Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

Abstract A thermocapillary model is used to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the menisci bounding the melt. The positions of the menisci and phase-change boundary are computed to satisfy the conservation laws rigorously. A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal–melt–gas triple phase line, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic shape stability is clarified.

[1]  J. Derby,et al.  Influence of thermal phenomena on crystal reattachment during dewetted Bridgman growth , 2009 .

[2]  T. Duffar,et al.  Bridgman growth without crucible contact using the dewetting phenomenon , 2000 .

[3]  F. Voltmer,et al.  Influence of gravity-free solidification on solute microsegregation , 1975 .

[4]  T. Surek,et al.  The growth of shaped crystals from the melt , 1980 .

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

[6]  Andrew Yeckel,et al.  Effect of steady crucible rotation on segregation in high-pressure vertical Bridgman growth of cadmium zinc telluride , 1999 .

[7]  Martin P. Volz,et al.  Detached growth of germanium by directional solidification , 2005 .

[8]  M. Volz,et al.  Bridgman Growth of Detached GeSi Crystals , 2002 .

[9]  Simon Brandon,et al.  Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling , 2008 .

[10]  J. Hale,et al.  Dynamics and Bifurcations , 1991 .

[11]  G. Roosen,et al.  DEWETTING AND STRUCTURAL QUALITY OF CdTe:Zn:V GROWN IN SPACE ☆ , 2001 .

[12]  P. Schweizer,et al.  Liquid film coating : scientific principles and their technological implications , 1997 .

[13]  R. Abbaschian,et al.  Detached crystal growth from melt by the axial heat processing technique , 2004 .

[14]  Liliana Braescu,et al.  On the capillary stability of the crystal-crucible gap during dewetted Bridgman process , 2010 .

[15]  Olf Pätzold,et al.  Detached growth behaviour of 2-in germanium crystals , 2005 .

[16]  Liliana Braescu,et al.  Shape of menisci in terrestrial dewetted Bridgman growth. , 2008, Journal of colloid and interface science.

[17]  L. Bizet,et al.  Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions , 2004 .

[18]  J. Garandet,et al.  Dewetting application to CdTe single crystal growth on earth , 2004 .

[19]  J. Szmelter Incompressible flow and the finite element method , 2001 .

[20]  Conyers Herring,et al.  Surface Tension as a Motivation for Sintering , 1999 .

[21]  W. Wilcox,et al.  Surface tension and contact angle of molten semiconductor compounds. I. cadmium telluride , 1990 .

[22]  Thomas A. Read,et al.  Physics of Powder Metallurgy , 1949 .

[23]  Liliana Braescu,et al.  Comparison between analytical and numeric determination of the interface curvature during dewetted Bridgman crystal growth , 2008 .

[24]  P. Schunk,et al.  Advances in Computational Methods for Free-Surface Flows , 1997 .

[25]  T. Duffar,et al.  Growth of GaSb single crystals by an improved dewetting process , 2001 .

[26]  Arun Pandy,et al.  Analysis of the growth of cadmium zinc telluride in an electrodynamic gradient freeze furnace via a self-consistent, multi-scale numerical model , 2005 .

[27]  M. Volz,et al.  Stability of detached-grown germanium single crystals , 2002 .

[28]  W. Wilcox,et al.  Approximate material-balance solution to the moving meniscus model of detached solidification , 2002 .

[29]  Long Chen FINITE ELEMENT METHOD , 2013 .

[30]  Daniel R. Lynch,et al.  Continuously deforming finite elements for the solution of parabolic problems, with and without phase change , 1981 .

[31]  A. B. Crowley,et al.  Mathematical Modelling of Heat Flow in Czochralski Crystal Pulling , 1983 .

[32]  M. Volz,et al.  Detached Bridgman Growth—A Standard Crystal Growth Method with a New Twist , 2009 .

[33]  G. Satunkin Determination of growth angles, wetting angles, interfacial tensions and capillary constant values of melts , 2003 .

[34]  Pierre Dusserre,et al.  Crucible de-wetting during Bridgman growth in microgravity. II. Smooth crucibles , 1997 .

[35]  J. Derby,et al.  Theoretical analysis and design considerations for float-zone refinement of electronic grade silicon sheets , 1995 .

[36]  Liliana Braescu,et al.  On the pressure difference ranges which assure a specified gap size for semiconductor crystals grown in terrestrial dewetted Bridgman , 2010 .

[37]  T. Duffar Bulk Crystal Growth under Microgravity Conditions , 2010 .

[38]  P. Dusserre,et al.  Crucible de-wetting during bridgman growth of semiconductors in microgravity , 1990 .

[39]  William H. Press,et al.  Numerical recipes , 1990 .

[40]  Jeffrey J. Derby,et al.  Finite Element Analysis of a Thermal‐Capillary Model for Liquid Encapsulated Czochralski Growth , 1985 .

[41]  Lamine Sylla,et al.  Numerical simulation of temperature and pressure fields in CdTe growth experiment in the Material Science Laboratory (MSL) onboard the International Space Station in relation to dewetting , 2007 .

[42]  S. Brandon,et al.  Basic Principles of Capillarity in Relation to Crystal Growth , 2010 .

[43]  Klaus-Werner Benz,et al.  Dewetted growth and characterisation of high-resistivity CdTe , 2004 .

[44]  D. Hurle Crystal pulling from the melt , 1993 .

[45]  J. Derby,et al.  On the dynamics of Czochralski crystal growth , 1987 .

[46]  C. Lan Flow and segregation control by accelerated rotation for vertical Bridgman growth of cadmium zinc telluride: ACRT versus vibration , 2005 .

[47]  Joe F. Thompson,et al.  Numerical grid generation , 1985 .

[48]  K. Benz,et al.  Detached growth of gallium doped germanium , 2002 .

[49]  W. Wilcox,et al.  Influence of Contact Angle, Growth Angle and Melt Surface Tension on Detached Solidification of InSb , 2000 .