Investigating the Effects of Inverted Temperature Dependence (ITD) on Clock Distribution Networks

The aggressive scaling of CMOS technology toward nanometer lengths contributed to the surfacing of many effects that were not appreciable at the micrometer regime. Among them, Inverted Temperature Dependence (ITD) is certainly the most unusual. It manifests itself as a speed up of CMOS gates when the temperature increases, resulting in a reversal of the worst-case condition, i.e., CMOS gates show the largest delay at low temperatures. On the other hand, for metal interconnects an high temperature still holds as worst case condition. The two contrasting behaviors may invalidate the results obtained through standard design flow which do not consider temperature as an explicit variable in their optimizations. In this paper we focus on the impact of ITD on clock distribution networks (CDN), whose function is vital to guarantee the synchronization among physically spaced sequential components of digital circuits. Using our simulation framework, we characterized the thermal behavior of a clock tree mapped onto an industrial 65nm CMOS technology and obtained using a standard synthesis tool. Results demonstrate the presence of ITD at low operating voltages and open new potential research scenarios into the EDA field.