Czochralski法是生長高品質矽單晶的重要技術。其中矽晶片的電阻率和差排密度與晶棒中雜質有很重要關係，特別是氧和碳的濃度。因此雜質控制便成為Czochralski法製造單晶矽中的重要問題，然而矽晶棒中的碳濃度流動與設定參數之間的關係在現存文獻中尚未確立，在這項研究中，軸對稱數值模型用於研究Cz過程中碳的質量傳遞現象，考慮晶體和坩堝的不同轉速和方向，研究不同流動模式下的質量傳遞現象。 我們研究晶體和坩堝旋轉的哪種組合具有較低的碳濃度，並分別進行晶體坩堝同向與反向旋轉，找到造成碳濃度降低的物理機制。我們發現晶體旋轉10 rpm和反向坩堝旋轉3 rpm具有最低的碳濃度。而碳傳輸的行為與熔融矽中的對流和晶體下方的速度有關，介面的溫度、熔湯氧濃度也會影響碳雜質溶入熔湯的多寡。其中有三個重要的渦流，首先是Taylor-Proudman cell在晶體 - 熔體界面下，它是碳濃度重要的來源。其次，浮力渦流將碳帶入熔體，熔湯的自由表面的範圍成為一個重要因素。這是因為碳在浮力渦流中也會再透過自由液面蒸發，如果被其他渦流抑制，碳便不會在一開始時蒸發而直接流入下個渦流。第三，二次渦流位於Taylor-Proudman cell和浮力渦流之間，適當大小的二次渦流能使碳滯流於此渦流，使碳有更多機會流回到浮力渦流讓碳蒸發。 ;Czochralski (Cz) method is widely used for the production of high quality silicon single crystal. Under high temperature condition of growth process, the undesirable impurities, such as oxygen and carbon, enter the silicon melt and their content strongly affects the resistivity and the dislocation density of the silicon wafer. A precise control of these impurities at a low concentration and uniform distribution, therefore, has played an important role for improving the quality of silicon crystals, especially large-sized crystals. To our best knowledge, there are few publications showing the effects of the operation parameters of CZ growth process on carbon concentration. In this study, a 2D axisymmetric numerical model is used to study the heat and carbon transport during the growth of a 6 inch-diameter silicon ingot. Different rotation speed and direction of the seed and crucible are considered to investigate their effects on the variation of heat, flow, and carbon characteristics. The numerical simulations show that the carbon concentration gets lowest when the counter rotation rates of seed and crucible are 10 rpm and -3rpm, respectively. The behavior of carbon movement is related to the melt convection and the velocity under crystal-melt interface. While the temperature on free melt surface and oxygen in the melt will affect the quantity of carbon. The flow structure is included three main vortices: Taylor-Proudman cell (1), under the crystal-melt interface, buoyancy driven cell near the crucible wall (3), and the secondary cell (2) between (1) and (3). It was found that the carbon atoms are carried by cell (3) into the silicon melt. The carbon atoms are got out of the melt from the free melt surface. The larger effective evaporation area may reduce the carbon content in the melt due to the larger evaporation rate of carbon. Moreover, the secondary vortex (2) also affects the carbon transportation. Appropriate cell (2) may keep the carbon atoms stay longer in the melt and buoyancy cell (3) is easier to bring them to the free melt surface.
