Reading the ripples of confined surface-state electrons: Profiles of constant integrated local density of states

Abstract

Atomically resolved scanning tunneling microscope images of a Ag(111) surface are presented, which simultaneously display standing-wave patterns arising from the confinement of surface-state electrons to nanoscale terraces. We show how the energy-dependent patterns develop from the superposition of allowed wave functions in the quantum box. A simple free-electron model is already sufficient to identify all major features in differential conductance $(dI/dV)$ maps and constant current topographic images, which both result from the superposition of up to eight allowed states. These results illustrate how the difference between $dI/dV$ and topographic measurements can be pronounced already for very low bias voltages. An analysis of $dI/dV$ spectra measured on large defect-free terraces yields a surface-state lifetime width of $\ensuremath{\Gamma}=4.9\ifmmode\pm\else\textpm\fi{}0.2\mathrm{meV},$ which is smaller than that previously reported.