  Using semi-analytical models we calculate the energy, effective Bohr radius
and radiative lifetime of neutral excitons confined in CdSe colloidal
nanoplatelets (NPLs). The excitonic properties are largely governed by the
electron-hole in-plane correlation, which in NPLs is enhanced by the
quasi-two-dimensional motion and the dielectric mismatch with the organic
environment. In NPLs with lateral size $L \gtrsim 20$ nm the exciton behavior
is essentially that in a quantum well, with superradiance leading to exciton
lifetimes of 1 ps or less, only limited by the NPL area. However, for $L < 20$
nm excitons enter an intermediate confinement regime, hence departing from the
quantum well behavior. In heterostructured NPLs, different response is observed
for core/shell and core/crown configurations. In the former, the strong
vertical confinement limits separation of electrons and holes even for type-II
band alignment. The exciton behavior is then similar to that in core-only NPL,
albeit with weakened dielectric effects. In the latter, charge separation is
also inefficient if band alignment is quasi-type-II (e.g. in CdSe/CdS), because
electron-hole interaction drives both carriers into the core. However, it
becomes very efficient for type-II alignment, for which we predict exciton
lifetimes reaching $\mu s$.
