of block copolymer self-assembly and its low thermodynamic driving force leads to the simultaneous formation of multiple uncorrelated grains with trapped defects at their boundaries, which significantly limits usability. Furthermore, in films, one of the blocks often preferentially wets the substrate surface, which may cause the formation of patterns that cannot be used for applications. These fundamental challenges to generating desired block copolymer patterns have motivated researchers to find ways to control orientation and ordering in films, resulting in various successful means to induce block copolymer alignment and defect elimination. [15,16] Alignment and ordering strategies include the application of external electric [17] or magnetic fields, [18] solvent vapor annealing, [19,20] and the use of patterned substrates. [21][22][23] The use of either chemically [24] or topographically [25][26][27][28] patterned substrates to direct block copolymer selfassembly in films is particularly interesting as it allows the control of domain orientation, the creation of defect-free patterns, and precise pattern registration on a substrate (Figure 2), which is especially interesting for applications requiring addressability of nanoscale features. The use of substrates with particular chemical patterns allows directing block copolymers to perfectly replicate the underlying pattern [24] (Figure 2c) and has therefore been termed epitaxial self-assembly or "chemoepitaxy." Guiding the assembly of block copolymers by topographical features of lithographically defined substrate patterns is also known as "graphoepitaxy" [25] -it refers to the use of a topographic substrate to, for example, preferentially align block copolymer lamellae parallel to the trenches (Figure 2d). These hybrid approaches combine bottom-up self-assembly with topdown patterning to precisely define desired substrate patterns. This concept focuses on directing the self-assembly of block copolymers using chemically and topographically patterned substrates. The reader is referred to recent reviews for details on the fabrication of chemical [22,29,30] and topographic patterns, [31] as well as alternative approaches to controlling block copolymer self-assembly, e.g., by using interfacial effects, solvents, film deposition processes, and advanced thermal annealing. [15,16,21,32]
Chemical Patterning: ChemoepitaxyThe chemical patterning of block copolymers has been closely linked to one specific diblock copolymer, namely, polystyreneb-poly(methyl methacrylate) (PS-b-PMMA). The chemical Self-assembling block copolymer films provide access to a variety of different nanostructured patterns in one, two, and three dimensions. However, in the absence of any templating, these nanostructures suffer from defects, often limiting utility. Directed block copolymer self-assembly uses patterned substrates that effectively suppress defect formation and allow the creation of desired patterns. The two main directed self-assembly techniques, chemoepitaxy and graphoepitaxy, employ...