Repeater Insertion in Tree Structured Inductive Interconnect: Underlying Theory

The effects of inductance on repeater insertion in RLC trees is the focus of this paper. An algorithm is introduced to insert and size repeaters within an RLC tree to optimize a variety of possible cost functions such as minimizing the maximum path delay, the skew between branches, or a combination of area, power, and delay. The algorithm has a complexity proportional to the square of the number of possible repeater positions and determines a repeater solution that is close to the global minimum. The repeater insertion algorithm is used to insert repeaters within several copper-based interconnect trees to minimize the maximum path delay based on both an RC model and an RLC model. The two buffering solutions are compared using the AS/X dynamic circuit simulator. It is shown that as inductance effects increase, the area and power consumed by the inserted repeaters to minimize the path delays of an RLC tree decreases. By including inductance in the repeater insertion methodology, the interconnect is modeled more accurately as compared to an RC model, permitting average savings in area, power, and delay of 40.8%, 15.6%, and 6.7%, respectively, for a variety of copper-based interconnect trees from a 0.25 μm CMOS technology. The average savings in area, power, and delay increases to 62.2%, 57.2%, and 9.4%, respectively, when using five times faster devices with the same interconnect trees.