A continuum theory of multispecies thin solid film growth by chemical vapor deposition

Journal of Elasticity

Volumn 73, Issue 1-3, 2003, Pages 13-74

  Jabbour, Michel E ^a   Bhattacharya, Kaushik ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Anisotropic interface; Chemical reaction; Chemical vapor deposition; Ideal lattice gas; Multispecies thin film

Indexed keywords

CHEMICAL VAPOR DEPOSITION; CONTINUUM MECHANICS; FILM GROWTH; KINETIC THEORY; MORPHOLOGY; PARTIAL DIFFERENTIAL EQUATIONS; SURFACE PHENOMENA; THERMODYNAMIC PROPERTIES;

ANISOTROPIC INTERFACES; CHEMICAL REACTION; IDEAL LATTICE GASES; MULTISPECIES THIN FILMS;

THIN FILMS;

EID: 3543085003     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000030018.40095.d5     Document Type: Article

References (47)

1. R. Abeyaratne and J.K. Knowles, On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (1990) 345-360.
2. G.S. Bales and A. Zangwill, Morphological instability of a terrace edge during step-flow growth. Phys. Rev. B 41 (1990) 5500-5508.
3. A. Bedford and D.S. Drumheller, Theories of immiscible and structured mixtures. Internat. J. Engrg. Sci. 8 (1983) 863-960.
4. W.K. Burton, N. Cabrera and F.C. Frank, The growth of crystals and the equilibrium structure of their surfaces. Philos. Trans. Roy. Soc. London A 243 (1951 ) 299-358.
5. H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. Wiley, New York (1985).
6. B.D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13 (1963) 167-178.
7. M.E. Coltrin and R.J. Kee, A mathematical model of the gas-phase and surface chemistry in GaAs MOCVD. In: Math. Res. Soc. Symp. Proc. 145 (1989) pp. 119-124.
8. M.E. Coltrin, R.J. Kee and J.A. Miller, A mathematical model of the coupled fluid mechanics and chemical kinetics in a chemical vapor deposition reactor. J. Electrochem. Soc. 131 (1984) 425-434.
9. M.E. Coltrin, R.J. Kee and J.A. Miller, A mathematical model of Silicon chemical vapor deposition. Further refinements and the effects of thermal diffusion. J. Electrochem. Soc. 113 (1986) 1206-1213.
10. F. Davi and M.E. Gurtin, On the motion of a phase interface by surface diffusion. J. Appl. Math. Phys. 41 (1990) 782-811.
11. G. Evans and R. Greif, A numerical model of the flow and heat transfer in a rotating disk chemical vapor deposition reactor. Trans. ASME 109 (1987) 928-935.
12. A. Ern, V. Giovangigli and M.D. Smooke, Detailed modeling of three-dimensional chemical vapor deposition. J. Cryst. Growth 180 (1997) 670-679.
13. E. Fried and M.E. Gurtin, The role of the configurational force balance in the nonequilibrium epitaxy of films. J. Mech. Phys. Solids 51 (2003) 487-517.
14. E. Fried and M.E. Gurtin, A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain boundaries and epitaxy. Adv. Appl. Mech. (2003) to appear.
15. J.W. Gibbs, The Collected Works of J. Willard Gibbs. Longman, Green and Co. (1928) pp. 55-354.
16. V. Giovangigli, Multicomponent Flow Modeling. Modeling and Simulation in Science, Engineering and Technology. Birkhauser, Basel (1999).
17. D.G. Goodwin and G.G. Gavillet, Numerical modeling of the filament-assisted diamond growth environment. J. Appl. Phys. 68 (1990) 6393-6400.
18. M.E. Gurtin, An Introduction to Continuum Mechanics. Mathematics in Science and Engineering 158. Academic Press, New York (1981).
19. M.E. Gurtin, The nature of configurational forces. Arch. Rational Mech. Anal. 131 (1995) 67-100.
20. M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Physics. Applied Mathematical Sciences 137. Springer, New York (2000).
21. M.E. Gurtin and M.E. Jabbour, Interface evolution in three dimensions with curvature dependent energy and surface diffusion: Inerface-controlled evolution, phase transitions, epitaxial growth of elastic films. Arch. Rational Mech. Anal. 163 (2002) 171-208.
22. M.E. Gurtin and A. Struthers, Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation. Arch. Rational Mech. Anal. 112 (1990) 97-160.
23. M.E. Gurtin, A. Struthers and W.O. Williams, A transport theorem for moving interfaces. Quart. Appl. Math. 47 (1989) 773-777.
24. M.E. Gurtin and P.W. Voorhees, The continuum mechanics of coherent two-phase elastic solids with mass transport. Proc. Roy. Soc. London 440 (1993) 323-343.
25. M.E. Gurtin and P.W. Voorhees, The thermodynamics of evolving interfaces far from equilibrium. Acta Mater. 44 (1996) 235-247.
26. J.E. Guyer and P.W. Voorhees, Morphological stability of alloy thin films. Phys. Rev. B 54 (1996) 11710-11724.
27. C. Herring, Surface tension as a motivation for sintering. In: W.E. Kingston (ed.), The Physics of Powder Metallurgy. McGraw-Hill, New Deltaork (1951) 143-179.
28. T.L. Hill, An Introduction to Statistical Thermodynamics. Dover, New York (1986).
29. W.G. Houf, J.F. Grcar and W.G. Breiland, A model for low pressure chemical vapor deposition in a hot-wall tubular reactor. Mater. Sci. Engrg. B17 (1993) 163-171.
30. C. Houtman, D.B. Graves and K.F. Jensen, CVD in stagnation point flow. J. Electrochem. Soc. 133 (1986) 961-970.
31. C.R. Kleijn, Chemical vapor deposition processes. In: M. Meyyappan (ed.), Computational Modeling in Semiconductor Processing. The Artech House Materials Science Library (1995) 97-145.
32. G. Maugin, Material Inhomogeneities in Elasticity. Applied Mathematics and Mathematical Computations 3. Chapman & Hall, London (1993).
33. T.J. Mountziaris and K.F. Jensen, Gas-phase and surface reaction mechanisms in MOCVD of GaAs with trimethyl-gallium and arsine. J. Electrochem. Soc. 138 (1991) 2426-2439.
34. W.W. Mullins, Theory of thermal grooving. J. Appl. Phys. 28 (1957) 333-339.
35. W.W. Mullins and R.F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 34 (1963) 323-329.
36. R. Omstead, P.M. van Sickle, P.W. Lee and K.F. Jensen, Gas phase and surface reactions in the MOCVD of GaAs from triethylgallium trimethylgallium, and tertiarybutylarsine. J. Cryst. Growth 93 (1998) 20-28.
37. R. Pollard and J. Newman, Silicon deposition on a rotating disk. J. Electrochem. Soc. 127 (1980) 744-752.
38. c Superconducting Systems. Springer, Berlin (1993) 28-70.
39. Y. Saito, Statistical Physics of Crystal Growth. World Scientific, Singapore (1996).
40. B.J. Spencer, P.W. Voorhees and S.H. Davis, Morphological instability in epitaxially strained dislocation-free solid films: Linear stability theory. J. Appl. Phys. 73 (1993) 4955-4970.
41. B.J. Spencer, P.W. Voorhees and J. Tersoff, Morphological instability theory for strained alloy film growth: The effect of compositional stresses and species-dependent surface mobilities on ripple formation during epitaxial film deposition. Phys. Rev. B 64 (2001) 235-318.
42. C. Truesdell, Rational Thermodynamics, 2nd ed. Springer, Berlin (1984).
43. J. Villain, Continuum models of crystal growth from atomic beams with and without desorption. J.Phys. 11 (1991) 19-42.
44. J. Villain and A. Pimpinelli, Physics of Crystal Growth. Cambridge Univ. Press, Cambridge (1998).
45. D.D. Vvedensky, Atomistic modeling of epitaxial growth: Comparisons between lattice models and experiments. Comp. Mater. Sci. 6 (1996) 182-187.
46. 7-δ thin layers grown by metal organic chemical vapor deposition. J. Appl. Phys. 75 (1994) 54092-54096.
47. A. Zangwill, Theory of growth-induced surface roughness. In: H.A. Atwater and C.V. Thompson (eds), Microstructural Evolution of Thin Films. Academic Press, New York (1995) to appear.