Substrate Step Induced Strain in Heteroepitaxial Growth
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SUBSTRATE STEP INDUCED STRAIN IN HETEROEPITAXIAL GROWTH W. R. L. LAMBRECHT*, B. SEGALL*,
and P.
PIROUZ t
* Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106 t Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106 ABSTRACT During epitaxial growth of lattice-mismatched materials, substrate surface steps induce verticalmisfit between substrate and epilayer. It is shown that the resulting strain is accomodated by an interface dislocation, which is of the Read-Shockley type for a complete step and supplemetary displacement type for a demistep, using R.C. Pond's classification. Alternative models for the strain accomodation are considered. A localized "displacement boundary" is shown to be unfavorable irrespective of the film-thickness. Residual shear strain in the film requires debonding from the substrate, which is shown to be unfavorable with respect to the dislocation model. The distribution of strain between film and substrate is shown to depend weakly on film-thickness but strongly on the material's elastic constants. INTRODUCTION Recently, there has been considerable interest in the role of substrate surface steps in semiconductor heteroepitaxy [1-71. In the case of a sphalerite semiconductor grown on a Si (001) substrate, monoatomic steps induce Inversion Domain Boundaries (IDB) between neighboring domains which have grown independently on different terraces and coalesced. A slight tilt of the substrate surface off the low index plane, which favors diatomic steps, was therefore found to be beneficial because it eliminates the IDB's [2]. The energetics and structure of single and double steps on Si surfaces have been studied by means of tight-binding atomistic calculations by Chadi [5]. An electronic structure study of the (110) IDB in SiC is presented in another contribution to this Meeting [8]. In a recent paper, Pirouz et al. [71 pointed out that, in addition to the "chemical bond" mismatch, the step also induces a vertical displacement between domains growing on neighboring terraces if the materials are lattice-mismatched. This should lead to stress in the epitaxial film and possibly also in the substrate. This effect also exists for even-numbered steps in which case there is no IDB. In fact, the vertical misfit increases with the step size. In general the vertical misfit is given by:
v = nd, - mde,
(1)
where n is the order of the substrate step and m the number of layers deposited, and d, and d, are the interplanar spacings in substrate and epilayer respectively for the set of planes parallel to the film-substrate interface. For small steps and reasonable lattice-mismatch n = m. The defect introduced by the vertical displacement was tentatively called a displacement boundary (DB) [7], and the question was raised at which critical thickness of the film it would become favorable to form a dislocation in order to release the strain energy associated with the DB. The question was posed in a similar context as the problem of latera
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