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Abstract:
Graphene, which consists of just a single atomic layer of carbon atoms bound into crystal lattice, is the hottest new material system considered for applications in future electronics and sensors. The properties, which make graphene so desirable for future electronics, are its extremely high electrical and thermal conductivities. For any transistor to be useful for communications or information processing, the level of the electronic low-frequency noise (also referred to as 1/f or flicker noise) has to be reduced to an acceptable level defined by the Hooge parameter. Although modern electronic devices such as cell phones and radars operate at very higher frequencies (GHz range), the low-frequency 1/f noise is extremely important. Due to unavoidable non-linearities in devices and systems, the low frequency noise up-converts to higher requencies, and contributes to the phase noise of the system, thus limiting its performance. The same is true for the proposed applications of graphene as a material for ultra-sensitive detectors.
1. INTRODUCTION
GRAPHENE TRANSISTOR:-
A graphene transistor is a nanoscale device based on graphene, a component of graphite with electronic properties far superior to those of silicon. The device is a single-electron transistor, which means that a single electron passes through it at any one time. A research team led by Professor Andre Geim of the Manchester Centre for Mesoscience and Nanotechnology built a graphene transistor. Scientists have predicted that graphene transistors could scale to transistor channels as small as two nanometers (nm) with terahertz speeds. The base of the graphene transistor is graphene.
Now before going to discuss about grapheme transistor(carbon nanotubes) lets take a brief introduction about GRAPHENE.
2.GRAPHENE
2.1.Introduction:-
Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. It can be viewed as an atomic-scale chicken wire made of carbon atoms and their bonds. The name comes from GRAPHITE + -ENE; graphite itself consists of many graphene sheets stacked together. Carbon is one of the most versatile chemical elements. Because it can form single, double and triple bonds, it forms thousands of chemical compounds, and has numerous elemental structures, or allotropes. The most common allotropes of carbon are diamond and graphite. Diamond consists of carbon atoms single-bonded to four other carbon atoms producing a tetrahedral crystal lattice. Its structure leads to its extreme hardness and thermal conductivity, but diamond is a very poor electrical conductor. In contrast, graphite consists of stacked layers of carbon sheets. Within an individual carbon sheet, known as graphene, the carbon atoms are sp2 hybridized and form a planar hexagonal lattice. The sp2 hybridization means that the carbons are -bonded in the plane, but are also -bonded above and below the plane. Graphene thus possesses one of the strongest bonds in nature and has a very high tensile strength. Graphene’s perpendicular p-orbitals lead to electron delocalization because there is no distinction between neighboring  bonds, as indicated in Figure below.
Fig.1 Aromatic hydrocarbons like benzene shown here, share electrons in the p-orbitals with many neighboring atoms.
This conjugated  orbital system permits the electrons to travel freely above and below the plane of carbon atoms with minimal scattering. Because of the minimal scattering and strong delocalization of the electrons, graphite is a good conductor along the plane. However, in graphite, electrostatic forces bind the layers together only very weakly, and graphite is a very soft mineral. In addition, the other layers interfere with the behavior of the single sheets, even if not strongly. An ideal system would be to study free single-layer graphene, but until a few years ago, two-dimensional systems like free graphene were believed to be impossible.
In recent years, the two most familiar allotropes of carbon have been joined by a number of newly discovered graphene-like materials. The first major graphene-related substance discovered was C60, also known as buckminsterfullerene, buckyball, and fullerene, a soccer-ball-like configuration of carbon atoms found in common lamp soot and known to be very stable. Soon, the scientific community encountered similar fullerene-type carbon structures called a carbon nanotubes. Carbon nanotubes are needle-like tubes of rolled up graphene sheets that exhibit many unusual and useful properties such as extreme tensile strength and high conductivity. .
2.2 Graphene’s Charge Carriers Are Relativistic
But why is there such interest in graphene? Aside from the obvious interest in the novelty of a two-dimensional crystal, graphene crystals exhibit unusual electrical properties that may prove useful both theoretically and practically. In particular, graphene’s charge carriers are very unusual in that they behave like massless Driac fermions and are most effectively described by the Dirac equation rather than the non-relativistic Schrödinger equation:
EN = [2ehc2 B(N+1/21/2)]1/2.
Fig.3 Formation of 0D, 1D and 3D carbon materials from Graphene.
2.3 Anomalous Quantum Hall Effect in Graphene
In addition, graphene also exhibits an anomalous quantum hall effect. In classical electromagnetism, the Hall effect arises when a magnetic field is applied perpendicular to the surface of a solid carrying a current parallel to the surface. The Lorentz force causes positive and negative charges to build up on opposite sides of the solid, parallel to the current, producing a potential difference known as the Hall voltage. The direction the voltage points determines the charge of the charge carriers in the material. The quantum Hall effect (QHE) is identical to the classical Hall effect except that the Hall voltage (and consequently the Hall resistivity and the Hall conductivity) occurs only in discrete steps equal to an integer times e2/h. In addition to the integer quantum Hall effect, there is another effect known as the fractional quantum Hall effect in which the Hall conductivity is equal to e2/h times a rational fraction that is less well understood. In the presence of a magnetic field, graphene produces yet another quantum Hall effect known as an anomalous quantum Hall effect. In the case of graphene, the Hall conductivity occurs in discrete integer steps like the conventional QHE, but is shifted by one-half of an integer as shown below in figure
Figure.4 A plot of the Hall conductivity xy (red) and the Hall resistivity xy (green) as a function of carrier concentration.
Graphene is an ideal system for examining the quantum Hall effect for a number of reasons. First, graphene samples are available in such purity that the charge carrier concentration can be tuned continuously from high concentrations of electrons to high concentrations of holes simply by changing the gate voltage. Second, the purity of the graphene samples is so high that the QHE can be observed even at room temperature, whereas most materials only exhibit the QHE at much lower temperatures. Finally, graphene’s anomalous quantum Hall effect, by being shifted by half compared to most systems, exhibits non-zero conductivity even as the charge carriers change from electrons to holes (the neutrality point or the Dirac point). For most materials, as the charge carrier concentration tends towards zero, so does the conductivity, so that there is a metal to insulator transition at no temperatures. But graphene has shown no signs of a metal-insulator transition even down to liquid helium temperatures.
2.4 The Future Of Graphene
Aside from the anomalous quantum Hall effect, one of the most exciting prospects for graphene is that it may eventually prove useful in electronic applications. Graphene’s high conductivity and its unusual electronic properties may lead to unexpected advances in processor and electronic technologies. After carbon nanotubes have so far failed to revolutionize the field, scientists are cautious in advertising the possible future applications of graphene. For graphene, it is too early to tell whether graphene will significantly affect the field of commercial electronics, but it’s small scale and unusual properties may contribute to the development of nanoscopic electronic components or quantum computing. Graphene has been used to produce a functional transistor even though this initial proof of concept transistor leaks electrons and is highly inefficient.
Scientists acknowledge that graphene will be an important material in future technologies. It might be used to store hydrogen in fuel cells or in batteries as electrodes. It may serve a use in the production of ultra-thin fabrics that require great strength. If glues are used between the graphene layers, it might be possible to assemble very strong materials. Its chemistry can be controlled to change its electrical properties to be conducting, insulating or semiconducting. It may even prove useful in the possible development of quantum computing. Graphene’s immense potential is especially exciting considering how easy and cheap it is to produce.