Abstract
A major issue in the growth of semiconductor crystals is the presence of line defects or dislocations. Dislocations are a major impediment to the usage of III–V and other compound semiconductor crystals in electronic, optical, and other applications. This chapter reviews the origins of dislocations in melt-based growth processes and models for stress-driven dislocation multiplication. These models are presented from the point of view of dislocations as the agents of plastic deformation required to relieve the thermal stresses generated in the crystal during melt-based growth processes. Consequently they take the form of viscoplastic constitutive equations for the deformation of the crystal taking into account the microdynamical details of dislocations such as dislocation velocities and interactions. The various aspects of these models are dealt in detail, and finally some representative numerical results are presented for the liquid encapsulated Czochralski (LEC) growth of InP crystals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- CFD:
-
computational fluid dynamics
- CFD:
-
cumulative failure distribution
- CRSS:
-
critical-resolved shear stress
- CZ:
-
Czochralski
- IC:
-
integrated circuit
- IC:
-
ion chamber
- LEC:
-
liquid encapsulation Czochralski
- LED:
-
light-emitting diode
- MASTRAPP:
-
multizone adaptive scheme for transport and phase change processes
- ODE:
-
ordinary differential equation
- SWBXT:
-
synchrotron white beam x-ray topography
- TEM:
-
transmission electron microscopy
- VCZ:
-
vapor pressure controlled Czochralski
- fcc:
-
face-centered cubic
References
J. Czochralski: Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle, Z. Phys. Chem. 92, 219–221 (1917), in German
G.K. Teal, J.B. Little: Growth of germanium single crystals, Phys. Rev. 78, 647 (1950)
W.C. Dash: Dislocation free silicon crystals. In: Growth and Perfection of Crystals, ed. by R.M. Doremus, B.W. Roberts, D. Turnbull (Wiley, New York 1958)
V. Swaminathan, A.S. Jordan: Dislocations in III/V compounds, Semicond. Semimet. 38, 293–341 (1993)
R.J. Roedel, A.R. Von Neida, R. Caruso, L.R. Dawson: The effect of dislocations in Ga_1-xAl_xAs:Si light-emitting diodes, J. Electrochem. Soc. 126, 637–641 (1979)
J.P. Hirth, J. Lothe: Theory of Dislocations (Krieger, Malabar 1992)
H. Alexander: On dislocation generation in semiconductor crystals, Radiat. Eff. Defects Solids 112(1/2), 1–12 (1989)
B.T. Lee, R. Gronsky, E.D. Bourret: Dislocation loops and precipitates associated with excess arsenic in GaAs, J. Appl. Phys. 64(1), 114–118 (1988)
J. Lagowski, H.C. Gatos, T. Aoyama, D.G. Lin: Fermi energy control of vacancy coalescence and dislocation density in melt-grown GaAs, Appl. Phys. Lett. 45(6), 680–682 (1984)
W. Zulehner: Czochralski growth of silicon, J. Cryst. Growth 65(1–3), 189–213 (1983)
M.F. Ashby, L. Johnson: On the generation of dislocations at misfitting particles in a ductile matrix, Philos. Mag. 20, 1009–1022 (1969)
A.S. Jordan, R. Caruso, A.R. Von Neida: A thermoelastic analysis of dislocation generation in pulled GaAs crystals, Bell Syst. Technol. J. 59(4), 593–637 (1980)
N. Kobayashi, T. Iwaki: A thermoelastic analysis of the thermal stress produced in a semi-infinite cylindrical single crystal during the Czochralski growth, J. Cryst. Growth 73, 96–110 (1985)
M. Duseaux: Temperature profile and thermal-stress calculations in GaAs crystals growing from the melt, J. Cryst. Growth 61(3), 576–590 (1983)
J.C. Lambropoulos: Stresses near the solid-liquid interface during the growth of a Czochralski crystal, J. Cryst. Growth 80, 245–256 (1987)
C.E. Schvezov, I.V. Samarasekera, F. Weinberg: Calculation of the shear stress distribution in LEC gallium arsenide for different growth conditions, J. Cryst. Growth 92, 479–488 (1988)
G.O. Meduoye, K.E. Evans, D.J. Bacon: Modelling of the growth of the LEC technique II. Thermal stress distribution and influence of interface shape, J. Cryst. Growth 97, 709–719 (1989)
G.O. Meduoye, D.J. Bacon, K.E. Evans: Computer modelling of temperature and stress distributions in LEC-grown GaAs crystals, J. Cryst. Growth 108, 627–636 (1991)
S. Motakef, K.W. Kelly, K. Koai: Comparison of calculated and measured dislocation density in LEC-grown GaAs crystals, J. Cryst. Growth 113, 279–288 (1991)
F. Dupret, P. Necodeme, Y. Ryckmans: Numerical method for reducing stress level in GaAs crystals, J. Cryst. Growth 97, 162–172 (1989)
D.E. Bornside, T.A. Kinney, R.A. Brown: Minimization of thermoelastic stresses in Czochralski grown silicon: Application of the integrated system model, J. Cryst. Growth 108, 779–805 (1991)
Y.F. Zou, H. Zhang, V. Prasad: Dynamics of melt-crystal interface and coupled convection-stress predictions for Czochralski crystal growth processes, J. Cryst. Growth 166, 476–482 (1996)
I. Yonenaga, K. Sumino: Impurity effects on the generation, velocity, and immobilization of dislocations in GaAs, J. Appl. Phys. 65, 85–92 (1989)
J. Lubliner: Plasticity Theory (Macmillan, New York 1990)
K. Sumino: Mechanical behavior of semiconductors. In: Handbook on Semiconductors, Vol. 3a, ed. by S. Mahajan, T.S. Moss (Elsevier, Amsterdam 1994) pp. 73–181
J. Hornstra: Dislocations in the diamond lattice, J. Phys. Chem. Solids 5, 129–141 (1958)
H. Alexander: Dislocations in covalent crystals. In: Dislocations in Solids, Vol. 7, ed. by F.R.N. Nabarro (North-Holland, Amsterdam 1986) pp. 113–234
D.J.H. Cockayne, A. Hons: Dislocations in semiconductors as studied by weak-beam electron-microscopy, J. Phys. 40(6), 11–18 (1979)
H. Gottschalk, G. Patzer, H. Alexander: Stacking-fault energy and ionicity of cubic III–V compounds, Phys. Status Solidi (a) 45(1), 207–217 (1978)
R. Meingast, H. Alexander: Dissociated dislocations in germanium, Phys. Status Solidi (a) 17(1), 229–236 (1973)
A. George, J. Rabier: Dislocations and plasticity in semiconductors. I – Dislocation structures and dynamics, Rev. Phys. Appl. 22, 941–966 (1987)
W.G. Johnston, J.J. Gilman: Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals, J. Appl. Phys. 30, 129–144 (1959)
H. Alexander, P. Haasen: Dislocations and plastic flow in the diamond structure. In: Solid State Physics, Vol. 22, ed. by F. Seitz, D. Turnbull, H. Ehrenreich (Academic, New York 1968) pp. 28–158
A.R. Chaudhuri, J.R. Patel, L.G. Rubin: Velocities and densities of dislocations in germanium and other semiconductor crystals, J. Appl. Phys. 33, 2736–2746 (1962)
G.I. Taylor: The mechanism of plastic deformation of crystals. Part I – Theoretical, Proc. R. Soc. Lond. Ser. A 145, 362–387 (1934)
F.R.N. Babarro, Z.S. Basinski, D.B. Holt: The plasticity of pure single crystals, Adv. Phys. 13, 193–323 (1964)
E. Peissker, P. Haasen, H. Alexander: Anisotropic plastic deformation of indium antimonide, Philos. Mag. 7, 1279 (1962)
I. Yonenaga, K. Sumino: Effects of in impurity on the dynamic behavior of dislocations in GaAs, J. Appl. Phys. 62(4), 1212–1219 (1987)
I. Yonenaga, K. Sumino: Mechanical properties and dislocation dynamics of GaP, J. Mater. Res. 4(2), 355–360 (1989)
J. Völkl: Stress in the cooling crystal. In: Handbook of Crystal Growth, Vol. 2, ed. by D.T.J. Hurle (North Holland, Amsterdam 1994) pp. 823–874
H. Siethoff, W. Schröter: Work-hardening and dynamical recovery in silicon and germanium at high-temperatures and comparison with FCC metals, Scr. Metall. 17(3), 393–398 (1983)
H. Siethoff, R. Behrensmeier: Plasticity of undoped GaAs deformed under liquid encapsulation, J. Appl. Phys. 67(8), 3673–3680 (1990)
H. Siethoff, K. Ahlborn, H.G. Brion, J. Völkl: Dynamical recovery and self-diffusion in InP, Philos. Mag. A 57(2), 235–244 (1988)
H. Siethoff, W. Schröeter: New phenomena in the plasticity of semiconductors and FCC metals at high temperatures, Z. Metall. 75(7), 475–491 (1984)
A.K. Mukherjee, J.E. Bird, J.E. Dorn: Experimental correlations for high temperature creep, ASM Transactions 62, 155–179 (1969)
C.R. Barrett, W.D. Nix: A Model for steady state creep based on the motion of jogged screw dislocations, Acta Metall. 13, 1247–1258 (1965)
H.G. Brion, H. Siethoff, W. Schröter: New stages in stress–strain curves of germanium at high-temperatures, Philos. Mag. A 43(6), 1505–1513 (1981)
H. Siethoff: Cross-slip in the high-temperature deformation of germanium, silicon and indium-antimonide, Philos. Mag. A 47(5), 657–669 (1983)
B. Escaig: Cross-slip processes in the fcc structure. In: Dislocation Dynamics, ed. by A.R. Rosenfield, R. Alan (McGraw-Hill, London 1968) pp. 655–677
D. Maroudas, R.A. Brown: On the prediction of dislocation formation in semiconductor crystals grown from the melt – Analysis of the Haasen model for plastic deformation dynamics, J. Cryst. Growth 108, 399–415 (1991)
C.T. Tsai: On the finite-element modeling of dislocation dynamics during semiconductor-crystal growth, J. Cryst. Growth 113, 499–507 (1991)
C.T. Tsai, A.N. Gulluoglu, C.S. Hertley: A crystallographic methodology for modeling dislocation dynamics in GaAs crystals grown from the melt, J. Appl. Phys. 73, 1650–1656 (1993)
J.C. Lambropoulos, C.H. Wu: Mechanics of shaped crystal growth from the melt, J. Mater. Res. 11, 2163–2176 (1996)
N. Miyazaki, Y. Kuroda: Dislocation density simulations for bulk single crystal growth process, Met. Mater. Int. 4(4), 883–890 (1998)
J.C. Moosbrugger: Continuum slip viscoplasticity with the Haasen constitutive model – application to single-crystal inelasticity, Int. J. Plast. 11, 799–826 (1995)
J.C. Moosbrugger, A. Levy: Constitutive modelling for CdTe single-crystals, Metall. Mater. Trans. A 26(10), 2687–2697 (1995)
H. Chung, W. Si, M. Dudley, A. Anselmo, D.F. Bliss, A. Maniatty, H. Zhang, V. Prasad: Characterization of structural defects in MLEK grown InP single crystals using synchotron beam x-ray topography, J. Cryst. Growth 174(1–4), 230–237 (1997)
H. Chung, W. Si, M. Dudley, D.F. Bliss, R. Kalan, A. Maniatty, H. Zhang, V. Prasad: Characterization of defect structures in magnetic liquid encapsulated Kyropoulos grown InP single crystals, J. Cryst. Growth 181(1-2), 17–25 (1997)
H. Steinhardt, P. Haasen: Creep and dislocation velocities in GaAs, Phys. Status Solidi (a) 49, 93–101 (1978)
I. Yonenaga, U. Unose, K. Sumino: Mechanical properties of GaAs crystals, J. Mater. Res. 2, 252–261 (1987)
A. George, C. Escaravage, G. Champier, W. Schröter: Velocities of screw and 60°-dislocations in silicon, Phys. Status Solidi (b) 53, 483–496 (1972)
M. Imai, K. Sumino: Insitu x-ray topographic study of the dislocation mobility in high-purity and impurity-doped silicon-crystals, Philos. Mag. A 47(4), 599–621 (1983)
B.Y. Farber, V.I. Nikitenko: Change of dislocation mobility characteristics in silicon single-crystals at elevated-temperatures, Phys. Status Solidi (a) 73(1), K141–144 (1982)
I. Yonenaga, K. Sumino: Dislocation velocity in indium-phospide, Appl. Phys. Lett. 58(1), 48–50 (1991)
H. Nagai: Dislocation velocities in indium phospide, Jpn. J. Appl. Phys. 20(4), 793–794 (1981)
K. Maeda, S. Takeuchi: Recombination enhanced glide in InP single crystals, Appl. Phys. Lett. 42(8), 664–666 (1983)
F. Louchet: On the mobility of dislocations in silicon by insitu straining in a high-voltage electron-microscope, Philos. Mag. 43(5), 1289–1297 (1981)
V. Celli, M. Kabler, T. Ninoyama, R. Thomson: Theory of dislocation mobility in semiconductors, Phys. Rev. 131(1), 58–72 (1963)
V.V. Rybin, A.N. Orlov: Theory of dislocation motion in low-velocity range, Sov. Phys. Solid State 11, 2635–2641 (1970)
S. Öberg, P.K. Sitch, R. Jones, M.I. Heggie: First-principles calculations of the energy barrier to dislocation motion in Si and GaAs, Phys. Rev. B 51(19), 13138–13145 (1995)
V.V. Bulatov, S. Yip, A.S. Argon: Atomic modes of dislocation mobility in silicon, Philos. Mag. A 72(2), 453–496 (1995)
H.R. Kolar, J.C.H. Spencer, H. Alexander: Observation of moving dislocation kinks and unpinning, Phys. Rev. Lett. 77(19), 4031–4034 (1996)
H.J. Möller: The movement of dissociated dislocations in the diamond–cubic structure, Acta Metall. 26, 963–973 (1977)
P. Haasen: Kink formation in charged dislocation, Phys. Status Solidi (a) 28(1), 145–155 (1975)
P.B. Hirsch: Mechanism for the effect of doping on dislocation mobility, J. Phys. 40(6), 117–121 (1979)
K. Sumino, I. Yonenaga: Dislocation dynamics and mechanical behavior of elemental and compound semiconductors, Phys. Status Solidi (a) 138, 573–581 (1993)
K. Sumino, H. Harada: In situ x-ray topographic studies of the generation and the multiplication processes of dislocations in silicon crystals at elevated temperature, Philos. Mag. A 44(6), 1319–1334 (1981)
P. Franciosi, A. Zaoui: Multislip in fcc. crystals: A theoretical approach compared with experimental data, Acta Metall. 30, 1627–1637 (1982)
A. Moulin, M. Condat, L.P. Kubin: Mesoscale modelling of the yield point properties of silicon crystals, Acta Metall. 47(10), 2879–2888 (1999)
H. Alexander, J.J. Crawford: Latent hardening of germanium crystals, Phys. Status Solidi (b) 222, 41–49 (2000)
A.A. Chernov: Modern Crystallography III. Crystal Growth (Springer, Berlin 1984)
H. Klapper: Generation and propagation of dislocations during crystal growth, Mater. Chem. Phys. 66, 101–109 (2000)
G. Dhanaraj, B. Raghothamachar, J. Bai, H. Chung, M. Dudley: Synchrotron x-ray topographic characterization of defects in InP bulk crystals, Proc. Int. Conf. Indium Phosphide Relat. Mater. (2005) pp. 643–648
G.T. Brown, B. Cockayne, W.R. Macewan: Deformation behavior of single crystals of InP in uniaxial compression, J. Mater. Sci. 15, 1469–1477 (1980)
S. Pendurti: Modeling Dislocation Generation in High Pressure Czochralski Growth of InP Single Crystals. Ph.D. Thesis (State University of New York, Stony Brook 2003)
A.S. Jordan: Some thermal and mechanical properties of InP essential to crystal growth modeling, J. Cryst. Growth 71, 559–565 (1985)
H. Siethoff: The plasticity of elemental and compound semiconductors, Semicond. Semimet. 37, 143–187 (1992)
J.C. Simo, T.J.R. Hughes: Computational Inelasticity (Springer, New York 1998)
H. Zhang, V. Prasad: A multizone adaptive process model for low and high pressure crystal growth, J. Cryst. Growth 155, 47–65 (1995)
P. Rudolph, M. Jurisch: Bulk growth of GaAs – An overview, J. Cryst. Growth 199(1), 325–335 (1999)
V.A. Antonov, V.G. Elsakov, T.I. Olkhovikova, V.V. Selin: Dislocations and 90°-twins in LEC-grown InP crystals, J. Cryst. Growth 235(1–4), 35–39 (2002)
T.-C. Chen, H.-C. Wu, C.-I. Weng: The effect of interface shape on anisotropic thermal stress of bulk single crystal during Czochralski growth, J. Cryst. Growth 173, 367–379 (1997)
J. Matsui: Study of strain variation in LEC-grown GaAs bulk crystals by synchotron radiation x-ray, Appl. Surf. Sci. 50, 1–8 (1991)
H.M. Buchheit, A. Khoukh, M. Bejar, S.K. Krawczyk, R.C. Blanchet: Residual strain mapping in III–V materials by spectrally resolving scanning photoluminescence, Microelectron. J. 30(7), 651–657 (1999)
S. Pendurti, V. Prasad, H. Zhang: Modelling dislocation generation in high pressure Czochralski growth of InP single crystals: Part I. Construction of a visco-plastic deformation model, Model. Simul. Mater. Sci. Eng. 13, 249–266 (2005)
V. Prasad, H. Zhang: Transport phenomena in Czochralski crystal growth processes, Adv. Heat Transf. 30, 313–435 (1997)
A.G. Elliot, A. Flat, D.A. Vanderwater: Silicon incorporation in LEC growth of single-crystal gallium-arsenide, J. Cryst. Growth 121(3), 349–359 (1992)
M. Neubert, P. Rudolph: Growth of semi-insulating GaAs crystals in low temperature gradients by using the vapour pressure controlled Czochralski method (VCZ), Prog. Cryst. Growth Charact. Mater. 43(2/3), 119–185 (2001)
G. Müller, J. Völkl, E. Tomzig: Thermal analysis of LEC InP growth, J. Cryst. Growth 64(1), 40–47 (1983)
A.R. Von Neida, A.S. Jordan: Reducing dislocations in GaAs and InP, J. Met. 38, 35–40 (1986)
A.G. Elliot, C.L. Wei, R. Farraro, G. Woolhouse, M. Scott, R. Hiskes: Low dislocation density, large diameter, liquid encapsulated Czochralski growth of GaAs, J. Cryst. Growth 70, 169–178 (1984)
K. Katagiri, S. Yamazaki, A. Takagi, O. Oda, H. Araki, I. Tsuboya: LEC growth of large diameter InP single crystals doped with Sn and with S, Inst. Phys. Conf. Ser. 79, 67–72 (1986)
R. Hirano, M. Uchida: Reduction of dislocation densities in InP single crystals by the LEC method using thermal baffles, J. Electron. Mater. 25, 347–351 (1996)
R. Hirano: Growth of low etch pit density homogeneous 2′′ InP crystals using a newly developed thermal baffle, Jpn. J. Appl. Phys. 38(2B), 969–971 (1999)
K. Terashima, T. Fukuda: A new magnetic–field applied pulling apparatus for LEC GaAs single-crystal growth, J. Cryst. Growth 63, 423–425 (1983)
H. Miyairi, T. Inada, M. Eguchi, T. Fukuda: Growth and properties of InP single crystals grown by the magnetic-field applied LEC method, J. Cryst. Growth 79(1–3), 291–295 (1986)
J. Osaka, H. Kohda, T. Kobayashi, K. Hoshikawa: Homogeneity of vertical magnetic-field applied LEC GaAs crystal, Jpn. J. Appl. Phys. Part 2 – Lett. 23(4), L194–197 (1984)
S. Ozawa, T. Kimura, J. Kobayashi, T. Fukuda: Programmed magnetic-field applied liquid encapsulated Czochralski crystal-growth, Appl. Phys. Lett. 50(6), 329–331 (1987)
H. Kohda, K. Yamada, H. Nakanishi, T. Kobayashi, J. Osaka, K. Hoshikawa: Crystal-growth of completely dislocation-free and striation-free GaAs, J. Cryst. Growth 71(3), 813–816 (1985)
S. Pendurti, H. Zhang, V. Prasad: Modeling dislocation generation in high pressure Czochralski growth of InP single crystals: Part II, Model. Simul. Mater. Sci. Eng. 13, 267–297 (2005)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag
About this chapter
Cite this chapter
Prasad, V.(., Pendurti, S. (2010). Models for Stress and Dislocation Generation in Melt Based Compound Crystal Growth. In: Dhanaraj, G., Byrappa, K., Prasad, V., Dudley, M. (eds) Springer Handbook of Crystal Growth. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74761-1_39
Download citation
DOI: https://doi.org/10.1007/978-3-540-74761-1_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74182-4
Online ISBN: 978-3-540-74761-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)