Theoretical optimisation of the side-wall of micropillar array columns using computational fluid dynamics

The present study provides an overview of the ideal side-wall position in micro-pillar array columns for the case of semi-embedded side-walls. The position has been determined using computational fluid dynamics simulations of the flow field in flow domains with different side-wall shifts. Optimal side-wall shift values are presented for a wide range of shapes (cylinders, and diamonds and hexagons with different aspect ratios) and packing densities. Simple linear correlations that allow calculating the optimised side-wall geometries for the different considered variety of shapes and packing densities could be established. Interestingly, only two correlations are needed to represent all investigated cases: one correlation for all diamonds, and one correlation for the cylinders and all hexagons. Compared to the case of a flat side-wall, the minimal feature size on the mask can be increased by a factor of 2.5 in the case of cylindrical pillar bed with external porosity ɛ = 0.4, implying that that much smaller pillar diameters can be used in the bulk of the bed before the minimal feature size on the mask falls below the lithography resolution.