Reduction of dark current at high-temperature operation is a great challenge in conventional quantum dot infrared photodetectors, as the rate of thermal excitations resulting in the dark current increases exponentially with temperature. A resonant tunneling barrier is the best candidate for suppression of dark current, enhancement in signal-to-noise ratio, and selective extraction of different wavelength response. In this paper, we use a physical model developed by the authors recently to design a proper resonant tunneling barrier for quantum infrared photodetectors and to study and analyze the spectral response of these devices. The calculated transmission coefficient of electrons by this model and its dependency on bias voltage are in agreement with experimental results. Furthermore, based on the calculated transmission coefficient, the dark current of a quantum dot infrared photodetector with a resonant tunneling barrier is calculated and compared with the experimental data. The validity of our model is proven through this comparison. Theoretical dark current by our model shows better agreement with the experimental data and is more accurate than the previously developed model. Moreover, noise in the device is calculated. Finally, the effect of different parameters, such as temperature, size of quantum dots, and bias voltage, on the performance of the device is simulated and studied.