探索單層及雙層石墨烯中長程庫倫交互作用

Abstract

本實驗使用機械式剝離法製備少數層石墨烯於二氧化矽厚度為300 nm之矽基板上，利用高畫素顯微相機拍攝石墨烯光學顯微鏡影像圖，藉由石墨烯高透光的特性以Image J軟體分析石墨烯樣品與基板色彩差異度，配合實驗室色彩差異度與厚度對應數據庫挑選單層及雙層石墨烯作為本實驗樣品，製成石墨烯元件。 本實驗欲透過正交四點量測，在水平方向即源極-汲極兩端輸出電流量測垂直方向之電壓差，藉此量測單純在電場下由長程庫倫交互作用所造成的非局域性效應 (Nonlocal Effect)，長程庫倫交互作用通常發生在絕緣體中，但是石墨烯為一個乾淨的二維電子氣系統，且狄拉克點具有半金屬之特性，所以有一定機率量到Nonlocal訊號。 實驗觀測到單層石墨烯樣品Nonlocal訊號出現在狄拉克點附近，並非每組樣品都會量測到Nonlocal訊號，目前統計結果Nonlocal訊號出現在最小電導率介於7.0 e2/h及12.9 e2/h的樣品，藉由歸一化比較不同樣品之間Nonlocal訊號量測之大小，發現當雜質濃度較低樣品 (無序性低)的Nonlocal訊號較大。另外觀測溫度與Nonlocal訊號之關係，當溫度越低Nonlocal訊號越大。除此之外，本實驗也在部份300 K沒量測到Nonlocal訊號樣品中發現隨溫度下降過程中出現Nonlocal訊號，並逐漸增大。可知最小電導率、雜質濃度、熱能會影響Nonlocal訊號量測。 二維材料不同層數間會有不同的電性表現，本實驗也從雙層石墨烯元件中於狄拉克點附近之垂直方向電壓差量測到Nonlocal訊號，變溫量測結果發現熱能影響雙層石墨烯元件的Nonlocal訊號與單層結果相同，當熱能增加到大於長程庫倫交互作用產生的能量，使得Nonlocal訊號不易被觀察到。

By using mechanical exfoliation with highly oriented pyrolytic graphite, we disperse few-layer graphene sheets on silicon substrates capped with a 300-nm thick SiO2 layer. High resolution optical microscope was used to identify the number of layer of those graphene sheets. The number of layer was simply determined by the contact difference in the optical microscope images. We then employed a standard electron-beam lithography and thermal evaporation to make four gold contact electrodes (100-nm thick) on graphene sheets for four-probe electrical measurements. We applied a constant current on the source and drain electrodes and collected a voltage difference between two electrodes that are arranged in the direction orthogonal to the current path. The measurements are commonly used to detect nonlocality such as that of Hall effects due to external magnetic fields. Here we applied this differential voltage measurement to study nonlocality due to long range Coulomb interactions between electrons and holes near the Dirac point of graphene. It was observed that the nonlocality is strongly dependent on minimum conductivity and impurity carrier concentrations of the graphene, and it is reduced with increasing thermal energy. For example, the nonlocality was observed in single-layer graphene with minimum conductivities in the range between 7.0 e2/h and 12.9 e2/h. In addition, both of high impurity carrier concentrations and high temperature cause decreases of the nonlocal effect. On the other hand, the nonlocality was observed in bilayer graphene as well. We inspected temperature dependent behaviors which are similar to that of single-layer graphene.