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

Abstract

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 () and Ni () lattices grown at temperatures 800 K, despite the lower temperature behaviour of quantum dots seeming to suggest further driving forces taking part in such processes.