化學機械平坦化之最佳化操作：動態規劃法

Abstract

在本論文中，我們探討在一片二氧化矽或銅晶圓的研磨過程中， 改變向下壓力與旋轉速度對不平坦度的影響。因為向下壓力與旋轉速 度的大小皆有其限制的範圍，我們運用動態規劃設計有限向下壓力及 旋轉速度的化學機械研磨之最佳化操作，並藉由更精確描述化學機械 研磨的模型，在其他參數皆為固定的條件下，計算出輸入的改變量與 時間，接著將最佳化計算結果在控片上作實驗，並與傳統的固定移除 率操作方法作比較。此外，在有圖案的銅晶圓研磨，運用高處所受的 向下壓力比低處高的假設，建立階梯高度的模型，並藉由模擬的結果 說明向下壓力對平坦化效率的影響。

In this thesis, the impact on non-planarization index by the down force and rotational speed during a SiO2 or Cu CMP process was investigated. Since the magnitudes of down force and rotational speed have limits, we choose the dynamic programming approach because of its ability to achieve constrained optimization by the down force and rotational speed. The duration and the amount of input were computed based on the more accurate chemical mechanical polishing model when the other parameters were fixed. Experiments based on dynamic programming were done for blanket wafers and the conventional operation was compared with the dynamic programming operation. Besides, the model for the step height reduction was established in the case of pattern wafer. The model was based on the assumption that at the feature scale, high areas on the wafer experience higher pressure than the lower areas. The influence of the planarization efficiency by the down force was discussed based on the simulation result.