Theoretical Model for Calculating the Thickness of the Nanoscale Chemical Reaction Layer on Sapphire Substrate for Different Slurry Dipping Durations and Experiments

計算浸泡不同研磨液時間的藍寶石化學反應層厚度理論模式及實驗

林榮慶(Zone-Ching Lin) ； 丁皓洋(Hao-Yang Ding) ； 馬士閎(Shih-Hung Ma)

《中國機械工程學刊》 39卷5期 (2018/10) Pp. 477-486

摘要

An innovative theoretical model and experimental method were proposed to calculate nanoscale thickness of the chemical reaction layer of sapphire substrates and analyze the various slurry dipping durations (dipping 5,10,20,30,60,90 min.)affecting the thickness of the chemical reaction layer. It involved applying small down force to cut sapphire substrates dipped in slurry for varying dipping durations it to obtain the SDFE values corresponding to the thickness of chemical reaction layer. The measured SDFE values of performing with a cutting depth interval of 0.05nm were then used to develop a theoretical method for calculating the thickness of the chemical reaction layer of sapphire substrate according to the various dipping durations of dipping slurry. Finally, an AFM nanoscale cutting experiment was conducted with a cutting depth interval of approximately 0.01 nm for each cutting pass to determine the changes in the SDFE values, which were used to measure the thickness of the chemical reaction layer for each slurry dipping time. The results verify that the proposed theoretical method is feasible. Next, it conducted a regression analysis and a regression equation for the thickness of the chemical reaction layer and various dipping durations. The results indicate that at longer slurry dipping duration, the chemical reaction layer thickened; specifically, the chemical reaction layer thickness at dipping duration less than 20 min increased rapidly with the dipping time, but at dipping duration longer than 30 min, the increase was approximately linear.

關鍵字

Specific down force energy ； atomic force microscopy ； sapphire substrate ； thickness of chemical reaction layer

並列摘要

本文提出計算浸泡不同研磨液時間的藍寶石化學反應層厚度之理論模式和實驗方法。將浸泡不同研磨液時間的藍寶石用較小的下壓力切削藍寶石，以獲得浸泡不同研磨液時間的化學反應層內的此下壓能值(SDFE)。再用原子力顯微鏡(AFM)進行切削深度間隔0.05nm的藍寶石實驗，以獲得浸泡不同研磨液時間之不同切削深度的比下壓能值，用所得之SDFE值計算浸泡不同研磨液時間的化學反應層厚度理論模式，計算出浸泡不同研磨液時間的藍寶石化學反應層厚度值。最後再用AFM實驗切削藍寶石，其中的切削深度間隔為0.01nm，並觀察其SDFE值的變化，決定浸泡不同研磨液時間的藍寶石化學反應層厚度的實驗值。最後驗證本文之計算浸泡不同研磨液時間的藍寶石化學反應層厚度理論模式為合理的。本文亦將所得之浸泡不同研磨液時間的藍寶石化學反應層厚度值進行迴歸分析，並獲得迴歸公式。迴歸分析結果可看出在浸泡時間小於20分鐘時，其化學反應層厚度增加很快，但在浸泡時間大大於30分鐘後，其化學反應層厚度的增加近似直線增加