Electric Field Effect in Atomically Thin Carbon Films

TL;DR

Monocrystalline graphitic films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands and they exhibit a strong ambipolar electric field effect.

Abstract

We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic transport at submicron distances even at room temperature.

Figures (3)

• Figure 1: Graphene films. (A) Photograph (in normal white light) of a relatively large multilayer graphene flake with thickness$\approx 3 \mathrm{~nm}$ on top of an oxidized Si wafer. (B) AFM image of $2 \times 2 \mu \mathrm{~m}^{2}$ area of this flake near its edge. Colors: dark brown is $\mathrm{SiO}_{2}$ surface; orange corresponds to 3 nm height above the $\mathrm{SiO}_{2}$ surface. (C) AFM image of single-layer graphene. Colors: dark brown - $\mathrm{SiO}_{2}$ surface; brown-red (central area) - 0.8 nm height; yellow-brown (bottom-left) - 1.2 nm ; orange (top-left) - 2.5 nm . Notice the folded part of the film near the bottom, which exhibits a differential height of $\approx 0.4 \mathrm{~nm}$. For details of AFM imaging of single-layer graphene, see [15]. (D) SEM micrograph of one of our experimental devices prepared from FLG, and (E) their schematic view.
• Figure 2: Field effect in few-layer graphene. (A) Typical dependences of graphene's resistivity$\rho$ on gate voltage for different temperatures ( $T=5,70$ and 300 K for top to bottom curves, respectively). (B) Example of changes in the film's conductivity $\sigma=1 / \rho\left(V_{\mathrm{g}}\right)$ obtained by inverting the 70 K curve (dots). (C) Hall coefficient $R_{\mathrm{H}}$ vs $V_{\mathrm{g}}$ for the same film. (D) Temperature dependence of carrier concentration $n_{0}$ in the mixed state for the film in (A) (open circles), a thicker FLG film (squares) and multilayer graphene ( $d \approx 5 \mathrm{~nm}$; solid circles). Red curves in (B) to (D) are the dependences calculated from our model of a 2D semimetal illustrated by insets in (B).
• Figure 3: (A) Examples of Shubnikov-de Haas oscillations for one of our FLG devices for different gate voltages;$T=3 \mathrm{~K}$ and $B$ is the magnetic field. As the black curve shows, we often observed pronounced plateau-like features in $\rho_{\mathrm{xy}}$ at values close to $\left(h / 4 e^{2}\right) / v$ (in this case, $\varepsilon_{\mathrm{F}}$ matches the Landau level with $v=2$ at around 9T). Such not-fully developed Hall plateaus are usually seen as an early indication of the quantum Hall effect in the situations where $\rho_{\mathrm{xx}}$ does not yet reach the zero-resistance state. (B) Dependence of the frequency of ShdH oscillations $B_{\mathrm{F}}$ on gate voltage. Solid and open symbols are for samples with $\delta \varepsilon \approx 6$ and 20 meV , respectively. Solid lines are guides to the eye. The linear dependence $B_{\mathrm{F}} \propto V_{\mathrm{g}}$ proves a constant (i.e., 2D) density of states [15]. The observed slopes (solid lines) account for the entire external charge $n$ induced by gate voltage, confirming that there are no other types of carriers and yielding the double-valley degeneracy for both electrons and holes [15]. The inset shows an example of the temperature dependence of amplitude $\Delta$ of ShdH oscillations (symbols), which is fitted by the standard dependence $T / \sinh \left(2 \pi^{2} k_{B} T / \hbar \omega_{C}\right)$ where $\omega_{C}$ is their cyclotron frequency. The fit (solid curve) yields light holes' mass of $0.03 m_{0}$.