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

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.

Effect of the pulling, crystal and crucible rotation rate on the thermal stress and the melt–crystal interface in the Czochralski growth of germanium crystals

The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.

Effect of crucible rotation on the temperature and oxygen distributions in Czochralski grown silicon for photovoltaic applications

Oxygen concentration is sensitive to changes in the rotation rate for Czochralski grown silicon crystals.

Growth of Single-Crystal Cd0.9Zn0.1Te Ingots Using Pressure Controlled Bridgman Method

We report growth of single-crystal Cd0.9Zn0.1Te ingots while using the pressure-controlled Bridgman method. The Cd pressure was controlled during growth to suppress its evaporation from the melt and reduce the size of Te inclusions in the as-grown crystals. The accelerated crucible rotation technique (ACRT) was used to suppress constitutional supercooling. The fast accelerating and slow decelerating rotation speeds were optimized. Two-inch Cd0.9Zn0.1Te single-crystal ingots without grain boundaries or twins were grown reproducibly. Glow discharge mass spectrometry results indicate the effective segregation coefficients of Zn and In dopants are 1.24 and 0.18, respectively. The full width half maximum (FWHM) of X-ray rocking curve was approximately 22.5 ″, and the IR transmittance was approximately 61%, indicating high crystallinity. The mean size of the Te inclusions was approximately 13.4 μm. Single-crystal wafers were cut into 5 × 5 × 2 mm3 slices and then used to fabricate gamma ray detectors. The energy resolution and peak-to-valley ratio maps were constructed while using 59.5 keV gamma ray measurements, which proved the high uniformity of detection performance.

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration

A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.