Clock tree embedding for 3D ICs

This paper addresses a fundamental problem of zero skew clock tree embedding problem in 3D ICs. We propose an algorithm, called ZCTE-3D, for solving the zero skew clock tree embedding problem in 3D ICs for a given tree topology. The primary objective is to minimize the cost of TSVs together with finding embedding layers and the secondary objective is to minimize the cost of wirelength. We show that ZCTE-3D solves the problem optimally in polynomial time under the linear delay model, while it solves the problem suboptimally under the Elmore delay model. We also propose an effective 3D clock tree synthesis flow by integrating a multi-layer tree topology generation algorithm, called MMM-3D, into ZCTE-3D. Through an extensive exploitation of ZCTE-3D in experiments, we have analyzed the relation between the number of TSVs, the total wirelength, and tree topology. When compared with the results produced by the previous 3D clock tree synthesis algorithm BURITO, experimental results show that ZCTE-3D uses on average 10% less number of TSVs with similar wirelength and delay for the same tree topologies. Furthermore, by generating tree topologies with MMM-3D, we are able to reduce the number of TSVs by 10% on average even with 4% shorter wirelength and 2% reduced delay.