Decay of Shockley surface state by randomly adsorbed Bi atoms at Ag(111) surfaces

The decay of the Shockley surface state by randomly adsorbed Bi atoms at Ag(111) surfaces was investigated. As the Bi coverage (theta(Bi)) increased, the energy dispersion E(k) was observed to deviate from the intrinsic downward parabolic dispersion of the Ag(111) Shockley surface state at the low-energy side in scanning tunneling microscopy dI/dV images. Meanwhile, scanning tunneling spectroscopy revealed that the bottom of the parabolic dispersion was broadened but still persistent. The criterion for the occurrence of the E(k) deviation was found to be given by the condition where the coherent length L-phi of the surface electrons becomes shorter than the wavelength of the Shockley surface-state electron.