週期性二維液膜解析解用以計算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。在一個有週期性結構的晶圓上旋塗薄膜，並以一個非線性的偏微分方程式描述其流體行為。取結構上的一小部分，分做四個子區塊，可以將非線性的偏微分方程式線性化，且首先解出其符號解，以一個無因次參數 描繪不同條件下的平坦度。 是表示離心力與表面張力的比，當 趨近於無窮大，表面張力趨近於零，液膜是順形液膜，即在每一個位置液膜厚度一樣。當 趨近於零，表面張力趨近無窮大，則得到平坦液膜。窄形或方形特徵中，低 時，X方向間距越小，平坦度越差；相對於Y方向間距越小，平坦度越好。特徵高度對平坦度則不會有太大影響。此外，於大部分情形中，高 時，平坦度就固定在-25%，不再隨 變化了。文獻中一維模型解析解視結構在Y方向為無窮遠，故其解析解只適於窄形結構。本論文所提之二維模型不僅適用於窄形的結構，對於方形或長形結構亦可考慮到在其Y方向結構的變化而加以描繪。 This thesis is the first one to present “a 2-D analytical solution of film planarizatsion 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. The thin film on the wafer which has period structures is coated by spin coating. We can describe the phenomenon by four order partial differential equation. And it can be used to solve out the symbolic solution by linearizing the partial differential equation at four subregions which is the part of the period structure. We describe the DOP by using the governing dimensionless parameter at different conditions. The represents the ratio of centrifugal force to surface tension force during spin coating. When approach to infinite, surface tension is zero, and the film is always conformal. When approach to zero, surface tension is infinite, and the film is planar The DOP of narrow rectangular or square feature decreases with decrease of the space between two features on X direction. A comparison shows that DOP will increase with decrease of the space between two features on Y direction. And for height of the feature, DOP changes slightly with increase of the .Finally, for the most conditions, no matter how the features and parameters change, at high , DOP will steady at -25% and not change with any more.
