Dependence of the intrinsic line width of surface states on the wave vector: the Cu surfaces

The dependence of the intrinsic line width Γ of electron and hole states due to inelastic scattering on the wave vector [k.sub.∥] in the occupied surface state and the first image potential state on the Cu(111) and Ag(111) surfaces has been calculated using the GW approximation, which simulates the self-energy of the quasiparticles by the product of the Green's function and the dynamically screened Coulomb potential. Different contributions to the relaxation of electron and hole excitations have been analyzed. It has been demonstrated that, for both surfaces, the main channel of relaxation of holes in the occupied surface states is intraband scattering and that, for electrons in the image potential states, the interband transitions play a decisive role. A sharp decrease in the intrinsic line width of the hole state with an increase in [k.sub.∥] is caused by a decrease in the number of final states, whereas an increase in Γ of the image potential state is predominantly determined by an increase of its overlap with bulk states.