Tube Redundancy in Statistical Evaluation of Critical Path Delay of CNFET Circuits in the Presence of Tube variations

Due to limited controllability over the tube growth process, Carbon Nanotube Field-Effect Transistors (CNFET) show large variations in their behavior. These variations are primarily caused by variation in CNT diameter and the presence of metallic tubes (m-CNT) in, what it should be, purely semi-conducting (s-CNT) arrays. For proper operation of a CNFET metallic tubes have to be removed, unintentionally reducing transistor strength. This work proposes to use a calculated minimum CNT redundancy at the transistor level to improve functional yield for a given failure rate. We focus our evaluation on a critical path that in reality, due to metallic tube presence, could be a different path in each circuit. We limit the redundancy to a minimum required, to avoid unnecessary increase in the channel area. The calculated minimum number of redundant CNTs are added to each CNFET to achieve only slightly increased statistical critical path delay after m-CNT removal, compared to the ideal critical path delay. We use a statistical approach to improve prediction accuracy for both critical path delay and functional yield. With proposed minimum redundancy we are able to reduce the allowed delay degradation (tolerance) by 15-25% and still have a good functional yield. Results show a reduction of 7-10% in critical path delay variation of ISCAS'85 logic benchmark circuits with >99% functional yield (Yf).