Circuit propagation delay estimation through multivariate regression-based modeling under spatio-temporal variability

Abstract

With every process generation, the problem of variability in physical parameters and environmental conditions poses a great challenge to the design of fast and reliable circuits. Propagation delays which decide circuit performance are likely to suffer the most from this phenomena. While Statistical static timing analysis (SSTA) is used extensively for this purpose, it does not account for dynamic conditions during operation. In this paper, we present a multivariate regression based technique that computes the propagation delay of circuits subject to manufacturing process variations in the presence of temporal variations like temperature. It can be used to predict the dynamic behavior of circuits under changing operating conditions. The median error between the proposed model and circuit-level simulations is below 5%. With this model, we ran a study of the effect of temperature on access time delays for 500 cache samples. The study was run in 0.557 seconds, compared to the 20h and 4min of the SPICE simulation achieving a speedup of over 1×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> . As a case study, we show that the access times of caches can vary as much as 2.03× at high temperatures in future technologies under process variations.