Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene

We theoretically calculate the phonon scattering limited electron mobility in extrinsic (i.e., gated or doped with a tunable and finite carrier density) two-dimensional graphene layers as a function of temperature $\left(T\right)$ and carrier density $\left(n\right)$. We find a temperature-dependent phonon-limited resistivity ${\rho }_{\mathit{ph}}\left(T\right)$ to be linear in temperature for $T\gtrsim 50\mathrm{K}$ with the room-temperature intrinsic mobility reaching the values of above ${10}^5{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$. We comment on the low-temperature Bloch–Grüneisen behavior where ${\rho }_{\mathit{ph}}\left(T\right)\sim T^4$ for unscreened electron-phonon coupling.

Figure 1

(Color online) Calculated inverse relaxation times as a function of energy for different temperatures $T∕T_{\mathit{BG}}=0.2$, 0.5, 1.0, and 1.5 for an electron density $n={10}^{12}{\mathrm{cm}}^{-2}$ with $T_{\mathit{BG}}=54\mathrm{K}$. The deformation-potential coupling constant $D=19\mathrm{eV}$ and the phonon velocity $v_{\mathit{ph}}=2\times {10}^6\mathrm{cm}∕\mathrm{s}$ are used in this calculation.

Figure 2

(Color online) (a) Calculated graphene resistivity as a function of temperature for several densities $n=1\times {10}^{12}$, $3\times {10}^{12}$, and $5\times {10}^{12}{\mathrm{cm}}^{-2}$. We use the deformation potential $D=19\mathrm{eV}$. Note that in BG regime $(T<T_{\mathit{BG}})$, $\rho \sim T^4$ and in EP regime $(T>100\mathrm{K})$, $\rho \sim T$. (b) The same as (a) in linear scale. The inset shows the resistivity in low-temperature limits $(T<80\mathrm{K})$.

Figure 3

(Color online) Calculated mobility limited by the acoustic phonon with the deformation-potential coupling constant $D=19\mathrm{eV}$ (a) as a function of temperature for different densities $n=1\times {10}^{12}$, $3\times {10}^{12}$, and $5\times {10}^{12}{\mathrm{cm}}^{-2}$ and (b) as a function of density for different temperatures $T=77\mathrm{K}$ and $T=300\mathrm{K}$.

Figure 4

(Color online) The deviations from Mattiessen’s rule for two different densities, (a) $n={10}^{12}{\mathrm{cm}}^{-2}$ and (b) $n=7\times {10}^{11}{\mathrm{cm}}^{-2}$. Here, ${\rho }_i$ $\left({\rho }_{\mathit{ph}}\right)$ represents the resistivity due to impurity (phonon) scattering.

Figure 5

(Color online) Calculated resistivity with both the acoustic phonon scattering and the intervalley phonon scattering. See Appendix for details.