GeSn/Ge p-i-n photodetectors with practical Ge0.964Sn0.036 active layers are theoretically investigated. First, we calculated the electronic band parameters for the heterointerfaces between strained Ge1−xSnx and relaxed (001)-oriented Ge. The carrier transport in a p-i-n photodiode built on a ten-period Ge0.964Sn0.036/Ge multiple quantum well absorber was then analyzed and numerically simulated within the Tsu−Esaki formalism by self-consistently solving the Schrödinger and Poisson equations, coupled to the kinetic rate equations. Photodetection up to a 2.1 μm cut-off wavelength is achieved. High responsivities of 0.62 A W−1 and 0.71 A W−1 were obtained under a reverse bias voltage of −3 V at peak wavelengths of 1550 nm and 1781 nm, respectively. Even for this low Sn-fraction, it is found that the photodetector quantum efficiency (49%@1.55 μm) is higher than those of comparable pure-Ge devices at room temperature. Detectivity of 3.8 × 1010 cm Hz1/2 W−1 and 7.9 × 1010 cm Hz1/2 W−1 at −1 V and −0.5 V, respectively, is achievable at room temperature for a 1550 nm wavelength peak of responsivity. This work represents a step forward in developing GeSn/Ge based infrared photodetectors.