Knowledge of nanopore size and shape is critical for many implementations of these single-molecule sensing elements. Geometry determination by fitting the electrolyte-concentration-dependence of the conductance of surface-charged, solid-state nanopores has been proposed to replace demanding electron microscope-based methods. The functional form of the conductance poses challenges for this method by restricting the number of free parameters used to characterize the nanopore. We calculated the electrolyte-dependent conductance of nanopores with an exponential-cylindrical radial profile using three free geometric parameters; this profile, itself, could not be uniquely geometry-optimized by the conductance. Several different structurally simplified models, however, generated quantitative agreement with the conductance, but with errors exceeding 40% for estimates of key geometrical parameters. A tractable conical-cylindrical model afforded a good characterization of the nanopore size and shape, with errors of less than 1% for the limiting radius. Understanding these performance limits provides a basis for using and extending analytical nanopore conductance models.

The performance of nanopore single-molecule sensing elements depends intimately on their physical dimensions and surface chemical properties. These factors underpin the dependence of the nanopore ionic conductance on electrolyte concentration, yet the measured, or modeled, dependence only partially illuminates the details of geometry and surface chemistry. Using the electrolyte-dependent conductance data before and after selective surface functionalization of solid-state nanopores, however, introduces more degrees of freedom and improves the performance of conductance-based nanopore characterizations. Sets of representative nanopore profiles were used to generate conductance data, and the nanopore shape and exact dimensions were identified, through conductance alone, by orders-of-magnitude reductions in the geometry optimization metrics. The optimization framework could similarly be used to evaluate the nanopore surface coating thickness.