Abstract
The bulk single crystab of semiconductors (e.g. Si, GaAs) and oxides which are at present commercially produced have mostly non-uniform properties in the microscale (e.g. doping striations) and in the macroscale (longitudinal and lateral segregation). Such inhomogeneities are deleterious for the performance of the devices produced from these crystals. This book gives a review of the various origins of inhomogeneities occuring during crystal growth from the melt. It is shown that convection is the major source of the non-uniformities in the technically used growth configurations, e.g. Czochralski-, zone- and Bridgman-methods, because the growth rate is controlled by the heat transport. The formalism of hydrodynamics, especially dimensionless numbers, is used for a modeling of melt growth, giving a correlation between the occurrence of inhomogeneities and relevant growth parameters.
The results of the theoretical and experimental modeling are found to be in correlation to results of real crystal growth, especially for cases of dominating buoyancy convection.
Various measures in avoiding inhomogeneities are derived from the models and are discussed with respect to their efficiency and practical applicability.
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References
Müller, G.: Über die Entstehung von Inhomogenitäten in Halbleiterkristallen bei der Herstellung aus Schmelzen, Selisch Fachbuch-Verlag, Langensendelbach 1986
Czochralski, J.: Z. Physik. Chem. (Leipzig) 92, 219 (1917)
Zulehner, W., Huber, D.: Crystals Vol. 8 (ed. J. Grabmaier) Springer-Verlag, Berlin 1982, pp. 3–143
Keck, P. H., Golay, M. J. E.: Phys. Rev. 89, 1297 (1953)
Emeis, R.: Z. Naturforsch. 9a, 67 (1954)
Dietze, W., Keller, W., Mühlbauer, A.: Crystals Vol. 5 (ed. H. C. Freyhardt) Springer-Verlag, Berlin 1981, pp. 1–42
Werkfoto of Wacker Chemitronic GmbH, Burghausen (unpublished) 1986
Stapper, C. H.: IBM J. Res. Development 29, 87 (1985)
Liaw, H. M.: Solid State Technol. July, 65 (1982)
Olsen, G. H., Ban, V. S.: ibid. Febr. 99 (1987)
Müller, G., Jacob, H.: in Landolt-Börnstein, n.s. Group III, Vol. 17d (eds. Schulz, M., Weiss, H.) Springer-Verlag, Berlin 1984, pp. 12–63
Gault, W. A., Monberg, E. M., Clemens, J. E.: J. Crystal Growth 74, 491 (1986)
Zulehner, W.: in Landolt-Börnstein, n.s. Group III, Vol. 17c (eds. M. Schulz, H. Weiss) Springer-Verlag, Berlin 1984
Mühlbauer, A.: see Ref. 13
Walter, H. U.: ESA Journal 7, 235 (1983)
Druminsky, M.: private communication
Dannhäuser, F., Krausse, J., Mayer, K.: Solid State Electron. 15, 1383 (1972)
Obreimov, J., Schubnikov, L.: Z. Physik 25, 31 (1924)
Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 60, 305, 385, 423 (1925)
Stöber, F.: Z. Kristallogr. 61, 299 (1925)
Stockbarger, D. C.: Rev. Sci. Instr. 7, 133 (1936)
Kapitza, P.: Proc. Roy. Soc. (London) A119, 358 (1928)
Pfann, W. G.: Trans. AIME 194, 747 (1952)
Nacken, R.: Z. Instrumentenkunde 36, 12 (1916)
Kyropoulos, S.: Z. Anorg. Allgem. Chem. 154, 308 (1926)
Gilman, J. J. (ed.): The Art and Science of Growing Crystals, John Wiley, New York and London 1963
Maier, H., Hesse, J.: Crystals Vol. 3 (ed. Freyhardt, H. C.) Springer-Verlag, Berlin 1980, pp. 145–220
Rosenberger, F.: Interfacial Aspects of Phase Transformations (ed. Mutaftschiev, B.) Reidel Publ. Comp. 1982, pp. 315–364
Jackson, K. A.: J. Crystal Growth 24/25, 130 (1974)
Bauser, E., Strunk, H. P.: ibid. 69, 561 (1984)
Rosenberger, F.: Fundamentals of Crystal Growth I, Springer Series in Solid-State Sciences Vol. 5, Springer-Verlag, Berlin 1979
Parker, R. L.: Solid State Physics Vol. 25 (eds. Ehrenreich, H., Seitz, F., Turnbull, D.) Academic Press, New York 1970, pp. 151–299
Cornell, S. R., McFadden, G. B., Rehmand, R. G., Glicksman, M. E.: see Ref. 85, pp. 102–126
Müller, G., Neumann, G.: J. Crystal Growth 63, 58 (1983)
Budo, A.: Theoretische Mechanik, VEB Deut. Verl. d. Wissenschaften, Berlin 1963
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability, Chlarendon Press, Oxford 1961
Oertel, H.: Convective Transport and Instability Phenomena (eds. Zierep, J., Oertel, H., jr.) Braun-Verlag, Karlsruhe 1982, pp. 3–24
Velarde, M. G., Castillo, J. L.: see Ref. 37, pp. 235–264
Schwabe, D., Scharmann, A., Peisser, F., Oeder, R.: J. Crystal Growth 43, 305 (1978)
Schwabe, D.: Physico Chemical Hydrodynamics 2, 263 (1981)
Schwabe, D., Scharmann, A.: J. Crystal Growth 52, 435 (1981)
Chun, C. H., Schwabe, D.: see Ref. 37, pp. 397–318
Mihelcic, M., Wingerath, K., Pirron, C.: J. Crystal Growth 69, 473 (1984)
Polezhaev, V. J.: Crystals Vol. 10 (ed. Freyhardt, H. C.) Springer-Verlag, Berlin 1984, pp. 87–150
Rosenberger, F., Müller, G.: J. Crystal Growth 65, 91 (1983)
Müller, G., Neumann, G., Weber, W.: ibid. 70, 78 (1984)
Krishnamurti, R.: J. Fluid Mech. 60, 285 (1973)
Müller, G., Neumann, G., Matz, H.: J. Crystal Growth 84, 36 (1987)
Carruthers, J. R.: Preparation and Properties of Solid State Materials Vol. 3 (eds. Wilcox, W. R., Lefever, R. A.) Dekker, New York 1977, pp. 1–121
Dietl, J., Helmreich, D., Sirtl, E.: see Ref. 6, pp. 43–107
Schmid, F.: german patent, DE 3001815, filed 18. 1. 80
Neumann, G.: Ph. D. thesis, Institut für Werkstoffwissenschaften, Universität Erlangen-Nürnberg 1986
Lehoczky, S. L., Szofran, F. R.: J. Crystal Growth 69, 201 (1984)
Morizane, K., Witt, A. F., Gatos, H. C.: J. Electrochem. Soc. 115, 747 (1968)
Mühlbauer, A., Sirtl, E.: phys. stat. sol. (a) 23, 555 (1974)
Cisek, T. F.: in Semiconductor Silicon (eds. Haberecht, R. R., Kern, E. L.) Electrochem. Soc, New York 1969, 156
Holmes, P. J.: J. Phys. Chem. Solids 24, 1239 (1963)
Rosztoczy, R. E., Wolfstirn, K. B.: J. Appl. Phys. 42, 426 (1971)
Bloem, J.: J. Crystal Growth 13/14, 302 (1972)
Longini, R. L., Greene, R. F.: Phys. Rev. 102, 992 (1956)
Zschauer, K.-H.: Festkörperprobleme, Advances in Solid State Physics Vol. 15 (ed. Queiser, H. J.) Pergamon/Vieweg-Verlag, Braunschweig 1975, pp. 1–20
Zschauer, K.-H., Vogel, A.: Proc. 3rd. Int. Symp. on GaAs and Related Compounds, Inst. Phys. Conf. Ser. 9, 100 (1971)
Burton, J. A., Prim, R. C., Slichter, W. P.: J. Chem. Phys. 21, 1987 (1953)
Favier, J. J., Wilson, L. O.: J. Crystal Growth 58, 103 (1982)
Wilcox, W. R.: Fractional Solidification (eds. Zief, M., Wilcox, W. R.) Dekker, New York 1967, pp. 47–117
Kodera, H.: J. Appl. Phys. 2, 527 (1963)
Scheil, E.: Z. Metallkunde 14, 70 (1942)
Pfann, W. G.: Zone Melting, (2nd ed.) John Wiley, New York 1966
Müller, G.: Proc. Europ. Materials Research Society Conf., Strasbourg, June 2–5 (1987) Les Editions de Physique, Paris 1987, Vol. XVI, pp. 117–130
Wilson, L. O., Schryer, N. L.: J. Fluid Mech. 85, 479 (1978)
Wilson, L. O.: J. Crystal Growth 44, 371 (1978)
Favier, J. J.: Acta Met. 29, 197 (1981)
Camel, D., Favier, J. J.: J. Crystal Growth 67, 42 (1984)
Camel, D., Favier, J. J.: ibid. 67, 57 (1984)
Müller, G., Kyr, P.: Proc. of Scientific Results of the German Spacelab Mission D1, Norderney, Aug. 27–29,1986, (eds.) Sahm, P. R., Jansen, R., Keller, M. H., Wissenschaftl. Projektführung D1 c/o DFVLR-Köln, 1987, p. 246
Hunt, J. D., Jackson, K. A.: Trans. Met. Soc. AIME 263, 843 (1966)
Favier, J. J., de Goer, J.: Proc. 5th European Symp. Materials Sciences Under Microgravity, Elmau (1984) ESA-SP 222/ISSN = 379–656, pp. 127–134
Kyr, P.: Ph. D. thesis, Institut für Werkstoffwissenschaften, Universität Erlangen-Nürnberg 1985
Cochran, W. G.: Proc. Comb. Phil. Soc. 30, 365 (1934)
Olson, J. M., Rosenberger, R.: J. Fluid Mech. 92, 609 (1979)
Charlson, G. S., Sani, R. L.: Int. J. Heat Mass Transfer 14, 2157 (1971)
Neumann, G., Müller, G.: to be published
Kölker, H.: J. Crystal Growth 50, 852 (1980)
Hirata, H., Inoue, N.: Jap. J. Appl. Phys. 23, L527 (1984)
Brown, R. A., Ungar, L. H., Adornato, P. M.: Workshop on “Solidification and Fluid Dynamics in the Earth’s and the Space Laboratory”, Aachen, RWTH, March 8–9 (1984), pp. 127–157
Ettouney, H. M., Brown, R. A.: Comput. Phys. 49, 118 (1983)
Holmes, D. E., Gatos, H. C.: J. Electrochem. Soc. 128, 429 (1981)
Wang, C. A., Witt, A. F., Carruthers, J. R.: J. Crystal Growth 66, 299 (1984)
Müller, G.: Tiegel zum Herstellen von Kristallen und Verwendung des Tiegels, German patent P3441707.9, filed 15. 11. 1984
Fig. 44 in Ref. 36
Fig. 43 and p. 191 in Ref. 36
Oreper, G. M., Szekely, J.: J. Crystal Growth 67, 405 (1984)
Witt, A. F., Gatos, H. C., Lichtensteiger, M., Lavine, M. C., Herman, C. J.: J. Electrochem. Soc. 122, 276 (1975)
Fiegl, G.: Solid State Technol. August, 121 (1983)
Holmes, D. E., Kamath, G. S.: J. Crystal Growth 57, 607 (1982)
Yip, V. F. S., Wilcox, W. R.: ibid. 36, 29 (1976)
Burton, J. A., Kolb, E. D., Slichter, W. P., Struthers, J. D.: J. Chem. Phys. 21, 1991 (1953)
Ozawa, S., Kimura, T., Kobayashi, J., Fukuda, T.: Appl. Phys. Lett. 50, 329 (1987)
Maier, H., Hesse, J.: Crystals Vol. 3 (ed. H. C. Freyhardt) Springer-Verlag, Berlin 1980, pp. 145–220
Bachmann, K. J. Thiel, F. A., Schreiber, H.: Prog. Crystal Growth Char. 2, 171 (1979)
Benz, K. W., Müller, G.: J. Crystal Growth 46, 35 (1979)
Zschauer, K.-H., Sell, H.-J.: to be published
Müller, G., Weiss, H.: German patent DE 2842605 C2, filed 29. 9. 78, given 8. 12. 83, additional patent DE 2933976 A1 US-Patent 4, 267, 154; filed Aug. 20, 1979; given 12. 5. 81
Hoshikawa, K., Kohda, H., Hirata, H.: J. Appl. Phys. 23, L37 (1984)
Mazur, R. G., Dickey, D. H.: J. Electrochem. Soc. 113, 255 (1966)
Murgai, A., Gatos, H. C., Westdorp, W. A.: ibid. 126, 2240 (1979)
Burke, J. R., Jensen, J. D., Houston, B.: ibid. 120, 431 (1973)
Tan, T. Y., Gösele, U.: Appl. Phys. A 37, 1 (1985)
Müller, G.: see Ref. 37, pp. 441–468
Camel, D., Favier, J. J.: J. Crystal Growth 61, 125 (1983)
Favier, J. J.: Acta Met. 29, 205 (1981)
Favier, J. J.: J. Crystal Growth 49, 373 (1980)
Van Run, A. M. J. G.: ibid. 47, 680 (1979)
Wilson, L. O.: ibid. 48, 363 (1980)
Wilson, L. O.: ibid. 48, 435 (1980)
Wilson, L. O.: ibid. 48, 451 (1980)
Wilson, L. O.: ibid. 56, 219 (Erratum) (1982)
Wheeler, A. A.: ibid. 56, 67 (1982)
Wheeler, A. A.: Proc. R. Soc. Lond. A 379, 305 (1982)
Wheeler, A. A.: ibid. 379, 325 (1982)
Hurle, D. T. J., Jakeman, E., Pike, E. R.: J. Crystal Growth 34, 633 (1968)
Witt, A. F., Gatos, H. C.: J. Electrochem. Soc. 115, 70 (1968)
Fu, T. W., Wilcox, W. R.: J. Crystal Growth 51, 557 (1981)
Fu, T. W., Wilcox, W. R.: ibid. 57, 91 (1982)
Hayakawa, Y., Sone, Y., Tatsumi, K., Kumagawa, M.: Jap. J. Appl. Phys. 21, 1273 (1982)
Hurle, D. T. J.: Adv. Space Res. Vol. 3, No. 5, 43 (1983)
Sing, R., Witt, A. F., Gatos, H. C.: J. Electrochem. Soc. 121, 380 (1974)
Murgai, A., Gatos, H. C., Witt, A. F.: ibid. 123, 224 (1976)
Martin, E. P., Jr.: Ph. D. thesis, Massachusetts Institute of Technology 1977
Hurle, D. T. J.: Phil. Mag. 13, 305 (1966)
Hurle, D. T. J.: Crystal Growth (ed. H. S. Peiser) Pergamon, Oxford 1967, 659
Busse, F. H.: see Ref. 37, pp. 149–170
see Ref. 37 Chap. 2.1, pp. 233–317
Schwabe, D., Scharmann, A.: Proc. 4th European Symp. on Materials Sciences Under Microgravity (ESA SP-191) Madrid, Aprü 1983, pp.213–218
Eyer, A., Leiste, H., Nitsche, R.: see Ref. 77, pp. 173–182
Eyer, A., Leiste, H., Nitsche, R.: J. Crystal Growth 71, 173 (1985)
Eyer, A., Leiste, H.: ibid. 71, 249 (1985)
Kölker, H.: Proc. 5th Europ. Symp. on Materials Sciences Under Microgravity, Elmau (1984) ESA-SP 222/ISSN 0379–6566, pp. 169–172
Walter, H. U.: J. Electrochem. Soc. 123, 1098 (1976)
Garcia-Ybarra, P. L., Velarde, M.: Phys. Fluids (submitted)
Chun, Ch-H.: J. Crystal Growth 48, 600 (1980)
Schwabe, D.: Habilitationsschrift, Justus-Liebig-Universität Giessen 1981
Turner, J. S.: Buoyancy Effects in Fluids, Cambridge University Press 1973
Huppert, H. E., Turner, J. S.: Nature 271, 46 (1978)
Huppert, H. E., Turner, J. S.: J. Fluid Mech. 100, 367 (1980)
Huppert, H. E., Turner, J. S.: ibid. 106, 299 (1981)
Müller, G., Neumann, G.: J. Crystal Growth 59, 548 (1982)
Cherepanova, T. A., Didrikson, T. A.: Krist. Tech. 14, 1501 (1979)
Chernov, A. A., Ruzakin, M. P.: J. Crystal Growth 52, 185 (1981)
Carruthers, J. R., Witt, A. F.: Crystal Growth and Characterization (eds. Ueda, R., Mullin, J. B.) North-Holland Publ. Comp., Amsterdam 1975, pp. 107–154
Kyr, P., Müller, G.: Z. Flugwiss. Weltraumforsch. 6, 152 (1982)
Tiller, W. A., Jackson, K. A., Rutter, J. W., Chalmers, B.: Acta Met. 1, 428 (1953)
Ueda, H.: J. Phys. Soc. Japan 16, 61 (1961)
Komarov, G. V., Regel, A. R.: Sov. Phys. Sol. State 5, 563 (1963)
Bardsley, W., Hurle, D. T. J., Hart, M., Lang, A. R.: J. Crystal Growth 49, 612 (1980)
Haken, H. (editor): Chaos and Order in Nature, Springer-Verlag Berlin 1984
Schuster, H. G.: Deterministic Chaos, Physik-Verlag, Weinheim 1984
Hurle, D. T. J.: see Ref. 85, pp. 55–76
Lorenz, E. N.: J. Atmos. Sci. 20, 130 (1963)
Saltzman, B.: ibid. 19, 329 (1981)
Swinney, H. L., Gollub, J. P.: Physics Today 31, August, 41 (1978)
Hellemann, R. H. G.: Fundamental Problems in Statistical Mechanics, Vol. 5 (ed. Cohen, E. G. D.) North-Holland, Amsterdam — New York 1980, 165
Hellemann, R. H. G., Joos, G. (eds.): Chaotic Behaviour in Deterministic Systems, North-Holland, Amsterdam 1983
Swinney, H. L., Gollub, J. P.: Hydrodynamic Instabilities and the Transition to Turbulence, Springer-Verlag, Berlin 1981
Carruthers, J. R.: J. Crystal Growth 32, 13 (1976)
Müller, G., Neumann, G.: Proc. 4th Europ. Symp. on Material Sciences Under Microgravity (ESA SP-191), Madrid, April 1983, pp. 285–294
Weber, W.: Ph. D. thesis, Institut für Werkstoffwissenschaften, Universität Erlangen-Nürnberg 1988
Verhoeven, J. D.: Physics Fluids 12, 1733 (1969)
Fauve, S., Libchaber, A.: Chaos and Order in Nature (ed. H. Haken) Springer-Verlag, Berlin 1984
Wilcox, W. R., Fullmer, L. D.: J. Appl. Phys. 36, 2201 (1965)
Cockayne, B., Plant, J. G., Vere, A. W.: J. Crystal Growth 15, 167 (1972)
Cole, G. S., Winegard, W. C.: J. Inst. Metals 93, 153 (1964)
Kim, K. M., Witt, A. F., Gatos, H. C.: J. Electrochem. Soc. 119, 1218 (1972)
Carruthers, J. R., Witt, A. F., Reusser, R. E.: Semiconductor Silicon, Proc. 3. Int. Symp. on Silicon Materials Science and Technology, Philadelphia, 1977, Vol. 77–2, p. 61
Zulehner, W.: Crystal Growth 1983, Proc. 7. Int. Conf. on Crystal Growth, Stuttgart, Sept. 12–16 (1983) J. Crystal Growth 65, 189 (1983)
Whiffîn, P. A. C., Brice, J. C.: J. Crystal Growth 10, 91 (1971)
Mateika, D., Laurien, R., Liehr, M.: ibid. 65, 237 (1983)
Cockayne, B., Gates, M. P.: J. Mater. Sci. 2, 118 (1967)
Cockayne, B., Chesswas, M., Plant, J. G., Vere, A. W.: ibid. 4, 565 (1969)
Utech, H. P., Flemings, M. C.: Crystal Growth (ed. H. S. Peiser) Pergamon, Oxford 1967, 651
Witt, A. F., Herman, C. J., Gatos, H. C.: J. Mater. Sci. 5, 822 (1970)
Cohen, C.: Electronics, July 3 (1980), 83
Kim, K. M.: J. Electrochem. Soc. 129, 421 (1982)
Walter, H.: private communication
Hoshi, K., Isawa, N., Suzuki, T., Ohkubo, Y.: J. Electrochem. Soc. 132, 693 (1985)
Mihelcic, M., Wingerath, K.: J. Crystal Growth 82, 318 (1987)
Hoshikawa, K.: Jap. J. Appl. Phys. 21, L545 (1982)
Osaka, J., Kohda, H., Kobayashi, T., Hoshikawa, K.: ibid. 23, L195 (1984)
Terashima, K., Katsumata, T., Orito, F.: ibid. 23, L302 (1984)
Mihelcic, M., Wingerath, K.: J. Crystal Growth 71, 163 (1985)
Berge, P., Dubois, M., Croquette, V.: see Ref. 37, pp. 123–148
Müller, G., Schmidt, E., Kyr, P.: J. Crystal Growth 49, 387 (1980)
Müller, G.: Adv. Space Res. 3, 51 (1983)
Ozawa, S., Eguchi, M., Fujii, T., Fukuda, T.: Appl. Phys. Lett. 51, 197 (1987)
Chedsey, H. A., Robertson, D. S.: J. Phys. D5, 325 (1972)
Kumagawa, M., Tamaki, M., Hayakawa, Y.: Japan J. Appl. Phys. 26, 180 (1987)
Müller, G., Rupp, R., Volkl, J., Wolf, H., Blum, W.: J. Crystal Growth 71, 771 (1985)
Völkl, J., Müller, G.: see Ref. 69, pp. 141–150
Chang, C. J., Brown, R. A.: J. Crystal Growth 63, 343 (1983)
Hofmann, D., Mosel, F., Müller, G.: to be published
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Müller, G. (1988). Convection and Inhomogeneities in Crystal Growth from the Melt. In: Crystal Growth from the Melt. Crystals, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73208-9_1
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