Electron Transport in Graphene

Graphene, a single sheet of carbon, has properties that suggest it may have an important role to play in future electronic devices. The low scattering rates and the electronic structure of graphene give rise to good electronic transport that is easy to modify by doping or electrostatic fields. Its high conductivity could allow it to serve as interconnects. It can be gated so it could be used as the channel in novel transistors. Graphene is quite stable and inert so it is possible to prepare large areas that have low defect densities and low electronic scattering rates.

At the present, most graphene samples are prepared by stripping layers off of graphite, which consists of multilayers of graphene and is the ground state of carbon. An alternate way to prepare large areas of graphene is by evaporating silicon from silicon carbide. As the silicon evaporates, it leaves behind sheets of graphene. The number of graphene layers can be controlled by the evaporation temperature and time. The ability to prepare large areas of high quality graphene on a substrate is a necessary step toward using graphene in future electronics.

Graphene’s electronic structure has a number of properties that have excited intense research into its physical properties. The energy-momentum dispersion of graphene leads to charge carriers that can be understood as two-dimensional Dirac particles with internal symmetries. In some ways, the electrons behave like massless particles of light, which have a similar dispersion. Electrons in graphene have a property called chirality, which is like the helicity of light. However, the electrons in graphene also have a new quantum degree of freedom called pseudo-spin, which does not have a related property in light particles, and is analogous to the real spin of an electron.

Understanding the role of defects in the transport properties of graphene is central to realizing future electronics based on carbon. Using scanning tunneling spectroscopy, we have observed quasiparticle interference patterns in epitaxial graphene grown on silicon carbide. Energy-resolved maps of the local density of states reveal modulations on two different length scales, reflecting both intravalley and intervalley scattering (see Fig. 1). Although such scattering in graphene can be suppressed because of the symmetries of the Dirac quasiparticles, we have shown that, when its source is atomic-scale lattice defects, wave functions of different symmetries can mix.

Figure 1. Defect scattering in bilayer epitaxial graphene. (A) STM topography and (B-E) simultaneously-acquired spectroscopic dI/dV maps. Mound-type defects below the graphene are labeled with red arrows and do not display much scattering, whereas lattice defects labeled with blue arrows display large scattering and give rise to the interference patterns observed in the dI/dV images of B-E. Sample biases are: (B) -90 mV, (C) -60 mV, (D) -30 mV, and (E) 30 mV.

When graphene is grown by evaporating silicon from silicon carbide, the interface between the graphene and the remaining silicon carbide can play an important role in the properties of the graphene. Using scanning tunneling microscopy, we have imaged this interface (see Fig. 2) and correlated the structure of the interface with its electronic properties. It is somewhat surprising and encouraging that the interface can possess a lot of non-trivial structure without any corresponding disturbance in the transport properties of the graphene. First principles electronic structure calculations clarify why it is possible to image the interface below the graphene and explain the energetics of the different interface structures that have been observed (see Fig. 3).

Figure 2. STM topographic image of the first graphene layer showing a combination of SiC interface features along with the graphene lattice due to the transparency of tunneling into the graphene layer. Typical adatom features are tetramers (red arrows) and hexagons (green arrows).

Figure 3. Wavefunction contours calculated for a model of the graphene-SiC interface showing how graphene becomes transparent at certain tunneling energies (see publications for details). (d) Top-down view of a 5x5 cell with a tetramer and neighboring adatom at the interface displayed in red. (e) The total calculated charge density above the graphene layer displays the same superstructure modulation observed in the STM images of graphene due to the SiC interface reconstruction. Here red indicates regions of highest charge density and blue corresponds to lowest charge density.

Imaging the Interface Beneath Expitaxial Graphene
Scattering and Interference in Epitaxial Graphene



Joseph A. Stroscio - NIST
Gregory Rutter  - Georgia Institute of Technology
Mark D. Stiles - NIST


Jason Crain
Nathan Guisinger - Argonne National Laboratory
Emily Jarvis - Gordon College


Phillip First - Georgia Institute of Technology

---

Online: January 2008
Last Updated: February 2008

egpwebmaster@nist.gov