A semiconductor device having a logic section and a memory section that are formed on the same semiconductor chip, including: a first transistor formed in the logic section and having gate electrodes and source and drain regions, and a second transistor formed in the memory section having gate electrodes, source and drain regions and a capacitor, the capacitor being of a MIM structure and having an upper and a lower metal electrode and a capacitor dielectric film sandwiched therebetween, the capacitor dielectric film being formed of a dielectric material which is selected from the group consisting of ZrO2, Hf92, (Zrx, Hf1-x)O2 (0