Modeling precursor diffusion and reaction of atomic layer deposition in porous structures

Atomic layer deposition (ALD) is a technique for depositing thin films of materials with a precise thickness control and uniformity using the self-limitation of the underlying reactions. Usually, it is difficult to predict the result of the ALD process for given external parameters, e.g., the precursor exposure time or the size of the precursor molecules. Therefore, a deeper insight into ALD by modeling the process is needed to improve process control and to achieve more economical coatings. In this paper, a detailed, microscopic approach based on the model developed by Yanguas-Gil and Elam is presented and additionally compared with the experiment. Precursor diffusion and second-order reaction kinetics are combined to identify the influence of the porous substrate's microstructural parameters and the influence of precursor properties on the coating. The thickness of the deposited film is calculated for different depths inside the porous structure in relation to the precursor exposure time, the precursor vapor pressure, and other parameters. Good agreement with experimental results was obtained for ALD zirconiumdioxide (ZrO2) films using the precursors tetrakis(ethylmethylamido)zirconium and O2. The derivation can be adjusted to describe other features of ALD processes, e.g., precursor and reactive site losses, different growth modes, pore size reduction, and surface diffusion