高轉換效率的太陽能電池是其中一種潛在性的永續能源，多數的太陽能電池由結晶矽太陽(單晶矽或多晶矽)所製造。因為單晶矽太陽能電池由矽最高等級所製造而成，單晶矽太陽能電池具有最高的轉換效率；而多晶矽太陽能電池由於從便宜的原料所生產，則它們則有較多的優選方位。定向凝固是一種可考慮為最佳的方式，生產較大的尺寸與較高品質的矽晶錠，由於它們在原料中的雜質有較大耐受性。
熱交換法是最好的鑄造方法，因為它具有簡單操作、成本低廉與原料送進機器內的機動性等優點。在定向凝固的熱交換系統中，溫度分佈是由爐內條件、加熱器功率與冷卻系統所影響。冷卻條件、加熱區的設計與雜質的偏析從鑄造過程中，藉由熱交換法會有意義的影響多晶矽鑄錠的品質。固、液界面的型狀在成長矽晶錠的定向凝固過程中，具有重要的雜質偏析影響。
固液界面的形狀和位置是受到加熱器的功率與坩鍋壁的熱性質影響。在這個研究中，使用一個二維數值模擬的有限差分法，研究多晶矽鑄錠在凝固過程中溫度的變化/分佈，結果與實驗量測結果進行比較。藉由調整加熱功率與不同固、液界面側壁的熱性質進行模擬。熱模擬結果顯示，使用有限差分法所建立的程式碼，在凝固過程中能夠計算碳濃度的分佈。碳濃度的分佈已經能夠研究三種鑄錠不同界面形狀的成長。
關鍵字：多晶，矽晶錠，定向凝固，熱交換爐，數值模擬，有限差分法。

High efficiency solar cells are one of the renewable energy potential. The majority of solar cells are made by crystalline silicon (either mono or poly crystalline). Although mono-crystalline cells have the highest efficiency since they are made by the highest grade of silicon, the poly-crystalline are more preferable since they are made by cheaper raw materials. Directional solidification is considered the best way to produce large scale and high quality ingot. Since it has a great tolerance to the impurities in the feedstock.
The heat exchange method is the best casting method since it has the advantages of an easy operation, low cost and flexibility of the materials in the feedstock. During directional solidification in the (HEM) system the temperature distribution is affected by the condition of the furnace and the power of the heaters and cooling system in the furnace. The cooling condition and the design of the hot zone and the impurities segregation have a significant effect on the quality of polycrystalline silicon ingot from casting process by heat exchange method (HEM). The shape of solid-liquid interface has a great impact on the impurity segregation in the grown ingot during directional solidification.
The solid-liquid interface shape and position are effected by the power of the heaters and the thermal property of the crucible walls. In this study a 2D numerical simulation using FE method has been performed to investigate the temperature variation/distribution in the solidification process of polycrystalline silicon ingot and the results are compared to the experimental measurements. By adjusting the power of the heaters and thermal properties of the side walls different solid-liquid interface has been simulated. The result from the thermal simulation has been incorporated to establish a code using finite difference method (FDM) to calculate the carbon concentration distribution during the solidification process. The distribution of the carbon has been investigated for three ingots grown with different interface shapes.

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