Design method and algorithms for directed self-assembly aware via layout decomposition in sub-7 nm circuits

Multiple patterning via layout decomposition method for directed self-assembly lithography

“…To satisfy these restrictive rules, it is necessary to implement a decomposition algorithm that can group vias/contacts into guiding templates and assign templates to different masks while using the minimum number of masks. 4 Although general decomposition problems fall under the category of NP-hard, indicating that their inherent complexity cannot be feasibly solved within polynomial time, various efficient algorithms have been proposed to provide high-quality solutions. Conventional approaches can be divided into two categories: mathematical modeling and graph-based approaches.…”

“…These three algorithms are used in a series of sequential steps. 4 All of these methods have demonstrated the high efficiency of the decomposition problem. However, to fit the VLSI design or dense layout, there are still some shortages as follows.…”

“…For example, if 193-nm immersion (193i) lithography is used, then only the collinear contacts in the horizontal or vertical directions can be patterned in one guiding template, whereas the shape of the guiding template can be more complicated if E-beam or EUV lithography is used (e.g., L-shaped templates and templates with arbitrary directions). To satisfy these restrictive rules, it is necessary to implement a decomposition algorithm that can group vias/contacts into guiding templates and assign templates to different masks while using the minimum number of masks 4 …”

“…proposed a method that incorporates exhaustion, path solving, and generational solving to solve the complex layout. These three algorithms are used in a series of sequential steps 4 …”

Commensurability-Driven Orientation Control during Block Copolymer Directed Self-Assembly

“…Block copolymer (BCP) self-assembly can generate a range of nanostructures that have many potential applications in photonics, − plasmonics, , electronics, , nanometrology, filtration membranes, , and energy devices. , Directed self-assembly (DSA) of BCPs using topographic or chemical prepatterns to render long-range order has been intensively studied because it is a promising next-generation lithography technique that can offer sub-photolithographic resolution with minimum cost. − For example, a recent DSA study using line templates successfully demonstrated finFET fabrication at the 7 nm node, in which the device performance is comparable to that of the finFETs manufactured using photolithography . DSA has also been used as a complementary lithographic method for contact hole patterning in two-dimensional (2D) templates. − Two-dimensional templates have been used to generate interesting nanostructures including spirals, rings, and line patterns with 90° bends and T-junctions. − In particular, we showed that structures with two degenerate orientations could be formed using a square template, and the degeneracy could be broken (i.e., one of the possible orientations selected) by placing openings around the edges of the templates . However, the controllability of orientation via the wall openings is limited in the sense that the orientation of neighboring cells cannot always be controlled independently.…”