Flexural-Phonon Scattering Induced by Electrostatic Gating in Graphene

Graphene has an extremely high carrier mobility partly due to its planar mirror symmetry inhibiting scattering by the highly occupied acoustic flexural phonons. Electrostatic gating of a graphene device can break the planar mirror symmetry, yielding a coupling mechanism to the flexural phonons. We examine the effect of the gate-induced one-phonon scattering on the mobility for several gate geometries and dielectric environments using first-principles calculations based on density functional theory and the Boltzmann equation. We demonstrate that this scattering mechanism can be a mobility-limiting factor, and show how the carrier density and temperature scaling of the mobility depends on the electrostatic environment. Our findings may explain the high deformation potential for in-plane acoustic phonons extracted from experiments and, furthermore, suggest a direct relation between device symmetry and resulting mobility.

Figure 1

Broken ${\sigma }_h$ symmetry and mobility degradation in gated graphene devices. (a) Potential profile across the device in (b) for different dielectric substrates and a graphene carrier density of $n_0=2\times 10^{13}$ ${\mathrm{cm}}^{-2}$. The asymmetry in the potential across graphene triggers scattering with the out-of-plane flexural modes. (b) Device geometry with graphene separated from the gate electrode with voltage $V_G$ by a dielectric region with dielectric constant $\kappa$. (c) Mobility versus temperature at different carrier densities (in ${\mathrm{cm}}^{-2}$) for a graphene device with $\kappa =2.5$ (circle) and isolated graphene with preserved ${\sigma }_h$ symmetry (left pointing triangle), respectively, with and without field-induced flexural-phonon scattering.

Figure 2

Field-induced $e$-ph couplings to flexural phonons. (a),(b) Coupling matrix element $M_{\mathbf{k}{\mathbf{k}}^{\prime }}^{\lambda }$ for the (a) ZA and (b) ZO phonons at a carrier density of $n_0=2\times 10^{13}{\mathrm{cm}}^{-2}$ and $\kappa =2.5$. The $\mathbf{k}$ point is positioned 300 meV above the Dirac point and the circles indicate constant energy surfaces on the Dirac cones. (c) $q$ dependence of the coupling to the ZA phonon along the dashed line in (a) for different electrostatic conditions and carrier densities.

Figure 3

Temperature dependence of the field-induced ZA scattering limited mobility. (a) Scattering rate near the Fermi level for the in-plane $\mathrm{TA}+\mathrm{LA}$ and the flexural ZA phonons at low and room temperature, $n_0=2\times 10^{13}{\mathrm{cm}}^{-2}$ and $\kappa =22$. (b) Temperature exponent, $\alpha =-d\log ({\mu }_e)/d\log (T)$, as a function of temperature for the mobilities in Fig. 1. The field-induced ZA scattering dominates at room temperature and changes the temperature exponent in the low-temperature regime.

Figure 4

Electrode stack setup of a graphene device. (a) Potential profile across the graphene device in a symmetric and asymmetric arrangement. (b) Arrangement consisting of graphene and two electrodes. In the symmetric mode, the electrodes are kept at the same potential $V_1=V_2$ and a charge is added to the graphene layer. In the asymmetric mode, an electric field is generated by a potential difference between the two electrodes $V_1=-V_2$. The mobility is only degraded in the asymmetric mode. (c) Mobility at two different temperatures without ($\mathrm{TA}+\mathrm{LA}$) and with ZA scattering in a device with graphene sandwiched between two different dielectrics. The dielectric regions have ${\kappa }_A=2.5$ and ${\kappa }_B=22$.