Amorphous thin film growth: effects of density inhomogeneities

Temperature behaviour of the average size of nanoparticle lattices co-deposited with an amorphous matrix. Analysis of Ge + Al2O3 and Ni + Al2O3 thin films

We theoretically interpret the thermal behaviour of the average radius versus substrate temperature of regular quantum dot/nanocluster arrays formed by sputtering semiconductor/metal atoms with oxide molecules. The analysis relies on a continuum theory for amorphous films with given surface quantities, perturbed by a nanoparticle lattice. An account of the basic thermodynamic contributions is given in terms of force-flux phenomenological coefficients of each phase (Ge, Ni, Al₂O₃). Average radii turn out to be expressible by a characteristic length scale and a dimensionless parameter, which mainly depend upon temperature through diffusion lengths, film pressures and finite-size corrections to interfacial tensions. The numerical agreement is good in both Ge ([Formula: see text]) and Ni ([Formula: see text]) lattices grown at temperatures [Formula: see text]800 K, despite the lower temperature behaviour of quantum dots seeming to suggest further driving forces taking part in such processes.

APPROXIMATION OF THE STOCHASTIC RAYLEIGH–BÉNARD PROBLEM NEAR THE ONSET OF CONVECTION AND RELATED PROBLEMS

It is well known that complicated stochastic evolution systems near a change of stability are often dominated by slow modes. We rigorously approximate the evolution of the system by stochastic ordinary differential equations describing the amplitudes of the dominating modes on a slow time-scale.

In this paper we focus on equations with quadratic nonlinearity and give applications to the Rayleigh–Bénard problem and a model from surface growth perturbed by fractional noise.The unique existence of global solutions is not necessary.

Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

A local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.

Nonlinear ripple dynamics on amorphous surfaces patterned by ion beam sputtering

Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripples on aeolian sand dunes. A suitable generalization of continuum descriptions of the latter allows us to describe theoretically for the first time the main nonlinear features of ripple dynamics by IBS, namely, wavelength coarsening and nonuniform translation velocity, that agree with similar results in experiments and discrete models. These properties are seen to be the anisotropic counterparts of in-plane ordering and (interrupted) pattern coarsening in IBS experiments on rotating substrates and at normal incidence.