In this paper, reliability of the two sandwiched MIM capacitors of $Al_2O_3-HfO_2-Al_2O_3$ (AHA) and $SiO_2-HfO_2-SiO_2$ (SHS) with hafnium-based dielectrics was analyzed using two kinds of voltage stress; DC and AC voltage stresses. Two MIM capacitors have high capacitance density (8.1 fF/${mu}m^2$ and 5.2 fF/${mu}m^2$) over the entire frequency range and low leakage current density of ~1 nA/$cm^2$ at room temperature and 1 V. The charge trapping in the dielectric shows that the relative variation of capacitance (${Delta}C/C_0$) increases and the variation of voltage linearity (${alpha}$/${alpha}_0$) gradually decreases with stress-time under two types of voltage stress. It is also shown that DC voltage stress induced greater variation of capacitance density and voltage linearity than AC voltage stress.