在電子封裝技術演進下晶圓重組製程因為晶片設計功能的提升而成為主要趨勢，然而在製程中會產生晶圓翹曲現象。為了解決此問題會使用數值模擬的方法進行分析，但是封裝結構為高度非均質，需要利用網格數極高的三維有限元素模擬求解，導致計算量過大。因此，如何將原始複雜模型進行簡化，並且結合解析式預測形成高效率有效的計算方式，其中利用材料等效方法進行簡化為重要的發展。此外，目前預測晶圓非對稱翹曲的方式是以有限元素模擬的非線性分析為主，若欲使用挫曲與後挫曲分析角度進行探討，以此尋求不同的解決方式作為有其潛力所在的替代方案來研究晶圓翹曲問題，則可以對於實際製程上的情況進行更全面的分析。有鑑於此，本文發展一基於能量角度的材料結構等效方法，將原始晶圓複雜結構轉換成簡化等效雙層結構模型，搭配修正型解析解預測非對稱翹曲，並且與其他等效方法做比對。由結果顯示，使用Che與Park的等效方法搭配修正型解析式最有效，可以成功預測重組晶圓的分歧溫度和翹曲狀況，達到快速有效的分析和預測。並且以挫曲與後挫曲分析探討晶圓挫曲發生時機和翹曲狀況，並且和非線性分析進行比對，模擬的結果顯示兩者分析的分歧溫度和最終翹曲值誤差分別為14%和6%，誤差在可接受範圍內所以可以驗證其可行性，因此後挫曲分析可以作為發展晶圓重組製程非對稱翹曲的分析工具。後續建立含挫曲與後挫曲分析的製程模擬器，在大變形區域預測其翹曲幅度，並且與非線性分析相比對，誤差為3%以內因此可以驗證模擬結果和規劃流程的可行性，則能對於產線的實際情況做更全面的分析。未來在材料等效部分將針對剛性進行等效，另外建立符合剛性等效的模型，達成在電子封裝領域中提升晶圓翹曲的預測性，將其擴展至其他工程領域上。在挫曲與後挫曲分析部分探討更多不同數值模型對其參數的影響研究敏感度的分析，更真實描述實際製程的內容與變形行為。

Asymmetric warping is an annoying phenomenon causing defects and reducing process yield of wafers and it must be prevented. Traditionally, full-scale 3D finite element simulations and nonlinear analysis are usually used for addressing this concern but it is extremely expensive. Therefore, alternative effective approaches should be sought. The purpose of this thesis is to perform structure and material equivalences for converting the original highly complex 3D structure into a bi-layered structure with equivalent uniform materials for conducting semi-analytical prediction and efficient finite element simulations for addressing the above needs. In addition, the buckling and post-buckling analysis methods are also hired to predict the asymmetric warpage of packaged wafers as an alternative approach for warpage analysis in the future. To achieve the goal, material equivalence methods using a self-developed energy-based approach is developed along with traditional arithmetic average as well as the methods proposed by Che [6] and Park [7] et al for predicting asymmetric warpage with semi-analytical solution. In comparison while the proposed energy-based approach is feasible, its performance still could not match with that provided by Che [6] and Park [7] methods. Nevertheless, it is expected that such the proposed approach could be further improved. Furthermore, the warpage predicting scheme based on buckling and post-buckling analyses have shown consisted results with current nonlinear bifurcation approach [9,10] and benchmark finite element solutions. Therefore, the feasibility has been confirmed although the computational cost should be further reduced in the future. Finally, a process emulator with buckling and post-buckling analysis is established to highlight the applicability of such an approach in whole process wafer warpage prediction. It is believed that with the investigation results of this work should have strong impact for future fan-out reconstituted packaging process optimization.

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