High-Mobility Few-Layer Graphene Field Effect Transistors Fabricated on Epitaxial Ferroelectric Gate Oxides

The carrier mobility $\mu$ of few-layer graphene (FLG) field-effect transistors increases tenfold when the ${\mathrm{SiO}}_2$ substrate is replaced by single-crystal epitaxial $\mathrm{Pb}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_3$ (PZT). In the electron-only regime of the FLG, $\mu$ reaches $7\times {10}^4{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at 300 K for $n=2.4\times {10}^{12}/{\mathrm{cm}}^2$, 70% of the intrinsic limit set by longitudinal acoustic (LA) phonons; it increases to $1.4\times {10}^5{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at low temperature. The temperature-dependent resistivity $\rho (T)$ reveals a clear signature of LA phonon scattering, yielding a deformation potential $D=7.8\pm 0.5\mathrm{eV}$.

Figure 1

AFM contact mode image of a 2.4 nm FLG flake (center) on a 400 nm PZT film. Inset: optical image of the whole flake with the area in (a) circled. The PZT surface shows smooth terraces separated by $a$-axis lines, with a root-mean-square (rms) surface roughness of 3–4 Å over a $1\mu {\mathrm{m}}^2$ area. FLG has a roughness of 2–3 Å. (b) Device schematics. (c) Hall bar configuration of a FLG-FET with current ($I_1$, $I_2$) and voltage electrodes for resistance ($V_1$ and $V_2$) and Hall ($V_1$ and $V_H$) measurements. We determine the thickness of this FLG to be $(2.4\pm 0.3)\mathrm{nm}$ based on its optical transparency.

Figure 2

(a) $\rho (V_g)$ at selected temperatures taken on the device shown in Fig. 1c. Inset: schematics of the band structure of FLG of this thickness. (b) $\rho (V_g)$ at 4 K. The kink at $V_g^T=1.1\mathrm{V}$ (dash-dotted line) marks the boundary between regimes I and II. (c) $\rho (V_g)$ at 10 K (open symbols) with a fitting curve (solid line) combining Eqs. (1, 3) with $\beta =0.9$ and $r=0.6$. The dashed line is calculated from Eq. (1) assuming a density-independent mobility ${\mu }_e={\mu }_h=1\times {10}^5{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$.

Figure 3

$\rho (T)$ at electron densities of (from top to bottom) $n=1.89$, 2.02, 2.16, 2.30, and $2.43\times {10}^{12}/{\mathrm{cm}}^2$. The solid lines are fittings to Eq. (4) for $T>100\mathrm{K}$, with the corrections due to a nondegenerate Fermi gas included. Inset: Low-$T$ residual mobility ${\mu }_0(n)$ in a double-log plot. Open squares are data taken in regime II. The dashed line plots the fitting [Eq. (3), electrons] obtained in regime I.

Figure 4

Comparison of $\mu (T)$ in various graphitic materials. Solid squares: PZT-gated FLG shown in Fig. 3 at $n=2.4\times {10}^{12}/{\mathrm{cm}}^2$. Open triangles: a ${\mathrm{SiO}}_2$-gated FLG of the same thickness and density [17]. Open circles: single-layer graphene on ${\mathrm{SiO}}_2$ reported in Ref. 10. Crosses: mobility of bulk graphite from Ref. 21. Solid line: LA phonon-limited mobility calculated from Eq. (4).