Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

The role of high-energy phonons in electron–phonon interaction at conducting surfaces with helium-atom scattering

“…The experimental HAS data for the DW exponent plotted in Fig. 4 as a function of temperature for odd values of n from 3 to 17 (the Pb films, after forming a wetting monolayer, tend to grow as a bilayer sequence, 2 ) with an n sat, f of about 9, are also reasonably well fitted, within the fairly large experimental error, by Eqs. ( 6), (10) and 11).…”

“…For sufficiently large temperatures, meaning T comparable or greater than the Debye temperature, the DW exponent 2W eff (k f ,k i ,T) is essentially linear in T as in eqn (8). However, eqn (2) shows that all phonon modes which have polarization components parallel to Dk contribute, even high energy modes which are neglected in the standard treatments. Here it is demonstrated that the electron-phonon interaction method of treating the DW factor allows one to readily estimate the contributions of high energy phonon modes such as, for example, optical modes.…”

“…27 With λ HAS, f = 0.18 and λ HAS,s = 0.19 given for Cs and Cu in Ref. 2 (Table 3 and 2), respectively, and sat, f = 4 for Cs films on Cu(111), 2 the best fits (red curves) with Eq. ( 6) and the substitutions of Eqs.…”

“…The venerable concept of Debye-Waller (DW) factor, by which Piet Debye (1913) and Ivar Waller a Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal, 4,20018 (in his 1923 thesis) correctly attributed to thermal vibrations the attenuation of Roentgen rays, in the case of HAS from conducting surfaces presently allows for a direct measurement of the e-ph mass-enhancement factor λ -a basic parameter for conducting materials. 2 This is made possible by the theoretical demonstration that the linear decay of the DW exponent 2W (T ) with the surface temperature T is approximately proportional to λ , with the proportionality constant estimated from known parameters of the surface.…”

Time-dependent density functional theory calculations of electronic friction in non-homogeneous media

“…Aside from the electronic excitations, another energy dissipation channel that is frequently neglected is the excitation of phonons at the surface. There is a broad spectrum of theoretical models that have been successfully used to describe the energy exchange between incident atoms and molecules and the surface lattice: semiclassical approximations with atomic interaction potentials, 28 stochastic descriptions based on the Generalized Langevin Oscillation model, 29 or ab initio molecular dynamics simulations 30 are among them.…”