Czochralski Silicon Crystal Growth Research Articles

Influence of Thermal Conductivity and Emissivity of Heat Shield Surface Material on the Thermal Field of Czochralski Silicon Crystal Growth

Influence of Thermal Conductivity and Emissivity of Heat Shield Surface Material on the Thermal Field of Czochralski Silicon Crystal Growth

Effect of horizontal magnetic field position on oxygen distribution in CZ silicon crystal growth

The horizontal magnetic field-assisted Czochralski(CZ) method is gaining significant popularity in the semiconductor industry for producing 200 mm semiconductor-grade silicon wafers. In this study, the impact of the horizontal magnetic field position on the oxygen content and radial uniformity of semiconductor-grade silicon crystals produced by the CZ method was investigated. Three-dimensional simulations were conducted using finite element software to calculate the melt convection and oxygen content before and after adjustment of the magnetic field position, respectively. The simulations results predicted a decrease in the oxygen content of the crystals following the adjustment of the magnetic field position from 0 to 75 mm below the free surface, and this was experimentally verified. The velocity distribution of the free melt surface exhibits better uniformity when lowering the magnetic field position. The influence of the magnetic field position on the temperature distribution and Marangoni flow in the melt was investigated, and the result of oxygen concentration difference identified the adjustment of the magnetic field position promoted the greater Marangoni flow below the free melt surface, which promoted the volatilization of SiO gas and thus reduced the oxygen concentration in the silicon ingot. Therefore, adjusting the position of the magnetic field is an effective way to increase the Marangoni flow and to obtain semiconductor-grade silicon crystal with lower oxygen content and better oxygen radial homogeneity.

The effects on heat and oxygen transport of different heat shield and sidewall insulation designs during continuous Czochralski silicon crystal growth

Numerical work has been done to optimize the hot zone for the continuous Czochralski growth of 8-inch diameter silicon crystals using a double-crucible system. Thicker insulation layers on a high-heel-shaped heat shield and the sidewall insulation led to a reduction in the heater power of more than 40%, a decrease in the oxygen content, and a significant flattening of the growth interface. This design also allowed a stronger argon gas flow near the outer free melt surface and the quartz crucible wall, which prevented the generation of an argon gas vortex in this area. Stronger flow of argon gas would assist in moving more SiO gas and dust out of the chamber. However, the reduction in the outer melt temperature compared to the original design could slow down the melting of the silicon granules.

Adjustment of oxygen transport phenomena for Czochralski silicon crystal growth

During silicon crystal growth, oxygen, a well-known major impurity, affects the final silicon wafer's mechanical and electrical properties. This study focused on regulation of discharge of different concentrations of oxygen from the quartz crucible into the silicon melt while considering the crucible angular speed and the friction at the melt–crucible interface. The three-dimensional transient governing equations for heat transfer, fluid flow, and impurity transportation in the Czochralski (CZ) puller were solved numerically. The oxygen solvation equation representing the crucible to silicon melt was modified to evaluate the accuracy of oxygen concentration calculations during the CZ process. Experimental measurements using the Fourier-transform infrared (FTIR) technique were used to confirm the simulation results. The results demonstrate that the crucible angular speed affects the oxygen concentration near the crucible wall and therefore in the silicon ingot. The proposed modifications for evaluating oxygen concentration offer a more comprehensive understanding of the oxygen dynamics during the CZ crystal growth.

Reduction of oxygen concentration in 300 mm diameter n-type Czochralski silicon crystal growth using an optimized heating zone with dual side-heaters

In this study, the modified heating zone structure for 300 mm diameter Cz-Si crystal growth with dual side-heaters has been proposed. Based on it, 300 mm diameter n-type RCz-Si crystals with the oxygen concentration of 9.5–10.5 ppma were obtained.

Effects of different crucible shapes on heat and oxygen transport during continuous Czochralski silicon crystal growth

The effects of different quartz crucible geometries on continuous Czochralski growth of 8-inch silicon crystals in a double-crucible system are investigated. The numerical results show that a design in which the bottom and the side walls of the crucible are flat lowers the oxygen content, saves energy, and weakens the melt flow turbulence. Moreover, the lowest von Mises thermal stress in the crucible system was obtained with this crucible design. The flat crucible side wall reduces heat loss from the outer melt surface, facilitating heat transfer from the side heater into the melt. The differences in crucible geometry change the temperature distribution and flow pattern in the outer melt but have an insignificant effect on the deflection of the crystal-melt interface.

Effects of Induced Current in Crystals on the Melt Flow and the Melt–Crystal Interface during Industrial 300 mm Czochralski Silicon Crystal Growth under a Transverse Magnetic Field

Due to the high magnetic field intensity during industrial 300 mm silicon crystal growth, typically up to 0.3 T, the crystal’s rotation under this transverse magnetic field (TMF) induces a current that is strong enough to impact both the melt flow and the melt/crystal interface (m/c interface) shape. This paper investigates the influence of TMF-induced current in crystals on the melt flow, temperature distribution, and interface shape through the conduction of three sets of 3D simulations that vary in the electrical conductivity of crystals, TMF intensities, and crystal rotation rates. Combined with experiments, the accuracy of the model has been validated, and a reasonable electrical conductivity of the crystal has been predicted. The study findings reveal a shift in the driving force of forced convection from centrifugal to Lorentz force when the induced current in crystal is augmented. This alteration affects the melt flow and the m/c interface shape. Notably, this study serves as a significant complement to the conventional model, which overlooks the induced current in crystals, enhancing the accuracy and comprehensiveness of the simulation outcomes to provide a robust theoretical underpinning for industrial production.

Effect of water-cooled jacket on the oxygen transport during the Czochralski silicon crystal growth process

Nowadays, the water-cooled jacket is widely used in the large industrial Czochralski (Cz) furnace to enhance the pulling rate of the monocrystalline silicon crystal for solar cells. It is an efficient tool to increase productivity and reduce the production cost of the photovoltaic industry. However, the water-cooled jacket would affect the oxygen concentration of the grown silicon crystals. In this study, a two-dimensional numerical model was used to investigate the influence of the water-cooled jacket on the heat and oxygen transport in the silicon melt during the crystal growth process. The results demonstrate that the water-cooled jacket significantly enhances the heat loss from the melt-crystal and melt-gas interfaces, resulting in a larger temperature difference and stronger buoyancy convection in the melt, compared to the case without water-cooled jacket. The strong buoyancy convection causes the higher turbulent viscosity in the melt. Consequently, the oxygen transport in the melt is strengthened. By using the water-cooled jacket, the oxygen concentration in the grown crystals was increased by about 2.6 ppma at the crystal length of 400 mm. The simulation results agree reasonably with the experimental data.

Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

A method including a polynomial fitting step was proposed for crystallization interface correction of Czochralski crystal growth simulation, which can obtain an axisymmetric interface under a non-axisymmetric flow when the crystal rotates.

Controlling the heat, flow, and oxygen transport by double-partitions during continuous Czochralski (CCz) silicon crystal growth

The effect of the depths of two partitions on the heat, flow, and oxygen transport during the CCz growth of an 8-inch diameter silicon crystal is numerically investigated. A crucible in which two partitions are immersed in the silicon melt is so-called a triple-crucible. The different depths of two partitions change the effective wall surface area, which is the main source of oxygen at the growth interface, melt motion, and heat transfer within the crucible. The diffusion and convection of oxygen from the partitions and crucible wall towards the free surface and the crystal-melt (c-m) interface are also affected. The amount of oxygen that dissolves from the effective wall surface into the melt is proportional to the surface temperature and the surface area. The choice of at least one long partition will prevent the entry of unmelted granular silicon into the melt region under the c-m interface. Comparison of various cases shows that when the partition near the c-m interface is longer (90 mm) and the partition near the crucible sidewall is shorter (40 mm), the power consumption and the content of oxygen along the growth interface are lower.

Effects of different partition depths on heat and oxygen transport during continuous Czochralski (CCz) silicon crystal growth

A series of quasi-steady numerical simulations of the CCz growth of 8-in.-diameter silicon crystals are performed. A quartz partition is installed inside the melt to prevent the solid silicon that is being continuously added during growth from being transported to the crystal-melt interface without being melted. The effects of different partition depths on the heat, flow, and oxygen distributions are investigated. The simulation results show that the oxygen content increases when the depth of partition is increased from 20 mm to 80 mm. The trend is reversed for higher partition depths. This is due to the variation in the thermal field and flow structure. As the depth of the partition increases, there is a more significant change in the velocity under the free surface of the melt in the region inside the partition than in the outer melt region.

Advanced approach for oxygen transport and crystallization front calculation in Cz silicon crystal growth

Modeling of oxygen transport during Czochralski (Cz) silicon crystal growth still is a big challenge due to oxygen evacuation from the melt free surface, affected by strong anisotropy of turbulent mass transport. To predict the crystal oxygen concentration and crystallization front geometry with reasonable accuracy usually a 3D unsteady LES or DNS approach is required which demands significant computation resources and time. We present a new steady turbulence model using the extended hypothesis for modeling the Reynolds stress tensor, which accounts for different mechanisms of Reynolds stresses anisotropy and can be used in fast 2D engineering calculations. Several 8″ silicon crystals were grown in EKZ 3500 furnace with varying operating parameters. Wafers have been cut from different parts of the crystals and analyzed using the Fourier-transform infrared spectroscopy (FTIR) for oxygen concentration in facilities of Fraunhofer CSP and iTechSolar. The comparison between experimental and calculated results, which include oxygen concentration and interface deflection, is discussed in details. Time-averaged Reynolds stress tensor components as well as the turbulent heat fluxes components are compared between unsteady LES and steady RANS approaches.

Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

ILES of melt turbulent convection with conjugated heat transfer in the crucible and gas flow for Czochralski silicon crystal growth system

Results of Implicit Large Eddy Simulation (ILES) of buoyancy, rotation, and surface tension driven turbulent melt convection during Czochralski (Cz) silicon crystal growth are presented. Convective and conductive heat transfer in the melt is coupled with heat transfer in surrounding crystal, crucible, and gas flow. Distributions of resolved turbulence kinetic energy (TKE), Reynolds stress tensor, production terms and dissipation rate in the silicon melt are discussed and compared to published results. We have found significant anisotropy of the melt velocity fluctuations along the melt free surface and the crucible. Conjugated heat transfer in the melt flow and in the crucible has provided important results of the temperature fluctuation intensity along the liquid/solid interface. Our ILES results have also shown that there are significant regions in the melt with negative values of the shear production term. To estimate the quality of calculations using a conventional turbulence model for a Cz configuration, we have compared our ILES data to respective results obtained within the Boussinesq eddy viscosity assumption. As well we have evaluated how precise are available approximations of the production terms and dissipation rate of TKE for Si melt turbulent convection.

Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth

The influences of cusp magnetic field on the turbulent melt flow and the crystal/melt interface are studied by three-dimensional unsteady simulations for 300 mm industrial Czochralski silicon crystal growth. Detailed comparisons are implemented for the melt flow pattern, temperature and velocity oscillations as well as the crystal/melt interface with and without magnetic field. It is found that the melt flow is complex and irregular in this system, accompanied with rich flow structures and large temperature and velocity fluctuations. Under the application of cusp magnetic field, the turbulent melt flow is significantly inhibited with the simple flow structure as well as the periodic temperature and velocity fluctuations. The anticlockwise periodical flow in the melt induced by cusp magnetic field can help to reduce the impurity in the crystal and suppress the crystal/melt interface deformation. In particular, the thermal waves on the melt free surface are firstly observed with cusp magnetic field for large-size Czochralski silicon crystal growth, traveling in the direction of crucible rotation.

Factors influencing the gas bubble evolution and the cristobalite formation in quartz glass Cz crucibles for Czochralski growth of silicon crystals

Long-term Czochralski (Cz) silicon crystallization processes like multi-pulling demand high qualities and performances of fused quartz crucibles. Crucial issues are the gas bubble evolution and cristobalite (Crs) formation within the bulk and on the inner crucible surfaces. Here, crucibles by four suppliers were investigated using vacuum bake-out tests (VBT), for which crucible samples are heat-treated under vacuum at 1450 °C for different holding times with and without direct Si contact.An improved data analysis showed that the bubbles in all crucibles grow with process time; however, the expansion is more pronounced in the bulk material than in the critical surface-near region. Further, we observed that the final bubble size is higher in natural than in synthetic SiO2 material.Crs formation could be observed at all crucibles' surfaces, distinguishable into brownish Crs at sites with Si contact and white Crs without Si contact. The resulting Crs layer thickness and the surface covering increased with longer holding times; however, too thick layers could cause chipping. Further, the observed Crs growth rate is different for all crucible types. Finally, the crucibles were evaluated for their highest application potential for long-term Cz experiments.

Control of Oxygen Impurities in a Continuous-Feeding Czochralski-Silicon Crystal Growth by the Double-Crucible Method

The continuous-feeding Czochralski method is a cost-effective method to grow single silicon crystals. An inner crucible is used to prevent the un-melted silicon feedstock from transferring to the melt-crystal interface in this method. A series of global simulations were carried out to investigate the impact of the inner crucible on the oxygen impurity distributions at the melt-crystal interface. The results indicate that, the inner crucible plays a more important role in affecting the O concentration at the melt-crystal interface than the outer crucible. It can prevent the oxygen impurities from being transported from the outer crucible wall effectively. Meanwhile, it also introduces as a new source of oxygen impurity in the melt, likely resulting in a high oxygen concentration zone under the melt-crystal interface. We proposed to enlarge the inner crucible diameter so that the oxygen concentration at the melt-crystal interface can be controlled at low levels.

Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm

The melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process significantly influence the crystal quality. In this paper, an optimization system with the combination of an artificial neural network and a genetic algorithm is proposed to optimize the growth parameters during the growth process. Flattening the melt/crystal interface and reducing the oxygen concentration along the interface were chosen as the optimization targets. Two important growth parameters, the crystal rotation rate and crucible rotation rate, were chosen as optimization variables. First, a global heat and mass transfer model was developed to simulate the crystal growth process and then tested with experimental data. The verified heat and mass transfer model was then used to train an artificial neural network with the aim of rapidly assessing the complex nonlinear dependence of the interface shape and oxygen concentration on the growth parameters. The trained neural network combined with a genetic algorithm was then used to obtain the optimal growth parameters. Both deflection of the melt/crystal interface and the oxygen concentration along the interface decreased after optimization. Finally, the optimal growth parameters were checked in the heat and mass transfer model to evaluate the performance of the optimization system. The proposed method will also be useful for optimization of other crystal growth processes.

Investigation of gas bubble growth in fused silica crucibles for silicon Czochralski crystal growth

Abstract Gas bubbles in crucibles for Czochralski (Cz) silicon growth are both necessary and detrimental: In the outer, bubble-containing (BC) layer of the crucible, they are required for mechanical stability, while in the inner, bubble-free (BF) layer, bubbles can cause the release of particles from the crucible into the melt which may disrupt the single-crystalline growth. In this work, a vacuum bake-out test (VBT) procedure was set up for unused crucible parts and a microscopic characterization routine was developed to systematically investigate bubble formation and growth. Longer process time, higher temperature, and lower atmospheric pressure lead to an increased bubble growth in both, the BC and BF layer. During the VBT, no new bubbles form in the BF layer, while existing bubbles grow. The comparison to experimental data from crucibles used in an industrial Cz process indicates that VBTs can simulate this process. This allows the prediction of the gas-bubble formation in Cz crucibles using a cost-effective and less time-consuming analyzation method.

Transient global modeling for the pulling process of Czochralski silicon crystal growth. I. Principles, formulation, and implementation of the model

Abstract A transient global model for the crystal pulling process was developed for magnetic-field-applied Czochralski silicon (CZ-Si) growth. Heat transfer by solid conduction, melt convection, and diffuse gray radiation is taken into account for the crystal, melt, and other components in the furnace. The mesh adaption and view factor updating for the dynamic pulling process were realized by the structured grid deformations for different domains. By imposing the thermal boundary conditions in the vicinity of the triple point, the inverse control by the virtual proportional integral derivative controller and heat flux is acceptable for the transient global simulation of the pulling process in CZ-Si crystal growth. The applied cusp-shaped magnetic field (CMF) suppressed the turbulent melt flow and stabilized the heat and mass transport. CMF with different zero-Gauss-plane locations resulted in different flow patterns, which could affect the impurity transport during the pulling process. This developed transient global model can be applied for the segregation predictions of impurities (oxygen and carbon) and dopants in the CZ-Si growing process.