nach oben

Erschienen in:

2010 | OriginalPaper | Buchkapitel

40. Mass and Heat Transport in BS and EFG Systems

verfasst von : Thomas F. George, Stefan Balint, Liliana Braescu

Erschienen in: Springer Handbook of Crystal Growth

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this chapter several mathematical models describing processes which take place in the Bridgman–Stockbarger (BS) and edge-defined film-fed growth (EFG) systems are presented. Predictions are made concerning the impurity repartition in the crystal in the framework of each of the models. First, a short description of the real processes which are modeled is given, along with the equations, boundary conditions, and initial values defining the mathematical model. After that, numerical results obtained by computations in the framework of the model are provided, making a comparison between the computed results and those obtained in other models, and with the experimental data.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Models for Stress and Dislocation Generation in Melt Based Compound Crystal Growth

Nächstes Kapitel Crystalline Layer Structures with X-Ray Diffractometry

40.1.

J.A. Burton, R.C. Prim, W.P. Slichter: The distribution of solute on crystals grown from the melt, J. Chem. Phys. 21, 1987–1996 (1953)ADSCrossRef

40.2.

C. Wagner: Theoretical analysis of diffusion of solutes during the solidification of alloys, J. Met. 6, 154–160 (1954)

40.3.

K.M. Kim, A.F. Witt, M. Lichtensteiger, H.C. Gatos: Quantitative analysis of the thermo-hydrodynamic effects on crystal growth and segregation under destabilizing vertical thermal gradients: Ga-doped germanium, J. Electrochem. Soc. 125, 475–480 (1974)CrossRef

40.4.

J.J. Favier: Macrosegregation-I: Unified analysis during non-steady state. Solidification, Acta Metall. 29, 197–204 (1981)CrossRef

40.5.

J.J. Favier: Macrosegregation-II: A comparative study of theories, Acta Metall. 29, 205–214 (1981)CrossRef

40.6.

D.E. Holmes, H.C. Gatos: Convective interference and "effective" diffusion-controlled segregation during directional solidification under stabilizing vertical thermal gradients; Ge, J. Electrochem. Soc. 128, 429–437 (1981)CrossRef

40.7.

C.J. Chang, R.A. Brown: Radial segregation induced by natural convection and melt/solid interface shape in vertical Bridgman growth, J. Cryst. Growth 63, 343–364 (1983)ADSCrossRef

40.8.

W.A. Tiller, K.A. Jackson, J.W. Rutter, B. Chalmers: The redistribution of solute atoms during the solidification of metals, Acta Metall. 1, 428–437 (1953)CrossRef

40.9.

P.R. Griffin, S. Motakef: Influence of non-steady gravity on natural convection during micro-gravity solidification of semiconductors. Part I. Time Scale Analysis, J. Appl. Microgravity II 3, 121–127 (1989)

40.10.

P.R. Griffin, S. Motakef: Influence of non-steady gravity on natural convection during micro-gravity solidification of semiconductors. Part II. Implications for crystal growth experiments, J. Appl. Microgravity II 3, 128–132 (1989)

40.11.

A.F. Witt, H.C. Gatos, M. Lichtensteiger, M.C. Lavine, C.J. Herman: Crystal growth and steady-state segregation under zero gravity, J. Electrochem. Soc. 122, 276–283 (1975)ADSCrossRef

40.12.

P.M. Adornato, R.A. Brown: Convection and segregation in directional solidification of dilute and non-dilute binary alloys, J. Cryst. Growth 80, 155–190 (1987)ADSCrossRef

40.13.

P.A. Clark, W.R. Wilcox: Influence of gravity on thermocapillary convection in floating zone melting of silicon, J. Cryst. Growth 50, 461–469 (1980)ADSCrossRef

40.14.

S.A.I. Nikitin, V. Polezhayev, A.I. Fedyushkin: Mathematical simulation of impurity distribution in crystals prepared under microgravity conditions, J. Cryst. Growth 52, 471–477 (1981)ADSCrossRef

40.15.

S.R. Coriell, R.F. Sekerka: Lateral solute segregation during unidirectional solidification of a binary alloy with a curved solid-liquid interface, J. Cryst. Growth 46, 479–482 (1979)ADSCrossRef

40.16.

S.R. Coriell, R.F. Boisvert, R.G. Rehm, R.F. Sekerka: Lateral solute segregation during unidirectional solidification of a binary alloy with a curved solid-liquid interface II. Large departures from planarity, J. Cryst. Growth 54, 167–175 (1981)ADSCrossRef

40.17.

H.M. Ettouney, R.A. Brown: Effect of heat transfer on melt/solid interface shape and solute segregation in edge-defined film-fed growth: Finite element analysis, J. Cryst. Growth 58, 313–329 (1982)ADSCrossRef

40.18.

J.P. Kalejs, L.Y. Chin, F.M. Carlson: Interface shape studies for silicon ribbon growth by the EFG technique I. Transport phenomena modeling, J. Cryst. Growth 61, 473–484 (1983)ADSCrossRef

40.19.

C.E. Chang, W.R. Wilcox: Control of interface shape in the vertical Bridgman-Stockbarger technique, J. Cryst. Growth 21, 135–140 (1974)ADSCrossRef

40.20.

T.W. Fu, W.R. Wilcox: Influence of insulation on stability of interface shape and position in the vertical Bridgman-Stockbarger technique, J. Cryst. Growth 48, 416–424 (1980)ADSCrossRef

40.21.

T.W. Clyne: Heat flow in controlled directional solidification of metals I. Experimental investigation, J. Cryst. Growth 50, 684–690 (1980)ADSCrossRef

40.22.

T.W. Clyne: Heat flow in controlled directional solidification of metals II. Mathematical model, J. Cryst. Growth 50, 691–700 (1980)ADSCrossRef

40.23.

P.C. Sukanek: Deviation of freezing rate from translation rate in the Bridgman-Stockbarger technique I. Very low translation rates, J. Cryst. Growth 58, 208–218 (1982)ADSCrossRef

40.24.

P.C. Sukanek: Deviation of freezing rate from translation rate in the Bridgman-Stockbarger technique II. Moderate translation rates, J. Cryst. Growth 58, 219–228 (1982)ADSCrossRef

40.25.

T. Jasinski, W.M. Rohsenow, A.F. Witt: Heat transfer analysis of the Bridgman-Stockbarger configuration for crystal growth I. Analytical treatment of the axial temperature profile, J. Cryst. Growth 61, 339–354 (1983)ADSCrossRef

40.26.

L.R. Morris, W.C. Winegard: The development of cells during the solidification dilute Pb-Sb alloy, J. Cryst. Growth 5, 361–375 (1969)ADSCrossRef

40.27.

A.F. Witt, H.C. Gatos, M. Lichtensteiger, C.J. Herman: Crystal growth and segregation under zero gravity, J. Electrochem. Soc. 125, 1832–1840 (1978)CrossRef

40.28.

A.M. Balint, D.G. Baltean, T. Levy, M. Mihailovici, A. Neculae, S. Balint: The dopant fields in uniform-diffusion-layer, global-thermal-convection and precrystallization-zone models, Mater. Sci. Semicond. Process. 3, 115–121 (2000)CrossRef

40.29.

D.T.J. Hurle, E. Jakeman, C.P. Johnson: Convective temperature oscillations in molten gallium, J. Fluid Mech. 64, 565–576 (1974)ADSCrossRef

40.30.

C.A. Wang, A.F. Witt: Annual Report Material Processing Center (Massachusetts Institute of Technology, Massachusetts 1984)

40.31.

M.M. Mihailovici, A.M. Balint, S. Balint: The axial and radial segregation due to the thermo-convection, the decrease of the melt in the ampoule and the effect of the precrystallization-zone in the semiconductor crystals grown in a Bridgman-Stockbarger system in a low gravity environment, J. Cryst. Growth 237–239, 1752–1756 (2002)CrossRef

40.32.

M.M. Mihailovici, A.M. Balint, S. Balint: On the controllability of the level of the dopant concentration and of the compositional uniformity of a doped crystal, grown in a low gravity environment by Bridgman-Stockbarger method, Int. J. Theor. Physics, Group Theory Nonlin. Opt. 10, 425–436 (2003)

40.33.

A.M. Balint, M.M. Mihailovici, D.G. Baltean, S. Balint: A modified Chang-Brown model for the determination of the dopant distribution in a Bridgman-Stockbarger semiconductor crystal growth system, J. Cryst. Growth 230, 195–201 (2001)ADSCrossRef

40.34.

A.M. Balint, M.M. Mihailovici, D.G. Baltean, S. Balint: Interface structure in the growth of semiconductor crystals using the Bridgman-Stockbarger method, Thin Solid Films 380, 108–110 (2000)ADSCrossRef

40.35.

M.M. Mihailovici, A.M. Balint, S. Balint: The dopant distribution computed in the modified Chang-Brown model using quasi-steady state approximation, Comput. Mater. Sci. 24, 262–267 (2002)CrossRef

40.36.

D.G. Baltean, T. Levy, S. Balint: Transport de masse par convection et diffusion dans un milieu multiporeux, C. r. Acad. Sci. Paris, Ser. IIB 326, 821–826 (1998)ADSMATH

40.37.

K. Moutsopoulos, S. Bories: Dispersion en milieux poreux hétérogènes, C. R. Acad. Sci. Paris, Ser. IIB 316, 1667–1672 (1993), in FrenchMATH

40.38.

J.C. Maxwell: Electricity and Magnetism (Clarendon, Oxford 1873)MATH

40.39.

V.I. Avetisov, Mendeleev Institute Moscow (personal communication)

40.40.

M.M. Mihailovici, A.M. Balint, S. Balint: Way to improve the compositional uniformity of doped crystals grown by Bridgman-Stockbarger method in a low gravity environment, Int. J. Theor. Phys. Group Theory Nonlinear Opt. 11, 109–119 (2004)MATH

40.41.

D.J. Larson, J. Bethin, B.S. Dressler: Shuttle Mission 51-G, Experiment MRS77F055, Flight Sample Characterization (Grumman Corporate Research Center, Bethpage 1988), NASA Report RE-753

40.42.

P.S. Dutta, A.G. Ostrogorsky: Segregation of Ga in Ge and InSb in GaSb, J. Cryst. Growth 217, 360–365 (2000)ADSCrossRef

40.43.

L.L. Zheng, D.J. Larson Jr., H. Zhang: Role of thermotransport (Sorret effect) in macrosegregation during eutectic/off-eutectic directional solidification, J. Cryst. Growth 191, 243–251 (1998)ADSCrossRef

40.44.

L. Braescu: The dependence of the dopant distribution on the pulling rate and on the capillary channel radius in the case of a Nd:YVO₄ cylindrical bar grown from the melt by the EFG method, Mater. Sci. Eng. B 146, 41–44 (2008)CrossRef

40.45.

E. Tulcan-Paulescu, A.M. Balint, S. Balint: The effect of the initial dopant distribution in the melt on the axial compositional uniformity of a thin doped crystal grown in strictly zero-gravity environment by Bridgman-Stockbarger method, J. Cryst. Growth 247, 313–319 (2003)ADSCrossRefMATH

40.46.

V.A. Tatarchenko: Shaped Crystal Growth (Kluwer, Dordecht 1993)CrossRef

40.47.

H.E. LaBelle Jr., A.I. Mlavsky, B. Chalmers: Growth of controlled profile crystals from the melt: Part I – Sapphire filaments, Mater. Res. Bull 6, 571–579 (1971)CrossRef

40.48.

H.E. LaBelle Jr., A.I. Mlavsky, B. Chalmers: Growth of controlled profile crystals from the melt: Part II – Edge-defined, film-fed growth (EFG), Mater. Res. Bull. 6, 581 (1971)CrossRef

40.49.

B. Chalmers, H.E. LaBelle Jr., A.I. Mlavsky: Edge-defined, film-fed crystal growth, J. Cryst. Growth 13/14, 84–87 (1972)ADSCrossRef

40.50.

J.P. Kalejs: Impurity redistribution in EFG, J. Cryst. Growth 44, 329–344 (1978)ADSCrossRef

40.51.

J.P. Kalejs, G.M. Freedman, F.V. Wald: Aluminium redistribution in EFG silicon ribbon, J. Cryst. Growth 48, 74–84 (1980)ADSCrossRef

40.52.

B. Chalmers: Transient solute effects in shaped crystal growth of silicon, J. Cryst. Growth 82, 70–73 (1987)ADSCrossRef

40.53.

J. Cao, M. Prince, J.P. Kalejs: Impurity transients in multiple crystal growth from a single crucible for EFG silicon octagons, J. Cryst. Growth 174, 170–175 (1997)ADSCrossRef

40.54.

J.P. Kalejs: Interface shape studies for silicon ribbon growth by the EFG technique II. Effect of die asymmetry, J. Cryst. Growth 61, 485–493 (1983)ADSCrossRef

40.55.

J.P. Kalejs: Modeling contribution in commercialization of silicon ribbon growth from the melt, J. Cryst. Growth 230, 10–21 (2001)ADSCrossRef

40.56.

O. Bunoiu, I. Nicoara, J.L. Santailler, T. Duffar: Fluid flow and solute segregation in EFG crystal growth process, J. Cryst. Growth 275, 799–805 (2005)ADSCrossRef

40.57.

L. Braescu, S. Balint, L. Tanasie: Numerical studies concerning the dependence of the impurity distribution on the pulling rate and on the radius of the capillary channel in the case of a thin rod grown from the melt by edge-defined film-fed growth (EFG) method, J. Cryst. Growth 291, 52–59 (2006)ADSCrossRef

40.58.

L. Braescu, T.F. George, S. Balint: Evaluation and control of the dopant distribution in a Nd:LiNbO₃ fiber grown from the melt by the edge-defined film-fed growth (EFG) method, Photonic Fiber and Crystal Devices: Advances in Materials and Innovations in Device Applications I (Optics and Photonics 2007), SPIE Proc. 6698, 669803:1–8 (2007)CrossRef

40.59.

L. Braescu, T. Duffar: Effect of buoyancy and Marangoni forces on the dopant distribution in the case of a single crystal fiber grown from the melt by the edge-defined film-fed growth (EFG) method, J. Cryst. Growth 310, 484–489 (2008)ADSCrossRef

40.60.

T.F. George, L. Braescu: Sapphire fibers grown from the melt by the EFG technique: Dependence of the impurity distribution on temperature and surface tension gradients, Photonic Fiber and Crystal Devices: Advances in Materials and Innovations in Device Applications II (Optics and Photonics 2008), SPIE Proc. 7056, 705603–1–705603–10 (2008)CrossRef

40.61.

L. Braescu, T.F. George: Arbitrary Lagrangian-Eulerian method for coupled Navier-Stokes and convection-diffusion equations with moving boundaries, Proc. 12nd WSEAS Int. Conf. Appl. Math. – Mathʼ07 (2007) pp.33–36

40.62.

F. Duarte, R. Gormaz, S. Natesan: Arbitrary Lagrangian-Eulerian method for Naver-Stokes equations with moving boundaries, Comput. Methods Appl. Mech. Eng. 193, 4819–4836 (2004)ADSMathSciNetCrossRefMATH

40.63.

M. Fernandez, M. Moubachir: Sensitivity analysis for an incompressible aeroelastic system, Math. Models Methods Appl. Sci. 12, 1109–1130 (2002)MathSciNetCrossRefMATH

Titel: Mass and Heat Transport in BS and EFG Systems
verfasst von: Thomas F. George
Stefan Balint
Liliana Braescu
Verlag: Springer Berlin Heidelberg
Buch: Springer Handbook of Crystal Growth
Print ISBN: 978-3-540-74182-4

Electronic ISBN: 978-3-540-74761-1

Copyright-Jahr: 2010
DOI: https://doi.org/10.1007/978-3-540-74761-1_40

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht