To investigate the possibility of the $ZrO_2$ buffer layer as the insulator for the Metal-Ferroelectric-Insulator-semiconductor (MFIS) structure, $ZrO_2$ and $SrBi_2Ta_2O_9$ (SBT) thin films were deposited on the P-type Si(111) wafer by the R.F. magnetron-sputtering method. According to the process with and without the post-annealing of the $ZrO_2$ buffer layer and SBT thin film, the diffusion amount of Sr, Bi, Ta elements show slight difference through the Glow Discharge Spectrometer (GDS) analysis. From X-ray Photoelectron Spectroscopy (XPS) results, we could confirm that the post-annealing process affects the chemical binding condition of the interface between the $ZrO_2$ thin film and the Si substrate. Compared to the MFIS structure without the post-annealing of the $ZrO_2$ buffer layer, memory window value of MFlS structure with post-annealing of the $ZrO_2$ buffer layer were considerably improved. The window memory of the Pt/SBT (260 nm, $800^{circ}C)/ZrO_2$ (20 nm) structure increases from 0.75 to 2.2 V under the applied voltage of 9 V after post-annealing.