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We present the results of kinetics experiments on quantum-size-effects (QSE) Pb islands formed on Si(111). We have looked at the evolution of seven-layer Pb islands from five-layer Pb islands due to the transport of Pb atoms from the interisland region, overcoming a barrier at the island edges, and moving to the island tops. By analyzing low-energy electron-diffraction and scanning-tunneling microscopy data, we have estimated the barrier for layer formation in this system to be ∼0.32eV. This energy is much larger than that expected from QSE electronic contributions alone.