Line Roughness in Lamellae-Forming Block Copolymer Films

We study the line roughness in poly(styrene-b-methyl methacrylate) symmetric block copolymer thin films and propose a phenomenological model to fit and describe the observed line edge, width, and placement roughness. Owing to the layering structure of symmetric block copolymers, we build from the model used to describe the thermal fluctuations in bilayer membranes and add a term for the bulk composition fluctuations in a phase segregated system. We use the peristaltic and undulatory modes of bilayer membranes to describe the width and placement roughness, respectively. We also include the correlations between adjacent domains to capture the cross-talk between alternating domains. We find that the model reproduces most of the main features observed in the power spectral density of our block copolymer films, providing a baseline to understand the physical properties that influence line roughness in a system relevant to nanolithography.