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標題: | 使用有限差分法與格林函數之3D IC熱模擬演算法 3D IC Thermal Simulation Algorithm Using the Finite Difference Method and the Green's Function |
作者: | Wilson Jin 陳星圻 |
指導教授: | 盧奕璋(Yi-Chang Lu),李建模(Chien-Mo Li),黃俊郎(Jiun-Lang Huang),陳中平(Chung-Ping Chen) |
關鍵字: | 3D IC的熱模擬, 有限差分法, 格林函數, TSV和威盛的, LU分解, 快速傅立葉變換, 離散餘弦變換., 3DIC, Thermal Simulation, Finite Difference Method, Green’s Function, Virtual Power Source, Analytical Method, TSV and Via’s, LU Decomposition, Fast Fourier Transform and Discrete cosine transform., |
出版年 : | 2012 |
學位: | 碩士 |
摘要: | 近年來,在多核心處理器的設計過程中,晶片核心熱效應溫度模擬顯得越來越重要,是不允許被忽視的重點之一。一個完整的晶片核心熱效應溫度模擬,通常必須考慮單位體積超過以一百萬個3D平面網格單位的三維積體電路(IC),而在這個單一封裝晶片中,往往包含了眾多複雜的模組,因此熱傳導產生的問題,已造成效能上的一個瓶頸。若使用2D圖層的3D圖層與三維積體電路的架構來增加設備的密度,這個問題則會更加嚴重。因此,高分辨率和全晶片模擬與數以百萬計的網格熱模擬成為設計一個高效能積體電路不可或缺的工具。在設計滿足這些性能要求的同時,現有的熱模擬算法往往需要相當大的計算資源來獲得勉強可接受的結果,例如需要極大量的記憶體運算空間、更高時脈的中央核心處理器......等,即使如此,傳統的演算法仍須消耗大量時間來完成運算,此外還有插入電源限制和無插入TSV問題。
目前文獻上已經有人提出基於有限差分法的3D IC基板熱模擬分析方法,有限元方法和格林函數的泊松方程式法。其中格林函數法採用離散餘弦變換,大大的加速了熱模擬執行時間,比傳統的有限差分法快上了不少。但格林的分析方法有插入TSV的3D IC全芯片基板和有限差分法的限制問題。另外,有限元方法也需要大量的內存記憶體資源和高性能CPU性能支援。 本論文研究提出了一個折衷的混合模擬方法,同時使用兩個或兩個以上的熱模擬分析,克服了像一層均勻問題、TSV插入問題、限制網目尺寸......等限制。 首先,用格林方程式法提高在高分辨率熱應用的計算時間;提出了快速傅立葉變換的數值計算方法。格林的熱模擬基礎上的高分辨率網格和均勻材料,電源和電流的網格之間的熱阻。正因為如此,所有軍裝網格電導率可以被替換成基於格林函數的積分方程解二維層。 其次,如3D IC的插入通過硅通孔(TSV)和虛擬電源(VPS),多層熱,導熱異構建議使用傳統的有限差分法,共同利用空間域的LUT方法。 TSV技術的高導熱材料的IC內層的多層三維集成電路驅散熱量。 TSV的芯片上的溫度分佈的影響可能使模型為減少集中電源引起的最高溫度。如此一來可以得到更快和更準確的熱模擬精度分析,採用混合方法可以應用到3D全晶片的積體電路設計,在不犧牲模擬速度的情況下,同時得到高精確的溫度分佈計算結果。 Nowadays, in the design of many-core processor, it is necessary to make temperature simulation of full die for the design of one core. It is requested to see more than one million mesh grids in a 3D plane in a full chip thermal simulation. For packing more devices per unit volume of modern integrated 3D circuits (ICs), heat conduction has become a big issue of limiting factors. This problem is exacerbated with the emergence of 3D IC where from 2D layers to 3D layer, increasing device density. To develop modern multi-core system on chip architecture, high resolution and full chip thermal simulation with millions of mesh grids, 3D IC thermal simulation becomes an important tool for micro IC design. When facing these performance demands, existing thermal simulation algorithms often requires excessive amount of computation resources to get acceptable results like huge memory, higher performance of CPU, long calculation time, limitation of inserting power source and without inserting TSV. Accurate and efficient full-chip thermal simulation for a 3D IC is of particular importance. Until now, an analytical thermal simulation method for 3D IC substrates based using the finite difference method, the finite element method and the Green’s function of a Poisson equation has been developed. The Green’s function using discrete cosine transform significantly improved the execution time of thermal simulation compared to the conventional finite difference method. But the Green's analytical method has a limitation on inserting TSV's in 3D IC full chip substrate and finite difference method. Finite element methods also have limitation on requiring huge memory resources and high CPU performance. The specific goal of this research is pursued with developing hybrid method utilized together two or more the analytical thermal simulation methods, aiming to overcome limitation like, uniform layer issue, TSV insertions problem, limitation of mesh size and etc. First, to improve calculation time of applications at high resolution thermal profile is used a Green's function method; numerical method of Fast Fourier Transform is proposed. The Green's thermal simulation is based on the high resolution mesh and uniform material that the thermal resistance between power source and current mesh grid. As such, all uniformed conductivity of mesh grids could be replaced from 2D layer into a Green function based integral equation solution. Secondly, such as 3D ICs inserting thermal through silicon via’s (TSV) and virtual power source (VPS) of multi-layer, the heterogeneous thermal conductivity is proposed using the conventional finite difference method utilizing spatial domain LUT method together. TSV’s are high thermal conductivity material of IC to disperse heat from inner layers of a multi-layer 3D IC. The effects of TSV on the chip temperature distribution could make the model as decreasing highest temperature induced by concentrating the power sources. This analytical thermal simulation from faster and better accuracy using hybrid method can be applied to 3D full-chip IC design, offering speed-up computation while delivering accurate temperature profile. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63780 |
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顯示於系所單位: | 電子工程學研究所 |
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