Shrinking Core Model for Knudsen Diffusion-Limited Atomic Layer Deposition on a Nanoporous Monolith with an Ultrahigh Aspect Ratio

ZnO was grown on nanoporous alumina monoliths by atomic layer deposition (ALD) from diethylzinc (DEZ) and water. The alumina monolith has a cylindrical shape with a length of 6.2 ± 2.0 mm and a diameter of 1.93 ± 0.78 mm, of which the average pore diameter and specific surface area are 8.9 nm and 256 m2/g, respectively. The ALD process in the nanoporous monolith, of which the aspect ratio is higher than 105, was limited by the Knudsen diffusion of DEZ within the pores. The minimum exposure time (τcy) of DEZ for the complete coverage of ZnO on the cylindrical monolith was predicted to be τcy = ρOH R 2/4D e C o by using the shrinking core model (SCM) where ρOH is a molar volumetric density of OH groups, R is a radius of the monolithic cylinder, D e is an effective diffusion coefficient of DEZ in porous alumina, and C o is a concentration of DEZ on the exterior surface. Using a value of D e (1.4 × 10−2 cm2/s) obtained from the SCM, the minimum exposure time was predicted to be ∼66 min. Indeed, the complete coverage of ZnO was experimentally accomplished in an exposure time of 70 min. In addition, it is also demonstrated that the minimum exposure time is largely dependent in the shape (e.g., planar, cylindrical, or spherical) of the monolith.