The mechanics of thin film epitaxy is developed using an equilibrium thermodynamics formalism and linear elasticity. A virtual variation approach is employed that leads to a direct identification of the important volume and surface thermodynamic parameters characterizing mechanical equilibrium. In particular, the equilibrium volume stress state of an epitaxial film as a function of the film thickness, surface free energies, and surface stresses is obtained. It is shown how this formalism can be used to determine the critical thickness for epitaxy.

1.
Matthews, J. M., 1975, “Coherent Interfaces and Misfit Dislocations,” Epitaxial Growth, Part B, J. M. Matthews, eds., Academic Press, San Diego, CA, pp. 559–609.
2.
Cammarata
,
R. C.
,
1994
, “
Surface and Interface Stress Effects in Thin Films
,”
Prog. Surf. Sci.
,
46
, pp.
1
38
.
3.
Cammarata
,
R. C.
,
Sieradzki
,
K.
, and
Speapen
,
F.
,
2000
, “
Simple Model for Interface Stresses With Application to Misfit Dislocation Generation in Epitaxial Thin Films
,”
J. Appl. Phys.
,
87
, pp.
1227
1234
.
4.
Shuttleworth
,
R.
,
1950
, “
The Surface Tension of Solids
,”
Proc. R. Soc. London, Ser. A
,
63
, pp.
444
457
.
5.
Herring, C., 1952, “The Use of Classical Macroscopic Concepts in Surface-Energy Problems,” Structure and Properties of Solid Surfaces, edited by R. Gomer and C. S. Smith, eds., University of Chicago Press, Chicago, pp. 5–81.
6.
Brooks, H., 1963, “Theory of Boundaries,” Metals Interfaces, American Society of Metals, Metals Park, Ohio, pp. 20–64.
7.
Mullins, W. W., 1963, “Solid Surface Morphologies Governed by Capillarity,” Metal Surfaces: Structure, Energetics, and Kinetics, ASM, Cleveland, OH, pp. 17–64.
8.
Cahn
,
J. W.
,
1980
, “
Surface Stress and the Chemical Equilibrium of Small Crystals: I. The Case of the Isotropic Surface
,”
Acta Metall.
,
28
, pp.
1333
1338
.
9.
Cahn
,
J. W.
, and
Larche´
,
F.
,
1982
, “
Surface Stress and Chemical Equilibrium of Small Crystals. II. Solid Particles Embedded in a Solid Matrix
,”
Acta Metall.
,
30
, pp.
51
56
.
10.
Suo
,
Z.
, and
Lu
,
W.
,
2000
, “
Composition Modulation and Nanophase Separation in a Binary Epilayer
,”
J. Mech. Phys. Solids
,
48
, pp.
211
232
.
11.
Kouris
,
D.
,
Peralta
,
P.
, and
Sieradzki
,
K.
,
2000
, “
Surface Islands and Their Elastic Interaction With Adatoms
,”
Surf. Sci.
,
445
, pp.
420
429
.
12.
Spaepen
,
F.
,
2000
, “
Interfaces and Stresses in Thin Films
,”
Acta Mater.
,
48
, pp.
31
42
.
13.
Cammarata
,
R. C.
,
Trimble
,
T. M.
, and
Srolovitz
,
D. J.
,
2000
, “
Surface Stress Model for Intrinsic Stresses in Thin Films
,”
J. Mater. Sci.
,
15
, pp.
2468
2474
.
14.
Gibbs, J. W., 1961, “On the Equilibrium of Heterogeneous Substances,” The Scientific Papers of J. Willard Gibbs, Volume 1: Thermodynamics, Dover, New York, pp. 55–353.
15.
Callen, H. B., 1985, Thermodynamics and an Introduction to Thermostatics, John Wiley and Sons, New York.
16.
Reiss, H., 1996, Methods of Thermodynamics, Dover, New York.
17.
Tschoegl, N. W., 2000, Fundamentals of Equilibrium and Steady State Thermodynamics, Elsevier, Amsterdam.
18.
Larche´
,
F. C.
, and
Cahn
,
J. W.
,
1985
, “
The Interactions of Composition and Stress in Crystalline Solids
,”
Acta Metall.
,
33
, pp.
331
357
.
19.
Zangwill, A., 1988, Physics at Surface, Cambridge University Press, Cambridge, UK, pp. 7–12.
20.
Johnson
,
W. C.
,
2000
, “
Superficial Stress and Strain at Coherent Interfaces
,”
Acta. Mater.
,
48
, pp.
434
444
.
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