Temperature Distribution In Melt Research Articles

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.

Simulation to confirm the existence of distinct low-temperature regions in a Si melt using an insulating plate under the crucible bottom for the noncontact crucible method

The noncontact crucible (NOC) method has a large and deep low-temperature region in the upper central part of a Si melt to allow natural crystal growth inside it. Thanks to the low-temperature region, the NOC method can grow a uniform large Si single ingot without contact with the crucible wall. Using simulation of the temperature distribution in the Si melt, the establishment of the low-temperature region is clearly shown on basis of controlling the heat flow from the bottom heater into the Si melt using an insulating plate locally set under the crucible bottom. The heat from the bottom heater can be effectively weaken especially for the heat flow from the crucible center, resulting in the quite large low-temperature region in the melt. The effectiveness of such heat-flow control was proved by the growth of several Si single ingots using the NOC method. The effects of the heat power balance and the thickness of the insulating plate are also shown by the simulation. The temperature gradient in the NOC ingot is clearly smaller than that in an ingot grown by the Czochralski (CZ) growth mode.

On Dynamic Temperature Distributions in the Molten Bath of the Magnesite Ores

The relevance of this article is due to the enormous value of refractories in the national economy. Refractory materials are the materials produced of mineral raw materials and are capable of retaining their functional properties under a variety of conditions at high temperatures without significant deformations; such materials are used for metallurgical processes, furnace designing, and high-temperature units. There is solved a partial differential equation of parabolic type, non-linear in the second derivatives. The solution is carried out by using the MATLAB software. The article presents the results of researching temperature distribution in conductive magnesite melt, depending on the current leads location.

Computational Study of Contact Solidification for Silicon Film Growth in the Ribbon Growth on Substrate System

Ribbon growth on substrate (RGS) has emerged as a new method for growing silicon films at low cost for photovoltaic applications by contact solidification. Thermal conditions play an important role in determining the thickness and quality of the as-grown films. In this study, we have developed a mathematical model for heat transfer, fluid flow, and solidification in the RGS process. In particular, a semi-analytical approach is used in this model to predict solidification with a sharp solid–liquid interface without using a moving grid system. A more realistic analytical relationship that considers the varying rate of heat removal at the interface has been developed to evaluate the effective heat transfer rate, solidification rate, and solidification front. These models were used to predict the flow patterns in the crucible, the temperature distributions in the system, the velocity fields in the crucible, the solidification rates, and the film thicknesses. The effects of important operational parameters, such as pulling speed, preheat temperature, and thermal properties of the substrate material, have been examined. In addition, an order of magnitude analysis has been performed to understand heat transfer in the growing film and substrate. This analysis leads to a simplified mathematical model for heat transfer and solidification, which can be resolved analytically to derive theoretical solutions for the effective heat transfer coefficient, the rate of solidification, and the film thickness. The results show that the solidification rate varies largely on the substrate. The non-uniformity can be mitigated by altering the temperature distribution in the silicon melt through manipulating heat generation in the top heater. The rates of solidification and film thickness are very sensitive to both the thermal conductivity and preheat temperature of the substrate. Increasing pulling velocity will increase the rate of solidification at the leading edge but reduce the film thickness. The numerical model and the theoretical solution provide an important tool for thermal design and optimization of the RGS system.

An ultrasound-based system for temperature distribution measurements in injection moulding: system design, simulations and off-line test measurements in water

The polymer melt temperature in the screw ante-chamber of an injection moulding machine influences a number of parameters during the polymer process and therefore the final product quality. For measurement of this temperature, a sensor must be non-invasive (because of the axial moved screw during the injection of the plasticized polymer into the mould) and withstand the high pressure (>1000 bar) and temperature (>200 °C) during the injection moulding process. It is well known that the temperature of the polymer melt in the screw ante-chamber is inhomogeneous, and for that reason the sensor system must be able to measure the temperature spatially resolved. Due to the fact that sound velocity is temperature dependent, we developed a non-invasive tomography system using the transit times of ultrasonic pulses along different sound paths for calculating the temperature distribution in a polymer melt. Simulation results and example experiments at a test measurement setup are shown. Moreover, different strategies for the ultrasonic probe design (buffer rods, generation of wide beam angle) are discussed. The results of the proposed system are important for the validation of numerical simulations, a better understanding of the plasticizing process and can be used for the input of a novel temperature control system.

Modeling of axial vibrational control technique for CdTe VGF crystal growth under controlled cadmium partial pressure

A VGF growth setup assisted by axial vibrations of baffle submerged into CdTe melt with controlled Cd partial pressure was designed. An influence of baffle shape on flow velocity map, temperature distribution in CdTe melt and interface shape of growing crystal was analyzed by numerical simulation and physical modeling. To produce the desirable shape of crystal melt interface we slant under different angles vertical generatrix in a cylindrical disk and made chasing on faceplates of a disk. It was ascertained that a disk with conical generatrix formed more intensive convective flows from a faceplate with larger diameter. It was shown that at CdTe VGF crystal growth rate about 10mm/h application of AVC technique made it possible to produce convex interface for 2in. crystal diameter.

D215 GaAs単結晶成長に及ぼす融液流動および温度分布の影響(OS-2:複合対流)

2D computer simulation assists in the decision of growth parameters to reduce the crystal defects of GaAs crystal in liquid encapsulated Czochralski (LEC) method. In this paper, we numerically investigated the reason why the 450mm-long crystal has more crystal defects than the 350mm-long crystal by comparing heat exchange, temperature distribution and velocity vector in the source melt at several stage of the growth. The simulation results indicated that large heat release from crystal and small heat release from crucible bottom are advantageous to the crystal growth with few defects. It is also necessary that forced convection and natural convection of GaAs melt is delicately controlled by the crucible rotation rate and the temperature distribution.

Influence of Marangoni convection on the flow pattern in the melt during growth of Y3Al5O12 single crystals by the Czochralski method

A melt flow taking place during growth of Y3Al5O12 crystals by the Czochralski method including the Marangoni convection is analyzed using a finite element method. The presence of even weak Marangoni convection strongly affects the flow pattern and temperature distribution in the YAG melt. A superposition of thermocapillary and buoyancy forces causes the interface to be 20% more convex towards the melt compared to that situation without Marangoni convection. This effect is more pronounced if the melt level is low. A quasi-planar interface is obtained by using higher rotation rates if Marangoni convection is not included in the analysis. However, the planar interface cannot be easily achieved even if small Marangoni convection is present; the interface is concave at the centre and convex at the edge of the crystal causing the whole interface to be wave-like in shape. Such shape of the interface indicates difficulties in determining a point of interface inversion.

Observation of Marangoni convection in a half-zone silicon melt

Marangoni flows in a half-zone silicon bridge under highly super-critical conditions are observed by using a X-ray radiography with Zirconium-core tracers. The flow structure changes from melting process of silicon to cylindrical half-zone. The tracer during the melting process fluctuated between positions separated by 90-degree azimuthal angles. The tracer in the cylindrical bridge tends to stay positions with 180-degree azimuthal angles. This observation is thought to reveal asymmetric temperature distribution in the silicon half-zone melt.

Numerical calculation of the crystal rotation effect on YBa2Cu3O7−x single crystal growth by the pulling method

A series of numerical calculations of convection were performed for the YBa2Cu3O7−x (Y123) single crystal growth by the modified pulling method (Solute Rich Liquid Crystal Pulling method; SRL-CP method). The finite-difference method was used to calculate the steady state of the axisymmetric two-dimensional incompressible viscous fluid system. The effect of the crystal rotation on the flow pattern and the temperature distribution in the melt was studied. An increase of the crystal diameter and/or the crystal rotation rate increased the strength of the forced convection in the melt, and as a result, the temperature at the crystal growth interface increased. These results were consistent with the experimental results.

Visualization of solidification process in kinetics control system with interferometry

The behavior of a solid-liquid interface and temperature distribution in the supercooled melt during solidification were observed. Salol, an organic material, was solidified in a temperature gradient environment, where the process was controlled by both kinetics and diffusion. The thickness of the temperature-reversed layer in front of the interface was measured by interferometry with the moire technique. It was found that as the interface advanced, the macroscopic roughness of the interface increased markedly in the flight experiment on a sounding rocket. Heat transfer during solidification was numerically calculated and was compared with experimental data.

Three-dimensional simulations of the Czochralski bulk flow in a stationary transverse field and in a vertical magnetic field: Effects on the asymmetry of the flow and temperature distribution in the Si melt

The quantitative difference between the influence of a stationary transverse field and a vertical magnetic field on the flow and temperature distribution in the Si melt was studied by means of numerical simulations in a three-dimensional mathematical model of the Czochralski crystal growth. The flow and temperature distribution were forced to be asymmetric due to an asymmetric temperature boundary condition at the crucible wall. It was found that the vertical magnetic field decreases the asymmetry in the system, especially in the vicinity of the growth interface, more intensely than the stationary transverrse managnetic field. Besides, it was also shown that both magnetic fields damp out the flow and temperature oscillations in the model.

The temperature distribution in a simulated garnet Czochralski melt

An open cylindrical container of water with an aspect ratio of 1.3 was heated from the side while the temperature of the bottom of the vessel was controlled independently. It was found that when the temperature of the bottom surface is below that of the side, the liquid divides itself into three regions, an upper region which is thoroughly mixed by convection and is essentially uniform in temperature; a thin surface layer; and a bottom region in which there is no mixing, whose height is controlled by the bottom surface temperature. The temperature in this region increases from the vessel bottom to the mixed region boundary. Changes in the bottom temperature have only a slight effect on the mixed region temperature. As the total liquid level is reduced, the mixed region temperature and the thickness of the bottom or stagnant region both decrease until the mixed region disappears and only the stagnant and thin surface layers remain. These results can be used to help explain the behavior of garnet melts.

Temperature distribution in melt and crystal during crystal growth by the kyropoulos method

Temperature distribution in melt and crystal during crystal growth by the kyropoulos method

Semiconductor sheets for the manufacture of semiconductor devices

The temperature distribution in a supercooled melt is qualitatively described. Properly shaped heat shields are shown to overcome parasitic wall growth and thermal shock, besides being an additional means of controlling thermal conditions. Using such a setup, it is possible to grow material in continuous sheets with a wide range of physical dimensions. The sheets are single crystals, dislocation-free, and have excellent surfaces.