A Finite-Point Method for Efficient Gate Characterization Under Multiple Input Switching

Abstract

Timing characterization of standard cells is one of the essential steps in VLSI design. The traditional static timing analysis (STA) tool assumes single input switching models for the characterization of multiple input gates. However, due to technology scaling, increasing operating frequency, and process variation, the probability of the occurrence of multiple input switching (MIS) is increasing. On the other hand, considering all possible MIS scenarios for the characterization of multiple input logic gates, is computationally intensive. To improve the efficiency, this work proposes a finite-point-based characterization methodology for multiple input gates with the effects of MIS. Furthermore, delay variation due to MIS is integrated into the STA flow through propagation of switching windows. The proposed modeling methodology is validated using benchmark circuits at the 45nm technology node for various operating conditions. Experimental results demonstrate significant reduction in computation cost and data volume with less than ∼10% error compared to that of traditional SPICE simulation.

A Simple Hybrid Model for Accurate Delay Modeling of a Multi-Input Gate

“…Note that δ ↓ S (−∞) = δ ↓ S (∞) is mainly caused by transistor T 2 , which is closed in one case, connecting nodes N and O, while in the other it is open (see Section III). Although the absolute values differ, our results fit very well 2 to previous investigations in other technologies [7], [8], [9].…”

“…A less visible phenomenon of the speed-up MIS effect deserve to be mentioned here: Simulations for an older 65 nm technology and results reported in the literature (e.g. in [7], [8]) reveal local delay maxima for medium-sized |∆|. We conjecture these to be caused by input-output coupling capacitances, which introduce a current working against the intended behavior of the gate.…”

“…Multiple approaches have been proposed to cover MIS effects in literature, ranging from linear [7] or quadratic fitting [8] over higher-dimensional model representation [9] to recent machine learning methods [10]. However, none of these naturally generalizes to multi-input involution channels.…”