Methods are provided for manufacturing well-controlled, solid-state nanopores and arrays of well-controlled, solid-state nanopores by a cyclic process including atomic layer deposition (ALD), or chemical vapor deposition (CVD), and etching. One or more features are formed in a thin film deposited on a topside of a substrate. A dielectric material is deposited over the substrate having the one or more features in the thin film. An etching process is then used to etch a portion of the dielectric material deposited over the substrate having the one or more features in the thin film. The dielectric material deposition and etching processes are optionally repeated to reduce the size of the features until a well-controlled nanopore is formed through the thin film on the substrate.