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  • 學位論文

應用第一原理計算於摻鎳Cu6Sn5介金屬破裂韌性之研究

First-principles Calculations on Fracture Toughness Prediction of Ni-doped Cu6Sn5 Intermetallic Compounds

指導教授 : 陳俊杉

摘要


介金屬化合物常見於電子構裝中的錫焊料及銅基板,並對電子構裝之品 質控制有莫大的影響。過往的研究中發現,在此系統中摻入鎳後,介金屬將會固定在eta相的Cu6Sn5,並能夠阻絕形成其他種類可能會造成介面劣化的介金屬。因此,了解eta相Cu6Sn5及其摻入鎳後的破裂性質(亦即破裂韌性)便極為重要。同時,由於缺乏摻鎳後的破裂韌性實驗數據,密度泛函理論的計算模擬在此問題上便為一方便而有效的工具。然而eta相Cu6Sn5本身在Sn位置的分數占據特性及摻入鎳後所形成的非整數化學當量使得密度泛函理論計算需建置一十分龐大的原子模型,並需要大量的計算時間。為了克服此問題,本研究採用混合非整數化學當量的原子之膺勢的虛擬晶體近似法以縮小模型,同時進一步驗證虛擬晶體近似法在此系統中之適用性。本研究藉由密度泛函理論結合虛擬晶體近似法研究eta相Cu6Sn5在摻入不同比例之鎳時的物理性質。首先本研究從驗證虛擬晶體近似法出發,接著討論eta相Cu6Sn5摻入不同比例鎳時的體積變化;隨後計算並討論計算破裂韌性時所需之楊氏模數在eta相Cu6Sn5中隨不同摻鎳比變化的趨勢;最後計算eta相Cu6Sn5在不同摻鎳比下之破裂韌性的變化情形。我們發現隨著摻鎳量的增加,eta相Cu6Sn5之體積會收縮,其彈性模數與破裂韌性亦有增加的趨勢;此趨勢將於正文中透過銅鎳間的鍵結增強加以解釋並討論。

並列摘要


Intermetallic compounds (IMC) which appear in the interface of Sn solders and Cu substrate play an important role in quality control in electronic packaging industry. In the system, it has been reported that IMC can be stabilized in eta phase Cu6Sn5 by adding Ni dopant. This can prevent the interface from being degraded by other IMCs. It is thus important to understand the fracture properties, i.e. fracture toughness, of eta-Cu6Sn5 and Ni-doped eta-Cu6Sn5. However, the fracture experiments in Ni-doped eta-Cu6Sn5 are lacking. Computational simulation with density functional theory (DFT) is thus a powerful tool to look into this system. Because of the fractional occupancy in eta-Cu6Sn5 and Nidoped eta-Cu6Sn5, it needs a large model to reproduce the fraction occupancy crystal, which requires tremendous computational efforts. Virtual crystal approximation (VCA) is thus involved to ease the computation in this research. However, the suitability of VCA to a system needs to be validated before conducting further computation. In this research, we conduct a DFT simulation. The suitability of VCA in eta-Cu6Sn5 with different amounts of Ni-dopant is first validated. Then the structural variations of eta-Cu6Sn5 under different percentages of Ni-dopant are also presented. The necessary mechanical properties to get fracture toughness, including Young’s modulus are examined. Finally, the fracture toughness of eta-Cu6Sn5 under different Ni-dopants is investigated. We found that eta-Cu6Sn5 experiences a shrinkage in volume and enhancement in Young’s modulus and fracture toughness as the percentage of Ni-dopant increases. The trend will be further discussed by the bond-strengthening mechanism between Cu and Ni atoms in this thesis.

並列關鍵字

DFT ab initio VCA Cu6Sn5 Fracture toughness

參考文獻


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