Range of Excited Electrons in Metals

Decay of electronic excitations at metal surfaces

“…In the 3D EGM the decay rate scales as ðE F À EÞ 2 [71,76], while in 2D the dependence is modified to ðE F À EÞ 2 ln jE F À Ej [296,297]. For Be the 3D EGM gives G ee ¼ 90 meV at G that is significantly smaller than the intraband contribution of 225 meV, but larger than the interband one (40 meV).…”

“…0) the increase of the lifetimes is negligible. That this is the case can easily be understood by looking at the small o expansion [72,76] of the imaginary part of the bulk RPA response function. In this approximation the real (E 1 ) and imaginary (E 2 ) parts of the dielectric function are given by…”

“…Previous estimates of the electron-electron contribution have assumed the hole to be filled by interband transitions involving the bulk electrons near the surface (Fig. 30) and have calculated the decay rate using the degenerate electron-gas model of an isotropic Fermi liquid [76]. In a new treatment (see Section 2.3), both band-structure and surface effects were included to correctly describe both 2D and 3D decay processes.…”

Long lived electronic states

“…In the present work, the deexcitation probability of an excited state with arbitrary spatial extension is calculated inside a free-electron-like metal described by the Lindhard response function. In the limit of complete delocalization the result obtained by Quinn [8] for free electrons is retrieved while a fully localized state almost lives forever.…”

“…The transition rate, probability per unit time P, of this deexcitation process is a property of the excited state directly related with the imaginary part of its self-energy S 2 [8] …”