利用等效原理與格林第三恆等式之階層電感宏觀建模

Abstract

現今的封裝技術已經發展到三維堆疊的時代，各種複雜的繞線結構帶給寄生參數萃取越來越多的挑戰，電腦輔助工具需要考量到更加棘手的問題，過去可以忽視的問題逐漸需要受到正視。因此，如何快速地萃取精確(誤差小於1%)的電感參數是本作的重點。除此之外，技術與資訊的發達使得半導體產業日益競爭，如何妥善保護企業之間的商業機密亦是非常重要的議題。 主流的商業或學術軟體中的電感萃取方法都需要輸入完整的電路設計圖，因而潛在IP被竊取的風險。此外，若電路中發生某種程度上的變更，參數萃取的結果也會連帶受到影響，因此這些萃取步驟可能需要隨著變動不斷重複執行而耗費大量的時間。 基於上述的考量，我們發展出不同以往的萃取模式，我們借鑒了電磁理論中的等效原理，透過建構虛擬的等效面及邊界上的物理機制發展出新穎的演算法，可以將電路隱藏在等效面中，並在等效面的邊界上產生一組不可回溯的資料使其成為一個全新獨立的模組，在不需知道電路真實幾何結構的情況下得出精確的電感值。同時，這些建立在等效面上的模組也取代了原先大量複雜的金屬連線，降低計算的複雜度、提升後續處理的彈性。因此，我們可以透過這樣的方法有效地簡化未來先進封裝中可能帶來的挑戰。

The advanced packaging technology has developed into the three-dimensional stacking. The complicated routing structure brings more and more challenges to parasitic parameter extraction. Computer-aided tools need to consider more realistic issues, that could be ignored in the past become increasingly important. How to efficiently extract the accurate (less than 1%) parameters is one of the motivations for this work. In addition, the development of technology and information has made the semiconductor industry increasingly competitive. How to protect confidential commercial information is also important. The mainstream commercial or academic software inductance extraction methods require the complete circuit layout, so there is potential risk of IP theft. In addition, if there are certain changes in the circuit, the parameters will change accordingly, the extraction steps will need to be repeated again, which might consume a lot of time. Based on the above considerations, we developed a parameter extraction macromodeling that is different from the past. We drew on the equivalence principle in electromagnetic theory to build a virtual equivalent surface and using the physical mechanism on the boundary to develop this novel algorithm. Therefore, we can hide the circuits in the equivalent surface and generate a set of non-retroactive data on the boundary to make it become an independent module. We can use this information to accurately extract the parameters without knowing the actual geometric design. Simultaneously, the information based on the equivalent surface also reduces the complexity. Therefore, we can address the challenges brought by advanced packaging in the future through this method.