柴氏長晶法是現今用以生長大尺寸矽單晶的一個主要方法。為了提高晶體的品量，則需要有效的控制晶錠之氧濃度以及其電性。矽晶圓片最佳電阻率可以透過於晶棒生長過程中，加入一些常見的摻雜劑（硼，砷，磷，銻，...）於矽熔湯中來達成。 在本研究中，有限體積法（FVM）數值模擬方法，用於研究砷的摻雜對固液界面氧氣濃度的影響使用進行了。本研究的實驗數據由SAS公司提供，而在砷濃度中電阻率的轉換是透過轉換公式來計算，並將實驗數據與模擬結果進行比較。將模擬結果與實驗數值相比較後，很顯然，兩者於晶棒的電阻率之變化趨勢是一致。 矽熔湯重摻砷之氧濃度含量比非摻雜的情況下熔湯中的氧濃度明顯偏低，主要原因是由於砷的摻雜會降低二氧化矽中氧的活度係數，進而降低氧的熔解。由於砷的偏析係數較小，所以砷的濃度隨生長晶體高度增加而增加。砷部分會集中在晶錠的中間，而相較於晶體邊緣則較少。 此外，若增加於熔湯中砷的含量，將降低在晶體中之氧含量，但增加徑向砷之含量。砷摻雜量與電阻率之間是成反比關係。 最後，提拉速度和旋轉率對於電阻率之影響亦被考慮。在結果中顯示出晶錠中電阻率，隨生長速率及坩堝的旋轉速度增加而增加，但隨晶k體的旋轉速率增加而降低。 ;Nowadays the Czochralski (Cz) technique has become a main method to grow large single silicon crystal. In order to enhance the quality of crystal, the level of oxygen concentration in the ingot as well as its electric properties has to be controlled. The optimal resistivity for the silicon epitaxial wafers can be obtained by adding directly some common dopants (boron, arsenic, phosphorus, antimony …) into the liquid silicon during the growth process. In this study, the effect of doping arsenic on the oxygen concentration along the freezing interface is numerically investigated by finite volume method (FVM). In order to compare with the experimental resistivity provided by SAS Company, the conversion of crystal resistivity from arsenic concentration is made by using the standard transformation formulation. It is clear that the simulation predictions have similar tendency with the experimental ones in crystal resistivity. The computational results show the mechanism of oxygen content reduction in heavily arsenic-doped Cz silicon melt as compared with non-doped melt. This is because arsenic doping decreases the thermodynamic activity coefficient of oxygen dissolved into the bulk melt from silica. Arsenic content also increases along the length of crystal due to its small segregation coefficient (k0=0.3). The arsenic atoms concentrated in the ingot center are much more than their concentration in the region of crystal edge. Furthermore, the increase in doping level causes a decrease of oxygen content in the growth direction while this increases the radial segregation of arsenic. There is an inverse relationship between dopant concentration and crystal resistivity. Last but not least, the effect of pulling rate and rotation rate on the resistivity is also predicted numerically. The results indicate that the radial resistivity variation of ingot increases with increasing the growth rate as well as crucible rotation rate while this trend is reversed as the crystal rotation rate is accelerated.
