Lamellar Diblock Copolymers on Rough Substrates: Self-consistent Field Theory Studies

TL;DR

This study uses self-consistent field theory to analyze how substrate roughness influences the orientation of lamellar diblock copolymers, revealing conditions that favor perpendicular alignment for nanolithography applications.

Contribution

It provides a quantitative analysis of the critical substrate roughness needed for lamellar orientation transition, considering surface preference, film thickness, and polymer parameters.

Findings

Critical roughness increases with surface preference and film thickness.

Rough substrates can induce perpendicular lamellae even with surface preference.

Results align with experimental observations and inform nanolithography techniques.

Abstract

We present numerical calculations of lamellar phases of di-block copolymers (BCP) confined between two surfaces, where the top surface is flat and the bottom one is corrugated. The corrugated substrate is assumed to have a single $q$-mode of lateral undulations with a wavenumber q_s and amplitude R. We focus on the effects of substrate roughness, parameterized by the dimensionless quantity, q_sR, on the relative stability between parallel and perpendicular orientations of the lamellar phase. The competition between film confinement, energy cost of elastic deformation and gain in surface energy induces a parallel-to-perpendicular transition of the BCP lamellae. Employing self-consistent field theory (SCFT), we study the critical substrate roughness value corresponding to this transition. The critical value increases as function of the surface preference towards one of the two BCP components, and as function of film thickness. But, it decreases with increasing values of the Flory-Huggins parameter. Our findings are equivalent to stating that the critical value decreases as the BCP molecular weight or the natural BCP periodicity increases. We further show that the rough substrate can overcome the formation of parallel lamellae in cases where the top surface has a preference towards one of the two BCP components. Our results are in good agreement with previous experiments, and highlight the physical conditions behind the perpendicular orientation of lamellar phases, as is desired in nanolithography and other industrial applications.