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Electron-beam lithography and reactive ion etching were used to process silicon-on-insulator substrates for the fabrication of single cylindrical high-aspect-ratio solid-state nanopores and high-packing-density nanopore arrays. Minimum pore diameters of 40 nm were readily achieved with a high yield. The electrolyte concentration dependence of ion transport through single nanopores was measured for pores with diameters ranging from 40 to 140 nm. Measured single-nanopore conductances in high salt concentrations were compared to a simple model using a cylindrical resistance path and bulk solution conductivity. Electrochemical impedance spectroscopy was used to study the ac response of the device.