Contact doping, Klein tunneling, and asymmetry of shot noise in suspended graphene

Abstract

The inherent asymmetry of the electric transport in graphene is attributed to Klein tunneling across barriers defined by $pn$ interfaces between positively and negatively charged regions. By combining conductance and shot noise experiments, we determine the main characteristics of the tunneling barrier (height and slope) in a high-quality suspended sample with Au/Cr/Au contacts. We observe an asymmetric resistance ${R}_{\mathrm{odd}}=100\ensuremath{-}70\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Omega}}$ across the Dirac point of the suspended graphene at carrier density $|{n}_{\mathrm{G}}|=(0.3\ensuremath{-}4)\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$, while the Fano factor displays a nonmonotonic asymmetry in the range ${F}_{\mathrm{odd}}\ensuremath{\sim}0.03$--0.1. Our findings agree with analytical calculations based on the Dirac equation with a trapezoidal barrier. Comparison between the model and the data yields the barrier height for tunneling, an estimate of the thickness of the $pn$ interface $d<20$ nm, and the contact region doping corresponding to a Fermi level offset of $\ensuremath{\sim}\ensuremath{-}18$ meV. The strength of pinning of the Fermi level under the metallic contact is characterized in terms of the contact capacitance ${C}_{c}=19\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} \text{F}/{\mathrm{cm}}^{2}$. Additionally, we show that the gate voltage corresponding to the Dirac point is given by the difference in work functions between the backgate material and graphene.