Infrared Spectroscopic Probe of Charge Distribution in Gated Multilayer Graphene: Evidence of Nonlinear Screening

We characterize the charge distribution in ion-gated turbostratic multilayer graphene employing broadband infrared transmittance spectroscopy. The experimental results evince the nonlinear screening of graphene and are in agreement with a theoretical model that accounts for the electrostatic coupling between the layers and the quantum capacitance of the graphene. We find that descriptions of charge distributions in these systems in the high-density regimes accessed experimentally via the formation of an electric double layer must include the capacitance of the multilayer graphene channel, which varies with charge and thickness. Specifically, the graphene-channel capacitance increases with thickness but tends to saturate after three layers, underscoring graphene’s qualities for ultrathin charge-storage applications. Through accurate determination of the layer-resolved carrier density in multilayer graphene, this sensitive technique may prove useful for the study of charge distributions in other two-dimensional multilayer devices.

Figure 1

(a) Optical transmittance of MLG samples ($N=1$ to 5) measured without ionic liquid over a wide energy range, 0.25–6.2 eV. The inset shows an image of an actual device with ionic liquid. The red dotted line indicates the region of the graphene channel ($3\times 3{\mathrm{mm}}^2$). (b) Illustration of IL-gated MLG device with infrared transmission measurement. (c) Schematic band diagram of gated MLG stack for $N=4$. The induced charge $Q$ is distributed across the layers, shifting the position of the chemical potential of each layer relative to its charge-neutrality (Dirac) point. Optical transitions promote electrons in the valence band to the conduction band when the photon energy $E\ge 2|{\mu }_i|$ (green circle) and are suppressed if $E<2|{\mu }_i|$ (red cross). The thickness of the EDL is labeled $d$. (d) The equivalent capacitor network of the MLG devices includes the capacitance of the dielectric (ionic liquid, $C_d$), the charge-dependent quantum capacitance of each graphene monolayer ($C_{q,i}$), and the capacitance due to the interlayer spacing ($C_{\mathrm{il}}$). The total capacitance $C_G$ and the series arrangement of the capacitance $C_{\mathrm{MLG}}$ are indicated by red and blue dashed lines, respectively. (e) Transmission ratio ${\mathcal{T}}_{V_G}/{\mathcal{T}}_{\mathrm{CNP}}$ as a function of photon energy $E$ for different gate voltages $V_G$ measured for a monolayer ($N=1$) device. The experimental data and corresponding fit are shown by symbols and lines, respectively. The inset shows the $I$–$V_G$ characteristics of the IL-gated device for $V_{DS}=10$ mV. (f) Normalized optical conductivity as a function of gate bias as derived from the experimental fit. (g) Chemical potential $\mu$ (solid line) and temperature $T$ (open circles) obtained from the fit.

Figure 2

(a) Experimental data for ${\mathcal{T}}_V/{\mathcal{T}}_{\mathrm{CNP}}$ (symbols) and theoretical fitting curves (gray lines) in IL-gated bilayer graphene ($N=2$) for different gate biases ($\mathrm{\Delta }{V}_G=V_G-V_{\mathrm{CNP}}$). The inset shows the $I$–$V_G$ characteristics of the IL-gated device for $V_{\mathrm{DS}}=10\mathrm{mV}$. (b) Optical conductivity obtained from the fit for weak gating $\mathrm{\Delta }{V}_G=-0.3$ V (dashed line) and strong gating $\mathrm{\Delta }{V}_G=-1.8$ V (solid line). Here $i=1$ (2) stands for the top (bottom) graphene layer as defined in Fig. 1. (c) Chemical potential ${\mu }_i$ and temperature $T_i$ (inset) obtained from the fit.

Figure 3

(a)–(d) Carrier density in the $i\mathrm{th}$ layer in IL-gated MLG at different gate biases $\mathrm{\Delta }{V}_G$, where the thickness of the MLG runs from $N=2$ (left) to $N=5$ (right). (e)–(h) Corresponding normalized carrier density $n_i/n_{\mathrm{tot}}$.

Figure 4

(a) Total carrier density in the MLG channel as a function of gate bias for different MLG thicknesses ($N=1$ to 5). (b) Total carrier density as a function of voltage drop across the dielectric layer $V_d$, as obtained from the experiments. (c) Ratio of the dielectric voltage drop $V_d$ to the gate bias, ${\nu }_d$ (${\nu }_d\equiv V_d/\mathrm{\Delta }{V}_G$), for $N=1$ to 5.

Figure 5

Capacitances of the system extracted from experiments: (a) total capacitance $C_G$ (stars), dielectric capacitance $C_d$ (diamonds), and MLG capacitance $C_{\mathrm{MLG}}$ (circles) as a function of $\mathrm{\Delta }{V}_G$. Different colors denote different layer thicknesses $N$. (b) MLG capacitance $C_{\mathrm{MLG}}$ as a function of $N$ for different charge densities $n_{\mathrm{tot}}$, extracted from interpolation of the experimental data. (c) Theoretical estimates of the gate-dependent capacitances $C_d$ and $C_{\mathrm{MLG}}$, where $C_d=2.6\mu {\mathrm{F/cm}}^2$ is taken from experiment. (d) MLG capacitance $C_{\mathrm{MLG}}$ theoretically determined from minimization of the total energy as a function of channel thickness.