1. A chemically-sensitive field effect transistor having a multi-layered structure, comprising: a substrate layer having an extended body; a first insulating layer positioned above the extended body of the substrate layer; a second insulating layer positioned above the first insulating layer; a source electrode and a drain electrode each having a top surface and a bottom surface, the top surface separated from the bottom surface by opposing outer and inner side portions, each of the opposed side portions and each of the bottom surfaces of the source and drain electrodes being disposed within the first insulating layer, the source electrode being separated from the drain electrode by a distance; a graphene layer positioned between the first and second insulating layers and extending between the outer side portion of the source electrode and the outer side portion of the drain electrode thereby forming a channel between the source and drain electrodes, the graphene layer contacting the top surface of the source and drain electrodes; and a well structure provided in the second insulating layer, the well structure having a bottom surface positioned above and in contact with the graphene layer, a top surface opposed to the bottom surface, and a chamber, the chamber extending from the top surface to the bottom surface of the well structure and exposing the graphene layer within the chamber, the graphene layer forming a bottom surface of the chamber.