Using the Leibler-Ohta-Kawasaki (LOK) phase-field model of block copolymers (BCPs), we characterize how a chemoepitaxial template with parallel lines of arbitrary width affects the BCP microdomain shape. We apply boundary conditions that account for the interactions of the polymers with the templated substrate and a neutral top-coat. We derive formulas for the monomer density and the microdomain interface profile of periodic, lamellar BCP melts whose template lines are wider or narrower than the bulk microdomain width. For such systems, our analysis (i) shows that mass conservation causes the microdomain interfaces to oscillate about their bulk positions and (ii) determines the length scale λ over which these oscillations decay away from the substrate.
Block copolymers oer an appealing alternative to current lithographic techniques with regard to fabrication of the next generation micro-processors. However, if copolymers are to be useful on an industrial manufacturing scale, they must meet or exceed lithography specications for placement and line edge roughness (LER) of resist features. Here we discuss a eld theoretic approach to modeling the LER of lamellar microdomain interfaces in a strongly segregated block copolymer system; specically, we derive a formula for the LER as a functions of the Flory Huggins parameter and the index of polymerization N. Our model is based on the Leibler-Ohta-Kawasaki energy functional. We consider a system with a nite number of phase separated microdomains and also show how the LER depends on distance of the microdomain interface from the system boundary. Our results suggest that in order to meet target LER goals at the 15 nm, 11 nm, and 6 nm nodes, must be increased by a factor of at least 5 above currently attainable values.