Modeling multiple input switching of CMOS gates in DSM technology using HDMR

Continuing scaling of CMOS technology has allowed aggressive pursuant of increased clock rate in DSM chips. The ever shorter clock period has made switching times of different inputs on a logic gate ever closer to each other. The traditional method of static timing analysis assuming single input switching is no longer adequate enough to capture gate level delays accurately. Gate delay models considering multiple input switching are needed for DSM chips. We propose a new method of systematically modeling gate delays using the high dimensional model representation (HDMR) method. The proposed method models gate delays with respect to the relative signal arrival times (RSAT) of its inputs. The systematic nature of the proposed algorithm allows gate delay characterization with more inputs switching close to each other. This paper will show, for the first time, gate delay models of up to 5 inputs. In addition, the proposed model is extended to allow the input signal slope and process variations to be taken into account for statistical static timing analysis. Our results show that the proposed HDMR model gives an error between 2.2% to 12.9% for a variety of static and dynamic logic gates as compared to SPICE results, depending on the number of inputs involved in switching