A numerical analysis of the ripening of multilayer islands on Cu(111) shows
that the Ehrlich-Schwoebel barrier for interlayer mass transport is indepe
ndent of the terrace width w as long as w > w(c) = 14 +/- 2 Angstrom, but v
anishes for w < w(c). The critical width we corresponds exactly to the terr
ace width below which the surface state is pushed above the Fermi level due
to quantum confinement. The Ehrlich-Schwoebel barrier is therefore correla
ted with the occupation of surface states.