Infrared spectroscopic study of carrier scattering in gated CVD graphene

We measured Drude absorption of gated CVD graphene using far-infrared transmission spectroscopy and determined the carrier scattering rate ($\gamma$) as a function of the varied carrier density ($n$). The $n$-dependent $\gamma \left(n\right)$ was obtained for a series of conditions systematically changed as (10 K, vacuum) $\to$ (300 K, vacuum) $\to$ (300 K, ambient pressure), which reveals that (1) at low-T, charged impurity ($=A/\sqrt{n}$) and short-range defect ($=B\sqrt{n}$) are the major scattering sources which constitute the total scattering $\gamma =A/\sqrt{n}+B\sqrt{n}$, (2) among various kinds of phonons populated at room-$T$, surface polar phonon of the ${\mathrm{SiO}}_2$ substrate is the dominantly scattering source, and (3) in air, the gas molecules adsorbed on graphene play a dual role in carrier scattering as charged impurity center and resonant scattering center. We present the absolute scattering strengths of those individual scattering sources, which provides the complete map of scattering mechanism of CVD graphene. This scattering map allows us to find out practical measures to suppress the individual scatterings, the mobility gains accompanied by them, and finally the ultimate attainable carrier mobility for CVD graphene.

Figure 1

(a) FIR transmission $T(V_{\mathrm{G}},\omega )$ measured with the gating voltage applied negatively $V_{\mathrm{G}}<0$ V. Inset shows schematically how the $V_{\mathrm{G}}$-dependent transmission measurement is made. (b) Optical conductivity ${\sigma }_1(V_{\mathrm{G}},\omega )$ calculated from $T(V_{\mathrm{G}},\omega )$. Dashed curve shows the Drude-model fitting result. The squared symbol at $\omega =0{\mathrm{cm}}^{-1}$ shows the DC conductivity ${\sigma }_{\mathrm{DC}}$(IR). In the inset we compare the ${\sigma }_{\mathrm{DC}}$ calculated from the $I\text{−}V$ curve with ${\sigma }_{\mathrm{DC}}$(IR).

Figure 2

(a) Optical conductivity ${\sigma }_1\left(\omega \right)$ is normalized by the DC conductivity ${\sigma }_{\mathrm{DC}}$. The curve width measured at ${\sigma }_1\left(\omega \right)/{\sigma }_{\mathrm{DC}}=1/2$ represents the scattering rate $\gamma$. (b) Plot of $1/{\sigma }_1\left(\omega \right)$ versus ${\omega }^2$. Dashed lines are the linear fit using the Drude relation $1/{\sigma }_1\left(\omega \right)=a{\omega }^2+b$. The $x$-axis intercept (squared symbol) shows $-{\gamma }^2$ determined for each $V_{\mathrm{G}}$. Inset shows carrier density $n$ measured from the $y$-axis intercept and from two other methods (see Supplemental Material, Fig. S3 [12]).

Figure 3

Scattering rate $\gamma$ plotted against carrier density $n$ for the hole doping ($n<0{\mathrm{cm}}^{-2}$) and electron doping ($n>0{\mathrm{cm}}^{-2}$). The dashed curves show $\gamma ={\gamma }_{\mathrm{CI}}+{\gamma }_{\mathrm{SR}}$ where ${\gamma }_{\mathrm{CI}}=A/\sqrt{n}$ and ${\gamma }_{\mathrm{SR}}=B\sqrt{n}$ represent the Coulomb scattering and short range scattering rate, respectively. Inset shows the linear relation $\gamma \sqrt{n}=A+Bn$.

Figure 4

Scattering function $\gamma \left(n\right)$ measured at $T=300$ K and $P={10}^{-6}$ Torr. The temperature-induced scattering $\mathrm{\Delta }\gamma \equiv \gamma \left(300\mathrm{K}\right)-\gamma \left(10\mathrm{K}\right)$ is shown by the red curve.

Figure 5

(a) $\gamma$ measured before and after graphene is exposed to air. The difference $\mathrm{\Delta }\gamma =\gamma \left(\mathrm{air}\right)-\gamma \left(\mathrm{vacuum}\right)$ shows the scattering due to the gas adsorbed on graphene, ${\gamma }_{\mathrm{AD}}$. Inset shows the evolution of the $I\text{−}V$ curve with the time elapsed since exposure. (b) ${\gamma }_{\mathrm{AD}}$ is analyzed in terms of two components ${\gamma }_{\mathrm{AD}}={\gamma }_{\mathrm{CI}}+{\gamma }_{\mathrm{RS}}$, where ${\gamma }_{\mathrm{CI}}$ and ${\gamma }_{\mathrm{RS}}$ are the Coulomb scattering and resonant scattering, respectively. In the inset we reproduce the theoretical ${\gamma }_{\mathrm{RS}}$ calculated for ${\mathrm{H}}^{+}$-adsorbed graphene with permission from the authors [9].

Figure 6

The four scattering sources and their $\gamma \left(n\right)$'s identified and measured in this work: ${\gamma }_{\mathrm{CI}}$ for charged impurity, ${\gamma }_{\mathrm{SR}}$ for short-range disorder, ${\gamma }_{\mathrm{SPP}}$ for surface polar phonon of ${\mathrm{SiO}}_2$, and ${\gamma }_{\mathrm{AD}}$ for gas adsorbate in air. The total scattering $\gamma ={\gamma }_{\mathrm{CI}}+{\gamma }_{\mathrm{SR}}+{\gamma }_{\mathrm{SPP}}+{\gamma }_{\mathrm{AD}}$ is shown by the black curve.