Resonance Popsci

7/29/2019 Resonance Popsci

1/16

238 RESONANCE March 2011

GENERAL ARTICLE

Graphene An Exciting Two-Dimensional Material forScience and Technology

Mandar M Deshmukh and Vibhor Singh

Keywords

Graphene, nanoelectronics,

massless electrons, NEMS.

Vibhor is a PhD student at

TIFR and got his MSc

from IIT Roorkee.

Mandar is a faculty

member at TIFR and is

interested in the broad

area of nanoscience. His

hobbies include photogra-

phy and long distance

running.

One atom thick graphene is derived from graphite

and is a new material; however, graphite has

been a part of human history for centuries. In

this article we discuss why it generates so much

excitement in a wide variety of scientic disci-

plines. We emphasize its electronic and mechan-

ical properties with an eye towards applications

that may impact our lives sooner, rather than

later. We also review methods to make this won-

der material, including the famous `scotch-tape'

technique that led to the Nobel-Prize winning

research.

1. Introduction

An intriguing question that researchers working in nano-

science are trying to answer is { how do electrons owdierently when they are conned to ow through struc-tures that are only about 10 nm in one of their dimen-sions? In most contemporary electronic devices, say ina computer's processor, the electrons ow through thedevices and interconnects in a manner very similar towater owing through the pipes in the plumbing systemof a typical home. What the connement at nanometerlengthscale does is to accentuate the wave-like natureof electrons, described by quantum mechanics. Answers

to questions like these are very pertinent as they willhelp in the development of the next generation of ma-terials and devices { this will aid in the miniaturizationand scaling of electronic components in line with theprediction of Moore's law [1]. Some of the answers tothe question also suggest that a completely new kind ofdevice based on qubits { smallest unit of computation


2/16

239RESONANCE March 2011

GENERAL ARTICLE

based on the ideas in the eld of quantum computing {are realizable in research labs.

In this quest for studying nanostructures several break-throughs have been made in the eld of materials sci-ence. The Nobel Prize winning discovery in 1996 ofa new form of carbon, C60, in the shape of a soccerball, besides already-known allotropes like diamond andgraphite, has led to a renewed focus on carbon-basednanostructures. Carbon with an atomic number of 6 hasan electronic conguration of 1s22s22p2. The outer shell

of 2s2 2p2 is very adaptable and can hybridize to formmolecular orbitals (starting with half-lled 2s1 2p3) thathave the hybridized character of both s and p orbitals.A hybridization of sp3 character leads to four orbitalswith tetrahedral symmetry as seen in diamond, sp2 hy-bridization leads to a hexagonal symmetry as seen ingraphite, graphene (we will revisit this in further detailshortly), carbon nanotubes and C60, and sp hybridiza-tion leads to organic molecules like acetylene.

The malleable nature of carbon's molecular orbitals canbe seen in the world around us dominated by carbonwhich is the key ingredient of the living world. As aresult of the discovery of C60, there is a push to devel-opment of electronics based on carbon. Ijima discoveredin 1991 another allotrope of carbon called carbon nan-otubes. Carbon nanotubes (CNT) with single walls con-sist of a single atom thick sheet of graphite (also calledgraphene) rolled into a seamless cylinder. Depending onthe diameter and the axis of rolling, these carbon nan-otubes were either metallic or semiconducting. As a nat-

ural sequence of scientic evolution researchers workedin several teams all over the world to isolate a singlelayer of graphene. This was a daunting task as makingmaterials that are atomically thick had not been donebefore { certainly not at the scale required to make elec-tronic devices [2].

sp

2

hybridizationleads to a

hexagonal

symmetry as seen

in graphite,

graphene, carbon

nanotubes and

C60.

Carbon nanotubes

(CNT) with single

walls consist of asingle atom thick

sheet of graphite

(also called

graphene) rolled

into a seamless

cylinder.


3/16


GENERAL ARTICLE

Figure 1. The lattice struc-

ture of graphene has hex-

agonal symmetry as indi-

cated by the red and bluecolored atoms taken to-

gether. This class of lattice

is not a Bravais lattice but

can be constructed from

two interpenetrating lat-

t ices o f eq uilateral t ri-

angles.

Andre Geim and Konstantin Novolselov came up withan ingenious method after years of eort [3] to isolatemonolayer graphene akes. As we discuss in more detaillater, they developed the `scotch tape' method whichrelies on taking a large crystal of graphite and peelingthe crystal repeatedly by using an adhesive tape to gen-erate a large number of thin crystals. Depositing thistape on a substrate of choice, like the 300 nm coating ofSiO2 on silicon allows one to optically image the layersand fabricate electrical devices. This simple idea behindthe discovery has led to a new eld that is growing veryrapidly and recently Geim and Novolselov were awardedthe Nobel Prize for their discovery [4]. It is important tounderstand the underlying science behind the materialto appreciate the impact of this discovery.

2. Understanding Graphene's Electronic Prop-

erties

It is interesting to note that the basic structure thatgives rise to graphite, carbon nanotubes and C60 isgraphene with sp2 hybridized molecular orbital; how-

ever, it was the last to be isolated. Figure 1 shows thehexagonal lattice structure of graphene that results from

Andre Geim andKonstantinNovolselov

came up with the

scotch tape method

which relies on taking

a large crystal of

graphite and peeling

the crystal repeatedly

by using an adhesive

tape to generate a

large number of thincrystals.


4/16


GENERAL ARTICLE

It is the half-filledshell of unhybridized

pz

that gives the

state its unique

electrical property

due to the overlap

with nearest

neighbours to form S

orbital.

the sp2

hybridization of the molecular orbitals startingfrom the half-lled outer shell of 2s1 2p3 (one can thinkof this as an intermediate state from the outer shell 2s2

2p2 prior to hybridization). The p orbital that is not hy-bridized is the pz orbital and is oriented perpendicularto the plane of the two-dimensional sheet. The hexago-nal lattice is not a Bravais lattice and that implies thatone can describe it only in terms of two interpenetratinglattices of equilateral triangles { one atom of red latticeat the centroid of the blue lattice (see Figure 1). Thesp2 bonds between the nearest neighbour atoms havea strong wavefunction overlap and give rise to a verystrong covalent bond. However, it is the half-lled shellof unhybridized pz that gives the state its unique electri-cal property due to the overlap with nearest neighboursto form orbital.

In order to better understand the electronic propertiesof any material it is important to understand the energy

(E) and momentum (!k ) relationship for dierent

!k {

also known as band structure of the material. The ori-

gin of the band structure is simply related to the factthat unhybridized pz, perpendicular to the plane, over-lap with nearest neighbours to form orbitals spreadout in energy and give rise to a band of states extendedover a range of energies. The result of such a calcula-tion, using the tight-binding approach, involves startingwith a linear combination of wavefunctions at blue andred sites (shown in Figure 1) and nding the energymomentum relationship taking into account the crystalstructures symmetry. Here it is incorporated by usingthe fact that a blue lattice point has three next nearestneighbours (in red) that have an angular spread of 120o.The result of such a calculation is shown in Figure 2a.

In general for a three-dimensional material the plot ofband structure is a 4-dimensional object as E(kx; ky; kz),an object that is dicult to visualize, whereas in the caseof graphene it is a 3-dimensional object as E(kx; ky).

In order to better

understand the

electronic properties

of any material it is

important to

understand the

energy (E) andmomentum

relationship for

different also

known as band

structure of the

material.

(!k )

!k


5/16


GENERAL ARTICLE

(a)

(b)

(c)

Figure 2. Understanding the bandstructure, essentially the energy and momentum relationship for

the electrons, of graphene. a) The plot of the two symmetric bands, namely conduction and

valence bands which meet at six points. The horizontal plane shows the position of the Fermi

energy of pristine undoped graphene. The electronic states, below the Fermi level, in the v alence

band are completely filled. b) The contour plot of the band-gap difference in the energy of

conduction and valence band at various values of electronic momentum. The dark purple region

at the center of six-triangular region indicates the region where the band-gap is zero. Of these, two

marked K and K are distinct and rest are mirror images of these two fundamentally distinct

Fermi-points. c) The electronic excitations take place at the top of the Fermi sea and consequently

the region of the bandstructure shown ina) that is most relevant is one near the Fermi energy. The

clear linear relationship very close to the Fermi energy between energy and momentum of the

electron leads to exciting physics. This linear E vs K relationship allows us to use the Dirac

equation by invoking the analogy with relativistic physics where the dispersion relationship is

similar. The electronic excitations inside graphene behave as if they have no mass.

The key things to notice are the fact that there are twobands (lower one in Figure2a is the valence band and the

upper one is the conduction band). The plane throughthe middle is the position of the Fermi energy, indicatingthat the valence band is completely lled and the con-duction band is empty. The reason behind a completelylled valence band and completely empty conductionband is that the starting set ofpz are exactly half-lledresulting in the nal bands of the solid being lled only


6/16


GENERAL ARTICLE

upto the valence band. The second key feature is thatthe conduction and valence bands touch at six points.Figure 2b shows the contour plot of the bandgap { thedierence in energy between the conduction and valenceband. We see that at six points the bandgap is zero andthe symmetry of the hexagonal crystal structure, in realspace, is reected in the symmetry in the momentum (k)space, as expected. The six points are also the points atwhich the Fermi energy cuts two bands and so the solidhas six Fermi points. From the symmetry of the startingproblem where we had to start with two lattices of redand blue sites to solve for E(kx; ky) there are only twodistinct Fermi points indicated by K and K0 while theother four are essentially mirror images of these two fun-damentally distinct Fermi points. The presence of thesetwo points has a profound eect on the degeneracy ofstates in graphene and carbon nanotubes { any statecould belong to either the K or K0 valley. Like the spinof an electron that has a two-fold degeneracy of up(")and down(#) spin, now there is an additional degree offreedom with K points. This additional degree of free-

dom is referred to as `pseudospin' { essentially a `fake'spin introduced to take care of the algebra associatedwith the quantum mechanics. So, for a pristine undis-torted (to preserve the hexagonal symmetry) graphenein the absence of a magnetic eld, the electronic statesof electrons are four-fold degenerate: 2 (from spin) 2(from pseudospin associated with K and K0 sites).

We now move further to another aspect of graphene'sE and k relationship that makes it very special. Tounderstand the electronic properties of any system oneneeds to only look at the excitations close to the Fermienergy because far away from EF (energies much largerthan kBT, with kB being the Boltzmann constant andT is the temperature), the states are either completelylled, or are completely empty, and hence unable to par-ticipate in `transitions' between states required for the

At six points thebandgap is zero and

the symmetry of the

hexagonal crystal

structure, in real

space, is reflected in

the symmetry in the

momentum (k)

space.

To understand the

electronic

properties of any

system one needs

to only look at the

excitations close to

the Fermi energy.


7/16


GENERAL ARTICLE

The electronicproperties are

determinedby

excitations,like

waves, on the

surface of the Fermi

sea; the states deep

below, or high

above the Fermi

energy are mostly

irrelevant forelectrical transport.

Graphene is a

wonderland for

studyingv ery

interesting quantum

mechanicalphenomena that

typically cannot be

studied in solid-state

devices, but could

only be seen in

particle accelerators.

spatial movement of electrons. Eectively the electronicproperties are determined by excitations, like waves, onthe surface of the Fermi sea; the states deep below, orhigh above the Fermi energy are mostly irrelevant forelectrical transport. The aforementioned fact is a subtleeect due to the Fermionic nature of electrons. So, tounderstand graphene's electronic properties one needsto `zoom-in' in very close to the Fermi energy and checkthe energy and momentum relationship of the electrons.

Figure 2c shows the `view' of the bandstructure close to

one of the Fermi points and one nds that the bandslook like two upturned cones. This implies that E/ kfor the excitations close to the Fermi energy. As a re-sult, the electronic excitations inside graphene behaveas if they are massless as their energy and momentumare linearly related, unlike electrons in most materials,where energy and momentum are quadratically related E / k2. This peculiar nature of electron's energyand momentum relationship makes them analogous torelativistic particles, say photons, where the energy and

momentum are linearly related. However, the electronsin graphene do not ow anywhere close to the velocity oflight (they travel at roughly 106 m/s, i.e., about 1/300the speed of light); they are analogous only because oftheir linear energy momentum (E/ k) relationship. Asa result graphene is a `wonderland' for studying very in-teresting quantum mechanical phenomena that typicallycannot be studied in solid-state devices, but could onlybe seen in particle accelerators. This unique E/ k rela-tionship implies that one cannot use Schrodinger equa-tion to describe the quantum mechanics of electrons but

have to use Dirac equation { a more appropriate quan-tum mechanical description.

In addition to the interesting nature of electrons, graph-ene is electronically an exciting material because it isstrictly a 2D (2-dimensional) system of electrons, mean-ing the electrons can move only in the plane and


8/16


GENERAL ARTICLE

Some very uniqueexperiments like the

quantum Hall effect,

which require a

2-dimensional

electron gas, can be

seen in graphene.

The basic recipe for

making graphene

using scotch tape

technique requires

using 300 nm of

SiO2-coated siliconwafer as a substrate

and cleaning it with a

harsh etchant to

remove any residue

that is adhering to the

wafer.

cannot move out of the plane { the degree of freedom is2-dimensional for translational motion of electrons. Asa result some very unique experiments like the quantumHall eect, which require a 2-dimensional electron gas,can be seen in graphene.

3. Making Graphene and Fabricating a Transis-

tor

How does one isolate a monolayer of graphene and char-acterize it? This is a question that several researchershave spent a lot of time thinking about. Several dier-ent techniques have been developed to isolate graphene.We discuss two techniques for making graphene { therst one, known as the `scotch-tape' technique [5], isa method that Nobel laureates Andre Geim and Kon-stantin Novoselov used for their work, and the secondone is based on CVD (chemical vapour deposition) andutilizes methane's pyrolysis over copper.

The basic `recipe' for making graphene using `scotchtape' technique requires using 300 nm of SiO2-coated

silicon wafer as a substrate and cleaning it with a harshetchant to remove any residue that is adhering to thewafer. Following this one patiently peels graphite bysandwiching it between scotch tape (something very sim-ilar to cellotape in India) repeatedly till the tape istranslucent. Dabbing the tape on the SiO2 wafer andpeeling it o leads to deposition of an assortment ofakes of dierent thicknesses on the surface. Examin-ing the surface with a simple optical microscope allowsone to sift through the debris and locate the very thinakes of graphene [5]. Figure 3a shows an optical mi-

croscope image of such a deposition. One can clearlysee that there are several akes with diering colours.The thickest ake at the bottom of the image hassilver color, like a typical metal, and is very thick( 500 nm), whereas ones that have a dark blue colorare 50 nm thick and the triangular ake that is


9/16


GENERAL ARTICLE

Figure 3. Making graphene.

a) An optical microscope

image of graphene after

peeling using the scotch-

t ap e t ec hn iq u e. T h e

300nm thick SiO2-coatedSi

wafer has a purple color

andthe color changessub-

tly w here lay ers of

graphene are deposited.

The triangular flapof mono-

layer graphene is clearly

s e en . O th e r fl ak e s o f

graphene show varying

color. b) Optical micro-

scope image of few layer

graphene grown using py-

rolysis of methane in a re-

ducing atmosphere of H2.

c) The steps behind the

CVD growth showing how

the pyrolyzed methane

leads to incorporation of

carbon atoms inside cop-per. As the growth system

is cooled to room tempera-

ture these carbon atoms

come to the surface due to

reduced solubility of car-

bon in copper; this leads

to the formatio n of

graphene on thesurface of

copper.

barely visible is monoloayer graphene. The `scotch-tape' method has evolved signicantly since the earlydays; meaning that as the technique has spread, researchgroups have adapted it to their `taste' by adding new in-sights and modifying the recipe. Much like the pav bhajion the streets of Mumbai { each one tastes slightly dif-ferent and is made dierently.

The `scotch tape' technique is an easy means to realizesmall-area akes of graphene. However, for applicationsand research one needs an alternate method to makegraphene on a large scale repeatably. In the last coupleof years scientists have developed a CVD process [6,7] toovercome the limitations of the `scotch tape' technique.Figure 3b shows graphene grown using the CVD tech-nique that uses the pyrolysis of methane in a reducingatmosphere at 1000oC on a copper foil. Figure 3c showsthe schematic of the key steps in CVD growth. Pyrol-ysis of methane leads to the solubility of carbon atomsin small concentration, into the copper foil. The key

reason behind using copper is that it supports a self-limiting concentration of carbon atoms to be dissolvedin the metal. As the temperature is reduced the solu-bility of carbon atoms reduces and they accumulate atthe surface forming monolayer and multilayer graphene.Following this the copper can be etched using a vari-ety of methods to realize a freestanding membrane of


10/16


GENERAL ARTICLE

Figure 4. How is graphene

visible? a) Cross-section

of the layer of graphene

deposited ona SiO2-coated

wafer. The ray diagram

shows one of a very large

number of paths a ray of

light tracedthoughthe mul-

tilayer. Graphene is visible

when the reflected light on

and off graphene (contrast

light) has a difference in

intensity for a given wave-

length of light. b) Contour

plot of contrast light (dif-

ference in the intensity of

reflected light on and off

graphene) as a function of

wavelength of light and the

thickness of the dielectric.

A large peak indicates a

high contrast and an in-

creased ability to see

graphene. The most com-monsubstrate for optically

o b servin g g rap hen e is

300nm of SiO2

and exhibits

large contrast.

(b)(a)

graphene. Peeled graphene is still the best way to getclean graphene. The mobility of electrons in CVD gra-phene is signicantly lower due to higher number of de-fects. One expects this to be xed as more research isdone on graphene growth. The advantage of the CVDprocess is that one can get large pieces of graphene. Re-cently, researchers in Korea have made 30inch30inchgraphene sheet using this technique.

We now try to understand how we can optically observesomething that is only one atom thick. A schematic ofthe stack of layers of lms modeling graphene [8] on aSiO2-coated wafer is seen in Figure4a. The colour of the

very thin ones has a specic colour due to interferenceof light and the physics of the colour of graphene is verysimilar to why one sees colourful bands when oil oatson water. Calculating the intensity of reected light othe surface of a stack of dielectric is done by summingup various `paths' by considering that at each interfacepart of the light is reected, and remaining transmittedwith the transmission in a medium leading to a relativephase dierence with the incident light as the opticalpathlength travelled will be dierent. Figure 4a showsone such `path' that contributes to reected light inten-sity. One can see graphene if the intensity of reectedlight on and o graphene is dierent [8] { note that thisis no dierent from a criterion one would use to see anyobject. Figure 4 shows a contour plot of dierence inthe intensity of light reected on and o graphene (acontrast function) [8]. One observes that whenever thecontrast function peaks for a given choice of thickness

Researchers in

Korea have made

30 inch u 30 inch

graphene sheet

using the CVD

technique.


11/16


GENERAL ARTICLE

Figure 5. Characterization of graphene transistor. a) After deposition of graphene the coordinates

of the flake are recorded and the electrodes patterned on it using electron beam lithography. This

is followed by deposition of chromium and gold to form the ohmic contacts and the electrodes are

clearly seen. b) Schematic of the circuit used to characterize a graphene transistor. A voltage VSD

is applied across the source (S) and drain (D) and the current (I) is measured. A voltage (VG) is

applied across the gate electrode. An applied negative voltage at the gate depletes the electrons

in graphene. c) Transistor response

of a graphene device.The resistance

of graphene device shows a peak in

resistance as the gate voltage is

swept from negative values of gate

voltage to positive values. This

changes the conduction in the de-vice from holes to electrons and

pa sses th ou gh the po int whe re

graphene has very few carrier giving

rise to the peak in resistance. The

insets show theposition ofthe Fermi

energy on the bond diagram for dif-

ferent gate voltages.

of SiO2 we can locate graphene using the optical tech-nique. The most popular substrate for making graphenedevices is 300 nm thick SiO2 as it has a large peak incontrast function over the visible wavelength range of400{600 nm. Optical observation just narrows downthe `very thin' graphene that may be a couple of mono-layers thick. To be sure that a ake is monolayer onehas to do further characterization { like Raman spec-troscopy which probes unique vibrational ngerprint ofthe hexagonal lattice of graphene, or study the quantumHall eect, as monolayer graphene has a very uniquequantum Hall signature [2,9,10].

Once a monolayer graphene ake is located, standardlithographic processes are used to pattern electrodes tomake a device. The result of such fabrication is seenin Figure 5a where the device was fabricated using theake shown in Figure 3a. The heavily-doped Si belowthe SiO2 serves as a gate for this transistor fabricated

Once a monolayergraphene flake is

located, standard

lithographic

processes are

used to pattern

electrodes to make

a device.

( )

( )

( )


12/16


GENERAL ARTICLE

The fact that agraphene transistor

cannot be turned off

is related to its band

structure and the fact

that it does not have

a band gap.

Another

consequence of the

strong covalent

bonds due to a large

overlap between the

nearest-neighbourcarbon atoms that

are sp2 hybridized, is

that the in-plane

Youngs modulus of

graphene is

~1 TPa.

using graphene. Figure 5b shows a schematic of thecircuit used to test the electrical response of the transis-tor. The resistance of monolayer graphene is monitoredas the gate is swept from negative to positive voltage.The most important feature of the data shown in Figure5c is that the resistance does not become very large {implying that the transistor never turns o. The factthat a graphene transistor cannot be turned `o' is re-lated to its band structure and the fact that it does nothave a band gap. As one starts from a negative valueof gate voltage the conduction occurs due to holes andthe Fermi energy EF is in the valence band (as seen ininset ofFigure 5c). When the gate voltage is reduced to0 V the Fermi energy is swept past the point where theconduction and valence bands meet at a point shown inFigure 2a and Figure 2c. At positive values of gate volt-age electrons are induced in graphene and eventually thedensity of carriers increases, leading to reduction in theresistance. The electrical properties are a direct reec-tion of the bandstructure that we discussed earlier.

No `o-state' of a graphene transistor means that sili-con transistors will not be replaced soon with graphenedevices. However, the big advantage that graphene tran-sistors oer is that they have very high mobility as theelectrons travel longer without undergoing scattering.So, graphene transistors are good candidates for veryspecialized high frequency applications where the tran-sistor needs to modulate the signal at very high frequen-cies 10 GHz { typical frequencies at which communi-cation using mobile phones takes place.

4. Mechanics Using Graphene Membrane

So far we have discussed the electronic properties ofgraphene; however, another consequence of the strongcovalent bonds due to a large overlap between the nearest-neighbour carbon atoms that are sp2 hybridized, is thatthe in-plane Young's modulus of graphene is 1 TPa.


13/16


GENERAL ARTICLE

Figure 6. Making a guitar

s tr in g u si ng a b e lt o f

graphene. a) Scanning

electronmicroscope image

of a suspended graphene

device. The scale bar cor-

responds to2Pm.b)Acolor

scale plot of the current

through the device as it is

driven at different frequen-

cies as g ate vo ltag e istuned to modify the in-

d u ce d t en s i on . c ) T h e

equivalence between vari-

ous resonant systems like

mass attached to a spring

and a percussion instru-

ment like sitar.

Due to the porousstructure of the light

carbon atoms and

immense structural

strength graphene is

emerging as a

desirable material for

composites to make

next generation of

airplanes that are

strong and light.

In addition to this, graphene can sustain 20% strain be-fore undergoing permanent deformation [11]. Due tothe `porous' structure of the light carbon atoms and im-mense structural strength graphene is emerging as a de-sirable material for composites to make next generationof airplanes that are strong and light.

At nanoscale as well, graphene possesses desirable me-chanical properties that are useful for making mechani-cal devices that can serve as very ne balances to mea-sure mass of small molecules. A large eld has devel-

oped over the last several decades studying nano elec-tromechanical systems (NEMS); graphene has a lot tooer to this exciting area. An example of such a sim-ple NEMS device is shown in Figure 6a which showsthe scanning electron microscope (SEM) image of sus-pended graphene tethered to conducting posts andhanging 150 nm above the substrate. Such a device isfabricated by rst making graphene much in the sameway Geim and Novoselov described and then followingsteps of nanofabrication to etch the surface underneath

to suspend it. This device is very similar to a sitar, or a


14/16


GENERAL ARTICLE

guitar string, but a million times smaller. Once this de-vice is realized one can resonantly excite, akin to pluck-ing, by sending electrical pulses to electrical connectionsand then detect, akin to hearing a pure note, by mea-suring some electrical signals, like the current throughthe device. What is this useful for? Such NEMS devicesare very sensitive detectors of mass and stress. Figure6b shows the `tuning' of the resonant frequency of thisdevice with a gate voltage that changes the tension {a small change in gate voltage results in a large changein frequency. The physics here is very similar to thechange in frequency of the sound that comes from a gui-tar string as the musician tightens the peg holding thestring. One interesting result we found in our researchwas to `listen to the note' as a function of tempera-ture and noticing that the note changes as the length ofthe graphene changes. By measuring the rate of changeof this `note' we could measure expansion coecient ofgraphene over a wide temperature range; we found itto be negative, meaning graphene will contract as oneheats it and expands when one cools it; another pecu-

liarity of graphene. Figure 6c shows a cartoon picturethat shows the equivalence between the resonance phe-nomenon in a mass attached to a spring and a guitarstring. As explained earlier the guitar strings and thegraphene NEMS device shown in Figure6a are very sim-ilar as well.

How does a NEMS device measure mass? It is easyto understand the principle if one looks at the spring-mass system in Figure6c and monitors the resonant fre-quency; one can detect when the buttery lands on it.The relative change in the resonant frequency f

f m

m,

where m is the change in mass and m is the mass of theresonator. To get the most sensitivity, implying large f

f

one would really like a small m so that even a small ad-ditional mass m leads to a large change in frequency.This sensitivity is the main reason why resonators based

One can resonantlyexcite, akin to

plucking, by sending

electrical pulses to

electrical connections

and then detect, akin

to hearing a pure

note, by measuring

some electrical

signals, like the

current through thedevice.

We could measure

expansion

coefficientof

graphene over a

wide temperature

range; we found it

to be negative,

meaning graphenewill contract as

one heats it and

expands when one

cools it; another

peculiarity of

graphene.


15/16


GENERAL ARTICLE

Suggested Reading

[1] http://en.wikipedia.org/wiki/Moore%27s_law

[2] K S Novoselov, A K Geim, S V Morozov, D Jiang,Y Zhang,S V Dubonos,

I V Grigorieva and A A Firsov, Science, Vol.306, p.666, 2004.

http://www.sciencemag.org/content/306/5696/666.abstract

[3] K S Novoselov, D Jiang, F Schedin, T J Booth, V V Khotkevich, S V

Morozov and A K Geim, Proceedings of the National Academy of

Sciences of the United States of Americ a, Vol.102, p.10451, 2005,

http://www.pnas.org/content/102/30/10451.abstract

[4] http://nobelprize.org/nobel_prizes/physics/laureates/2010/

[5] http://www.youtube.com/watch?v=rphiCdR68TE

The optical propertiesand the fact that

graphene can

transmit close to 97%

of light makes it a

good candidate for

electrodes for solar

cells.

The inherentflexibilityof the

material makes it

a leading

candidate for

realizingflexible

displays.

on graphene are desirable { they oer very low m andthe ability to detect small molecules.

5. Other Exciting Properties and What Future

Holds

We have pointed out only a small subset of propertiesthat make graphene exciting. However, the optical prop-erties and the fact that it can transmit close to 97% oflight makes it a good candidate for electrodes for solarcells. Graphene has very unique chemical properties andthe fact that it is chemically very stable makes it a verygood candidate for chemically resistant coatings. Theinherent exibility of the material makes it a leadingcandidate for realizing exible displays. Imagine a verythin display the size of a newspaper that you can foldand put in your wallet. Research in graphene is at itsinfancy and the coming ve years will indicate whetherthe research will impact a common person.

Irrespective of how the future of graphene turns out,the discovery and ongoing experimental research has a

common theme that simple ideas and ingenuity drivecutting edge research { not sophisticated equipments.Six years ago nobody could have imagined that fertileimagination, scotch tape and a small crystal of graphitecould lead to a Nobel Prize and also on the way energizea wide variety of research.


16/16


GENERAL ARTICLE

[6] X Li, W Cai, J An, S Kim, J Nah, D Yang, R Piner, A Velamakanni, I

Jung, E Tutuc et al., Science, Vol.324, p.1312, 2009,


[7] C Soldano, A Mahmood and E Dujardin, Carbon, Vol.48, p.2127, 2010.

http://www.sciencedirect.com/science/article/B6TWD-4Y9SVX0-1/2/

6c72d93b29a210eefa164f0be3d5337c;

http://arxiv.org/abs/1002.0370

[8] P Blake, E WHill,A HC Neto,K SNovoselov, D Jiang, RYang,T JBooth

and A K Geim, Applied Physics Letters, Vol.91, p.063124, 2007.

http://link.aip.org/link/APPLAB/v91/i6/p063124/s1 &Agg=doi;http://

arxiv.org/abs/0705.0259

[9] Y Zhang,. Y Tan, H L Stormer and P Kim, Nature, Vol.438, p.201, 2005.

http://dx.doi.org/10.1038/nature04235

[10] A H C Neto, F Guinea, N M R Peres, K S Novoselov and A K Geim,

Reviews of Modern Physics, Vol.81, p.109, 2009.

http://link.aps.org/doi/10.1103/RevModPhys.81.109;http://arxiv.org/

abs/0709.1163

[11] C Lee, X Wei, J W Kysar and J Hone, Science, Vol.321, p.385, 2008.


Address for Correspondence

Mandar M Deshmukh

and Vibhor Singh

Department of Condensed

Matter Physics and Materials

Science

Tata Institute of Fundamental

Research

Homi Bhabha Road

Mumbai 400005, India.

Email: [email protected]

[email protected]

Acknowledgements

This work was supported by

the G overnment of India.

Andre Geim was born in Sochi, Russia on October 1,

1958. Both his parents were Russian Germans engi-

neers. He obtained his PhD in 1987 in metal physics

from the Institute of Solid State Physics (ISS)) at the

Russian Academy of Sciences (RAS) in Chernogolovka.

In 2001 he became a professor of physics at the Univer-

sity of Manchester in UK and was appointed director of

t h e M an c he st er C en t re f or M e so sc ie n ce a n d

Nanotechnology in 2002.

Konstantin Novoselov was born in Nizhny Tagil, So-

viet Union, in 1974 in a Russian family. He received a

Diploma from the Moscow Institute of Physics and

Technology, and undertook his PhD studies at the

University of Nijmegen in the Netherlands before mov-

ing to the University of Manchester in UK with his

doctoral advisor Andre Geim in 2001. He now holds

both Russian and British citizenship.

The Two Physicists Sharing the Honour

Date post:	03-Apr-2018
Category:	Documents
Upload:	vishwas-gupta
View:	219 times
Download:	0 times

Resonance Popsci

Documents