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Strained multilayers composed of two misfitting layers and a third, thin interlayer are considered. With appropriate intermediate lattice parameters for the interlayer, the latter is shown to stabilize the structure with respect to misfit dislocation formation. Cases of misfit corresponding both to balanced biaxial stress and to pure shear stress in the interface are treated.

I. INTRODUCTION There has been extensive work on the stability of strained multilayer structures. Typically, a criterion for such stability is the critical thickness above which a coherently strained (or commensurate) layer structure becomes thermodynamically unstable with respect to injection of a misfit dislocation dipole.1 Recent attention has focused on the findings that critical thicknesses are successively greater than that for a single dipole for cases of equilibrium or constrained equilibrium arrays of dislocations in single embedded layers2"4 and in multilayers.5'6 In the present work, we show that the coherently strained state is stabilized, i.e., the critical thickness is increased, by the presence between the constituent layers of a thin interlayer with lattice constants intermediate between those of the constituent layers. The physical implications of the results apply to any case of strained layers, including a single deposited overlayer. However, the case that we treat explicitly is that of two constituent layers in which the strain is partitioned between the two. The layers could be thought of as interior members of a large multilayer structure. The standard case of multilayers strained in biaxial tension and compression is considered. In addition, results are presented for layers that are out of registry by a pure shear in the interface plane. Together, these solutions superpose to describe the general case of misfitting layer structures. The results are presented for the single misfit dislocation dipole case, but can be extended by analogy to the multiple dislocation cases.

would apply for two hexagonal, tetragonal, or rhombohedral crystals with basal plane habits. The strains for a given layer are e = en = e22, while the stresses are a = an = (T22 with cr33 = 0. Hooke's law gives a = 2/JLK€ =

ce

(1)

where //, is the shear modulus, K = (1 + ^)(1 — v), and v is Poisson's ratio. In each layer, the coherency strain is e = (a — at)/'a,- where a is the in-plane lattice parameter of the coherent bilayer, and a, is the stress-free lattice parameter of layer i. If we assume, without loss of generality, that aA < aB, then aA < a < aB, and2"4 aAeA + aB\eB\ = aB = aA = Aa.

(2)

Since force balance also requires that aAhA + aBhB = 0,

(3)

X2

II. BIAXIALLY STRAINED LAYERS A. Elastic field Bilayer case The first case is that of layers under equal biaxial tension or compression (Fig. 1). As a specific example, we consider two face-centered cubic crystals with {100} habit planes of the interface. An equivalent treatment 1572

http://journals.cambridge.org

J. Mater. Res., Vol. 8, No. 7, Jul 1993

Downloaded: 15 Mar 2015

FIG. 1. Two