Absolute step and kink formation energies of Pb derived from step roughening of two-dimensional islands and facets

Abstract

The shapes of (111) oriented two-dimensional (2D) islands and facets, the latter being part of three-dimensional (3D) crystallites of Pb, were equilibrated at 104--520 K. Island sizes were in the range of 15--90 nm radius, facets typically at 100--270 nm radius. They were imaged by scanning tunneling microscopy to provide the exact outline of the bounding step. Increased step roughening with increasing temperature decreases the radius anisotropy of islands and facets in a consistent manner. Products of island/facet radius times local step curvature versus temperature were obtained experimentally, serving as the basis of absolute step and kink energies at 0 K. They are ${f}_{1A}(0)=128.3\ifmmode\pm\else\textpm\fi{}0.3\mathrm{meV},$ ${f}_{1B}(0)=115.7\ifmmode\pm\else\textpm\fi{}5.8\mathrm{meV},$ and ${\ensuremath{\varepsilon}}_{\mathrm{kA}}=42.5\ifmmode\pm\else\textpm\fi{}1.0\mathrm{meV},$ ${\ensuremath{\varepsilon}}_{\mathrm{kB}}=60.6\ifmmode\pm\else\textpm\fi{}1.6\mathrm{meV},$ respectively. The combination of studying small 2D islands (unstable at high temperature) and large 2D facets allows measurements over a very large range of temperatures.