Numerical Study on Flow Field and Temperature Distribution in Growth Process of 200 mm Czochralski Silicon Crystals

The melt flow and temperature distribution in a 200 mm silicon Czochralski furnace with a cusp magnetic field was modeled and simulated by using a finite-volume based FLUTRAPP ( Fluid Flow and Transport Phenomena Program) code. The melt flow in the crucible was focused, which is a result of the competition of buoyancy, the centrifugal forces caused by the rotations of the crucible and crystal, the thermocapillary force on the free surfaces and the Lorentz force induced by the cusp magnetic field. The zonal method for radiative heat transfer was used in the growth chamber, which was confined by the crystal surface, melt surface, crucible, heat shield, and pull chamber. It was found that the cusp magnetic field could strength the dominant counter-rotating swirling flow cell in the crucible and reduce the flow oscillation and the pulling-rate fluctuation. The fluctuation of dopant and oxygen concentration in the growing crystal could thus be smoothed.

3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Effects of Thermocapillary Convection on the Growth Process in Industrial 8-inch Silicon Czochralski Growth

Czochralski (CZ) crystal growth process is a widely used technique in manufacturing of silicon crystals and other semiconductor materials. The ultimate goal of the IC industry is to have the highest quality substrates, which are free of point defect, impurities and micro defect clusters. The scale up of silicon wafer size from 200 mm to 300 mm requires large crucible size and more heat power. Transport phenomena in crystal growth processes are quite complex due to melt and gas flows that may be oscillatory and/or turbulent, coupled convection and radiation, impurities and dopant distributions, unsteady kinetics of the growth process, melt crystal interface dynamics, free surface and meniscus, stoichiometry in the case of compound materials. A global model has been developed to simulate the temperature distribution and melt flow in an 8-inch system. The present program features the fluid convection, magnetohydrodynamics, and radiation models. A multi-zone method is used to divide the Cz system into different zones, e.g., the melt, the crystal and the hot zone. For calculation of temperature distribution, the whole system inside the stainless chamber is considered. For the convective flow, only the melt is considered. The widely used zonal method divides the surface of the radiation enclosure into a number of zones, which has a uniform distribution of temperature, radiative properties and composition. The integro-differential equations for the radiative heat transfer are solved using the matrix inversion technique. The zonal method for radiative heat transfer is used in the growth chamber, which is confined by crystal surface, melt surface, heat shield, and pull chamber. Free surface and crystal/melt interface are tracked using adaptive grid generation. The competition between the thermocapillary convection induced by non-uniform temperature distributions on the free surface and the forced convection by the rotation of the crystal determines the interface shape, dopant distribution, and striation pattern. The temperature gradients on the free surface are influenced by the effects of the thermocapillary force on the free surface and the rotation of the crystal and the crucible.

Gamma-ray induced color centers in Yb : YAG crystals grown by Czochralski method

20 at.% Yb:YAG single crystals have been grown by the CZ method and gamma-ray irradiation induced color centers and valence change of Fe3+ and Yb3+ ions in Yb:YAG have been studied. One significant 255 nm absorption band was observed in as-grown crystals and was attributed to Fe3+ ions. Two additional absorption (AA) bands located at 255 nm and 345 nm, respectively, were produced after gamma irradiation. The changes in the AA spectra after gamma irradiation and air annealing are mainly related to the charge exchange of the Fe3+, Fe2+, oxygen vacancies and F-type color centers. Analysis shows that the broad AA band is associated with Fe2+ ions and F-type color centers. The transition Yb3+ Yb2+ takes place as an effect of recharging of one of the Yb3+ ions from a pair in the process of gamma irradiation. (C) 2006 Elsevier Ltd. All rights reserved.

gamma-LiAlO2 single crystal grown by Czochralski technique and modified by vapor transport equilibration (VTE) technique

Large-sized (similar to 2 inch, 50.8 mm) gamma-UA102 single crystal has been grown by conventional Czochralski (Cz) method, but the crystal ha's a milky, dendriform center. The samples taken from transparent and milky parts were ground and examined by X-ray diffraction. All diffraction peaks could be indexed in gamma-LiAlO2. The crystal quality was characterized by X-ray rocking curve. The full-width at half-maximum (FWHM) values are 116.9 and 132.0 arcsec for transparent and milky parts, respectively. The vapor transport equilibrium (VTE) technique was introduced to modify the crystal quality. After 1000 degrees C/48 h, 1100 degrees C/48 h, 1200 degrees C/48 h VTE processes, the FWHM values dropped to 44.2 and 55.2 arcsec for transparent and milky part, respectively. The optical transmission of transparent part was greatly enhanced from 85% to 90%, and transmission of milky part from 75% to 80% in the range of 190 similar to 1900 nm at room temperature. When the VTE temperature was raised to 1300 degrees C, the sample cracked and FWHM values of transparent and milky parts were increased to 55.2 and 80.9 arcsec, respectively. By combining Cz technique with VTE technique, large-sized and high quality gamma-LiAlO2 crystal can be obtained.

Czochralski growth and crystal structure of cerium-doped Lu2Si2O7 scintillator

Cerium-doped lutetium pyrosilicate crystal, Ce:Lu2Si2O7 (Ce:LPS), was grown by the Czochralski method. The segregation coefficient of Ce3+ ion was studied by the ICP-AES method. X-ray diffraction analysis showed that the structure of Ce:LPS crystal was monoclinic symmetry with space group of C2/m. Perfect cleavage planes (110) and imperfect cleavage planes (001) were observed by optical microscope. The reasons why it is difficult to grow crack-free crystals were studied. After optimized growth parameters, a Ce:LPS crystal with dimension of Phi 25 x 30 mm was grown, which is colorless, high optical quality, cracking-free and no inclusions. The transmittance of Ce:LPS crystal from 380 to 800 nm is over 82% and there is no observable absorption. (c) 2005 Elsevier B.V. All rights reserved.

Defect analysis in Czochralski-grown Yb : FAP crystal

Growth-induced defects in Yb:FAP crystals grown by the Czochralski method have been investigated by optical microscopy, chemical etching, scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS). Anisotropic etching features have been observed on two FAP crystal planes: (0001) and (1010). The shape of etch pits on the (0001) plane is hexagonal, while the etch pits on the (1010) plane have a variety of irregular shapes. It is also found that the density of etch pit varies along the boule. Based on the experimental observations, the formation mechanisnis of growth defects are discussed, and methods for reducing the growth-induced defect concentration is proposed. (c) 2005 Elsevier B.V. All rights reserved.

Effects and numerical analysis of argon gas flow on the oxygen concentration in Czochralski silicon single crystal growth

Argon gas, as a protective environment and carrier of latent heat, has an important effect on the temperature distribution in crystals and melts. Numeric simulation is a potent tool for solving engineering problems. In this paper, the relationship between argon gas flow and oxygen concentration in silicon crystals was studied systematically. A flowing stream of argon gas is described by numeric simulation for the first time. Therefore, the results of experiments can be explained, and the optimum argon flow with the lowest oxygen concentration can be achieved. (C) 2002 Elsevier Science B.V. All rights reserved.

Compensation ratio-dependent concentration of a VInH4 complex in n-type liquid encapsulated Czochralski InP

The concentration of hydroen-indium vacancy complex VInH4 in liquid encapsulated Czochralski undoped and Fe-doped n-type InP has been studied by low-temperature infrared absorption spectroscopy. The VInH4 complex is found to be a dominant intrinsic shallow donor defect with concentrations up to similar to 10(16) cm(-3) in as-grown liquid encapsulated Czochralski InP. The concentration of the VInH4 complex is found to increase with the compensation ratio in good agreement with the proposed defect formation model of Walukiewicz [W. Walukiewicz, Phys. Rev. B 37, 4760 (1998); Appl. Phys. Lett. 54, 2094 (1989)], which predicts a Fermi-level-dependent concentration of amphoteric defects. (C) 1998 American Institute of Physics, [S0003-6951(98)04435-0].

Void-like defects in annealed Czochralski silicon

Void-like defects of octahedron structure having {111} facets were observed in annealed Czochralski silicon. The amorphous coverage of SiOx and SiCx on the inner surface of the defects was identified using transmission electron microscopy and electron energy-loss spectroscopy. It is suggested that these defects are a kind of amorphous precipitate origin. A mechanism for the generation of these defects and the previously reported solid amorphous precipitates is proposed. (C) 1998 American Institute of Physics. [S0003-6951(98)02842-3].