Modeling rough surfaces as a strategy to control the crystal quality, spatial and size distribution in semiconductor nanoparticles growth: A theoretical-experimental approach

The growth of germanium nanoparticles’ thin films on rough SiO \(_{2}\) ${}_2$ surfaces through the sputtering technique was analyzed based on thermodynamic principles. The study proposes a predictive model that allows controlling the size, distribution, and crystalline quality of nanoparticles embedded in oxides by adjusting the corresponding growth parameters in reactive sputtering. Surfaces based on two-dimensional Brownian motion, a precise modeling technique, were used to model the rough surface. A mathematical relation between the Hurst exponent and root mean square of a surface measured is used to reconstruct theoretical roughness surfaces. The modeling predictions were compared with statistical results obtained through atomic force microscopy measurements. Additionally, we find that the interfacial thin film-surface energy impacts the crystallization process.