本文提出一種混合拉式轉換法（Laplace transform technique）和中央差分法（Central difference method）的數值方法，並配合最小平方法（Least-squares scheme）來預測12吋晶圓中所加入的熱通量。首先利用拉式轉換法處理系統之時間域而後再以有限差分法處理系統轉換後之時間域，最後再以數值逆拉式轉換法求得測試物件之溫度場分佈以便預測出所加入的熱通量。拉式轉換法的優點是可以求得在某一特定時間的溫度值，而不需要由初始時間慢慢地求解。最小平方法的應用在於使數值結果能較快速地收斂。本文的數值模擬採用晶圓上下兩邊都受到對稱均勻的20 W/cm²光源照射熱通量，周圍環境溫度為27℃，晶圓從27℃被快速的加熱到1097℃，12吋晶圓的厚度為0.725 mm。由結果顯示，晶圓上所需的照射熱通量可有效地經由此逆向模式評估計算出來。

The present study introduces a hybrid scheme of the Laplace transform technique and central difference method in conjunction with the least-squares scheme is used to predict the heat flux of 12-in wafer. Time-dependent terms in the governing equation are removed by using the Laplace transform technique, and then the resulting differential equation is solved by using the finite-difference method. Temperature distributions in the domain are obtained by using the numerical inversion of Laplace transform. Due to the application of the Laplace transform technique, the temperature can be calculated at a specific time without step-by-step computation in the time domain. By the least-squares scheme, the convergence of iteration can become fast and stable. In this thesis, both sides of the wafer were subjected to a uniform heat flux of 20 W/cm² from 27℃ transition to a steady state of 1097℃ via simulation with an ambient temperature 27℃. The incident-heat-flux profile required for temperature uniformity across 12-in-diameter （0.775-mm-thick） silicon wafer were intuitively evaluated using inverse modeling. Our numerical result show that the incident heat fluxes on the wafer can be efficiently achieved using inverse modeling.

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