Continued scaling of semiconductor devices in logic and memory applications requires the introduction of high-k (HK) dielectrics to enhance the capacitance density while maintaining a low leakage. Of particular concern in DRAM memory applications is the so called `dielectric relaxation current', which is significantly enhanced with HfO2 dielectrics as compared to SiO2. In this paper, it is shown that these relaxation currents arise from electron trapping/detrapping by/from oxygen vacancy defects in the HfO2 dielectric from/to the contact electrodes. This understanding is utilized to minimize `dielectric relaxation currents' by optimizing the defect structure in the HK dielectric. By creating trap-free dielectric films with N or La doping, we show that substantial reductions in the relaxation currents can be achieved. For the first time, it is demonstrated that a HK dielectric stack formed as a result of these treatments can have reduced relaxation currents similar to SiO2, thus providing a pathway to solving a fundamental paradigm associated with HK dielectrics that has persisted for several years.