# Circuit design algorithm compensates for tangled nanotubes

SAN DIEGO — Researchers from Stanford University reported Thursday (June 7) at the Design Automation Conference here on a way to design circuits that should work even when many of the nanotubes in them are twisted and misaligned.

Nanotubes tend to grow with unpredictable kinks and bends that can cause bad wiring connections. The resarchers came to the conclusion that engineers will have to design circuits that will work regardless of where and how the tubes lie.

They came up with a single circuit element—a NAND gate—that was immune from the vagaries of its underlying nanotube layout. From that single element, they abstracted and generalized the math to come up with an algorithm that they say can guarantee a working design for any circuit element, despite the presence of misaligned tubes.

The key to determining whether a circuit element is immune to nanotube misalignment is breaking up each circuit element into a fine grid that can be analyzed mathematically. Doing this in the abstract with models allows engineers to determine which grid squares nanotubes must pass through and which they shouldn't traverse to make a design work correctly.

To eliminate unwanted connections, nanotubes in so-called illegal regions can then be either chemically etched away or rendered electrically irrelevant by other means.

The Stanford algorithm takes the concept several steps further, applying sophisticated mathematics to determine automatically where the legal and illegal regions should be in the design of a circuit element with a particular function.

While the algorithm can overcome all the bad connections that errant nanotubes make, it cannot guarantee that a nanotube will always make a desired connection.

The group's next step is to move beyond simulation to build and test real circuit elements according to the algorithm's output.

Microelectronics Advanced Research Corp. supported the research.