籽晶离轴角度对顶部籽晶溶液法SiC晶体中基平面位错分布的影响

doi:10.16553/j.cnki.issn1000-985x.xb2026.0021

摘要/Abstract

摘要： 基平面位错是影响4H-碳化硅（SiC）晶体质量及其器件性能的重要缺陷。为探究籽晶离轴角度对顶部籽晶溶液法4H-SiC晶体生长中基平面位错分布的影响，本文通过构建全局传热、三维热弹性应力分析与Alexander-Haasen位错演化的多物理场耦合模型，系统地研究了不同离轴角度（0°、4°、60°、90°）下晶体中剪切应力及基平面位错的分布规律。结果表明，正轴（0°）生长时晶体剪切应力与基平面位错最低且呈现六重对称分布；随着离轴角度的增大，剪切应力逐渐转变为四重对称分布，高应力区域集中在晶体边缘。同时，基平面位错密度随离轴角度的增加而显著上升，离轴角度较大（60°、90°）的基平面位错密度比离轴角度较小（≤4°）的情况提高了两个数量级，说明采用小离轴角度籽晶生长4H-SiC晶体可以有效抑制基平面位错的产生。本研究揭示了籽晶离轴角度-应力场-基平面位错的关联机制，为制备低缺陷密度的4H-SiC单晶提供了理论依据与工艺指导。

关键词: 顶部籽晶溶液法; SiC晶体; 数值模拟; 离轴角度; 剪切应力; 基平面位错

Abstract: Basal plane dislocations （BPDs） are critical defects that severely degrade the quality of 4H-silicon carbide （SiC） crystal and the performance of 4H-SiC based devices. The top-seeded solution growth （TSSG） method is promising for high-quality SiC crystals with its near-thermodynamic equilibrium conditions. However，the distribution of thermal stress and BPDs is not fully understood in the TSSG growth of 4H-SiC crystals. Both on-axis and off-axis seeds are widely used in the industrial TSSG processes. To investigate the effect of seed off-axis angle （θ_off） on thermal stress and BPDs in 4H-SiC crystals grown by the TSSG method，a multi-physics coupled model was developed in this study by integrating global heat transfer，three-dimensional thermoelastic stress analysis，and the Alexander-Haasen dislocation evolution model. The resolved shear stress （RSS） and BPDs density distributions in 4H-SiC crystals grown at off-axis angles of 0°，4°，60°，and 90° were systematically simulated and analyzed. The results show that the seed off-axis angle critically affects the RSS distribution at the growth interface. Under on-axis （θ_off=0°） growth，the RSS exhibits a highly symmetric，low-stress state，with stress near the center approaching zero and only minor perturbations at the edge. At the θ_off is 4°，the RSS shows axisymmetric regional patterns. At the θ_off is 60°，the RSS transitions to a fourfold symmetric distribution with alternating tensile and compressive stresses，and the stress amplitude increases by an order of magnitude compared to that at θ_off ≤4°. At the θ_off is 90°，the RSS becomes fully fourfold symmetric distribution. Under all conditions，the maximum RSS on the growth surface is lower than that on the seed back surface，and high-stress regions consistently concentrate at the crystal periphery. The density and distribution of BPDs closely correlate with RSS. Under on-axis growth，BPDs exhibit a sixfold symmetric distribution. As the θ_off increases，the BPDs distribution gradually transitions to fourfold symmetric distribution，and the overall BPDs density increases significantly. At the θ_off are 60° and 90°，the maximum BPDs density reaches approximately 10⁵ cm^-2，which is two orders of magnitude higher than that at 4° （approximately 10³ cm^-2）. This substantial increase indicates that large θ_off promote BPDs multiplication and are detrimental to high-quality crystal growth. In addition，the BPDs density is consistently higher on the seed back surface than on the growth surface，and high-BPDs regions coincide with high-RSS regions at the crystal periphery. This study elucidates the correlation among the seed off-axis angle，thermal stress field，and BPDs distribution in 4H-SiC crystals grown by the TSSG method. The findings demonstrate that using a seed with a small off-axis angle （≤4°） effectively suppresses BPD generation，thereby facilitating the growth of high-quality 4H-SiC single crystals. These results provide theoretical guidance for optimizing the TSSG process to achieve low defect density and high crystalline perfection.

Key words: top-seeded solution growth; SiC crystal; numerical simulation; off-axis angle; shear stress; basal plane dislocation

中图分类号:

O782

栾森, 齐小方, 马文成, 徐永宽. 籽晶离轴角度对顶部籽晶溶液法SiC晶体中基平面位错分布的影响[J]. 人工晶体学报, 2026, 55(6): 886-897.

LUAN Sen, QI Xiaofang, MA Wencheng, XU Yongkuan. Effect of Seed Off-Axis Angles on Distribution of Basal Plane Dislocations in Top-Seeded Solution Growth of SiC Crystals[J]. Journal of Synthetic Crystals, 2026, 55(6): 886-897.

图/表 11

图1 TSSG法SiC晶体生长炉结构示意图

Fig.1 Schematic diagram of growth furnace structure for SiC crystal by TSSG method

表1 数值模拟中材料的物性参数

Table 1 Material physical property parameters in numerical simulation

Material	Property	Value	Unit
Si-40% （mole fraction） Cr	Density，ρ	5 199-0.552T	kg/m³
	Specific heat capacity，C_p	1 196	J/（kg∙K）
	Thermal conductivity，λ	-68.28+5.4×10^-2T	W/（m∙K）
	Dynamic viscosity，μ	1.266×10^-3exp（1 982/T）	Pa∙s
Graphite	Density，ρ	1 950	kg/m³
	Specific heat capacity，C_p	710	J/（kg∙K）
	Thermal conductivity，λ	150	W/（m∙K）
Graphite felt	Density，ρ	120	kg/m³
	Specific heat capacity，C_p	200	J/（kg∙K）
	Thermal conductivity，λ	0.336	W/（m∙K）
SiC	Density，ρ	3 215	kg/m³
	Specific heat capacity，C_p	1 463.9	J/（kg∙K）
	Thermal conductivity，λ	6.11×10 000/（T-115）	W/（m∙K）
Argon	Specific heat capacity，C_p	520.33	J/（kg∙K）
Argon	Thermal conductivity，λ	0.07	W/（m∙K）

图2 晶体生长模拟模型。（a）晶体二维温度分布；（b）二维温度数据导入后三维模型的温度分布；（c）热应力模拟三维网格和边界条件

Fig.2 Crystal growth simulation model. （a） Two-dimensional temperature distribution of crystal；（b） temperature distribution in three-dimensional model after importing two-dimensional temperature data；（c） three-dimensional mesh and boundary conditions for thermal stress simulation

图3 六方晶系基平面滑移系示意图

Fig.3 Schematic diagram of slip systems in basal plane of hexagonal crystal system

表2 A-H模型相关参数

Table 2 Parameters for A-H model

Property	Value and unit
Burgers vector，b	3.073×10^-10 m
Stress exponential factor，m	2.8
Activation enthalpy，Q	3.3 eV at T>1 000 ℃ 2.6 eV at T<1 000 ℃
Dislocation velocity，v	m/s
Multiplication constant，K	7×10^-5
BPDs density in $a k$ direction， $N m (a k)$	m^-2
Boltzmann constant， $k B$	8.615×10^-5 eV/K

表2 A-H模型相关参数

Table 2 Parameters for A-H model

Property	Value and unit
Burgers vector，b	3.073×10^-10 m
Stress exponential factor，m	2.8
Activation enthalpy，Q	3.3 eV at T>1 000 ℃ 2.6 eV at T<1 000 ℃
Dislocation velocity，v	m/s
Multiplication constant，K	7×10^-5
BPDs density in $a k$ direction， $N m (a k)$	m^-2
Boltzmann constant， $k B$	8.615×10^-5 eV/K

图4 不同离轴角度下晶体不同滑移方向的分解剪切应力（τRSS）分布

Fig.4 Distribution of resolved shear stress （τRSS） in different slip directions of crystals under different off-axis angles

图5 不同离轴角度下晶体剪切应力最大值（a）和不同滑移方向的分解剪切应力（b）

Fig.5 Maximum shear stress in crystals under different off-axis angles （a） and resolved shear stress in different slip directions （b）

图6 不同离轴角度下晶体总剪切应力分布。（a）籽晶背面|τtotal|；（b）生长面|τtotal|

Fig.6 Distribution of total shear stress in crystals under different off-axis angels. （a） Back surface of seed |τtotal|；（b） growth surface |τtotal|

图7 不同离轴角度下4H-SiC晶体内BPDs密度分布。（a） 0°；（b） 4°；（c）；60°；（d） 90°

Fig.7 Distribution of BPDs density in 4H-SiC crystals under different off-axis angles. （a） 0°；（b） 4°；（c） 60°；（d） 90°

图8 不同离轴角度下不同截面BPDs密度分布。（a）籽晶背面；（b）生长面

Fig.8 Distribution of BPDs density under different off-axis angles for different cross-sections. （a） Back surface of seed；（b） growth surface

图9 不同离轴角度下BPDs密度沿不同截面的最大值分布

Fig.9 Distribution of maximum values of BPDs density along various cross-sections under different off-axis angles

参考文献 23

[1]	张福生，杨　昆，刘新辉，等. 无微管缺陷六英寸SiC单晶的制备［J］. 硅酸盐学报， 2021， 49（4）： 736-742.
	ZHANG F S， YANG K， LIU X H， et al. Growth of six inches SiC single crystals without micropipe defect［J］. Journal of the Chinese Ceramic Society， 2021， 49（4）： 736-742 （in Chinese）.
[2]	彭　燕，陈秀芳，谢雪健，等. 半绝缘碳化硅单晶衬底的研究进展［J］. 人工晶体学报， 2021， 50（4）： 619-628.
	PENG Y， CHEN X F， XIE X J， et al. Research progress of semi-insulating silicon carbide single crystal substrate［J］. Journal of Synthetic Crystals， 2021， 50（4）： 619-628 （in Chinese）.
[3]	BÖTTCHER K， CLIFFE K A. Three-dimensional resolved shear stresses in off-axis grown SiC single crystals［J］. Journal of Crystal Growth， 2007， 303（1）： 310-313.
[4]	SEKI K， KUSUNOKI K， HARADA S， et al. Evaluation of basal plane dislocation behavior in the epitaxial layer on a 4H-SiС wafer fabricated by the solution growth method［J］. Materials Science Forum， 2019， 963： 80-84.
[5]	SONG H Z， SUDARSHAN T S. Basal plane dislocation conversion near the epilayer/substrate interface in epitaxial growth of 4° off-axis 4H-SiC［J］. Journal of Crystal Growth， 2013， 371： 94-101.
[6]	YANG G， XU L B， CUI C， et al. Anisotropic etching mechanisms of 4H-SiC： experimental and first-principles insights［J］. Journal of Semiconductors， 2024， 45（1）： 012502.
[7]	YANG Y W， LI K Q， TONG Z Y， et al. The effect of shear on nucleation and movement of basal plane dislocations in 4H-SiC［J］. Journal of Applied Physics， 2024， 136（4）： 045706.
[8]	LU S O， CHEN H Y， HANG W， et al. Numerical analysis of the dislocation density in n-type 4H-SiC［J］. CrystEngComm， 2023， 25（26）： 3718-3725.
[9]	GAO B， KAKIMOTO K. Three-dimensional modeling of basal plane dislocations in 4H-SiC single crystals grown by the physical vapor transport method［J］. Crystal Growth & Design， 2014， 14（3）： 1272-1278.
[10]	LU S O， XU B J， XUAN L L， et al. Comparing basal and prismatic slips induced by thermal stresses in 4H-SiC crystals［J］. CrystEngComm， 2024， 26（44）： 6244-6254.
[11]	LU S O， XU B J， WANG Y Z， et al. Distribution of basal plane dislocations in 4-degree off-axis 4H-SiC single crystals［J］. CrystEngComm， 2024， 26（16）： 2143-2154.
[12]	KAKIMOTO K， NAKANO S. Numerical analysis of dislocation density of SiC crystals tilted from ［0001］ toward ［1210］ and ［1100］ grown by physical vapor transport［J］. Crystal Research and Technology， 2022， 57（4）： 2100219.
[13]	XU B J， LU S O， CUI H， et al. The fracture stress of 8-inch silicon carbide during the PVT growth［J］. CrystEngComm， 2024， 26（39）： 5550-5560.
[14]	LU S O， XU B J， XUAN L L， et al. Numerical analysis on the thermal stress and dislocation density of a 300 mm SiC single crystal grown by the PVT method［J］. CrystEngComm， 2025， 27（36）： 6019-6029.
[15]	杨　垚，李早阳，高俊浩，等. 晶体旋转影响下的溶液法6英寸SiC单晶生长研究［J］. 物理学报， 2025， 74（15）： 158101.
	YANG Y， LI Z Y， GAO J H， et al. Effects of crystal rotation on 6-inch SiC crystal growth by top-seeded solution growth method［J］. Acta Physica Sinica， 2025， 74（15）： 158101 （in Chinese）.
[16]	LIU B T， YU Y， TANG X， et al. Optimization of crucible and heating model for large-sized silicon carbide ingot growth in top-seeded solution growth［J］. Journal of Crystal Growth， 2020， 533： 125406.
[17]	SUI Z R， XU L B， CUI C， et al. Effects of solution height and crystal rotation on the solution flow behavior in the top-seeded solution growth of SiC single crystals［J］. CrystEngComm， 2024， 26（7）： 1022-1031.
[18]	LI F C， HE L， YAN Z Y， et al. Effects of crystal rotation on the carbon transport in the top-seeded solution growth of SiC single crystal［J］. Journal of Crystal Growth， 2023， 607： 127112.
[19]	LIU Y H， LI M Y， YAN Z Y， et al. Effects of coil frequency on the carbon transport in the top-seeded solution growth of SiC single crystal［J］. Journal of Crystal Growth， 2024， 643： 127801.
[20]	LI M Y， LIU Y H， QI X F， et al. Suppression of the surface roughness by adjusting the temperature distribution in the top-seeded solution growth of SiC crystal［J］. Journal of Materiomics， 2025， 11（5）： 100994.
[21]	YANG Y， LI Z Y， WANG J L， et al. Thermal-magnetic effects in the SiC crystal growth by top-seeded solution growth method with induction heating［J］. International Communications in Heat and Mass Transfer， 2026， 172： 110624.
[22]	ZHU C， HARADA S， SEKI K， et al. Influence of solution flow on step bunching in solution growth of SiC crystals［J］. Crystal Growth & Design， 2013， 13（8）： 3691-3696.
[23]	LIU X B， ZHU C， HARADA S， et al. Application of C-face dislocation conversion to 2 inch SiC crystal growth on an off-axis seed crystal［J］. CrystEngComm， 2019， 21（47）： 7260-7265.