In the OSTI Collections: Graphene

Article Acknowledgement: Dr. William N. Watson, Physicist DOE Office of Scientific and Technical Information

Properties of graphene determined from experiments

Mathematical predictions of graphene behavior

Graphene in technology

Graphene as a guide to understanding other things

References

Research Organizations

Reports available through OSTI's SciTech Connect, DOepatents, and DOE PAGES^Beta

Peer-Reviewed Journals

Additional References

OSTI Services

Although a huge variety of substances are made of carbon chemically bound with other elements, materials made of nothing but carbon atoms can be categorized into just a few types.  In diamond, the carbon atoms’ arrangement looks essentially the same with respect to all three dimensions, but other forms of carbon consist of distinct plane or curved layers, each just one atom thick, each of which exhibits one set of symmetries within its own two dimensions but have a different kind of symmetry along the third dimension—graphite being a common, long-known example that consists of weakly-bound plane layers, each made of carbon atoms that are tightly bound to their neighbors in the same layer. 

Pure carbon can also exist as a single one-atom-thick layer.  Fullerenes^[Wikipedia], which consist of a type of carbon molecule discovered a few decades ago, are more or less spherelike structures.  Single-atom thicknesses of carbon needn’t take the form of spheres or spheroids, though.  Tubes that each consist of a single layer of carbon atoms just a few nanometers in circumference but of various longer lengths are objects of extensive study and technological interest, particularly as structural and functional elements for nanotechnology.  And there is one other monatomically thick form of carbon whose size spans many atoms in both length and width, called graphene.  Graphene is basically what you’d have if you took a piece of graphite and removed one of its layers intact from the stack. Indeed, this process is what some methods for obtaining graphene amount to. 

Graphene has physical and chemical properties that make it worth obtaining.  Within the bulk of a piece of pure three-dimensional graphite, each atom has two electrons bound to it exclusively, while three electrons per atom are shared between pairs of neighboring atoms within a single layer, and one electron per atom is shared by pairs of neighboring atoms in adjoining layers.  But when a layer of graphite is separated from the rest of the material to become graphene, its electrons are no longer attracted by atoms in adjoining layers; instead, the electrons previously shared between layers are shared among all the atoms in the separated layer.  This single change gives graphene a set of potentially useful properties quite different from those of graphite or other forms of pure carbon.  Some of these properties were expected from theoretical calculations made long before practical techniques for isolating graphene were discovered; other properties have been more recently calculated or determined from experiment. 

The characteristics and possible uses of graphene are being widely and intensively explored.  Much of this work is being supported through the U. S. Department of Energy, with current results becoming available from technical reports, conference presentations, graduate-student theses, patents, and papers published in research journals.  OSTI’s SciTech Connect service provides reports of all these types, as it has for nearly two years.  DOepatents, an older service, has a narrower focus on just the patents that result from Energy Department research.  And for reports of Department-sponsored work published as papers in peer-reviewed scientific and technical journals, OSTI now has a new service in beta version, called DOE PAGES.  All these services provide access to reports about various problems and questions related to graphene; a sample of these is illustrated by the reports described below.  The first reports in this sample discuss things learned from experiment and mathematical analysis about graphene’s properties; afterwards we’ll examine reports on developments in graphene technology.  Finally, we’ll see how graphene, though different from other materials, has enough similarities to some of them to serve as a useful, more accessible analog to help us understand them. 

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Properties of graphene determined from experiments

If a graphene sample is given some extra energy, those electrons that are shared among all its atoms may gain some of the energy and change their state of motion.  With the extra energy, the electrons’ set of possible motions also becomes larger—i.e., the graphene’s entropy increases.  The increases with energy in the sample’s entropy and in the number of electrons executing new motions are reflected in the values of the electrons’ temperature and chemical potential^[Wikipedia].  The electrons don’t retain their extra energy indefinitely, though; the widely-shared electrons’ interactions with the more restricted electrons and the carbon atoms’ nuclei dissipate their energy, so that their temperature and chemical potential decrease with time.  The slide presentation “Time-resolved carrier distributions in graphene”^{[SciTech Connect]} from Los Alamos National Laboratory documents the sudden increase and more gradual decrease in graphene electrons’ temperature and chemical potential as found from experiments.  The variations in these two quantities were observed not to follow the same pattern; the authors note that this finding is important for graphene applications. 

Some of these applications involve how graphene conducts electricity (i.e., how electrons flow along the plane) and how it interacts with light.  Graphene’s electronic and optical behavior might be satisfactory for some purposes but not others.  A possibility for changing graphene into something with a more suitable combination of properties motivated experiments by a different Los Alamos group, which they presented in “Real-Time Electronic Structure Evolution of Thermally Reduced Graphene Oxide (GO)”^{[SciTech Connect]}.  The electron configuration of graphene is altered when some of the electrons that were shared among all its carbon atoms are localized by forming bonds between particular carbon atoms and oxygen atoms, thus making the graphene and oxygen into graphene oxide.  Binding of the oxygen atoms to one side, the other side, or both sides of the carbon-atom plane, as well as the oxygen atoms’ number and spacing, affects how the remaining widely-shared electrons can move in response to the electric fields^[Wikipedia] of a generator, battery, or light wave^[Wikipedia].  The presentation shows how different methods of producing graphene oxide yield materials with different oxygen placement and different optoelectronic properties. 

A paper published in Physical Review Xby authors at Columbia University describes details of a particular optical process in graphene:  absorbing light of one frequency to generate light of triple that frequency (third-harmonic generation^[Wikipedia]).  Earlier experiments had shown how this process occurs when light shining perpendicularly onto the graphene plane is absorbed by shared electrons whose differing energies are nearly proportional to their momenta.  The Columbia group’s paper, “Optical Third-Harmonic Generation in Graphene”^{[DOE PAGES Beta]}, describes frequency-tripling in graphene when the light shines on it at other angles and is absorbed by sets of electrons whose momenta differ while their energies are nearly the same.  The intensity of the graphene’s frequency-tripling of light coming from different directions and having different polarizations^[Wikipedia] indicate not only the more obvious symmetries of the graphene atoms’ spatial arrangement, but the less obvious related symmetries of their electromagnetic properties.  In these experiments, the graphene samples were grown from vapor deposited on glass, whose quite different response to light made graphene’s frequency-tripling easy to identify.  But the response was so clear that the researchers expect the technique to be useful for determining the orientation of graphene grown on substrates made of materials other than glass, or examined under less optimal observational conditions. 

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Mathematical predictions of graphene behavior

The reports just described all relate to experimental discoveries.  Other studies have been able to deduce certain behaviors of graphene as mathematical consequences of some of its known properties.  One such study is reported in an Iowa State University master’s thesis by Meng-Chieh Ling, “Hot electron dynamics in graphene”^{[SciTech Connect]}. 

Wherever an electric field exists, any charged particles, like electrons, that happen to be in the field will accelerate at a rate directly proportional to the strength of the field.  This direct proportionality is easiest to discern when the electric field is uniform in strength and direction, as it might be in otherwise empty space.  In a material, though, the electrons and atomic nuclei that constitute the material all have electric fields of their own, so the total electric field at any location in the material differs in strength and direction from that at other locations, according to which other particles are nearby.  Any electron in the material would thus be accelerated at one rate and direction at any one point, and at different rates and directions at other points.  In fact, electric fields in the material will in general not be constant at any one point, since they change with the random motion of the material’s particles. 

The accelerations of the material’s electrons due to these internal fields tend to cancel out overall, so that any electrons that are more or less stationary tend to stay more or less stationary in the material.  But if any electrons within the material are free to move—like the widely-shared electrons in a graphene sheet, for example—they may respond to an additional electric field generated from outside the material by accelerating until their interactions with the material’s other particles via the internal fields make them dissipate some of their energy to other particles in the material, leaving the shared electrons with a drift velocity that fluctuates around some finite value.  In many materials in our usual ambient conditions, this drift velocity (rather than the acceleration) will be proportional to the superimposed electric field, but for some materials, or under different ambient conditions, even the electrons’ drift velocity won’t be proportional to the additional field.  Such a nonproportionality is characteristic of graphene when its temperature is low enough.  Ling’s thesis describes an initial calculation of exactly how electrons in graphene do behave under such conditions.  It shows key features of how the electron momenta are distributed, and how the electron current is related to the strength of the superimposed electric field and to the strength of the electrons’ interaction with other particles in the graphene.  The thesis also describes how taking more details of graphene into account would serve to determine additional features of the electron current. 

A group of researchers working at the University of Illinois at Urbana-Champaign and at Harvard University reported their findings on “Stability of edge states in strained graphene”^{[DOE PAGES Beta]} in the journal Physical Review B.  As they note in their paper’s introduction, graphene’s electronic properties can be tuned through deformations and strains, which change the relative positions of the graphene’s carbon atoms, thus changing the probabilities that electrons will “hop” between carbon atoms.  Certain deformation patterns have, in fact, been found to mimic the effect of magnetic fields^[Wikipedia] on the electrons’ motion to some extent.  The authors examined the similarity of these two influences when the graphene’s edges affect the electrons’ motion.  It turns out that differently shaped edges make considerable difference in the possible patterns of electron distribution in the graphene, so the different edge shapes affect the extent to which deformation of the graphene resembles magnetism in its effect on the electrons’ motion.  In graphene that has the “zigzag” edge type, shown on the right in Figure 1, the effect of strain is much like that of a magnetic field, but not in graphene that has “armchair” edges (Figure 1, left).  The authors note that present experimental techniques for distinguishing different electron behaviors in graphene should make different graphene edge shapes easily detectable. 

A mathematical prediction of graphene behavior made by physicists at the University of Texas and the University of Science and Technology of China is more directly aimed at seeing how graphene might be used in a specific kind of electronic device.  Their report in Physical Review B, entitled “Gate-tunable exchange coupling between cobalt clusters on graphene”^{[DOE PAGES Beta]}, shows that magnetic metal clusters placed on a graphene sheet can interact in ways that can be controlled by applying an electric field to the graphene-metal system.  Such a system would offer advantages for making spintronic^[Wikipedia] devices (devices that function by affecting the orientations of electrons’ spins^[Wikipedia], which are directly related to the directions of the electrons’ magnetic fields).  Among the advantages listed by the authors: 

• Clusters of magnetic transition elements like cobalt form readily on graphene surfaces. 
• The interfaces between graphene and magnetic transition metals have potentially attractive properties—e.g., on graphene, the magnetic fields of particles in thin transition-metal layers are predicted to have very different energies for different field orientations. 
• In graphene, the electrons’ motion within and among the carbon atoms causes only a weak magnetic disturbance of the electrons’ spins. 

Calculations described in the paper reveal in some detail how the cobalt clusters’ interactions depend on various parameters of the cobalt-graphene system. 

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Graphene in technology

The reports described above focus on theoretical and experimental findings that could guide the design of various kinds of devices made with graphene.  The following reports focus on graphene-based technology more directly.   

The report “Enabling Graphene Nanoelectronics”^{[SciTech Connect]} from Sandia National Laboratories addresses the problem of mass fabrication, specifically the development of techniques to deposit and synthesize graphene over large areas so that the graphene exhibits highly uniform electronic properties and record-setting mobility (i.e., drift speed per unit electric field)^[Wikipedia] of its electric-charge carriers^[Wikipedia].  (Here, the “large” areas are large in microelectronic terms—in this case, areas of about 100 square micrometers, equal to 0.01 millimeters by 0.01 millimeters.)  The report’s authors “combined an array of growth approaches and characterization resources to investigate several innovative and synergistic approaches for the synthesis of high quality graphene films on technologically relevant substrates (SiC^[Wikipedia] and metals)”, and also focused on developing ways to transfer graphene onto other substrates.  In a three-year project funded by Sandia, researchers

• developed a scalable synthesis route for monolayer and bilayer graphene on silicon carbide using atmospheric argon^[Wikipedia], achieving 100  in size and “excellent electronic uniformity” across the sample, and developing a strategy for bilayer graphene growth at the size scale of wafers^[Wikipedia] manufactured in the semiconductor industry,
• developed a fundamental understanding of graphene growth mechanisms on silicon carbide and metal (particularly copper) substrates,
• developed a scalable electrostatic process to transfer graphene from silicon carbide to Pyrex,
• demonstrated graphene-based field-effect transistors^[Wikipedia] that operated at room temperature,
• observed the Integer Quantum Hall Effect^[Wikipedia] and a record charge-carrier mobility, or drift speed per unit electric field, of 14,000 cm²/Vs—that is, 14,000 (centimeters per second) per (volts per centimeter)—for device arrays.  (For comparison, charge-carrier mobility for standard semiconductors is about 1,500 cm²/Vs for silicon and about 8,500 cm²/Vs for gallium arsenide.  Even 14,000 cm²/Vs isn’t necessarily the ultimate mobility for graphene; it’s expected that, when graphene is defect-free, its charge-carrier mobility would be about 200,000 cm²/Vs.) 

The new techniques for making graphene would enable more than nanoelectronics.  A later Sandia report, “Graphene resonators:  analysis and film transfer” ^{[SciTech Connect]}, discusses transferring graphene grown on copper by chemical vapor deposition^[Wikipedia] onto a substrate in order to make and characterize mechanical resonators^[Wikipedia].  The substrate is made with gaps in its surface so that the portions of graphene extending over the gaps will be free to vibrate as resonators.  Figure 4 shows a scanning electron microscope image^[Wikipedia] of such resonators, which appear as indentations.  The report describes the relation of a resonator’s frequency to its size, mass, density, stiffness, and tension.  This last parameter, which depends on the resonator-fabrication process, has not been precisely calculated from existing theory, but can be determined from experiment.  The report mentions two ways to get the resonators vibrating for such experiments or for actual use.  One way is to use laser pulses to alternately heat and cool the resonators; the resonators’ resulting expansion and contraction, if correctly timed, will set them to vibrating at one of their natural frequencies.  The resonators could also be electrostatically actuated if they were integrated with electrodes. 

Figure 4 also shows cracks and wrinkles in the graphene sheet, which are evidence of problems with the graphene transfer method.  The report describes these problems and proposes some changes in the transfer process to eliminate them. 

The analysis of cobalt clusters on graphene and their electronic behavior described above^{[DOE PAGES Beta]}  represents the use of known laws of physics to work out how a device of a particular design might function.  A less analytic way to design a device still takes account of known physics, but arrives at a design by experiment instead of calculation.  This approach is exemplified by work described in a slide presentation by Los Alamos National Laboratory researcher Shaojin Guo prepared for the 247th National Meeting and Exposition of the American Chemical Society.  “Graphene-Au Nanoparticles Composite-Based Electrochemical Aptamer Biosensors”^{[SciTech Connect]} illustrates the use of graphene as a component in new types of sensors that involve the use of aptamers^[Wikipedia]—molecules designed specifically to fit with other molecules that one wants to detect—attached to a platform made of graphene, a particular form of porous silicon dioxide^[Wikipedia], and gold nanoparticles^[Wikipedia].  Papers referred to in Guo’s presentation, such as “Solid-State Label-Free Integrated Aptasensor Based on Graphene-Mesoporous Silica–Gold Nanoparticle Hybrids and Silver Microspheres”^{[abstract, ACS]}, provide more detail about how the devices work.  When molecules to be detected react with aptamers in the device, the platform reacts to the interaction and electronically produces an amplified signal.  The electronic amplification, together with other signal-enhancing features of the sensor designs, enable the sensors to register the presence of very small amounts of the substances they’re designed to detect. 

Another use of graphene as part of a composite material in a device is represented by United States Patent 8,778,538, “Electrode material comprising graphene-composite materials in a graphite network”^[DOepatents].  This patent addresses the problem of improving lithium-ion batteries’^[Wikipedia] performance with respect to their electric-charge storage capacity, power density, retention of storage capacity and power density over many discharge-and-recharge cycles, and safety.  The first three of these properties depend strongly on the nature of the battery’s electrically active material, how that material is supported, and how it’s electrically connected to the current collector that transfers electrons between it and the outside world.  Substitutes for standard electrically active materials have been found that are superior in the first two properties but inferior in the third:  the batteries that use them lose nearly all their capacity after a few recharge cycles.  The patent describes a new material that avoids this problem, namely “a network of graphite regions that are in good electrical and physical contact with … a composite of graphene sheets and nanoparticles of … and/or thin films of an [electrically active material] … dispersed in, and supported by, the graphene sheets.”  Figure 5 is a schematic diagram of one version of such a network, using silicon for the electrically active material in the form of nanoparticles instead of thin films. 

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Graphene as a guide to understanding other things

Analyzing graphene and using it in new devices lets us learn about more than just graphene itself.  Two other papers published in Physical Review B provide examples of how understanding this material can help researchers understand the nature and behavior of other materials as well. 

The arrangement of a material’s atoms has a great deal to do with how that material behaves.  One way to observe atomic arrangements is with a transmission electron microscope^[Wikipedia], in which beams of electrons play much the same role that beams of light do in optical microscopes.  Because the spatial resolution of a microscope increases with the momentum of the particles it uses to illuminate the objects observed, electron beams offer an advantage over photon beams:  providing enough momentum per beam particle to resolve individual atoms takes less energy if the beam particles are electrons instead of photons.  (In fact, photons with that much momentum constitute, not visible light, but x-rays.)  However, electrons with that much momentum, if they collide with the atoms of the observed material, can move the atoms out of their places, disrupting the arrangement one intends to observe.  Even with techniques that use very few electrons per atom per second to minimize the atoms’ displacement while still providing enough image contrast between atoms and empty spaces to show where the atoms are, some disturbance turns out to be unavoidable. 

The minimum extent and nature of such disturbances was explored by a collaboration of researchers at Lawrence Berkeley National Laboratory, the University of California—Berkeley, the National Polytechnic Institute in Mexico City, the FEI Company, and the Dow Chemical Company and discussed in their paper “Real-time sub-Ångstrom imaging of reversible and irreversible conformations in rhodium catalysts and graphene”^{[DOE PAGES Beta]}.  They found that in a film made of rhodium^[Wikipedia] just 2-3 atoms thick, some atoms were temporarily displaced when exposed to the microscope’s electron beam.  To better understand the details of the process, the researchers examined their electron microscope’s effect on a simpler system:  graphene, with its single layer of less-massive carbon atoms.  Careful analysis of the atomic motions observed in graphene indicated that displacements can come about when even weak electron beams set the entire graphene sheet into random vibrations.  The vibrations can combine in ways that result in some atoms occasionally being displaced into relatively stable positions away from their regular locations in the standard graphene lattice. 

While monatomic graphene layers have enough similarity to few-layer rhodium to help clarify the latter’s behavior, graphene apparently has even more similarity to another substance of increasing interest:  phase IV solid hydrogen, which exists at slightly above room temperature at very high pressures (above 220 gigapascals, or about 2.2 million atmospheres) and is expected to be superconducting at high temperatures and have other exotic properties.  The exact atomic structure of this form of hydrogen has been debated, with several specific candidate structures being proposed, but all the proposals involve layers of weakly interacting H₂ molecules sandwiched in some fashion between graphenelike layers.  Researchers at the Geophysical Laboratory of the Carnegie Institution of Washington, D.C. note that electron structures in a hydrogenic honeycomb lattice and in graphene’s honeycomb lattice are “identical both topologically and by symmetry” in their paper “Graphene physics and insulator-metal transition in compressed hydrogen”^{[DOE PAGES Beta]}.   Their calculations show that the electronic properties of all the proposed structures for solid high-density molecular hydrogen can be understood by studying a single graphene layer and/or simple systems composed of such layers.  From this analysis, the authors identify two new factors that affect how compressed hydrogen can reach a semimetallic state.  They note that while their analysis doesn’t take certain types of random effects into account, these effects should have opposing influences that will at least partly cancel, and that the graphenelike layers of hydrogen should dominate the behavior of high-pressure hydrogen, its metallization, and its other optical and electronic properties. 

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References

Wikipedia

• Graphene
• Fullerene
• Chemical potential:  Overview
• Electric field
• Electric field of light wave [Polarization (waves):  Transverse electromagnetic waves]
• Optical frequency multiplier [third-harmonic generation]
• Polarization (waves)
• Spintronics
• Magnetic field
• Spin (physics)
• Electron mobility
• Charge carrier
• Silicon carbide [SiC]
• Argon
• Wafer (electronics)
• Field-effect transistor
• Quantum Hall effect
• Chemical vapor deposition
• Dielectric
• Resonator
• Scanning electron microscope
• Aptamer
• Meosporous silica
• Nanoparticle
• Lithium-ion battery
• Transmission electron microscopy
• Rhodium

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Research Organizations

• Los Alamos National Laboratory
• Columbia University
• Iowa State University
• University of Illinois at Urbana-Champaign
• Harvard University
• University of Texas
• University of Science and Technology of China
• Sandia National Laboratories
• Northwestern University, assignee of United States Patent 8,778,538
• Lawrence Berkeley National Laboratory
• University of California—Berkeley
• Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional [English]
• FEI Company
• Dow Chemical Company
• Geophysical Laboratory, Carnegie Institution of Washington

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Peer-Reviewed Journals

• Physical Review B
• Physical Review Letters
• Physical Review X
• Analytical Chemistry

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Additional References

• “Electronic Life on the Edge”^[LBNL] (Lawrence Berkeley National Laboratory news release, May 8, 2011)
• American Chemical Society:  247th National Meeting and Exposition
• “Solid-State Label-Free Integrated Aptasensor Based on Graphene-Mesoporous Silica–Gold Nanoparticle Hybrids and Silver Microspheres” (abstract, Analytical Chemistry, 2011, 83 (20), pp. 8035–8040)

OSTI Services

• SciTech Connect
• DOepatents
• DOE PAGES^Beta

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