The systems and methods described herein include a sensor for suitable for sensing chemical and biological substances. The sensor comprises a semiconductor layer formed in or on a substrate and a channel having nano-scale dimensions formed in the semiconductor layer, where the structure creates an electrically conducting pathway between a first contact and a second contact on the semiconductor layer. In certain preferred embodiments, the nano-scale channel has a trapezoidal cross-section with an effective width and exposed lateral faces, where the effective width is selected to have same order of magnitude as a Debye length (LD) of the semiconductor material of which the semiconductor layer is formed.