隨著積體電路製程技術持續向先進節點邁進，傳統半導體元件中所使用的鋁合金導線因其較高的電阻率以及嚴重的阻容延遲（RC Delay）效應，已無法滿足現代高速運算與低功耗的性能需求。因此，具備更低電阻率與優異抗電遷移（Electromigration, EM）特性的銅製程已全面成為現今晶片互連線路的主流材料。然而，當導線的線寬縮減至奈米尺度時，材料的尺寸效應將引發顯著的物理變化，導致導線表面散射（Surface Scattering）與晶界散射（Grain Boundary Scattering）的機率大幅飙升，進而造成銅導線的電阻率急遽上升，嚴重限制了訊號傳輸速率並加劇了晶片的可靠度問題。為了克服這一瓶頸，近年來的學術界與產業研究多聚焦於開發自形成阻障層，或嘗試導入如釕（Ru）、鈷（Co）等新型替代金屬。然而，不論是製程調整或是新材料開發，深入探討金屬內部微觀結構與晶界構型對原子擴散的影響，皆是評估導線抗電遷移可靠度的關鍵問題。
本研究聚焦於純銅導線內部的一般晶界（General Grain Boundaries），透過原子尺度的理論模擬探討晶界形貌對銅晶界擴散係數的關聯。研究結果顯示，於單晶與一般晶界模型中，本研究計算所得之點空缺生成能、生成熵以及躍遷能障與前人研究結果相符，證實了本研究所採用之原子勢能與建模的合理性。在 78 種扭轉接合的一般晶界中，本研究篩選出六種晶界能最低的穩定結構進行後續擴散係數計算。然而，微觀過渡態（NEB）計算發現，(210)|(320)、(310)|(210) 以及 (321)|(211) 三種具備較高晶界能的模型中，其能量最高之鞍點（Saddle point）構型會出現一個或以上振動頻率為負值的虛頻模式（Imaginary modes），顯示出高能晶界內部的點空缺躍遷機制可能較複雜，難以單純用單一原子跳躍模式描述。
在 500K 至 1000K 的溫度區間，此六種晶界的擴散係數介於文獻記載的單晶結構與多晶模型之間。此結果可歸因於此六種晶界本質上屬於能量極低的穩定結構，其內部的點空缺躍遷能障較高，故其擴散係數低於包含高能晶界與三叉點（Triple Junctions）的多晶模型。此項模擬數據完美符合了 Borisov 關聯性的巨觀預測，即晶界自擴散係數會隨著晶界能的上升而增加。此外點空缺擴散的難易與空缺結構優化過程後的能量下降幅度以及其局域空缺體積之間並無顯著的直接關聯，且由於靜態過渡態計算方法本質上無法全面捕捉高溫下點空缺的連續性協同跳躍行為，使得此靜態預測方法對晶界擴散係數存在一定程度的低估，需進一步納入更高晶界能的模型以獲取更完整的分析內容。另外在不同晶面組合對應的晶界形貌變化，雖然對總體擴散係數的數量級並無顯著影響，但卻會影響晶界擴散的異向性。綜上所述，若欲預測純銅導線中晶界的抗電遷移（EM）失效特性，以晶界能而非晶界幾何構型作為判斷晶界擴散的難易度是更合理的作法。

As integrated circuit manufacturing advances toward sub-nanometer nodes, traditional aluminum interconnects suffer from severe resistance-capacitance (RC) delay and high resistivity. Although copper interconnects offer lower resistivity and superior electromigration (EM) resistance, nanoscale linewidth shrinking significantly increases surface and grain boundary scattering, leading to a sharp rise in resistivity and reliability concerns. Understanding the impact of grain boundary morphology on atomic diffusion remains crucial for evaluating EM reliability.
This study investigates the correlation between grain boundary morphology and diffusion coefficients in pure copper using atomistic theoretical simulations. The calculated vacancy formation energy, formation entropy, and migration barriers in single-crystal and general grain boundary models align well with literature, confirming the model validity. Among 78 general grain boundaries, six low-energy stable structures were selected for diffusion analysis. Nudged elastic band (NEB) calculations reveal that higher-energy grain boundaries exhibit saddle points with imaginary vibrational modes, indicating complex vacancy migration mechanisms beyond single-atomic jumps.
Between 500 K and 1000 K, the calculated diffusion coefficients of these low-energy grain boundaries lie between single-crystal and polycrystalline literature values, consistent with Borisov's correlation that grain boundary self-diffusion increases with grain boundary energy. Vacancy mobility shows no direct correlation with energy drop during relaxation or local vacancy volume. Furthermore, while grain boundary orientation does not alter the overall diffusion order of magnitude, it influences diffusion anisotropy. In conclusion, grain boundary energy serves as a more reliable metric than geometric configuration for evaluating diffusion resistance and EM reliability in copper interconnects.

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