The electrical characteristics and annealing effects of tunneling dielectrics stacked with $SiO_2$ and $Si_{3}N_{4}$ were investigated. I-V characteristics of band gap engineered tunneling gate stacks consisted of $Si_{3}N_{4}/SiO_2/Si_{3}N_{4}$ (NON), $SiO_2/Si_{3}N_{4}/SiO_2$ (ONO) dielectrics were evaluated and compared with $SiO_2$ single layer using the MOS (metal-oxide-semiconductor) capacitor structure. The leakage currents of engineered tunneling barriers (ONO, NON stacks) are lower than that of the conventional $SiO_2$ single layer at low electrical field. Meanwhile, the engineered tunneling barriers have larger tunneling current at high electrical field. Furthermore, the increased tunneling current through engineered tunneling barriers related to high speed operation can be achieved by annealing processes.