy of such a defect as a function of the Flory- Huggins parameter (χ) and the total degree of polymerization (N) for the block copolymer is also calculated. It is found that high pitch multiplying underlayers do not show significant decreases in defect free energy relative to a simple pitch doubling underlayer. It is also found that χN is not the best descriptor for correlating defect free energy since simultaneous variation in chain length (N) and χ value while maintaining a constant χN product produces significantly different defect free energies. Instead, the defect free energy seems to be directly correlated to the χ value of the diblock copolymer used. This means that as higher χ systems are produced and utilized for DSA, the limiting defect level will likely decrease even though DSA processes may still operate at similar χN values to achieve ever smaller feature sizes.