Self Heating-Aware Optimal Wire Sizing under Elmore Delay Model

Global interconnect temperature keeps rising in the current and future technologies due to self-heating and the adiabatic property of top metal layers. The thermal effects impact adversely both reliability and performance of the interconnect wire, shortening the interconnect lifetime and increasing the interconnect delay. Such effects must be considered during the process of interconnect design. In this paper, one important argument is that the traditional linear dependence between wire resistance and wire width is no longer adequate for high layer interconnects due to the adiabatic property of these wires. By using curve fitting technique, we propose a quadratic model to represent the resistance of interconnect, which is aware of the thermal effects. Based on this model and the Elmore delay model, we derived a linear optimal wire sizing formula in form of f(x) = ax + b. Compared to non-thermal-aware exponential wire sizing formula inform of f(x) = ae
^-bx
, we observed a 49.7% average delay gain with different choices of physical parameters