The invention relates to a method for the production of a nanoelement field effect transistor, a nanoelement field effect transistor and a nanoelement arrangement. According to the method for the production of a nanoelement field effect transistor, a nanoelement is formed, a first and a second source-/drain area is coupled to the nanoelement, a surface area of a substrate is removed, such that a region of the nanoelement is exposed, and a gate-insulating structure and a gate structure are formed in a covered manner fully encompassing the nanoelement.