本論文包含兩個部分。首先，我們建立一個二維的模型，利用潤滑理論及接觸力學去計算化學機械研磨(chemical mechanical planarization; CMP)製程中晶圓表面和研磨墊表面之間的接觸應力及流體(研磨液)壓力分佈。我們著重在等效晶圓剛性(含晶圓剛性及研磨頭結構結合而成的等效剛性)，晶圓扣環寬度及其背壓，和多區段晶圓背壓等參數，對接觸應力均勻度的影響。接觸應力均勻度與晶圓表面材料磨除率均勻度成正相關的關係。

我們的數值結果指出，對任一給定的等效晶圓剛性而言，都可以找出晶圓扣環寬度及其背壓的最佳組合以得到最小的接觸應力不均勻度。此外，等效晶圓剛性愈小，可以得到的最小接觸應力不均勻度的值愈小，所以使用氣囊式的浮動研磨頭設計，以期產生最小的等效晶圓剛性，將是較佳的選擇。在較小的等效晶圓剛性下，多區段晶圓背壓對於減小接觸應力不均勻度的成效將會較改變晶圓扣環寬度及其背壓為佳，當然兩種方法同時使用效果更佳。

另一方面，我們從具溝槽表面研磨墊的CMP問題做延伸，探討一個上平板為有限長度平板，而下平板為一具溝槽表面之無限長度平板的潤滑問題。在這一部分的研究中，我們不考慮接觸應力，純粹探討溝槽表面對上平板的運動行為及流體壓力的影響。在此，我們忽略上平板的重量，並且以一直線彈簧及一扭矩彈簧去處理上平板的力及力矩平衡。我們用微擾法去求解此一問題。結果指出，下平板表面溝槽的存在會使得流體壓力在空間分佈上有溝槽尺度的變異並且會隨時間而改變。因此，流體壓力所造成的力及力矩都會隨著時間改變，並使得上平板隨著時間振盪。

This dissertation includes two parts. First, we use two-dimensional models of fluid film lubrication and contact mechanics to calculate the contact stress and fluid (i.e., slurry) pressure distributions on the wafer–pad interface in chemical mechanical planarization (CMP). In particular, the effective rigidity of the wafer (determined by the wafer carrier structure), the retaining ring width and its back pressure are taken to be the design parameters. The purpose is to study the synergetic effects of such parameters on the contact stress uniformity, which directly affects the spatial uniformity of the material removal rate on the wafer surface.

Our numerical results indicate that, for a given wafer rigidity, one may choose the retaining ring width and back pressure to minimize the contact stress non-uniformity (NU). Also, the resulting minimum NU decreases with the effective wafer rigidity, suggesting that it is beneficial to use a soft (e.g., floating-type) wafer carrier. Moreover, for a soft wafer carrier, it is demonstrated that using a multi-zone wafer-back pressure profile is even more effective in reducing NU. Of course, it is better to use both methods simultaneously.

Moreover, we also construct a grooved-surface fluid film lubrication model to study the fluid lubrication mechanics. In particular, we correlate the attitude of the upper plate (representing the wafer) to the down force and moment. This lubrication model is motivated by the CMP model, but does not really model the CMP problem. The most interesting effect we would like to know is the effect of the lower plate surface grooves on the upper plate motion, which is analyzed by perturbation method. Our results indicate that the existence of the grooves on the lower plate will induce the spacial and temporal variations of the fluid pressure distribution, and hence temporal variations of the force and moment on the upper plate, which, in turn, cause the upper plate to oscillate.

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