The thin films of high permitivity in ferroelectric materials using a capacitor are applied to DRAMs and FRAMs. (Ba, Sr)TiO$_3$ thin as ferroelectric materials were prepared by the sol-gel method and made by spin-coating on the Pt/Sio$_2$/Si substrate at 4,000 [rpm] for 10 seconds. The structural characteristics of the surface were analyzed by fractal dimension. The thickness of BST ceramics thin films was about 260∼280 [nm]. The property of the leakage current was stable with 10-9∼10-11[A] when the applied voltage was 0∼3[V]. BST thin films ha low leakage current properties when fractal dimension was low and a coating area was high.