臺灣博碩士論文加值系統

電遷移效應係指電流誘發的原子擴散現象，富饒基礎學理探究及產業科技上的應用。探討電遷移效應的理論模型自1960年起相繼被提出，包含Huntington等人提出的碰撞模型、Bosvieux等人提出的電荷極化模型、Sorbello提出的以贗勢法為基礎的理論模型，此些模型用以描述電流之於金屬內原子的作用力關係。Blech, Korhonen, Clement,等人則奠基於前述微觀作用力之理論模型，進而推導出巨觀上因電遷移效應造成的導線應力隨空間、時間的變化，及解釋著名的Blech效應。儘管上述的數學模型可以完整的描述實驗上觀察到具方向性的現象如孔洞/突起物生成、界面反應上的極化效應，但卻不能有效解釋非方向性的現象如合金過飽和現象、界面反應上的非極化效應。由此，現存電遷移理論模式似乎尚不全解釋所有觀測到的現象，而電流誘導之材料晶格相穩定性變化之基礎研究亦有待系統性理解。因此，本論文利用臨場通電同步輻射X光、臨場通電電子顯微鏡、臨場通電奈米壓痕試驗，並結合第一原理計算、機器學習技法、有限元素分析法，旨在重新檢視材料晶格相穩定性變化的機制。本論文首先利用機器學習技法建立有效電荷之理論模型，並重新解析有效電荷之物理意義，並提出新穎的觀點。本論文隨後在臨場實驗的觀測下，發現電流將誘發晶格產生非均勻的本質晶格應變，且該應變將顯著的提升原子擴散係數。我們發現當晶格應變來到一個臨界值時，原子擴散將被顯著的觀測到。進一步，由於電流誘發晶格形變，我們以臨場通電背向散射電子繞射圖譜並結合傳統機械力學的理論成功預測電流誘發形變。以施密德定律分析通電誘發之凸塊及雙晶形變生成，認為電流誘發凸塊生長係藉由滑移形變生成，當晶格受力達一臨界值時，材料便以應力釋放的方式誘發擴散發生，形成凸塊；當電流密度提高時，雙晶形變被觀察到。藉此，通電將如傳統應力理論行為誘發彈性/滑移/雙晶形變之轉換。更進一步，本論文建構以虎克定律為基礎定性模型以計算在面心立方晶體中發生電遷移的臨界應變值，該理論計算與實驗相當吻合。總結而言，本研究認為材料在通電初期會誘發本質且非均勻之晶格應變，非均勻的晶格應變提供擴散驅動力且該應變將增加擴散係數，當晶格應變累積到一臨界值時，應力釋放誘發之擴散現象會顯著發生，且該應力釋放將遵守傳統機械應力理論。本研究因此提出電流誘發形變可與傳統機械力學以相同脈絡討論，並認為誘發電致擴散的關鍵因子並不只有電性，更包含了材料的機械性質。本論文作者希望能藉由此論文的研究能提供通電對材料晶格穩定性之影響理論基礎，並能提供關鍵因子以協助次世代電子連結材料之設計。

Electromigration (EM) effect is the atomic diffusion induced by electric current. It involves both fundamental and technology interests. Theoretical models including the ballistic model, charge polarization model, and pseudopotential-based analytical model, have been proposed by Huntington el al., Bosvieux et al., and Sorbello, respectively, to tack on the EM effect microscopically. Macroscopic stress models proposed subsequently by Blech et al., Korhonen et al., Clement et al., etc., describes the critical points for EM occurrence, and stress evolution during EM. These models intend to reasonably interpret directional phenomena including the voids/hillocks formation, and polarity effect; however, they fail to explain the non-directional phenomena including the supersaturation effect, and non-polarity effect. It seems that some parts of the existing EM theories are missing to well and generally explain all the phenomena. The fundamental understanding to the electric current-induced lattice stability change is urgent to be pursued. In this study, in situ electric current synchrotron radiation-based X-ray diffraction (XRD), in situ electric current scanning electron microscopic (SEM) equipped with electron backscattering diffraction pattern (EBSD), in situ nano indentation were employed with combination of first principles calculation, machine learning method and finite element analysis to study the lattice stability change induced by electric current. This study first developed a machine learning model to explore the effective charge and deciphered the complex physic of it. We then found that electric current would induce intrinsic non-uniform lattice strain, which would significantly increase the atomic diffusivity. When the lattice strain exceeded a critical value, diffusion was significantly observed. The electric current-induced deformation was able to be predicted by applying the theories from conventional solid mechanics. Hillock formation and twin deformation were analyzed by using Schmid’s Law, which suggested the elastic/slip/twin transition induced by electric current. Hillock formation was identified as a slip deformation and was likely to result from the stress relaxation-induced diffusion. Twin deformation was found induced at higher current density. The Hooke’s Law was further employed to establish a qualitative model to predict the EM occurrence in face-centered cubic metals. The model worked well to describe the critical lattice strain for EM occurrence. It is remarkable to suggest that not only the electrical properties, but the mechanical properties of materials govern the EM-resistance. The electric current-induced deformation can be discussed in the same context with the conventional solid mechanics. The author hopes that the study provides a fundamental understanding to the electric current-induced lattice stability change and may provide new guideline for next-generation interconnection materials’ design.

CHAPTER I: INTRODUCTION 1
I.1 Background 1
CHAPTER II: LITERATURE REVIEW 5
II.1 EM effect in Back-end-of-line (BEOL) processing of Integrated Circuits 5
II.2 EM effect in the electronic packaging materials 7
II.3 Theoretical models for EM 11
II.4 Effective charge 28
II.5 EM occurrence induced stress evolution 32
II.6 EM-induced lattice deformation measurement 43
II.7 Correlation between the EM occurrence and mechanical properties 51
II.8 Electroplastic effect 52
II.9 Electric current effect upon phase stability change 55
II.10 Summary 63
II.11 Objectives of the present thesis 64
CHAPTER III: RESEARCH METHODOLOGIES 66
III.1 In situ current stressing synchrotron radiation-based X-ray techniques 66
III.2 In situ current stressing scanning electron microscopy 67
III.3 In situ current stressing nano-indentation 68
III.4 Ab initio calculations 70
III.5 Finite-element analysis 70
III.6 Machine learning method 72
III.7 Sample preparation 89
CHAPTER IV: RESULTS AND DISCUSSIONS 90
IV.1 Exploring effective charge in electromigration using machine learning 90
IV.2 The electromigration effect revisited: non-uniform local tensile stress-driven diffusion 114
IV.3 Electric current-induced elastic/slip/twin deformation of Cu 149
IV.4 In situ investigation on the isotropy of the electric current-induced lattice strain 180
IV.5 Electric current-induced lattice strain in fcc metals and electromigration occurrence 188
IV.6 The Blech effect revisited – critical voltage drop induced electromigration occurrence 198
IV.7 Gradient electro-hardening of copper revealed by in situ nano-indentation 226
IV.8 General model for electric current-induced materials lattice stability change 239
CHAPTER V: CONCLUSION 242
Reference 243

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