Analytical model for island growth mode in thin film deposition

An analytical model for 3D island growth in Atomic Layer Deposition (ALD) was derived from geometric and statistical principles. The model: (i) accounts for a random island distribution and spontaneous nucleation; (ii) expresses surface coverage, deposited mass, mass gain per cycle and surface roughness in closed-form equations; (iii) is expandable to alternative island shapes or processes beyond ALD, including variants of chemical vapor deposition. A Monte-Carlo simulation enabled visualization of the deposit morphology at distinct features of the derived analytical curve corresponding to various growth stages: separate island growth, onset of coalescence, peak mass gain per cycle and convergence to a continuous film. The model can fit experimentally measured signals in-or ex-situ relating to mass uptake or surface roughness during the nucleation process. The fit to literature data of HfO2, Al2O3 and ZrO2 island growth on H-terminated Si showcased the insights that the model gives, such as estimation of island size, island nucleation density and spontaneous island nucleation rate. The model serves as a valuable tool to guide process design and optimization, whether the goal is to obtain specific nanoparticle morphologies, as for fields of catalysis or optics, or thin continuous films, for areas of semiconductor and coating technologies.