Flat-surface, step-edge, facet-facet, and facet-step diffusion barriers in growth of a Pb mesa

We obtain important energy parameters for understanding growth kinetics of a faceted Pb mesa. Specifically, extensive calculations of diffusion barriers are performed for a Pb adatom: (i) on a flat Pb(1 1 1) or Pb(0 0 1) surface; (ii) crossing a single A- or B-step edge on Pb(1 1 1) surface; (iii) crossing a facet-facet edge between Pb(1 1 1) facet and Pb(0 0 1) facet, or between Pb(1 1 1) facet and Pb (11 over(1, ̄)) facet; (iv) crossing a facet-step joint between Pb(0 0 1) facet and A-step, or between Pb (11 over(1, ̄)) facet and B-step, using a modified embedded atom method. We investigate two different diffusion modes: direct hopping of an adatom, and exchange mechanism between an adatom and substrate atom(s). Direct hopping diffusion is more favorable over exchange mechanism for an adatom on a flat (1 1 1) or (0 0 1) surface. Diffusion crossing A-step edge favors direct hopping, while diffusion crossing B-step edge favors exchange mechanism. For facet-facet or facet-step diffusion, the exchange mechanism is always favorable over direct hopping. The diffusion barriers obtained here have been used to reasonably explain the intriguing kinetic growth of a Pb mesa in recent experiments. In addition, we also discuss low-index planes of Pb [over(1, ̄) 10] crystallographic zone related to the choices of sidewalls in the formation of a Pb mesa by calculating corresponding surface free energies.