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.     

Axial macrosegregation in Ga‐doped germanium grown by the vertical gradient freeze technique with a rotating magnetic field

The impact of a rotating magnetic field (RMF) on the axial segregation in Vertical Gradient Freeze (VGF) grown, Ga doped germanium is investigated. Growth experiments were performed using the VGF‐RMF as well as the conventional VGF technique. Carrier concentration profiles characterising the Ga segregation were measured by the Spreading Resistance method and calibrated using Hall values of carrier concentration and mobility. The Ga concentration rises more gradually under RMF action, i.e., the dopant segregation is significantly reduced by the rotating field. This effect is attributed to a better mixing of the melt. Numerical results on the flow velocity confirm this explanation. The RMF induced flow is much more intense than the natural buoyant convection due to the radial temperature gradient and leads to a pronounced decrease of the effective partition coefficient k_eff. In the early stages of growth a k_eff value close to k₀ was obtained, i.e., the gallium was almost homogeneously distributed within the melt. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of the isothermal melt flow due to rotating magnetic fields in crystal growth

The use of a rotating magnetic field promises the feature of a contactless flow control in crystal growth especially for configurations where an increase of the material transport in a definite way is desired. This paper gives the comparison of numerically calculated and experimentally obtained results on the flow due to a rotating magnetic field as well as numerical results on the influence of the field parameters (frequency, amplitude) on the fluid flow in the melt.     

Silicon transport under rotating and combined magnetic fields in liquid phase diffusion growth of SiGe

The effect of applied rotating and combined (rotating and static) magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. 72‐hour growth periods produced some single crystal sections. Single and polycrystalline sections of the processed samples were examined for silicon composition. Results show that the application of a rotating magnetic field enhances silicon transport in the melt. It also has a slight positive effect on flattening the initial growth interface. For comparison, growth experiments were also conducted under combined (rotating and static) magnetic fields. The processed samples revealed that the addition of static field altered the thermal characteristics of the system significantly and led to a complete melt back of the germanium seed. Silicon transport in the melt was also enhanced under combined fields compared with experiments with no magnetic field. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of system parameters on MHD flows in rotating magnetic fields

A numerical study is presented of the electromagnetic and hydrodynamic field distributions induced by rotating magnetic fields in a conducting fluid contained in a cylindrical vessel with insulated and conducting walls and ends. Simulations are carried out to determine the effect of various rotating electromagnetic field configuration parameters on magnetohydrodynamic melt flow structure and velocity distributions. Results show that the flow motion consists of the primary azimuthal and secondary meridional flows and that the detailed pattern of these flows changes with the system parameters such as the electric conductivities of the container and the liquids, and the relative positions of the inductor and melts. It is found that the basic structure of the melt velocity distribution is not affected noticeably by the distribution of electromagnetic forces in the case of symmetric distribution, but it changes significantly if this symmetry breaks.     

Crystal growth of rare-earth orthovanadate (RVO4) by the floating-zone method

Single crystals of rare-earth orthovanadate, RVO₄ where R=Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, with the cross-sectional size of about 7×7 mm² and 20–50 mm length have been successfully grown by the floating-zone method. Fluorescence properties at room temperature and dielectric and elastic properties along the c-axis of some grown crystals have been reported.     

Crystal growth by the travelling heater method using tapered crucibles and applied rotating magnetic field

Crystal growth experiments were carried out by the Travelling Heater Method using tapered growth ampoules with and without the application of a rotating magnetic field. The objective was to enhance its commercial potential by reducing the size of required seed crystals and increasing the growth rate. To this end, a number of GaSb crystals were grown using either 25 mm diameter straight, or 10 mm to 25 mm tapered growth ampoules. Growth rates of 2 mm/day and 5 mm/day were employed. The effect of rotating magnetic fields of several strengths and frequencies was examined. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport properties of amorphous germanium prepared by the glow discharge technique

The paper deals with conductivity, thermoelectric power and field effect measurements on amorphous Ge specimens prepared by the decomposition of germane gas in a rf glow discharge. Substrate temperatures T_d of 300, 400 and 500 K were used during deposition. The sign of the thermoelectric power S is negative throughout the temperature range investigated (200–500 K). Above 300 K, the conductivity activation energy in specimens prepared at T_d = 500 K lies between 0.40 and 0.43 eV; it is equal to the gradient of the S versus 1/T curves, suggesting transport in the extended electron states. Below room temperature there is an increasing contribution in all specimens from electron hopping transport in localized states lying about 0.25 eV below ?_C. Both conductivity and thermoelectric power results can be interpreted satisfactorily in terms of these two current paths. Hopping at the Fermi level has not been observed. The preliminary field effect measurements indicate that, as in amorphous Si, ?_f lies near a density of state minimum. The density of states at ?_f is appreciably higher than that in similarly prepared Si specimens.     

Mechanism of macrostep formation in solution growth of compound semiconductor and the evidence given by space experiment

The behavior of macrostep and its formation mechanism are discussed taking solution growth of compound semiconductor as an example. The macrosteps are created by the bunching of atomic steps on a misoriented substrate and they coalesce to form larger macrosteps. At a steady state, the vertical growth of the macrostep terrace is carried out by the atomic steps supplied from a screw dislocation. Space experiments conducted by the group of Professor K. W. Benz showed that the macrostep disappears under a temperature gradient when the growth rate is decreased below a certain value. It is concluded that the non‐uniform bulk diffusion of the solute is the driving force to create the macrostep.     

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.     

Determination of kinetic parameters of crystal growth rate of borax in aqueous solution by using the rotating disc technique

Growth rate of polycrystalline disc of borax compressed at different pressure and rotated at various speed has been measured in a rotating disc crystallizer under well-defined conditions of supersaturation. It was found that the mass transfer coefficient, K, increased while overall growth rate constant, K_g, and surface reaction constant, k_r, decreased with increasing smoothness of the disc. It was also determined that kinetic parameters (k_r,r,K,g) of crystal growth rate of borax decreased with increasing rotating speed of the polycrystalline disc. The effectiveness factor was calculated from the growth rate data to evaluate the relative magnitude of the steps in series bulk diffusion through the mass transfer boundary layer and the surface integration. At low rotating speed of disc, the crystal growth rate of borax is mainly controlled by integration. However, both diffusion and integration steps affect the growth rate of borax at higher rotating speed of polycrystalline disc.     

Heteroepitaxial growth of ZnS on GaP by the close-spaced technique

Heteroepitaxial growth of ZnS on GaP substrates was achieved with high growth rate by the close-spaced technique. Source temperatures were between 900 and 1150° C. The apparent enthalpy change of 36.6 kcal/mol obtained from the temperature dependence of the evaporation rate of source ZnS powder suggests that the material transport is carried out via the reaction between the source and hydrogen by diffusion and convection. The dependence of the growth rate on the substrate orientation is (100) > (111)Ga > (111)P, and the growth rates on these faces at a source temperature of 1000° C are about 1.6, 0.85, and 0.4 μm/min, respectively. The growth kinetics on the (111)Ga face are close to the mass transport limited case. The growth kinetics on the (111)P face are close to the surface reaction limited case, and that on the (100) face are almost the mass transport limited case. The surface morphology and X-ray analysis show that the crystal structure depends on the orientation of the substrate. The (0001) oriented α (hexagonal) modification of ZnS is obtained on the (111)Ga face, the (111) oriented β (cubic) modification on the (111)P face, and the (100) oriented β modification on the (100) face in the studied range of temperature.     

Crystalline growth of germanium thin films on single crystal silicon substrates by solid phase crystallization

We have studied the epitaxial-like growth of germanium (Ge), due to solid phase crystallization (SPC) from amorphous Ge (a-Ge) deposited on single crystal silicon (Si) substrate. The crystalline growth of Ge following the orientation of Si substrates was successfully obtained by the SPC at 400 °C or higher. The preferential growth on Si (111) substrates continues up to 10,000 Å. Different orientations from the substrate orientation in XRD patterns are slightly observed in the growth on Si (100) substrates at 450 °C, but the preferential growth of (100) orientation continued in the whole film thickness in TEM images. The epitaxial-like growth of Ge may be more preferable on the Si (111) substrate than the (100) one.     

Shaped crystal growth of PbTe by the open tube technique

The possibility of growing shaped A^IVB^VI crystals from the vapour phase by the open tube technique was investigated on PbTe. The thermodynamic conditions to reproducible prepare several habits of PbTe crystals — whiskers, tetrahedral prisms and cubes, platelets (a), dendrites, cubic and octahedral skeletons (b) as well as their properties were examined. The crystalline habits (a) are characterized by perfectly mirror-like (100) surfaces and low dislocation densities. The type and concentration of charge carriers are mainly determined by the vapour composition within the crystallization zone and very from n = 3 × 10¹⁷ to p = 1 × 10¹⁹cm⁻³. These properties are the reason of the interest in shaped PbTe crystals for the aim of IR optoelectronic devices.     

Direct observation and numerical simulation of molten silicon flow during crystal growth under magnetic fields by x-ray radiography and large-scale computation

Control of melt flow during Czochralski (CZ) crystal growth by application of magnetic fields is an important technique for large-diameter (>300 mm) silicon single crystals. Melt convection under magnetic fields is an interesting problem for electromagnetic-hydrodynamics. This paper reviews the effects of a vertical magnetic field and a cusp-shaped magnetic field on melt flow during CZ crystal growth. Melt flow in vertical magnetic fields or cusp-shaped magnetic fields was investigated by the direct observation method based on X-ray radiography and by numerical simulation. The first part of this review shows the result of direct observation of molten silicon flow under magnetic fields. It also compares the results of experimental and numerical simulation. The second part shows the details of the numerical simulation of the behavior of molten silicon in magnetic fields.     

Crystal growth from the vapour phase: Confrontation of theory with experiment

Starting with the BCF theory recent crystal growth models based on computer simulations are discussed. These models are confronted with experiments for growth from the vapour concerning rates of growth and the direct observations of step patterns, growth spirals and etch pits.     

Levitation of metallic melt by using the simultaneous imposition of the alternating and the static magnetic fields

This study developed a new levitation method, which used the simultaneous imposition of static and alternating magnetic fields. Dynamic behavior was measured for pure Cu and pure Ni melts levitated by the proposed method. The oscillation due to surface tension and convection in levitated Cu melts were hardly observed at static magnetic fields exceeding 1 T. Only the rotation of this axis parallel to the static magnetic field was observed under high static magnetic fields. The proposed method demonstrated that metallic melt could be statically levitated like a solid sphere. It was also found that stable levitation of paramagnetic Ni melt was rather difficult at static magnetic fields exceeding 5 T, because of the magnetization force.     

Epitaxial growth of magnetic semiconductor EuO on silicon by molecular beam epitaxy

Functional oxides demonstrate a wide range of magnetic, optical and transport properties. Their integration with silicon promises significant advances in electronics. An important key in enabling brand‐new oxide technologies is the utilization of silicon/oxide epitaxy, thus making quality of the interface a critical issue. The progress depends on our ability to avoid formation of impurity phases at the interface and to tackle structural mismatch of the oxide and Si. We design a novel chemical protection of Si (001) surface on the submonolayer scale based on the surface metal silicide with the (1×5) reconstruction. This new technique is applied to the long‐standing problem of integration of a ferromagnetic semiconductor with Si. Direct epitaxial growth of EuO on Si without any buffer layer, so far inaccessible, is achieved by molecular beam epitaxy. The nucleation step, comprising first 10 monolayers of EuO, is followed by a distillation‐controlled growth. An alternative to standard capping procedures for EuO, based on controlled formation of an amorphous Eu₂O₃ layer, is devised. Crystal perfection of the films is established ex situ by x‐ray diffraction and Rutherford backscattering. Magnetic properties of the EuO films match those of the bulk.