臺灣博碩士論文加值系統

半導體製造產業在近年來迅速蓬勃的發展，並同時是一個投資額極高的產業，由於在大部分實際製程中，往往存在產品設定點的改變及製程老化衰退變動等決定性變化，並伴隨著非高斯外界干擾與不確定量測延遲所造成製程輸出產品資訊擷取之延宕等隨機性變數影響，因此發展一套控制策略提升製程的控制效能絕對有其必要性。基於以上理由，本研究主要針對具有不確定量測延遲變異與非高斯分佈外界干擾等隨機分佈特性的半導體生產製程發展一混合型逐批控制策略，稱之為結合決定性 (deterministic) 與隨機性 (stochastic) 之模式基礎控制 (Model based control, MBC) 的逐批控制策略 (DSMBC)，藉由決定性模式與隨機性模式其優缺互補之特性，提升製程的控制效能。

決定性模式為基礎的逐批控制如指數加權移動平均 (EWMA) 控制，針對設定點改變等決定性變化能快速的反應及追跡，但無法克服量測延遲變異造成系統輸出資訊回饋之延宕所帶來的控制效能遲滯及不穩定控制；而以隨機性模式為基礎的逐批控制如最小熵控制 (MEC)，其能有效的將隨機性外界干擾及不確定量測延遲變異對控制系統的影響降至最低，卻缺乏當系統設定點發生改變後快速追跡之能力。故DSMBC將決定性的預測系統平方誤差與隨機性的系統信息熵及控制能量約束項之結合作為一創新的系統性能指標，以設計最適化逐批控制器；且為了避免製程隨批次之進行而產生老化衰退的飄移，與模式誤差 (model mismatch) 造成控制效能的影響，DSMBC藉由每一批次擷取到的輸出回饋資訊完成數據導向的模式自我更新。除此之外，由於時下半導體產業多以多機台設備同時並行生產不同產品，本研究亦將DSMBC數據導向逐批控制策略延伸至多機台多產品 (MTMP) 系統，並利用觀察向量處理方式共享每個機台上於各批次所擷取到的系統輸出資訊，以建立決定性的MTMP系統模式。

最後，本研究於單一機台單一產品系統與多機台多產品系統分別以ㄧ鎢化學氣相沈積製程及淺層溝渠隔離製程驗證本論文所擬DSMBC數據導向逐批控制策略於真實製程上之有效性與可行性。

In recent years, semiconductor manufacturing has swiftly evolved as a lucrative industry with high capital investment. Most actual manufacturing processes experience deterministic changes, such as set-point changes and process drifts. In addition, the output variable of the process is usually subject to random inputs, such as metrology delay of uncertain duration and non-Gaussian disturbances which can be treated as random variables that follow a specific probability density function (PDF). Conventional control is unable to minimize both sources of variation. Therefore, it is necessary to develop a novel control method to improve the performance of conventional control. In response to this need, this research proposes a hybrid run-to-run (RtR) controller called deterministic and stochastic model based control (DSMBC) strategy for the semiconductor production processes with the stochastic distribution characteristics. The DSMBC strategy merges the features of both models into an effective process control method.

The deterministic RtR controller (exponentially weighted moving average or EWMA controller) responds quickly to deterministic changes, such as set-point changes and drifts. But it could not overcome the hysteresis of control performance and closed loop instability caused by delay of information feedback of process outputs due to metrology delay of uncertain duration. The stochastic model based controller (minimum entropy control or MEC) is effective in minimizing effects due to the random disturbances and metrology lag of varying duration. But it is slow in responding to set-point changes. In designing an optimal controller that has the strengths of both controllers, the proposed DSMBC strategy formulates a novel performance index into a weighted sum of stochastic entropy of output errors, deterministic prediction of square of the output errors and the control energy constraint. This modification also allows the optimal controller to counteract the effects caused by the drift of aging of the process with batch processing and model mismatch. Model mismatch is eliminated as the DSMBC strategy uses the feedback information of the measured process output from every batch to accomplish the data-driven updating of the model parameters. In addition, the proposed data-driven RtR controller of the DSMBC strategy can also be applied to semiconductor industries which use multi-devices for parallel production of different products (also called MTMP processes). The observation vector is used to pool together the measured output information obtained at each batch to construct the deterministic and stochastic MTMP models.

Finally, simulations of the tungsten chemical-vapor deposition process and shallow trench isolation process demonstrate the power, effectiveness and feasibility of the proposed data-driven RtR controller employing the DSMBC strategy in STSP and MTMP processes.

目錄

摘要 .............................................................................................................................. I
Abstract ........................................................................................................................ II
致謝 ........................................................................................................................... III
目錄 ........................................................................................................................... IV
圖目錄 ...................................................................................................................... VII
表目錄 ....................................................................................................................... IX

第一章 前言 ............................................................................................................... 1

1.1 引言 .................................................................................................................. 1
1.2 文獻回顧 .......................................................................................................... 2
1.3 研究動機 .......................................................................................................... 5

第二章 背景理論 ....................................................................................................... 7

2.1 單一機台單一產品製程的EWMA逐批控制 ................................................ 7
2.2 多機台多產品製程的逐批控制 ...................................................................... 9
2.2.1 JADE於多機台多產品製程的系統模式 ................................................ 10
2.2.2 RLS於多機台多產品製程的系統模式 .................................................. 13
2.2.3 State estimation的逐批控制策略 ............................................................ 15
2.3 隨機分佈系統控制 ........................................................................................ 17
2.3.1 系統輸出的機率密度函數 ..................................................................... 17
2.3.2 形狀追跡控制策略 ................................................................................. 18
2.3.3 最小熵控制策略 ..................................................................................... 19

第三章 混合型逐批控制器於單一機台單一產品系統 ......................................... 21

3.1 系統描述 ........................................................................................................ 21
3.2 結合決定性與隨機性之模式基礎控制的逐批控制策略 ............................ 24
3.2.1 性能指標 ................................................................................................. 24
3.2.2 真實系統輸出誤差的機率密度函數 ..................................................... 26
3.2.3 最適化逐批控制器設計與穩定性分析 ................................................. 28
3.3 結合決定性與隨機性之模式基礎控制的數據導向逐批控制策略 ............ 33
3.3.1 真實系統輸出誤差的機率密度函數之遞迴更新 ................................. 34
3.3.2 系統模式的遞迴更新 ............................................................................. 36
3.3.3 數據導向的最適化逐批控制器設計 ..................................................... 38
3.4 測試範例 ........................................................................................................ 42
3.4.1 數學測試範例 ......................................................................................... 42
3.4.2 鎢化學氣相沈積製程 ............................................................................. 58

第四章 混合型逐批控制器於多機台多產品系統 ................................................. 70

4.1 DSMBC逐批控制策略於MTMP系統 ......................................................... 71
4.1.1 MTMP系統描述 ...................................................................................... 71
4.1.2 最適化逐批控制器設計於MTMP系統 ................................................ 76
4.2 DSMBC數據導向逐批控制策略於MTMP系統 ......................................... 79
4.2.1 遞迴更新MTMP系統模式 .................................................................... 80
4.2.2 遞迴更新MTMP系統輸出誤差的機率密度函數 ................................ 86
4.2.3 數據導向的最適化逐批控制器設計於MTMP系統 ............................ 95
4.3 測試範例 – 淺層溝渠隔離製程 .............................................................. 100
4.3.1 淺層溝渠隔離製程介紹 ....................................................................... 100
4.3.2 淺層溝渠隔離製程測試 ....................................................................... 101

第五章 結果與討論 ............................................................................................... 120

參考文獻 ................................................................................................................. 122

作者自述 ................................................................................................................. 126



圖目錄

Figure 2.1 EWMA逐批控制策略的系統流程方塊圖 ........................................ 9
Figure 3.1 DSMBC逐批控制策略之系統流程方塊圖 ..................................... 24
Figure 3.2 DSMBC數據導向逐批控制策略之系統流程方塊圖 ..................... 33
Figure 3.3 非高斯分佈的隨機外界干擾 ........................................................... 44
Figure 3.4 非高斯分佈的不確定量測延遲變異 ............................................... 45
Figure 3.5 EWMA逐批控制策略於量測延遲系統之控制流程方塊圖 .......... 47
Figure 3.6 EWMA控制器於 的模擬結果 .......................... 48

Figure 3.7 EWMA控制器於 的模擬結果 ........................... 49

Figure 3.8 SMBC 逐批控制策略的模擬結果 .................................................. 53
Figure 3.9 DSMBC 逐批控制策略的模擬結果 ............................................... 55
Figure 3.10 真實系統輸出誤差的變化程度於DSMBC逐批控制策略 ............ 56
Figure 3.11 真實系統輸出誤差PDF的3D-mesh圖 .......................................... 57
Figure 3.12 初始與最終的真實系統輸出誤差PDF比較圖 ............................... 57
Figure 3.13 非高斯分佈的隨機外界干擾 ........................................................... 60
Figure 3.14 EWMA控制器於CVD製程的模擬結果 ........................................ 62
Figure 3.15 SMBC 逐批控制策略於CVD製程的模擬結果 ............................. 64
Figure 3.16 DSMBC 逐批控制策略於CVD製程的模擬結果 .......................... 66
Figure 3.17 CVD製程輸出誤差的變化程度於DSMBC逐批控制策略 ........... 67
Figure 3.18 CVD製程輸出誤差PDF的3D-mesh圖 ......................................... 68
Figure 3.19 初始與最終的CVD製程輸出誤差PDF比較圖 ............................ 68
Figure 4.1 MTMP系統的生產排程示意圖 ....................................................... 70

Figure 4.2 DSMBC逐批控制策略於MTMP系統下第m機台的控制流程方
塊圖 ................................................................................................... 72
Figure 4.3 第m機台下每一批次生產不同產品的生產排程示意圖 ............... 73
Figure 4.4 DSMBC數據導向逐批控制策略於MTMP系統之控制流程方塊
圖 ....................................................................................................... 80
Figure 4.5 MTMP系統之歷史數據處理示意圖 ............................................... 82
Figure 4.6 MTMP系統各機台真實測量到的輸出誤差計算方法示意圖 ....... 87
Figure 4.7 數學符號各下標說明圖 ................................................................... 90
Figure 4.8 MTMP系統歷史數據的真實輸出誤差計算流程示意圖 ............... 92
Figure 4.9 STI製程中矽溝槽深度示意圖 ....................................................... 100
Figure 4.10 非高斯分佈隨機外界干擾之機率密度函數 (PDF) ...................... 102
Figure 4.11 量測延遲於每批操作數據 ............................................................. 104
Figure 4.12 各機台的產品生產排程 ................................................................. 105
Figure 4.13 JADE控制器的控制效能 ............................................................... 109
Figure 4.14 JADE控制器的控制作動 ............................................................... 110
Figure 4.15 SMBC控制器的控制效能 .............................................................. 112
Figure 4.16 SMBC控制器的控制作動 .............................................................. 113
Figure 4.17 DSMBC 控制器的控制效能 ......................................................... 116
Figure 4.18 DSMBC 控制器的控制作動 ......................................................... 117
Figure 4.19 MTMP系統輸出誤差的information potential與熵值之變化 ...... 118
Figure 4.20 MTMP系統輸出誤差PDF的3D-mesh圖 .................................... 118
Figure 4.21 初始與最終的MTMP系統輸出誤差PDF比較圖 ........................ 119



表目錄

Table 3.1 各逐批控制策略於數學測試範例之控制效能比較表 ................... 58
Table 3.2 各逐批控制策略於CVD製程之控制效能比較表 .......................... 69
Table 4.1 各機台的產品生產排程表 ............................................................. 106
Table 4.2 各逐批控制策略於MTMP之STI製程的控制效能比較表 .......... 119

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