探討石墨烯在電場下所造成的橫向電壓

Abstract

本實驗使用機械剝離法製備少數層石墨烯於矽基板上，透過原子力顯微鏡確認樣品為少數層石墨烯，經由光學顯微鏡定位、電子束微影及熱蒸鍍系統，完成場效電晶體結構之石墨烯元件。先利用兩點量測法確認樣品電性傳輸，接著改用四點量測法探討其橫向方向之電壓差值變化。 透過兩點量測法，在施加背向閘極偏壓時，可明顯觀察到石墨烯雙極性(bipolar)的物理特性，且樣品電導率約為7-22 e2/h。透過四點量測法，在汲極/源極兩端輸出電流，並在橫向方向量測電壓差值，發現所量測值與石墨烯場效應呈現一致性，透過積分形式去估算樣品不對稱性所造成的電壓差值，且隨著閘極偏壓造成費米能階的改變，載子濃度的上升與下降皆會影響其變化，並定義出△V34(Vg)，其為閘極偏壓之函數。 發現當石墨烯樣品本身品質較好時，有機會在正交方向量測到與△V34(Vg)完全相反的逆向偏壓值，且此逆向偏壓值在狄拉克點處達最大值，此現象有別於磁場所造成之霍爾電壓，而是單純透過電場所造成之橫向電壓，可能與石墨烯非局域效應下所產生之電壓差有關，且當石墨烯樣品本身品質較好時，此一現象表現得更明顯。最後從不同電極位置上進行四點正交量測，發現相同元件上，此橫向電壓與電極所在位置相關。

Graphene sheets are dispersed on SiO2 (300±15 nm) / Si substrates. Electron-beam lithography and thermal evaporation are applied to make devices with Au (80 nm) electrodes for four-probe electrical measurements. The device is measured at room temperature. The few-layer graphene sheets show little disorder with resistances and conductivity in the range of 1-3x103 Ω and 7-20 e2 / h, respectively. By applying back gate voltage, graphene field-effect transistors show typical ambipolar features. To probe transverse voltage, two electrodes arranged perpendicular to the source-drain current direction are used to measure the voltage difference. There are two different results as described below. One is that a voltage difference shows up owing to the geometry asymmetry in graphene devices. We call it the edge effect. The other result shows a transverse voltage which is maximum at the Dirac point and is opposite to the edge effect. It is much more evident especially in high-quality graphene devices. This transverse voltage may be related to the nonlocality due to the long-range electron-electron interactions and the linear dispersion relation in graphene. Actually, the difference between the edge effect and nonlocal effect can be separated apart. The nonlocal effect also shows a strong dependency on the position of the two perpendicular, probing electrodes.