Statistical processing of nanoporous templates with high-yield single-pore resolution

We address the statistical patterning of nanoscale lattices and discuss the probability to overlap a finite number of lattice features with a given entity. The experimental exemplification is done through selective nanowire growth using nanoporous alumina templates. This random patterning approach is found to provide rigorous selection rules for locating definite sets of objects into nanoporous templates. Remarkably, no alignment with respect to the template's features is required to achieve single-nanopore resolution with probabilities as high as 92% upon properly choosing the size of the processing mask. The approach is found to be scale-invariant with a minimal influence of the masking item symmetry and with good reliability of the mask-to-nanopore overlapping threshold. Routed in surface optimization, this study dives into the discrete geometry of quasi-periodic lattices through simple technological processing and analytical approaches.