The current-voltage (I-V) characteristics and spectral dependences of the photocurrent of p-i-n structures, including GeSiSn/Si multiple quantum wells (MQWs) with the Sn content up to 15%, are studied. It is shown that the increase in the Sn content from 4.5 to 13% leads to a gradual increase in the dark current density from 6×10−6 A/cm2 to 5×10−5 A/cm2 at the reverse bias of 1 V. The further rise in the Sn content to 15% results in the increase of the dark current density to 5×10−4 A/cm2, which is an order of magnitude lower than the known values for GeSn-based photodiodes. The shift of the cutoff wavelength of the photoresponse with the Sn content increase in heterostructures is demonstrated. The photoresponse spectrum of the detector extends up to wavelengths of larger than 2 μm at the Sn content of more than 10%.