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The combinatorial nature of many important mathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecularmotor-propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NPcomplete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology.parallel computing | molecular motors | NP complete | biocomputation | nanotechnology M any combinatorial problems of practical importance, such as the design and verification of circuits (1), the folding (2) and design (3) of proteins, and optimal network routing (4), require that a large number of possible candidate solutions are explored in a brute-force manner to discover the actual solution. Because the time required for solving these problems grows exponentially with their size, they are intractable for conventional electronic computers, which operate sequentially, leading to impractical computing times even for medium-sized problems. Solving such problems therefore requires efficient parallel-computation approaches (5). However, the approaches proposed so far suffer from drawbacks that have prevented their implementation. For example, DNA computation, which generates mathematical solutions by recombining DNA strands (6, 7), or DNA static (8) or dynamic (9) nanostructures, is limited by the need for impractically large amounts of DNA (10-13). Quantum computation is limited in scale by decoherence and by the small number of qubits that can be integrated (14). Microfluidics-based parallel computation (15) is difficult to scale up in practice due to rapidly diverging physical size and complexity of the computation devices with the size of the problem, as well as the need for impractically large external pressure.Here, we propose a parallel-computation approach, which is based on encoding combinatorial problems into the geometry of a physical network of lithographically defined channels, followed by exploration of the network in a par...

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A bilayer resist system, consisting of hydrogen silsesquioxane (HSQ) as negative tone electron (e)-beam resist top coat and hard baked novolak resist as bottom coat, has been investigated for its ability to yield high aspect ratio nanoscale structures. For comparison, single layer HSQ (hard mask) has been investigated for its resolution, contrast, and process latitude. In single layer HSQ, dense lines and spaces (1:1) have been resolved down to 20 nm and single lines have been obtained with widths less than 15 nm. Processing conditions which result in higher contrasts in HSQ also result in higher horizontal contrasts, i.e., in poorer process latitudes; this effect has previously been observed for other negative tone e-beam resists as well. In the bilayer combination, HSQ allows nanoscale structures with an aspect ratio exceeding 15 to be etched in hard baked novolak resist. Single lines with 800 nm height and 40 nm width, semidense lines and spaces (1:2) with 155 nm height and 25 nm width, and dense lines and spaces (1:1) with 130 nm height and 40 nm width have been patterned in this bilayer system. Both the single layer HSQ and the HSQ/novolak bilayer system appear to be suitable as e-beam resists for research on nanoscale gates in complementary metal–oxide–semiconductor (CMOS) and other devices.