Numerical Simulation of Influence of Different Shoulder Shapes on Quality of Czochralski Silicon Single Crystals

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

Abstract

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

CLC Number:

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.

Figures/Tables 13

References 25

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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

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

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

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