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Topic Name: UM Physicists Showed Electrons Can Travel More Than 100 Times Faster in Graphene, the Intrinsic Limit to the Mobility

Category: Organic electronics

Research persons: Professor Michael S. Fuhrer

Location: University of Maryland, United States

Details

University of Maryland physicists have shown that in graphene the intrinsic limit to the mobility, a measure of how well a material conducts electricity, is higher than any other known material at room temperature. Graphene, a single-atom-thick sheet of graphite, is a new material which combines aspects of semiconductors and metals.

Their results, published online in the journal Nature Nanotechnology, indicate that graphene holds great promise for replacing conventional semiconductor materials such as silicon in applications ranging from high-speed computer chips to biochemical sensors.

A team of researchers led by physics professor Michael S. Fuhrer of the university's Center for Nanophysics and Advanced Materials, and the Maryland NanoCenter said the findings are the first measurement of the effect of thermal vibrations on the conduction of electrons in graphene, and show that thermal vibrations have an extraordinarily small effect on the electrons in graphene.

In any material, the energy associated with the temperature of the material causes the atoms of the material to vibrate in place. As electrons travel through the material, they can bounce off these vibrating atoms, giving rise to electrical resistance. This electrical resistance is "intrinsic" to the material: it cannot be eliminated unless the material is cooled to absolute zero temperature, and hence sets the upper limit to how well a material can conduct electricity.

In graphene, the vibrating atoms at room temperature produce a resistivity of about 1.0 microOhm-cm (resistivity is a specific measure of resistance; the resistance of a piece material is its resistivity times its length and divided by its cross-sectional area). This is about 35 percent less than the resistivity of copper, the lowest resistivity material known at room temperature.

"Other extrinsic sources in today's fairly dirty graphene samples add some extra resistivity to graphene," explained Fuhrer, "so the overall resistivity isn't quite as low as copper's at room temperature yet. However, graphene has far fewer electrons than copper, so in graphene the electrical current is carried by only a few electrons moving much faster than the electrons in copper."

In semiconductors, a different measure, mobility, is used to quantify how fast electrons move. The limit to mobility of electrons in graphene is set by thermal vibration of the atoms and is about 200,000 cm2/Vs at room temperature, compared to about 1,400 cm2/Vs in silicon, and 77,000 cm2/Vs in indium antimonide, the highest mobility conventional semiconductor known.

"Interestingly, in semiconducting carbon nanotubes, which may be thought of as graphene rolled into a cylinder, we've shown that the mobility at room temperature is over 100,000 cm2/Vs" said Fuhrer (T. Dürkop, S. A. Getty, Enrique Cobas, and M. S. Fuhrer, Nano Letters 4, 35 (2004)).

Mobility determines the speed at which an electronic device (for instance, a field-effect transistor, which forms the basis of modern computer chips) can turn on and off. The very high mobility makes graphene promising for applications in which transistors much switch extremely fast, such as in processing extremely high frequency signals.

Mobility can also be expressed as the conductivity of a material per electronic charge carrier, and so high mobility is also advantageous for chemical or bio-chemical sensing applications in which a charge signal from, for instance, a molecule adsorbed on the device, is translated into an electrical signal by changing the conductivity of the device.

Graphene is therefore a very promising material for chemical and bio-chemical sensing applications. The low resitivity and extremely thin nature of graphene also promises applications in thin, mechanically tough, electrically conducting, transparent films. Such films are sorely needed in a variety of electronics applications from touch screens to photovoltaic cells.

Fuhrer and co-workers showed that although the room temperature limit of mobility in graphene is as high as 200,000 cm2/Vs, in present-day samples the actual mobility is lower, around 10,000 cm2/Vs, leaving significant room for improvement. Because graphene is only one atom thick, current samples must sit on a substrate, in this case silicon dioxide.

Trapped electrical charges in the silicon dioxide (a sort of atomic-scale dirt) can affect the electrons in graphene and reduce the mobility. Also, vibrations of the silicon dioxide atoms themselves can also have an effect on the graphene which is stronger than the effect of graphene’s own atomic vibrations. This so-called “remote interfacial phonon scattering” effect is only a small correction to the mobility in a silicon transistor, but because the phonons in graphene itself are so ineffective at scattering electrons, this effect becomes very important in graphene.

“We believe that this work points out the importance of these extrinsic effects, and creates a roadmap for finding better substrates for future graphene devices in order to reduce the effects of charged impurity scattering and remote interfacial phonon scattering.” Fuhrer said.

Note for Graphene
Graphene is a single planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. It can also be viewed as an atomic-scale chicken wire made of carbon atoms and their bonds. The carbon-carbon bond length in graphene is approximately 1.42 Å. From a physicist point of view, graphene is the basic structural element for all other graphitic materials including graphite, carbon nanotubes and fullerenes. For a chemist, graphene is an infinitely large aromatic molecule, an extension of a family of flat polycyclic aromatic hydrocarbons called graphenes.

Perfect graphenes consist exclusively of hexagonal cells; pentagonal and heptagonal cells constitute defects. If an isolated pentagonal cell is present, then the plane warps into a cone shape; insertion of 12 pentagons would create a fullerene. Likewise, insertion of an isolated heptagon causes the sheet to become saddle-shaped. Controlled addition of pentagons and heptagons would allow a wide variety of complex shapes to be made, for instance carbon NanoBuds. Single walled carbon nanotubes may be considered to be graphene cylinders; some have a hemispherical graphene cap (that includes 6 pentagons) at each end.

The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene…it is not correct to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed". In this regard, graphene has been referred to as an infinite alternant (only six-member carbon ring) polycyclic aromatic hydrocarbon. The onset of graphene properties, as compared to those of a polycyclic aromatic hydrocarbon are not known. PAHs of 60, 78, and 120 carbon atoms have UV absorbance spectra that show a discrete PAH electronic structure, but a PAH of 222 carbon atoms has Raman bands similar to those in graphite.

Physicists from the University of Manchester who first found and studied graphene (rather than PAH) in 2004, defined it in Science as:

Graphene is the name given to a single layer of carbon atoms densely packed into a benzene-ring structure, and is widely used to describe properties of many carbon-based materials, including graphite, large fullerenes, nanotubes, etc. (e.g., carbon nanotubes are usually thought of as graphene sheets rolled up into nanometer-sized cylinders). Planar graphene itself has been presumed not to exist in the free state, being unstable with respect to the formation of curved structures such as soot, fullerenes, and nanotubes.

The British researchers obtained relatively large graphene sheets (eventually, up to 100 microns in size and visible through a magnifying glass) by mechanical exfoliation (repeated peeling) of 3D graphite crystals; their motivation was allegedly to study the electrical properties of thin graphite films and, as purely two-dimensional crystals were unknown before and presumed not to exist, their discovery of individual planes of graphite was presumably accidental. Both theory and experiment previously suggested that perfect 2D structures could not exist in the free state. It is believed that intrinsic microscopic roughening on the scale of 1 nm could be important for the stability of 2D crystals.

Similar work is ongoing at many universities and the results obtained by the Manchester group in their PNAS paper "Two-dimensional atomic crystals" have been confirmed by several groups. For an example of a sample on the order of a monolayer, see figure 1.

Graphene sheets in solid form (e.g. density > 1g/cc) usually show evidence in diffraction for graphite's 0.34 nm (002) layering. This is true even of some single-walled carbon nanostructures. However unlayered graphene with only (hk0) rings has been found in the core of presolar graphite onions. Transmission electron microscope studies show faceting at defects in flat graphene sheets, and suggest a possible role in this unlayered-graphene for two-dimensional dendritic crystallization from a melt.

Note for Carbon Nanotube
Carbon nanotubes (CNTs) are allotropes of carbon. This results in a nanostructure where the length-to-diameter ratio exceeds 1,000,000. Such cylindrical carbon molecules have novel properties that make them potentially useful in many applications in nanotechnology, electronics, optics and other fields of materials science. They exhibit extraordinary strength and unique electrical properties, and are efficient conductors of heat. Inorganic nanotubes have also been synthesized.

Nanotubes are members of the fullerene structural family, which also includes buckyballs. Whereas buckyballs are spherical in shape, a nanotube is cylindrical, with at least one end typically capped with a hemisphere of the buckyball structure. Their name is derived from their size, since the diameter of a nanotube is in the order of a few nanometers (approximately 1/50,000th of the width of a human hair), while they can be up to several millimeters in length. Nanotubes are categorized as single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs).

The nature of the bonding of a nanotube is described by applied quantum chemistry, specifically, orbital hybridization. The chemical bonding of nanotubes are composed entirely of sp2 bonds, similar to those of graphite. This bonding structure, which is stronger than the sp3 bonds found in diamond, provides the molecules with their unique strength. Nanotubes naturally align themselves into "ropes" held together by Van der Waals forces. Under high pressure, nanotubes can merge together, trading some sp² bonds for sp³ bonds, giving great possibility for producing strong, unlimited-length wires through high-pressure nanotube linking. Carbon Nanotubes are said to have the strength of diamonds and research is being made into weaving them into clothes to create stab and bulletproof clothing. The Nanotubes would effectively stop the bullet from penetrating the body but the force and velocity of the bullet would be likely to cause broken bones and internal bleeding.

The strength and flexibility of carbon nanotubes makes them of potential use in controlling other nanoscale structures, which suggests they will have an important role in nanotechnology engineering. The highest tensile strength an individual multi-walled carbon nanotube has been tested to be is 63 GPa. Bulk nanotube materials may never achieve a tensile strength similar to that of individual tubes, but such composites may nevertheless yield strengths sufficient for many applications. Carbon nanotubes have already been used as composite fibers in polymers to improve the mechanical, thermal and electrical properties of the bulk product. A 2006 study published in Nature determined that some carbon nanotubes are present in damascus steel, possibly helping to account for the legendary strength of the (almost ancient) swords made of it.

Carbon nanotubes have many properties—from their unique dimensions to an unusual current conduction mechanism—that make them ideal components of electrical circuits.

Nanotube based transistors have been made that operate at room temperature and that are capable of digital switching using a single electron.

One major obstacle to realization of nanotubes has been the lack of technology for mass production. However, in 2001 IBM researchers demonstrated how nanotube transistors can be grown in bulk, not very differently from silicon transistors. The process they used is called "constructive destruction" which includes the automatic destruction of defective nanotubes on the wafer.

This has since then been developed further and single-chip wafers with over ten billion correctly aligned nanotube junctions have been created. In addition it has been demonstrated that incorrectly aligned nanotubes can be removed automatically using standard photolithography equipment.

The first nanotube integrated memory circuit was made in 2004. One of the main challenges has been regulating the conductivity of nanotubes. Depending on subtle surface features a nanotube may act as a plain conductor or as a semiconductor. A fully automated method has however been developed to remove non-semiconductor tubes.

An alternative way to make transistors out of carbon nanotubes has been to use random networks of them. By doing so one average all of their electrical differences and one can produce devices in large scale at the wafer level. This approach was first patented by Nanomix Inc. It was first published in the academic literature by the Naval Research Laboratory in 2003 through independant research work. This approach also enabled Nanomix to make the first transistor on a flexible and transparent substrate.

UM Physicists Showed Electrons Can Travel More Than 100 Times Faster in Graphene, the Intrinsic Limit to the Mobility

In figure 1, Graphene is an atomic-scale chicken wire made of carbon atoms

In figure 2, Optical micrograph image of single and bilayer graphene