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arXiv 1502.04330cond-mat.mes-hall
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悬浮石墨烯中的接触掺杂、Klein隧穿和散粒噪声的不对称性

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

Antti Laitinen, G. S. Paraoanu, Mika Oksanen, Monica F. Craciun, Saverio Russo, Edouard Sonin, Pertti Hakonen

备注：
15 pages, 7 figures
发表信息：
Phys. Rev. B 93 ,115413 (2016)
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摘要：

石墨烯中的电输运的固有不对称性归因于穿过由正电荷区域和负电荷区域之间的$\textit{pn}$ -界面限定的势垒的克莱因隧穿。通过结合电导和散粒噪声实验，我们确定了高品质的悬浮样品与Au/Cr/Au接触的隧穿势垒（高度和斜率）的主要特征。我们观察到在载流子密度$|n_{\rm G}|=0.3-4 \cdot 10^{11}$ cm $^{-2}$处的悬浮石墨烯的狄拉克点上的不对称电阻$R_{\textrm{odd}}=100-70$ $Ω$，而Fano因子在$F_{\textrm{odd}} \sim 0.03 - 0.1$范围内显示非单调不对称性。我们的研究结果同意与狄拉克方程的梯形障碍的基础上的分析计算。模型和数据之间的比较产生隧穿的势垒高度，估计的厚度的$\textit{pn}$界面$d < 20$ nm，和接触区掺杂对应的费米能级偏移$\sim - 18$毫电子伏。金属接触下费米能级的钉扎强度以接触电容$C_c=19 \times 10^{-6}$ F/cm $^2$来表征。此外，我们表明，对应于狄拉克点的栅极电压是由背栅材料和石墨烯之间的功函数差。

英文摘要：

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 $R_{\textrm{odd}}=100-70$ $Ω$ 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.

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