The self-trapping of bulk and surface excitons is considered. Both the
initial free exciton state and the final state (diatomic quasi-molecu
le) are formed via resonant binding. Under self-trapping, the binding
is redistributed to concentrate mainly inside the molecule, forming a
strong intra-molecule bond. But some of the weak resonant bonds persis
t in the vicinity of the molecule, which results in a lowering of the
self-trapping barrier. These phenomena manifest themselves differently
in the three- and two-dimensional cases, being better pronounced in t
he latter case.