Single-mode silicon p-i-n waveguides with varying cross-sections have been studied experimentally for on-chip photodetection at an operating wavelength k * 1550 nm. It has been shown that the quantum efficiency increases with decreasing waveguide cross-section. The performance of such a photodetector can be modelled in terms of density of surface states, bulk two photon absorption co-efficient, and waveguide loss parameters. © Springer Nature Switzerland AG 2019.