The intersubband optical absorption and Stark effect of square and step quantum wells in the presence of applied electric field have been investigated theoretically. By considering the tunneling of photoexcited electrons under the influence of electric field in the quantum well, we obtain a shifted and broadened absorption spectrum from the tunneling of electrons. Such broadening leads to a decrease of absorption coefficient when the applied electric field is increased. For detector application of multiple quantum well devices, if efficient tunneling of the photoexcited electrons is desirable for high responsivity, the sharpness of the absorption peak needs to be compromised. Our results provide insight to this broadening and thus the optimization guideline for detector design.