The Al2O3 thin films were deposited on the Si3N4 (radical- Si3N4) prepared by the direct nitridation of a Si substrate using atomic nitrogen radicals. Because the radical- Si3N4 is highly resistive against the oxidation process, we can completely eliminate the metal phase in Al2O3 that degrades the insulating properties of Al2O3. The 1.3nm thick Al2O3 film was found to have a permittivity of 9.76 in this stacked Al2O3/Si3N4 structure. It was also found that no oxidation took place at the interface of Si3N4 and the Si substrate during the deposition and post-oxidation of the Al2O3 film on the radical-Si3N4/Si substrates. As a result, highly capacitive MIS (Metal-Insulator-Semiconductor) structures were realized using the Al2O3/Si3N4 stacked insulator. The MIS diode with Al2O3/Si3N4 is found to have 105 times less leakage current compared to the diode with Si3N4 insulator film with similar capacitance density. We have shown that the insulating properties of the Al2O3/radical-Si3N4 stack are suitable for the MFIS (Metal-Ferroelectric-Insulator-Semiconductor) transistors.