In this paper, we present a self-consistent theoretical model for a metal-insulator semiconductor (MIS) dual band ultraviolet (UV) photodetector with a modified structure implying an arbitrarily defined insulating potential barrier as its active region. Utilizing our proposed model, the dark and photocurrent density-voltage (J-V) characteristics of MIS UV photodetectors with multi-quantum wells of silicon (MQWs) are calculated. We demonstrate that dark current is reduced in the suggested structure, because the electron-tunneling probability becomes unity at energies coincident with the peak detection wavelength. This is due to the resonant tunneling and decreases at energies that are significantly smaller than this optimum value. In consequence, the number of carriers contributing to the dark current, which have a broad energy distribution at high temperatures, will decrease. It is also shown that the designed structure could detect two individual UV wavelengths, simultaneously. The width of each Si quantum well has been considered at around 1.2 nm, in order to observe these two absorption peaks in the middle and near UV regions of photon spectrum (about 365 nm, 175 nm).