三維積體電路中具時序考量的功能與修復路徑訊號指派方法：結合最小成本最大流與模擬退火法

Abstract

隨著高效能運算的興起以及跨晶片連線數量的急遽增加，3D IC封裝已成為整合技術的關鍵。然而，大量的互連也帶來更高的故障風險，使得互連修復成為不可或缺的技術。 本論文提出一種專為3D IC跨晶片修復鏈設計的訊號指派方法。該方法首先利用最小成本最大流（MCMF）演算法產生初始連線解，接著結合模擬退火（SA）針對時序要求進行優化。 與僅針對功能性訊號指派的過往研究不同，本方法同時考慮訊號的功能與修復路徑、滿足時序要求以及總線長最小化。實驗結果顯示，與整數線性規劃（ILP）相比，所提出方法在執行時間上有超過數千倍的加速，且維持高修復能力與低連線成本，展現良好的可擴展性，適用於實際3D IC修復應用場景。

With the rise of high-performance computing and the rapid increase in inter-die connections, 3D IC packaging has become a key integration technology. However, the large number of interconnects also introduces higher risk of faults, making interconnect repair a necessity technique. This paper proposes a signal assignment method specifically designed for inter-die repair chains in 3D ICs. The method first generates an initial routing solution using the min-cost max-flow (MCMF) algorithm, and then applies simulated annealing (SA) to optimize for timing requirements. Unlike previous studies that focus solely on functional signal assignment, the proposed method simultaneously considers functional and repair paths, satisfies timing constraints, and minimizes total wirelength. Experimental results show that compared to integer linear programming (ILP), the proposed method achieves over 1000 times speedup in runtime while maintaining high repairability and low routing cost. This demonstrates strong scalability and practical applicability in real-world 3D IC repair scenarios.