Spare-cell-aware multilevel analytical placement

Post-silicon validation has recently drawn designers´ attention due to its increasing impacts on the VLSI design cycle and cost. One key feature of the post-silicon validation is the use of spare cells. In the literature, most existing works focus on developing new delicate spare cell structures. On the other hand, the placement of spare cells has a crucial impact on the design cycle and cost of the post-silicon debugging; however, there exists not much work on this placement problem. In this paper, we propose the first spare-cell-aware analytical placement framework which predicts the spare cell requirement and considers spare cell insertion during global placement. We also propose a multilevel spare cell insertion technique which provides a more efficient spare cell planning and a better control of quality impact due to spare cell insertion. To guide the selection of available spare cell positions during insertion, we propose a mixed-integer-linear-programming formulation to determine the optimal spare cell positions. Experimental results show that our algorithm can averagely achieve 17-33% and 1.77-2.61X better quality of spare cell insertion than that of the existing spare cell insertion algorithms, UniSpare and PostSpare , on the tested real designs with 1-5% spare cell insertion rates.