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We have fabricated and demonstrated ultrathin In-Ga-Zn-O (IGZO) channel ferroelectric HfO₂ field effect transistor (FET) with memory operation. Ultrathin-body IGZO ferroelectric FET (FeFET) shows high mobility and nearly ideal subthreshold slop with minimum 8 nm channel thickness, thanks to the properties of IGZO material, junctionless FET operation, nearly-zero low-k interfacial layer on metal-oxide channel and effective capping for realizing ferroelectric phase formation with HfZrO₂ (HZO). The controllable memory operations are achieved with the use of back gate. The design guideline of IGZO FeFET is proposed by discussing the thickness of front gate oxide HZO and back gate oxide SiO₂ using TCAD simulation. The material and electrical properties of metal/HZO/IGZO/metal capacitor are also investigated. Metal/HZO/IGZO/metal capacitor has up to 10⁸ endurance and over one-year retention. IGZO FeFET shows a potential for high-density and low-power memory application.