Identifying Electronic Doorway States in the Secondary Electron Emission from Layered Materials

Abstract

We investigate the secondary low-energy electron emission induced by inelastic electron scattering from graphene and layered materials thereof. By applying a coincidence detection of the primary scattered and the emitted secondary electron we unravel pronounced resonance features otherwise overshadowed by the largely structureless secondary electron energy distribution. Supported by density functional theory calculations we show that these structures are the signature of prominent Feshbach resonances above the vacuum threshold which originate from interlayer states acting as a doorway state for electron emission. Remarkably, some of these doorway states open up only for samples with more than five layers.

Figures (9)

• Figure 1: Low-energy electron spectroscopy. (a) Schematic of the experimental setup: 173 eV electrons impact on a sample surface under 60$^\circ$ with respect to the sample surface normal: Either one electron ($E\textsubscript{1}$) or two coincident secondary electrons ($E\textsubscript{1}$,$E\textsubscript{2}$) are detected energy-resolved with a hemispherical energy analyser (HEA, $E\textsubscript{1}$) and a multichannel plate (MCP) detector using a time-of-flight (TOF) approach ($E\textsubscript{2}$), respectively. Reflection electron energy loss spectra (rEELS) are shown for quasi-freestanding single-layer graphene (SLG, green), bilayer graphene (BLG, blue) and highly-oriented pyrolitic graphite (HOPG, red) in panel (b). Corresponding ($E\textsubscript{1}$, $E\textsubscript{2}$) correlation maps for all three materials are shown in panels (c), (d), and (e), respectively. All heat maps use the color scheme indicated on top of panel (c) adapted to represent the logarithm of the respective electron yield counts.
• Figure 2: Secondary low-energy (LEE) spectra for (a) SLG, (b) BLG and (c) HOPG. These $E\textsubscript{2}$ spectra were obtained by integrating the double differential data in Fig. \ref{['fig:Fig1']} (c)-(e) over $E\textsubscript{1}$ in the range $[0,140]$ eV and normalised to the bin at 18 eV. The inset for HOPG displays the second derivative of the energy spectrum. (d) Density of states (DOS) and projected DOS (pDOS) for $sp\textsuperscript{2}$ and $p\textsubscript{z}$ orbitals, shifted vertically for better visibility.
• Figure 3: The logarithm of the magnitude of the coupling matrix element of quasi-bound states above the vacuum level $|\phi_{\mathrm{R}}\rangle$ and continuum states $|\phi_{\mathrm{cont}}\rangle$, $\delta_C$, see Eq. \ref{['eq:defdeltaC']}, is shown. Connecting lines to guide the eye. In the panels on the right, we show for each material (each also representing a different coupling strength) a typical (avoided) crossing appearing at the $\Gamma$ point as $L_{\text{vac}}$ is varied. The data from Fig. \ref{['fig:App3']} is shown on a magnified scale in dependence of $\Delta L\textsubscript{vac}=L\textsubscript{vac}-L\textsubscript{vac, material}$ with $L\textsubscript{vac, SLG}=14.0$ Å, $L\textsubscript{vac, BLG}=17.8$ Å, and $L\textsubscript{vac, HOPG}=15.5$ Å.
• Figure 4: Wave functions of the quasi-bound states and the discretised vacuum continuum states of HOPG (red dots) undergoing an avoided crossing. In the frames ①-③ on the right, three exemplary wave functions are shown for an HOPG slab of 14 layers corresponding to the avoided crossing as function of $L_{\mathrm{vac}}$ labelled ①-③ in the left panel. Colours represent isosurfaces of increasing charge density (from blue to yellow). Rendered using the software Vesta momma_vesta_2011.
• Figure 5: $E\textsubscript{2}$ energy distribution projections for SLG (a), BLG (b) and HOPG (c). For the five different energy spectra, all counts in Fig. \ref{['fig:Fig1']} for a given $E\textsubscript{1}$ energy window labelled on the right-hand side of each panel are summed up. All spectra are normalised to the bin at 18 eV and shifted along the $y$-axis for better comparison.