By combining band gap engineering with the self-organized growth of quantum dots, we present a scheme of adjusting the mid-infrared absorption properties to desired energy transitions in quantum dot based photodetectors. Embedding the self organized InAs quantum dots into an AlAs/GaAs superlattice enables us to tune the optical transition energy by changing the superlattice period as well as by changing the growth conditions of the dots. Using a one band envelope function framework we are able, in a fully three dimensional calculation, to predict the photocurrent spectra of these devices as well as their polarization properties. The calculations further predict a strong impact of the dots on the superlattices minibands. The impact of vertical dot alignment or misalignment on the absorption properties of this dot/superlattice structure is investigated. The observed photocurrent spectra of vertically coupled quantum dot stacks show very good agreement with the calculations.In these experiments, vertically coupled quantum dot stacks show the best performance in the desired photodetector application.