| 摘要: | 本論文是第一個針對旋轉塗佈液膜平坦化之二維模型求得解析解，用以計算旋轉塗佈液膜平坦化之程度與描述液膜之分佈。在半導體的製程中，應用旋轉塗佈可得微米級之薄膜，再逐步逐層的經過沉積、顯影與蝕刻等步驟，製得半導體之元件。因此在元件設計上、良率控制及量產效率都繫於對旋轉塗佈機制的了解。本論文的模型可以掌握更多的參數，比如：線排的長寬比與線排在晶圓上的位置。突破以往一維解析解只能針對極為狹窄的線排預測其平坦度以及液膜分佈的情形。受限於符號計算軟體的限制，本論文提出的方法所求得的數值解與前人針對各式線排之平坦度大略相符；而整體液膜分佈與實際狀況則有差距。本論文發現方孔或方台的平坦度在任何角度上沒有很大的變化，而狹窄矩形的平坦度隨著角位置愈大，其平坦度愈趨向狹長矩形於低角位置之平坦度。相反的，狹長矩形線排隨著角位置愈大，其平坦度愈趨向狹窄矩形於低角位置之平坦度。此現象肇因於液膜所流經的跨距會隨著在晶圓位置上的不同而有差異。狹窄線排的平坦度在相同的離心力與表面張力比的條件下較狹長線排的平坦度差，顯示表面張力的作用距離較長而有較平坦的效果。各式線排於某個的角度下，其平坦度的表現不分軒輊。這表示角度影響了離心力、牆面效應與表面張力的綜合作用，使得該位置下的液膜所受的合力是一樣的，因此平坦度的表現相同。這些現象的發現，有助於改善半導體業界於設計積體電路元件的案紋形式與位置上的安排，也可解決許多關於錯位的控制問題。總而言之，本論文所提出的二維解析解，揭示了模型於維度上的拓展是可行的，並證明存在一個數學物理方法來了解旋轉塗佈的機制，因此在應用上更有依據。 This thesis is the first one to present “a 2-D analytical solution of film planarization for spin coating”. This analytical solution is used for predicting the degree of planarization (abbreviated as DOP), and describing the film distribution. Among semiconductor manufacturing process, utilizing spin coating can obtain the micro-thick film, and help other process to produce the elements. Thus, for the demand of design, quality, and productivity, understanding more about the mechanism of spin coating is required. This thesis can account more parameters than 1-D can. Hence, it won’t only describe the DOP of the very narrow feature, and the film profile. Due to the limit the symbolic computation application program, this thesis proposes an alternative approach for getting the DOP and film profile. The DOP is almost consistent with the former research, but inconsistent in film profile. We find that the square type feature is little of varied on arbitrary position. The DOP of the narrow rectangular feature will behave as that of longer rectangular one in lower angular position while its angular position becomes higher. On the contrast, when the longer rectangular feature raises its position, its DOP will be similar with that of the narrow rectangular one. This is because of the length of the distance across which the film flows. The DOP of the narrow feature is worse than that of the longer feature under the same condition of the ratio of centrifugal force to surface tension. This shows that the longer active length of surface tension can makes it more flatten. On certain position, the DOP becomes the same for various features. This means the angular position will effects the synthetic performance of the centrifugal force, wall effects, and surface tension, and make them the same. Those phenomena can help semiconductor industry for their pattern design and the arrangements, and resolve the problem of the miss alignment. To sum up, this thesis successfully illustrates the exploring of the feasibility of 2-D analytical solution. Moreover, it shows that there exists a mathematical physical approach to understand the mechanics of spin coating. Hence, offering a base for its relative applications. |
