Silicon nanoribbons were fabricated using standard optical lithography from silicon on insulator material with top silicon layer thicknesses of 100, 60 and 45 nm. Electrically these work as Schottky-barrier field-effect transistors and, depending on the substrate voltage, electron or hole injection is possible. The current through the nanoribbon is extremely sensitive to charge changes at the oxidized top surface and can be used for biomolecule detection in a liquid. We show that for detection of streptavidin molecules the response is larger in the accumulation mode than in the inversion mode, although not leading to higher detection sensitivity due to increased noise. The effect is attributed to the location in depth of the conducting channel, which for holes is closer to the screened surface charges of the biomolecules. Furthermore, the response increases for decreasing silicon thickness in both the accumulation mode and the inversion mode. The results are verified qualitatively and quantitatively through a two-dimensional simulation model on a cross section along the nanoribbon device.