The metal-insulator-silicon (MIS) capacitors with $SiO_2$ and high-k dielectrics ($HfO_2$, $Al_2O_3$) were fabricated, and the current-voltage characteristics were investigated. Especially, an effective barrier height between metal gate and dielectric was extracted by using Fowler-Nordheim (FN) plot and Direct Tunneling (DT) plot of quantum mechanical(QM) modeling. The calculated barrier heights of thermal $SiO_2$, ALD $SiO_2$, $HfO_2$ and $Al_2O_3$ are 3.35 eV, 0.6 eV, 1.75 eV, and 2.65 eV, respectively. Therefore, the performance of non-volatile memory devices can be improved by using engineered tunnel barrier which is considered effective barrier height of high-k materials.