Graphoepitaxial Control of Lamellar Block Copolymer Alignment in Wide Trenches: Effects of Trench Width and Sidewall Tilt

Graphoepitaxy provides a robust route to align lamellar block copolymers in topographic trenches, yet alignment often degrades rapidly as the trench width increases into the wide-trench regime. Here, mesoscale density functional simulations under thermal annealing are used to quantify width- and geometry-dependent ordering of symmetric lamella-forming block copolymers confined in trenches. A Fourier-based alignment metric reveals a sharp, sigmoidal decay of alignment with trench width normalized by the natural lamellar period, indicating a crossover between (i) a globally aligned state established by wall-guided propagation and (ii) a misoriented, kinetically trapped state produced by bulk-like interior nucleation followed by domain impingement. This width dependence is well captured by a logistic form, yielding a characteristic crossover width and transition sharpness that compactly describe the accessible alignment window. Parameter sweeps show that increasing incompatibility shifts the crossover to smaller widths, whereas stronger sidewall surface fields extend the accessible width range with diminishing returns at large fields; in the range examined, film thickness has little influence on the crossover. Finally, simulations in trapezoidal trenches demonstrate that high alignment persists for moderate sidewall taper, while larger taper promotes lamellar bending and defects. A geometric criterion based on the variation in trench width across the film thickness, using a numerical threshold derived from strong-segregation theory, rationalizes the observed onset of degradation when this variation approaches approximately 1.4 lamellar periods. These results provide a mechanistic framework and quantitative guidelines for extending graphoepitaxial lamellar alignment beyond the narrow-confinement regime.