A Czochralski crystal puller automated by the weighing method

The automated crystal growing equipment makes use of a commercial electronic balance equipped with a microprocessor. The mode of operation is explained and experiences got on the occasion of crystal growth experiments are presented.     

A novel method of temperature control for a crystal growth puller

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.     

Investigations of the crystal growth of PbMoO4 by the Czochralski method

The thermal conditions at the liquid/solid interface are characterized by temperature measurements in the melt and on the growing crystal with 〈001〉-seed orientation. The thermal boundary layer was determined, from which the relation of effective thermal conductivity of the liquid and solid phase was found to be λ_l,eff/λ_s,eff = 0.25. The liquid/solid interface is extremly convex towards the melt and has a conical shape. When the crystal diameter reaches a certain value the cone was truncated with the formation of a facet in the centre. This typical interface shape is mainly the result of a difference between the effective thermal conductivity of melt and crystal.     

Algorithm for crystal-profile control in automated crystal growth by the Czochralski method

Growth setups of the new generation should provide crystal growth in the automated mode. One of the necessary conditions for growing quality crystals is the rigorous maintenance of the given boule profile. In the systems with weight control, the model weight is compared with the weight measured by the weight sensor. Below, we describe an algorithm for calculating the model weight based on the numerical solution of the Bardsley equation. The algorithm allows one to set the crystal profile either by a function or a point set.     

Dopant concentration profile in a Czochralski flow of liquid metal in a vertical or a horizontal magnetic field

Dopant concentration profiles are obtained for a Czochralski flow of liquid metal in a static crucible under either an axisymmetric vertical magnetic field or a horizontal uniform magnetic field. The latter magnetic field inevitably requires fully three-dimensional cylindrical coordinate model equations, which are successfully solved for the representative parameters Gr = 10⁷, Pr = 0.01, Re = 1620 and Ha 1000. Asymmetric concentration profiles are obtained. The average heat flux decreased with the Hartmann number. The circumferential rotational direction was found to be reversed in a lower regime against that of a top rotating crystal rod in a strong lateral magnetic field. In a vertical magnetic field, the concentration profile approached the pure diffusion state.     

Growth of Na modified potassium lithium niobate crystal by the Czochralski method

Transparent Na modified potassium lithium niobate (Na_0.23K_2.60Li_1.82Nb_5.35O_15.70; NKLN) crystal was successively grown by the Czochralski method using RF induction heating from melt composition Na₂O:K₂O : Li₂O:Nb₂O₅=2:30:25:43 mol%. NKLN crystal showed a tetragonal tungsten bronze structure with lattice constants a=12.5446±0.0010 Å and c=4.0129±0.0005 Å at room temperature. The dielectric constant along the c-axis ε₃₃ showed a sharp maximum around 480 °C. Optical transmission edge was 370 nm and optical transmission spectra showed no absorption at wavelengths ranging from 380 to 800 nm. The structural and optical properties of NKLN were similar to those of the near stoichiometric KLN crystals. We believe that the growth of NKLN by the Czochralski method has an advantage for a large size and high-quality crystal.     

Three dimensional simulation of melt flow in Czochralski crystal growth with steady magnetic fields

Three-dimensional transient numerical simulations were carried out to investigate the melt convection and temperature fluctuations within an industrial Czochralski crucible. To study the magnetic damping effects on the growth process, a vertical magnetic field and a cusp magnetic field were considered. Due to our special interest in the melt convection, only local simulation was conducted. The melt flow was calculated by large-eddy simulation (LES) and the magnetic forces were implemented in the CFD code by solving a set of user-defined scalar (UDS) functions. In the absence of magnetic fields, the numerical results show that the buoyant plumes rise from the crucible to the free surface and the crystal–melt interface, which indicates that the heat and mass transfer phenomena in Si melt can be characterized by the turbulent flow patterns. In the presence of a vertical magnetic field, the temperature fluctuations in the melt are significantly damped, with the buoyant plumes forming regular cylindrical geometries. The cusp magnetic field could also markedly reduce the temperature fluctuations, but the buoyant plumes would break into smaller vortical structures, which gather around the crystal as well as in the center of the crucible bottom. With the present crucible configurations, it is found that the vertical magnetic field with an intensity of 128 mT can damp the temperature fluctuations more effectively than the 40 mT cusp magnetic field, especially in the region near the growing crystal.     

Growth of large dimension BaWO4 crystal by the Czochralski method

In this paper, polycrystalline materials of BaWO₄ were synthesized by solid-state phase method, and a single crystal of BaWO₄ was successfully grown along a and c-axis direction by using the Czochralski method. Up to 20×22×80 mm³ BaWO₄ crystal was obtained, and X-ray powder diffraction results show that the as-grown BaWO₄ crystal belongs to the scheelite structure. The effective segregation coefficients of Ba and W of the BaWO₄ crystal were measured by the X-ray fluorescence method, and the effective segregation coefficients of Ba and W were near 1. The rocking curve from (2 0 0) diffraction plane of as-grown BaWO₄ single crystal was measured on the High-resolution X-ray diffractometer D5005, and the full-width at half-maximum value was found to be 26.64′′ The density and hardness of the BaWO₄ crystal was measured, the measured density was in agreement with the calculated result, and the Mohs hardness was about 4.     

Stresses near the solid-liquid interface during the growth of a Czochralski crystal

Numerical and analytical techniques are used in order to calculate the thermal stresses near the solid-liquid interface during the growth of a crystal by the Czochralski method. We first assume the crystal to be elastically isotropic, and then we discuss the case of elastic anisotropy. We establish the conditions for the achievement of steady state near the solid-liquid interface and then we show the effect of high temperature inelastic deformation by explicitly accounting for the relaxation of the stresses by creep asymptotically close to the center of the solid-liquid interface.     

Application of rotating magnetic fields in Czochralski crystal growth

The physical principles of electromagnetic stirring with a rotating magnetic field are explained and a mathematical model to calculate the electromagnetic volume force, the fluid flow and the transport of heat and solutes is outlined. For the electromagnetic volume force and for the order of magnitude of the flow velocities approximative analytical expressions are given. A high flexibility in configuring the volume force in order to achieve a desired flow distribution is obtained by multi-frequency stirring that is by superposition of two or several magnetic fields with different frequencies and/or sense of rotation. Results of experimental investigation and mathematical simulation of multi-frequency stirring are given. Numerical simulation of the fluid flow, the temperature and the oxygen distribution in a Czochralski process crucible was performed including the effect of single mode and multi-frequency stirring. The results indicate that electromagnetic stirring should offer large potentials for the optimization of the flow configuration in a Czochralski process crucible. Finally examples from literature of practical application of rotating magnetic fields in crystal growth are presented.     

Control of diameter in Czochralski and related crystal growth techniques

The various published methods for the automatic control of the diameter of crystals growing by the Czochralski technique are critically reviewed. The form of the meniscus in Czochralski growth is described and it is argued that the most successful servo-control techniques are those which sense changes in meniscus shape rather than changes in diameter only.     

Large eddy simulation of Marangoni convection in Czochralski crystal growth

Large eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global simulation of a Czochralski furnace for silicon crystal growth against the assumed thermophysical properties

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite‐element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the flow velocity,supersaturation and temperature on the crystal growth from solutions

This paper is a review of our experimental research on the influence of the supersaturation, flow velocity and temperature on the linear crystallization rate of different faces of model crystal systems. The obtained experimental results are discussed in the light of the new theoretical treatments on crystal growth from low temperature solutions.     

Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and seed crystal. At first, the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF‐coil was calculated. Using this heat generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed‐melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of the eddy current sensing of gallium arsenide Czochralski crystal growth

The feasibility of eddy current sensing of (1) the melt surface position and (2) the liquid-solid interface shape of 3-inch gallium arsenide crystals being grown by the Czochralski technique has been investigated using an axisymmetric finite element method. The results show clearly that differential sensor designs operating at high frequency ( ≈ 1 MHz) are very sensitive to the distance between the sensor and the surface of the melt providing the opportunity to precisely monitor and control this important variable of the growth process. The calculations also show a weaker effect of interface shape upon the imaginary impedance component at lower frequencies (1–10 kHz). Its physical basis is due to the different skin depths of solid and liquid GaAs. We show that a sensor's response to this interface effect can be enhanced by appropriate design of the differential sensor's pick-up coils.     

Dislocations of salol crystals grown by the Czochralski method

Crystals of salol were grown by the Czochralski method in three different pulling directions to examine the crystallographic orientation effect of the seed. They were characterized by the etch pit method and X-ray projection topography. It was found that the dislocation density was 2 × 10³−1 × 10⁴/cm² and that the configuration of dislocations was straight. The running directions of dislocations strongly depend on the pulling directions; i.e., [11 0] and [1 10] for the crystal grown in [100] axis, [11 0], [1 10] and [110] for the crystal pulled along [112] axis and [010] for [010] axis crystal.     

Global simulation of coupled carbon and oxygen transport in a Czochralski furnace for silicon crystal growth

For accurate prediction of carbon and oxygen impurities in a single crystal produced by the Czochralski method, global simulation of coupled oxygen and carbon transport in the whole furnace was implemented. Both gas-phase transportation and liquid-phase transportation of oxygen and carbon were considered. With five chemical reactions considered, SiO and CO concentrations in gas and C and O atom concentrations in silicon melt were solved simultaneously. The simulation results show good agreement with experimental data.     

Growth of KCl crystal by Czochralski method and influence of nanodiamond impurity on its hardness and optical properties

KCl alkali halide crystal with different nanodiamond impurity was grown by Czochralski method. X‐Ray diffraction of the outcome samples reveals that they are still single crystal. Also crystal hardness observation reveals that the hardness of KCl single crystal has been increased by adding different percentage of nanodiamond impurity. In addition, the study of FTIR spectrums of the pure and doped crystals represents that the KCl optical properties has not changed.