• 作者： 趙一雄
• 作者服務機構： 私立大同工學院
• 中文摘要： 鋁銅合金薄膜於電場作用下，晶界處銅離子之擴散速率遠大於鋁離子之擴散速率，而在擴散
  過程中，銅離子或與鋁離子結合形成第二相CuAl2，或自第二相CuAl2中離析出來。本文即是
  討論薄膜在電場作用下銅離子擴散的動態情形，並計算銅離子濃度沿晶界之分佈。若外加電場並
  非很大時，由於第二相CuAl2中銅離子之被離析出來，沿晶界之銅離子濃度並沒有明顯遞減，
  所以晶界處鋁離子之擴散將一直不會明顯，亦即鋁銅合金薄膜因電流引起質量遷移所生之破壞現
  象將不顯著。若外加之電場?大，則銅離子往正極方向堆聚，並維持其飽和濃度，致使負極附近
  之濃度逐漸減少，而負極附近鋁離子的擴散現象遂逐漸顯著，其質量遷移效應使得部份質量發散
  區域逐漸形成裂縫或溝槽。所以鋁銅合金薄膜因電流引起質量遷移所生之破壞現象多數發生於負
  極附近，這些破壞現象以鋁離子之質量發散為主要原因。因此延緩晶界處銅離子濃度隨時間之改
  變率，即可延緩晶界處鋁離子之擴散現象，因而增長了薄膜通電流後的使用壽命。單位體積之晶
  界中第二相CuAl2之個數增加時，可以延遲晶界處銅離子濃度隨時間之改變率，而第二相CuAl2
  猶如銅離子之供應者，它將銅離子離析出來時，亦可延遲晶界處銅離子濃度隨時間之改變率。d
• 英文摘要： Copper ion diffuses toward the anode at aconsiderably faster rate than aluminum ion inthe grain boundaries of aluminum-copper thinfilms under the influence of an applied electricfield. The diffusion of copper ion may locallyaccumulate or deplete the primary phase, result-ing in precipitation or dissolution of the second-phase CuAl2. From the results, the generaldiffusion equations for such process are derived,and the time dependent on distribution of copperion along the graim boundary of aluminum-copper thin film has been solved by rigorouslyusing the Laplace transformation. It is shownthat the number of precipitate particles per unitvolume and the dissolution coefficience of theprecipitate are the dominant factors to determinethe rate of concentration change of copper ionin the primary phase. When the applied fieldstrength is not large, the copper ion concentra-tion at the cathode region will not decreasebelow the solubility limit due to the dissolutionof the precipitate second-phase. On the contrary,if the applied field strength is large enough, thenthe copper ion will deplete from the cathodeand the aluminum ion starts to diffuse quicklyat this region. Finally, the failure mechanismsrelating copper additions to electromigrationlifetime are censidered.
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