Coupling-aware force driven placement of TSVs and shields in 3D-IC layouts

Abstract

In 3D ICs, TSV cross coupling can seriously degrade circuit performance if it is not sufficiently considered in a design. Cross coupling is heavily dependent on how TSVs are placed, and should be considered during the floorplanning of the chip. In this work we propose a coupling-aware TSV placement algorithm that attempts to reduce both wirelength and TSV cross coupling. TSV shielding is another method for coupling mitigation, and the proposed algorithm combines coupling-aware TSV placement with shield insertion to yield better results than either technique alone. With regard to the most heavily coupled TSV pair in a design, our results show that applying both techniques simultaneously produces a 12.3% improvement in maximum S-parameter compared to traditional TSV placement which optimizes wirelength only. Using coupling-aware TSV placement or shield insertion alone produces a 4.2% and 4.8% improvement respectively. The improvement offered by using both techniques simultaneously is actually more than the sum of the improvement offered by using each technique on its own. This implies that the two techniques are not independent of one another, and that when used simultaneously each technique increases the effectiveness of the other, giving strong motivation for using them both simultaneously. Furthermore, the percent increase in wirelength due to using these two techniques is an order of magnitude less than the percent improvement to coupling, justifying the tradeoff made by our algorithm.

TSV Replacement and Shield Insertion for TSV–TSV Coupling Reduction in 3-D Global Placement

“…As we observed in our original analysis of the results of the "Fixed Cells" algorithm [12], spreading TSVs can greatly increase the effectiveness of SI by providing more potential positions for shields. During the TSV spreading stage of the algorithm all standard cell positions are fixed and only the TSVs are movable.…”

“…For our first experiment, we ran all algorithm variations on the randomized benchmarks developed in [12]. For each algorithm and each benchmark, we report the maximum Table II that in all three algorithm variants, the newly proposed "Movable Cells" algorithm is able to reduce the worst case coupling more than the "Fixed Cells" algorithm.…”

“…the solution which minimizes the squared distance between two points also minimizes the HPWL of two points, but can be solved much easier as it is differentiable. Thus, we can model the WL objective as (12). The matrix notation for x is given in (13) and a similar equation exists for y where x and y are the vectors of the position of each TSV and standard cell.…”

“…First, we introduce the benchmarks and the metrics used to characterize a final placement, and then we discuss the results. For each set of benchmarks we run our two proposed algorithms to improve coupling: the "Fixed Cells" algorithm originally introduced in [12], and the newly proposed "Movable Cells" algorithm. For comparison, we implement three versions of each algorithm with certain stages disabled in order to quantify how each stage affects the results.…”