Structures for air-gap spacers in a field-effect transistor and methods for forming air-gap spacers in a field-effect transistor. A gate structure is formed on a top surface of a semiconductor body. A dielectric spacer is formed adjacent to a vertical sidewall of the gate structure. A semiconductor layer is formed on the top surface of the semiconductor body. The semiconductor layer is arranged relative to the vertical sidewall of the gate structure such that a first section of the first dielectric spacer is located in a space between the semiconductor layer and the vertical sidewall of the gate structure. A second section of the dielectric spacer that is located above a top surface of the semiconductor layer is removed. An air-gap spacer is formed in a space from which the second section of the dielectric spacer is removed.