應用區塊子模型建立嵌入式基板翹曲模擬及最適化設計之研究

Block-Based Finite Element Modeling, Simulation and Optimization of the Warpage of Embedded Trace Substrate

連健宇(Chien-Yu Lien)

指導教授 ： 姚遠

國立清華大學/工學院/化學工程學系/碩士(2019年)

摘要

由於現今電子裝置的製作重心在於更輕薄，一種無核芯(coreless)的基版技術被研發及發展、稱為嵌入式基板(Embedded Trace Substrate, ETS)，並廣泛應用於各式電子產品，如:通訊用具、智慧型手錶以及各式各樣消費型產品。然而，此種設計因為不同材料間的相異的物理性質會有嚴重的缺陷，舉例而言，銅線與與其他非金屬材料的熱膨脹係數(Coefficient of thermal expansion, CTE)不匹配，會造成產品發生嚴重的翹曲(warpage)，進而影響後續封裝製程(package processing)。近年來，有限元素分析法(Finite Element Analysis, FEA)是一種受歡迎且有效的方法幫助研究人員預測板彎翹曲和機械性質的研究。生產者可以應用有限元素方法去模擬基板的改良設計，以及能提供一個特定的翹曲數值滿足後續開發所需。儘管如此，對於高精度的模擬需耗費龐大的計算成本，因此，如果必須多次執行模擬研究（例如，靈敏度分析和翹曲優化），則模擬研究將成為漫長而艱鉅的任務。

在此篇論文中，可分為二部分。一是以代表性體積元素(Representative Volume Element, RVE)研究板材的材料性質，在材料的微觀組織結構下進行數值模擬分析，在經由逆向工程或是有限元素法得到此研究所需的材料物性，另外以貝茲曲線(Bézier curve)擬合玻璃轉移溫度(Tg)在溫度變化下對物質物性的影響。其二是提出了一個新的方法針對有限元素法分析機械性質的板材模擬及流程，並設計一種優化的策略對於板彎翹曲的控制。方法如下:首先將每層基板的Gerber檔轉換成高解析度的圖像，並且透過預先劃分好的區塊掃描每個圖像的銅區域進行二值化分析。接下來使用體積平均微觀力學方法計算每個子區塊的有效材料屬性，然後堆疊所有區塊構建出用於有限元素分析的模型。有別於傳統的軌跡劃分模擬，該方法大幅地降低計算資源的需求。此外，我們還能獲得與實際實驗相符、精準的翹曲預測結果。最後，文章的末端提出了一種優化策略，該策略能在封裝製程的預處理步驟，藉由參數的調整進行板彎翹曲的優化。本文的結果顯示出此一新的模擬方法是有效、實際且能降低計算成本的。

關鍵字

嵌入式基板 ； 有限元素模型 ； 翹曲優化 ； 翹曲模擬 ； 無核芯 ； 代表性體積元素 ； 貝茲曲線

並列摘要

As the electronic devices getting lighter and smaller, a coreless substrate technology, called Embedded Trace Substrate (ETS) is developed to meet the market requirement. However, this design causes severe warpage due to the large difference in CTEs (coefficient of thermal expansion) of build-up material and Cu plate. Recently, finite element analysis (FEA) is a popular and effective method used for substrate warpage prediction and mechanical studies. Manufacturers apply FEA simulation for substrate design improvements, and provide substrate warpage that satisfying the customer’s specification. Nevertheless, the computational resources needed for high-fidelity simulation are extremely expensive and time consuming. Hence the simulation study becomes a long and arduous task if it has to be performed many times, e.g., sensitivity analysis and warpage optimization.

In this paper, on the one hand, we research the material properties of composite material with RVE and carry out numerical simulation analysis under the microstructure of the material. In addition, the glass transition temperature (Tg) is fitted by Bézier curve in thermos Mechanical Analysis. On the other hand, we propose a new method for FEA modeling of mechanical behaviors of substrate, and present an optimization strategy for substrate warpage control. In the first step, the Gerber files of each layer of the substrate are converted into high resolution bitmap images, and the copper area of each image is divided and scanned by a pre-sized block window. After that, the effective material properties for each block are calculated with volume average micromechanics approach, and then all blocks are stacked-up to build block-based analysis model for FEA simulation. As comparing with conventional trace mapping simulation, the proposed method significantly decreases the demands of computing resource. Besides, we gained accurate warpage prediction results as validated by a real substrate experiment. Finally, we presented an optimization strategy that manipulates the thickness of each layer for substrate warpage optimization in pre-processing steps of packaging. In conclusion, the results show that the methodology for substrate simulation in this paper is practical, effective, and costless.

並列關鍵字

ETS substrate ； FEA modeling ； warpage optimization ； warpage simulation ； coreless ； RVE ； Bézier curve

參考文獻

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