(32c) Free Energy of Defects in Aligned Block Copolymer Systems Via Thermodynamic Integration of a Coarse Grained Block-Copolymer Model

Directed self-assembly (DSA) of block copolymers (BCPs) is a promising technique for producing nanoscale regular patterns.  In particular, DSA of block copolymers is a leading candidate for extending current optical lithography capabilities below the 20 nm feature size scale for producing device features in semiconductor manufacturing.  However, development of such techniques can be a time consuming and difficult proposition given the number of possible material and process variable combinations to explore, the limited knowledge of the fundamental behavior of such systems, and the difficulty in observing the assembled materials.  Thus, the development of such DSA techniques could benefit greatly from predictive computer simulation methods that can faithfully represent the behavior of such materials and processes.  One option for simulation of BCP-DSA is molecular  dynamics (MD), which, when combined with realistic potentials for polymer behavior, can potentially provide more accurate simulations of the inherent polymer  behavior, dynamics, and equilibrium states without oversimplifying interatomic interactions and without the  need to guess  modes of molecular movement.  An important issue in bringing such DSA techniques to fruition is developing an understanding of defectivity in such processes and what controls these defect rates.  In addition to determining equilibrium material structures and exploring the dynamics of such processes, MD models can also be used with thermodynamic integration techniques to calculate free energy differences between various states, provided a reversible path can be envisioned between them. Using such thermodynamic integration techniques, various equilibrium and metastable states can be compared.  In this work, MD combined with thermodynamic integration has been used to calculate defect state free energies in self-assembled block copolymer thin films.  Using such free energy data, defect densities can be calculated as functions of relevant system parameters such as the polymer and underlayer properties. In this work, defect free energies are calculated as a function of χ, N, and underlayer pattern properties (e.g. composition and multiplicity).  A more complete picture of defectivity in DSA systems has evolved from this work and will be discussed.  For example, though others have calculated free energies of defects as a function of χN, the independent contributions of χ and N are more informative. A high χ, low N system yields a significantly higher defect free energy than a low χ, high N system, even when χN is the same in the two systems.