A parametric study of vertical quantum dot infrared photodetectors (QDIPs) is presented. The properties of QDIPs are functions of the period of QD layers, the barrier thickness, and the buffer thickness. Optimum periods are found to exist for the responsivity (R) and the detectivity (D*), respectively. The optimum period for D* is larger than that for R because the noise decreases as the number of periods increases. Stacking of many QD layers is necessary for a higher D* because the optimum period for D* is quite large. In addition, a high absorption coefficient for the QD layers is very important because that improves both R and D* and decreases the optimum period.