MHD Effects in Semiconductor Crystal Growth and Alloy Solidification

Transcription

1 International Scientific Colloquium Modelling for Electromagnetic Processing Hannover, March 24-26, 2003 MHD Effects in Semiconductor Crystal Growth and Alloy Solidification M. Hainke, J. Friedrich, D. Vizman, G. Müller Abstract This paper gives a review of the R&D activities of the Crystal Growth Laboratory (CGL) in Erlangen in the field of the use of magnetic fields in crystal growth and in material research under microgravity conditions. Therefore, the experimental and numerical techniques will be presented. Results obtained by CGL in the fields Czochralski growth of Silicon crystals, growth of GaAs and InP crystals as well as solidification under microgravity conditions will be shown. Introduction Magnetic fields are widely used in semiconductor crystal growth, as well as in casting technologies to influence the convective heat and mass transport in the melt in a desired way. In the field of the growth of large diameter silicon crystals by the Czochralski (Cz) technique, steady magnetic fields are improving the process conditions by damping e.g. harmful temperature fluctuations in the melt as well as by controlling the oxygen distribution in the crystal. One disadvantage of such static magnetic fields is the relatively high magnetic induction, usually of some hundreds of milli-tesla, which is necessary for an efficient flow control. Much lower field strengths are needed if time-dependent fields are applied. Moreover, time-dependent fields allow to establish different flow regimes in the melt depending on the configuration of the magnetic field. The time-dependent magnetic fields are currently under investigation in Czochralski growth of Silicon, as well as in Vertical Gradient Freeze (VGF) growth of III-V semiconductors. In the VGF growth, their application increases the number of experimentally available parameters to modify the process conditions. The Crystal Growth Laboratory in Erlangen has a long tradition in the analysis of the effects of magnetic fields in crystal growth. In the following experimental and numerical tools for the investigation of the influence of magnetic fields in crystal growth and some results obtained by CGL will be presented. 1. Experimental and numerical tools for the analysis of magnetic fields in crystal growth Experimental investigations in simplified geometries representing typical configurations for crystal growth and alloy solidification allow an easy and systematic investigation of the basic interactions between magnetic fields and natural convection. Thereby, the effects of magnetic field on buoyant convection and on Marangoni convection is of interest for the crystal grower. The influence of steady magnetic fields [1-3] as well as of rotating magnetic fields[4-7] on the buoyant flow was analyzed intensively by using so-called convection cells filled with 73

2 liquid Gallium to which different boundary conditions can be applied. The measurement of the heat transport in such melts allowed to get a better understanding of the transport phenomena. Such results summarized in form of e.g. stability diagrams assisted the crystal grower to select proper parameters of the magnetic field in which a beneficial effect on the crystal growth process can be expected. Temperature measurements by using e.g. specially designed thermocouple set-ups are up to now the only technique by which the effects of magnetic fields on the heat transport in the melt can be studied in-situ during real crystal growth experiments [8-11]. This approach can be used even during industrial production of silicon crystals with 300mm diameter without disturbing the process. Another experimental technique consists in the analysis of doping striations and doping distributions of as grown crystals [12-16]. This ex-situ approach allows to determine the impacts of magnetic fields on the shape of the solid-liquid interface which is in general crucial for the crystal properties as well as on the homogeneity of dopant distributions. The investigation of doping striations is also a suitable way to analyze e.g. how temperature fluctuations caused by instationary Marangoni convection can be suppressed by using steady [e.g. 13, 14] or rotating magnetic fields [16]. A deeper understanding of the experimental results is obtained by a combined application of numerical simulation. On the other hand, the numerical models are improved and validated by experimental results obtained with the techniques mentioned above. At the CGL the software codes CrysVUn and STHAMAS2D were developed for global two dimensional, and STHAMAS3D for local three dimensional calculations of solidification processes [4-7, 11, 17,18]. All codes contain several models for different kinds of magnetic fields. In the following sections some typical examples will be illustrated where these methods have been applied to investigate the influence of magnetic fields in different crystal growth processes. 2. Basic investigation of the interaction of magnetic fields and natural convection in model experiments By experimental studies with the convection cells filled with Gallium and accompanying numerical simulations, stability diagrams including the transitions to time-dependent flow regimes were determined which describe the interaction of axial fields as well as rotating magnetic fields with buoyant convection in terms of dimensional characteristic numbers. Such stability diagrams were obtained for different aspect ratios of the melt and for different thermal boundary conditions. Rayleigh-Benard configurations were also analyzed as zone melting configurations as well as Bridgman configurations, in which the melt is heated from the top [1-6]. In a similar way stability diagrams were experimentally and numerically identified for the interaction of steady fields as well as of rotating magnetic fields and Marangoni convection. Thereby, the reduction of the intensity of doping striations in GaAs crystals grown by the Floating Zone technique served as an experimental measure to investigate the influence of these magnetic fields on temperature fluctuations [12-14, 16]. Currently, these fundamental studies are extended to alternating and travelling magnetic fields, because it seems that such systematic studies are still missing. 3. Application of magnetic fields in Czochralski growth of Silicon In Czochralski growth of Silicon crystals, the melt volumes and the corresponding crucible diameters were increased significantly in the last years. Today, crystals with a weight 74

3 of more than 200kg are grown. The result of this increased melt size is a highly turbulent melt during growth with strong temperature fluctuations. Therefore, steady magnetic fields, mainly cusp or horizontal configurations, are investigated and used to damp the undesired temperature fluctuations. For example, such temperature fluctuations are detrimental during the seeding process because they are causing for strong variations of the diameter of the growing crystal in the necking phase. These diameter variations can cause severe mechanical problems if one takes into account the weight of the growing crystal hanging at the small diameter seed. Recently, it was demonstrated that the uniformity of the diameter of the seed can be improved significantly due to the damping of the temperature fluctuations by using a steady magnetic field. The application of e.g. a horizontal magnetic field also influences the shape of the solidliquid interface in a positive way. In numerical simulations of a 300mm process it was observed that an increased field strength decreases the bending of the solid-liquid interface in the considered parameter range [19]. This means that the lateral uniformity of point defects which are an important quality criterion, can be improved by a horizontal magnetic field. From the numerical results it appears also, that the electrical conductivity of the crystal seems to play an important role for the convection and the interface shape. The solid-liquid interface is curved more convex if an electrically conducting crystal is taken into account for the calculation of the electrical potential [20]. But, so far the effect of the electrical conductivity of the crystal was not validated experimentally. However, the use of steady magnetic fields has not only a positive influence on the process conditions. The temperatures close to the crucible wall significantly increase due to the reduced convective heat transport [9-10]. This has a harmful impact on the yield because the crucible wall is overheated. Small particles of the crucible can be detached from the wall and be transported to the growth interface terminating single crystalline growth. Therefore, the crystal grower has to find a compromise concerning the reduction of temperature fluctuations and the increase of crucible overheating when applying steady magnetic fields. Recently, the application of time-dependent magnetic fields during CZ-growth of Si, mainly alternating and travelling field configurations, is also under investigation. It seems that there is still much work to be done to analyze the influence of these fields as well as of their super-position with steady fields on the process conditions. 4. Application of magnetic fields in III-V semiconductor crystal growth In opposite to microelectronic Si, where 95% of the material is produced by the Czochralski technique, three industrial crystal growth methods exist to grow the most important III-V semiconductors GaAs and InP. These methods are the Liquid Encapsulated Czochralski (LEC), the Vapor Controlled Czochralski (VCZ) and the Vertical Gradient Freeze Method (VGF) and its variants. The reader is referred to text books about crystal growth for more detailed information about the different techniques [e.g 25]. In the case of GaAs, magnetic fields are so far not industrially used to control the melt convection, while in the case of InP there are some research groups and even commercial suppliers of the material who claim to use magnetic fields during growth of the crystals by the LEC as well as by the VCZ method. In the case of InP, mainly axial steady magnetic fields are applied in order to damp the temperature fluctuation in the melt. These temperature fluctuations are again very harmful because they are the main reason for crystal defects like twinning and polycrystalline growth. Furthermore, the use of the axial fields can improve the uniformity of the electrical properties on a macroscopic and microscopic level [11]. 75

4 There is also a stronger interest, at least in the scientific community, to apply timedependent magnetic fields during VGF growth of both, GaAs and InP. In the VGF method, no means exist to influence the convective transport in the melt, like the crystal and crucible rotation in the Cz variants. Therefore, rotating magnetic fields were studied as one possibility to overcome this lack. It was found that the use of rotating magnetic fields influences the temperature and dopant distribution within the melt and the shape of the solid-liquid interface [15] in a positive way. Under optimized process conditions of the magnetic field an improved radial uniformity of the dopant distribution is observed. Furthermore, it was experimentally and numerically shown that the rotating magnetic field can lead to a reduction of the bending of the solid-liquid interface on a macroscopic level [15]. Therefore, the crystal can be grown under reduced thermal stress conditions and thus nominally with a lower defect density. However, it seems that this effect becomes obvious only at higher growth velocities [21]. Furthermore, the rotating magnetic field seems to be not the most proper configuration in order to minimize the strong concave curvature of the interface very close to the crucible wall. This local bending is determined mainly by the thermal properties of the crucible material, pyrolitic boron nitride. This local effect is connected with the growth of facets which are thought to be the origin of crystal defects like twins and polycrystalline growth. Therefore, it is of strong scientific and also industrial interest whether other magnetic field configurations would help to overcome this problem at the crucible wall. In this context, it should be mentioned, that this local bending close to the crucible wall was not observed in growth experiments in which an axial steady magnetic field was applied [22]. It might be that the importance of this result was underestimated and that it would be worth to enhance the R&D activities in this direction, too, especially to find a theoretical explanation for these experiments. 5. Application of magnetic fields under µg conditions Due to the damping effect of both, magnetic fields and microgravity conditions, there exists a close connection between these two research fields [23-25]. In former times, it was thought that strong steady magnetic fields could allow to achieve diffusive transport conditions on earth. However, systematic theoretical investigations showed that a pure diffusive mass transport during solidification of binary systems with especially very small distribution coefficients cannot be established by using steady magnetic fields [24]. Furthermore, additional effects can occur under high field strengths like thermoelectric convection. Magnetic fields were studied under microgravity conditions in order to suppress unsteady Marangoni convection [13-14] and the undesired disturbances resulting from steady as well as unsteady (g-jitter) residual accelerations [26]. Nowadays, especially rotating magnetic fields are of interest, because two furnace inserts in the Material Science Laboratory (MSL) on the International Space Station (ISS) will be equipped with this type of magnetic field. Within the European project MICAST (Microstructure Formation in Casting under Diffusive and Magnetically Controlled Convective Conditions) it is foreseen to use rotating magnetic fields to investigate the influence of the convective heat and species transport on the dendritic alloy solidification of technical Al alloys in a series of space experiments [24,27]. These investigations are of high industrial and scientific interest, as a quantitative description of the influence of flows during solidification on all length scales is still lacking due to the complexity of appearing phenomena. Due to the large number of parameters governing the solidification, like growth velocity, composition, temperature gradient and magnetic field 76

5 parameters, numerical simulation plays an important role for the development of a quantitative understanding of the appearing phenomena. The numerical results will serve as input data for the experimental investigations planned within the MICAST project. As a first milestone of the MICAST space experiments, a sounding rocket flight is scheduled on the mission TEXUS41 for spring 2004, in which the influence of the rotating magnetic field on the microstructure formation in an Al alloy will be analyzed. Conclusions An attempt was made to briefly summarize the current status of the use of magnetic fields in crystal growth and under microgravity conditions. Thereby, the main emphasis was put on the R&D contributions obtained by the Crystal growth Laboratory in these fields. It can be concluded that there is still a potential for future R&D activities. One focus might be the effects of alternating and travelling magnetic fields as well as the effects of super-positions of time-dependent fields with steady fields. Acknowledgements The contributions of our colleges to the different presented topics is gratefully acknowledged. The investigations presented are supported by DLR under contract no. 50WM0042, by ESA under contract no /00/NL/SH as well as by Wacker Siltronic. References [1] J. Baumgartl, W. Budweiser, G. Müller and G. Neumann, Studies of Buoyancy Driven Convection in a Vertical Cylinder with Parabolic Temperature Profile, Journal of Crystal Growth, 97, 9-17, 1989 [2] J. Baumgartl, M. Gewald, R. Rupp, J. Stierlein and G. Müller, The Use of Magnetic Fields and Microgravity in Melt Growth of Semiconductors: A Comparative Study, Proceedings VIIth European Symposium on Materials and Fluid Sciences under Microgravity, ESA SP-295, [3] J. Baumgartl, G. Müller, Calculation of the effects of magnetic field damping on fluid flow - comparison of magnetohydrodynamic models of different complexity, Microgravity Quarterly 2 (1992) 197 [4] B. Fischer, J. Friedrich, C. Kupfer, D. Vizman, G. Müller, Experimental and numerical analysis of the influence of rotating magnetic fields on heat transport in Rayleigh Benard configurations, Proc. 3rd Int. Conf. on Transfer Phenomena in Magnetohydro-dynamic & Electroconducting, Flows Aussois, France September 1997, [5] B. Fischer, J. Friedrich, C. Kupfer, G. Müller, D. Vizman, Experimental and numerical analysis of the influence of a rotating magnetic field on convection in Rayleigh Benard configurations, In: Transfer Phenomena in Magnetohydrodynamics and Electroconducting Flows, Kluwer, Dordrecht (1999) [6] J. Friedrich, Y. Lee, B. Fischer, C. Kupfer, D. Vizman, G. Müller, Experimental and numerical study of Rayleigh-Benard convection affected by a rotating magnetic field, Physics of Fluids 11 (1999) [7] B. Fischer, J. Friedrich, U. Hilburger, G. Müller, Systematic study of buoyant flows in vertical melt cylinders under the influence of rotating magnetic fields, Proc. EPM2000, Nagoya, Japan, (2000) [8] A. Seidl, G. McCord, G. Müller, H.-J. Leister, Experimental observation and numerical simulation of wave patterns in a Czochralski silicon melt, J. Cryst. Growth 137 (1994) 326 [9] A. Seidl, G. Müller, E. Dornberger, E. Tomzig, B. Rexer, W. v. Ammon, Turbulent melt convection and its implication on large diameter silicon Czochralski crystal growth, Proceedings of the Eighth International Symposium on Silicon Materials Science and Technology. Silicon Materials Science and Technology. Electrochem. Soc, Pennington, NJ, USA (1998)

6 [10] O. Grabner; G. Muller; J. Virbulis; E. Tomzig; W. v. Ammon, Effects of various magnetic field configurations on temperature distributions in Czochralski silicon melts, Microelectronic-Engineering. vol.56, no.1-2; May 2001; p.83-8 [11] D. Vizman, J. Friedrich, G. Müller, Comparison of the predictions from 3D numerical simulation with temperature distributions measured in Si Czochralski melts under the influence of different magnetic fields, Journal-of-Crystal-Growth. vol.230, no.1-2; Aug. 2001; p [12] F. Mosel; A. Seidl; D. Hofmann; G. Muller, LEC-growth and characterization of n- and p-type Fedoped InP, Third International Conference. Indium Phosphide and Related Materials (Cat. No.91CH2950-4) IEEE, New York, NY, USA; 1991; xxiv+678 pp.331 [13] R. Rupp, S. Auerochs, G. Müller, C. Weyrich, S. Leibenzeder, Growth of GaAs single crystals by the Floating Zone Technique under microgravity, Adv. Space Res. 11 (1991) 297 [14] F.M. Herrmann, J. Baumgartl, T. Feulner and G. Müller, The Use of Magnetic Fields for Damping Unsteady Marangoni Convection in GaAs Floating Zones Under µg, Proceedings VIIIth European Symposium on Materials and Fluid Science in Microgravity ESA SP-333, 57-60, 1992 [15] F. Herrmann, G. Müller, Growth of 20mm diameter GaAs crystals by the Floating Zone technique with controlled As-vapour pressure under microgravity, J. Cryst. Growth 156 (1995) 350 [16] J. Friedrich, C. Kupfer, B. Fischer, G. Müller, Influence of rotating magnetic fields on heat and species transport in crystal growth by the Vertical Gradient Freeze method, Proc. 3rd Int. Conf. on Transfer Phenomena in Magnetohydrodynamic & Electroconducting Flows, Aussois, France September 1997, [17] B. Fischer, J. Friedrich, H. Weimann, G. Müller, The use of time-dependent magnetic fields for control of convective flows in melt growth configurations, J. Crystal Growth 198/199 (1999) [18] M. Hainke, T. Jung, J. Friedrich, B. Fischer, M. Metzger, G. Müller, Equipment and Process Modelling of Industrial Crystal Growth Using the Finite Volume Codes CrysVUn and STHAMAS., Progress in Industrial Mathematics (Eds. Anile, A.M.; Capasso, V.; Greco, A.), Springer Verlag, ISBN (2002), [19] G. Mueller, O. Graebner, D. Vizman, Simulation of Crystal Pulling and Comparison to Experimental Analysis Cz-Process, Electrochemical Society Meeting, Ninth International Symposium on Silicon Materials Science and Technology, Philadelphia, May 12-17, 2002 [20] D. Vizman, J. Friedrich, G. Mueller, HMCZ and EMCZ in the Industrial Czochralski Growth of 300mm Si Crystals, Proceedings of the 5 th International Pamir Conference, Fundamental and Applied MHD, September, 2002, Ramatuelle, France, [21] M. Hainke, J. Friedrich, G. Mueller, Numerical Study of the Effects of Rotating Magnetic Fields during VGF Growth of 3" GaAs Crystals, Proc. of 5 th Int. Pamir Conference (2002) V-1 [22] Y. Park, E. Kim, M. Son, S. Min, Effects of an axial magnetic field on the growth interfaces in vertical gradient freeze GaAs crystal growth, J. Crystal growth ) [23] J. Friedrich, G. Müller, The use of magnetic fields in crystal growth and alloy solidification: Importance for industrial technologies and for microgravity research, Low G Journal 1 (1999) [24] J. Friedrich, G. Müller, The influence of steady and alternating magnetic fields in crystal growth and alloy solidification: Industrial importance, current industrial R&D topics, links to microgravity research, ESA SP 433 (1999) [25] G. Müller, Melt Growth of Semiconductors, Materials-Science-Forum.vol ; 1998; p [26] J. Baumgartl, G. Müller, The use of magnetic fields for damping the action of gravity fluctuations (gjitter) during crystal growth under microgravity., J. Crystal Growth 169 (1996) [27] J. Friedrich, R. Backofen, G. Mueller, Numerical simulation of grain structure and global heat transport during solidification of technical alloys in MSL inserts under diffusive conditions, Adv. Space Res. 29/4 (2002) Authors Marc Hainke, Jochen Friedrich, Georg Müller Daniel Vizman Crystal Growth Laboratory Dept. of Physics Fraunhofer Institute IISB West University of Timisoara Schottkystr. 10 Bd. V. Parvan Erlangen 1900 Timisoara Germany Romania marc.hainke@iis-b.fhg.de 78