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Perspectives:Graphene Nanoelectronics

[color=Red]Graphene Nanoelectronics[/color]a(r1IO$n iO
R. M. Westervelt*
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.LMwhE#T)h4? Semiconductor technology has taken us a long way by making devices of ever smaller size. But eventually, as the transistors approach the size of molecules, quantum effects become important. What will then be the form of future nanoelectronic devices? Can quantum mechanics be used to control device operation? And can they operate at reasonable temperatures? Nanoscale transistors made from graphene may provide ways to address these questions. [url=http://www.sciencemag.org/cgi/content/full/320/5874/356]On page 356 of this issue, Ponomarenko et al.[/url] (1) describe graphene [fly][fly][box=Red]single-electron transistors etched to sizes as small as ~30 nm[/box][/fly][/fly], which have quantum-confined energy states, and control the motion of single electrons (see the figure). This complements investigations of single-electron transistors from graphene flakes (2), quantum interference devices (3), and ~200-nm etched graphene dots (4).
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/C}\+B[X[_g Graphene is an unusually simple material with startling new properties (5). It consists of a single atomic layer of carbon atoms. One can prepare a graphene sample by pulling an atomic layer off of a graphite crystal with a piece of sticky tape, and then pressing the tape down onto a silicon substrate. After pulling the tape free, small islands of graphene remain, recognizable with an optical microscope. Graphene layers are tough--the carbon atoms bind together in a hexagonal lattice--and can be freely suspended over a trench in the substrate.

s;g4m4N$l0W&F It is the behavior of electrons in single graphene layers (5-9) that is opening the way for new kinds of devices. In a typical semiconductor, electrons and holes (the positively charged carriers) occupy the conduction and valence energy bands, respectively. A finite energy called the energy gap must be added to a particle to move it from the valence to the conductance band. Electrons and holes move like regular particles: They have a mass, their speed increases from zero as they are accelerated, and their kinetic energy is proportional to the square of their speed. [box=Red]In graphene, the behavior of electrons and holes is very different: The particles move with a constant speed vF that does not depend on their kinetic energy E.[/box] This is similar to the behavior of photons, which always travel at the speed of light c. In graphene, the speed of electrons and holes is slower than light by a factor of 300. Graphene also differs because there is [box=Red]no energy gap[/box]: The conduction and valence bands are shaped like an inverted pair of cones that meet in a single point at E = 0 in momentum space. The relativistic form of the energy bands is new for solids, and it changes the rules that govern how electrons move through a graphene-based device..pIA;zuc:t

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I.B1E![\i Novoselov et al. (8) found that one could control the carrier density in graphene in an unusual way. A positive gate voltage attracts electrons, so the Fermi energy lies at positive energies E > 0 in the cone-shaped conduction band. As the gate voltage is made less positive, the density of electrons decreases, but the conductance G does not fall to zero at E = 0, as it would in a normal semiconductor. Instead, it reaches a minimum value comparable to the quantum of conductance GQ = e2/ħ, where e is the electron charge, and ħ is Planck's constant. As the gate voltage is moved to negative values, the conductance increases again, because holes are attracted. Because there is no energy gap, it is not possible to deplete the carriers completely and drive the conductance to zero. New ways must then be found to make transistors.t`NT6I7YI'cb
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An even more unusual phenomenon occurs in graphene: The Klein paradox allows a relativistic particle to pass freely through a tall barrier of great width (10), whereas an ordinary particle would bounce backward, like a baseball after it hits a wall. As an electron approaches a potential barrier created by a gate, or by charged traps in the substrate, the electron's kinetic energy is reduced to zero as it hits the barrier. But instead of backscattering the electron, as one would expect, the barrier converts the electron into a hole, which is then attracted to the barrier potential and moves forward freely. When the hole exits the far side of the barrier, it turns back into an electron. The Klein paradox allows electrons to move through a graphene layer as if it were ideal. Graphene samples are not perfect, but are divided into pools of electrons or holes. Despite these imperfections, the charge carriers can move ~ 0.3 μm at room temperature with little scattering (5). This allows one to make ballistic transistors from such a simply prepared material."LiT"U\ w_6Y

2Eb9UAt7j Electrons in graphene show strong quantum behavior, even at room temperature, in part becaue of their freedom of motion. In the quantum Hall effect, the Hall conductance is quantized in integer multiples of GQ. To observe this effect, high quality samples, strong magnetic fields, and low temperatures ~4 K are usually needed. The quantum Hall effect has been observed in graphene (11, 12)--the quality of the data is very high, despite the simple methods used to produce the samples. It is interesting that the quantization of Hall conductance steps is different for graphene: They are spaced by 4GQ, with the lowest steps at ± 2GQ. These changes are caused by graphene's unusual band structure in which the electrons and holes travel at a constant speed. Recently, the quantum Hall effect in graphene has been observed at room temperature (13), which demonstrates its potential for quantum devices.*Gn-jxl1b*F
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The freedom of motion associated with the Klein paradox creates a problem: How does one confine charge carriers inside a device? A simple approach is to cut the graphene layer into the right shape, as for the quantum dot in the figure. Quantum confinement of electrons can also be used to control their motion. For example, a narrow ribbon of graphene (14) can effectively create an energy gap between the electron and hole bands, the magnitude of the gap being inversely proportional to the ribbon width. With an energy gap, one can then deplete the carrier concentrations with a barrier or gate, as with a conventional device.*eP`q9~(a?:Xmr'Z
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A quantum dot created by etching a graphene layer is shown on the left in the figure. A pool of electrons is confined inside a graphene disc that is connected to its leads by two narrow constrictions; a graphene side gate is used to tune the dot charge. Because they are very narrow, the conductance of these constrictions can be reduced to values <GQ, which allows the dot to trap individual electrons at low temperatures. In this regime, the quantum dot acts as a single-electron transistor, and its conductance shows a periodic set of peaks as the gate voltage is increased. By making very small graphene dots with sizes <100 nm, Pomonarenko et al. (1) were able to enter a regime where the conductance peaks are no longer periodic, but are instead controlled by the energy of the individual quantum states of electrons trapped inside. The measured energy distribution showed the electrons behaved as a chaotic quantum system (7), as one might expect for a dot that is not perfectly round. By etching the dots even smaller, they were able to achieve transistor operation at room temperature.e
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Graphene is an exciting new material with unusual properties that are promising for nanoelectronics. The carriers move freely, ignoring barriers created by imperfections, and they show quantum effects at room temperature. Through advances in fabrication and characterization building on those of Ponomarenko et al. (1), it may become possible to make quantum dots so small that they approach the molecular scale (see figure, right panel). The future should be very interesting.JzR*}R XT0I}L

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:capP$|%[;C [[i] 本帖最后由 dawnlight 于 2008-04-18 15:54 编辑 [/i]]

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[eK,\T{,M`8lQ+D Graphene is very prospective in electronic device application.

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11

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22

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