Structures for an edge coupler of a photonics chip and methods of forming an edge coupler for a photonics chip. The structure includes a waveguide core on a dielectric layer, as well as an interconnect structure including a interlayer dielectric layer positioned over the dielectric layer and an opening penetrating through the interlayer dielectric layer to the waveguide core. A region of the interlayer dielectric layer is positioned to overlap with a portion of the waveguide core. The region of the interlayer dielectric layer has a surface that is rounded with a curvature.