Measurement of Scattering Rate and Minimum Conductivity in Graphene

Measurement of Scattering Rate and Minimum Conductivity in Graphene

12 Jul 2007 | Y.-W. Tan1†, Y. Zhang1†, K. Bolotin1, Y. Zhao1, S. Adam2, E. H. Hwang2, S. Das Sarma2, H. L. Stormer1,3,4, and P. Kim1
This paper reports on the measurement of the scattering rate and minimum conductivity in graphene samples with varying levels of disorder. The study investigates the conductivity of graphene samples with mobility ranging from 1 to 20 × 10³ cm²/V·s. By comparing experimental data with theoretical transport calculations based on charged impurity scattering, the impurity concentration in the samples is estimated to be between 2 × 10¹¹ and 15 × 10¹¹ cm⁻². In the low carrier density limit, the conductivity ranges from 2 to 12e²/h, which is related to the residual density induced by inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain short-range disorder, while low mobility samples are dominated by long-range scatterers. The study uses 19 graphene devices with various levels of disorder. The scattering mechanisms are inferred from the density dependence of the mean free paths and phase coherence lengths. The sample mean free path is extracted from the conductivity measurements, and it is found that at high carrier density, two different scattering mechanisms determine the density-dependent conductivity. The graphene samples are extracted from bulk graphite crystals and deposited onto SiO₂/Si substrates. The samples are measured using lock-in amplifiers at an excitation current less than 50 nA to minimize heating effects. The resistivity of five representative samples is shown as a function of gate voltage. The resistivity curves are symmetric around a particular gate voltage, V_dirac, and show a maximum at this value. The actual carrier density induced by the gate voltage in the presence of impurity doping is obtained from n = C_g(V_g - V_dirac)/e. The mobility of the samples is estimated using the semi-classical Drude model. The mobility ranges from 2,000 to 20,000 cm²/V·s. The quality of the samples is determined by comparing their behavior of carrier density dependent conductivity. The minimum conductivity is found to be strongly sample dependent, yielding values an order of e²/h with a non-universal prefactor. The minimum conductivity is influenced by the impurity concentration and the inhomogeneous charge distribution near the Dirac point. The study concludes that the minimum conductivity in graphene samples is strongly dependent on the impurity concentration and the inhomogeneous charge distribution.This paper reports on the measurement of the scattering rate and minimum conductivity in graphene samples with varying levels of disorder. The study investigates the conductivity of graphene samples with mobility ranging from 1 to 20 × 10³ cm²/V·s. By comparing experimental data with theoretical transport calculations based on charged impurity scattering, the impurity concentration in the samples is estimated to be between 2 × 10¹¹ and 15 × 10¹¹ cm⁻². In the low carrier density limit, the conductivity ranges from 2 to 12e²/h, which is related to the residual density induced by inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain short-range disorder, while low mobility samples are dominated by long-range scatterers. The study uses 19 graphene devices with various levels of disorder. The scattering mechanisms are inferred from the density dependence of the mean free paths and phase coherence lengths. The sample mean free path is extracted from the conductivity measurements, and it is found that at high carrier density, two different scattering mechanisms determine the density-dependent conductivity. The graphene samples are extracted from bulk graphite crystals and deposited onto SiO₂/Si substrates. The samples are measured using lock-in amplifiers at an excitation current less than 50 nA to minimize heating effects. The resistivity of five representative samples is shown as a function of gate voltage. The resistivity curves are symmetric around a particular gate voltage, V_dirac, and show a maximum at this value. The actual carrier density induced by the gate voltage in the presence of impurity doping is obtained from n = C_g(V_g - V_dirac)/e. The mobility of the samples is estimated using the semi-classical Drude model. The mobility ranges from 2,000 to 20,000 cm²/V·s. The quality of the samples is determined by comparing their behavior of carrier density dependent conductivity. The minimum conductivity is found to be strongly sample dependent, yielding values an order of e²/h with a non-universal prefactor. The minimum conductivity is influenced by the impurity concentration and the inhomogeneous charge distribution near the Dirac point. The study concludes that the minimum conductivity in graphene samples is strongly dependent on the impurity concentration and the inhomogeneous charge distribution.
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