Structures for a photonics chip that include a photonic component and methods of forming such structures. The structure may comprise a photodetector on a substrate and a waveguide core. The photodetector includes a light-absorbing layer having a longitudinal axis, a first sidewall, and a second sidewall adjoined to the first sidewall at an interior angle. The first sidewall is slanted relative to the longitudinal axis, and the second sidewall is oriented transverse to the longitudinal axis. The waveguide core includes a tapered section adjacent to the first sidewall and the second sidewall of the light-absorbing layer.