The directed self-assembly (DSA) of a 20 nm full-pitch silicon-containing block copolymer (BCP), poly(4-methoxystyrene-b-4-trimethylsilylstyrene), was performed using a process that produces shallow topography for hybrid chemo-/grapho-epitaxy. This hybrid process produced DSA with fewer defects than the analogous conventional chemo-epitaxial process, and the resulting DSA was also more tolerant of variations in process parameters. Cross-sectional scanning transmission electron microscopy (STEM) with electron energy loss spectroscopy (EELS) confirmed that BCP features spanned the entire film thickness on hybrid process wafers. Both processes were implemented on 300 mm wafers initially prepatterned by 193 nm immersion lithography, which is necessary for economic viability in high-volume manufacturing. Computational analysis of DSA extracted from top-down SEM images demonstrates the influence of process parameters on DSA, facilitating the optimization of guide stripe width, guide stripe pitch, and prepattern surface energy. This work demonstrates the ability of a hybrid process to improve the DSA quality over a conventional chemo-epitaxial process and the potential for high-volume manufacturing with high-χ, silicon-containing BCPs.