Extensive theoretical and experimental studies have been made on layered graphite material to understand its complex electrical behavior. Recently, electronic properties of graphene nanostructures, such as nanotubes, carbon nanocones, fullerenes, and graphite edges, have attracted much attention from the point of view of basic research and applications. The motivation for studying carbon based nano-structures is to develop atomic or molecular nanometer scale electronic devices having a fundamentally different operating principle than conventional electronic devices. Due to its nanoscale size one can look at opportunities to increase the device density as well. The electronic property of nanoscale materials are strongly influenced by their geometries. The graphene sheets are generally self-assembled to arrive at various shaped nanotubes, fullerenes, nanocones, etc. The electronic properties of these graphene sheets are cut and joined at the edges. Any new information and understanding related to graphene sheets will have an impact on basic research and applications of carbon based materials.
Highly oriented pyrolytic graphite (HOPG) is a periodical stack of two-dimensional graphene sheets along the c axis. Each sheet is comprised of hexagonal lattice of carbon bonded by strong σ bonding in the a-b plane. The conduction occurs by the quantum mechanical hopping of these electrons. Each of these layers are weakly bonded to their neighboring layers by interlayer interaction forces. Because of the weak interlayer interaction forces, the graphene layers can easily slide against each other and peel off easily. In late 1950s and early 1960s the electronic property of graphite was evaluated using phenomenological models based on the symmetry of graphite. The dispersion relation of the bands was found to have a very slight overlap of the valence and conduction bands at the Fermi level, where the electron density is very low. This causes graphite to have semimetallic characteristics. Even though the charge carrier concentration is very low, the electrical mobility of these carriers is high and its electrical resistivity along the plane is -40 μΩcm. The temperature coefficient of resistivity of HOPG is positive along the sheet and ρ⊥/ρ∥≈104 at room temperature.
It has been pointed out that graphene sheet edges strongly affect the π electronic states. The edges of the graphene sheets are of two types armchair and zigzag edges. It was shown theoretically that graphene sheets having zigzag edges possess edge states localized at the zigzag edges, hence making the armchair edge less conducting than the zigzag edge.
With this introduction on graphite, we would like to address two main issues in the present paper:
- How does the electrical property of the graphite sheet change when the graphite layer is displaced by shear forces?
- How does the electrical property of the graphite sheet change across a step edge?
Scanning tunneling microscopy and atomic force microscope with a conducting tips can be used to study the local electronic properties of conducting surfaces. Using STM measurement one can obtain images and perform spectroscopy with very high spatial resolution. In the STM one adopts either a constant height mode or a constant current mode for mapping. Mapping conductivity across step edges using STM has some difficulties. In the constant height mode, the variation of current measured across the step is due mainly to the height variation and hence mapping local conductivity using constant height mode is impractical. In the constant current mode, since the current is kept constant it is difficult to map the local conductivity from the displacement of the z piezo because tunneling current decreases exponentially with distance, thus small current change from sheet to sheet will lead to very small displacement of the z piezo. But, since edge states have larger conductance, STM in the constant current mode can be used to see these edge states. Performing I-V measurements at every point by stopping the feed-back signal to map the local conductivity with high resolution is also difficult using STM. SFM with a conducting tip in the contact mode overcomes the above difficulties at the expense of spatial resolution. For the present investigation we have used AFM in contact mode with constant applied normal force on the tip.