Thermal aware placement in 3D ICs using quadratic uniformity modeling approach

Abstract

Three-dimensional (3D) ICs have the potential to reduce the interconnect delay, but thermal problem becomes one of the most serious challenges. In this paper, we proposed an efficient thermal aware 3D placement algorithm,which takes use of quadratic uniformity modeling approach. In this model, cell distribution and thermal dissipation are integrated and formulated as a quadratic function through discrete cosine transformation (DCT) with wirelength optimization. Quadratic programming method is utilized to solve the unified quadratic objective function. We update the unified cell distribution and thermal dissipation with each step of the iterative placement process. Thermal distribution was considered enough during placement process even when a cell was moved. To save time, two fast methods to reflect thermal change were proposed for thermal distribution computation. The experimental results show our thermal aware 3D placement algorithm is efficient with about 3% reduction in average temperature and 15% in max temperature but a little perturbation on wire length.