Numerical investigation of local defectiveness control of diblock copolymer patterns

TL;DR

This paper numerically studies how to control local defects in diblock copolymer patterns by designing substrates, using a nonlocal Cahn-Hilliard model and various boundary conditions to simulate phase separation.

Contribution

It introduces a finite difference scheme for the nonlocal Cahn-Hilliard equation applied to tapered trench designs for defect control in copolymer patterns.

Findings

Channel width affects defect formation

Boundary conditions influence phase separation dynamics

Simulation results align with experimental observations

Abstract

We numerically investigate local defectiveness control of self-assembled diblock copolymer patterns through appropriate substrate design. We use a nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of diblock copolymers. We discretize the nonlocal CH equation by an unconditionally stable finite difference scheme on a tapered trench design and, in particular, we use Dirichlet, Neumann, and periodic boundary conditions. The value at the Dirichlet boundary comes from an energy-minimizing equilibrium lamellar profile. We solve the resulting discrete equations using a Gauss-Seidel iterative method. We perform various numerical experiments such as effects of channel width, channel length, and angle on the phase separation dynamics. The simulation results are consistent with the previous experimental observations.