瞭解金屬材料中的自擴散機制，對提升微電子元件的可靠性、特別是降低電遷移所致之故障，至關重要。本研究以分子動力學（MD）方法，採用能有效描述多體交互作用的嵌入式原子模型（EAM）勢能函數，系統性探討銅（Cu）之自擴散行為。並以 LAMMPS 模擬套件進行大規模計算，分析空缺濃度、空缺簇形成與溫度對自擴散之影響，範圍涵蓋塊材與特定晶界——Σ13 與 Σ7。同時以多晶銅薄膜之示蹤擴散係數與活化能的實驗量測結果，對模擬進行驗證。
本研究結果顯示，隨空缺濃度提高，原子擴散性明顯增強；然而在較高濃度下雖形成空缺簇，但簇本身基本上保持不動。特別地，早期形成之簇常鬆弛為穩定四面體（由4個空缺構成）結構；當此類四面體或更大的魔數簇（如由6與13個空缺構成）生成並持續存在時，會作為不移動的「固定吸收點」(immobile sinks)，限制原子遷移，使後期均方位移（Mean Square Displacement, MSD）斜率趨於平坦，使反應速率與溫度的關係(Arrhenius linearity)不再呈現理想線性關係。
沿 Σ13/Σ7 晶界上的擴散顯著高於固體塊材(bulk)中的擴散，這個特性突顯微觀結構對傳輸行為的關鍵影響。此一晶界內擴散高於塊材內擴散的擴散階層關係會直接影響電遷移行為，快速晶界通道加速了質量傳輸並使得線路損傷得更快；而塊材中的原子低移動性(特別是在魔數穩定化條件下)則促進了局部空位得累積與固定住空洞位置。這些研究結果得到了實驗數據的支持，顯示模擬與實際測量的擴散係數與活化能之間具有良好的一致性。綜合而言，本研究透過闡明空位簇與微觀結構通道（塊材與 Σ13/Σ7 晶界之不同）在熱與機械應力下如何主導原子得自擴散行為。而透過研究空位簇與晶界如何影響原子擴散，可以幫助工程師設計出更耐用的電子元件，特別是在高溫或高電流密度下，減少因電遷移造成的損壞。

Understanding self-diffusion in metallic systems is crucial for improving the reliability of microelectronic devices, particularly by mitigating electromigration-related failures. This study presents a comprehensive molecular dynamics (MD) investigation of self-diffusion in copper (Cu) using an Embedded Atom Model (EAM) potential, widely employed for metals because it captures many-body interactions. Large-scale simulations were performed in LAMMPS to systematically analyze the effects of vacancy concentration, vacancy-cluster formation, and temperature on self-diffusion in both the bulk and along selected grain boundaries, specifically Σ13 and Σ7. Experimental measurements of tracer-diffusion coefficients and activation energies in polycrystalline Cu films were used to validate the simulations.
The results show that increasing vacancy concentration significantly enhances atomic diffusivity. Although vacancy clusters form at higher concentrations, the clusters themselves remain largely immobile. In particular, early-stage clusters frequently relax into a stable tetrahedral (4-vacancy) structure; when such tetrahedra—or larger magic-number clusters (6 and 13)—form and persist, they act as immobile sinks that restrict mobility, flatten late-time MSD slopes, and lead to deviations from ideal Arrhenius linearity.
Diffusion along Σ13/Σ7 grain boundaries is substantially higher than in the bulk, underscoring the critical role of microstructure in transport. This hierarchy of GB is greater than the bulk diffusivity directly affects electromigration and thermomigration, which is responsible for the fast GB pathways that accelerate mass flux and damage transport, while reduced bulk mobility—especially under magic-number stabilization—promotes localized vacancy accumulation and void pinning. These findings are supported by experimental data, showing good agreement between simulated and measured diffusion coefficients and activation energies. By elucidating how vacancy clusters and microstructural pathways (bulk vs. Σ13/Σ7 GBs) govern self-diffusion under thermal and mechanical stress, this work provides insights for designing more robust interconnects with improved resistance to electromigration-induced failure.

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