Modulating dopant segregation in floating-zone silicon growth in magnetic fields using rotation

The feasibility of modulating dopant segregation using rotation for floating-zone silicon growth in axisymmetric magnetic fields is investigated through computer simulation. In the model, heat and mass transfer, fluid flow, magnetic fields, melt/solid interfaces, and the free surface are solved globally by a robust finte-volume/Newton's method. Different rotation modes, single- and counter-rotations, are applied to the growth under both axial and cusp magnetic fields. Under the magnetic fields, it is observed that dopant mixing is poor in the quiescent core region of the molten zone, and the weak convection there is responsible for the segregation. Under an axial magnetic field, moderate counter-rotation or crystal rotation improves dopant uniformity. However, excess counter-rotation or feed rotation alone results in more complicated flow structures, and thus induces larger radial segregation. For the cusp fields, rotation can enhance more easily the dopant mixing in the core melt and thus improve dopant uniformity.     

System of Mathematical Models for the Analysis of Industrial FZ-Si-Crystal Growth Processes

A system of coupled mathematical models and the corresponding program package is developed to study the interface shape, heat transfer, thermal stresses, fluid flow as well as the transient dopant segregation in the floating zone (FZ) growth of large silicon crystals (diameter more than 100mm) grown by the needle-eye technique. The floating zone method with needle-eye technique is used to produce high-purity silicon single crystals for semiconductor devices to overcome the problems resulting from the use of crucibles. The high frequency electric current induced by the pancake induction coil, the temperature gradients and the feed/crystal rotation determine the free surface shape of the molten zone and cause the fluid motion. The quality of the growing crystal depends on the shape of the growth interface, the temperature gradients and corresponding thermal stresses in the single crystal, the fluid flow, and especially on the dopant segregation near the growth interface. From the calculated transient dopant concentration fields in the molten zone the macroscopic and microscopic resistivity distribution in the single crystal is derived. The numerical results of the resistivity distributions are compared with the resistivity distributions measured in the grown crystal.     

Rotating magnetic fields: Fluid flow and crystal growth applications

Rotating or alternating magnetic fields are widely used in the industrial steel casting process or in metallurgical manufacturing. For the growth of single crystals, these techniques attracted a rapidly increasing attention within the last years: a well defined melt flow leads to a more homogeneous temperature and concentration distribution in the melt and consequently improves the growth process. Rotating magnetic fields (RMF) might be used instead of crucible and/or crystal rotation avoiding mechanically induced disturbances or might be added to conventional rotation mechanisms to gain a further flow control parameter. Compared to static magnetic fields, rotating ones are distinguished by a much lower energy consumption and technical effort. Furthermore, there are no reports on detrimental effects such as the generation of thermoelectromagnetic convection or coring effects in the grown crystals. One advantage of rotating magnetic fields is the possibility to apply them even to melts with a rather low electrical conductivity like e.g. aqueous solutions. High flow velocities are already generated with moderate fields. Therefore the field strength has to be adjusted with care because otherwise undesirable Taylor vortices might be induced. In the last years, the potential of rotating magnetic fields for crystal growth processes was demonstrated for model arrangements using e.g. gallium or mercury as a test liquid as well as for a variety of growth techniques like Float Zone, Czochralski, Bridgman, or Travelling Heater Methods: Fluctuations of the heat transport due to time-dependent natural convection have could be reduced by more than an order of magnitude or the mass transport could be improved with respect to the a better radial symmetry and/or a more homogeneous microscopic segregation.     

Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method

A vertical gradient freeze apparatus was set up to investigate the influence of a vertical magnetc field on Te dopant segregation in InSb. Te-doped InSb crystals were grown in the presence and absence of an 80.0 kG magnetic field. The axial profile of the Te concentration in the crystal grown in the magnetic field was observed to be more uniform than that grown without magnetic field, which was attributed to the influence of the high magnetic field on Te dopant segregation by reducing convection in the melt.     

Dopant transport during semiconductor crystal growth: Axial versus transverse magnetic fields

The present study investigates the effects of magnetic field orientation, magnetic field strength and growth rate on the dopant segregation in semiconductor crystals, and presents results of dopant composition in the crystal and in the melt at several different times during growth for several combinations of process parameters. The crystal's lateral segregation depends on the magnetic field's orientation and strength while the axial segregation depends on the magnetic field's strength and the growth rate. If either convective or diffusive transport truly dominates, then the crystal's dopant distribution is laterally uniform. The axial distribution in the crystal approaches the well-mixed limit if the melt motion is strong and the growth rate is slow, and the distribution approaches the diffusion-controlled limit if the melt motion is slow and the growth rate is fast. The deviations of the dopant distribution in the crystal from lateral uniformity and from the classical limits are quantified for several combinations of process parameters.     

Analysis of the dopant segregation effects at the floating zone growth of large silicon crystals

A computer simulation is carried out to study the dopant concentration fields in the molten zone and in the growing crystal for the floating zone (FZ) growth of large (> 100 mm) Si crystals with the needle-eye technique and with feed/crystal rotation. The mathematical model developed in the previous work is used to calculate the shape of the molten zone and the velocity field in the melt. The influence of melt convection on the dopant concentration field is considered. The significance of the rotation scheme of the feed rod and crystal on the dopant distribution is investigated. The calculated dopant concentration directly at the growth interface is used to determine the normalized lateral resistivity distribution in the single crystal. The calculated resistivity distributions are compared with lateral spreading resistivity measurements in the single crystal.     

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.     

Distribution coefficient of boron in Si crystal ingots grown in cusp-magnetic Czochralski process

Silicon single crystals are grown by the Czochralski method with various growing conditions. Effective segregation coefficient of boron is found to depend on the magnetic field in cusp-magnetic Cz method. Effects of zero-Gauss plane (ZGP), ZGP shape and magnetic intensity (MI) on the dopant concentration and its distribution in the crystal are experimentally investigated. The shape of ZGP is not only flat but also parabolic due to the magnetic ratio (MR), which is the ratio of the lower to upper electric-current densities in the configurations of the cusp-magnetic field. Equilibrium distribution coefficient of boron calculated by BPS model is 0.698. With the crystal rotation (w) of 16 rpm and the crucible rotation of ?0.5 rpm, the effective distribution coefficient (k_e) is 0.728 in zero magnetic intensity and increases up to 0.8093 in the parabolic ZGP shape. Although the magnetic strength near the crystal–melt interface decreases with increasing MR, it increases in the bulk melt, and hence k_e increases. Flow stability in the bulk melt influences k_e. At the magnetic field and growing conditions, k_e increases with increasing initial charge size of the silicon melt. There is no significant influence of ZGP on the radial distribution of the boron concentration. Simulation results of melt flow in the presence of a parabolic ZGP are outlined, and the segregation results in the experiments are compared with published experimental data.     

A review of radial segregation in crystal growth during microgravity

This review describes radial segregation results from crystal growth experiments in microgravity, together with their corresponding theoretical treatments. The paper is structured in terms of the different factors influencing radial segregation during crystal growth, such as: curved growth interfaces, variations in boundary layer thickness, weak convection, facets and magnetic fields.In a number of experiments considerably stronger radial segregation occurs in space than is normally observed on earth. The theoretical treatments lead to a sound understanding of all of the results. Possible ways to avoid the problem, such as the application of magnetic fields, are outlined.     

Effect of steady ampoule rotation on radial dopant segregation in vertical Bridgman growth of GaSe

For vertical Bridgman growth of the nonlinear optical material GaSe in an ampoule sufficiently long that flow and dopant transport are not significantly influenced by the upper free surface, we show computationally that steady rotation about the ampoule axis strongly affects the flow and radial solid-phase dopant segregation. Radial segregation depends strongly on both growth rate U and rotation rate Ω over the ranges 0.25 μms⁻¹U3.0 μms⁻¹ and 0Ω270 rpm. For each growth rate considered, the overall radial segregation passes through two local maxima as Ω increases, before ultimately decreasing at large Ω. Rotation has only modest effects on interface deflection. Radial segregation computed using a model with isotropic conductivity (one-third the trace of the conductivity tensor) predicts much less radial segregation than the “correct” model using the anisotropic conductivity, with the segregation decreasing monotonically with Ω. Consideration of a model in which centrifugal acceleration is deliberately omitted shows that, as Ω increases, diminution and ultimately disappearance of the “secondary” vortex lying immediately above the interface is due to centrifugal buoyancy, while axial distension of the larger “primary” vortex above is due to Coriolis effects. These results, which are qualitatively different from those accounting for centrifugal buoyancy, suggest that several earlier computational and analytical predictions of rotating vertical Bridgman growth are either limited to rotation rates sufficiently low that centrifugal buoyancy is unimportant, or are artifacts associated with its neglect. The overall radial segregation depends approximately linearly on the product of and the growth rate U for the conditions considered, where is the segregation coefficient.     

Convection in melts and impurity distribution in semiconductor crystals

Impurity distributions in semiconductor melts and crystals grown from these melts are experimentally and numerically studied on an example of Ga-doped Ge crystals. It is shown that inhomogeneous dopant distribution is observed in the form of striations and is caused by the convective flows in the melt and their nonstationary rearrangement in the vicinity of the crystallization front. The character of heat and mass transfer under the microgravity conditions is predicted. The necessity of precision experiments under terrestrial and, especially, space conditions is emphasized.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modification of Fluid Flow and Heat Transport in Vertical Bridgman Configurations by Rotating Magnetic Fields

Applying a rotating magnetic field to an electrically conducting liquid, a Lorentz force is induced which generates a melt rotation of a certain angular velocity. A cylindrical gallium melt (aspect ratio 2.5) has been used as a model liquid. The melt has been heated from the bottom (Ra = 10⁶) or from the top (Ra = −10⁶) and the resulting temperature fluctuations in the melt have been measured in dependence on the rotating field strength (B_max = 30 mT). In the case of the unstable gradient 0.8 mT are sufficient to dominate the buoyancy driven convection and to reduce the amplitude of the buoyancy caused temperature oscillations for more than one order of magnitude. At the same time, the fluctuation frequency increases with the field strength. In the case of the stabilizing temperature gradient, low amplitude/high frequency temperature fluctuations are generated by the rotating magnetic field, indicating the transition to a time-dependent flow. In both cases we see an increase of the convective heat transport for magnetic inductions higher than approximately 5 m T. Applying the rotating magnetic field to the Bridgman growth of gallium doped germanium, the same behavior can be seen: Growing with a top-seeded arrangement, the intensity of the dopant striations is decreased and their frequency is increased. Growing with a bottom-seeded arrangement, the interface curvature changes from concave to convex and the flow becomes time-dependent.     

Radial segregation due to weak convection in a floating zone

The influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystals grown under microgravity conditions is studied numerically. The geometry considered corresponds to a floating-zone configuration with partially coated melt surfaces consisting of small evenly distributed spots of free surfaces. In order to distinguish dopant distribution due to weak convection clearly from distribution due to diffusion the spots only cover one quarter of the periphery. Thus, surface tension-driven convection is allowed only over one quarter of the floating-zone configuration resulting in an asymmetric dopant distribution. The percentage of free surfaces present is varied in order to alter the Marangoni flow rates. The maximum dopant concentration due to radial segregation is plotted as a function of a certain convection level. The results of the present numerical study are supposed to be used to design corresponding space experiments launched at the end of the year 2000.     

Investigations of impurity striations in potassium bichromate crystals

Impurity striations in potassium bichromate crystals (KBC, lopezite) formed during crystal growth from aqueous solution were revealed by chemical etching and analyzed. Striations were revealed as etch grooves, as rows of dislocation etch pits and as rows of flat‐bottomed etch pits. Various types and groups of striations have been visualized. Some striations were due to lateral segregation of impurities caused by convection flow of the mother solution, other were formed during growth stoppages whereas induced striations were generated by changes in hydrodynamical conditions. Growth rates changes resulted in zonal distribution of impurities, formation of planar lattice strain, rows of clusters of point defects and rows of dislocations. Generation of striations with different intensities in various sectors is a proof of the selective capture of impurities. Ratios of growth rates of various faces of KBC crystals growing in forced and free convection regimes were determined by induced striations. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axial Solute Transport during Bridgman Growth of BiSbTe3‐Mixed Crystals ‐ a comparison of analytical and numerical results

2D/3D‐transient finite‐element computer simulations of heat and mass transport including convection have been performed for a Bridgman configuration close to real growth conditions. The results for the axial distribution of the excessive tellurium in BiSbTe₃ semiconductor crystals grown from the melt are compared with the predictions of analytical segregation models.It is shown that Favier's model can be successfully applied for quantitatively estimating model parameters of segregation. Finally, the transition from normal gravity to microgravity conditions is discussed.     

A Study of Convection,Striations and Interface Shape in InP Crystals Grown by the Double-Crucible LEC Technique

A doublecrucible (DC) Czochralski setup has been used for the pulling of semi-insulating Fe-doped InP. The level of the Fe-doped melt in the growth crucible is replanished with the undoped InP from the reservoir crucible. In this way, since the distribution coefficient of iron is very small (about 0.001), the Fe concentration in the growth crucible is virtually unchanged during the pulling so that the axial Fe concentration is much more uniform than in standard LEC crystals. The use of two concentric crucibles has great implications in terms of convective flows, stability of the melt temperature and interface shape. In this paper we report the results of a study on striations and structural defects in InP grown from a double-crucible LEC arrangement. A dimensionless relationship for correlating striation features with melt motions is also proposed.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zone Melting of Bi0,5Sb1,5Te3 Crystals under Microgravity

Two samples of the thermoelectrical material Bi_0.5Sb_1.5Te₃ were grown by zone melting technique during a space flight of the russian space station “MIR” in 1994. By comparing the flight samples with the reference ground samples relevant conclusions regarding the influence of different mass transport situations in the melt on micro- and macrosegregation are possible. The samples were analyzed metallographically, by local resolved scanning of the SEEBECK-coefficient and by WDX measurements. Contrary to the ground samples the flight samples showed no convection-induced striations in the bulk. Consequently under microgravity unsteady flow in the melt has been avoided. The axial distribution of the Te component in the flight samples showed an unexpected Pfann -like behaviour, which points to a convection-controlled growth. Contrary to this the axial distribution of the metal components was diffusion-controlled. The axial macrosegregation of tellurium found in the flight samples can be explained by the high sensitivity of components with a low distribution coefficient to weakest convective flows. The radial distribution of the Te component in the flight samples is more homogeneous compared to the ground samples. The explanation of these differences succeeds only partly by the curvature of the interface and by the variation of the Te concentration boundary layer across the interface.