Computer Simulation of Radial Oxygen Distribution in Silicon Czochralski-grown Single Crystal

1. 研究目标：利用计算机模拟氧在奇克拉尔斯基生长单晶中的径向分布，以提高单晶的均匀性。(1)研究原理：考虑到Si熔体与高纯石英坩埚反应产生的氧加入-Si熔体中氧的对流扩散-Si熔体无表面sio蒸发-Si单晶中氧偏析的一系列过程，模拟了径向氧分布，并找到了解释测量分布的模拟条件。(2)简化模型的有限差分分析：我们模拟了矩形截面简化熔体形状的径向氧分布，模拟结果可以解释测量到的氧浓度分布。(3)实际复杂模型的有限元分析：对实际弯曲生长界面模型进行了径向氧分布模拟，模拟结果与实测氧浓度分布吻合无差异。(4)简化模型中掺杂剂浓度分布的有限差分分析：对简化后的矩形截面熔体形状进行了磷的径向分布模拟，模拟结果可以很好地解释实测的掺杂剂浓度分布，特别是在熔体中加入常规掺杂的基础上，在Si熔体自由表面加入PH_3后，其分布更加均匀。(5) Si单晶点阵图像和Si晶体缺陷图像的三维计算机图形化：实现了Si单晶点阵图像和co -晶源粒子等Si晶体缺陷图像的三维计算机图形化，这些内容对理解超大规模集成电路器件的原子尺度结构非常有效。

1. Research target : computer simulation of radial oxygen distribution in Si Czochralski-grown single crystal to improve its uniformity.2. Research main result(1) Research principle : we simulate a radial oxygen distribution taking a series of processes, incorporation of oxygen originated by reaction Si melt and high purity quartz crucible- convective diffusion of oxygen in Si melt-SiO evaporation through Si melt free surface-oxygen segregation into Si single crystal, into consideration and find the simulation condition to explain the measured distribution.(2) Finite difference analysis for simplified model : we simulated the radial oxygen distribution for the simplified melt shape of a rectangular cross section and the simulation results could explain the measured oxygen concentration profile.(3) Finite element analysis for actual, complex model : we simulated the radial oxygen distribution for the actual, curved growing interface model and the simulation results agreed with the measured oxygen concentration profile by no difference.(4) Finite difference analysis of dopant concentration profile for simplified model : we simulated the radial phosphorus distribution for the simplified melt shape of a rectangular cross section, and the simulation results could explain the measured dopant concentration profile, especially more uniform distribution when we added PH_3 through Si melt free surface in addition the conventional doping in the melt.(5) 3D computer graphics of Si single crystal lattice image and Si crystal defect image : we visualized 3D computer graphics of Si single crystal lattice image and Si crystal defect image such as COP-crystal-originated particle-and these contents are very effective to understand VLSI devices structure of atomic scale.