Modeling of heat transfer in a melt in growing single crystals by the stockbarger method using the accelerated crucible rotation technique (ACRT)

1998 ◽  
Vol 39 (1) ◽  
pp. 85-90 ◽  
Author(s):  
V. É. Distanov ◽  
A. G. Kirdyashkin
Keyword(s):  
Heat Transfer ◽  
Single Crystals ◽  
Stockbarger Method ◽  
Rotation Technique ◽  
Crucible Rotation

Numerical simulation of heat transfer processes during single crystal growth by the Bridgman - Stockbarger method in fixed and rotating crucibles

2021 ◽  
pp. 21-32
Author(s):  
Степан Александрович Кислицын ◽  
Константин Александрович Митин ◽  
Владимир Степанович Бердников
Keyword(s):  
Heat Transfer ◽  
Angular Velocity ◽  
Single Crystal ◽  
Convective Heat ◽  
System Of Equations ◽  
Axial Region ◽  
Thermogravitational Convection ◽  
Angular Velocities ◽  
Stockbarger Method ◽  
Crucible Rotation

Численно методом конечных элементов исследованы процессы кристаллизации кремния в плоскодонных неподвижных и равномерно вращающихся графитовых цилиндрических тиглях в режимах сопряженного конвективного теплообмена. Процессы кристаллизации кремния изучены при фиксированной скорости опускания тигля в холодную зону и различных скоростях его вращения. Опускание тигля имитировалось перемещением точки излома в распределении температуры на внешней стороне стенок тигля. Точка излома - это граница перехода от нагретого до начальной температуры участка стенки к области с заданным градиентом температуры. Использованы адаптивные сетки на треугольниках, отслеживающие положение фронта кристаллизации на каждом временном шаге. Использован пакет программ собственной разработки. The dependence of both spatial shape and intensity of the convective flow of silicon melt during the growth of a silicon ingot by the Bridgman-Stockbarger method was studied numerically by the finite element method. Stationary and uniformly rotating graphite crucible in conjugate convective heat transfer regines were examined. The simulation was carried out on the basis of dimensionless system of equations for the thermogravitational convection in the Boussinesq approximation using the bipolar approach. In the mixed convection regine, the system of equations was augmented by an equation for the azimuthal velocity. Adaptive grids on triangles were used to track the position of the crystal-melt interface at each time step. The calculations were carried out at a constant rate of lowering the crucible from the hot to the cold zone, equal to 2.81 cm/h, and at a constant temperature gradient equal to 35 K/cm. Lowering the crucible was simulated by moving the inflection point in the temperature distribution on the outside of the crucible walls. The range of angular velocities of crucible rotation from 0 to 10 rpm is considered. It is shown that as the angular velocity of crucible rotation in the axial region increases, both the velocity of the downward flow arising in the regines of thermogravitational convection gradually and the convective heat flux to the crystal-melt interface decrease. As a result, in the range of angular velocities from 2 to 10 rpm, the shape of the crystal-melt interface gradually approaches to the one typical for the thermal conductivity regime. It is shown that at the initial stage of the process at an angular velocity of 10 rpm in the axial region of the cooled crucible bottom, the nucleation of a single crystal is possible.

Mathematical Model of the Bridgman-Stockbarger Method to Growth Semiconductor Single Crystals

1992 ◽  
Vol 278 ◽  
Author(s):  
E. Vega ◽  
G. Muiñiz ◽  
F. Rabago
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Single Crystals ◽  
Transfer Equation ◽  
Point System ◽  
Two Dimensional ◽  
Heat Transfer Equation ◽  
Stability Problems ◽  
Stockbarger Method ◽  
Dimensional Equation

AbstractA two dimensional equation has been solved which represents the heat transfer equation for the growth of single crystals system called Bridgman- Stockbarger method. Two variations were analyzed with and without an insulation between heater and cooler. System without an insulation shows stability problems because it's directly affected by the boundary between the cooler and heater region, in this case we obtained a discontinuity in this point. System with an insulation shows higher stability.

Crystal growth of CuInSe2 by the Bridgman method

1989 ◽  
Vol 67 (4) ◽  
pp. 294-297 ◽  
Author(s):  
W. S. Weng ◽  
L. S. Yip ◽  
I. Shih ◽  
C. H. Champness
Keyword(s):  
Crystal Growth ◽  
Room Temperature ◽  
Amorphous Layer ◽  
Bridgman Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Vertical Bridgman ◽  
Hall Effect Measurements ◽  
Rotation Technique ◽  
Crucible Rotation

Single crystals of CuInSe2 have been fabricated by the vertical Bridgman method. A conventional Czochralski crystal-pulling system was adapted for this purpose. An accelerated crucible-rotation technique was employed for a better mixing of the melt during the growth. Void- and crack-free crystal grains with an area as large as 50 mm2 and a thickness of more than 5 mm could be selectively cut from the ingots. From room-temperature Hall-effect measurements, mobility values as large as 73 cm2 ∙ V−1 ∙ s−1 were obtained for the present samples. X-ray diffraction studies suggested that abrasive polishing might create an amorphous layer on the surface of the CuInSe2 crystals.

scholarly journals Characteristics of TlBr single crystals grown using the vertical Bridgman-Stockbarger method for semiconductor-based radiation detector applications

2016 ◽  
Vol 34 (2) ◽  
pp. 297-301 ◽  
Author(s):  
Dong Jin Kim ◽  
Joon-Ho Oh ◽  
Han Soo Kim ◽  
Young Soo Kim ◽  
Manhee Jeong ◽  
...  
Keyword(s):  
Single Crystals ◽  
High Performance ◽  
Radiation Detector ◽  
Radiation Detectors ◽  
Middle Part ◽  
High Quality ◽  
Single Crystalline ◽  
Crystalline Sample ◽  
Vertical Bridgman ◽  
Stockbarger Method

AbstractTlBr single crystals grown using the vertical Bridgman-Stockbarger method were characterized for semiconductor based radiation detector applications. It has been shown that the vertical Bridgman-Stockbarger method is effective to grow high-quality single crystalline ingots of TlBr. The TlBr single crystalline sample, which was located 6 cm from the tip of the ingot, exhibited lower impurity concentration, higher crystalline quality, high enough bandgap (>2.7 eV), and higher resistivity (2.5 × 1011 Ω·cm) which enables using the fabricated samples from the middle part of the TlBr ingot for fabricating high performance semiconductor radiation detectors.

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