Deposition of High-Quality ${\mathrm{HfO}}_2$ on Graphene and the Effect of Remote Oxide Phonon Scattering

We demonstrate atomic layer deposition of high-quality dielectric ${\mathrm{HfO}}_2$ films on graphene and determine the magnitude of remote oxide surface phonon scattering in dual-oxide structures. The carrier mobility in these ${\mathrm{HfO}}_2$-covered graphene samples reaches $20000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at low temperature. Distinct contributions to the resistivity from surface optical phonons in the ${\mathrm{SiO}}_2$ substrate and the ${\mathrm{HfO}}_2$ overlayer are isolated. At 300 K, surface phonon modes of the ${\mathrm{HfO}}_2$ film centered at 54 meV limit the mobility to approximately $20000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$.

Figure 1

(a) Optical micrograph of a GFET partially covered by 30 nm ${\mathrm{HfO}}_2$ film (bottom half, green). The graphene sheet is outlined in red. (b) Atomic force microscope image of the circled area in (a) and a line cut across the $\mathrm{\text{graphene}}/{\mathrm{SiO}}_2$ step. The rms roughness is 3–4 Å on graphene and 2–3 Å on ${\mathrm{SiO}}_2$.

Figure 2

(a) Low-$T$ sheet conductance $\sigma (V_{\mathrm{bg}})$ of the ${\mathrm{HfO}}_2$-covered side in three partially covered GFETs (samples $A$, $B$, and $C$ are black, red, and blue, respectively). The majority of our ${\mathrm{HfO}}_2$-covered samples exhibit Dirac points within $\pm 20\mathrm{V}$ and ${\mu }_{\mathrm{FE}}>6000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. (b) Well-developed half-integer quantum Hall states on the ${\mathrm{HfO}}_2$-covered side of sample $A$ at $B=8.9\mathrm{T}$ and $T=1.5\mathrm{K}$.

Figure 3

Resistivity $\rho (T)$ on the bare (a) and ${\mathrm{HfO}}_2$-covered (b) sides of sample $B$. From top to bottom: Hole density $n=1.0–3.0\times {10}^{12}/{\mathrm{cm}}^2$ in $5.0\times {10}^{11}/{\mathrm{cm}}^2$ steps. Error bars are smaller than the symbol size. (c) $\rho (T)$ at $n=3.0\times {10}^{12}/{\mathrm{cm}}^2$ for the bare (black) and covered sides (red). Solid lines are fits to Eq. (1).

Figure 4

(a) Resistivity coefficient vs density $C_1(n)$ of the ${\omega }_1=63\mathrm{meV}$ mode of the ${\mathrm{SiO}}_2$ surface on the bare side of three GFETs. (b) $C_3(n)$ of the ${\omega }_3=54\mathrm{meV}$ mode of the ${\mathrm{HfO}}_2$ surface on the covered side of the same GFETs. Open squares, solid circles, and solid triangles correspond to samples $A–C$, respectively. Dashed lines are empirical fittings to $n^{-\alpha }$, where $\alpha$ range from 1.1 to 1.6 for $C_1(n)$ and from 0.7 to 1.0 for $C_3(n)$. Electrons and holes exhibit similar $C(n)$.

Figure 5

Mobility limit imposed by LA and ROP scattering at 300 K in sample $B$. ${\omega }_1=63\mathrm{meV}$ is the dominant surface mode in graphene-on-${\mathrm{SiO}}_2$ samples (black). ${\omega }_1^{\prime }$ represents the corresponding screened mode in ${\mathrm{HfO}}_2/\mathrm{\text{graphene}}/{\mathrm{SiO}}_2$ structures (magenta). The ${\omega }_3=54\mathrm{meV}$ mode in ${\mathrm{HfO}}_2$ covered GFETs limits $\mu$ to $20000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ (red). The blue line represents $\mu$ set by LA phonons.