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# 大直径直拉硅单晶炉热场的改造及数值模拟

29 卷 第 4 期 　　　　　　　　 人 　 第 工 　 　 　 　 　　　　　　　Vol. 29 　No. 4 晶 体 学 报 　 2000 年 11 月 　　　　　　　　　　 JOURNAL OF SY NTHETIC CRYSTALS 　　　　　　　 November ,2000

( 河北工业大学半导体材料研究所 ,天津 300130)

has been suppressed by our new heat system with composite heater. Distribution of temperature

filed was calculated by numeric simulation. The result indicated that axial temperature gradient was decreased due to the decrease of thermal convection in the melt . The concentration of oxygen in CZSi has been reduced. simulation

1 　 　　 引 言

Abstract : In order to reduce oxygen content in large2diameter Czochralski Si single crystal ( CZSi ) ,we have modified the heat zone in 406mm ( 16in. ) system. Thermal convection of melt Key words : CZSi ; heat zone ; heater thermal convection ; oxygen concentration ; numeric

Improvement and Numeric Simulation for Heat Zone in Large2diameter Si Single Crystals Furnace
( Institute of Semiconductor Materials ,Hebei University of Technology ,Tianjin 300130 ,China)
( Received 10 March 2000 , accepted 15 June 2000)

REN Bing2yan , LIU Cai2chi , ZHANG Zhi2cheng , HAO Qiu2yan

382

Diameter of the crystals 154mm

2 　 　　 实 验

3　 实验结果

Table 1 　Basic experimental conditions
Parameter of the crystal Items Crucible size 406mm Charge size 45kg Crystal rotation rate 12r/ min Crucible rotation rate 5r/ min Pull speed conditions
P < 100 > 　 ～6 cm 3 Ω?

0. 6mm/ min

Fig. 1 　 Schematic diagram of the hot zone ( a) popular”hot zone ; ( b) modified”hot zone “ “

取普通和改造热场生长的晶体各一颗 , 去掉头尾以后 , 各自均分成 10 段 , 每段长 35mm 。 μ 分别取厚度为 600 m 的样品 ,并进行化学抛光和超净清洗 ,分别测试其纵向氧含量 ,并对第一

383

Fig. 2 　 Axial distribution of oxygen concentration in the crystals
(a) Axial distribution of oxygen concentration 　　　　　　(b) Difference in oxygen concentration of crystal 1 and crystal 2

4　 分析与讨论

?

Δ

Δ

Δ

384

Table 2 　Properties and processing parameters
Property/ Parameter Emissivity Value 0. 55 (Crystal ,chamber wall) 0. 318 (Melt) 0. 50 (Quartz crucible) 0. 90 (Components of graphite ,) Pedestal ,Radiation shield ,Supporter 0. 20 ( Puller) 0. 70 ( Insulator) 22. 0 (Crystal) 64. 0 (Melt) 2. 89 (Quartz crucible) 60. 0 (Components of crucible ,Pedestal , Radiation shield ,Supporter) 58. 94 ( Puller) 1. 31 × 3/ T ( Insulator) 10 1683 2. 3 × 3 10 1. 0 × 3 10 1. 8 × 6 10 1. 2 × 5 ( Graphite) 10 0. 3872 0. 1524 300

Thermal conductivity(W/ mK)

Melting temperature of silicon ( K) Density of solid silicon (kg/ m3) Specific heat of solid silicon (J/ kg K) Heat of fusion (J/ kg) Electric conductivity(1/ Ωm) Crucible inner diameter (m) Crystal diameter (m) Chamber wall temperature ( K)

在熔/ 晶界面 :
K1 ( T1 ) n ? T1 - Ks ( Ts ) n ? Ts = PeSt n ?e T1 = Ts = 1
?

Δ 　　 其中 n为单位长度矢量 , St 为 Stefan 数 ,由式Δ Hf / ( Cps Tm ) 得出 , Hf 为硅的熔化热 ; Tm 为 硅的熔点温度 。 在暴露表面 :

Ki ( Ti ) n ? Ti = qrad , i

在方程 ( 2c) 中 , qrad , i 是边界表面上单位面积由于辐射造成的热损失 ,用 Maruyama 提出的辐射传热模型来估算 。

GT = Δ t . g. α. b3 / v2

12K ,而右边温差为 - 4. 4K ,图 5 中左边温差为 7. 8K ,而右边为 - 6. 5K。热对流驱动力的大小 , 可用无量纲格拉斯霍夫数 ( Grasheff number) 来表示 :

其中 b 为熔体特征长度 , g 为重力加速度 ,α 为温度引起的体膨胀系数 , v 为运动粘滞系 数 , GT 随 b3 增加 。在其他参数不变的情况下 ,Δ T 明显减小 。从熔体中生长硅单晶时 ,Δ T 的

Δ

?

Δ

Δ

?

?

?

?

( 2 a) ( 2 b)

( 2 c)
[7 ,8 ]

385

Fig. 4 　 Temperature distributions in the hot zone (the height of melt 256mm ,the height of crystal 100mm)

Fig. 5 　 Temperature distributions in the hot zone (the height of melt 160mm ,the height of crystal 230mm)

5 　 　　 结 论

1 　Kanda Isao , Suzuki Takefumi , et al . Influence of Crucible and Crystal Rotation on Oxygen2concentration Distribution in Large2 2 　 ogawa Shinji ,Huang Xinming ,et al . Oxygen Transport Analysis in Czochralski Silicon Melt by Considerring the Oxygen Evaporation T from the Melt Surface. J . Crystal Growth , 1995 ,148 :70280 Surfaces. Int . J . Heat Mass Transfer 1994 ,37 :1723
Crystal Growth ,1998 ,191 :4132420

3 　Hirata H , Hoshikawa K. Three2dimension Numerical Analyses of the Effects of A Cups Magnetic Field on the Flows , Oxygen Transport and Heat Transfer in a Czochralski Silicon Melt . J . Crystal Growth , 1992 ,125 :181 5　 Hahn Seung2Ho ,Tsukada Takao ,et al . G lobal Analysis of Heat Transfer in Si CZ Furnace with Specular and Diffuse Surfaces. J . 6　 周永溶 . 半导体材料 . 1992 年 6 月第一版 ,北京 : 北京理工大学出版社 ,127 :128 7　 Maruyama S. A Three2dimension Numerical Method Based on the Superposition Principle. Numer. Heat Transfer ,1993 ,24 :181 Czochralski2grown Silicon Crystals. J . Crystal Growth , 1998 ,186 :3622368

4　 Machida Norihisa , Suzuki Y ouji , et al . The Effects of Argon Gas Flow Rate and Furnace Pressure on Oxygen Concentration in

8 　Maruyama S , Aihara T. Radiation Heat Transfer of a Czochralski Crystal Growth Furnance with Arbitrary Specula and Diffuse

diameter Silicon Single Crystal . J . Crystal Growth ,1996 ,166 :6692674

302河北工业大学材料学院信息功能材料研究所赵龙

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