多輸入多輸出化學機械研磨製程控制

Abstract

化學機械研磨(Chemical-Mechanical Polish, CMP)是一個極為複雜的製程，因為牽涉到物理、化學及機械的領域[1]；對於晶圓輸出參數(例如移除率)而言，影響它的輸入參數不只一種，對晶圓的不平坦度而言，可能需要考慮到兩個以上輸入參數；在一般的半導體廠裡，大多採用批次(Run-to-Run)製程控制來控制晶圓的品質如不均勻度或移除率等；所謂批次，就是由前一製程的資料來預測下一批製程所需輸入的參數值，逐步控制晶圓產品使得品質輸出更能符合目標需求。 本研究提出了多輸入多輸出批片(wafer to wafer)雙模式適應控制之架構：雙模式適應控制(Dual Mode Adaptive Control, DMAC) [2][3]利用適應模型跟隨控制模式及適應模型鑑定模式兩者達成控制目標。實驗條件為每片研磨完後都作研磨墊修整(pad conditioning)，輸入的變數為壓力、研磨墊速度及研磨頭速度，最終控制目標為研磨率及不平坦度，此設計以多輸入多輸出控制系統架構為基礎。文獻指出研磨墊速度及研磨頭速度一樣時可使晶圓研磨後達到最平坦的效果 [4]，因此控制變數選為下壓力及研磨轉速以將移除率及不平坦度控制在目標值。在此研究中設計解耦控制器，將雙輸入雙輸出系統解耦成為兩套單輸入單輸出的系統。根據模擬及實驗數據，加入解耦控制器比沒有加入解耦控制器能更有效的控制移除率及不平坦度。 模型跟隨控制模式中，模擬中加入解耦控制器，目標誤差值的SAE（summation of absolute error）改善35.9％，SSE （summation of squared error）改善48.5%，MAE（maximum of absolute error）改善23.5％；實驗中加入解耦控制器，目標誤差值的SAE（summation of absolute error）改善7.6％，SSE （summation of squared error）改善32.6%，MAE（maximum of absolute error）改善29.7％。在此說明一下SAE實驗跟模擬部分的誤差: 模擬部分，CMP 的Model乃利用內插法所計算出來的線性模型，可是實際上要去控制CMP的模型為非線性，所以才使得實驗的SAE改善值不如模擬的SAE改善值一般理想。 模型鑑定模式中，只要CMP狀態值超出理想值範圍20％以外就會立即停機，請工程師來勘查機台問題，此為雙模式適應控制比傳統的單模式適應控制多提供的額外監控功能。

Chemical-Mechanical Polish is an extremely complicated process because it involves physical, chemical, and mechanical field [1]. There are many complicated factors which may affect only one output parameter such as removal rate. For non-planarization index alone, it is necessary to consider more than two input parameters at the same time. In semiconductor industry, run-to-run process control is used extensively to control process outputs, such as non uniformity and removal rate. Run-to-run process control uses the previous run process recipe to predict the next run process recipe to control the next run product quality on the target. This research has proposed multi-input, multi-output wafer-to-wafer Dual Mode Adaptive Control. Dual Mode Adaptive Control （DMAC）[2][3] utilizes adaptive model following control mode and adaptive model identification mode to achieve the control target. The experiment is carried out based on conditioning the pad every wafer. According to literature [4], wafer non-uniformity can be minimized when the wafer polishing pad and the wafer carrier are rotated at the same speed in CMP process. In one two-inputs, two-outputs CMP process, the inputs are down force and rotation speed of the wafer, the outputs are removal rate and non-planarization index. This multiple–input, multiple–output system uses down force and rotational speed of the wafer to control removal rate and non-planarization index. This research proposes decoupled controller to turn this two-inputs, two-outputs system into two single input single output systems. In adaptive model following control, according to simulations and experiments, control system with decoupled controller can do a better job in controlling removal rate and non-planarization index than control system without decoupled controller. In adaptive model following control simulations, decoupled controller of this research improves the target error SAE（summation of absolute error）by 35.9％, SSE （summation of squared error）by 48.9％, MAE（maximum of absolute error）by 23.5％. In adaptive model following control experiments, decoupled controller of this research improves the target error SAE（summation of absolute error）by 7.6％, SSE （summation of squared error）by 32.6％, MAE（maximum of absolute error）by 29.7％. There is difference in improvement of SAE between simulation and experiment. The actual CMP plant is a nonlinear system in experiment, but a linear model is used in simulation. The improvement of SAE in experiment is not so ideal as it is in simulation. In adaptive model identification mode, if there shows more than 20% drift in system parameter, the CMP equipment will be shut down for diagnosis, this is one additional monitoring capability provided by DMAC than conventional single mode adaptive control(SMAC).