HfO2-based ferroelectric (FE-HfO2) is a promising material for low-power and high-capacity memory technology. Since thinner ferroelectric films are required for low voltage operation, the impact of film thickness on the switching kinetics of FE-HfO2 needs to be studied in detail. In this paper, metal/ferroelectric/metal capacitors are fabricated with several thicknesses of HfZrO2 (HZO) films and characterized to study the switching kinetics based on the nucleation limited switching (NLS) model. Thinner HZO capacitors show slower polarization switching and asymmetry in program and erase operation, although low-frequency polarization charge density is nearly the same for all thicknesses. Slow switching is due to the large variability of the activation field of FE domains and grain boundaries among small FE grains. The asymmetry is caused by the asymmetric interface property at the top and bottom interfaces. High-resolution TEM and electron diffraction mapping methods provide physical evidence for the above discussions.