Convection and Inhomogeneities in Crystal Growth from the Melt

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.

[1]  Kobayashi Takashi,et al.  Homogeneity of Vertical Magnetic Field Applied LEC GaAs Crystal , 1984 .

[2]  E. Sirtl,et al.  Lamellar growth phenomena in 〈111〉-oriented dislocation-free float-zoned silicon single crystals , 1974 .

[3]  Georg Müller,et al.  Tenfold growth rates in the travelling heater method of GaSb crystals by forced convection on a centrifuge , 1983 .

[4]  A. Wheeler The effect upon Czochralski growth of periodic modulation of the growth rate , 1982 .

[5]  C. Stapper The effects of wafer to wafer defect density variations on integrated circuit defect and fault distributions , 1985 .

[6]  D. Schwabe,et al.  Marangoni convection in open boat and crucible , 1981 .

[7]  M. Mihelčić,et al.  Three-dimensional simulations of the Czochralski bulk flow in a stationary transverse field and in a vertical magnetic field: Effects on the asymmetry of the flow and temperature distribution in the Si melt , 1987 .

[8]  W. Tiller,et al.  The redistribution of solute atoms during the solidification of metals , 1953 .

[9]  F. Rosenberger,et al.  Convective instabilities in a closed vertical cylinder heated from below. Part 1. Monocomponent gases , 1979, Journal of Fluid Mechanics.

[10]  G. Müller Convection in melts and crystal growth , 1982 .

[11]  G. Müller,et al.  A two-Rayleigh-number model of buoyancy-driven convection in vertical melt growth configurations , 1987 .

[12]  F. Stöber XVII. Künstliche Darstellung großer, fehlerfreier Kristalle , 2022 .

[13]  J. R. Burke,et al.  Striations Due to Compositional Variations in Czochralski‐Grown ( Pb1 − x Sn x ) 1 − y Te y , 1973 .

[14]  K. M. Kim Suppression of Thermal Convection by Transverse Magnetic Field , 1982 .

[15]  H. Ueda Resistivity Striations in Germanium Single Crystals , 1961 .

[16]  A. Eyer,et al.  Striation-free silicon crystals by float-zoning with surface-coated melt , 1985 .

[17]  A. Chernov,et al.  Adsorbed layers on (111)InAs faces in contact with In-As-Cl-H gas phase, and the possibility of phase transitions in the adsorbed layers , 1981 .

[18]  J. Szekely,et al.  The effect of a magnetic field on transport phenomena in a Bridgman-Stockbarger crystal growth , 1984 .

[19]  M. Mihelčić,et al.  Three-dimensional simulations of the Czochralski bulk flow , 1984 .

[20]  Qianying Wu,et al.  Crystal Growth and Characterization , 1980 .

[21]  S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability , 1961 .

[22]  W. Gault,et al.  A novel application of the vertical gradient freeze method to the growth of high quality III–V crystals , 1986 .

[23]  A. Scharmann,et al.  Experiments on surface tension driven flow in floating zone melting , 1978 .

[24]  J. C. Brice,et al.  The suppression of thermal oscillations in czochralski growth , 1971 .

[25]  Helmut Kölker The behaviour of nonrotational striations in silicon , 1980 .

[26]  L. Wilson Analysis of microsegregation in crystals , 1980 .

[27]  Herbert E. Huppert,et al.  Double-diffusive convection , 1981, Journal of Fluid Mechanics.

[28]  T. Fujii,et al.  Increase of effective viscosity of molten GaAs and InSb under an axial magnetic field , 1987 .

[29]  K. Hoshikawa Czochralski Silicon Crystal Growth in the Vertical Magnetic Field , 1982 .

[30]  A.M.J.G. Van Run Computation of striated impurity distributions in melt-grown crystals, taking account of periodic remelt , 1979 .

[31]  L. Wilson The effect of fluctuating growth rates on segregation in crystals grown from the melt: II. Backmelting , 1980 .

[32]  J. Favier Initial transient segregation during unidirectional solidification of a binary alloy in a furnace with thermal damping , 1980 .

[33]  C. Chun Marangoni convection in a floating zone under reduced gravity , 1980 .

[34]  P. Kapitza The Study of the Specific Resistance of Bismuth Crystals and Its Change in Strong Magnetic Fields and Some Allied Problems , 1928 .

[35]  H. Oertel,et al.  Convective transport and instability phenomena , 1982 .

[36]  F. Szofran,et al.  Further comments on segregation during Bridgman growth of Cd(x)Hg(1-x)Te , 1984 .

[37]  W. Zulehner,et al.  Czochralski growth of silicon , 1983 .

[38]  G. Müller,et al.  Suppression of doping striations in zone melting of InSb by enhanced convection on a centrifuge , 1982 .

[39]  A. Witt,et al.  Microscopic Rates of Growth in Single Crystals Pulled from the Melt: Indium Antimonide , 1968 .

[40]  W. Cochran The flow due to a rotating disc , 1934, Mathematical Proceedings of the Cambridge Philosophical Society.

[41]  Harry L. Swinney,et al.  Hydrodynamic instabilities and the transition to turbulence , 1981 .

[42]  R. Parker Crystal Growth Mechanisms: Energetics, Kinetics, and Transport , 1970 .

[43]  D. Camel,et al.  Thermal convection and longitudinal macrosegregation in horizontal bridgman crystal growth: II. Practical laws , 1984 .

[44]  D. Mateika,et al.  Czochralski growth by the double container technique , 1983 .

[45]  J. Favier Macrosegregation—II a comparative study of theories , 1981 .

[46]  A. Eyer,et al.  Floating zone growth of silicon under microgravity in a sounding rocket , 1985 .

[47]  D. Camel,et al.  Theoretical analysis of solute transport regimes during crystal growth from the melt in an ideal Czochralski configuration , 1983 .

[48]  E. R. Pike,et al.  Striated solute distributions produced by temperature oscillations during crystal growth from the melt , 1968 .

[49]  R. Rupp,et al.  Deformation behaviour and dislocation formation in undoped and doped (Zn, S)InP crystals , 1985 .

[50]  Hisham M. Ettouney,et al.  Finite-element methods for steady solidification problems , 1983 .

[51]  D. Camel,et al.  Thermal convection and longitudinal macrosegregation in horizontal Bridgman crystal growth: I. Order of magnitude analysis , 1984 .

[52]  W. Wilcox,et al.  Dislocation elimination in THM growth of GaAs , 1976 .

[53]  H. Kodera Constitutional Supercooling during the Crystal Growth of Germanium and Silicon , 1963 .

[54]  H. Huppert,et al.  On melting icebergs , 1978, Nature.

[55]  J. Carruthers Origins of convective temperature oscillations in crystal growth melts , 1976 .

[56]  Elisabeth Bauser,et al.  Microscopic growth mechanisms of semiconductors: Experiments and models , 1984 .

[57]  F. Rosztoczy,et al.  Distribution Coefficient of Germanium in Gallium Arsenide Crystals Grown from Gallium Solutions , 1971 .

[58]  R. Prim,et al.  The Distribution of Solute in Crystals Grown from the Melt. Part I. Theoretical , 1953 .

[59]  T. Fukuda,et al.  Programmed magnetic field applied liquid encapsulated Czochralski crystal growth , 1987 .

[60]  E. D. Kolb,et al.  Distribution of Solute in Crystals Grown from the Melt. Part II. Experimental , 1953 .

[61]  J. Favier Macrosegregation—I unified analysis during non-steady state solidification , 1981 .

[62]  K. M. Kim,et al.  Crystal Growth from the Melt under Destabilizing Thermal Gradients , 1972 .

[63]  Georg Müller,et al.  Natural convection in vertical Bridgman configurations , 1984 .

[64]  B. Pamplin Preparation and properties of solid state materials: Edited by William R. Wilcox Marcel Dekker Inc., New York and Basel , 1981 .

[65]  Hermann Haken,et al.  Chaos and Order in Nature , 1981 .

[66]  U. Gösele,et al.  Point defects, diffusion processes, and swirl defect formation in silicon , 1985 .

[67]  S. Kyropoulos Ein Verfahren zur Herstellung großer Kristalle , 1926 .

[68]  M. Golay,et al.  Crystallization of Silicon from a Floating Liquid Zone , 1953 .

[69]  Harry L. Swinney,et al.  The transition to turbulence , 1978 .

[70]  J. Krausse,et al.  Zum einfluss von temperprozessen auf widerstandsschwankungen in siliziumeinkristallen , 1972 .

[71]  J. Turner,et al.  Buoyancy Effects in Fluids , 1973 .

[72]  L. Fullmer,et al.  Turbulent Free Convection in Czochralski Crystal Growth , 1965 .

[73]  G. Kamath,et al.  Macrosegregation in solution-grown GaAs crystals , 1982 .

[74]  A. R. Lang,et al.  Structural and chemical inhomogeneities in germanium single crystals grown under conditions of constitutional supercooling , 1980 .

[75]  F. Rosenberger Crystal Growth Kinetics , 1982 .

[76]  K. A. Jackson The present state of the theory of crystal growth from the melt , 1974 .

[77]  H. Gatos,et al.  Effect of Microscopic Growth Rate on Oxygen Microsegregation and Swirl Defect Distribution in Czochralski‐Grown Silicon , 1979 .

[78]  B. Mutaftschiev Interfacial Aspects of Phase Transformations , 1982 .

[79]  August F. Witt,et al.  Analysis of crystal growth characteristics in a conventional vertical Bridgman configuration , 1984 .

[80]  A. Witt,et al.  Quantitative Analysis of Microsegregation in Silicon Grown by the Czochralski Method , 1976 .

[81]  G. Müller,et al.  GaSb and InSb crystals grown by vertical and horizontal travelling heater method , 1979 .

[82]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[83]  N. Schryer,et al.  Flow between a stationary and a rotating disk with suction , 1978, Journal of Fluid Mechanics.

[84]  W. Wilcox,et al.  Programmed and oscillatory motion in Bridgman-Stockbarger growth , 1982 .

[85]  A. W. Vere,et al.  Ferroelectric domains and growth striae in barium sodium niobate single crystals , 1969 .

[86]  Barry Saltzman,et al.  Finite Amplitude Free Convection as an Initial Value Problem—I , 1962 .

[87]  P. J. Holmes A competitive adsorption model of steady-state growth of a crystal from a lightly-doped melt , 1963 .

[88]  W. Wilcox,et al.  Rate change transients in Bridgman-Stockbarger growth , 1981 .

[89]  Book-Review - Hydrodynamic Instabilities and the Transition to Turbulence , 1982 .

[90]  D. T. J. Hurle,et al.  Temperature oscillations in molten metals and their relationship to growth striae in melt-grown crystals , 1966 .

[91]  P. W. Bridgman Certain Physical Properties of Single Crystals of Tungsten, Antimony, Bismuth, Tellurium, Cadmium, Zinc, and Tin , 1925 .

[92]  R. G. Mazur,et al.  A Spreading Resistance Technique for Resistivity Measurements on Silicon , 1966 .

[93]  B. Cockayne,et al.  Growth striations in vertically pulled oxide and fluoride single crystals , 1967 .

[94]  M. Mihelčić,et al.  Numerical simulations of the Czochralski bulk flow in an axial magnetic field: Effects on the flow and temperature oscillations in the melt , 1985 .

[95]  A. W. Vere,et al.  Crucible-base cooling: An aid to Czochralski crystal growth , 1972 .

[96]  J. D. Verhoeven Experimental Study of Thermal Convection in a Vertical Cylinder of Mercury Heated from Below , 1969 .

[97]  Y. Hayakawa,et al.  Effect of Ultrasonic Vibrations on Pulled Crystals , 1982 .

[98]  H. Huppert,et al.  Ice blocks melting into a salinity gradient , 1980, Journal of Fluid Mechanics.

[99]  D. Hurle Melt temperature fluctuations: Causes and response of the solidification front , 1983 .

[100]  A. Witt,et al.  Impurity Distribution in Single Crystals IV . Growth Characteristics and Impurity Incorporation During Facet Growth , 1966 .

[101]  G. Müller,et al.  Interfacial transport in crystal growth, a parametric comparison of convective effects , 1983 .

[102]  R. L. Longini,et al.  Ionization Interaction between Impurities in Semiconductors and Insulators , 1956 .

[103]  C. J. Chang,et al.  Radial segregation induced by natural convection and melt/solid interface shape in vertical bridgman growth , 1983 .

[104]  N. Inoue,et al.  Study of Thermal Symmetry in Czochralski Silicon Melt under a Vertical Magnetic Field , 1984 .

[105]  L. Wilson A new look at the Burton, Prim, and Slichter model of segregation during crystal growth from the melt , 1978 .

[106]  H. Walter A Mechanism for Generation of Pulsating Growth and Nonrotational Striations during Initial Transient of Solidification , 1976 .

[107]  J. Bloem Doping in chemically vapour deposited epitaxial silicon , 1972 .

[108]  L. Schubnikow,et al.  Eine Methode zur Herstellung einkristalliger Metalle , 1924 .

[109]  A. Witt,et al.  Czochralski-type crystal growth in transverse magnetic fields , 1970 .

[110]  Ruby Krishnamurti,et al.  Some further studies on the transition to turbulent convection , 1973, Journal of Fluid Mechanics.

[111]  L. Wilson,et al.  A test of the boundary layer model in unsteady Czochralski growth , 1982 .

[112]  J. Gilman The art and science of growing crystals , 1963 .

[113]  K. Bachmann,et al.  Melt and solution growth of bulk single crystals of quaternary III–V alloys , 1981 .

[114]  Toshihiko Suzuki,et al.  Czochralski Silicon Crystals Grown in a Transverse Magnetic Field , 1985 .

[115]  D. C. Stockbarger The Production of Large Single Crystals of Lithium Fluoride , 1936 .

[116]  N. Balazs,et al.  Fundamental Problems in Statistical Mechanics , 1962 .

[117]  G. Müller,et al.  Investigation of convection in melts and crystal growth under large inertial accelerations , 1980 .

[118]  Hiroshi Hirata,et al.  Homogeneous Dopant Distribution of Silicon Crystal Grown by Vertical Magnetic Field-Applied Czochralski Method , 1984 .

[119]  A. Witt,et al.  Crystal Growth and Steady‐State Segregation under Zero Gravity: InSb , 1975 .