Research Article Capacitance Variation of Electrolyte

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2013 Article ID 836315 5 pageshttpdxdoiorg1011552013836315

Research ArticleCapacitance Variation of Electrolyte-Gated BilayerGraphene Based Transistors

Hediyeh Karimi12 Rubiyah Yusof12 Mohammad Taghi Ahmadi34 Mehdi Saeidmanesh3

Meisam Rahmani5 Elnaz Akbari1 and Wong King Kiat5

1 Centre for Artificial Intelligence and Robotics Universiti Teknologi Malaysia 54100 Kuala Lumpur Malaysia2Malaysia-Japan International Institute of Technology Universiti Teknologi Malaysia 54100 Kuala Lumpur Malaysia3 Computational Nanoelectronic Research Group Faculty of Electrical Engineering Universiti Teknologi Malaysia81310 Johor Malaysia

4Nanotechnology Research Center Nanoelectronic Group Physics Department Urmia University Urmia 57147 Iran5 Faculty of Electrical Engineering Universiti Teknologi Malaysia 81310 Skudai Johor Malaysia

Correspondence should be addressed to Rubiyah Yusof rubiyahicutmmy

Received 15 March 2013 Accepted 8 July 2013

Academic Editor Raquel Verdejo

Copyright copy 2013 Hediyeh Karimi et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Quantum capacitance of electrolyte-gated bilayer graphene field-effect transistors is investigated in this paper Bilayer graphenehas received huge attention due to the fact that an energy gap could be opened by chemical doping or by applying externalperpendicular electric field So this extraordinary property can be exploited to use bilayer graphene as a channel in electrolyte-gatedfield-effect transistorsThe quantum capacitance of bi-layer graphene with an equivalent circuit is presented and also based on theanalytical model a numerical solution is reported We begin by modeling the DOS followed by carrier concentration as a function119881 in degenerate and nondegenerate regimes To further confirm this viewpoint the presented analytical model is compared withexperimental data and acceptable agreement is reported

1 Introduction

Recently graphene an atomic layer of carbon atoms arrangedin a two-dimensional (2D) honeycomb lattice has drawn re-searchersrsquo attention due to its exceptional mechanical andelectrical properties for new semiconductor materials anddevices [1ndash3] Bilayer graphene (BLG) the stacking of two-monolayer graphene as a newmaterial with outstanding elec-trical and physical properties holds the great promise to beused as a conducting channel in FETs [4 5] The energy dis-persion relation of conductance and valence bands of eachgraphene layer is linearly touching on Dirac points [6] Asshown in Figure 1 the two layers are arranged in Bernal stack-ing which its lattice constant within a layer is given by 119886 =

0246 nm and the layer spacing by 119889 = 0334 nm BLG is typ-ically arranged in AA-stacked and AB-stacked arrangementsA bandgap in BLGs can be created by applying a perpendic-ular electric field and incorporating the inversion symmetry

breaking between double layers in the atomic structure Twodifferent stacking shapes of the BLG (AA AB) in layers resultfrom interlayer coupling effects in low energy which showsa different band structure [7] The study had shown that AA-stacked BLG is gapless metallic [8] whereas AB-stacked BLGis semiconductingwith a bandgap and the bandgap is tunablein the presence of external electric field perpendicular to theBLG [9]

Nowadays electrolyte-gated bilayer graphene field-effecttransistors (EGFETs) have caughtmuch attention due to theiradvantages such as small size and the possibilities for massproduction Their short and consistent response times arevery favorable to the electronics industry EGFETs introducednew features such as the integration of compensation anddataprocessing circuits in the same circuit for this type of sensors[10] Recently microelectronic advances have been exploitedand applied to improve EGFETs fabrication Because of theelectrolyte ionic properties electrical parts of EGFETs cannot

2 Journal of Nanomaterials

Bilayer graphene

AA-stacking AB-stacking

d = 0334nm

Bilayer graphene

AB t ki

d =

Figure 1 Schematic of bilayer graphene AA- and AB-stacking

have contact with liquid only the gate area is open EGFETscan be based on many materials as their detectors such asmembrane and graphene [11] On the other hand in 2011Ye et al presented a comparative study of high carrier densitytransport in ion-gated mono- bi- and trilayer graphenesusing electric double-layer transistors [12]

In this paper EGFET has been employed to study theelectron transport of graphene [13] As shown in Figure 2 thebilayer graphene based electrolyte-gated transistor consists ofsource and drain (gold) in which anAB stacked of the bilayergraphene sheet which is employed as a conducting channelon an oxidized siliconSiO

2substrate is proposed Therefore

a back gate controlled the current through the graphene Aphotoresist layer as an insulator has been employed which re-sults in the creation of a small window which exposes theelectrolyte [14] The interfacial capacitance of the graphenewas measured by the standard three-electrode electrochemi-cal cell using a potentiostat which the potential of grapheneis controlled with respect to a reference electrode (a platinumelectrode) [15] By assuming that the source and substrate ter-minals are held at ground potential the channel region hasthe characteristics of the resistor in small voltage between thesource and drain (119881DS) [16] It is notable that by applyingthis configuration the background capacitance can be mini-mized and the graphene edges do not expose to the electro-lyte To control the gate voltage precisely a platinum counterelectrode is included to form the standard three-electrodeelectrochemical configuration

The focus of this paper is to model the quantum capacit-ance of bilayer graphene based EGFET To address this possi-bility two interfacial capacitances which arise from thedouble layer formed by ions at the graphene ionic liquid inter-face and the quantum capacitance of graphene have a stronginfluence on themeasurement of the total capacitance To un-derstand the electrical response of the bilayer graphenebased EGFET device an electrical equivalent circuit for thementioned structure is developed and discussed in Figure 3

It can be seen in Figure 3 that the equivalent circuit iscomposed of an ohmic resistance of a solution (119877s) in ser-ies with the double-layer capacitance and the quantum

capacitance of bilayer graphene In order to present the acc-umulation of a layer of counterions on a charged electrode119862double layer is defined [17] The capacitance versus potentialof a double-layer graphene device was measured in ionicliquid in 1-butyl-3-methylimidazolium hexafluorophosphate(BMIMPF6) which can be expressed as 119862double layer = 120576

0120576119905

where 1205760= 885 times 10

minus12 Fmminus1 is the dielectric constant of theionic liquid and it is the radius of the counterions [18] ForBMIM-PF

6ionic liquid 120576 asymp 7 and 119905 asymp 03 nm which leads

to double-layer capacitance of asymp 21 120583Fcmminus2 [16] It could bestated that the quantum capacitance of the bilayer graphenebased electrolyte-gated FETs can bemodeled holding the factthat the smaller of the two capacitances dominates the totalcapacitance [19] On one hand the double-layer capacitancecan be neglected compared to the predicted quantum capac-itance of bilayer graphene while on the other hand thedouble-layer capacitance is not strongly dependent on thepotential making it straightforward to determine the quan-tum capacitance of bilayer graphene In 2009 the quantumcapacitance of bilayer graphene in an ionic liquid electrolytewasmeasured byXia et al [18] He found out that in hismeas-urements Debye ionic screening length of the ionic liquid isvirtually zero which makes the quantum capacitance a domi-nant source of the measured capacitance The aim of thisstudy is to evaluate the quantum capacitance of bilayer gra-phene sheet as a function of voltage and validate theoreticalpredictions with the experimental results [18]

2 Proposed Model

An important quantity in the design of nanoscale devices isthe quantum capacitance To model a theoretical predictionof quantum capacitance for ideal bilayer graphene based elec-trolyte-gated FETs the expression for quantum capacitance isused [20] as follows

119862 =120597119876

120597119881 (1)

where 120597119876 = 119890 120597119899 is the charge measured in coulombs 119890is the charge of the electron 119899 is the BLGrsquos intrinsic carrier

Journal of Nanomaterials 3

Bilayer grapheneCE

Source-drain electrodes(Au)

VsdVref

Au

SiO2

Si

REIonic liquid electrolyte

Insulation layer

+

minus

Figure 2 Schematics of the proposed structure and the electrical circuit of the bilayer graphene based EGFET

Bilayer graphene

Bilayer graphene based EGFET Equivalent circuit

Back gate

Vref

Au AuSiO2

Si

Ioni

c liq

uid

elec

troly

te

SourceDrain

120576 d

Rs

CQ

Cdouble layer

Figure 3 Equivalent circuit of bilayer graphene based electrolyte-gated field-effect transistor

concentration and 120597119881 = 120597119864119890 is the voltage applied to thedevices where119864 is energy By the substitution of the quantumcapacitance model (2) can be expressed as

119862 = 1198902 120597119899

120597119864 (2)

According to (2) the carrier concentration and the energydispersion of BLG is necessary to be calculated for model-ing the quantum capacitance Understanding the electronicstructure of bilayer graphene starts with looking at its bandstructure It has been shown that the bandgap of BGNs canbe varied by means of an external perpendicular electric fieldand induced significant bandgap between the valence andconduction bands from a zero-gap semiconductor to an insu-lator [21ndash24] The energy band structure of AB which isstacking biased BGN using tight-binding method has beenstudied in [25] Equation (3) illustrates energy (119864) and biased

voltage (119881) relationship of BGN The energy dispersion ofBLG is expressed as

119864 (119896) =1198811+ 1198812

2

plusmn radic1205762

119896+1198812

4+1199052

perp

2plusmn1

2radic4 (1198812 + 1199052

perp) 1205762

119896+ 1199054perp

(3)

where 1205762119896= (V4(4 + V21199052

perp2))(V2 + 1199052

perp) is electronrsquos dispersion

in monolayer graphene [26] 119905perp= 035 eV is an interlayer

hopping energy [6]1198811and119881

2are the potential energy of first

and second layers respectively and 119881 is the potential energydifference between first and second layers (119881 = 119881

1minus 1198812) By

using the energy dispersion of BLG density of state (DOS) asa fundamental parameter of BLG indicates available energystates that can be defined as

DOS = ( ℎ2

119898lowast

(119896 minus 119896119892)

1198962120587)

minus1

(4)

where ℎ is the reduced Plankrsquos constant and 119898lowast is the

effective mass of electron in the BLG 119896119892is defined as 119896

119892=

(1198812120592119865ℎ)radic(119881

2+ 21199052perp)(1198812 + 1199052

perp) where 120592

119865= (radic23) at ℎ asymp

1 times 106m sdot sminus1 is the Fermi Velocity 119896 is defined as 119896 =

plusmn[2119898lowast(119864 minus 119864

119888)ℎ2]12

+119896119892where 119864

119888= 1198641198922+(119881

1+1198812)2 and

119864119892is the energy gap DOS indicates available energy states It

is notable that electrical property of materials from metallicto semiconducting is changing by the gradient of DOS nearthe Dirac point In the next step the carrier concentration ofBGL is given by

119899 = intDOS sdot 119891 (119864) 119889119864 (5)

where 119891(119864) = 1(1 + 119890(119864minus119864119891)119896119861119879) is the Fermi-Dirac distribu-tion function which gives the probability of occupation of astate at any energy level In this function119864

119891is the Fermi level

119896119861is Boltzmannrsquos Constant and 119879 is the temperature Using

DOS calculated from (4) the carrier concentration reads

119899 =119898lowast

ℎ22120587int

+infin

0

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

119889119864 (6)

where 1198961015840=(119896 minus 119896g) As depicted in Figure 4 the carrier con-centration is plotted for different values of 119881


5

4

3

2

1

0

times1017

Carr

ier c

once

ntra

tion

(mminus2)

0 05 1 15 2 25 3 35 4 45 5

E (eV)

V (eV)= 05

V (eV)= 04

V (eV)= 03

Figure 4 Carrier concentration versus energy (119864)

43

425

42

415minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)

Figure 5 The quantum capacitance of bilayer graphene basedelectrolyte-gated FETs

It is apparently seen that the calculated carrier concen-tration model points out the strong dependence of voltageshowing that the voltage increment effect will influence thecarrier concentration Substituting the carrier concentrationin (2) the quantum capacitance of BLG is expressed as

119862 =1199022119898lowast

ℎ22120587

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

(7)

Equation (7) provides a quantitative description of the quan-tum capacitance of bilayer graphene in terms of Fermi veloc-ity [27] carrier density temperature and fundamental physi-cal quantities According to the relation between energy bandstructure and the graphene potential the quantum capac-itance-voltage characteristic of bilayer graphene is depictedas shown in Figure 5

The overall quantum capacitance versus gate potential forthe bilayer graphene is similar to that of a single layer gra-phene To get a greater insight into the quantum capacitanceof bilayer graphene based electrolyte-gated FETs devices sev-eral outstanding features of the 119862-119881 characteristics are em-barked First of all the quantum capacitance possesses amin-imum value at the Dirac point which is close to zero On theother hand the linear increase of the capacitance with a volt-age which is symmetric with respect to the Dirac point canbe considered as the other perceptible feature of the quantumcapacitance model In order to validate the proposed model

43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)

ExperimentModel

Figure 6 Comparison between bilayer graphene quantum capaci-tance model with experimental extracted data

the comparison between the quantum capacitance model ofbilayer graphene based electrolyte-gated FETs with extractedexperiment data is done as illustrated in Figure 6 [18]

It is noteworthy that the theoretical slope is greater thanthe measured slope for bilayer graphene A possible explana-tion for thismight be that the suggestedmodel is based on thepure and ideal bilayer graphene in which in reality variousimpurities and defects exist It seems possible that these re-sults are due to the fact that the impurities can drasticallylower the slope for bilayer graphene However unlike singlelayer graphene a theory for treating impurities in bilayer gra-phene has not yet been developed [18]These findings furthersupport the idea of the effects of impurities on both the firstand second layers which requires a self-consistent theory toinclude the screening of the impurity field by the carriers inboth layers This is further complicated by the possibility ofimpurities intercalated between the two layers Further exper-imental studies should be done to investigate the quantitativeunderstanding of bilayer graphene It is apparently seen thatthere is a favorable agreement between the proposed modelof bilayer graphene based electrolyte-gated FETs and experi-mental results It can be concluded that the presented modelcan be applied as a powerful tool to optimize the bilayer gra-phene based electrolyte-gated FETs performance

3 Conclusion

BLGs can be employed in digital electronics because theirbandgap can be varied bymeans of an external perpendicularelectric field and can induce a significant bandgap betweenthe valence and conduction bands turning it from a zero-gapsemiconductor to an insulator Carriermobility values as highas 200000 cm2 (Vs)minus1 (200 times higher than in silicon) canbe achieved by graphene which are increased by increasingcarrier density [22] According to the graphene structure itcan satisfy our major requirement of a channel in electrolyte-gated FETs due to its large surface-to-volume ratio highconductivity high mobility and strong mechanical and elas-ticity properties The aim of this paper was to model the


quantum capacitance of bilayer graphene based electrolyte-gated FETs with an equivalent circuit of the proposed deviceFor purposes of verification a comparison study between themodel and experimental data was done and notable agree-ment is reported which shows that bilayer graphene basedelectrolyte-gated FETs model can be used to predict bilayergraphene behavior in graphene based devices

Acknowledgments

The authors would like to acknowledge the financial supportfrom the ResearchUniversity Grant of theMinistry of HigherEducation of Malaysia (MOHE) under Project MJIIT-4J010Also they thank the ResearchManagement Center (RMC) ofthe University of Technology Malaysia (UTM) for providingan excellent research environment to complete this work

References

[1] M Acik and Y J Chabal ldquoNature of graphene edges a reviewrdquoJapanese Journal of Applied Physics vol 50 no 7 Article ID070101 2011

[2] D Guo D Zhang and L Zhang ldquoSparse representation-basedclassification for breath sample identificationrdquo Sensors andActuators B vol 158 no 1 pp 43ndash53 2011

[3] T Jayasekera P K Pillalamarri JWMintmire and VMeunierldquoEffect of phase-breaking events on electron transport in meso-scopic and nanodevicesrdquo International Journal of QuantumChemistry vol 108 no 15 pp 2896ndash2905 2008

[4] K S Novoselov S VMorozov TM GMohinddin et al ldquoElec-tronic properties of graphenerdquo Physica Status Solidi B vol 244no 11 pp 4106ndash4111 2007

[5] K S Novoselov E McCann S V Morozov et al ldquoUnconven-tional quantum Hall effect and Berryrsquos phase of 2120587 in bilayergraphenerdquo Nature Physics vol 2 no 3 pp 177ndash180 2006

[6] K S Novoselov A K Geim S V Morozov et al ldquoTwo-dimen-sional gas of massless Dirac fermions in graphenerdquo Nature vol438 no 7065 pp 197ndash200 2005

[7] Y Xu ldquoInfrared and Raman spectra of AA-stacking bilayer gra-phenerdquo Nanotechnology vol 21 no 6 Article ID 065711 2010

[8] X Zhong R Pandey and S P Karna ldquoStacking dependent elec-tronic structure and transport in bilayer graphene nanorib-bonsrdquo Carbon vol 50 no 3 pp 784ndash790 2012

[9] Y GuoW Guo and C Chen ldquoSemiconducting to half-metallicto metallic transition on spin-resolved zigzag bilayer graphenenanoribbonsrdquo Journal of Physical Chemistry C vol 114 no 30pp 13098ndash13105 2010

[10] S C Chen Y-K Su and J S Tzeng ldquoThe fabrication and char-acterisation of ion-sensitive field-effect transistors with a silicondioxide gaterdquo Journal of Physics D vol 19 no 10 pp 1951ndash19561986

[11] S Martinoia and P Massobrio ldquoISFET-neuron junction circuitmodels and extracellular signal simulationsrdquo Biosensors andBioelectronics vol 19 no 11 pp 1487ndash1496 2004

[12] J Ye M F Craciun M Koshino et al ldquoAccessing the transportproperties of graphene and its multilayers at high carrier dens-ityrdquoProceedings of theNational Academy of Sciences of theUnitedStates of America vol 108 no 32 pp 13002ndash13006 2011

[13] T Ono Y Fujimoto and S Tsukamoto ldquoFirst-principles cal-culation methods for obtaining scattering waves to investigate

transport properties of nanostructuresrdquoQuantumMatter vol 1pp 4ndash19 2012

[14] Y Ouyang Y Yoon and J Guo ldquoScaling behaviors of graphenenanoribbon FETs a three-dimensional quantum simulationstudyrdquo IEEE Transactions on Electron Devices vol 54 no 9 pp2223ndash2231 2007

[15] I Heller S Chatoor J Mannik M A G Zevenbergen C Dek-ker and S G Lemay ldquoInfluence of electrolyte composition onliquid-gated carbon nanotube and graphene transistorsrdquo Jour-nal of the American Chemical Society vol 132 no 48 pp 17149ndash17156 2010

[16] F Karimi M T Ahmadi M Rahmani E Akbari M J Kianiand M Khalid ldquoAnalytical modeling of graphene-based DNAsensorrdquo Science of AdvancedMaterials vol 4 pp 1142ndash1147 2012

[17] E Dubuisson Z Yang and K P Loh ldquoOptimizing label-freeDNA electrical detection on graphene platformrdquo AnalyticalChemistry vol 83 no 7 pp 2452ndash2460 2011

[18] J Xia F Chen J Li and N Tao ldquoMeasurement of the quantumcapacitance of graphenerdquo Nature Nanotechnology vol 4 no 8pp 505ndash509 2009

[19] D Wei M J A Bailey P Andrew and T Ryhanen ldquoElectro-chemical biosensors at the nanoscalerdquo Lab on a Chip vol 9 no15 pp 2123ndash2131 2009

[20] D L John L C Castro and D L Pulfrey ldquoQuantum capaci-tance in nanoscale device modelingrdquo Journal of Applied Physicsvol 96 no 9 pp 5180ndash5184 2004

[21] H Y Xu T Heinzel and I V Zozoulenko ldquoEdge disorder andlocalization regimes in bilayer graphene nanoribbonsrdquo PhysicalReview B vol 80 no 4 Article ID 045308 2009

[22] W Zhu V Perebeinos M Freitag and P Avouris ldquoCarrier scat-tering mobilities and electrostatic potential in monolayer bi-layer and trilayer graphenerdquo Physical Review B vol 80 no 23Article ID 235402 2009

[23] G M Rutter J N Crain N P Guisinger P N First and J AStroscio ldquoStructural and electronic properties of bilayer epitax-ial graphenerdquo Journal of Vacuum Science and Technology A vol26 no 4 pp 938ndash943 2008

[24] S Russo M F Craciun M Yamamoto S Tarucha and A FMorpurgo ldquoDouble-gated graphene-based devicesrdquo New Jour-nal of Physics vol 11 Article ID 095018 2009

[25] J Nilsson A H Castro Neto F Guinea and N M R PeresldquoElectronic properties of bilayer and multilayer graphenerdquoPhysical Review B vol 78 no 4 Article ID 045405 2008

[26] E V Castro K S Novoselov S V Morozov et al ldquoElectronicproperties of a biased graphene bilayerrdquo Journal of PhysicsCondensed Matter vol 22 no 17 Article ID 175503 2010

[27] N Paitya S Bhattacharya D De and K P Ghatak ldquoInfluenceof quantizing magnetic field on the fowler-nordheim fieldemission from non-parabolic materialsrdquo Quantum Matter vol1 pp 63ndash85 2012

Submit your manuscripts athttpwwwhindawicom

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Biomaterials


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Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Bilayer graphene

AA-stacking AB-stacking

d = 0334nm

Bilayer graphene

AB t ki

d =

Figure 1 Schematic of bilayer graphene AA- and AB-stacking

have contact with liquid only the gate area is open EGFETscan be based on many materials as their detectors such asmembrane and graphene [11] On the other hand in 2011Ye et al presented a comparative study of high carrier densitytransport in ion-gated mono- bi- and trilayer graphenesusing electric double-layer transistors [12]

In this paper EGFET has been employed to study theelectron transport of graphene [13] As shown in Figure 2 thebilayer graphene based electrolyte-gated transistor consists ofsource and drain (gold) in which anAB stacked of the bilayergraphene sheet which is employed as a conducting channelon an oxidized siliconSiO

2substrate is proposed Therefore

a back gate controlled the current through the graphene Aphotoresist layer as an insulator has been employed which re-sults in the creation of a small window which exposes theelectrolyte [14] The interfacial capacitance of the graphenewas measured by the standard three-electrode electrochemi-cal cell using a potentiostat which the potential of grapheneis controlled with respect to a reference electrode (a platinumelectrode) [15] By assuming that the source and substrate ter-minals are held at ground potential the channel region hasthe characteristics of the resistor in small voltage between thesource and drain (119881DS) [16] It is notable that by applyingthis configuration the background capacitance can be mini-mized and the graphene edges do not expose to the electro-lyte To control the gate voltage precisely a platinum counterelectrode is included to form the standard three-electrodeelectrochemical configuration

The focus of this paper is to model the quantum capacit-ance of bilayer graphene based EGFET To address this possi-bility two interfacial capacitances which arise from thedouble layer formed by ions at the graphene ionic liquid inter-face and the quantum capacitance of graphene have a stronginfluence on themeasurement of the total capacitance To un-derstand the electrical response of the bilayer graphenebased EGFET device an electrical equivalent circuit for thementioned structure is developed and discussed in Figure 3

It can be seen in Figure 3 that the equivalent circuit iscomposed of an ohmic resistance of a solution (119877s) in ser-ies with the double-layer capacitance and the quantum

capacitance of bilayer graphene In order to present the acc-umulation of a layer of counterions on a charged electrode119862double layer is defined [17] The capacitance versus potentialof a double-layer graphene device was measured in ionicliquid in 1-butyl-3-methylimidazolium hexafluorophosphate(BMIMPF6) which can be expressed as 119862double layer = 120576

0120576119905

where 1205760= 885 times 10

minus12 Fmminus1 is the dielectric constant of theionic liquid and it is the radius of the counterions [18] ForBMIM-PF

6ionic liquid 120576 asymp 7 and 119905 asymp 03 nm which leads

to double-layer capacitance of asymp 21 120583Fcmminus2 [16] It could bestated that the quantum capacitance of the bilayer graphenebased electrolyte-gated FETs can bemodeled holding the factthat the smaller of the two capacitances dominates the totalcapacitance [19] On one hand the double-layer capacitancecan be neglected compared to the predicted quantum capac-itance of bilayer graphene while on the other hand thedouble-layer capacitance is not strongly dependent on thepotential making it straightforward to determine the quan-tum capacitance of bilayer graphene In 2009 the quantumcapacitance of bilayer graphene in an ionic liquid electrolytewasmeasured byXia et al [18] He found out that in hismeas-urements Debye ionic screening length of the ionic liquid isvirtually zero which makes the quantum capacitance a domi-nant source of the measured capacitance The aim of thisstudy is to evaluate the quantum capacitance of bilayer gra-phene sheet as a function of voltage and validate theoreticalpredictions with the experimental results [18]

2 Proposed Model

An important quantity in the design of nanoscale devices isthe quantum capacitance To model a theoretical predictionof quantum capacitance for ideal bilayer graphene based elec-trolyte-gated FETs the expression for quantum capacitance isused [20] as follows

119862 =120597119876

120597119881 (1)

where 120597119876 = 119890 120597119899 is the charge measured in coulombs 119890is the charge of the electron 119899 is the BLGrsquos intrinsic carrier


Bilayer grapheneCE


VsdVref

Au

SiO2

Si


Insulation layer

+

minus


Bilayer graphene


Back gate

Vref

Au AuSiO2

Si

Ioni

c liq

uid

elec

troly

te

SourceDrain

120576 d

Rs

CQ

Cdouble layer



119862 = 1198902 120597119899

120597119864 (2)



119864 (119896) =1198811+ 1198812

2

plusmn radic1205762

119896+1198812

4+1199052

perp

2plusmn1

2radic4 (1198812 + 1199052

perp) 1205762

119896+ 1199054perp

(3)

where 1205762119896= (V4(4 + V21199052

perp2))(V2 + 1199052






1minus 1198812) By


DOS = ( ℎ2

119898lowast

(119896 minus 119896119892)

1198962120587)

minus1

(4)



119892=

(1198812120592119865ℎ)radic(119881

2+ 21199052perp)(1198812 + 1199052

perp) where 120592




119888)ℎ2]12

+119896119892where 119864

119888= 1198641198922+(119881

1+1198812)2 and



119899 = intDOS sdot 119891 (119864) 119889119864 (5)





119899 =119898lowast

ℎ22120587int

+infin

0

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

119889119864 (6)



5

4

3

2

1

0

times1017

Carr

ier c

once

ntra

tion

(mminus2)

0 05 1 15 2 25 3 35 4 45 5

E (eV)

V (eV)= 05

V (eV)= 04

V (eV)= 03


43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)



119862 =1199022119898lowast

ℎ22120587

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

(7)



43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)

ExperimentModel




3 Conclusion




Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Bilayer grapheneCE


VsdVref

Au

SiO2

Si


Insulation layer

+

minus


Bilayer graphene


Back gate

Vref

Au AuSiO2

Si

Ioni

c liq

uid

elec

troly

te

SourceDrain

120576 d

Rs

CQ

Cdouble layer



119862 = 1198902 120597119899

120597119864 (2)



119864 (119896) =1198811+ 1198812

2

plusmn radic1205762

119896+1198812

4+1199052

perp

2plusmn1

2radic4 (1198812 + 1199052

perp) 1205762

119896+ 1199054perp

(3)

where 1205762119896= (V4(4 + V21199052

perp2))(V2 + 1199052






1minus 1198812) By


DOS = ( ℎ2

119898lowast

(119896 minus 119896119892)

1198962120587)

minus1

(4)



119892=

(1198812120592119865ℎ)radic(119881

2+ 21199052perp)(1198812 + 1199052

perp) where 120592




119888)ℎ2]12

+119896119892where 119864

119888= 1198641198922+(119881

1+1198812)2 and



119899 = intDOS sdot 119891 (119864) 119889119864 (5)





119899 =119898lowast

ℎ22120587int

+infin

0

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

119889119864 (6)



5

4

3

2

1

0

times1017

Carr

ier c

once

ntra

tion

(mminus2)

0 05 1 15 2 25 3 35 4 45 5

E (eV)

V (eV)= 05

V (eV)= 04

V (eV)= 03


43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)



119862 =1199022119898lowast

ℎ22120587

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

(7)



43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)

ExperimentModel




3 Conclusion




Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




5

4

3

2

1

0

times1017

Carr

ier c

once

ntra

tion

(mminus2)

0 05 1 15 2 25 3 35 4 45 5

E (eV)

V (eV)= 05

V (eV)= 04

V (eV)= 03


43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)



119862 =1199022119898lowast

ℎ22120587

119896

1198961015840

1

1 + 119890(119864minus119864119891)119896119861119879

(7)



43

425

42


Qua

ntum

capa

cita

nce (

Fcm

)

times10minus6

V (eV)

ExperimentModel




3 Conclusion




Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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