Minimum Coating Thickness in Pore Size Reduction of Inorganic Substrates through Particle Deposition

Abstract

The determination of minimum coating thickness for covering substrate holes through particle deposition is achieved with a combined, three-dimensional, on-lattice model, in which both deterministic and non-deterministic driving forces are taken into account. The relative importance of deterministic forces to non-deterministic forces is quantified by a dimensionless parameter, Peclet number. The minimum covering thickness normalized with the characteristic hole size (hc/Hw) is investigated subject to variation in Peclet number (Pe) and normalized size (Dp/L) of the depositing particle, normalized hole size (Hw/L), and degree of post-contact restructuring allowed (Nr). It is found that there exists a scaling relationship between the normalized minimum covering thickness and the normalized hole size as hc/Hw∼(Hw/L)E with E=0.53, 0.54, 0.96, and 1.42 for Pe of 1000, 10, 0.5, and 0.1, respectively. The magnitude of the scaling exponent implies that the hole covering ability of diffusive particle movement varies more than that of ballistic particle movement over variation in hole size. It is also found that hc/Hw increases with increasing Hw/L and Dp/L. At low Pe (<1), hc/Hw increases with increasing Pe for smaller holes, but decreases with increasing Pe for larger holes. For larger Pe, hc/Hw decreases with increasing Pe, implying that ballistic particle movement is more efficient in covering holes. Post-contact surface restructuring deteriorates the hole covering efficiency of particle deposition for ballistic movement dominated situations (large Pe). But for low Pe situations, there exists an optimal surface restructuring extent, at which hc/Hw is a minimum.