  Exciton-exciton annihilation (EEA) and Auger recombination are detrimental
processes occurring in semiconductor optoelectronic devices at high carrier
densities. Despite constituting one of the main obstacles for realizing lasing
in semiconductor nanocrystals (NCs), the dependencies on NC size are not fully
understood, especially for those with both weakly and strongly confined
dimensions. Here, we use differential transmission spectroscopy to investigate
the dependence of EEA on the physical dimensions of thickness-controlled 2D
halide perovskite nanoplatelets (NPls). We find the EEA lifetimes to be
extremely short on the order of 7-60 ps. Moreover, they are strongly determined
by the NPl thickness with a power-law dependence according to {\tau}_2~d^5.3.
Additional measurements show that the EEA lifetimes also increase for NPls with
larger lateral dimensions. These results show that a precise control of the
physical dimensions is critical for deciphering the fundamental laws governing
the process especially in 1D and 2D NCs.
