Reference plane for the electronic states in thin films on stepped surfaces

The question on whether there exists a unique photoelectron reference plane for a stepped solid surface is discussed on the basis of angle-resolved photoelectron spectroscopy data for Ag films grown on Pt(997). Different step morphologies at the surface and interface, revealed by low-energy electron diffraction measurements, result in distinctly different band dispersions of the $sp$-like quantum well states and of the Shockley surface state. Quantum well standing waves form between the parallel optical surface and interface planes, while the surface state follows the orientation of a local plane tilted with respect to the optical surface. These findings show the connection of the photoelectron reference plane with the local morphology of a solid surface and the spatial extent of the electron wave functions.

Figure 1

(a) Sum of micro-LEED images of clean Pt(997) taken every 1 eV in the range 20–60 eV of primary energy with the SPELEEM instrument. (b) LEED image taken at 51.5 eV primary energy across the sharp edge between the clean Pt(997) surface and a 9-ML Ag film grown on it with the conventional LEED apparatus of the ARPES end station (spot size ∼1 mm diameter). The coexisting patterns allow us to determine directly $K_{\mathrm{Ag}}$.

Figure 2

ARPES data for a 18-ML Ag film on Pt(997) along $k_x$. (a) Spectra at different photon energies (reported in the panels). Dashed lines mark the dispersion of the QW states. Arrows indicate the surface state. (b) Surface state band dispersion in the proximity of $k_{x,2}$ ($\hslash \omega =47.9$, 57.3, 87.2 eV from bottom to top). The green continuous line highlights the $k_x$ shift of the surface state band center. (c) Structure plot showing the position of the band center for the surface and QW states. (d) Same as (c), upon applying the direct rotation correction to the surface state data.

Figure 3

ARPES data for a 12-ML Ag film on Pt(997). (a) Spectra at different photon energies (reported in the panels). Dashed lines mark the dispersion of the QW state. (b) Structure plot showing the position of the band center for the surface and QW states. (c) Constant energy cut at 80 meV above $E_F$ (top) and band dispersion along the $k_x$ axis at $k_y=0$ and along the $k_y$ axis at $k_x=k_{x,2}$ (bottom). $\hslash \omega =48.0\mathrm{eV}$.

Figure 4

(a) Sketch of a stepped surface shown in profile view [step density corresponding to the Pt(997) surface]. The incidence direction of the electron beam makes an arbitrary angle β with the average surface normal. (b) Kinematic simulation of the intensity of the specular beam in the $q_x\text{−}{q}_{\mathrm{z}}$ plane (the two axes have different scales). Red and green lines mark the angles α + β and β. The numerical values refer to the Pt(997) surface.

Figure 5

Intensity of the (0,0) LEED spot of clean Pt(997) collected along the dotted line in Fig. 1. To compensate the strong intensity variations as a function of kinetic energy, the intensity is scaled differently in three regions of the image. Red dots highlight the position of the intensity maxima.

Figure 6

Intensity of the (0,0) LEED spot for (a) 9-ML and (b) 15-ML Ag films on Pt(997) in the $q_x\text{−}{q}_z$ plane. The intensity is scaled differently in two regions of the images to compensate the strong intensity variations as a function of primary electron energy. Green dots mark the positions of the experimental maxima. The dashed lines indicate the inclination of the diffraction rods with respect to the $q_z$ axis.

Figure 7

(a) Side view of the structural model of a Ag film on Pt(997). Yellow and red spheres represent Ag and Pt atoms. The unknown interface morphology is hidden by a stripe oriented parallel to the Pt(997) plane. Small arrows indicate the orientation of the parallel Ag[111] and Pt[111] axes. Large arrows indicate the orientation of the Ag [11,11,9] and Pt[997] axes, which are separated by the ${\beta }_{\mathrm{Ag}}$ angle. (b) Ag growth of 1D-like islands in contact with Pt(997). (c) Initial growth of the second Ag layer.