Coalescence of ultrathin films by atomic layer deposition or chemical vapor deposition: Models of the minimum thickness based on nucleation and growth rates

Ultrathin, pinhole-free, and atomically smooth films are essential for future development in microelectronic devices. However, film morphology and minimum thickness are compromised when growth begins with the formation of islands on the substrate, which is the case for atomic layer deposition or chemical vapor deposition (CVD) on relatively unreactive substrates. Film morphology at the point of coalescence is a function of several microscopic factors, which lead to measurable, macroscopic rates of island nucleation and growth. To quantify the effect of these rates on the morphology at the point of coalescence, we construct two models: (1) a Monte Carlo simulation generates the film height profile from spatially random nucleation events and a constant island growth rate; simulated films resemble AFM images of the physical films; (2) an analytical model uses Poisson point statistics to determine the film thickness required to cover the last bare site on the substrate as a function of the nucleation rate and growth rate. Both models predict the same maximum thickness required to reach 99% coverage and reveal a power law relationship between the maximum thickness and the ratio of the nucleation rate divided by the growth rate. The Monte Carlo simulation further shows that the roughness scales linearly with thickness at coverages below 100%. The results match well with experimental data for the low-temperature CVD of HfB2 on Al2O3 substrates, but there are significant discrepancies on SiO2 substrates, which indicate that additional surface mechanisms must play a role.