Travelling magnetic fields applied to bulk crystal growth from the melt: The step from basic research to industrial scale

ARTICLE IN PRESS

Journal of Crystal Growth 310 (2008) 1298–1306 www.elsevier.com/locate/jcrysgro

Travelling magnetic fields applied to bulk crystal growth from the melt: The step from basic research to industrial scale Peter Rudolph Institute for Crystal Growth, Max-Born-Street 2, D-12489 Berlin, Germany Available online 17 November 2007

Abstract After introduction of various types of magnetic fields in crystal growth, their main pros and cons for crystallization processes are discussed. It is shown that their further developments towards industrial maturity are bound up with the cardinal demands—increase of the process output, improvement of the crystal quality, and reduction of costs. In a further section, the advantages of travelling magnetic g project—the development of an internal fields are presented. The central chapter is devoted to the target of the current KRISTMAG heater–magnet module for coupled generation of temperature and a travelling magnetic field, suitable for incorporation into industrial Czochralski pullers and vertical gradient freeze equipments. Amplitude, frequency and phase shift of the three-phase current are all adjustable and are combined with a dc component to control the crystallization process effectively. Results of accompanying numeric modelling are presented. The current state of crystal growth experiments in travelling magnetic field and first encouraging results are given. r 2007 Elsevier B.V. All rights reserved. PACS: 81.10.F; 41.20.Jb; 07.55.Db Keywords: A1. Convection; A1. Heat transfer; A1. Mass transfer; A2. Magnetic field assisted method

1. Introduction One of the cardinal problems caused by scaling-up of crystal growth processes is the appearance of convective perturbations and even turbulences, which occur in the melt. They produce violent fluctuations in growth rate leading to compositional inhomogeneities, misoriented nucleations at the growing interface and, probably, twinning like in III–V and II–VI compounds. The use of both steady (permanent) and non-steady (variable) magnetic fields (Fig. 1) is being exploited to achieve damping of this turbulence. The application of magnetic fields in crystal growth of materials with electrical conductivity is well known for a long time [1–7]. After Suzuki et al. [8] for the first time described the Czochralski growth of Si crystals with significant reduced oxygen concentration by applying of a Tel.: +49 30 63923034; fax: +49 30 63923003.

E-mail address: [email protected] 0022-0248/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2007.11.036

transverse steady magnetic field (SMF) and after Kim and Smetana [9] demonstrated the applicability of air-cored solenoids for vertical field generation enormous research activities and several application tests of magnetic Czochralski (MCz) methods under industrial conditions were carried out. Also for LEC growth of III–V compounds like GaAs [10] and InP [11–13] SMFs were introduced very successfully. Characteristic thermal asymmetries, produced by axial and transversal fields, could be depressed by the use of cusp fields [14,15]. Even a spontaneous melt rotation (e.g. of silicon) without crucible movement can be achieved by electromagnetic force (EMF) [16]. Beneficial effects of magnetic fields have been also observed at crystallization of eutectics [17–19], high-temperature superconducting compounds [20–22] and organic crystals [23–25]. Nowadays even nanoparticles are solidified under SMF (e.g. Ref. [26]). Little is known about growth of dielectric crystals within magnetic fields due to the much smaller electrical melt conductivities [27,28]. A detailed overview on various types of SMF is given by Hurle and Series [29].

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magnetic fields in crystal growth steady (permanent) magnetic fields (SMF) vertical (axial, longitudinal) field (VMF, AxMF, LMF)

cusp field (CMF)

x

o

o

x

(1989) Series, Hirata, Hoshikawa

horizontal (transverse) field (HMF, TrMF)

non-steady (variable) magnetic fields (NSMF) rotating field (RMF)

travelling field (TMF)

alternating (pulsating) (AMF, PMF)

electromagneticfield (EMF)

+

(1985) Kim, Smetana

(1966) Utech, Flemings, Chedzey, Hurle (1981) Suzuki

(1958) Mullin, Hulme (1972) Shaskov, Shuslebina

(1997) Ono, Trapaga

(1992) Abritska, Gorbunov

(1999) Gelfgat

(1956) Pfann, Hagelbarger (1999) Wantanabe

Fig. 1. The various types of magnetic fields in crystal growth and their pioneers.

As has been found, also non-SMFs can harmonize the fluctuating natural convection streams very effectively. Whereas rotating magnetic fields (RMF) benefit controllable melt mixing [30,31] alternating (pulsating) magnetic fields (AMF) [32] and travelling magnetic fields (TMF) [33] are of special interest for acting on the diffusion boundary layer (AMF [34]), Marangoni flows [35] and curvature of the growing interface (TMF [36,58]). Thus, there is a wide range of applicabilities of magnetic fields in crystal growth processes. In addition to control of thermodynamic (temperature, pressure, composition), kinematic (translation, rotation, acceleration, vibration) and electrical (polarization, Peltier, Soret current) parameters, the use of magnetic fields is proving to be a sophisticated additional tool for achieving enhanced crystal quality during growth. However, today, after more than 50 years of basic research and diverse industrial tests arises the question ‘‘quo vadis’’ crystal growth in magnetic fields? Without doubt the experiments on laboratory scale and also the permanent improvement of accompanying numeric modelling will be still continued during the next years. This holds the more for the non-steady field variants, such as AMF and TMF, which were introduced in crystal growth only recently. In this paper, the capacity even of TMF for industrial applications will be discussed. Further, a higher versatility is expected from combined fields like SMF with RMF [37,38], SMF with AMF [39], RMF with TMF [40] or AMF and TMF with SMF [41]. Of course, in the end economical constrains decide over the applicability of such combinations in production. In general, further developments of magnetic fields for crystal growth must be focussed on their realizability in industry that depends on the cardinal demands such as increased process output, improved crystal quality, and reduced costs. For instance, an increase of the output per growth run can be achieved by two principal ways—(i) increase of the crystal diameter requiring, however, larger crucible widths or (ii) lengthening the crystal while

maintaining the diameter by pulling it from higher crucibles or containers (note: a further long-tested concept of continuous recharging will not be discussed here). Variant (i) is preferred for Czochralski growth of silicon. Meanwhile crystal diameters of 300 mm and crucible diameters between 711 and 914 mm are of industrial standard [42]. Next larger diameter will be 450 mm and will require such huge charges (4400 kg) and crucible sizes (36 in.) in which the thermal convective flows are strongly turbulent and, hence, not more controllable without magnetic fields [43]. However, the enormous costs, among others for the superconducting magnet around the growth chamber, lack a solution for the time being. From the point of view of power consumption, variant (ii) seems to be favoured due to the constancy of the heater diameter. Lengthened crucibles with increased melt heights, however, can cause convective turbulences, too. As it is well known that the Rayleight number Ra is proportional to the third power of the characteristic height H. Of course, in case of LEC an increased crucible rotation rate can help to maintain the flow stability [44] but due to the low thermal diffusivity of semiconductor compounds the stability is being lost already at much lower rotation rates compared to molten silicon. Therefore, melt heights over about 8–10 cm are not more controllable under conventional growth conditions and the application of a damping magnetic field becomes essential. Table 1 compiles characteristic flow parameters, which predominate the melt convection in crystal growth systems. Their force densities were recently estimated by Muiznieks et al. [45] for silicon melts in standard Czochralski pullers. Maximal force densities are generated by the buoyancyand rotation-driven flows of 142 and 150 N m3, respectively. Hence, before a magnet is produced first of all the estimation of the needed counter-acting magnetic force is required to equal it to the maximum convective flow force in the melt.

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Table 1 Estimated characteristic flow forces acting in silicon melt in generic Czochralski pullers (adapted from calculations in Ref. [45]) Force origin

Viscosity

Buoyancy (unstable density lamination due to temperature difference)

Rotation (suppression of meridional flow by rotationdriven azimuthal force)

Surface tension (Marangoni effect)

Equation Value (N m3)

Fv EZt Du 0.28

FbErbg DT 144

F sup  4ro2c Dr 150

ðF M =LÞ  ðqg=qTÞðDT=L2 Þ 0.06

Zt—turbulent dynamic viscosity, Du—velocity difference, r—density of the melt, b—volumetric expansion coefficient, g—gravitational acceleration, DT— temperature difference, oc—crucible rotation rate, Dr—radial position difference, qm/qT—Marangoni parameter, L—characteristic length.

2. Travelling magnetic field—principle and advantages Br (t)

A TMF is generated by means of applying out-of-phase ac currents to a number of coils which are arranged vertically one upon the other (Fig. 2). As a result, a meridional travelling Lorentz field is induced when a conducting melt is applied inside. The field line direction (up or downward), frequency f, phase shift j and amplitude I can be controlled very conveniently. The magnetic induction B can be described as a wave model consisting of axial and radial components B ¼ ðB2z þ B2r Þ1=2 with wavelength l ¼ 2p/k ¼ nh (k—wave number, nX2— number of coils, h—distance between coils). A conventional TMF arrangement, mainly tested under laboratory conditions, consists of three coils in delta connection. Supplying the standard three-phase ac current, a fixed frequency of f ¼ 50 Hz and a constant phase shift of j ¼ 1201 are given automatically. More variability, however, can be achieved when the coils are coupled in star connection. In this case, each coil can be supplied separately and frequency and phase shift can be varied in a wide range. This is important to create a Lorentz-force field, which is as best adapted to a particular growth situation (see Section 3). First theoretical and experimental studies on TMF in crystal growth started at the end of the 1990s [24,46,47]. Since that time main research is concentrated on its application in small-diameter vertical Bridgman (VB) and vertical gradient freeze (VGF) arrangements for fundamental studies in metallic alloys [48], Ge [49,50] and few semiconductor compounds such as GaAs [51] and InP [52]. As will be shown below, even for the VB and VGF growth variants the TMF mode proves to be well adjustable. Actually, until now there are not yet reports on use of TMF in LEC systems (note: recently the author’s team started the growth of GaAs in TMF by the modified LEC method named vapour pressure controlled Czochralski (VCz) technique; see Section 3). On contrary, the growth of silicon crystals by the Czochralski method under TMF began already in 2001 [53]. Until now, this mode is under further development [41,54]. The TMF proves to be favourable for convenient control of the temperature distribution, interface shape and oxygen incorporation by relative low power consumption. The advantage of TMF compared to all other modes is the creation of a Lorentz

Bz (t) Bz

 h

z Br

k = 2 / 

Fig. 2. The principle of a travelling magnetic field at crystal growth from melt by using of three axially parallel coils fed by a three-phase ac of given frequency f and phase shift j. (Bz, Br—axial and radial magnetic field components, respectively, l ¼ nh—magnetic wavelength, n—number of coils, h—distance between coils, k ¼ 2p/l—wave number).

force field, which is axisymmetric, i.e. toroidal (Fig. 4b), and has often a similar morphology like the buoyancy force field. This manifests its effective counter-acting property and is of essential advantage in comparison with horizontal or vertical SMF where asymmetric flow and temperature patterns are caused [55]. Compared to SMFs, the TMF shows a more effective interaction (coupling) factor N which describes the ratio between the induced EMF and prevalent buoyancy-driven convection (friction) force [56,57]. In a SMF, the interaction parameter is expressed by the Cowling number Co=Ha2/Re (Ha—Hartmann number, Re—Reynolds number) and becomes N SMF  Co ¼

B2 sL B2 s ¼ ru ro

(1)

with B—magnetic flow density (inductivity), s—electrical conductivity of the melt, L—characteristic length, r—melt density, u—convective stream velocity, o—convective (vertical) rotation frequency. Compared to that the interaction parameter of a TMF is given by the ratio

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between the TMF-related magnetic Taylor number Tam and Rayleight number Ra as N TMF ¼

Tam ðB2 sfL3 =rn2 kÞ B2 om  / Ra ðgb DTL3 =n2 aÞ k DT

(2)

with f—TMF translation frequency, k—TMF wave number, n—kinematic viscosity, b—coefficient of volumetric thermal expansion, DT—temperature difference. Due to the higher friction efficiency between a moving magnetic field and convection streams, the characteristic (critical) interaction factor N* of TMF at which the damping acts effectively is much smaller than in case of static magnetic field lines and equals N TMF  ð0:1  0:01Þ

(3a)

while in SMF N SMF  1

(3b)

(note: relation (3a) is also valid for another non-SMF like RMF and AMF). As a result, the required induction B is significantly reduced. Compared to SMF where B values in the range of 102–10 T are needed in the case of TMF inductions of only 103–101 T are sufficient to achieve a nearly identical damping efficiency. This turns out to be an enormous economical effect. To demonstrate the higher damping efficiency of TMF compared to SMF under realistic growth conditions, the considerations of Muiznieks et al. [45] for a standard silicon Czochralski system are cited (see also Table 1). In a static axisymmetric magnetic field, a required counteracting force density of FFSMFEsuB2 ¼ 150 N m3 is achieved when an induction strength of at least rffiffiffiffiffiffiffiffi 150 BSMF   28 mT (4a) su is generated (s—electrical conductivity ¼ 1.2  106 S m1, u—velocityE0.16 m s1). Against it in case of TMF an identical suppression force density FTMFEspfLB2 ¼ 150 N m3 demands only an induction intensity of sffiffiffiffiffiffiffiffiffiffiffi 150  1:4 mT; (4b) BTMF  spfL when f ¼ 50 Hz and L ¼ 0.4 m. Such favourable qualities enable an effective and stable control of the macroscopic interface morphology too. For instance, as it was demonstrated by a numeric study of Schwesig et al. [52], at VGF growth of 2 in. InP crystals under TMF with B of 4.5 mT (f ¼ 50 Hz) the downwardoriented Lorentz force led to a decreased flow velocity and interface flattening. As a result, the von Mises stress at the solid–liquid phase boundary was also reduced significantly. Similar results were obtained by Lyubimova et al. [51] for GaAs crystals by the same method, which calculated a more planar interface and reduced radial dopant segregation effect. Also Yesilyurt et al. [58] demonstrated that Ge

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crystals could be grown by VB under TMF with an interface of minimum tangential shear. A downward directed TMF also proves to be advantageous for silicon crystal growth. Tomzig et al. [41] showed that a nearly ideal uniform oxygen distribution along the grown crystals can be obtained being even better than under RMF and AMF conditions. After Krauze et al. [54], the temperature fluctuations particularly in the outer crucible region are significantly decreased. However, as the author’s team demonstrated by global numeric simulation [59] not only the peripheral perturbations can be depressed by TMF, but also those below the growing crystal when a well-optimized magnet set up is applied. As it is well known, during the processes of unidirectional solidification (Bridgman, Czochralski) the relation between melt and crystal volumes is continuously decreasing. With other words, the aspect ratio of the melt H/D (H—height, D—diameter) is reducing. As the result the acting convective force densities are decreasing and the flows are stabilizing too. Hence, the critical magnetic Taylor number Tacrit m , indicating the transition from stationary to time-dependent flows, increases with decreasing aspect ratio, i.e. towards the end of crystallization [52,60]. Surprisingly, in case of VGF growth under TMF, the Tacrit m (H/D) relation remains nearly constant over the whole solidification process [52]. Likewise, constant low deflection of the growing interface and von Mises stress at VGF growth of InP crystals were occured demonstrating the advantages of TMF over RMF very obviously. Of course, like in all time-dependent magnetic fields the danger of inherent flow instabilities must be considered. Effects of resonance and perturbations can appear when waves of natural convection and magnetic field do interact with each other. Whereas for RMF, the stability analysis is already well developed (e.g. [61–63]); for TMF, such studies are still at the beginning [64–66]. At low-frequency long-wave TMF, a body force of a non-vanishing curl is discussed [65]. Further, it was deduced theoretically [66] that in the range of wave numbers k ¼ 1–10 an increasing TMF frequency reduces the critical force density FT crit MF at which the axisymmetric flow patterns go over to a threedimensional instable flow body. Only at higher k410, the stability is slightly returning with increasing frequency. Indeed such an instability threshold was experimentally observed in a cylindrical GaInSb melt surrounded by TMF [67]. FT crit MF relates to a given field intensity, i.e. high enough induced axial flow velocity, and depends on the aspect ratio. For VGF growth of 2 in. InP crystals under TMF, a critical magnetic induction of 8 mT was calculated [52]. Generally, due to the practical importance for optimizing the inductor design a further more detailed stability analysis is required. g solution—a step to industrial scale 3. The KRISTMAG The usual method is to position the magnets outside the growth chamber (e.g. Refs. [29,43]). However, to produce a

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sufficient strong non-steady magnetic force density within the melt (see Eqs. (4a) and (4b)) requires that the magnet be designed for generation of higher induction force to compensate the field loss within the surrounding chamber wall, heat shields, heaters and crucible. In SMF, the shielding effect is proportional to the relative permeabilities mr and is, hence, minimal when materials with mrE1 (e.g. stainless steel, graphite) are arranged inside the magnet. In case of non-SMF, however, the frequency-induced eddy currents in electrically conducting materials increase the shielding factor S. Setting S as quadratic ratio between radius and skin depth R2/d2 with d=(2pmomrsf)1/2 becomes S ¼ 2pmo mr sfR2

(5) 7

1

with mo—magnetic field constant (=12.566  10 H m ). Especially in the case of high-pressure crystal growth of dissociating semiconductor compounds, e.g. III–Vs and II–VIs, very compact vessels with water-cooled walls of some cm thickness are used. As a result up to one order of magnitude lowered flow density will reach the melt column only [68]. Therefore, outside magnets must be able to generate very high induction forces that make such inductors for industrial growth machines very expensive (for a typical resistive system the cost is approximately proportional to the fourth power of the bore and to the square of the field [29]). Thus, an economical effect can be achieved when non-steady magnetic coils, such as a TMF generator, could be placed as close as possible to the melt to have a maximum efficiency of flow driving [65]. Therefore, for adoption in industrial growth machines a location of the coils inside the growth container is favoured. In fact, there were some attempts to arrange internal magnetic inductors. Bru¨ckner and Schwerdtfeger [69] used an electromagnetic wire-winded coil supplied by normal three-phase current of 50 Hz for generation of a RMF during Czochralski growth of Cu, Ge and Si with diameter of 10 mm. Such ‘‘stirrer’’ was positioned around a HF coil for heating. However, to overcome the problem of extensive heat-up caused by heat transfer from the melt a

special cooler was placed between both heater and magnet. Obviously, the temperature limit of the inductor parts (155 1C for the insulation of windings) stopped further developments of such RMF variant especially for the industry. On laboratory scale, however, some further modifications are described. For example the VB growth of Ga1xInxSb crystals in an accelerated magnetic field was realized by using of a 5 kHz HF coil positioned between melt container and resistance heater inside the container [34]. It is also well known from zone melting that there is no technical problem to add RMF coil or permanent magnets to the zone heater by their axially parallel placement [31,70]. For example in such a manner many space growth experiments were carried out [31]. However, until today there are no reports on TMF arrangements inside the growth chambers. g Currently, within the framework of the KRISTMAG project for the first time internal variants of TMF generators are under development. It was worked out that the best solution even for a possible industrial application proves to be an internal heater–magnet module for coupled generation of temperature and a TMF, suitable for incorporation into industrial Czochralski pullers and VGF equipments. Amplitude, frequency and phase shift of the three-phase current should be all adjustable and combined with a dc component to control the crystallization process effectively. The basic idea of combined heater–magnet is not new. Already in 1970 Fujimori and Ayusawa [71] proposed in a patent description to apply a ‘‘picket fence’’ (meandertype) graphite heater simultaneously as heating element and generator of a RMF when it is supplied with a threephase accelerating current (ac) power input. The RMF arises due to the phase shift between the three deltaconnected cylindrical body segments (Fig. 3a). In 1980 Hoshikawa et al. [72] and independently Hull [73] reported the first Czochralski silicon crystal growth experiments with such heater–magnet module made of graphite. Rotation rates of 20–30 rpm were observed at the Si melt surface in a 250 mm diameter crucible [72]. Both authors observed an improvement of the oxygen control in the

Fig. 3. Layouts of three graphite heaters for LEC growth of semiconductor compounds without (a) and with TMF (b and c). The nearly identical dimensions facilitate the replacement in one and the same puller vessel. (a) Conventional ‘‘picket fence’’ (meander) heater fed by three-phase current in delta connection, (b and c) magnet–heater modules with staircase-shaped current path, subdivided in three sections for TMF generation by feeding with three-phase current of given phase shift in delta (b) and star connection (b).

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as-grown crystals. Two years later, Kim et al. [74] used such three-segment heater for interrupting rotation of the melt by interchanging two phases of the three-phase ac power input. He also alluded to the possibility of simultaneous delivery of ac and dc components for RMF generation and growth heat production, respectively [75]. However, it must be mentioned that such ‘‘picket fence’’ heater is only of small RMF efficiency due to the antiparallel directed current lines in the vertical paths. As a result, within this heater part the induced Lorentz flows do neutralize each other. Hence, only the upper and below horizontally directed turning regions may contribute to an effective field coupling (Fig. 3a). This is obviously the reason that such concept was also not further pursued. Generally, for the generation of a vertically translating TMF the heater design must be changed completely, i.e. from a meander-like shape to a hole-cylindrical body with an upwards-winding slit forming a single layered spiral- or staircase-shaped current path. The path is subdivided in coil segments by contact points for the phase-shifted power supply in delta or star connection. For the first time, a construction scheme of such heater type made of graphite was proposed by Mu¨he et al. [76]. Slightly earlier, the principle was settled in a patent description of von Ammon et al. [77], too. These thoughts stimulated the technical g project realization within the framework of KRISTMAG essentially. However, numerous constructional, electrical and electronic originalities have to been solved by the author’s team [78–80]. For instance, asymmetry effects due to the passages between windings, and electric supply lines have to be obviate. Figs. 3b and c show schemes of heater–magnet modules for insertion in LEC vessels operating in delta and star connection, respectively. The 3D electromagnetic computer modelling by the commercial package ANSYS was used to optimize the inductor design and feeder arrangements for generation of a TMF with minimum features of asymmetry [81]. Different connections to the three-phase power supply were modelled considering input of current with variable

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phase, amplitude and frequency. Of course, the investigated effects required the using of the entire system geometry without any kind of simplifications by symmetry. Fig. 4b shows a velocity field of the pure induced Lorentz force in a VGF Ge melt with 110 mm in diameter when a downward translating TMF with f ¼ 250 Hz and j ¼ 601 is operating (note: here the thermal field is not yet considered). At a given induction of B ¼ 4 mT maximal Lorentz force densities of Fz180 and +150 N m3 have been obtained in the downward and upward directed stream toroids, respectively. Such values fulfil the demands in Section 2 very well. Based on the electromagnetic optimizations, a new suitable power unit and control system for supply of the heater–magnet module has been developed. It contains a 6pack integrated intelligent power system (SkiiP) impulse and frequency driven by an electronic control module. As a result, both a three-phase well-formed sinus ac of desired frequency and phase shift for TMF generation and a dc component for controlling the melting and crystallization temperature are supplied to the heater–magnet. At present, the following parameter range is available: maximum power P ¼ 40 kW, magnetic induction B ¼ 1–8 mT, voltage V ¼ 0–40 V, maximum current I ¼ 330 A per coil section, frequency f ¼ 10–600 Hz, and phase shift j ¼ 5–1201. Global numeric modelling is used to support and optimize the crystal growth experiments with heater– magnet modules. Figs. 4a and c compare the stream contours in a Ge melt within the VGF arrangement without (a) and with downward translating TMF (b) computed by the code CRYSMAS [82]. As can be seen, the growing interface morphology can be modified from an unfavourable concave one to a more promising slightly convex curvature. Figs. 5a and b show two snapshots of the flow and temperature fields in the LEC GaAs melt without (a) and with TMF (b) modelled by the programme NAVIER (based on data from WIAS-HiTNIHS) [59]. A more homogeneous stream and temperature distribution is

Fig. 4. Global numeric simulation of the TMF effect in a Ge melt with diameter of 100 mm in the VGF equipment. (a) Stream lines of buoyancy flow without TMF and interface shape within the left half cylinder, causing an undesirable concave interface curvature [82], (b) 3D velocity field of the pure Lorentz force (without thermal considerations) when the heater–magnet induces a downward translating TMF with f ¼ 250 Hz and j ¼ 601 [81], and (c) stream contour in a downward translating TMF and interface shape within the right half cylinder produced by the heater–magnet at f ¼ 20 Hz and j ¼ 601. A favourable convex interface is obtained [82].

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Fig. 5. Comparison of the computed temperature field in a half LEC crucible with 4 kg GaAs melt heated by the heater–magnet without (a) and with downward translating TMF of f ¼ 300 Hz and j ¼ 701 (b). A maximal Lorentz force density of 403 N m3 is induced. The crucible and crystal rotation is 5 and 5 rpm, respectively [59].

obvious when the TMF is used. Further, markedly reduced temperature oscillations below a growing GaAs LEC crystal were observed when an optimized TMF configuration is applied [59]. Nowadays, at the IKZ Berlin three crystal growth machines of industrial scale, i.e. CI 358 for LEC, LPA ‘‘Mark 3’’ for VCz and ‘‘Kronos’’ for VGF growth, are g heater–magnet modules. The equipped with KRISTMAG test phase is still running. However, recently, first encouraging results were obtained. Visual observations of the GaAs melt surface with floating particles in a VCz arrangement without B2O3 encapsulant revealed an agile reaction of the flow patterns to the variation of the TMF parameters. For instance, in contrast to the conventional mode without magnetic field a controllable outwards directed stream away from the seed could be achieved [83]. For the first time, VCz GaAs crystals were successfully grown in B2O3-free VCz regime under two different TMF modes. Fig. 6a shows a crystal grown in TMF operating in delta connection with f ¼ 50 Hz and j ¼ 1201. Fig. 6b presents the image of an example grown in TMF with star connection (f ¼ 400 Hz, j ¼ 701). A mean dislocation

Fig. 6. First GaAs crystals grown by a modified VCz method with g heater–magnet modules operating in: (a) delta-connection KRISTMAG with f ¼ 50 Hz and j ¼ 1201 and (b) in star connection with f ¼ 400 Hz, j ¼ 701 (courtesy of F. Kiessling, IKZ).

density of 104 cm2 of enhanced radial distribution homogeneity was detected in this crystal [83]. Forthcoming LEC and VGF growth experiments under TMFs will be carried out with GaAs and Ge, respectively.

4. Conclusions A combined heater–magnet module for installation in industrial crystal growth machines has been developed by g team. An appropriate system for power the KRISTMAG supply and process control was also constructed. Such module enables the simultaneous generation of heat for melting and of TMFs to counter-act the violent non-steady or even turbulent convection in the melt. It replaces the conventional meander heater by a coil consisting of a spiral- or staircase-shaped current path, which is subdivided, in segments by contact points for the phase-shifted power supply. Its placement close to the melt guarantees a

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maximum efficiency of flow driving and low cost of adaptation. With the aim to increase the melt height and, hence, the production output per run, the favourable effects of convection damping and interface flattening by such TMF module will be demonstrated. First melt flow observations and growth experiments show very encouraging results. Acknowledgements g team for high The author is indebted to the KRISTMAG professional competence and excellent cooperativeness. In particular he has to thank M. Czupalla, Ch. Frank-Rotsch, D. Jockel, F.-M. KieXling, U. Kupfer, R.-P. Lange, W. Miller, U. Rehse, O. Root, W. Schulze and M. Ziem from IKZ, O. Klein, Ch. Lechner and J. Sprekels from WIAS Berlin, G. Metzner, U. RoXbach, P. Scheel and V. Trautmann from Steremat GmbH Berlin, G. Bethin, M. Bethin, H. Borchert, B. Eberhardt and F. Senf from Auteam GmbH Vogelsdorf, H. Kasjanow and B. Nacke from the University Hanover, J. Fainberg, J. Friedrich and G. Mu¨ller from the Crystal Laboratory at the IISB of the FhG Erlangen. He is grateful to the Freiberger CM GmbH, CGS GmbH and CrysTec GmbH for continual interest, to Y. Israel (TimeKontor Berlin), V. Kopf, C. Pinho-Szmerlo and B. Schikorsky (FV Berlin) for project management and particularly to R. Fornari (Director of IKZ) for his continuous support. g project is co-financed by the European The KRISTMAG Regional Developments Fund (EFRE), ‘‘Zukunftsfonds’’ Berlin and ‘‘Zukunftsagentur’’ of the State Brandenburg. References [1] [2] [3] [4] [5] [6] [7] [8]

[9] [10] [11]

[12] [13] [14] [15] [16] [17]

W.G. Pfann, D.W. Hagelbarger, J. Appl. Phys. 27 (1956) 12. W.G. Pfann, D. Dorsi, Rev. Sci. Instrum. 28 (1957) 720. J.B. Mullin, K.F. Hulme, J. Electron. Control 4 (1958) 170. P. Gondi, G. Scacciati, Nuova Cimento 21 (1961) 829. W.C. Johnston, W. Tiller, Trans. AIME 221 (1961) 331; W.C. Johnston, W. Tiller, Trans. AIME 224 (1962) 214. H.P. Utech, M.C. Flemings, J. Appl. Phys. 37 (1966) 2021. H.A. Chedzey, D.T.J. Hurle, Nature 210 (1966) 933. T. Suzuki, N. Isawa, Y. Okubo, K. Hoshi, in: H.R. Huff, R.J. Kriegler, Y. Takeishi (Eds.), Semiconductor Silicon 1981, Electrochemical Society, Pennington, NJ, 1981. K.M. Kim, P. Smetana, J. Appl. Phys. 58 (1985) 2731. K. Terashima, T. Fukuda, J. Crystal Growth 63 (1983) 423. D. Hofmann, M. Mosel, G. Mu¨ller, in: G. Grossmann, L. Ledebo (Eds.), Semi-insulating III–V Materials, Malmo¨ 1988, Hilger, Bristol, 1988, p. 429. S. Ozawa, T. Kimura, J. Kobayashi, T. Fukuda, Appl. Phys. Lett. 50 (1987) 329. D.F. Bliss, R.M. Hilton, S. Bachowski, J.A. Adamski, J. Electron. Mater. 20 (1991) 967. R.W. Series, J. Crystal Growth 7 (1989) 92. H. Hirata, K. Hoshikawa, J. Crystal Growth 6 (1989) 747. M. Watanabe, W. Wang, M. Eguchi, T. Hybiya, Jpn. Appl. Phys. 38 (1999) L10. W.V. Youdelis, R.C. Dorward, Can. J. Phys. 44 (1966) 139.

1305

[18] D.R. Uhlmann, T.P. Seward, B. Chalmers, Trans. Met. Soc. AIME 236 (1966) 527. [19] D.T.J. Hurle, J.D. Hunt, The Solidification of Metals, ISI P110, Iron and Steel Institute, 1968, p. 162. [20] P. de Rango, M. Lee, P. Lejay, A. Sulpice, R. Tournier, M. Ingold, P. Germi, M. Pernet, Nature 349 (1991) 770. [21] Y. Ma, K. Watanabe, S. Awaji, M. Motokawa, Appl. Phys. Lett. 77 (2000) 192. [22] P. Badica, K. Togano, S. Awaji, K. Watanabe, A. Iyo, H. Kumakura, J. Crystal Growth 269 (2004) 518. [23] G. Sazaki, E. Yoshida, H. Komatsu, T. Takada, S. Miyashita, K. Watanabe, J. Crystal Growth 173 (1997) 231. [24] M. Ataka, E. Katoh, N.I. Wakayama, J. Crystal Growth 173 (1997) 592. [25] A. Moreno, B. Quiroz-Garcia, F. Yokaichiya, V. Stojanoff, P. Rudolph, Cryst. Res. Technol. 42 (2007) 231. [26] J. Wang, K. Zhang, Z. Peng, Q. Chen, J. Crystal Growth 266 (2004) 500. [27] M.S. Mwaba, J. Gu, M.R. Golriz, J. Crystal Growth 303 (2007) 381. [28] Y. Miyazawa, S. Morita, H. Sekiwa, J. Crystal Growth 166 (1996) 286. [29] D.T.J. Hurle, R.W. Series, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth, vol. 2a, Elsevier, North-Holland, 1994, p. 259. [30] Y.M. Shaskow, N.Y. Shulebina, Fiz. Khim. Obrab. Meter. 1 (1972) 34. [31] P. Dold, K.W. Benz, Prog. Cryst. Growth Charact. Mater. 38 (1999) 7. [32] M.Y. Abritska, L.A. Gorbunov, Magnetohydrodynamics 28 (1992) 398. [33] N. Ono, G. Trapaga, J. Electrochem. Soc. 144 (1997) 764. [34] A. Mitric, T. Duffar, C. Diaz-Guerra, V. Corregidor, L.C. Alves, C. Garnier, G. Vian, J. Crystal Growth 287 (2006) 224. [35] V. Galindo, G. Gerbeth, W. Von Ammon, E. Tomzig, J. Virbulis, in: Proceedings of the Fourth International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millenium, Presq’ile de Giens, France, 2000, p. 725. [36] P. Schwesig, M. Hainke, J. Friedrich, G. Mueller, J. Crystal Growth 266 (2004) 224. [37] I. Grants, A. Pedchenko, G. Gerbeth, Phys. Fluids 18 (2006) Art. No 124104. [38] X. Wang, N. Ma, D.F. Bliss, G.W. Iseler, P. Becla, J. Crystal Growth 287 (2006) 270. [39] V. Galindo, G. Gerbeth, W. von Ammon, E. Tomzig, J. Virbulis, Energy Convers. Manage. 43 (2002) 309. [40] A. Cramer, S. Eckert, Ch. Heinzelmann, C. Zhang, G. Gerbeth, in: Proceedings of the Fourth International Conference Electromagnetic Processing of Materials (EPM 2003), Lyon, 2003, p. 359. [41] E. Tomzig, J. Virbulis, W.V. Ammon, Y. Gelfgat, L. Gorbunov, Mater. Sci. Semicond. Process. 5 (2003) 347. [42] W. von Ammon, in: G. Mu¨ller, J.J. Metois, P. Rudolph (Eds.), Crystal Growth—From Fundamentals to Technology, Elsevier, Amsterdam, 2004, p. 239. [43] Y. Shiraishi, K. Takano, J. Matsubara, T. Iida, N. Takase, N. Machida, M. Kuramoto, H. Yamagishi, J. Crystal Growth 229 (2001) 17. [44] H.T. Rossby, J. Fluid Dyn. 36 (1969) 309. [45] A. Muiznieks, A. Krauze, B. Nacke, J. Crystal Growth 303 (2007) 211. [46] Y. Gelfgat, Yu. Kru¨mins, M. Abricka, Magnetohydrodynamics 35 (1999) 1. [47] N. Ramachandran, K. Mazuruk, M.P. Volz, J. Jpn. Soc. Microgravity Appl. 17 (2000) 98. [48] V. Galindo, I. Grants, R. Lantzsch, O. Pa¨tzold, G. Gerbeth, J. Crystal Growth 303 (2007) 258. [49] S. Yesilyurt, S. Motakef, R. Grugel, K. Mazuruk, J. Crystal Growth 263 (2004) 80. [50] R. Lantzsch, I. Grants, V. Galindo, O. Pa¨tzold, G. Gerbeth, M. Stelter, A. Cro¨ll, Magnetohydrodynamics 42 (2006) 445.

ARTICLE IN PRESS 1306

P. Rudolph / Journal of Crystal Growth 310 (2008) 1298–1306

[51] T.P. Lyubimova, A. Cro¨ll, P. Dold, O.A. Khlybov, I.S. Fayzrakhmanova, J. Crystal Growth 266 (2004) 404. [52] P. Schwesig, M. Hainke, J. Friedrich, G. Mueller, J. Crystal Growth 266 (2004) 224. [53] Th. Wetzel, Fortschritt-Berichte VDI, Reihe 9 (328) (2001) 1. [54] A. Krauze, A. Muiznieks, A. Mu¨hlbauer, Th. Wezel, L. Gorbunoov, A. Pedchenko, J. Virbulis, J. Crystal Growth 266 (2004) 40. [55] K. Kakimoto, in: G. Mu¨ller, J.J. Metois, P. Rudolph (Eds.), Crystal Growth—From Fundamentals to Technology, Elsevier, Amsterdam, 2004, p. 169. [56] P.A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge University Press, 2001. [57] B. Fischer, Thesis, University of Erlangen-Nu¨rnberg, 2001. [58] S. Yesilyurt, S. Motakef, R. Grugel, K. Mazuruk, J. Crystal Growth 263 (2004) 80. [59] O. Klein, Ch. Lechner, P.-E. Druet, P. Philip, J. Sprekels, Ch. FrankRotsch, F.M. KieXling, W. Miller, U. Rehse, P. Rudolph, in: Proceedings of the ICCG-15, Salt Lake City, 12–17 August 2007. [60] M. Hainke, J. Friedrich, G. Mueller, Mag. Hyd. 39 (2003) 615. [61] Th. Kaiser, K.W. Benz, Phys. Fluids 10 (1998) 1104. [62] B. Fischer, J. Friedrich, C. Kupfer, D. Vizman, G. Mu¨ller, Transfer Phenomena, in: A. Alemany, P. Marty, J.P. Thibault (Eds.), Magnetohydrodynamic and Electroconducting Flows, Kluwer Academic Publishers, 1999, p. 279. [63] I. Grants, G. Gerbeth, J. Fluid Mech. 463 (2002) 229. [64] K. Mazuruk, Adv. Space Res. 29 (2002) 541. [65] I. Grants, G. Gerbeth, J. Crystal Growth 269 (2004) 630. [66] A.Yu. Gelfgat, J. Crystal Growth 279 (2005) 276. [67] R. Lantzsch, V. Galindo, I. Grants, C. Zhang, O. Pa¨tzold, G. Gerbeth, M. Stelter, J. Crystal Growth 305 (2007) 249.

[68] G. Mu¨ller, private communication. [69] F.U. Bru¨ckner, K. Schwerdtfeger, J. Crystal Growth 139 (1994) 351. [70] R. Hermann, G. Behr, G. Gerbeth, J. Priede, H.J. Uhlemann, F. Fischer, L. Schultz, J. Crystal Growth 275 (2005) e1533. [71] K. Fujimori, T. Ayusawa, German patent 2107646 (1970). [72] K. Hoshikawa, H. Kohda, H. Hirata, H. Nakanishi, Jpn. J. Appl. Phys. 19 (1980) L33. [73] E.M. Hull, IBM Tech. Disclosure Bull. 23 (1980) 2756. [74] K.M. Kim, G.H. Schwuttke, P. Smetana, IBM Tech. Disclosure Bull. 25 (1982) 2277. [75] K.M. Kim, Patent DE 3750382 T2 (1987). [76] A. Mu¨he, B. Altekru¨ger, A. Vonhoff, Patent Descriptions DE 10349339 A1 (2003), US 0087125 A1 (2004). [77] W. von Ammon, J. Virbulis, E. Tomzig, Y. Gelfgat, L. Gorbunov, Patent Description DE 10102126 A1 (2001). [78] P. Rudolph, M. Ziem, P. Lange, Patent Description DE 10 2007 020 239.5 (2007). [79] P. Lange, M. Ziem, D. Jockel, P. Rudolph, F.M. Kiessling, Ch. Frank-Rotsch, M. Czupalla, B. Nacke, H. Kasjanow, A,. Mu¨he, Patent Application (2007). [80] P. Lange, P. Rudolph, Ch. Frank-Rotsch, B. Nacke, O. Klein, Patent Application (2007). [81] H. Kasjanow, B. Nacke, St. Eichler, D. Jockel, Ch. Frank-Rotsch, P. Lange, P. Rudolph, in: Proceedings of the ICCG-15, Salt Lake City, 12–17 August 2007. [82] Ch. Frank-Rotsch, D. Jockel, M. Ziem, P. Rudolph, in: Proceedings of the ICCG-15, Salt Lake City, 12–17 August 2007. [83] F.M. Kiessling, Nat. Status Seminar on Crystal Growth under Magnetic Fields, Berlin, 18–20 June 2007.