Metal-insulator-semiconductor-insulator-metal (MISIM) heterostructures, with rectifying current-voltage characteristics and photosensitivity in the visible and near-infrared spectra, are fabricated and studied. It is shown that the photocurrent can be enhanced by adding a multi-walled carbon nanotube film in the contact region to achieve a responsivity higher than 100 mA W − 1 under incandescent light of 0.1 mW cm − 2 . The optoelectrical characteristics of the MISIM heterostructures are investigated at lower and higher biases and are explained by a band model based on two asymmetric back-to-back Schottky barriers. The forward current of the heterojunctions is due to majority-carrier injection over the lower barrier, while the reverse current exhibits two different conduction regimes corresponding to the diffusion of thermal/photo generated carriers and majority-carrier tunneling through the higher Schottky barrier. The two conduction regimes in reverse bias generate two plateaus, over which the photocurrent increases linearly with the light intensity that endows the detector with bias-controlled photocurrent.