In this work, we report hafnium zirconium oxide (HZO)/indium gallium zinc oxide (IGZO)-based programmable ferroelectric (FE) diode memory array with ultra-fast sub-ns switching speed, thus extremely low sub-fJ switching energy for future in-memory and neuromorphic computing applications for the first time. The fabricated devices have electroresistance ratio of 3×105 and show robust cyclic endurance up to 109. In particular, we demonstrated a nonvolatile logic-in-memory circuit to implement NOT gate and incremental conductance changes to mimic analog nature of synaptic weights.