不同放肩形状对直拉硅单晶质量影响的数值模拟

doi:10.16553/j.cnki.issn1000-985x.2025.0188

摘要/Abstract

摘要： 直拉硅单晶放肩形状显著影响晶体质量。本研究利用CGSim软件，针对硅单晶生长过程中平放肩和缓放肩两种不同放肩形状进行模拟分析。结果表明，相比平放肩，缓放肩能形成理想的“M”形凸生长界面，促使熔体对流更均匀，固-液界面处氧含量富集程度提升约46.75%；该凸生长界面结构同时优化了晶体生长速率（V）与轴向温度梯度（G）的比值（V/G）分布，使缓放肩晶体应力最大值降幅约67.72%，且应力均匀性提升约62.73%。以上热力学（V/G调控）-溶质输运（氧输运行为）-结构稳定性（应力抑制）之间的协同优化机制，阐明了界面形状与应力场的动态耦合关系及缺陷演化规律。不同晶体长度的模拟结果进一步证实，该模式下的综合优化机制，为后续通过精确调控放肩形状来优化晶体质量提供了坚实基础。

关键词: 放肩; 生长界面; 直拉硅单晶; CGSim软件; 数值模拟

Abstract: The shoulder shape of Czochralski silicon single crystal significantly affects the crystal quality. In this study，CGSim software was used to simulate and analyze the two different shoulder shapes of abrupt shoulder and gradual shoulder during the growth of silicon single crystal. The results show that compared with the abrupt shoulder，the gradual shoulder can form an ideal “M” -shaped convex growth interface，which makes the melt convection more uniform，and the enrichment degree of oxygen content at the solid-liquid interface increases by about 46.75 %. The convex growth interface structure also optimizes the ratio value （V/G） distribution of crystal growth rate （V） to axial temperature gradient （G），which reduces the maximum stress of the gradual shoulder crystal by about 67.72% and increases the stress uniformity by about 62.73%. The above thermodynamic （V/G regulation）-solute transport （oxygen transport behavior）-structural stability （stress suppression） synergistic optimization mechanism clarifies the dynamic coupling relationship between interface shape and stress field and the evolution of defects. The simulation results of different crystal lengths further confirm that the comprehensive optimization mechanism in this mode lays a solid foundation for the subsequent optimization of crystal quality by accurately adjusting the shoulder shape.

Key words: shoulder; growth interface; Czochralski silicon crystal; CGSim software; numerical simulation

中图分类号:

马武祥, 郭可, 胡晓亮, 梅昊天, 李晓川, 范吉祥, 张倩. 不同放肩形状对直拉硅单晶质量影响的数值模拟[J]. 人工晶体学报, 2026, 55(2): 253-263.

MA Wuxiang, GUO Ke, HU Xiaoliang, MEI Haotian, LI Xiaochuan, FAN Jixiang, ZHANG Qian. Numerical Simulation of Influence of Different Shoulder Shapes on Quality of Czochralski Silicon Single Crystals[J]. Journal of Synthetic Crystals, 2026, 55(2): 253-263.

图/表 13

图1 晶体生长模型的几何结构及网格划分

Fig.1 Geometrical structure and mesh division of crystal growth model

表1 Cz硅晶体生长模拟计算中的主要材料物性参数

Table 1 Main material physical property parameters in Cz silicon crystal growth simulation calculation

Item	Silicon（crystal）	Silicon（melt）	Graphite	Quartz	Argon	Felt（solid）
Density/（kg·m^-3）	2 330	3 194-0.370 1T	1 830	2 200	Ideal gas	160
Thermal conductivity/ （W·m^-1·K^-1）	96 017/T^1.149	60~66	146.888 5-0.176 87T+ 0.000 127T²-4.689 9× 10^-8T³+6.665×10^-12T⁴	4	0.01+2.50×10^-5T	0.100（473 K）； 0.115（673 K）； 0.130（873 K）； 0.150（1 073 K）； 0.170（1 273 K）； 0.200（1 473 K）
Thermal expansion coefficient/K^-1	5.20×10^-6	1.40×10^-4
Thermal emissivity	0.9 016-2.6 208×10^-4T	0.30	0.80	0.85		0.80
Specific heat capacity/ （J·kg^-1·K^-1）	1 000	915	2 100	1 000	521	1 047
Elastic modulus/GPa	190
Poisson ratio	0.23
Melting point/K	1 686
Melt viscosity/（N·m^-1·K^-1）		7.00×10^-4
Surface tension/（N·m^-1）		8.75×10^-5
Crystallization latent Heat/（J·kg^-1）		1.80×10⁶

图2 平放肩（a）与缓放肩（b）的形貌和局部网格细化

Fig.2 Morphology and local mesh refinement of abrupt shoulder （a） and gradual shoulder （b）

图3 熔体的温度场和流场分布及固-液生长界面形状

Fig.3 Temperature field and flow field distribution of melt and solid-liquid growth interface shape

图4 固-液生长界面附近的氧分布、传输及熔体对流分布

Fig.4 Oxygen distribution，transport and melt convection distribution near solid-liquid growth interface

图5 界面形状及应力分布

Fig.5 Interface shape and stress distribution

图6 不同放肩形状下的界面高度和V/G值

Fig.6 Interface height and V/G value under different shoulder shapes

图7 不同放肩形状下的界面应力和氧含量

Fig.7 Interface stress and oxygen concentration under different shoulder shapes

表2 不同晶体长度下的主要拉晶工艺参数

Table 2 Main crystal pulling process parameters under different crystal lengths

Crystal length/mm	80	100	200	500	800	1 200
Seed crystal rotation rate/（r·min^-1）	-18	-18	-18	-18	-18	-18
Crucible rotation rate/（r·min^-1）	10	10	9	9	8	7
Growth rate/（mm·h^-1）	72	70	65	58	52	45
Melt gap/mm	30	30	30	30	30	30

图8 不同晶体长度下的界面形状、应力分布和温度分布

Fig.8 Interface shape，stress distribution and temperature distribution under different crystal lengths

图9 不同晶体长度下的界面高度及应力

Fig.9 Interface height and stress under different crystal lengths

表3 不同晶体长度条件下的界面中心高度和应力

Table 3 Interface center height and stress under different crystal lengths

Crystal length/mm	Gradual shoulder state	80	100	200	500	800	1 200
Interface center height/mm	-5.6	9.4	10.2	12.2	12.6	10.9	10.0
Center stress/（10⁷ Pa）	1.13	6.93	2.18	5.29	9.53	13.31	17.74
Stress amplification/（10⁵ Pa·mm^-1）		7.25	-23.75	3.11	1.41	1.26	1.11

图10 不同晶体长度下的缺陷浓度和尺寸分布

Fig.10 Defect concentration and size distribution under different crystal lengths

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