  Self-consistent field theory (SCFT) and strong segregation theory (SST) are
used to explore the parameter space governing the self-assembly of cylinder
forming block copolymers (BCPs) on a modulated substrate. The stability of
in-plane cylinders aligning parallel or perpendicular to substrate corrugation
is investigated for different barrier height and spacing for a weakly
preferential substrate. Within the conditions of our simulations, the results
indicate that cylinder alignment orthogonal to substrate undulation is promoted
at low barrier height when substrate is preferential to minority block,
independent of barrier spacing. Commensurability is shown to play a limited
role in the assembly of orthogonal meshes. Parallel alignment is readily
achieved at larger barrier height, near condition of commensuration between
barrier spacing and polymer equilibrium period. This is particularly true when
substrate is attractive to majority block. The interplay between barrier shape
and substrate affinity can be utilized in nanotechnology application such as
mesh creation, density multiplication, and 3D BCP morphologies.
