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.
Vxx
• Carrier density: n=-IB/eVH.
• Hall mobility: μ=σxx/en.
I
V
H
Review Hall effect
Electrons
Hall mobility
Field-effect mobility
Holes
Mobility and carrier scattering
• Coulomb scattering (impurity)(long-range
scattering)
• Defect (short-range scattering)
• Acoustic phonon scattering by graphene
phonons. (when μ~105 cm2/Vs)
• Substrate surface polar phonon scattering
• Midgap states (Metal-induced gap states,
defects, impurities, molecule adsorption)
e10-30nm
+
0.1-1nm
D
D
e-
D
D
+
Temperature dependent transport
• Low T: phonon scattering negligible.
– Coulomb scattering by impurities and short-range scattering by
defects dominate.
Scattering rate
• Matthiessen’s rule:
• Density of state:
– 1 layer:
– 2, 3 layers:
Coulomb
SR => V(q) = constant
• Mean free path at carrier density
n=3x1012 cm-1
– 1 layer : 70nm, 2, 3 layers : 10 nm.
Channel length ~μm => diffusive transport
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:
B.E. distribution
155 meV : 59 meV = 6.5 : 1
T increased => mobility decrease
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.
Short summary of mobility curve fitting
Monolayer
Low-T
High-T
Multilayer
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)
Carrier concentration
T increased -> the height of the peak is reduced.
(the slope |RH| vs VBG decrease => n increase)
1L
2, 3L
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.
Summary
Transport properties, carrier scattering mechanism in 1, 2, 3 layer graphenes
• 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