Monochromatic Electron Emission from Graphene-Insulator-Semiconductor-Structured Electron Source Utilizing Interference Efficets

TL;DR

The paper analyzes monochromatic electron emission from graphene-insulator-semiconductor (GIS) sources by numerically propagating electron wave packets through mono- and multilayer graphene. It identifies interlayer interference as a key factor that broadens energy distributions at certain energies (notably $E_0=13.4$ eV) and shows that first-order diffraction in monolayer graphene can yield narrow energy spreads when combined with angular confinement via a small aperture, achieving about $\Delta E \approx 0.22$ eV. Multilayer graphene further improves monochromaticity by effectively acting as an angular aperture, reducing the energy spread without external apertures as the number of layers increases. The results suggest a viable route to highly monochromatic GIS electron sources and motivate experimental validation with realistic parameters such as $\theta \approx 73^\circ$ and $\Delta E$ in the few-tenths of an eV range.

Abstract

The graphene-insulator-semiconductor-structured electron source has garnered significant attention due to its high electron emission efficiency and highly monochromatic electron emission. Graphene, with its c-axis orientation and well-defined interlayer spacing, exhibits electron interference effects that can influence the properties of emitted electrons. In this work, motion of an electron wave packet is numerically calculated to discuss the energy spread of the zero-order and first-order diffracted electron waves by mono- and multilayer graphene. It is found that the effects of multiple reflections of electron between the layers broaden the energy spread especially for the incident energy of 13.4 eV, and that highly monochromatic electron emission can be achieved by using diffracted electron wave with a small aperture.

Figures (10)

• Figure 1: (a)Monolayer graphene structure. $\vb*{a}_1$ and $\vb*{a}_2$ are primitive lattice vectors. $a = \abs{\vb*{a}_1} = \abs{\vb*{a}_2} = 2.46$ Å is the lattice constant. The A- and B-layers in the conventional unit cell for multi-layer graphene that is adopted in the present simulation are also shown. (b)The reciprocal lattice of monolayer graphene. $\vb*{b}_1$ and $\vb*{b}_2$ are primitive reciprocal lattice vectors. (c)3D reciprocal structure of monolayer graphene with Bragg scattering rods.
• Figure 2: Illustration of three-dimensional space used in the simulation. The unit cell in the $x$-$y$ plane is defined as $L_x \times L_y$, and is assumed to be periodic. The graphene is illustrated as ABA-stacked three-layer one, although the simulation is performed not only for three-layer one but also single or multi-layer one other than three-layer.
• Figure 3: Transmittance as a function of electron energy using monolayer to trilayer graphene. $\alpha_0 = 10$ Å, $E_0 = 10,20,\cdots70 \,\mathrm{eV}$. At the dotted lines, $\lambda /2 \times n = 3.35 \times (l-1)$ is satisfied, where $\lambda$ is wavelength, $l$ is the number of graphene layers, $n$ is positive integer. The numbers above the graphs represent ($l,n$).
• Figure 4: FWHMs of the EEDs transmitted through monolayer to five-layer graphene. $E_0=$13.4 eV, $\alpha_0 = 10$ Å.
• Figure 5: Electron wave packet with $E_0=40$ eV as a function of $z$ and time. The position $(x_0,y_0)$ is the center of the conventional unit cell. Monolayer graphene is placed at $z=85.7$ Å.