Defect-tolerant Logic with Nanoscale Crossbar Circuits

Crossbar architectures are one approach to molecular electronic circuits for memory and logic applications. However, currently feasible manufacturing technologies introduce numerous defects so insisting on defectfree crossbars would give unacceptably low yields. Instead, increasing the area of the crossbar provides enough redundancy to implement circuits in spite of the defects. We identify reliability thresholds in the ability of defective crossbars to implement boolean logic. These thresholds vary among different implementations of the same logical formula, allowing molecular circuit designers to trade-off reliability, circuit area and the computational complexity of locating functional components. We illustrate these choices for an AND gate and, of more practical interest, binary adders.