A solid state molecular sensor having an aperture extending through a thickness of a sensing region is configured with a sensing region thickness that corresponds to the characteristic extent of at least a component of a molecular species to be translocated through the aperture. A change in an electrical characteristic of the sensing region is measured during the molecular species translocation. The sensor can be configured as a field effect transistor molecular sensor. The sensing region can be a region of graphene including an aperture extending through a thickness of the graphene.