Structures for a field-effect transistor and methods of forming a structure for a field-effect transistor. The structure includes a semiconductor substrate having a first trench, and a trench isolation region positioned in the first trench. The trench isolation region contains a dielectric material, the trench isolation region includes a second trench surrounded by the dielectric material, and the trench isolation region includes openings that penetrate through the dielectric material. A semiconductor layer is positioned in the second trench of the trench isolation region. The semiconductor layer contains a single-crystal semiconductor material.