基於圖論針對二維定向自我組裝技術之電路同時擺置與繞線

Abstract

二維定向自我組裝 (two-dimensional directed self-assembly) 是一種用於次 2 奈米及以下的新興光刻技術。我們在使用二維定向自我組裝技術的過程中，可以通過決定雙重點狀圖樣 (double post) 的方向來引導嵌段共聚物形成可行的二維引導模板圖樣。在本篇論文中，我們提出首個方法來解決二維定向自我組裝電路之同時擺置與繞線的問題。首先，我們提出一種新穎的二維定向自我組裝結構圖來對可行的二維引導模板圖樣進行建模，該圖模型能於指定一個雙重點狀圖樣的方向後，在固定時間內完成圖模型的更新，以及能夠在線性時間內將圖形路徑轉換成符合定向自我組裝規範的繞線路徑。其次，我們基於圖模型提出一個二維定向自我組裝之同時擺置與繞線的演算法，該演算法包含有二維定向自我組裝單元放置時使用的基於廣播的成本函數，以及一個基於圖模型的方案來生成符合定向自我組裝規範的繞線。最終，我們使用強有效區域的特性來最小化在最終布局中金屬線末端之切斷點的數量。實驗結果顯示，我們的演算法可以高效率的生成具有高可繞性及零個雙重點狀圖樣之方向衝突的二維定向自我組裝電路之擺置與繞線的結果。

Two-dimensional directed self-assembly (2D-DSA) is an emerging lithography technology for the sub-2nm process node and beyond. We can determine the orientations of double posts to guide block copolymers to form feasible 2D guiding template patterns by the 2D-DSA process. In this thesis, we present the first work to handle the 2D-DSA simultaneous placement and routing problem. We first propose a novel 2D-DSA structure graph to model the feasible 2D-DSA guiding templates with a constant-time update scheme for each double post assignment and a linear-time scheme for a graph path transforming into a DSA-compliant routing path. Based on the graph modeling, we then present an algorithm flow for 2D-DSA simultaneous placement and routing, with a broadcast-based cost function for 2D-DSA cell placement and a graph-based scheme for DSA-compliant routing. Finally, we employ the strongly effective region property to minimize the line-end cuts in the final layout. Experimental results show that our algorithm can efficiently generate a 2D-DSA placement and routing solution with high routability and zero double-post conflict.