  Understanding exciton-exciton interaction in multiply-excited nanocrystals is
crucial to their utilization as functional materials. Yet, for lead halide
perovskite nanocrystals, which are promising candidates for nanocrystal-based
technologies, numerous contradicting values have been reported for the strength
and sign of their exciton-exciton interaction. In this work we unambiguously
determine the biexciton binding energy in single cesium lead halide perovskite
nanocrystals at room temperature. This is enabled by the recently introduced
SPAD array spectrometer, capable of temporally isolating biexciton-exciton
emission cascades while retaining spectral resolution. We demonstrate that
CsPbBr$_3$ nanocrystals feature an attractive exciton-exciton interaction, with
a mean biexciton binding energy of 10 meV. For CsPbI$_3$ nanocrystals we
observe a mean biexciton binding energy that is close to zero, and individual
nanocrystals show either weakly attractive or weakly repulsive exciton-exciton
interaction. We further show that within ensembles of both materials,
single-nanocrystal biexciton binding energies are correlated with the degree of
charge-carrier confinement.
