The Critical Thickness of Dislocation-Free Stranski-Krastanov Growth Atop a Deform Able Substrate

Abstract

We investigate the influence of mass forces (in particular, of gravitation and van der Waals forces) on the critical film thickness of thin films attached to solid substrates and establish corresponding corrections of the earlier published formula H_crit = σμ/τ² (where CT is the surface energy, μ - the shear modulus, and τ - the mismatch stress). It is assumed that the films’ particles are able to rearrange their relative positions in the lattices, and the equilibrium rearrangement is determined by minimizing the total static energy. Recently, it was demonstrated that morphological stability of interfaces in crystalline solids with the rearrangement is extremely sensitive to the presence of shear stresses. Equilibrium theory of elasticity of pre-stressed solids with the rearrangement of their material particles has already allowed the prediction of the appearance of corrugations in He⁴ films and to explain the dislocation-free Stranski-Krastanov pattern of epitaxial growth of thin solid films. The explicit asymptotic formulae announced here are especially useful in the case of small mass force, the effects of which can be detectable and even significant for some of the above mentioned phenomena.