To crystalize the HfZrOx (HZO) film into ferroelectric (FE) phase, the cooling down step of the crystallization annealing plays the vital part. Steeper cooling rate typically facilitates higher orthorhombic phase formation which requires large temperature difference in the cooling down step. To provide a sufficiently large temperature difference for BEOL compatible process, liquid nitrogen (LN2) was adopted for fast quenching in this work. Compared with conventional RTA chamber cooling (cooling rate of 3.1 oC/s), HZO-based FE capacitors by LN2 quenching (cooling rate of 49.6 oC/s) exhibit competitive advantages including an enhanced remanent polarization (Pr) by 25 % and improved switching speed by a factor of 2.5, charting a promising course towards improving the performance of ferroelectric devices.