Thermal damping of quantum interference patterns of surface-state electrons

Abstract

The temperature-dependent damping of quantum-mechanical interference patterns from surface-state electrons scattering off steps on Ag(111) and Cu(111) has been studied using scanning tunneling microscopy (STM) and spectroscopy in the temperature range 3.5–178 K. The thermal damping of the electron standing waves is described quantitatively within a simple plane-wave model accounting for thermal broadening due to the broadening of the Fermi-Dirac distributions of sample and tip, for beating effects between electrons with different (Formula presented) vectors, and for inelastic collisions of the electrons, e.g., with phonons. Our measurements reveal that Fermi-Dirac broadening fully explains the observed damping for Ag and Cu. From the analysis of our data, lower limits of the phase-relaxation lengths at the Fermi energy (Formula presented) of the two-dimensional electron gas of (Formula presented) at 3.5 K and (Formula presented) at 77 K for Ag(111), and of (Formula presented) at 77 K and (Formula presented) at 178 K for Cu(111) are deduced. In contrast to integral measurements such as photoemission we measure (Formula presented) close to (Formula presented) and also locally. The latter eliminates residual line widths due to surface defect scattering found in the integrating techniques. Our STM results, therefore, currently provide a very good absolute estimate of (Formula presented) and the inelastic lifetime (Formula presented) respectively. Our values can be combined with photoemission results on (Formula presented) to derive the inelastic lifetime of surface state electrons at any T. © 1999 The American Physical Society.