Quantum-Well Wave-Function Localization and the Electron-Phonon Interaction in Thin Ag Nanofilms

The electron-phonon interaction in thin Ag nanofilms epitaxially grown on Cu(111) is investigated by temperature-dependent and angle-resolved photoemission from silver quantum-well states. Clear oscillations in the electron-phonon coupling parameter as a function of the silver film thickness are observed. Different from other thin film systems where quantum oscillations are related to the Fermi-level crossing of quantum-well states, we can identify a new mechanism behind these oscillations, based on the wave-function localization of the quantum-well states in the film.

Figure 1

(a) Typical 2D photoemission map for 36 ML $\mathrm{Ag}/\mathrm{Cu}(111)$, $T=211\mathrm{K}$, $hv=6\mathrm{eV}$. (b) Transition of a QW resonance into a QW state with increasing Ag thickness. The shaded area indicates the projected Cu bulk bands to the surface. (c) Energies of the $\nu =1$ to $\nu =4$ QW states (dots) and QW resonances (squares) as a function of nominal film thickness [11]. The solid curves are calculations using the phase accumulation model with $m^{*}/m=0.65$, in agreement with data published before in 12. The dotted lines link the QW state QW resonance transitions occurring at 23 and 35 ML to the binding-energy scale.

Figure 2

(a) Temperature-dependent photoemission spectra of 36 ML $\mathrm{Ag}/\mathrm{Cu}(111)$ for 336 and 211 K. The $\nu =1$ and $\nu =2$ peaks shift in binding energy and the linewidth increases with increasing temperature. (b) Linewidths (dots) and linear fit (solid line) of the QW states and the Shockley surface state as a function of temperature for this film.

Figure 3

Electron-phonon coupling parameters for the QW states $\nu =1$ (closed circles) and $\nu =2$ (open circles) as a function of binding energy, deduced from $T$-dependent linewidth measurements as shown in the inset and Fig. 2b. Oscillations in $\lambda$ occur at binding energies (bold printed) at which a QW resonance to QW state transition occurs, as can be seen in Fig. 1c. For reference, the gray shaded areas mark the binding-energy regimes of increased electron-phonon scattering due the $\nu =1$ to $\nu =2$ QW state interaction (light gray) and due to the $\nu =1$ to $\nu =3$ QW state interaction (dark gray). The inset shows the temperature dependence of the linewidth of the $\nu =1$ QW state right before (a) and after (b) the $\lambda$-step at 0.5 eV binding energy.

Figure 4

Schematic illustration of the QW state hole relaxation paths. Hole states are indicated by open circles, while electrons are indicated by solid circles. The dark shaded area is the projected bulk band of the Cu(111)-substrate to the surface. (a) Phonon-mediated scattering into the delocalized $\nu =2$ QW resonance; (b) enhanced electron-phonon coupling due to phonon-mediated interband scattering into the localized $\nu =2$ QW state. The energy differences are highly exaggerated.