Nanowire addressing with randomized-contact decoders

Methods for assembling crossbars from nanowires (NWs) have been designed and implemented and methods for controlling individual NWs within a crossbar have also been proposed. However, implementation remains a challenge. A NW decoder is a device that controls many NWs with a much smaller number of lithographically produced mesoscale wires (MWs). Unlike traditional demultiplexers, all proposed NW decoders are assembled stochastically. In a randomized-contact decoder (RCD), for example, field-effect transistors are randomly created at about half of the NW/MW junctions. In this paper, we tightly bound the number of MWs required to produce a correctly functioning RCD with high probability. We show that the number of MWs is logarithmic in the number of NWs, even when manufacturing errors occur. We also analyze the overhead associated with controlling a stochastically assembled decoder. As we explain, lithographically-produced control circuitry must store information regarding which MWs control which NWs. This requires more area than the MWs themselves, but has received little attention elsewhere. Finally we analyze several simple testing algorithms for configuring this control circuitry. We demonstrate an unexpected tradeoff between testing time and the number of MWs required by an RCD.