Influence of the surface band structure on electron emission spectra from metal surfaces

Electron distributions produced by grazing impact of fast protons on Mg(0001), Cu(111), Ag(111), and Au(111) surfaces are investigated, focusing on the effects of the electronic band structure. The process is described within the band-structure-based approximation, which is a perturbative method that includes an accurate representation of the electron-surface interaction, incorporating information of the electronic band structure of the solid. For all the studied surfaces, the presence of partially occupied surface electronic states produces noticeable structures in double-differential—energy- and angle-resolved—electron emission probabilities from the valence band. For Mg, Cu, and Ag these structures remain visible in electron emission spectra after adding contributions coming from core electrons, which might make possible their experimental detection, but for Au they are hidden by inner-shell emission.

Figure 1

Comparison between the electronic density of the SES and the one corresponding to a bulklike state (multiplied by a factor 5, except in the case of Au) with the lowest-energy value corresponding to $n=1$ for (a) Mg(0001), (b) Cu(111), (c) Ag(111), and (d) Au(111). Dash-dotted line represents bulk and surface-state DFT results which are added in (a) and (b) as a reference.

Figure 2

Differential probability of electron emission from the valence band, as a function of the electron energy, for 100-keV protons impinging with the glancing angle $\alpha =0.1^{\circ }$ on (a) Mg(0001), (b) Cu(111), (c) Ag(111), and (d) Au(111). The electron ejection angle is ${\theta }_e={30}^{\circ }$, measured with respect to the surface in the scattering plane. Solid red line, BSB results including the SES contribution; dashed black line, BSB results without the SES contribution; dash-dot-dotted blue line, SES contribution; dash-dotted black line, results obtained within the jellium model [24].

Figure 3

Influence of the SES in differential electron emission probabilities for 100-keV protons impinging on a Cu(111) surface with an incidence angle $\alpha =0.5^{\mathrm{o}}$. Vertical scales of the right (left) panels are indicated on the right (left) side. The electron ejection angles are ${\theta }_e=20$, 30, 40, 50, 60, and ${70}^{\circ }$, respectively, all of them measured with respect to the surface in the scattering plane. Solid red line, BSB electron emission spectrum; dashed black line, BSB electron emission spectrum without including the SES contribution; dash-dot-dotted blue line, SES contribution.

Figure 4

Similar to Fig. 3 for total emission probability, including valence-band and inner-shell contributions. Vertical scales of the right (left) panels are indicated on the right (left) side. The ejection angles are ${\theta }_e=20$, 40, 60, and ${70}^{\circ }$, respectively. Solid thick gray line, total emission probability obtained by adding valence-band and core contributions, as explained in the text; solid thin red line, BSB valence emission probability; dashed black line, BSB probability without including the SES contribution; dot-dashed blue line, inner-shell emission probability.

Figure 5

Similar to Fig. 4 for a Ag(111) surface.

Figure 6

Similar to Fig. 4 for a Au(111) surface.

Figure 7

Similar to Fig. 4 for a Mg(0001) surface.

Figure 8

Influence of the incidence conditions on differential electron emission probabilities from the valence band of Cu(111). (a) Different impact velocities, keeping the incidence angle, $\alpha =0.5^{\circ }$, as a constant, for the ejection angle ${\theta }_e={60}^{\circ }$. (b) Different incidence angles, keeping the impact velocity, $v=2$ a.u., as a constant, for the ejection angle ${\theta }_e={30}^{\circ }$.