林永昌 2011.Dec.04

Experiment Hall-bar geometry was fabricated using oxygen plasma. Electrodes were made of Ti/Pd/Au. Gate length 2 to 4 μm, Hall-bar width from 0.5 to 4 μm. The magnetic field was ± 2T, and measured in high vacuum (10 -6 ~10 -8 Torr) in the temperature range of 4.2 K to 350K. Carrier density: n=-IB/eV H. Hall mobility: μ=σ xx /en. Vxx I VHVH

Review Hall effect Holes Electrons Hall mobility Field-effect mobility

Mobility and carrier scattering Coulomb scattering (impurity)(long-range scattering) Defect (short-range scattering) Acoustic phonon scattering by graphene phonons. (when μ~10 5 cm 2 /Vs) Substrate surface polar phonon scattering Midgap states (Metal-induced gap states, defects, impurities, molecule adsorption)

nm D D D D 0.1-1nm e-

Temperature dependent transport Low T: phonon scattering negligible. – Coulomb scattering by impurities and short-range scattering by defects dominate. Matthiessen’s rule: Density of state: – 1 layer: – 2, 3 layers: Mean free path at carrier density n=3x10 12 cm -1 – 1 layer : 70nm, 2, 3 layers : 10 nm. Channel length ~μm => diffusive transport Scattering rate Coulomb SR => V(q) = constant

Mobility and carrier scattering Difference in their density of states. 1 2, 3

Hall mobility for holes vs. Temperature Scattering by thermally excited surface polar optical phonon of the SiO2 substrate. Depends exponentially on the substrate graphene distance. (0.35 nm) Stronger than acoustic phonons of graphene. Scattering rate of 2 important surface phonons: 155 meV : 59 meV = 6.5 : 1 T increased => mobility decrease B.E. distribution Coulomb scattering is dominant. Substrate surface polar phonon induced field is screened by the additional graphene layers. Coulomb scattering time can result in the mobility increasing proportionally to temp.

High-T Low-T Monolayer Multilayer Short summary of mobility curve fitting Mobility limited (LRS, SRS) for 2, 3 layers graphene is inversely proportional to the square of the effective mass of carrier. More graphene layers => heavier the effective mass => higher degradation of the mobility limited by LR and SR for same impurity concentration. => If the impurity concentration is optimized low, the mobility of 2, 3 layers can higher than 1 layer graphene at room temperature on substrate.

Hall coefficient (variation of n) T increased -> the height of the peak is reduced. (the slope |R H | vs V BG decrease => n increase) Electron hole puddles was attributed to the intrinsic ripples in graphene and extrincsic charge-induced inhomogeneities in the carrier density. Another explanation is band overlaping in trilayer graphene. 1L 2, 3L Carrier concentration

Summary Carrier density increase => mobility decrease – 1 layer: mobility decrease. – 2, 3 layers: mobility increase. The different DOS for 1 and 2, 3 layer graphenes. Temperature increases – 1 layer: mobility decrease. Substrate surface polar phonon scattering – 2, 3 layers: mobility increase almost linearly with temperature. Coulomb scattering decreases with temperature due to their parabolic band structure and screening. Scattering by SiO2 phonons is significantly screened. Temperature dependence of the Hall coefficient Electron-hole puddles Transport properties, carrier scattering mechanism in 1, 2, 3 layer graphenes