CN107747122A - A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method - Google Patents

A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method Download PDF

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CN107747122A
CN107747122A CN201710811360.3A CN201710811360A CN107747122A CN 107747122 A CN107747122 A CN 107747122A CN 201710811360 A CN201710811360 A CN 201710811360A CN 107747122 A CN107747122 A CN 107747122A
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CN107747122B (en
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刘丁
任俊超
张新雨
张晶
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Xi'an Xinhui Equipment Technology Co ltd
Xian Eswin Material Technology Co Ltd
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    • C—CHEMISTRY; METALLURGY
    • C30—CRYSTAL GROWTH
    • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B15/00—Single-crystal growth by pulling from a melt, e.g. Czochralski method
    • C30B15/20—Controlling or regulating
    • C—CHEMISTRY; METALLURGY
    • C30—CRYSTAL GROWTH
    • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
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    • C30B29/06—Silicon
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    • C30—CRYSTAL GROWTH
    • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B30/00—Production of single crystals or homogeneous polycrystalline material with defined structure characterised by the action of electric or magnetic fields, wave energy or other specific physical conditions
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Abstract

本发明公开了一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，首先调节超导水平磁场强度，得到不同磁场强度下的固液界面氧浓度分布曲线，计算固液界面的平均氧浓度和固液界面径向氧浓度分布的均匀性，通过对比选取出合适的磁场强度，其次是在选取的磁场强度下分别调节晶体转速和坩埚转速，通过对比仿真结果得到适合降低固液界面氧浓度和提高固液界面氧浓度分布均匀性的晶体转速和坩埚转速，最后在所选取的超导磁场强度、晶体转速和坩埚转速三者的共同作用下，得到超导水平磁场下直拉硅单晶固液界面氧浓度分布信息，本发明解决了现有技术中存在的直拉硅单晶生长工艺参数调节时容易造成晶体中氧含量过高、氧分布不均匀的问题。

The invention discloses a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution of the solid-liquid interface. Firstly, the strength of the superconducting horizontal magnetic field is adjusted to obtain the oxygen concentration distribution curves of the solid-liquid interface under different magnetic field strengths, and the average value of the solid-liquid interface is calculated. Oxygen concentration and the uniformity of the radial oxygen concentration distribution of the solid-liquid interface, select the appropriate magnetic field strength by comparison, and then adjust the crystal rotation speed and the crucible rotation speed respectively under the selected magnetic field strength, and obtain the suitable reduction of the solid-liquid interface by comparing the simulation results Oxygen concentration and the crystal rotation speed and crucible rotation speed that improve the uniformity of the oxygen concentration distribution at the solid-liquid interface. Finally, under the joint action of the selected superconducting magnetic field strength, crystal rotation speed, and crucible rotation speed, the Czochralski silicon under the superconducting horizontal magnetic field is obtained. Single crystal solid-liquid interface oxygen concentration distribution information, the invention solves the problems in the prior art that the oxygen content in the crystal is too high and the oxygen distribution is uneven during the adjustment of the Czochralski silicon single crystal growth process parameters.

Description

一种直拉硅单晶生长工艺优化固液界面氧分布调节方法A Czochralski Silicon Single Crystal Growth Process Optimization Method for Adjusting the Oxygen Distribution at the Solid-Liquid Interface

技术领域technical field

本发明属于磁控直拉硅单晶固液界面氧分布生长工艺调节方法技术领域，具体涉及一种直拉硅单晶生长工艺优化固液界面氧分布调节方法。The invention belongs to the technical field of a method for adjusting the oxygen distribution growth process at the solid-liquid interface of a magnetically controlled Czochralski silicon single crystal, and in particular relates to a method for adjusting the oxygen distribution at the solid-liquid interface optimized for the Czochralski silicon single crystal growth process.

背景技术Background technique

直拉法是制备集成电路和光伏发电领域硅单晶半导体材料的主要方法。半导体行业对硅单晶的主要质量评价指标包括有降低晶圆片中各种有害杂质含量(氧、碳)和降低微缺陷，其中氧杂质含量所引起的二次缺陷会严重影响拉制的硅半导体材料的质量和生产的器件性能。为了尽可能减少晶体的微缺陷及确保晶体电阻率的均匀性，所以如何降低大尺寸晶体生长过程中固液界面(晶体与熔体交界面)的氧杂质含量和提高固液界面氧分布的均匀性，就具有十分重要的意义。The Czochralski method is the main method for preparing silicon single crystal semiconductor materials in the fields of integrated circuits and photovoltaic power generation. The main quality evaluation indicators for silicon single crystals in the semiconductor industry include reducing the content of various harmful impurities (oxygen, carbon) in the wafer and reducing micro-defects. Among them, the secondary defects caused by the content of oxygen impurities will seriously affect the drawn silicon. The quality of semiconductor materials and the performance of devices produced. In order to reduce the micro-defects of the crystal as much as possible and ensure the uniformity of the crystal resistivity, how to reduce the oxygen impurity content at the solid-liquid interface (crystal-melt interface) and improve the uniformity of oxygen distribution at the solid-liquid interface during the growth of large-sized crystals Sex is very important.

由于熔融硅处于高温、密封的炉体中，不能直接获取坩埚熔体内和固液界面的氧分布情况。目前，获取晶体中氧分布的方法主要有红外吸收法和数值模拟法。红外吸收法是通过测量硅晶圆片，对红外光谱进行分析，根据峰位置、吸收强度进行定量分析计算出硅晶圆片上的氧含量及氧分布均匀性，由于多次拉晶实验的方法费时费力,代价很大,只能直观地了解实验现象。数值模拟法是通过借助商业CFD软件对单晶炉热场进行建模，采用有限体积法(FVM)求解得到熔体内以及固液界面氧含量的分布情况，实验成本低、周期短，能够更好更快地认识晶体生长问题。目前数值模拟法中常规水平磁场下高晶体转速、低晶体转速的工艺调节方法容易导致晶体中氧含量升高，严重影响所制造的电子器件工作性能。因此，提出一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，在直拉硅单晶生长过程中降低固液界面的氧浓度和提高固液界面氧分布的均匀性，以满足市场对高品质硅单晶的需求是目前亟待解决的重要问题。Since the molten silicon is in a high-temperature, sealed furnace, the oxygen distribution in the crucible melt and at the solid-liquid interface cannot be obtained directly. At present, the methods to obtain the oxygen distribution in the crystal mainly include infrared absorption method and numerical simulation method. The infrared absorption method is to measure the silicon wafer, analyze the infrared spectrum, and calculate the oxygen content and oxygen distribution uniformity on the silicon wafer according to the peak position and absorption intensity quantitative analysis. Due to the time-consuming method of multiple crystal pulling experiments It is laborious and costly, and the experimental phenomenon can only be understood intuitively. The numerical simulation method is to model the thermal field of the single crystal furnace with the help of commercial CFD software, and use the finite volume method (FVM) to solve the distribution of oxygen content in the melt and the solid-liquid interface. The experiment cost is low, the cycle is short, and it can be more It is better to understand the crystal growth problem more quickly. At present, the process adjustment method of high crystal rotation speed and low crystal rotation speed under conventional horizontal magnetic field in the numerical simulation method will easily lead to an increase in the oxygen content in the crystal, which seriously affects the working performance of the manufactured electronic devices. Therefore, a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution at the solid-liquid interface is proposed, which reduces the oxygen concentration at the solid-liquid interface and improves the uniformity of the oxygen distribution at the solid-liquid interface during the Czochralski silicon single crystal growth process to meet The market's demand for high-quality silicon single crystals is an important issue that needs to be resolved urgently.

发明内容Contents of the invention

本发明的目的是提供一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，解决了现有技术中存在的直拉硅单晶生长工艺参数调节时容易造成晶体中氧含量过高、氧分布不均匀的问题。The purpose of the present invention is to provide a method for adjusting the oxygen distribution at the solid-liquid interface to optimize the Czochralski silicon single crystal growth process, which solves the problem that the oxygen content in the crystal is too high when the parameters of the Czochralski silicon single crystal growth process are adjusted in the prior art. , The problem of uneven oxygen distribution.

本发明所采用的技术方案是，一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，具体按照以下步骤实施：The technical solution adopted in the present invention is a method for adjusting the oxygen distribution of the Czochralski silicon single crystal growth process to optimize the solid-liquid interface, which is specifically implemented according to the following steps:

步骤1、构建直拉法硅单晶生长所需的三维局部物理模型；Step 1. Construct the three-dimensional local physical model required for Czochralski silicon single crystal growth;

步骤2、将三维局部物理模型导入CFX流体仿真模块，设置仿真模拟为稳态模拟，并设置硅熔体、硅晶体、石墨坩埚和石英坩埚的物性参数和超导磁场强度；Step 2. Import the three-dimensional local physical model into the CFX fluid simulation module, set the simulation simulation as steady-state simulation, and set the physical parameters and superconducting magnetic field strength of silicon melt, silicon crystal, graphite crucible and quartz crucible;

步骤3、求解不同超导水平磁场强度下固液界面径向氧浓度分布情况；Step 3, solving the radial oxygen concentration distribution of the solid-liquid interface under different superconducting level magnetic field strengths;

步骤4、分析晶体转速对固液界面形状和熔体内径向温度分布的影响；Step 4, analyzing the influence of the crystal rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt;

步骤5、分析坩埚转速对固液界面形状和熔体内径向温度分布的影响；Step 5, analyzing the influence of the crucible rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt;

步骤6、综合步骤3～5，结合所选取的超导水平磁场强度、晶体转速和坩埚转速三者的共同作用下，得到超导水平磁场下直拉硅单晶固液界面氧浓度分布信息。Step 6, combining steps 3 to 5, combined with the selected superconducting horizontal magnetic field strength, crystal rotation speed and crucible rotation speed, to obtain the oxygen concentration distribution information of the Czochralski silicon single crystal solid-liquid interface under the superconducting horizontal magnetic field.

本发明的特点还在于，The present invention is also characterized in that,

步骤1具体按照以下步骤实施：Step 1 is specifically implemented according to the following steps:

步骤1.1、利用Gambit软件网格生成直拉法硅单晶生长的三维局部物理模型，包含晶体、熔体、石英坩埚和石墨坩埚；Step 1.1, using the Gambit software grid to generate a three-dimensional local physical model of Czochralski silicon single crystal growth, including crystals, melts, quartz crucibles and graphite crucibles;

步骤1.2、设置石英坩埚半径为0.306m，石墨坩埚半径为0.32m，坩埚内熔体半径为0.3m，坩埚逆时针旋转，坩埚转速为ωc；晶体半径范围为0.15m～0.225m，晶体顺时针旋转，晶体转速为ωs，熔体高度为0.08m～0.22m，晶体长度为0m～0.6m，投料量160kg，自由界面为硅熔体和气体交界面，固液界面为晶体与熔体之间的相界面。步骤1.2中坩埚转速ωc为0～10rpm，晶体转速ωs为0～16rpm。Step 1.2, set the radius of the quartz crucible to 0.306m, the radius of the graphite crucible to 0.32m, the radius of the melt in the crucible to 0.3m, the crucible to rotate counterclockwise, and the crucible speed to be ωc ; the radius of the crystal is 0.15m to 0.225m, and the crystal is Clockwise rotation, the crystal rotation speed is ω s , the melt height is 0.08m~0.22m, the crystal length is 0m~0.6m, the feeding amount is 160kg, the free interface is the interface between silicon melt and gas, and the solid-liquid interface is crystal and melt the interface between them. In step 1.2, the rotation speed ω c of the crucible is 0-10 rpm, and the rotation speed ω s of the crystal is 0-16 rpm.

步骤2具体按照以下步骤实施：Step 2 is specifically implemented according to the following steps:

步骤2.1、设置坩埚为逆时针旋转，坩埚转速为ωc，晶体顺时针旋转，晶体转速为ωs；Step 2.1, set the crucible to rotate counterclockwise, the crucible rotation speed is ω c , the crystal rotates clockwise, and the crystal rotation speed is ω s ;

步骤2.2、假设硅熔体为不可压缩的牛顿流体；假设硅熔体满足Boussinesq近似；设置固液界面为平直面，在固液界面结晶时不发生过冷态，固液界面的温度为硅的熔点温度1685K；设置熔体与氩气交界面，即自由液面为平直面，其位置高度与固液界面高度相同，并向外界气氛环境辐射热量；石英坩埚底部和坩埚内壁与硅熔体满足无滑移边界条件；熔体内的氧输运过程对熔体流动与传热的影响忽略不计。Step 2.2, assuming that the silicon melt is an incompressible Newtonian fluid; assuming that the silicon melt satisfies the Boussinesq approximation; setting the solid-liquid interface as a flat surface, no supercooling occurs when the solid-liquid interface crystallizes, and the temperature of the solid-liquid interface is 1°C of silicon The melting point temperature is 1685K; the interface between the melt and argon is set, that is, the free liquid surface is a flat surface, and its position height is the same as that of the solid-liquid interface, and radiates heat to the external atmosphere; the bottom of the quartz crucible and the inner wall of the crucible meet the requirements of the silicon melt. No-slip boundary condition; the oxygen transport process in the melt has negligible influence on the melt flow and heat transfer.

步骤2.2中，仿真迭代求解过程中所用到的边界条件包括有氧浓度边界条件和温度边界条件，其中氧浓度边界条件如下：In step 2.2, the boundary conditions used in the simulation iterative solution process include oxygen concentration boundary conditions and temperature boundary conditions, where the oxygen concentration boundary conditions are as follows:

(1)硅熔液与石英坩埚内壁交界处的氧浓度边界条件：(1) Oxygen concentration boundary conditions at the junction of the silicon melt and the inner wall of the quartz crucible:

其中，NA为阿伏伽德罗常数，为氧分压，ao为氧体积分数，R为氧气体摩尔常数，T为化学反应温度，为化学反应自由能变化量。Among them, N A is Avogadro's constant, is the partial pressure of oxygen, a o is the volume fraction of oxygen, R is the molar constant of oxygen gas, T is the chemical reaction temperature, for chemical reaction free energy change.

(2)硅熔液与氩气交界面处的氧浓度边界条件：(2) Oxygen concentration boundary condition at the interface between silicon melt and argon:

式中，CO和Csurf分别是熔体中的氧浓度和自由液面的氧浓度；CSi是硅熔液浓度；DO和DSiO分别是氧在硅熔体中的扩散系数和SiO气体在氩气中的扩散系数；ΔG是化学反应式(Simelt+Omelt＝SiOgas)的自由能变化量，p0是一氧化硅气体的蒸汽压力，R为气体摩尔常数，T是化学反应温度；δg是自由液面边界层厚度；In the formula, C O and C surf are the oxygen concentration in the melt and the oxygen concentration of the free liquid surface, respectively; C Si is the silicon melt concentration; D O and D SiO are the diffusion coefficient of oxygen in the silicon melt and SiO Diffusion coefficient of gas in argon; ΔG is the free energy change of the chemical reaction formula (Si melt +O melt =SiO gas ), p 0 is the vapor pressure of silicon monoxide gas, R is the gas molar constant, T is the chemical Reaction temperature; δ g is the thickness of the free surface boundary layer;

在晶体实际生长环境过程中，自由液面的氧在氩气的吹拂下，自由液面的氧浓度Csurf仅为熔体内部氧浓度CO的万分数，因此将自由液面的氧浓度Csurf忽略不计，则自由液面的氧浓度边界条件简化为In the actual crystal growth environment process, the oxygen on the free liquid surface is blown by argon, and the oxygen concentration C surff on the free liquid surface is only a ten-thousandth fraction of the oxygen concentration C O in the melt, so the oxygen concentration C on the free liquid surface is Neglecting surf , the oxygen concentration boundary condition of the free liquid surface is simplified as

CO＝0mol/m3；C O = 0 mol/m 3 ;

(3)固液界面(晶体生长界面)处的氧浓度边界条件：(3) Oxygen concentration boundary condition at the solid-liquid interface (crystal growth interface):

式中，D为氧的扩散系数，Vg为固液界面的移动速度，k为氧的分凝系数，Co为熔体内的氧浓度。实验揭示氧的分凝系数接近单位1，且超过99％的氧气从自由液面挥发到氩气当中，所以在固液界面整体氧通量平衡中将掺入到晶体中的氧含量忽略不计，上式简化为In the formula, D is the diffusion coefficient of oxygen, V g is the moving velocity of the solid-liquid interface, k is the segregation coefficient of oxygen, and C o is the oxygen concentration in the melt. Experiments reveal that the segregation coefficient of oxygen is close to unit 1, and more than 99% of oxygen volatilizes from the free liquid surface into argon, so the oxygen content incorporated into the crystal is negligible in the overall oxygen flux balance at the solid-liquid interface, The above formula simplifies to

温度边界条件中石墨坩埚底部和石墨坩埚外壁施加等梯度温度分布值，在自由液面处建立热流密度方程，如下式：In the temperature boundary condition, an equal gradient temperature distribution value is applied to the bottom of the graphite crucible and the outer wall of the graphite crucible, and the heat flux density equation is established at the free liquid surface, as follows:

Ql'＝qout,k-qin,k＝σεT4-εqin,k Q l '＝q out,k -q in,k ＝σεT 4 -εq in,k

qin,k＝sumj＝1～N(Fk,jqout,j)q in,k =sum j=1～N (F k,j q out,j )

式中，β[T(r)-T0(r)]1.25用来描述由于气体对流而产生的热损耗，Ql′用来描述熔体液面由辐射而产生的热损耗，T为自由液面温度，T0为环境温度，Kl为硅熔体热传导系数，β为气体对流的热损耗系数，r为自由液面半径，ε为辐射系数，σ为Stefan-Boltzmann常数，Fk,j为k,j两个表面之间的角系数，qout,k是流出表面的热流量，qin,k是流入表面的热流量，x,z为空间直角坐标系方向变量，N为表面总个数；In the formula, β[T(r)-T 0 (r)] 1.25 is used to describe the heat loss due to gas convection, Q l 'is used to describe the heat loss of the melt surface due to radiation, and T is the free Liquid surface temperature, T 0 is the ambient temperature, K l is the thermal conductivity coefficient of silicon melt, β is the heat loss coefficient of gas convection, r is the radius of the free liquid surface, ε is the radiation coefficient, σ is the Stefan-Boltzmann constant, F k, j is the angle coefficient between k and j two surfaces, q out, k is the heat flow out of the surface, q in, k is the heat flow into the surface, x, z are the direction variables of the space Cartesian coordinate system, N is the surface The total number of;

在石墨坩埚和石英坩埚的顶表面，石英坩埚未与硅熔体接触的内表面以及晶体外表面等固体表面，也建立相似的热流密度方程，如下式：On the top surface of the graphite crucible and the quartz crucible, the inner surface of the quartz crucible that is not in contact with the silicon melt, and the outer surface of the crystal and other solid surfaces, a similar heat flux equation is also established, as follows:

Qs'＝qout,k-qin,k＝σεT4-εqin,k Q s '＝q out,k -q in,k ＝σεT 4 -εq in,k

其中，Qs′用来描述固体表面由辐射而产生的热损耗，Ks为硅熔体热传导系数，r为晶体半径或者石英坩埚的内半径，y为空间直角坐标系方向变量。Among them, Q s ′ is used to describe the heat loss caused by radiation on the solid surface, K s is the thermal conductivity coefficient of silicon melt, r is the crystal radius or the inner radius of the quartz crucible, and y is the direction variable of the spatial rectangular coordinate system.

在迭代求解控制中设置迭代次数为90000，时间因子为1，收敛曲线的残差值设置为1E-06。In the iterative solution control, set the number of iterations to 90000, the time factor to 1, and the residual value of the convergence curve to 1E-06.

步骤3具体按照以下步骤实施：Step 3 is specifically implemented according to the following steps:

步骤3.1、利用CFX模块的数值求解器，数值求解不同超导水平磁场强度下，晶体转速ωs和坩埚转速ωc均为0rpm时坩埚熔体内的流动与传热；Step 3.1, use the numerical solver of the CFX module to numerically solve the flow and heat transfer in the crucible melt when the crystal rotational speed ω s and the crucible rotational speed ω c are both 0 rpm under different superconducting horizontal magnetic field strengths;

步骤3.2、当迭代收敛后通过CFX模块的后处理得到熔体的温度分布云图以及氧浓度分布云图，在温度分布云图上追踪固液界面1685K等温线位置，获取固液界面上的氧浓度分布数据，得到氧浓度与晶体直径的关系曲线，即固液界面径向氧浓度分布曲线。依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的超导磁场强度。其中，平均氧浓度用来衡量固液界面氧浓度的高低，均方误差MSEO和梯度误差和δO用来衡量固液界面氧浓度分布的均匀性，如下式Step 3.2. After the iteration converges, obtain the temperature distribution cloud map and the oxygen concentration distribution cloud map of the melt through the post-processing of the CFX module, track the position of the 1685K isotherm at the solid-liquid interface on the temperature distribution cloud map, and obtain the oxygen concentration distribution data on the solid-liquid interface , to obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve at the solid-liquid interface. According to the average oxygen concentration at the solid-liquid interface The mean square error MSE O and the gradient error sum δ O of the radial oxygen concentration distribution curve are the minimum principles, and the appropriate superconducting magnetic field strength is selected. Among them, the average oxygen concentration Used to measure the level of oxygen concentration at the solid-liquid interface, the mean square error MSE O and gradient error and δ O are used to measure the uniformity of the oxygen concentration distribution at the solid-liquid interface, as shown in the following formula

其中，n为所采集到固液界面上的氧数据个数，ci为氧数据点，i为氧数据自变量；Among them, n is the number of oxygen data collected on the solid-liquid interface, c i is the oxygen data point, and i is the independent variable of the oxygen data;

其中，gradOi是固液界面径向氧浓度分布曲线上各氧数据点的梯度，gradOmin是固液界面径向氧浓度分布曲线的最小梯度，梯度误差和δO越小，则说明固液界面径向氧浓度分布的均匀性越均匀。Among them, gradO i is the gradient of each oxygen data point on the radial oxygen concentration distribution curve of the solid-liquid interface, and gradO min is the minimum gradient of the radial oxygen concentration distribution curve of the solid-liquid interface. The smaller the gradient error and δ O , the smaller the solid-liquid interface The uniformity of the oxygen concentration distribution in the radial direction of the interface is more uniform.

步骤4具体按照以下步骤实施：Step 4 is specifically implemented according to the following steps:

步骤4.1、在CFX前处理设置中，设置磁场强度为步骤3所选取的合适磁场强度，将坩埚转速ωc设置为0rpm，调节不同晶体转速ωs，迭代求解至残差曲线收敛，从而获取固液界面1685K等温线上的氧浓度数据；Step 4.1. In the CFX pre-processing setting, set the magnetic field strength to the appropriate magnetic field strength selected in step 3, set the crucible rotation speed ω c to 0 rpm, adjust the rotation speed ω s of different crystals, and iteratively solve until the residual curve converges, so as to obtain solid Oxygen concentration data on the 1685K isotherm at the liquid interface;

步骤4.2、得到氧浓度与晶体直径之间的关系曲线，即固液界面径向氧浓度分布曲线，为了分析晶体转速对固液界面形状和熔体内径向温度分布的影响，温度检测位置取自熔体内部，距离熔体与氩气交界面0.08m，长度为0.3m，方向由坩埚与熔体交界面指向晶体生长轴，依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的晶体转速。Step 4.2. Obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve of the solid-liquid interface. In order to analyze the influence of crystal rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, the temperature detection position is taken from Inside the melt, the distance from the interface between the melt and argon is 0.08m, the length is 0.3m, and the direction is from the interface between the crucible and the melt to the crystal growth axis, according to the average oxygen concentration of the solid-liquid interface The mean square error MSE O and the gradient error sum δ O of the radial oxygen concentration distribution curve are the minimum principles, and the appropriate crystal rotation speed is selected.

步骤5具体按照以下步骤实施：Step 5 is specifically implemented according to the following steps:

步骤5.1、在CFX前处理设置中，设置磁场强度为步骤3所选取的合适磁场强度，设置晶体转速ωs为0rpm，调节坩埚转速ωc，通过数值求解器迭代求解至残差曲线收敛，从而获取固液界面1685K等温线上的氧浓度数据；Step 5.1. In the CFX pre-processing setting, set the magnetic field strength to the appropriate magnetic field strength selected in step 3, set the crystal rotation speed ω s to 0 rpm, adjust the crucible rotation speed ω c , and solve iteratively through the numerical solver until the residual curve converges, thereby Obtain the oxygen concentration data on the 1685K isotherm at the solid-liquid interface;

步骤5.2、得到氧浓度与晶体直径之间的关系曲线，即固液界面径向氧浓度分布曲线，为了分析坩埚转速对固液界面形状和熔体内径向温度分布的影响，温度检测位置取自熔体内部，高度距离熔体与氩气交界面为0.08m，长度为0.3m，方向由坩埚与熔体交界面指向晶体生长轴，依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的晶体转速。Step 5.2. Obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve of the solid-liquid interface. In order to analyze the influence of crucible rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, the temperature detection position is taken from Inside the melt, the height is 0.08m from the interface between the melt and argon, the length is 0.3m, and the direction is from the interface between the crucible and the melt to the crystal growth axis, according to the average oxygen concentration of the solid-liquid interface The mean square error MSE O and the gradient error sum δ O of the radial oxygen concentration distribution curve are the minimum principles, and the appropriate crystal rotation speed is selected.

步骤6具体按照以下步骤实施：Step 6 is specifically implemented according to the following steps:

步骤6.1、在CFX前处理设置中，设置超导水平磁场强度和坩埚转速为步骤3、步骤5所选取的合适超导水平磁场强度和坩埚转速，由于高晶转有利于提高固液界面的一致性，所以首先将晶体转速ωs设置为高晶转，通过数值迭代求解和MATLAB作图得到固液界面径向氧浓度分布曲线；Step 6.1, in the CFX pre-processing settings, set the superconducting horizontal magnetic field strength and crucible rotation speed to the appropriate superconducting horizontal magnetic field strength and crucible rotation speed selected in steps 3 and 5, because high crystal rotation is conducive to improving the consistency of the solid-liquid interface Therefore, firstly, the crystal rotation speed ω s is set to high crystal rotation, and the radial oxygen concentration distribution curve of the solid-liquid interface is obtained through numerical iterative solution and MATLAB drawing;

步骤6.2、将晶体转速ωs设置为低晶转，通过数值迭代求解和MATLAB作图得到固液界面径向氧浓度分布曲线；Step 6.2, set the crystal rotation speed ω s to low crystal rotation, and obtain the radial oxygen concentration distribution curve of the solid-liquid interface through numerical iterative solution and MATLAB drawing;

步骤6.3、分别计算晶体转速ωs为高晶转和低晶转时固液界面径向氧浓度分布曲线中固液界面的平均氧浓度和与氧浓度分布均匀性相关的均方误差MSEO和梯度误差和δO，通过定量和定性的对比分析，选取得到既适合降低固液界面氧浓度又能提高固液界面径向氧浓度分布均匀性的超导水平磁场强度、晶体转速和坩埚转速。Step 6.3, calculate the average oxygen concentration of the solid-liquid interface in the radial oxygen concentration distribution curve of the solid-liquid interface when the crystal rotation speed ω s is high crystal rotation and low crystal rotation respectively and the mean square error MSE O and the gradient error and δ O related to the uniformity of oxygen concentration distribution, through quantitative and qualitative comparative analysis, the selection is suitable for both reducing the oxygen concentration of the solid-liquid interface and improving the radial oxygen concentration distribution of the solid-liquid interface Uniform superconducting horizontal magnetic field strength, crystal rotational speed and crucible rotational speed.

本发明的有益效果是，一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，通过建立三维数值模拟直拉硅单晶生长过程，更能直观准确得认识到坩埚熔体内氧浓度分布状态和固液界面氧浓度分布信息，且根据固液界面氧浓度分布曲线，可以定性的分析出晶体当中氧含量的高低以及氧杂质分布的均匀性。并且从定量的分析基础上利用氧浓度数据的算术平均值衡量固液界面的氧浓度高低和利用氧浓度数据的均方误差和氧浓度分布曲线的梯度误差和衡量固液界面氧浓度分布的均匀性。结合定性分析和定量分析结果发现，在所选取的合适磁场强度下低晶体转速和低坩埚转速的工艺调节方法，可以有效降低固液界面的氧浓度以及提高固液界面径向氧浓度分布的均匀性，达到降低硅晶体中氧杂质含量以及提高晶体中氧分布均匀性的目的，从而提高大尺寸硅单晶品质。The beneficial effect of the present invention is that a Czochralski silicon single crystal growth process optimizes the oxygen distribution adjustment method at the solid-liquid interface. By establishing a three-dimensional numerical simulation of the Czochralski silicon single crystal growth process, the oxygen in the crucible melt can be more intuitively and accurately recognized. Concentration distribution state and solid-liquid interface oxygen concentration distribution information, and according to the solid-liquid interface oxygen concentration distribution curve, the level of oxygen content in the crystal and the uniformity of oxygen impurity distribution can be qualitatively analyzed. And on the basis of quantitative analysis, the arithmetic mean value of the oxygen concentration data is used to measure the oxygen concentration of the solid-liquid interface, and the mean square error of the oxygen concentration data and the gradient error of the oxygen concentration distribution curve are used to measure the uniformity of the oxygen concentration distribution of the solid-liquid interface. sex. Combining the results of qualitative analysis and quantitative analysis, it is found that under the selected appropriate magnetic field strength, the process adjustment method of low crystal rotation speed and low crucible rotation speed can effectively reduce the oxygen concentration at the solid-liquid interface and improve the uniformity of the radial oxygen concentration distribution at the solid-liquid interface. To achieve the purpose of reducing the content of oxygen impurities in silicon crystals and improving the uniformity of oxygen distribution in the crystals, thereby improving the quality of large-size silicon single crystals.

附图说明Description of drawings

图1是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法三维数值模拟硅单晶生长原理图；Fig. 1 is a three-dimensional numerical simulation silicon single crystal growth schematic diagram of a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution at the solid-liquid interface of the present invention;

图2(a)～图2(b)是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法中不同超导磁场强度下固液界面氧浓度分布曲线图；Fig. 2 (a) ~ Fig. 2 (b) are a kind of Czochralski silicon single crystal growth process optimization solid-liquid interface oxygen distribution adjustment method in the present invention, under different superconducting magnetic field strengths, solid-liquid interface oxygen concentration distribution curve;

图3(a)～图3(d)是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法中不同晶体转速下固液界面氧浓度分布曲线图；Fig. 3 (a) ~ Fig. 3 (d) are a kind of Czochralski silicon single crystal growth process optimization solid-liquid interface oxygen distribution adjusting method in the present invention, the curve diagram of oxygen concentration distribution at solid-liquid interface under different crystal rotational speeds;

图4(a)～图4(d)是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法中不同坩埚转速下固液界面氧浓度分布曲线图；Fig. 4 (a) ~ Fig. 4 (d) are a kind of Czochralski silicon single crystal growth process optimization solid-liquid interface oxygen distribution adjustment method in the present invention, the oxygen concentration distribution curve of solid-liquid interface under different crucible rotating speed;

图5是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法中高晶转、低埚转下固液界面氧浓度分布曲线图；Fig. 5 is a curve diagram of oxygen concentration distribution at the solid-liquid interface in a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution at the solid-liquid interface of the present invention under high crystal rotation and low crucible rotation;

图6是本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法中低晶转、低埚转下固液界面氧浓度分布曲线图。Fig. 6 is a curve diagram of the oxygen concentration distribution at the solid-liquid interface under low crystal rotation and low crucible rotation in a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution at the solid-liquid interface of the present invention.

具体实施方式Detailed ways

下面结合附图和具体实施方式对本发明进行详细说明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

本发明一种直拉硅单晶生长工艺优化固液界面氧分布调节方法，具体按照以下步骤实施：The present invention provides a Czochralski silicon single crystal growth process optimization method for adjusting the oxygen distribution at the solid-liquid interface, which is specifically implemented according to the following steps:

步骤1、构建直拉法硅单晶生长所需的三维局部物理模型，具体按照以下步骤实施：Step 1. Construct the three-dimensional local physical model required for the growth of Czochralski method silicon single crystal, and implement it according to the following steps:

步骤1.1、如图1所示，利用Gambit软件网格生成直拉法硅单晶生长的三维局部物理模型，包含晶体、熔体、石英坩埚和石墨坩埚；Step 1.1, as shown in Figure 1, use the Gambit software grid to generate a three-dimensional local physical model of Czochralski silicon single crystal growth, including crystals, melts, quartz crucibles and graphite crucibles;

步骤1.2、设置石英坩埚半径为0.306m，石墨坩埚半径为0.32m，坩埚内熔体半径为0.3m，坩埚逆时针旋转，坩埚转速为ωc；晶体半径范围为0.15m～0.225m，晶体顺时针旋转，晶体转速为ωs，熔体高度为0.08m～0.22m，晶体长度为0m～0.6m，投料量160kg，自由界面为硅熔体和气体交界面，固液界面为晶体与熔体之间的相界面。其中，坩埚转速ωc为0～10rpm，晶体转速ωs为0～16rpm。在本发明仿真实验中，晶体半径设置为0.15m，晶体长度设置为0.2m。Step 1.2, set the radius of the quartz crucible to 0.306m, the radius of the graphite crucible to 0.32m, the radius of the melt in the crucible to 0.3m, the crucible to rotate counterclockwise, and the crucible speed to be ωc ; the radius of the crystal is 0.15m to 0.225m, and the crystal is Clockwise rotation, the crystal rotation speed is ω s , the melt height is 0.08m~0.22m, the crystal length is 0m~0.6m, the feeding amount is 160kg, the free interface is the interface between silicon melt and gas, and the solid-liquid interface is crystal and melt the interface between them. Wherein, the rotation speed ω c of the crucible is 0-10 rpm, and the rotation speed ω s of the crystal is 0-16 rpm. In the simulation experiment of the present invention, the crystal radius is set to 0.15m, and the crystal length is set to 0.2m.

步骤2、将三维局部物理模型导入CFX流体仿真模块，设置仿真模拟为稳态模拟，并设置硅熔体、硅晶体、石墨坩埚和石英坩埚的物性参数和超导磁场强度，其中物性参数设置如表1所示：Step 2. Import the 3D local physical model into the CFX fluid simulation module, set the simulation to steady-state simulation, and set the physical parameters and superconducting magnetic field strength of silicon melt, silicon crystal, graphite crucible and quartz crucible. The physical parameter settings are as follows: Table 1 shows:

表1物性参数Table 1 physical parameters

具体按照以下步骤实施：Specifically follow the steps below:

步骤2.1、设置坩埚为逆时针旋转，坩埚转速为ωc，晶体顺时针旋转，晶体转速为ωs；Step 2.1, set the crucible to rotate counterclockwise, the crucible rotation speed is ω c , the crystal rotates clockwise, and the crystal rotation speed is ω s ;

步骤2.2、假设硅熔体为不可压缩的牛顿流体；假设硅熔体满足Boussinesq近似；设置固液界面为平直面，在固液界面结晶时不发生过冷态，固液界面的温度为硅的熔点温度1685K；设置熔体与氩气交界面，即自由液面为平直面，其位置高度与固液界面高度相同，并向外界气氛环境辐射热量；石英坩埚底部和坩埚内壁与硅熔体满足无滑移边界条件；熔体内的氧输运过程对熔体流动与传热的影响忽略不计，Step 2.2, assuming that the silicon melt is an incompressible Newtonian fluid; assuming that the silicon melt satisfies the Boussinesq approximation; setting the solid-liquid interface as a flat surface, no supercooling occurs when the solid-liquid interface crystallizes, and the temperature of the solid-liquid interface is 1°C of silicon The melting point temperature is 1685K; the interface between the melt and argon is set, that is, the free liquid surface is a flat surface, and its position height is the same as that of the solid-liquid interface, and radiates heat to the external atmosphere; the bottom of the quartz crucible and the inner wall of the crucible meet the requirements of the silicon melt. No-slip boundary condition; the influence of the oxygen transport process in the melt on the flow and heat transfer of the melt is negligible,

步骤2.2中，仿真迭代求解过程中所用到的边界条件包括有氧浓度边界条件和温度边界条件，其中氧浓度边界条件如下：In step 2.2, the boundary conditions used in the simulation iterative solution process include oxygen concentration boundary conditions and temperature boundary conditions, where the oxygen concentration boundary conditions are as follows:

(1)硅熔液与石英坩埚内壁交界处的氧浓度边界条件：(1) Oxygen concentration boundary conditions at the junction of the silicon melt and the inner wall of the quartz crucible:

其中，NA为阿伏伽德罗常数，为氧分压，ao为氧体积分数，R为氧气体摩尔常数，T为化学反应温度，为化学反应自由能变化量。Among them, N A is Avogadro's constant, is the partial pressure of oxygen, a o is the volume fraction of oxygen, R is the molar constant of oxygen gas, T is the chemical reaction temperature, for chemical reaction free energy change.

(2)硅熔液与氩气交界面处的氧浓度边界条件：(2) Oxygen concentration boundary condition at the interface between silicon melt and argon:

式中，CO和Csurf分别是熔体中的氧浓度和自由液面的氧浓度；CSi是硅熔液浓度；DO和DSiO分别是氧在硅熔体中的扩散系数和SiO气体在氩气中的扩散系数；ΔG是化学反应式(Simelt+Omelt＝SiOgas)的自由能变化量，p0是一氧化硅气体的蒸汽压力，R为气体摩尔常数，T是化学反应温度；δg是自由液面边界层厚度；In the formula, C O and C surf are the oxygen concentration in the melt and the oxygen concentration of the free liquid surface, respectively; C Si is the silicon melt concentration; D O and D SiO are the diffusion coefficient of oxygen in the silicon melt and SiO Diffusion coefficient of gas in argon; ΔG is the free energy change of the chemical reaction formula (Si melt +O melt =SiO gas ), p 0 is the vapor pressure of silicon monoxide gas, R is the gas molar constant, T is the chemical Reaction temperature; δ g is the thickness of the free surface boundary layer;

在晶体实际生长环境过程中，自由液面的氧在氩气的吹拂下，自由液面的氧浓度Csurf仅为熔体内部氧浓度CO的万分数，因此将自由液面的氧浓度Csurf忽略不计，则自由液面的氧浓度边界条件简化为In the actual crystal growth environment process, the oxygen on the free liquid surface is blown by argon, and the oxygen concentration C surff on the free liquid surface is only a ten-thousandth fraction of the oxygen concentration C O in the melt, so the oxygen concentration C on the free liquid surface is Neglecting surf , the oxygen concentration boundary condition of the free liquid surface is simplified as

CO＝0mol/m3；C O = 0 mol/m 3 ;

(3)固液界面(晶体生长界面)处的氧浓度边界条件：(3) Oxygen concentration boundary condition at the solid-liquid interface (crystal growth interface):

式中，D为氧的扩散系数，Vg为固液界面的移动速度，k为氧的分凝系数，Co为熔体内的氧浓度。实验揭示氧的分凝系数接近单位1，且超过99％的氧气从自由液面挥发到氩气当中，所以在固液界面整体氧通量平衡中将掺入到晶体中的氧含量忽略不计，上式简化为In the formula, D is the diffusion coefficient of oxygen, V g is the moving velocity of the solid-liquid interface, k is the segregation coefficient of oxygen, and C o is the oxygen concentration in the melt. Experiments reveal that the segregation coefficient of oxygen is close to unit 1, and more than 99% of oxygen volatilizes from the free liquid surface into argon, so the oxygen content incorporated into the crystal is negligible in the overall oxygen flux balance at the solid-liquid interface, The above formula simplifies to

温度边界条件中石墨坩埚底部和石墨坩埚外壁施加等梯度温度分布值，在自由液面处建立热流密度方程，如下式：In the temperature boundary conditions, the bottom of the graphite crucible and the outer wall of the graphite crucible are applied with equal gradient temperature distribution values, and the heat flux density equation is established at the free liquid surface, as follows:

Ql'＝qout,k-qin,k＝σεT4-εqin,k Q l '＝q out,k -q in,k ＝σεT 4 -εq in,k

qin,k＝sumj＝1～N(Fk,jqout,j)q in,k =sum j=1～N (F k,j q out,j )

式中，β[T(r)-T0(r)]1.25用来描述由于气体对流而产生的热损耗，Ql′用来描述熔体液面由辐射而产生的热损耗，T为自由液面温度，T0为环境温度，Kl为硅熔体热传导系数，β为气体对流的热损耗系数，r为自由液面半径，ε为辐射系数，σ为Stefan-Boltzmann常数，Fk,j为k,j两个表面之间的角系数，qout,k是流出表面的热流量，qin,k是流入表面的热流量，x,z为空间直角坐标系方向变量，N为表面总个数；In the formula, β[T(r)-T 0 (r)] 1.25 is used to describe the heat loss due to gas convection, Q l 'is used to describe the heat loss of the melt surface due to radiation, and T is the free Liquid surface temperature, T 0 is the ambient temperature, K l is the thermal conductivity coefficient of silicon melt, β is the heat loss coefficient of gas convection, r is the radius of the free liquid surface, ε is the radiation coefficient, σ is the Stefan-Boltzmann constant, F k, j is the angle coefficient between k and j two surfaces, q out, k is the heat flow out of the surface, q in, k is the heat flow into the surface, x, z are the direction variables of the space Cartesian coordinate system, N is the surface The total number of;

在石墨坩埚和石英坩埚的顶表面，石英坩埚未与硅熔体接触的内表面以及晶体外表面等固体表面，也建立相似的热流密度方程，如下式：On the top surface of the graphite crucible and the quartz crucible, the inner surface of the quartz crucible that is not in contact with the silicon melt, and the outer surface of the crystal and other solid surfaces, a similar heat flux equation is also established, as follows:

Qs'＝qout,k-qin,k＝σεT4-εqin,k Q s '＝q out,k -q in,k ＝σεT 4 -εq in,k

其中，Qs′用来描述固体表面由辐射而产生的热损耗，Ks为硅熔体热传导系数，r为晶体半径或者石英坩埚的内半径，y为空间直角坐标系方向变量。Among them, Q s ′ is used to describe the heat loss caused by radiation on the solid surface, K s is the thermal conductivity coefficient of silicon melt, r is the crystal radius or the inner radius of the quartz crucible, and y is the direction variable of the spatial rectangular coordinate system.

在迭代求解控制中设置迭代次数为90000，时间因子为1，收敛曲线的残差值设置为1E-06；In the iterative solution control, set the number of iterations to 90000, the time factor to 1, and the residual value of the convergence curve to 1E-06;

步骤3、求解不同超导水平磁场强度下固液界面径向氧浓度分布情况，具体按照以下步骤实施：Step 3. Solve the distribution of radial oxygen concentration at the solid-liquid interface under different superconducting horizontal magnetic field strengths. Specifically, follow the steps below:

步骤3.1、利用CFX模块的数值求解器，数值求解不同超导水平磁场强度下，晶体转速ωs和坩埚转速ωc均为0rpm时坩埚熔体内的流动与传热；Step 3.1, use the numerical solver of the CFX module to numerically solve the flow and heat transfer in the crucible melt when the crystal rotational speed ω s and the crucible rotational speed ω c are both 0 rpm under different superconducting horizontal magnetic field strengths;

步骤3.2、当迭代收敛后通过CFX模块的后处理得到熔体的温度分布云图以及氧浓度分布云图，在温度分布云图上追踪固液界面1685K等温线位置，获取固液界面上的氧浓度分布数据，得到氧浓度与晶体直径的关系曲线，即固液界面径向氧浓度分布曲线，如图2所示，其中图2(a)是固液界面0°-180°平面中(平行于磁场方向)径向氧浓度分布曲线，图2(b)是固液界面90°-270°平面中(垂直于磁场方向)径向氧浓度分布曲线，依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的超导磁场强度，如下式Step 3.2. After the iteration converges, obtain the temperature distribution cloud map and the oxygen concentration distribution cloud map of the melt through the post-processing of the CFX module, track the position of the 1685K isotherm at the solid-liquid interface on the temperature distribution cloud map, and obtain the oxygen concentration distribution data on the solid-liquid interface , to obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve of the solid-liquid interface, as shown in Figure 2, where Figure 2(a) is the solid-liquid interface in the 0°-180° plane (parallel to the direction of the magnetic field ) radial oxygen concentration distribution curve, Fig. 2(b) is the radial oxygen concentration distribution curve in the 90°-270° plane (perpendicular to the direction of the magnetic field) of the solid-liquid interface, according to the average oxygen concentration of the solid-liquid interface The mean square error MSE O and the gradient error sum δ O of the radial oxygen concentration distribution curve are the minimum principles, and the appropriate superconducting magnetic field strength is selected, as shown in the following formula

其中，n为所采集到固液界面上的氧数据个数，ci为氧数据点，i为氧数据自变量；Among them, n is the number of oxygen data collected on the solid-liquid interface, c i is the oxygen data point, and i is the independent variable of the oxygen data;

其中，gradOi是固液界面径向氧浓度分布曲线上各氧数据点的梯度，gradOmin是固液界面径向氧浓度分布曲线的最小梯度，梯度误差和δO越小，则说明固液界面径向氧浓度分布的均匀性越均匀；Among them, gradO i is the gradient of each oxygen data point on the radial oxygen concentration distribution curve of the solid-liquid interface, and gradO min is the minimum gradient of the radial oxygen concentration distribution curve of the solid-liquid interface. The smaller the gradient error and δ O , the smaller the solid-liquid interface The uniformity of the radial oxygen concentration distribution at the interface is more uniform;

步骤4、分析晶体转速对固液界面形状和熔体内径向温度分布的影响，具体按照以下步骤实施：Step 4. Analyze the influence of the crystal rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, specifically in accordance with the following steps:

步骤4.1、在CFX前处理设置中，设置磁场强度为步骤3所选取的合适磁场强度，将坩埚转速ωc设置为0rpm，调节不同晶体转速ωs，迭代求解至残差曲线收敛，从而获取固液界面1685K等温线上的氧浓度数据；Step 4.1. In the CFX pre-processing setting, set the magnetic field strength to the appropriate magnetic field strength selected in step 3, set the crucible rotation speed ω c to 0 rpm, adjust the rotation speed ω s of different crystals, and iteratively solve until the residual curve converges, so as to obtain solid Oxygen concentration data on the 1685K isotherm at the liquid interface;

步骤4.2、得到氧浓度与晶体直径之间的关系曲线，即固液界面径向氧浓度分布曲线，为了分析晶体转速对固液界面形状和熔体内径向温度分布的影响，温度检测位置取自熔体内部，距离熔体与氩气交界面0.08m，长度为0.3m，方向由坩埚与熔体交界面指向晶体生长轴，图3(a)-3(d)分别是固液界面0°-180°平面中径向氧浓度分布曲线、固液界面90°-270°平面中径向氧浓度分布曲线以及固液界面形状和熔体内温度检测处径向温度分布曲线，依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的晶体转速；Step 4.2. Obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve of the solid-liquid interface. In order to analyze the influence of crystal rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, the temperature detection position is taken from Inside the melt, the distance from the interface between the melt and argon is 0.08m, the length is 0.3m, and the direction is from the interface between the crucible and the melt to the crystal growth axis. Figure 3(a)-3(d) are the solid-liquid interface 0° The radial oxygen concentration distribution curve in the -180° plane, the radial oxygen concentration distribution curve in the 90°-270° plane of the solid-liquid interface, the shape of the solid-liquid interface and the radial temperature distribution curve at the temperature detection point in the melt, according to the solid-liquid interface average oxygen concentration The mean square error MSE O of the radial oxygen concentration distribution curve and the gradient error and δ O are the minimum principle, and the appropriate crystal rotation speed is selected;

步骤5、分析坩埚转速对固液界面形状和熔体内径向温度分布的影响，具体按照以下步骤实施：Step 5. Analyze the influence of the crucible rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, specifically in accordance with the following steps:

步骤5.1、在CFX前处理设置中，设置磁场强度为步骤3所选取的合适磁场强度，设置晶体转速ωs为0rpm，调节坩埚转速ωc，通过数值求解器迭代求解至残差曲线收敛，从而获取固液界面1685K等温线上的氧浓度数据；Step 5.1. In the CFX pre-processing setting, set the magnetic field strength to the appropriate magnetic field strength selected in step 3, set the crystal rotation speed ω s to 0 rpm, adjust the crucible rotation speed ω c , and solve iteratively through the numerical solver until the residual curve converges, thereby Obtain the oxygen concentration data on the 1685K isotherm at the solid-liquid interface;

步骤5.2、得到氧浓度与晶体直径之间的关系曲线，即固液界面径向氧浓度分布曲线，为了分析坩埚转速对固液界面形状和熔体内径向温度分布的影响，温度检测位置取自熔体内部，高度距离熔体与氩气交界面为0.08m，长度为0.3m，方向由坩埚与熔体交界面指向晶体生长轴，图4(a)-4(d)分别是不同坩埚转速下固液界面0°-180°平面中径向氧浓度分布曲线、固液界面90°-270°平面中径向氧浓度分布曲线以及固液界面形状和熔体内温度检测处径向温度分布曲线，依据固液界面平均氧浓度径向氧浓度分布曲线的均方误差MSEO和梯度误差和δO为最小原则，选取合适的晶体转速；Step 5.2. Obtain the relationship curve between oxygen concentration and crystal diameter, that is, the radial oxygen concentration distribution curve of the solid-liquid interface. In order to analyze the influence of crucible rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, the temperature detection position is taken from Inside the melt, the height is 0.08m from the interface between the melt and argon, and the length is 0.3m. The direction is from the interface between the crucible and the melt to the crystal growth axis. Figures 4(a)-4(d) are different crucible rotation speeds The radial oxygen concentration distribution curve in the 0°-180° plane of the lower solid-liquid interface, the radial oxygen concentration distribution curve in the 90°-270° plane of the solid-liquid interface, the shape of the solid-liquid interface and the radial temperature distribution at the temperature detection point in the melt curve, based on the average oxygen concentration at the solid-liquid interface The mean square error MSE O of the radial oxygen concentration distribution curve and the gradient error and δ O are the minimum principle, and the appropriate crystal rotation speed is selected;

步骤6、综合步骤3～5，结合所选取的超导水平磁场强度、晶体转速和坩埚转速三者的共同作用下，得到超导水平磁场下直拉硅单晶固液界面氧浓度分布信息，具体按照以下步骤实施：Step 6, combining steps 3 to 5, combined with the selected superconducting horizontal magnetic field strength, crystal rotation speed and crucible rotation speed, to obtain the oxygen concentration distribution information of the Czochralski silicon single crystal solid-liquid interface under the superconducting horizontal magnetic field, Specifically follow the steps below:

步骤6.1、在CFX前处理设置中，设置超导水平磁场强度和坩埚转速为步骤3、步骤5所选取的合适超导水平磁场强度和坩埚转速，由于高晶转有利于提高固液界面的一致性，所以首先将晶体转速ωs设置为高晶转，通过数值迭代求解和MATLAB作图得到固液界面径向氧浓度分布曲线，如图5所示；Step 6.1, in the CFX pre-processing settings, set the superconducting horizontal magnetic field strength and crucible rotation speed to the appropriate superconducting horizontal magnetic field strength and crucible rotation speed selected in steps 3 and 5, because high crystal rotation is conducive to improving the consistency of the solid-liquid interface Therefore, firstly, the crystal rotation speed ω s is set to high crystal rotation, and the radial oxygen concentration distribution curve of the solid-liquid interface is obtained through numerical iterative solution and MATLAB drawing, as shown in Figure 5;

步骤6.2、将晶体转速ωs设置为低晶转，通过数值迭代求解和MATLAB作图得到固液界面径向氧浓度分布曲线，如图6所示；Step 6.2, set the crystal rotation speed ω s to low crystal rotation, and obtain the radial oxygen concentration distribution curve of the solid-liquid interface through numerical iterative solution and MATLAB drawing, as shown in Figure 6;

步骤6.3、分别计算晶体转速ωs为高晶转和低晶转时固液界面径向氧浓度分布曲线中固液界面的平均氧浓度和与氧浓度分布均匀性相关的均方误差MSEO和梯度误差和δO，通过定量和定性的对比分析，选取得到既适合降低固液界面氧浓度又能提高固液界面径向氧浓度分布均匀性的超导水平磁场强度、晶体转速和坩埚转速。Step 6.3, calculate the average oxygen concentration of the solid-liquid interface in the radial oxygen concentration distribution curve of the solid-liquid interface when the crystal rotation speed ω s is high crystal rotation and low crystal rotation respectively and the mean square error MSE O and the gradient error and δ O related to the uniformity of oxygen concentration distribution, through quantitative and qualitative comparative analysis, the selection is suitable for both reducing the oxygen concentration of the solid-liquid interface and improving the radial oxygen concentration distribution of the solid-liquid interface Uniform superconducting horizontal magnetic field strength, crystal rotational speed and crucible rotational speed.

为了研究分析超导磁场对直拉硅单晶生长的影响，本发明的数值仿真模型以西安理工大学TDR-120全自动CZ-Si单晶炉为原型，加入水平超导磁场。为了数值计算方便，对部分结构进行适当简化。建立直拉硅单晶生长中期的三维物理模型，具体物理参数包括：晶体直径300mm，投料量160kg，晶体长度200mm，晶体生长速度为0.52mm/min，X方向为水平超导磁场，Y轴为晶体生长轴方向，超导磁感应强度最高可达0.5T，如图1所示。In order to study and analyze the influence of superconducting magnetic field on the growth of Czochralski silicon single crystal, the numerical simulation model of the present invention takes the TDR-120 automatic CZ-Si single crystal furnace of Xi'an University of Technology as the prototype, and adds the horizontal superconducting magnetic field. For the convenience of numerical calculation, some structures are simplified appropriately. Establish a three-dimensional physical model for the middle stage of Czochralski silicon single crystal growth. The specific physical parameters include: crystal diameter 300mm, feeding amount 160kg, crystal length 200mm, crystal growth rate 0.52mm/min, X direction is the horizontal superconducting magnetic field, Y axis is In the direction of the crystal growth axis, the superconducting magnetic induction intensity can reach up to 0.5T, as shown in Figure 1.

通过数值仿真软件ANSYS中的CFX流体仿真模块，将埚转ωc和晶转ωs设置为0rpm，调节超导磁感应强度分别在0.25T和0.5T，得到不同磁场强度下固液界面径向氧浓度分布曲线，如图2所示，图2(a)-2(b)分别是固液界面0°-180°平面和90°-270°平面中径向氧浓度分布曲线。磁场强度越高，固液界面平均氧浓度越低，氧浓度均匀性越好；将埚转ωc设置为0rpm，调节晶转ωs分别为6rpm、8rpm和16rpm，迭代求解得到固液界面氧浓度分布信息。晶转ωs越高，固液界面平均氧浓度越高，氧浓度分布的均匀性越差，图3(a)-3(d)分别是不同晶转ωs下固液界面0°-180°平面中径向氧浓度分布曲线、固液界面90°-270°平面中径向氧浓度分布曲线、固液界面形状和熔体内检测温度分布，再将晶转ωs设置为0rpm，调节埚转ωc分别为0.5rpm、2rpm和4rpm，迭代求解得到固液界面氧浓度分布结果。埚转ωc越高，则固液界面边缘区域氧浓度升高，氧浓度均匀性变好，图4(a)-4(d)分别是不同埚转ωc下固液界面径向氧浓度分布曲线、固液界面形状和熔体内检测温度分布。经过综合考虑固液界面氧浓度低和径向氧浓度分布更均匀的原则，选取超导磁感应强度0.5T和坩埚转速0.5rpm，设置晶转ωs为16rpm，得到高晶转ωs、低埚转ωc下的固液界面氧浓度分布曲线，如图5所示，在同样的超导磁感应强度0.5T和坩埚转速0.5rpm下，设置晶转ωs为6rpm，得到低晶转ωs、低埚转ωc下的固液界面氧浓度分布曲线，如图6所示。Through the CFX fluid simulation module in the numerical simulation software ANSYS, set the crucible rotation ω c and crystal rotation ω s to 0 rpm, adjust the superconducting magnetic induction intensity at 0.25T and 0.5T respectively, and obtain the radial oxygen at the solid-liquid interface under different magnetic field intensities. The concentration distribution curve is shown in Figure 2. Figures 2(a)-2(b) are the radial oxygen concentration distribution curves in the solid-liquid interface 0°-180° plane and 90°-270° plane respectively. The higher the magnetic field strength, the lower the average oxygen concentration at the solid-liquid interface, and the better the uniformity of oxygen concentration; set the crucible rotation ωc to 0rpm, adjust the crystal rotation ωs to 6rpm, 8rpm and 16rpm respectively, and iteratively solve to obtain the solid-liquid interface oxygen Concentration distribution information. The higher the crystal rotation ω s , the higher the average oxygen concentration at the solid-liquid interface, and the worse the uniformity of the oxygen concentration distribution. Fig. 3(a)-3(d) respectively show the 0°-180 The radial oxygen concentration distribution curve in the ° plane, the radial oxygen concentration distribution curve in the solid-liquid interface 90°-270° plane, the shape of the solid-liquid interface and the detected temperature distribution in the melt, and then set the crystal rotation ω s to 0rpm, adjust The crucible rotation ω c is 0.5rpm, 2rpm and 4rpm respectively, and the oxygen concentration distribution results of the solid-liquid interface are obtained by iterative solution. The higher the crucible rotation ωc , the higher the oxygen concentration in the edge region of the solid-liquid interface, and the better the uniformity of oxygen concentration. Figure 4(a)-4(d) are the radial oxygen concentration at the solid-liquid interface under different crucible rotation ωc Distribution curve, shape of solid-liquid interface and detected temperature distribution in the melt. After comprehensively considering the principle of low oxygen concentration at the solid-liquid interface and more uniform distribution of radial oxygen concentration, the superconducting magnetic induction intensity is selected to be 0.5T and the crucible rotation speed is 0.5rpm, and the crystal rotation ω s is set to 16rpm to obtain high crystal rotation ω s and low crucible rotation speed The oxygen concentration distribution curve at the solid-liquid interface under rotation ω c is shown in Figure 5. Under the same superconducting magnetic induction intensity of 0.5T and crucible rotation speed of 0.5rpm, the crystal rotation ω s is set to 6rpm, and a low crystal rotation ω s , The oxygen concentration distribution curve at the solid-liquid interface at low crucible rotation ω c is shown in Figure 6.

在图5中，对于高晶转、低埚转下的仿真结果，分别用和表示固液界面0°-180°平面和90°-270°平面的平均氧浓度为In Fig. 5, for the simulation results under high crystal rotation and low crucible rotation, use and Indicates that the average oxygen concentration on the 0°-180° plane and 90°-270° plane of the solid-liquid interface is

分别用均方误差MSEO和梯度误差和δO进行评价固液界面0°-180°平面和90°-270°平面中径向氧浓度分布的均匀性。The uniformity of radial oxygen concentration distribution in the 0°-180° plane and 90°-270° plane of the solid-liquid interface was evaluated by mean square error MSE O and gradient error and δ O , respectively.

(1)利用MSEOxy和MSEOyz分别表示固液界面0°-180°平面和90°-270°平面中径向氧浓度分布均匀性，即(1) Use MSE Oxy and MSE Oyz to represent the uniformity of radial oxygen concentration distribution in the 0°-180° plane and 90°-270° plane of the solid-liquid interface, respectively, that is

(2)利用δOxy和δOyz分别表示固液界面0°-180°平面和90°-270°平面中径向氧浓度分布均匀性，即(2) Use δ Oxy and δ Oyz to represent the uniformity of radial oxygen concentration distribution in the 0°-180° plane and 90°-270° plane of the solid-liquid interface, respectively, that is

而在图6中，对于低晶转、低埚转下的仿真结果，固液界面的平均氧浓度和径向氧浓度分布均匀性MSEO和δO分别为In Figure 6, for the simulation results under low crystal rotation and low crucible rotation, the average oxygen concentration at the solid-liquid interface and radial oxygen concentration distribution uniformity MSE O and δ O are respectively

MSEOxy＝0.0073,MSEOyz＝0.0020MSE Oxy ＝0.0073, MSE Oyz ＝0.0020

δOxy＝0.7316,δOyz＝0.6539δ Oxy = 0.7316, δ Oyz = 0.6539

通过与传统高晶转，低埚转的工艺调节下的仿真结果对比，结果发现低晶转、低埚转的工艺调节方法下，固液界面的平均氧浓度更低，固液界面径向氧浓度分布均匀性更为均匀，同时满足大尺寸电子级直拉硅单晶对晶体中氧杂质含量的要求(量级)。By comparing with the simulation results under the process adjustment of traditional high crystal rotation and low pot rotation, it is found that under the process adjustment method of low crystal rotation and low pot rotation, the average oxygen concentration at the solid-liquid interface is lower, and the radial oxygen concentration at the solid-liquid interface is lower. The uniformity of concentration distribution is more uniform, and at the same time, it meets the requirements of large-scale electronic-grade Czochralski silicon single crystal for the content of oxygen impurities in the crystal ( order of magnitude).

Claims (9)

  1. A kind of 1. Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method, it is characterised in that specifically according to Lower step is implemented：
    Three-dimensional Local physical model needed for step 1, structure crystal for straight drawing monocrystal growth；
    Step 2, by three-dimensional Local physical model import CFX fluid emulation modules, setting analogue simulation is steady-state simulation, and is set Silicon melt, silicon crystal, the physical parameter and cryogenic magnetic field intensity of graphite crucible and silica crucible；
    Step 3, solve solid liquid interface radial direction oxygen concentration distribution situation under different superconduction horizontal magnetic intensities；
    The influence of step 4, analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt；
    The influence of step 5, analysis crucible rotation to radial temperature profile in solid-liquid interface shape and melt；
    Step 6, combining step 3~5, with reference to selected superconduction horizontal magnetic intensity, crystal rotation and crucible rotation three Under collective effect, czochralski silicon monocrystal solid liquid interface oxygen concentration distributed intelligence under superconduction horizontal magnetic field is obtained.
  2. 2. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 1 is specifically implemented according to following steps：
    Step 1.1, the three-dimensional Local physical model using Gambit software mess generation crystal for straight drawing monocrystal growth, include crystalline substance Body, melt, silica crucible and graphite crucible；
    Step 1.2, to set silica crucible radius be 0.306m, and graphite crucible radius is 0.32m, and melt radius is in crucible 0.3m, crucible rotate counterclockwise, crucible rotation ωc；Crystal radius scope is 0.15m~0.225m, and crystal turns clockwise, Crystal rotation is ωs, melt height is 0.08m~0.22m, and crystal length is 0m~0.6m, inventory 160kg, free interface For silicon melt and gas interface, boundary of the solid liquid interface between crystal and melt.
  3. 3. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 2, its It is characterised by, crucible rotation ω in the step 1.2cFor 0~10rpm, crystal rotation ωsFor 0~16rpm.
  4. 4. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 2 is specifically implemented according to following steps：
    Step 2.1, setting crucible are rotate counterclockwise, crucible rotation ωc, crystal turns clockwise, crystal rotation ωs；
    Step 2.2, hypothesis silicon melt are incompressible Newtonian fluid；Assuming that silicon melt meets Boussinesq approximations；Set Solid liquid interface is flat face, and supercooled state does not occur when solid liquid interface crystallizes, and the temperature of solid liquid interface is the melting temperature of silicon 1685K；Melt and argon gas interface are set, i.e. free surface is flat face, and its position height is highly identical with solid liquid interface, and Outwardly atmosphere radiations heat energy；Silica crucible bottom and crucible internal walls meet without slip boundary condition with silicon melt；Melt Interior oxygen transport process is ignored to melt flows with the influence conducted heat.
  5. 5. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 4, its It is characterised by, in the step 2.2, used boundary condition includes oxygen concentration boundary condition in iteration of simulations solution procedure And temperature boundary condition, wherein oxygen concentration boundary condition are as follows：
    (1) the oxygen concentration boundary condition of melted silicon and inner wall of quartz crucible intersection：
    <mrow> <msub> <mi>C</mi> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.5</mn> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mn>23</mn> </msup> </mrow> <msub> <mi>N</mi> <mi>A</mi> </msub> </mfrac> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> <mo>&amp;times;</mo> <mfrac> <msub> <mi>a</mi> <mi>O</mi> </msub> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>a</mi> <mi>O</mi> </msub> </mrow> </mfrac> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo>/</mo> <msup> <mi>m</mi> <mn>3</mn> </msup> </mrow>
    <mrow> <msub> <mi>a</mi> <mi>O</mi> </msub> <mo>=</mo> <msqrt> <msub> <mi>P</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </msub> </msqrt> <mo>&amp;CenterDot;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msubsup> <mi>&amp;Delta;G</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>3200</mn> <mo>/</mo> <mi>T</mi> <mo>-</mo> <mn>8.19</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>P</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>113.826</mn> <mo>/</mo> <mi>T</mi> <mo>+</mo> <mn>24.32</mn> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>&amp;Delta;G</mi> <mn>2</mn> <mn>0</mn> </msubsup> <mo>=</mo> <mo>-</mo> <mn>446570</mn> <mo>+</mo> <mn>169.19</mn> <mi>T</mi> <mo>.</mo> </mrow>
    Wherein, NAFor Avgadro constant,For partial pressure of oxygen, aoFor oxysome fraction, R is carrier of oxygen mole constant, and T is change Learn reaction temperature,For chemical reactionGibbs free amount.
    (2) melted silicon and the oxygen concentration boundary condition at argon gas interface：
    <mrow> <mo>-</mo> <msub> <mi>D</mi> <mi>O</mi> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>D</mi> <mrow> <mi>S</mi> <mi>i</mi> <mi>O</mi> </mrow> </msub> <mrow> <msub> <mi>RT&amp;delta;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mfrac> <msub> <mi>p</mi> <mn>0</mn> </msub> <msub> <mi>C</mi> <mrow> <mi>S</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>G</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>C</mi> <mrow> <mi>s</mi> <mi>u</mi> <mi>r</mi> <mi>f</mi> </mrow> </msub> </mrow>
    In formula, COAnd CsurfIt is the oxygen concentration of oxygen concentration in melt and free surface respectively；CSiIt is melted silicon concentration；DOAnd DSiO It is diffusion coefficient and SiO gas diffusion coefficient in argon gas of the oxygen in silicon melt respectively；Δ G is chemical equation (Simelt +Omelt=SiOgas) Gibbs free amount, p0It is the steam pressure of silicon monoxide gas, R is gas molar constant, and T is chemistry Reaction temperature；δgIt is free surface boundary layer thickness；
    During the actual growing environment of crystal, the oxygen of free surface is under the brushing of argon gas, the oxygen concentration C of free surfacesurfOnly For melt inside oxygen concentration COCount very much, therefore by the oxygen concentration C of free surfacesurfIgnore, then the oxygen of free surface is dense Degree boundary condition is reduced to
    CO=0mol/m3；
    (3) the oxygen concentration boundary condition at solid liquid interface (crystal growth interface) place：
    <mrow> <mi>D</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>V</mi> <mi>g</mi> </msub> <msub> <mi>C</mi> <mi>O</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow>
    In formula, D be oxygen diffusion coefficient, VgFor the translational speed of solid liquid interface, k is the segregation coefficient of oxygen, CoFor the oxygen in melt Concentration.Experiment discloses the segregation coefficient of oxygen close to unit 1, and the oxygen more than 99% is evaporate among argon gas from free surface, So the oxygen content being incorporated into crystal is ignored in solid liquid interface Whole Oxygen flux equilibrium, above formula is reduced to
    <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo>/</mo> <msup> <mi>m</mi> <mn>3</mn> </msup> </mrow>
    Graphite crucible bottom and graphite crucible outer wall apply constant gradient Temperature Distribution value in temperature boundary condition, at free surface Establish heat flow density equation, such as following formula：
    <mrow> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mi>l</mi> </msub> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mi>&amp;beta;</mi> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>1.25</mn> </msup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mi>s</mi> <mi>q</mi> <mi>r</mi> <mi>t</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>
    Q′l=qout,k-qin,k=σ ε T4-εqin,k
    qin,k=sumJ=1~N(Fk,jqout,j)
    In formula, β [T (r)-T0(r)]1.25For describing due to gaseous exchange and caused thermal losses, Q 'lFor describing melt liquid Face caused thermal losses by radiation, T are free surface temperature, T0For environment temperature, KlFor the silicon melt coefficient of heat conduction, β is gas The thermal losses coefficient of body convection current, r are free surface radius, and ε is radiation coefficient, and σ is Stefan-Boltzmann constants, Fk,jFor Ascent between two surfaces of k, j, qout,kIt is the heat flow of flux surface, qin,kIt is the heat flow for flowing into surface, x, z are sky Between rectangular coordinate system direction variable, N is surface total number；
    The inner surface not contacted in graphite crucible and the top surface of silica crucible, silica crucible with silicon melt and crystal outer surface Deng the surface of solids, similar heat flow density equation, such as following formula are also established：
    <mrow> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mi>&amp;beta;</mi> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>1.25</mn> </msup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>s</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mi>c</mi> <mi>r</mi> <mi>y</mi> <mi>s</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> <mo>/</mo> <mi>c</mi> <mi>r</mi> <mi>u</mi> <mi>c</mi> <mi>i</mi> <mi>b</mi> <mi>l</mi> <mi>e</mi> <mi> </mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>u</mi> <mi>s</mi> </mrow>
    Q′s=qout,k-qin,k=σ ε T4-εqin,k
    Wherein, Q 'sFor describing the surface of solids caused thermal losses by radiation, KsFor the silicon melt coefficient of heat conduction, r is crystal The inside radius of radius or silica crucible, y are rectangular coordinate system in space direction variable.
    It is 90000 that iterations is set in iterative controls, and time factor 1, the residual values of convergence curve are arranged to 1E- 06。
  6. 6. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 3 is specifically implemented according to following steps：
    Step 3.1, the numerical solver using CFX modules, under numerical solution difference superconduction horizontal magnetic intensity, crystal rotation ωs With crucible rotation ωcFlowing and heat transfer when being 0rpm in crucible melt；
    Step 3.2, the Temperature Distribution cloud atlas and oxygen concentration point of melt are obtained by the post processing of CFX modules after iteration convergence Cloth cloud atlas, solid liquid interface 1685K isothermal line positions are followed the trail of on Temperature Distribution cloud atlas, obtain the oxygen concentration distribution in solid liquid interface Data, the relation curve of oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, according to solid liquid interface Average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor minimum principle, choose and close Suitable cryogenic magnetic field intensity, such as following formula
    <mrow> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>c</mi> <mi>i</mi> </msub> </mrow>
    Wherein, n is the oxygen data amount check in collected solid liquid interface, ciFor oxygen data point, i is oxygen data arguments；
    <mrow> <msub> <mi>MSE</mi> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>c</mi> <mo>&amp;OverBar;</mo> </mover> <mi>O</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>
    <mrow> <msub> <mi>&amp;delta;</mi> <mi>O</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>gradO</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>gradO</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    Wherein, gradOiIt is the gradient of each oxygen data point on solid liquid interface radial direction oxygen concentration distribution curve, gradOminIt is solid-liquid circle Face diameter is to the minimal gradient of oxygen concentration distribution curve, gradient error and δOIt is smaller, then illustrate that solid liquid interface radial direction oxygen concentration is distributed Uniformity it is more uniform.
  7. 7. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 4 is specifically implemented according to following steps：
    Step 4.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, by crucible Rotational speed omegac0rpm is arranged to, adjusts different crystal rotational speed omegas, iterative to residual error curve convergence, so as to obtain solid liquid interface Oxygen concentration data on 1685K thermoisopleths；
    Step 4.2, the relation curve between oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, For influence of the analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from melt Inside, apart from melt and argon gas interface 0.08m, length 0.3m, crystal growth is pointed in direction by crucible and melt interface Axle, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor Minimum principle, choose suitable crystal rotation.
  8. 8. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 5 is specifically implemented according to following steps：
    Step 5.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, set brilliant Body rotational speed omegasFor 0rpm, regulation crucible rotation ωc, by numerical solver iterative to residual error curve convergence, so as to obtain Oxygen concentration data on solid liquid interface 1685K thermoisopleths；
    Step 5.2, the relation curve between oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, In order to analyze influence of the crucible rotation to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from melt Inside, height distance melt are 0.08m with argon gas interface, and length 0.3m, direction is pointed to brilliant by crucible and melt interface Body growth axis, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOAnd gradient error And δOFor minimum principle, suitable crystal rotation is chosen.
  9. 9. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 6 is specifically implemented according to following steps：
    Step 6.1, during processing is set before CFX, superconduction horizontal magnetic intensity and crucible rotation are set for selected by step 3, step 5 Suitable the superconduction horizontal magnetic intensity and crucible rotation taken, because Gao Jingzhuan is advantageous to improve the uniformity of solid liquid interface, so First by crystal rotation ωsGao Jingzhuan is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface radial direction oxygen Concentration profile；
    Step 6.2, by crystal rotation ωsLow brilliant turn is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface Radial direction oxygen concentration distribution curve；
    Step 6.3, crystal rotation ω is calculated respectivelysWhen turning for high brilliant turn with low crystalline substance in solid liquid interface radial direction oxygen concentration distribution curve The average oxygen concentration of solid liquid interfaceThe mean square error MSE related to oxygen concentration distributing homogeneityOWith gradient error and δO, lead to Comparative analysis qualitatively and quantitatively is crossed, selection is both adapted to reduce solid liquid interface oxygen concentration and can raising solid liquid interface radial direction oxygen Superconduction horizontal magnetic intensity, crystal rotation and the crucible rotation of uniform concentration distribution.
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CN108914201A (en) * 2018-08-29 2018-11-30 西安理工大学 A kind of Modelling of Crystal Growth in CZ-Si Pulling process parameter optimization method
CN109576785A (en) * 2018-12-29 2019-04-05 徐州鑫晶半导体科技有限公司 The method of oxygen content during adjusting monocrystalline silicon growing
CN110512278A (en) * 2019-09-12 2019-11-29 西安奕斯伟硅片技术有限公司 A kind of crystal pulling apparatus, device and method
CN111926384A (en) * 2020-06-05 2020-11-13 徐州鑫晶半导体科技有限公司 Single crystal furnace, method for determining operating parameters of single crystal furnace in growth process of single crystal silicon and method for preparing single crystal silicon
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CN101923591A (en) * 2010-08-09 2010-12-22 西安理工大学 Three-dimensional optimization design method of asymmetric hook-shaped magnetic field for MCZ single crystal furnace
CN103678890A (en) * 2013-11-28 2014-03-26 西北工业大学 Method for simulating influence of heating technology on premelting and melting of crystal boundaries by aid of crystal phase-field process

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US20060243192A1 (en) * 2003-05-28 2006-11-02 Kounosuke Kitamura Method of simulation with respect to density distribution and size distribution of void defect within single crystal and oxygen precipitation nucleus within single crystal
CN101923591A (en) * 2010-08-09 2010-12-22 西安理工大学 Three-dimensional optimization design method of asymmetric hook-shaped magnetic field for MCZ single crystal furnace
CN103678890A (en) * 2013-11-28 2014-03-26 西北工业大学 Method for simulating influence of heating technology on premelting and melting of crystal boundaries by aid of crystal phase-field process

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CN108914201A (en) * 2018-08-29 2018-11-30 西安理工大学 A kind of Modelling of Crystal Growth in CZ-Si Pulling process parameter optimization method
CN108914201B (en) * 2018-08-29 2019-09-27 西安理工大学 A Method for Optimizing Process Parameters of Czochralski Silicon Single Crystal Growth Process
CN109576785A (en) * 2018-12-29 2019-04-05 徐州鑫晶半导体科技有限公司 The method of oxygen content during adjusting monocrystalline silicon growing
CN110512278A (en) * 2019-09-12 2019-11-29 西安奕斯伟硅片技术有限公司 A kind of crystal pulling apparatus, device and method
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CN118658570B (en) * 2024-08-19 2024-12-06 西安交通大学 Method and device for determining shape of inner wall surface of crucible for growing silicon carbide by liquid phase method

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