Using Lyapunov Exponents to Estimate Sensitivity to Process Variability

The scaling of integrated circuits makes them more susceptible to faults, as the ones due to the effects of radiation and process variability. Failures related to process variability can cause circuits to operate outside their specification ranges. In most cases, simulations are used to analyze such effects, but simulations have high computational costs. This work aims to use Mathematical Chaos Theory through Lyapunov's Exponents to estimate analytically the effects caused by manufacturing process variability, resulting in a method that can estimate transistor variability with an accuracy equivalent to simulation-based methods but one hundred times faster, on average. The main physical factors that impact the on and off-current variations are analyzed. So, there is no need for simulations when using the proposed approach. As it has been proved that the functions representing the currents are contractions, it is possible to estimate the distortions using the derivative of the functions at a specific point. The applications are carried out for FinFET technology, and the results show that variations in the work function represent the most significant impact.