Green's function approach to the lifetimes of image potential resonances at metal surfaces

Abstract

We present a theoretical study of the image potential resonances (IPRs) at metal surfaces. We develop the Green's functions approach allowing us to calculate binding energies E n and lifetimes τ n of IPRs with high quantum numbers n (up to 10 in this work). A systematic study is performed at the point for the close-packed metal surfaces: Cu(111), Ag(111), Au(111), Al(001), Al(111), Be(0001), Mg(0001), Na(110), Li (110), and also at the Y point on Cu(110). The calculated lifetimes of IPRs on close-packed surfaces demonstrate the scaling law τ n ∝ n 3 . Our results are in agreement with available experimental data. We show that at the Y point on Cu(110) each quantum number n corresponds to a pair of IPRs n + and n − , where the energy difference E n+ − E n− is proportional to n −3 . The lifetimes τ n+ and τ n− differ significantly, however, they both obey the scaling law τ n± ∝ n 3 . Since the electrons trapped in the long-lived IPRs are strongly localized on the vacuum side, we argue that the inelastic electron-electron and electron-phonon scattering have a small contribution to the decay rate of these IPRs. The latter is dominated by the resonant electron transfer into the bulk.

Image potential states at transition metal oxide surfaces: A time-resolved two-photon photoemission study on ultrathin NiO films

“…Theoretically, the IPS are well understood and it is also possible to calculate the dynamics of electrons in IPS [21][22][23] . Image potential states of clean metal surfaces can be described using the so called bulk penetration model.…”

Resolubility of image-potential resonances

“…Since resonant elastic channels are expected to dominate electron transfer processes at interfaces in most applications, model studies of the decay of image-potential resonances are most interesting. These perspectives are, however, seriously hampered by the lack of a rigorous theoretical description which goes beyond appropriately tuned model potentials [18,19]. The multiple scattering theory of Echenique and Pendry [2] to free-electron-like metals as well as density functional theory at the level of the GW approximation predict just one broad resonance [20,21].…”