Epitaxial Volmer-Weber growth modelling

As-deposited epitaxial thin III-nitride films grown on silicon substrates by vapor deposition often exhibit large intrinsic stress that can lead to film failure. The stress created in a III-nitride film is strictly related to its crystal structure evolution during its epitaxial Volmer-Weber growth on the Si substrate. Sensitive real-time measurements of stress evolution during the deposition show that the crystal structure evolution of the film can be divided into three main stages: an initial compressive stage caused by the nucleation of several islands of the film material on the substrate; a subsequent tensile stage associated with the coalescence of these islands ending at the percolation point with the formation of a continous film; a final third compressive stage caused by the flux-driven incorporation of excess atoms within grain boundaries of the film. We propose a physically based analytical equation in order to obtain more insight into the stress-microstructure relation of the tensile stage of the growth, taking into account the epitaxial relation between the film and the substrate. The calculated values of the stress are compared with experimentally determined values of stress from the literature for an AlN thin film grown on a Si(111) substrate obtained through sensitive real-time measurements of the wafer bow. A comparison of the present model with experimental observations shows very good agreement using only a single fit parameter.