在IC封裝的製程中，介金屬化合物扮演著重要的角色，其可以增加兩金屬之間的黏著強度以及韌性，但是厚度太厚或是不均勻都會影響到IC封裝的品質，因此許多研究藉由實驗或數值模擬的方法來分析其可靠度和破壞行為。若是使用數值模擬，材料的機械性質是必須的，但這些機械性質是與溫度有關，而這些機械相關性質不易由實驗獲得，且很多介金屬化合物與溫度相關之機械性質也無法由文獻中求得，因此本研究之目的為利用密度泛函理論及第一原理計算，建構一套數值模擬程序，以求得純金屬與介金屬化合物在不同溫度下之楊氏係數、蒲松比及熱膨脹係數。
本研究利用VASP和Phonopy兩軟體建立數值模擬的程序，並以純金屬銅、鋁、介金屬化合Cu3Sn和鐵鋁介金屬化合物為例子，做為此模擬程序之驗證。由模擬結果所示在沒有溫度效應下純金屬銅之楊氏係數誤差絕對值為5%，蒲松比誤差絕對值為1%；介金屬化合物Cu3Sn之楊氏係數與Microindentation實驗值之誤差絕對值為3%，其蒲松比符合實驗值之範圍。
有溫度效應下銅之楊氏係數在不同溫度下最大誤差絕對值為12%，而蒲松比在常溫下300K是符合實驗值的，銅之熱膨脹係數在300K下誤差絕對值為3.7%，當溫度達到600K時誤差絕對值達10%；鋁之熱膨脹係數由300K到600K誤差絕對值都在10%以內。介金屬化合物Cu3Sn其楊氏係數與蒲松比沒有高溫實驗值可比對，但熱膨脹係數在300K下與實驗值誤差絕對值為5.7%。為彌補缺少Cu3Sn之實驗數因此以鐵鋁介金屬化合物做為驗證，楊氏係數在300K、450K和500K時誤差絕對值為1%左右；最後本研究利用非線性擬合的方法提出楊氏係數與溫度之間的關係式，以預測在任意溫度下之楊氏係數。

The characteristics of the intermetallic compound in an IC package are very important. When it is too thick or non-uniformly distributed, the reliability of the IC package may be degraded. Hence, many studies have experimentally investigated or numerically simulated intermetallic compound. If one intended to use numerical simulation approach, the material properties are integral. Experimentally determining mechanical properties at high temperature is difficult and takes a long time. Therefore, in this study, density functional theory and a method based on first principles are used to build a model of various metals and intermetallic compounds and to simulate them numerically to determine their Young’s modulus, Poisson’s ratios and coefficients of thermal expansion at reflow temperature. The simulation is conducted using the software VASP and Phonopy.
Four materials, Cu, Al, Cu3Sn and FeAl were considered. Comparing the Young’s modulus simulated results for Cu and Cu3Sn at room temperature with the relevant data in the literatures reveals errors in 10% for Cu and around 12% for Cu3Sn. The Poisson’s ratio is conformed to the reference. Experimental data at the reflow temperature of the intermetallic compound are hard to find: only the Young’s modulus of FeAl is in fact available, and the simulated error in that value is less than 1%. The coefficients of thermal expansion of Cu and Al from 300K to 600K have an error of about 10%. At 300K, the coefficient of thermal expansion of Cu3Sn has an error of 5.7% relative to experimental data. Nonlinear curve fitting also yield the temperature-dependent functions of Young’s modulus, Poisson’s ratio and coefficient of thermal expansion.

誌謝 i
摘要 ii
Abstract iii
目錄 iv
表目錄 v
圖目錄 vii
第一章 緒論 1
1.1背景介紹 1
1.2 文獻回顧 2
1.2.1 介金屬化合物之相關研究 2
1.2.2 介金屬化合物機械性質實驗研究 4
1.2.3運用分子動力學於材料機械性質之研究回顧 5
1.2.4 密度泛函理論運用於材料機械性質之研究回顧 6
1.3 研究目的 7
1.4 全文架構 8
第二章 基本理論介紹 13
2.1 密度泛函理論 13
2.1.1 電子密度 13
2.1.2 Thomas-Fermi模型 14
2.1.3 Hohenberg-Kohn模型 15
2.1.4 Kohn-Sham方程式 15
2.1.5 交換關連函數與贋勢能 17
2.2 彈性常數與機械性質的關係 19
2.3密度泛函微擾理論 21
2.3.1 晶格動力學 21
2.3.2 晶格振動聲子推導熱力學性質 23
2.3.3 熱膨脹係數 24
2.3.4高溫彈性常數[54] 25
2.4 軟體介紹 25
2.4.1 VASP介紹 26
2.4.2 VASP指令編輯流程 26
2.4.3 Phonopy介紹 28
第三章 研究流程 33
3.1 模擬流程 33
3.2 模擬設定 35
3.3 參數設定與收斂分析 37
第四章 結果與討論 50
4.1 不考慮溫度效應機械性質之計算 50
4.1.1純金屬之晶體結構與機械性質 50
4.1.2 介金屬化合物之晶體結構與機械性質 52
4.2 考慮溫度效應機械性質之計算 54
4.2.1 純金屬之機械性質與溫度之關係 55
4.2.2 介金屬化合物之機械性質與溫度之關係 56
第五章 結論與未來展望 89
5.1 結論 89
5.2 未來展望 90
參考文獻 92
附錄A 98
附錄B 99
附錄C 101

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