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 1 ¯ ) facet; (iv) crossing a facet–step joint between Pb(0 0 1) facet and A-step, or between Pb ( 11 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 [ 1 ¯ 10 ] crystallographic zone related to the choices of sidewalls in the formation of a Pb mesa by calculating corresponding surface free energies.