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

The inherent asymmetry of the electric transport in graphene is attributed to Klein tunneling across barriers defined by $\mathit{\text{pn}}$-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 $R_{\text{odd}}=100-70$ $\mathrm{\Omega }$ across the Dirac point of the suspended graphene at carrier density $\mathrm{\mid }{n}_{\mathrm{G}}\mathrm{\mid }=0.3-4\cdot {10}^{11}$ cm${}^{-2}$, while the Fano factor displays a non-monotonic asymmetry in the range $F_{\text{odd}}\sim 0.03-0.1$. 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 $\mathit{\text{pn}}$-interface $d<20$ nm, and the contact region doping corresponding to a Fermi level offset of $\sim -18$ meV. The strength of pinning of the Fermi level under the metallic contact is characterized in terms of the contact capacitance $C_c=19\times {10}^{-6}$ F/cm${}^2$. Additionally, we show that the gate voltage corresponding to the Dirac point is given by the work function difference between the backgate material and graphene.