The Influence of Mass Forces on the Critical Thickness of Pre-Stressed He 4 and Solid Epitaxial Films

Publisher Website
Google Scholar
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. It is assumed that the film's particles are able to rearrange their relative positions in the lattices, and the equilibrium rearrangement is determined my 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 to predict the appearance of corrugations in He4 films and to shed light on the dislocation-free Stranski-Krastanov pattern of epitaxial growth of thin solid films. We establish the corrections of the earlier published formula Hcrit = σμ/τ2 (where σ is the surface energy, μ the shear modulus, and τ the mismatch stress) relating to rigid substrates and announce a novel formula of the critical thickness for deformable substrates.