Reliability evaluation of logic circuits using probabilistic gate models

Logic circuits built using nanoscale technologies have significant reliability limitations due to fundamental physical and manufacturing constraints of their constituent devices. This paper presents a probabilistic gate model (PGM), which relates the output probability to the error and input probabilities of an unreliable logic gate. The PGM is used to obtain computational algorithms, one being approximate and the other accurate, for the evaluation of circuit reliability. The complexity of the approximate algorithm, which does not consider dependencies among signals, increases linearly with the number of gates in a circuit. The accurate algorithm, which accounts for signal dependencies due to reconvergent fanouts and/or correlated inputs, has a worst-case complexity that is exponential in the numbers of dependent reconvergent fanouts and correlated inputs. By leveraging the fact that many large circuits consist of common logic modules, a modular approach that hierarchically decomposes a circuit into smaller modules and subsequently applies the accurate PGM algorithm to each module, is further proposed. Simulation results are presented for applications on the LGSynth91 and ISCAS85 benchmark circuits. It is shown that the modular PGM approach provides highly accurate results with a moderate computational complexity. It can further be embedded into an early design flow and is scalable for use in the reliability evaluation of large circuits.