  A model of submonolayer thin film growth is studied, where the attachment of
atoms to island edges is hindered by an energy barrier. A novel behavior of the
density of islands, N_s, is predicted as a function of flux F and temperature
T. For example, N_s scales as F^X with X=2i^*/(i^*+3), where i^* is the
critical island size, in contrast with the standard result X=i^*/(i^*+2). The
theory is applicable to surfactant mediated growth and chemical vapor
deposition. It explains recent experiments, which are inconsistent with the
standard theory.
