  Optical measurements and first-principles calculations of the band structure
and exciton states in direct-gap bulk and few-layer PbI2 indicate that the n =
1 exciton is Frenkel-like in nature in that its energy exhibits a weak
dependence on thickness down to atomic-length scales. Results reveal large
increases of the gap and exciton binding energy with decreasing number of
layers, and a transition of the fundamental gap, which becomes indirect for 1-2
monolayers. Calculated values are in reasonable agreement with a
particle-in-a-box model relying on the Wannier-Mott theory of exciton
formation. General arguments and existing data suggest that the Frenkel-like
character of the lowest exciton is a universal feature of wide-gap layered
semiconductors whose effective masses and dielectric constants give bulk Bohr
radii that are on the order of the layer spacing.
