NUMANA - 結合數值法與解析法的三維度積體電路熱分析技術

Abstract

藉由結合數值法與解析法的分析技術，本篇論文發展出一套熱分析技術NUMANA，可以處理複雜的材質與結構，並有效率地分析三維度積體電路的溫度分佈。根據材質分佈的複雜程度，可以選擇使用單點展開或多點展開遞迴式解析法，以減少近似項數達到有效率地分析。與一套能夠快速解對稱正定矩陣的軟體 SuperLU 4.3版比較，所有實驗中 NUMANA的最大誤差在 2.2% 以下，而分析速率加倍15倍以上。此外，為了展示分析效率，以含有一百六十萬節點數的三維度積體電路等效熱模組為例，NUMANA 不但精準地得到溫度分佈，比之 SuperLU 也加速了850倍。

By combining analytical and numerical simulation techniques, this work develops a hybrid thermal simulator, NUMANA, which can effectively deal with complicated material structures, to estimate the temperature profile of a three-dimensional integrated circuit (3-D IC). In different complexity of material distribution, NUMANA can execute single point expansion or multi-point expansions recursive analytical based simulation to reduce truncation order and achieve efficient simulation. Compared with a fast SPD (symmetric positive definite) matrix solver, SuperLU_v4.3, the maximum error of NUMANA for all test cases is under 2.2%, and its speedup is over 15 times. Furthermore, to demonstrate its efficiency, given an equivalent thermal model of 3-D IC with control volumes of 1.6 million, NUMANA not only can accurately estimate its temperature profile, but also can achieve 850 times speedup over SuperLU.