Conductivity landscape of highly oriented pyrolytic graphite surfaces containing ribbons and edges

We present an extensive study on electrical spectroscopy of graphene ribbons and edges of highly oriented pyrolytic graphite (HOPG) using atomic force microscope (AFM). We have addressed in the present study two main issues (1) How does the electrical property of the graphite (graphene) sheet change when the graphite layer is displaced by shear forces? and (2) How does the electrical property of the graphite sheet change across a step edge? While addressing these two issues we observed (1) variation of conductance among the graphite ribbons on the surface of HOPG. The top layer always exhibits more conductance than the lower layers, (2) two different monolayer ribbons on the same sheet of graphite shows different conductance, (3) certain ribbon/sheet edges show sharp rise in current, (4) certain ribbons/sheets on the same edge shows both presence and absense of the sharp rise in the current, and (5) some lower layers at the interface near a step edge shows a strange dip in the current/conductance (depletion of charge). We discuss possible reasons for such rich conducting landscape on the surface of graphite.

Figure 1

(a) Carbon atoms showing $s{p}^2$ hybridized $\sigma$ orbitals in the $a\text{−}b$ plane and nonhybridized $\pi$ orbitals along the $c$ axis of the graphite layer. Graphite sheet/ribbons showing (b) armchair (cis) edge and (c) zigzag (trans) edge. (d) Six points in the Brillouin zone showing zero gap and having zero overlap of the conduction band (CB) and the valence band (VB) at Fermi energy $\left(E_F\right)$, i.e., zero density of state (DOS) at $E_F$ and (e) finite overlap of CB and VB leading to finite DOS at $E_F$.

Figure 2

Atomic force microscopic image (a) topographic (b) conductivity landscape of highly oriented pyrolytic graphite (HOPG).

Figure 3

(a) Topographic two-dimensional (2D) and (b) three-dimensional (3D) images of a selected region containing two monolayer steps/edges (staircaselike) on the surface of the HOPG sample. (c) Two height profiles along the lines marked in (a) as A and B. The arrows indicate the 0.4 nm step height. [Note: The tilt in the step (line profile) is an artifact of processing (linear line fit along the scan $x$ direction).]

Figure 4

(a) Local conductance map of steps of Fig. 3 for the forward and (c) for the reverse bias conditions, respectively. Contrast inversion and reversal of the current direction is observed on reversing the bias. The higher current is indicated by bright shade and lower current by darker shade in the forward bias condition and the scale is shown on the right-hand side of the image. In the reverse bias condition the higher negative current value is indicated by the darker shade and low negative value is shown as the brighter shade. The brightest layer in (a) is the top layer and the darkest is the lowest layer. (b) and (d) current profile along the lines marked in the conductance images [(a) and (c), respectively]. We see distinct changes (drop) in the current profile at the step edges in comparison to the height change in the topography [see Fig. 3c]. The arrows show distinct dips in the current/conductance occuring at the lower layers at each of the interface of the step edges.

Figure 5

Inset shows conductance map showing bright current streak appearing on certain edges as indicated by arrows. This observation indicates clearly the presence of two distinct type of edges on this graphite ribbons. We also show line profiles of the conductance current of the lines marked A and B, respectively, in the inset.

Figure 6

(a) Local conductance map for the forward bias condition. Labels 1 to 8 are the spots where current vs voltage $\left(I\text{−}V\right)$ measurements were carried out. (b) The current profile along the lines marked in (a) with labels A to C for forward bias condition. The arrow indicates the bright streak abruptly ending along the edge for the forward bias condition on the same ribbon.

Figure 7

(a) and (b) current-voltage $\left(I\text{−}V\right)$ measurement carried out at various regions of ribbons/terraces marked in Fig. 5 inset and Fig. 6b, respectively. Low slope value in the $I\text{−}V$ curve at zero-bias indicates a lower conducting region than the region having higher slope. (Note: All the $I\text{−}V$ measurements were carried at same value of constant force.)

Figure 8

In (a), (b), and (c) we show schematically the step edges of different kinds that can give rise to the corresponding current versus distance $\left(x\right)$ profile across the step edges and layers.