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

TL;DR

This study investigates the asymmetry in electric transport in suspended graphene caused by Klein tunneling across pn-interfaces, using conductance and shot noise measurements to characterize tunneling barriers and contact doping effects.

Contribution

It provides a detailed experimental and theoretical analysis of Klein tunneling and contact doping effects in suspended graphene, including barrier parameters and Fermi level pinning.

Findings

Asymmetric resistance across the Dirac point measured.

Non-monotonic asymmetry in shot noise Fano factor.

Estimated pn-interface thickness less than 20 nm.

Abstract

The inherent asymmetry of the electric transport in graphene is attributed to Klein tunneling across barriers defined by $\textit{pn}$-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 $R_{\textrm{odd}}=100-70$ $\Omega$ across the Dirac point of the suspended graphene at carrier density $|n_{\rm G}|=0.3-4 \cdot 10^{11}$ cm$^{-2}$, while the Fano factor displays a non-monotonic asymmetry in the range $F_{\textrm{odd}} \sim 0.03 - 0.1$. 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 $\textit{pn}$-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.