MBE Growth and Surface Diffusion

There has been much recent interest in the statistical properties of nonequilibrium surfaces. In particular, much attention has been focussed on theoretical models to describe thin film growth by Molecular Beam Epitaxy. A number of groups 1,2,3 have proposed that the statistical properties of MBE growth are given by the fourth order continuum equation1 h⋅=−D4∇4h+λ4∇2(∇h)2+η h⋅=−D4∇4h+λ4∇2(∇h)2+η (1) where h(x⃗ ∥,t)h(x→∥,t) is the height of the surface and η is a noise source with correlations ⟨η(x⃗ ∥,t)⟩=0⟨η(x⃗ ∥,t)η(x⃗ ′∥,t′)⟩=Sδd(x⃗ ∥−x⃗ ′∥)δ(t−t′) ⟨η(x→∥,t)⟩=0⟨η(x→∥,t)η(x→′∥,t′)⟩=Sδd(x→∥−x→′∥)δ(t−t′) (2)