數值模擬柴氏長晶法之熱流場與氧濃度分佈

Abstract

本研究以商用軟體CGSim作柴氏長晶法之動態模擬，以及晶爐內的氧濃度分佈。動態長晶的研究將比較模擬和實際測量之晶身長度變化，氧濃度則探討在熔湯內部及氣體流場的分佈現象。網格繪製皆採用二維軸對稱，統御方程式包含連續方程式、動量方程式、能量方程式及質傳方程式。柴氏長晶法過程非常複雜，液固界面形狀、熱流場及氧濃度分佈難以觀察，若能將長晶之物理參數搭配電腦模擬，便可及早推估長晶過程中熱流場與雜質濃度場之變化。除了CGSim之外，亦利用商用軟體Fluent做初步的熱流場模擬。

This study outlines the dynamics of CZ crystal growth and oxygen concentration by simulation of commercial software CGSim. The dynamics of CZ crystal growth are illustrated by the influence of the heater and the pull velocity, and the discussions on the oxygen concentration involve in silicon melt and gas flow distributions. The meshes of the system are constructed in 2D-axisymmetric model. The governing equations include continuity equation, momentum equation, energy equation, and mass transfer equation. Due to the complication of the CZ crystal growth process, it is difficult to observe the thermo-fluid flow field and oxygen concentration. By utilizing the simulation results, we can predict and estimate the variation of the thermo-fluid flows field and oxygen concentration. In addition to the simulation of CGSim, we also use the other commercial software Fluent to simulate the thermo-fluid flows field.