Graphene Flatland_Alice's Wonderland

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Information about Graphene Flatland_Alice's Wonderland

Published on March 4, 2014

Author: bijay_maniari


Flatland of Graphene is Alice’s Wonderland: Flatland of Graphene is Alice’s Wonderland Bijay Kumar Sharma, Emeritus Fellow, Electronics and Communication Engineering Department, National Institute of Technology,Patna-800005 E- 1 semiconductor industry - the main engine of growth of the World Economy: semiconductor industry - the main engine of growth of the World Economy Electronics Devices, Circuits and Systems and their related services are worth $5 Trillion which is 10% of total World’s real money market worth $50 Trillion. Electronics Circuits and Systems evolution and growth are driven by constantly shrinking device geometries and increased functionality that larger and denser Silicon IC Chips provide. 2 Impasse of 2025AD: Impasse of 2025AD This is becoming increasingly challenging and prohibitively costly and scaling below 9nm will come to a dead end sometime in near foreseeable future perhaps by 2025AD because of the physical limit. Graphene IC Chips are one of the alternatives which may become the enabling technology for further evolution of Electronics Systems. Graphene Technology may enableElectronics Industry retain its commanding position in World Economy . Hence urgent need to explore Graphene IC Chip Technology. 3 Conspicuous Absence of Graphene.: Conspicuous Absence of Graphene . Graphite and Diamond allotropes of Carbon were known from Ancient times. Recently Carbon Nano -Tubes and Fullerenes had been discovered. Three-dimensional (diamond, graphite), one-dimensional ( nanotubes ), and zero-dimensional (fullerenes) allotropes of carbon were known. The two-dimensional form was conspicuously missing, 4 Material Science of Graphene: Material Science of Graphene In 2004, Andre Geim and Konstantin Novoselov , two chemist at the University of Manchester in UK, peeled out a layer of graphite which we call graphene . Mechanical peeling is called EXFOLIATION. These are flat mono-layer of Carbon atoms, tightly packed into 2D honey-comb lattice, a living embodiment of 2D geometry in real life and taught in our text books. scientists believed that such a 2D structure would be unstable. 5 Graphene not known to exist.: Graphene not known to exist. Graphene was known to be an integral part of 3D Graphite. Graphene sheet was presumed not to exist in a free state. It was largely considered to be an “academic material” and believed to be unstable in real life. The melting temperature of the film rapidly decreases with decreasing thickness and they become unstable(segregate into islands or decompose) at a thickness of dozen of atomic layers. 6 0D,1D,2D and 3D allotropes of Carbon.: 0D,1D,2D and 3D allotropes of Carbon. 7 Exfoliation of Graphene.: Exfoliation of Graphene . Unexpectedly in 2004 free-standing graphene could be exfoliated . Follow up experiments proved that the charge carriers in graphene were indeed zero rest-mass Dirac Fermions and not Schrodinger Fermions . 8 Electrons and Holes in Si or GaAs: Electrons and Holes in Si or GaAs Electrons and Holes have nearly the mass of free electron. Electrons and holes are two separate entities. Electrons have much larger mobility than that of Holes. Independent Schrodinger Wave Functions have to be used to describe Electrons and Holes. 9 Graphene is an Exotic Condensed Matter System and Quantum Electrodynamic System even at Room Temperature.: Graphene is an Exotic Condensed Matter System and Quantum Electrodynamic System even at Room Temperature. Superconductor is an Exotic condensed Matter System at Liquid He Temperature i.e. at 4Kelvin. But Graphene is an Exotic condensed Matter System at Room Temperature of 300K. 10 Charge Conjugate Symmetry in Graphene.: Charge Conjugate Symmetry in Graphene . Charge Conjugate Symmetry is part of C(conjugate)-P(parity)-T(Time-Reversal) Invariance. Electron-Positron obey Conjugate Symmetry. Neutrino- antiNeutrino obey Conjugate Symmetry. Similarly electron- hole obey Conjugate Symmetry. Electron-Hole pair is equivalent to Electron-Positron pair. Hence Graphene behaves like Quantum- Electrodynamical system 11 Graphene is Relativistic: Graphene is Relativistic Electron and Holes are massless . Their weights are 0.007mass of free electron. Their velocities are c/3. 12 Graphene is Ambipolar: Graphene is Ambipolar Graphene is ambi -polar At zero-Voltage i.e. at charge neutrality point it is intrinsic; but becomes unipolar when it is electrically stressed. It can become n-type when positively biased and p-type when negatively biased. 13 Other Free-standing 2D monolayers: Other Free-standing 2D monolayers Soon after, free-standing 2D atomic crystals of other compounds were also discovered such as single layer Boron Nitride and half layer Bi 2 Sr 2 CaCu 2 O x [ Novoselov]. 14 Graphene is materia prima for other forms of Carbon.: Graphene is materia prima for other forms of Carbon. By creating topological defects, it can be wrapped up into 0D fullerenes, rolled into 1D carbon nanotubes (CNT) and stacked into 3D graphites . 15 0D Fullerenes: 0D Fullerenes 0D fullerenes are also known as Buckeyballs and have 60 C atoms. 12 pentagon plaquettes are required in addition to hexagonal plaquettes to produce the spherical configuration shown in Figure 2. Graphene rolled into 1D CNT , armchair or zigzag configuration, is shown in Figure 2. 16 Nano-tube of arm chair type (b) and of zigzag type(c).It is not necessary to introduce pentagons for producing nano-tubes as they have zero curvature. :  Nano -tube of arm chair type (b) and of zigzag type(c).It is not necessary to introduce pentagons for producing nano -tubes as they have zero curvature. 17 Zero Band Gap Graphene: Zero Band Gap Graphene 18 Graphene is amazingly tunable:: Graphene is amazingly tunable: E F can be tuned by chemical doping. E F can be tuned by the gate voltage. K (dielectric constant- strength of electron to electron interaction) depends on the substrate on which graphene is epitaxially grown. This ‘K’ introduces an asymmetry to ‘A’ and ‘B’ sub-lattices which in turn introduces a band gap in the otherwise metallic graphene . 19 Conductivity of Graphene: Conductivity of Graphene At 300K, mean free path of electron in graphene is several microns, an order of magnitude better than that in semi-conductors because of reduced phonon-electron interaction at 300K and hence this leads to intrinsic resistivity ρ(300K) = 30 ohm [Chen]. This corresponds to 1×10 -6 Ω-cm in 3D metal which is lower than that of Silver , Graphene is the most electrically conductive material till date. 20 Graphene Transmittance is governed by Fine Structure Constant.: Graphene Transmittance is governed by Fine Structure Constant. 21 Fine Structure Constant a Proof that Graphene is Quantum-electrodynamical: Fine Structure Constant a Proof that Graphene is Quantum- electrodynamical Fine structure constant α = e 2 /(4πε 0 ħc) ~ (1/137) shows the coupling between light and relativistic electron and it is traditionally associated with Quantum ElectroDynamics and not with material science. That graphene opacity is governed by the fine structure constant proves that graphene is a relativistic system and Quantum- electrodynamical system. 22 condensed matter physics which are governed by fundamental constants only and have nothing to do with material parametrers – these are Exotic: condensed matter physics which are governed by fundamental constants only and have nothing to do with material parametrers – these are Exotic (h/e 2 ) is the resisitivity quantum and appears in Quantum Hall Effect and in Universal Conductance fluctuations. (h/(2e)) is the magnetic flux quantum and appears in super conductivity. Similarly opacity of a single graphene is 1/137 determined by Fine Structure Constant. 23 electron-phonon scattering is independent of EF and nS (carrier concentration).: electron-phonon scattering is independent of E F and n S (carrier concentration). At n S = 1×10 12 /cm 2 , mean free path is greater than 2 micron and this results in intrinsic mobility of 200,000 cm 2 /(V-s). InSb mobility at room temperature which is 77,000 cm 2 /(V-s) and larger than that of Carbon Nano Tube (CNT) which is 100,000 cm 2 /(V-s). 24 Superlative Qualities of Graphene: Superlative Qualities of Graphene It has 100× tensile strength as compared to that of Steel. It has much better thermal conductivity than that of Diamond which till now was the most thermally conductive material. It is also most closely packed structure. It is impermeable to the smallest atom like Helium but it can stretch. 25 Tabulated Parameters of Graphene: Tabulated Parameters of Graphene Tensile Strength Young’s Modulus mobility Thermal Conductivity MPa GPa Cm^2/ (V-s) W/(m-K) Graphene 10^8 CNT 3000 Graphene 200,000 Graphene 3000- 5000 CNT 20,000 Diamond 3000 GaAs 8,000 Cu 300 Si 8,000 Graphene 1000 Diamond 2,000 Ag 280 Diamond 2,500 Steel 200 Si 1,450 Au 220 Steel 2,000 Si 180 Diamond 1500 26 graphene is a relativistic system goverened by Dirac Equations.: graphene is a relativistic system goverened by Dirac Equations. we can conclude that graphene is the thinnest, strongest, stiffest, most stretchable (almost 10%), having record thermal conductivity, permissible current density at 300K is 10 8 A/cm 2 million times higher than that of copper, highest intrinsic mobility (100 times that in Silicon), conducts electricity with zero carrier density, 27 Grahene is Quantum Electrodynamic System: Grahene is Quantum Electrodynamic System electrons and holes carriers behave like electron and positron in Quantum ElectroDynamic Systems and also behave like Dirac quasi particles, carriers have longest mean free path of the order of micron and are most impervious hence they cannot host interstitial dopents . 28 PowerPoint Presentation: Graphene is highly simplified and conceptually easy to visualize. Dirac Equation is obeyed by massless relativistic carriers even at Room Temperature. Psuedospin degree of freedom plays the role of relativistic spin. Dispersion of Electronics Band is described by a single parameter v F (Fermi Velocity) . The combination of simplicity and tunability makes graphene an ideal test bed for demonstrating fundamental condensed matter phenomena. 29

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