arX

iv:1

108.

2012

v1 [

cond

-mat

.mes

-hal

l] 9

Aug

201

1

Electrically Controlled Adsorption of Oxygen in Bilayer Graphene Devices

Yoshiaki Sato,1, ∗ Kazuyuki Takai,1 and Toshiaki Enoki1

1Department of Chemistry, Tokyo Institute of Technology, 2-12-1 Ookayama,

Meguro-ku, Tokyo, 152-8551, Japan

We investigate the chemisorptions of oxygen molecules on bilayer graphene (BLG) and its elec-trically modified charge-doping effect using conductivity measurement of the field effect transistorchanneled with BLG. We demonstrate that the change of the Fermi level by manipulating the gateelectric field significantly affects not only the rate of molecular adsorption but also the carrier-scattering strength of adsorbed molecules. Exploration of the charge transfer kinetics reveals theelectrochemical nature of the oxygen adsorption on BLG. [This document is the unedited Au-thor’s version of a Submitted Work that was subsequently accepted for publication in Nano Letters,c©American Chemical Society after peer review. To access the final edited and published work seehttp://dx.doi.org/10.1021/nl202002p .]

Keywords: Graphene; charge transfer; field effect transistor; electron transport; mobility; band gap

It has been a central topic of surface science how tocontrol the adsorption and desorption in order to tobring out desirable features and functionalities by ad-sorbed molecules. Tuning the electronic features of solidsurfaces has an important implication in that molec-ular chemisorptions and catalytic reactions are deter-mined by them1,2. In particular for graphene, the two-dimensional honeycomb carbon lattice, in which the con-duction π∗-band and the valence π-band contact to eachother at the “Dirac point” giving a feature of zero-gapsemiconductor3, the control of chemisorption is a criticalissue since chemisorption directly leads to altering everyelectronic property of graphene. Other than the elec-tron/hole doping4 owing to the charge transfer betweengraphene and the adsorbed molecules, widely known arethe charged impurity effect on the electron transport5–7,lattice deformation8, and opening the band gap dueto asymmetric adsorption9–11. Aside from the macro-scopic spatially-controlled adsorption that is achieved us-ing nano-device fabrication technique12, microscopic con-trol of adsorption structure is of great importance be-cause the aforementioned adsorption effects are alteredby the local structure of adsorbate, e.g., whether theadsorbed molecules are arranged in a random or su-perlattice structure10,13, or whether the molecules areadsorbed individually4,14 or collectively (in dimers15 orclusters16,17). For the first step to realize such anadvanced control of adsorption, the methods to uti-lize the interaction between the adsorbed molecules andgraphene for it are to be explored.

The principal impetus in the present study is to con-trol the charge transfer between graphene and the ad-sorbed molecules by tuning the Fermi level of graphene,which is readily accomplished in the field effect transis-tor (FET) structure. When SiO2/Si substrate is usedas the back-gate insulator of the FET, the tuning rangeof the Fermi level of graphene by the application of thegate voltage is at the extent of several ±0.1 eV18 whichwould be sufficient to alter the chemical reactivity onthe surface. Besides, the additional charge and the gra-dient of electric potential generated by the gate electric

SiO2SiO2SiO2

Vg,ad+−

−+

gatevoltage

200

240

280

320

360

0

0

100

12

34

5

200

300

400

500

600

Doping Density (×1012cm−2)

Mob

ility

(V

scm

−2 )

O2 E

xp

osu

re T

ime

(m

in)

−50 V

0 V

+40 V

+80 V

field are expected to change the polarization of adsorbedmolecules19,20 and to modify the charge distribution ongraphene layers and the adsorbed molecules21–25 leadingto, e.g., the change in the ease of migration of moleculesadsorbed on graphene26. Some research27–29 argues thatthe change in the Fermi level caused by a gate electricfield activates electrochemical redox reactions and theaccompanying charge transfer causes hysteresis of thesource–drain current in graphene FET, yet there has beenno investigation that elucidates the relation between thekinetics of adsorption to graphene and gate electric field.In this study we investigated gate-tuned molecular oxy-gen adsorption through systematic measurements of con-ductivity using mainly bilayer graphene (BLG).The back-gated BLG-FETs were fabricated on SiO2

(300 nm thick) on heavily n-doped silicon substrate bymeans of photolithography. The channel length andwidth were 6 µm and 3.5 µm, respectively. Prior to mea-surement, we repeated vacuum annealing (210◦C, 10 h)to remove the adsorbed moisture and contaminants onthe surface until no more changes in the gate-dependentconductivity σ were eventually seen. After the anneal-ing, the BLG-FET exhibited its pristine nature, that is,ambipolar transport properties with a conductivity min-imum around Vg = V

0CNP < 8 V giving the “ charge neu-

trality point (CNP)” with electrons and holes in BLGbeing equal in density. The Drude mobility µ(n) wasestimated to be ∼ 1 × 103 cm2V−1s−1 from the equa-tion µ(n) = σ/e|n|, where n is the carrier density withn = (cg/e)(Vg − VCNP) (cg/e = 7 × 1010 cm−2V−1;

http://arxiv.org/abs/1108.2012v1http://dx.doi.org/10.1021/nl202002p

2

1 atmroom temperature

Vg,ad+

−

Vg(sweep)

VDSA

in vacuumin O2

measuring conductivity

0

0 40 80−80 −40

2

4

6

Vg−V0CNP (V)

0

2

4

6

0

2

4

6 pristine

0.5-min exposure

1-min exposure

+80 V

+80 V

+40 V

+40 V

−50 V

+80 V

+40 V

−50 V

−50 V

Vg,ad

Co

nd

uctivity (

×10

–4

Ω–

1)

−60 −40 −20 0 20 40 60 80

0

1

2

3

4

5

6

7

Co

nd

uctivity (

×1

0−

4Ω

−1)

Vg (V)

1 min

pristine

5.5 min

31 min

178 min

O2 Exposure

a

b

c

FIG. 1: (a) Schematic of the measurement cycle. First, the field effect transistor channeled by bilayer graphene (BLG-FET) isexposed to gaseous O2 while the gate voltage Vg,ad is applied (left panel). Then the system is evacuated and the source–drainconductivity of the BLG-FET is measured by sweeping the gate voltage Vg (right panel). Subsequently gaseous O2 is againintroduced, and the cycle is repeated. The gas introduction and evacuation are completed in a shorter time than ∼ 10 s toprevent additional gas from adsorption. The whole cycle is executed at room temperature. (b) Change of the field effectbehavior due to the O2 exposure with Vg,ad = 0 V (run 1). The gate voltage giving the minimum conductivity (the chargeneutrality point), is shifted from Vg = V

0CNP (< 8 V) (marked by a brown triangle, before O2 exposure) to the positive direction

(green triangles) upon O2 exposure. Circles on the curves represent the conductivity at the hole density of 2.5 × 1012 cm−2

that are used to calculate Drude conductivity shown in Figure 4a. (c) The same measurement as in the panel (b) with applyingthe finite Vg,ad . All the curves are shifted by −V

0CNP (V

0CNP = 13, 9, and 11 V for the run of Vg,ad = +80, +40, and −50 V,

respectively) in Vg direction, i.e., the charge neutrality points of the pristine graphene without the adsorbed oxygen are taken aszero gate voltage. The top panel of (c) represents the σ vs Vg −V

0CNP for the pristine graphene. The changes of σ vs Vg −V

0CNP

curve after a single and a double exposure to O2 (the time duration of a single exposure is 30 s) are shown in the center andthe lower panel of (c), respectively. Filled circles indicate Vshift = VCNP − V

0CNP (the shift of the CNP) for each curve.

cg is the capacitance per unit area for the back-gatedgraphene FET on 300 nm-thick SiO2 )

22, It is in therange of the values for BLG-FET in two-probe config-uration previously reported6, and therefore we confirmthat the graphene of the present BLG-FET has few de-fects that may extremely enhance the chemical reactivityof graphene30.

Next we exposed the BLG-FET to 1 atm of high-purity (>99.9995%) oxygen in the measurement cham-ber at room temperature. Instead of measuring conduc-tivity with graphene kept in the O2 environment, weperformed the short-time interval exposure–evacuationcycles schematically shown in Figure 1a; O2 exposurewas done under the dc gate voltage Vg,ad, followed byrapid evacuation in less than 10 s (the physisorbed O2molecules would be removed immediately without chargetransfer), and eventually the σ vs Vg measurement was

done with sweeping Vg under vacuum. In this cycle, wecan rule out the possibility of the additional oxygen ad-sorption during sweeping gate voltage for the σ vs Vgmeasurement since the system was evacuated then. Inaddition, we found that the σ vs Vg curve did not varyunder vacuum at room temperature at least for morethan several hours, so that we can also rule out the pos-sibility of the oxygen desorption during σ vs Vg mea-surement (taking ca. 10 min to obtain a single σ vsVg curve). Therefore, just repeating the cycles substan-tially realizes the long-time O2 exposure under Vg,ad, thelength of which is denoted by total O2 exposure time,t. Figure 1b shows the change in σ vs Vg by repeat-ing the O2 exposure-evacuation cycles without applyinggate voltage during O2 exposure (run 1, Vg,ad = 0 V).The shift of the charge neutrality point by the amountof Vshift(t) = VCNP(t) − V 0CNP toward the positive di-

3

---- --

++

+

0

10

20

30

40

50

60

70

O2 Exposure Time (min)

0.1 1 10 100 1000 10000

1

2

3

4

5

0

no

x (

×1

01

2 c

m−

2)

Vg,a

d =

−50

V

Vg,a

d =

+80

V

Vg,a

d =

+40

V

Vg,a

d =

0V

electrondominant

hole dominant

Vsh

ift (V

)

Run 1

Run 4

Run 5

Run 2

Run 3

2

5

3

FIG. 2: Time dependence of Vshift and doping density nox with doping due to the O2 exposure under application of variousVg,ad. Solid and dotted curves are the fits based on the H kinetics and the P kinetics (see text), respectively. The curve fittingis made in the range of exposure time below 2000 min. The electron-dominant region, where the Fermi level of BLG is higherthan the CNP (Vg,ad > VCNP), is painted blue and the hole-dominant region (Vg,ad < VCNP) is painted white. Carrier type isinverted between electron and hole at the point indicated by arrows (numbers aside correspond to the run number) during theevolution of the oxygen adsorption.

rection was observed (Figure 1b), which represents holedoping to graphene. Prolonged exposure brought furtherhole doping, and eventually the doping density (inducedcharge by the oxygen adsorption) nox(t) = (cg/e)Vshift(t)reached more than 5 × 1012 cm−2 within a time scaleof 103 min. Note that any hysteresis as observed ingraphene FET in moist atmosphere29,31–34 was not foundin the observed σ vs Vg curve, so that we can uniquely de-termine VCNP(t) as a function of t. Another remarkablefeature is the hole conductivity in highly doped regime,Vg − VCNP(t) < −40 V (i.e., |n| > 3 × 1012 cm−2). Theσ vs Vg curve distorted and exhibited the sublinear de-pendence in this regime for the pristine BLG-FET as canbe seen in Figure 1b. Yet it disappeared only after theexposure to O2 for 1 min, whereas the carrier doping hasnot proceeded much at that time. Thus this rapid changein conductivity feature is discriminated from the slowerchange causing the shift of the CNP; one possibility isthat the former is due to rapid oxidation of the metal–graphene interface35,36, which does not shift the Fermilevel of graphene but asymmetrically varies the conduc-tivity.

Both VCNP and the mobility of the BLG-FET withthe oxygen adsorbed were reset to the value for the pris-tine BLG-FET by annealing the O2-exposed BLG-FETin vacuum at 200 ◦C, indicating that O2 desorption read-ily proceeds at high temperature without making anydefects. By virtue of this reversibility of the oxygen ad-

sorption, we can repeat the conductivity measurementsin the exposure–evacuation cycles as described above forthe same device and compare the results. We addition-ally carried out four consecutive measurements under thesame condition except that a finite gate voltage Vg,ad wasapplied during O2 exposure; Vg,ad was +80 V (run 2 andrun 3), −50 V (run 4) and +40 V (run 5). Figure 1crepresents the change of the gate-dependent conductiv-ity σ vs Vg − V 0CNP at the initial step of the runs 2, 4,5: before O2 exposure, (i.e., after vacuum annealing)and after the first and second exposure–evacuation cy-cles (the duration time for O2 exposure in each cycle is30 s, i.e., t = 0.5, 1 min, after the first and second cycle,respectively). All the σ vs Vg − V 0CNP curves collapsedonto almost the identical curve in the pristine grapheneas shown in the top panel of Figure 1c. Since V 0CNP waswithin 10±3 V for each run (see the caption of Figure 1),the BLG-FET was realized to exhibit its pristine featurebefore O2 exposure. After the O2 exposure (the centerand the bottom panel of Figure 1c) the gate-dependentconductivity changes similarly as was also observed forrun 1 (Figure 1b), but the effect of applying Vg,ad duringO2 exposure is marked by the clear difference in Vshift(t).There is a tendency that Vshift(t) is larger for higher Vg,adand smaller for lower Vg,ad, indicating that hole dopingproceeds more intensively to graphene with higher Fermilevel. This trend is pronounced on the increase in the ex-posure time, as confirmed by comparing the center and

4

+80 V

+40 V

±00 V

−50 V

Vg,ad

0.1 1 10 100 1000

1013

1012

1011

1010

109

O2 exposure time (min)

dn

ox

/ d

t (c

m−

2 m

in−

1)

FIG. 3: Double logarithmic plot of time dependence ofdnox/dt. Symbols are taken in common with Figure 2. Weestimate dnox/dt from the differential between the neighbor-ing data points for each run in Figure 2. Lines are linear fitsfor all the differential data. The slope of each curve gives u =1.02, 0.91, 0.86, and 0.77 (dnox/dt ∝ t

−u) for the gate voltageVg,ad = +80, +40, 0, and −50 V, respectively.

the bottom panel of Figure 1(c).

We tracked the temporal evolution of the gate-dependent conductivity over a wide time range between100–103 min. Figure 2 represents Vshift for runs 1–5 withrespect to O2 exposure time, in which the correspond-ing doping density owing to the oxygen adsorption, nox,is also shown in the right axis. The tendency that thehigh Vg,ad leads to rapid doping can be seen clearly overa whole time range; e.g., to reach the doping level ofVshift = 40 V, it took ca. 300 min for nonbiased BLG-FET. In contrast, hole doping is so enhanced for theBLG-FET of Vg,ad = 80 V that it took only 4 min, on theother hand so suppressed for that of Vg,ad = −50 V thatit took more than 1000 min. The doping density increasesalmost linearly with respect to log t for Vg,ad = +80 Vand +40 V, whereas superlinearly for Vg,ad = 0 V and−50 V. The plots for runs 2 and 3, having commonVg,ad = +80 V, are completely on the same line, whichverifies that the thermal annealing in vacuum for the re-producing of the undoped state in the BLG does notaffect the behavior of adsorption.

Figure 3 shows the time dependence of the dopingrate dnox/dt estimated from the differential betweenthe neighboring data points in Figure 2. It is obvi-ous that the doping rate changes in accordance withdnox/dt ∝ t−u. The power u is dependent on Vg,ad; u ≈ 1for Vg,ad = +80 V and it decreases for the runs withlower Vg,ad. This deviates from the conventional Lang-murian kinetics for molecular adsorption which wouldgive dnox/dt ∝ exp(−t/τ) with a constant τ .Careful verification is necessary to inquire the gate-

voltage-dependent and non-Langmurian temporal change

of the molecular doping since the rate for doping densitydnox/dt is related to both of the rate for the chemisorp-tion of molecules (dNox/dt, whereNox is the areal densityof the adsorbed oxygen molecules) and the transferredcharge per adsorbed molecule (the charge/molecular ra-tio, Z). Therefore, we analyze the mobility that in-cludes the information of the scattering mechanism ofthe conducting electrons and the charge of the adsorbedmolecules. Within a standard Boltzmann approach37,the mobility is changed inversely proportional to thedensity of the scattering centers (i.e., the adsorbedmolecules), Nox. In the realistic case, the inverse mobil-ity is given as a function of Nox and the carrier densityn, which reads5

1

µ(n,Nox)=

NoxC(n)

+1

µ0(n)(1)

Here µ0(n) represents the mobility of the pristinegraphene without the adsorbed oxygen. The coefficientC(n) represents the feature of carrier scattering by theadsorbed oxygen. On the one hand, the charged-impurityscattering38 gives C(n) ∝ [1 + 6.53√n (d+ λTF)]/Z2for the BLG in the low-carrier-density regime andin the limit of d → 0 within the Thomas–Fermiapproximation38, where d is the distance between theimpurities and the center of the two layers of the BLG(see the inset of Figure 4a for the definition), and thescreening length λTF = κh̄

2/4m∗e ≈ 1 nm (κ: dielectricconstant)38. On the other hand, the short-range delta-correlated scatterers give the constant C(n) ≡ Cs38, orthe strong impurities with the potential radius R giveC(n) ∝ [ln(R√πn)]2 in the off-resonance condition39,which is a decreasing function of n in the regime ofn ∼ 1012 cm−2 taking R to be several angstroms. As forthe relation between the concentration of the adsorbedoxygen molecules Nox and the O2-induced doping den-sity nox, we assume that the charge Ze of each adsorbedoxygen molecule dopes the carriers −Ze in the BLG, no-tably, nox = −ZNox. To be exact, the amount of theinduced charge is not such a simple function6 propor-tional to the number of adsorbed molecules due to theenergy-dependent DOS of BLG40,41 and the anomalis-tic screening effect therein5,6,42. Yet in the low energyregime of BLG where the DOS is envisaged to be con-stant, the assumption above is appropriate.Figure 4a shows the inverse Drude mobility µ−1 vs

nox plots at the carrier density of n = 2.5 × 1012 cm−2(marked by the open circles in Figure 1b for run 1:Vg,ad =0 V) for Vg,ad = +80, +40, 0, and −50 V. Linear increasein µ−1 with respect to nox was found. This, along withthe linearity between µ−1 and Nox given by Eq. (1), im-plies that Z is not a function ofNox, i.e., invariant againstthe increase of the adsorbed molecules. Interestingly, theslope of µ−1 vs nox plot (the inverse of the slope corre-sponds to C(n)|Z| in Eq. (1)) depends on Vg,ad. Notethat before O2 was introduced (nox = 0), we observedµ−1 ≈ 28 V sm−2 irrespective of Vg,ad, and thus the dif-ference in the mobility by Vg,ad genuinely results from

5

10 5

50

40

30

20

2 3 4

Doping density, nox (×1012 cm−2)

1/μ

(V

sm

−2

)

SiO2 AdsorbedMolecules

BLGd

Ze Ze Ze Ze Ze

+80 V

+40 V

0 V

−50 V

+80 V

+40 V

±00 V

−50 V

Vg,ad

Vg,ad

a

b

0 1 2 3 4 5 60

2

4

6

C|Z

| (×

10

15 V

−1

s−

1)

Carrier density, n (×1012 cm−2)

FIG. 4: (a) Inverse mobility µ−1 vs the doping density noxfor each run in Figure 2. Symbols are taken in common withFigure 2. Lines are linear fits (as for Vg,ad = +80 V, thedata for both run 2 and run 3 are included). Inset: Adsorbedoxygen species with charge Ze positioned at the distance daway from the center of BLG. (b) C|Z| vs the carrier densityn (see Eq. (1)). For Vg,ad = +80 V, C|Z| is acquired bygathering the data for run 2 and run 3. Theoretical resultsbased on a charged-impurity scattering mechanism are shownwith the various distance d and charge/molecular ratio Z: thesolid line represents the result for d = 0.43 nm and Z = 0.38,the dashed line for d = 0.73 nm and Z = 0.38, and the dottedline for d = 0.43 nm and Z = 0.28, respectively.

the adsorbed oxygen instead of other unintentional im-purities on the BLG or the SiO2 substrate. In Figure 4b,the inverse of the slope, C(n)|Z|, is shown for the var-ious carrier densities, n. Therein we omit the data inthe low carrier regime of n < 2.5 × 1012 cm−2, in whichthe residual carriers due to electron–hole puddles can-not be disregarded and the carrier density n (and thusalso the Drude mobility) cannot be correctly estimatedonly by considering the gate electric field effect43. Sim-ilarly to the charged impurity model rather than oth-erwise, C(n)|Z| is increasing with n. The dependenceexperimentally observed, however, still deviates from thetheoretical calculated results within the charged impuritymodel plotted in Figure 4b for various d and Z (assumingd and Z are invariant to n).

The difference in C(n)|Z| depending upon Vg,ad indi-cates that the electronic polarity of graphene varies theadsorption states of oxygen molecules, leading to the vari-ation of d and Z. When the positive (negative) Vg,ad isapplied, negative (positive) carrier is electrically inducedon graphene, which may modify the interaction betweengraphene and the adsorbed oxygen molecules with thenegative charge, e.g., the Coulomb interaction and theoverlap of the orbitals. Eventually, the stable adsorptionstate is varied by Vg,ad, leading to the difference in mo-bility. Besides, let us recall that conductivity measure-ment process is set apart from the O2 adsorption processand that constant Vg,ad is not applied when the mobilityis measured (Figure 1a). Accordingly, whereas the sta-ble adsorption state of oxygen during the conductivitymeasurement may differ from that during adsorption, theadsorbed oxygen molecules are kept in the former stateduring conductivity measurement, and the mobility vary-ing by Vg,ad is actually observed. This indicates that theenergetic barrier exists for charge redistribution betweengraphene and the adsorbed oxygen molecules (shown be-low), and once the adsorption is accomplished, the chargeZe on each adsorbed oxygen molecules will not immedi-ately change just after switching on/off the gate voltage.One possible reason for the deviation between the ex-perimental results and theoretical curve is that d variesaccompanied with the change in n (or sweeping Vg). Yetactually, since modifying d by several angstroms resultsin the small change in (C(n)|Z|) as shown in Figure 4b,it is necessary to investigate more about the behavior ofthe adsorbed oxygen molecules in the gate electric fieldin a the future study.

It is controversial what kind of oxygen species does ac-tually cause the hole doping to graphene. Because theelectron affinity of O2 (0.44 eV

44) is much lower thanthe work function of graphene (4.6 eV45), direct chargetransfer between them seems unfavorable. Instead, withan analogy of the charge doping of diamond surface46,there is a widely accepted28,33,47 hypothesis that the holedoping proceeds through an electrochemical reaction46

such as: O2+2H2O+4e− = 4OH−, by which the charge

transfer is favorable due to the lowered free energy change∆G = −0.7 eV28 on the condition that the oxygen pres-sure is 1 atm and pH = 7. This electrochemical reactionneeds the aid of water that is mostly eliminated in the ex-periment by annealing (we observed no hysteresis in theσ vs Vg curve, that is, there are few charge traps oftenattributed to residual moisture on graphene or its sub-strate). Yet as for graphene deposited on the hydrophilicSiO2 substrate

32, it is possible that a small amount ofresidual water molecules (more than the chemical equiv-alent of O2) are trapped on SiO2 surface or voids, whichcannot be easily removed by the vacuum annealing at200 ◦C in comparison with those on graphene surface.We suggest that the electrochemical mechanism is plau-sible also in our case, yet the adsorbed molecule couldbe other chemical species than OH−, the charge of whichmay be dependent on Vg,ad.

6

e−

A

ζTS

ζG

ζCNP

‡E

ζads

T

∆G

Vg,ad > 0

cg

DOS of BLG

εF

0 0

‡E(εF(0))+ε

F(0)

‡E(εF(0))

‡E(εF(t))+ε

F(t)

DOS

nox

DOS

O2

εF(0)

εF(t)

‡E(εF(t))

a

b

FIG. 5: Schematic energy diagrams of the kinetics of O2adsorption (H kinetics). (a) Path for electron transfer inthis model is shown by the blue dotted arrow; electrons inBLG (the electrochemical potential ζG) are transferred toO2 molecules via the transition state (the circled T at thelevel of ζTS ), giving the adsorbed oxygen species (the cir-cled A at the level of ζads). The activation energy, the freeenergy change, and the level of the CNP are denoted by ‡E,∆G and ζCNP, respectively. The Fermi level is defined byεF = ζG− ζCNP. As a demonstration, the case for Vg,ad > 0 ispresented. (b) Temporal change in the activation energy andthe Fermi energy due to the adsorption of oxygen moleculesto BLG negatively doped by the positive gate voltage (as incase of panel a). The left panel represents the case beforeoxygen adsorption (t = 0), and the right panel represents theoxygen exposure for the time t. Here the energy is measuredfrom the CNP. The red and the blue tick marks denote thelevel for the transition state and the Fermi level, respectively.Oxygen adsorption lowers the Fermi level, accompanied withthe increase in hole doping of nox (equal to the area of grayed

part,∫ εF(0)εF(t)

D(εF) dεF), and the activation energy increases

according to Eq. (2)

In light of the discussion above, the electrochemicaldescription33,48 is expected to be applicable for the ob-served adsorption kinetics of oxygen to the BLG. Herewe premise that the molecular adsorption is determinedby the electrochemical potential of graphene, and con-sider the charge transfer kinetics in an approach basedon Butler–Volmer theory49,50. The model is schemati-cally depicted in Figure 5. The probability of the adsorp-tion reaction is determined by the electrochemical poten-tial of graphene (ζG) and that in the equilibrium condi-tion of the oxygen-chemisorption reaction (ζads). When

∆G = ζads − ζG < 0, the electrons favorably transferfrom of graphene to the adsorbed oxygen (denoted by“A” in Figure 5a), and the oxygen-adsorption reactionproceeds. For charge transfer, the electrons should gothrough some energy barrier; we assume that electronstunnel from BLG to the O2 molecules via a single transi-tion state (denoted by “T”), whose electrochemical po-tential is ζTS. The difference

‡E = ζTS − ζG correspondsto the activation energy of the oxygen-chemisorption re-action, which determines the frequency of the electrontransfer. Whereas ζG is dependent on the Fermi level εFas ζG = εF+ ζCNP (ζCNP is the electrochemical potentialof the CNP), we envisage that ζTS (or

‡E) is a functionof εF as well. In the framework of the Butler–Volmertheory, we obtain the dependence of ‡E on εF as

‡E(εF + dεF) =‡E(εF)− α dεF, (2)

where α(> 0) is a constant related to the “transfer coef-ficient” in the Butler–Volmer theory that associates theactivation energy with the electrochemical potential (notthe Fermi energy); thus herein we call α as “pseudo trans-fer coefficient” (see Supporting Information for detail inthe derivation). That is, we have the assumption thatthe activation energy scales linearly with the Fermi en-ergy. Further assuming that the molecular adsorptionrate dNox/dt is controlled by the electron transfer pro-cess and is not strongly affected by other contributionssuch as molecular diffusion14, it is given by

dNoxdt

= χD(

εF +‡E(εF)

)

f(

εF +‡E(εF); εF

)

, (3)

where D(ε) is the density of states (DOS) of BLG (ε isthe energy measured from ζCNP) and f(ε; εF) = [1 +(ε− εF)/kBT ]−1 is the Fermi–Dirac distribution func-tion. The coefficient χ does not depend on εF (if thedistance between the adsorbing molecules and BLG var-ied depending on εF or Vg,ad, the tunneling frequencywould be affected so that χ might be dependent on themas well; yet herein we ignore such effect for simplicity).The right-side of Eq. (3) represents the tunneling rate ofthe electron from the graphene to oxygen at the energylevel of transition state, ε = εF +

‡E(εF) = ζTS − ζCNP.According to Eq. (2) and Eq. (3), the molecular adsorp-tion rate is dependent on the Fermi level of graphene.Using them, we can explain both the temporal evolutionof the doping rate and its dependence on the gate voltageVg,ad.Let us discuss the temporal change in the doping rate.

The Fermi level of graphene is lowered with the increaseof the adsorbed oxygen molecules, because the positivecharge is induced on graphene by the charge Ze theypossess. Recalling that nox = −ZNox, the doping rateis given by dnox/dt. Furthermore, since

‡E ≫ kBT isfulfilled as shown later, we also approximate that f(εF+‡E(εF); εF) ≃ exp(−‡E(εF)/kBT ). Using the relationdnox = −D(εF)dεF, we acquire a formula describing thetemporal change of the Fermi level:

7

−D (εF(t))dεF(t)

dt=

pkBT

αteD

(

εF(t) +‡E (εF(t))

)

exp

(

αteεF(t)− εF(0)

kBT

)

, (4)

where εF(t) = εF(t, Vg,ad), expressing that the Fermilevel is a function of the exposure time t and the gatevoltage Vg,ad, and εF(0) = εF(0, Vg,ad), the Fermi levelat t = 0. We have specifically defined two constants, thepseudo transfer coefficient αte (the subscript “te” abbre-viates “temporal evolution”) and

p = −αteZχkBT

exp

(

−‡E (εF(0))

kBT

)

(5)

The right side of Eq. (4) represents the product of thecharge transfer frequency and the amount of charge peradsorbed molecule, whereas the left side does the resul-tant amount of the doped charge. Because BLG (or alsosingle layer graphene) has the low DOS around the CNPcompared to metal, the small amount of carrier dopingresults in the large shift in the Fermi level, which effec-tively controls the kinetics. Thus the adsorption kineticsis well described by Eq. (4), the equation focusing on theFermi level. When we envisage that the BLG is approx-imately described by two-dimensional parabolic disper-sion of the free electron, the DOS becomes constant asD ≡ DP = γ⊥/π(h̄vF)2, where vF = (

√3/2)γ0a/h̄ is the

Fermi velocity in SLG, a = 2.46 Å is the in-plane latticeconstant, and γ0 = 3.16 eV and γ⊥ ≈ 0.4 eV51,52 are theintrasheet and intersheet transfer integrals, respectively.In this case (hereafter labeled as P kinetics), Eq. (6) isreadily integrated, giving

nox(t) = −{εF(t)− εF(0)}DP =(

kBTDPαte

)

ln(1 + pt)

(6)Note that Eq. (6) satisfies dnox/dt ∝exp[−αtenox(t)/kBTD] and is equivalent to the in-tegrated form of Elovich equation53,54, the empiricalequation that is widely applicable to chemisorptionsonto semiconductors. When the hyperbolic DOS ofBLG41 is reflected to Eq. (4), more accurate but morecomplicated expression of εF(t) is acquired (denoted asH kinetics), given by

− αtekBT

exp

(

αteεF(0)

kBT

)

S[εF(0), εF(t)] + pt = 0, (7)

where S[εF(0), εF(t)] is a function that depends on theDOS at the Fermi level and that at the transition statelevel (derived in the Supporting Information).We performed curve fitting of the experimental results

of nox(t) with Eq. (6) and Eq. (7) for P kinetics andH kinetics, respectively. The difference in Vg,ad by runsis simulated by the dependence of εF(0) on Vg,ad firstwithout considering the gap-opening effect55,56, that is,

we calculate εF(0) using the relation that the charge ofcg(Vg,ad−V 0CNP) doped on BLG by applying Vg,ad is equalto

∫

εF(0)

0D(ε)dε. Irrespective of the kinetic models, All

the theoretical curves are well fitted to the experimentalresults except those for run 4 in the range above 103

min. Eq. (4) is invalid in the first place in the long-time regime in which the adsorption rate is almost aslow as the desorption rate, since the present treatmentincludes no contribution of desorption. The deviationis, however, contrary to the expectation; the desorptionshould suppress the evolution of the hole doping yet theenhanced doping was actually observed. Thus we suspectthat it is due to long-time scale chemisorption of oxygenonto graphene which is ubiquitously observed in carbonmaterials57,58. Note that the several volts of offsets areadded in Vshift (corresponding to the doping density of 2×1011 cm−2) to improve the fitting in the time range of t ≤100 min. This small offset corresponds to a fast reactionthat finishes at the very initial stage of adsorption, e.g.,due to the reactive chemisorption of O2 to the defect oredge site of graphene59,60.

Figure 6 shows the profiles of the fitting results. Prac-tically, the fitting parameters are following two: αte andp, but in order to derive the initial activation energy be-fore the oxygen adsorption, ‡E(εF(0)), from p based onEq. (6), we briefly assume that the charge/molecular ra-tio is independent of the gate voltage and determine thatZχγ⊥ = 1×105 eV2 min−1 from the pre-exponential fac-tor in the literature33, coxνκel ∼ 1017 cm−2s−1 (coxνκelin the literature corresponds to χγ⊥/π(h̄vF)

2 in this pa-per). Note that if we assume another value than Zχγ⊥ =1 × 105 eV2 min−1, it results in a uniform shift of thecalculated ‡E(εF(0)). In addition, the charge/molecularratio of the adsorbed molecule Z is likely dependent onVg,ad from the discussion about the mobility, but it leadsthe shift of ‡E(εF(0)) only by ∼ kBT = 0.026 eV. Onthe one hand, αte (representing the temporal change ofthe activation energy) exhibits a significant deviation be-tween the H kinetics and the P kinetics(Figure 6a), or de-pends on the treatment of the DOS of BLG. This devia-tion is understood as follows: H kinetics reflects the DOSof BLG that is a monotonically increasing function withrespect to |εF| having a minimum (D = DP) at the CNP(Figure 6(c)), yet P kinetics does not. Since the down-ward shift of the Fermi level upon the oxygen adsorptiondepends on the DOS at the Fermi level, the range of thechange in the Fermi level differs between two kineticsmodels (Figure 6(c)). Thus αte, related with the Fermilevel by Eq. (2), is calculated differently. This result iscontrasted with the conventional electrochemical reactionon the metal electrodes in which the kinetics is not signif-

8

0 31 2DOS /DP

P H

0.2

0.1

0

+80 V+40 V0 V–50 V

–0.1

–0.2

–0.3

Vg,ad

εF (

eV

)

CNP

−50 0 50

0

2

4

Vg,ad (V)

αte

H

P

αgf

−0.2 0 0.2

0.5

0.4

0.3

εF(0) (eV)

‡E

(εF(0

))

(eV

)

H

P

a

c

b

FIG. 6: Summary of parameters obtained by the curve fittingin Figure 2 with P kinetics (P) and H kinetics (H) compared.(a) Dependence of the pseudo transfer coefficient αte on Vg,ad.The pseudo transfer coefficient αgf acquired by the linear fit-ting to panel b is also plotted. (b) Initial activation energy‡E(εF(0)) plotted as a function of εF(0) = εF(0, Vg). (c) (Leftpanel) Density of states (DOS, solid line) for BLG as a func-tion of the Fermi energy, where DP (DOS at the energy ofεF = 0) is taken as unit of the DOS. The solid line denotesthe DOS applied for the H kinetics. In P kinetics the DOSis treated as constant; D = DP (dotted line). (Right panel)Change of the Fermi level by oxygen adsorption as a functionof Vg,ad. Bars and boxes represent the range calculated underP kinetics and H kinetics, respectively, assuming γ⊥ = 0.4 eV.The Fermi level before the oxygen adsorption (εF(0)) is at thepoint indicated by triangles (black squares) for H (P) kinetics,whereas the Fermi level shifts downward with the increase ofthe adsorbed oxygen, and eventually reaches the bottom endof the boxes (bars) in the end of the oxygen adsorption forthe H (P) kinetics. The energy is measured from the CNP(dashed line), and the gap-opening effect is not considered.

icantly affected by the DOS of the electrodes and is justowing to the low DOS of the BLG with comparison to themetal. On the other hand, we found that ‡E(εF(0)) is adecreasing function of εF(0) = εF(0, Vg,ad) (shown in Fig-ure 6b, therein we plot ‡E(εF(0)) with respect to εF(0)instead of Vg,ad). From Eq. (2), the slope of the plots inFigure 6b corresponds to the pseudo transfer coefficientα, and we found that αgf = 0.36 and 0.42 for P kineticsand H kinetics, respectively (the subscript “gf” abbrevi-ates “gate electric field”). Herein we distinguish αgf fromαte; being different from αte that is calculated based on

the temporal Fermi level shift by oxygen adsorption (thusαte inevitably includes the oxygen adsorption effect), αgfis acquired by tuning the Fermi level electrically at t = 0before oxygen adsorption. We found that αgf is muchsmaller than αte(≥ 1), or rather near 0.5, a typical trans-fer coefficient for simple redox reactions48,49 (Figure 6a).Specifically, the oxygen adsorption effect included onlyin αte but not in αgf is attributed, e.g., to the electricdipole layer61 formed between graphene and the adsorbedmolecules and the Coulomb interaction between the ad-sorbed oxygen molecules. We expect that these effectsalso raise the activation energy roughly in proportionalto the number of molecules Nox (or the doping densitynox), and thus we have the expression for the additionaladsorption effect: d‡E = ξmoldnox = −ξmolD(εF)dεF(ξmol: the proportional coefficient; herein we use therelation dnox = −D(εF)dεF again). Then we acquireαte ≃ αgf + ξmol〈D(εF)〉 (〈D(εF)〉 denotes the averageDOS in the range of the Fermi level for each run), whichindicates that αte is large when the DOS is large inthe level far away from the CNP (see Figure 6c). In-deed, as shown in Figure 6a, αte for H kinetics showsthe V-shaped dependence on Vg,ad with the minimum forVg,ad = +40 V, which gives the smallest average DOS.Though the kinetics for the molecular adsorption is af-fected by various effects as mentioned above, we representthem by the parameter αte and succeed in accounting forthe observed kinetics in a facile way.

Finally let us account for the power-law dependenceof dnox/dt ∝ t−u shown in Figure 3. It is helpful tolook on the simpler P kinetics for the assessment ofdnox/dt; from Eq. (6), we obtain dnox/dt ∝ p/(1 + pt).Approximately we have dnox/dt ∝

(

u〈t〉u−1)

t−u where

u ≃ [1 + (1/p〈t〉)]−1 ≤ 1 (the time 〈t〉 is the center ofthe expansion of ln(dnox/dt) in terms of ln t, and it is agood approximation if p〈t〉 ≫ 1, or otherwise if p〈t〉 ≃ 1in the time range such that t = [10−1〈t〉, 10〈t〉]). Sincep is intensively dependent on Vg,ad (recall that (i) p isexponentially decaying against ‡E(εF(0)) as representedin Eq. (5), (ii) ‡E(εF(0)) linearly decreases with respectto εF(0) with the slope of −αgf as shown in Figure 6c,(iii) εF(0) is an increasing function of Vg,ad. We acquiredp =19.6, 2.9, 0.98 and 0.32 for Vg,ad = +80, +40, 0,and −50 V, respectively, by fitting within the P kineticsmodel), we can find that u is almost unity for a positivelyhigh Vg,ad and tends be smaller for negatively high Vg,adwithin the time range experimentally scoped, which isconsistent with the observed behavior. When the elec-trochemical mechanism governs the kinetics of the oxy-gen adsorption, the activation energy of the charge trans-fer continually increases with the O2 exposure time in-creasing. This effect leads to non-Langmurian kineticsof the oxygen adsorption and the power-law decrease ofdnox/dt, even though neither the desorption process northe saturation limit of adsorption are taken into consid-eration.

In BLG, it is known that a band gap opens due to theenergy difference between two layers9. The gate electric

9

field as well as the adsorbed oxygen may produce sucha strong energy difference that the eventual band gapshould affect the time evolution of molecular adsorption.The band gap opening effect is expected to exhibit mostprominently when the Fermi level goes across the CNP(at the point shown by arrows in Figure 2), while we can-not find such behavior obviously. We guess it is partly be-cause most of the adsorbed oxygen molecules exist in theinterface between graphene and the gate dielectric SiO2.For the band gap opening effect to appear, it is neces-sary that the gate electric field and the molecular fieldenhance each other when the Fermi level is near the CNP(i.e., the charge induced by the gate electric field and thatby the adsorbed molecules including unintentional resid-ual impurities on the SiO2 substrate are balanced), yet itis possible only when the molecules mainly adsorb on thetop surface of BLG, and not for the molecules adsorbedin the interface (Figure S2, Supporting Information). Orit may be partly because the disordered potential dueto the impurities in the substrate fluctuates the energylevel around which the band gap exists62, eventually blur-ring band gap opening effects and chemical reactivity63

of BLG. Details about the band-gap opening effects arediscussed in the Supporting Information.In summary, we investigated the weak chemisorption of

O2 molecules on bilayer graphene by measuring its trans-port properties. The hole doping due to O2 chemisorp-tion is remarkably dependent on the gate voltage, andthe amount of the doped carrier increases with O2 ex-posure time, the rate of which is in accordance with∝ t−u(u ≤ 1) rather than with conventional Langmuiriankinetics. We conclude from these that an electrochem-

ical reaction governs the O2 chemisorption process, inwhich the rate of the chemisorption is determined bythe Fermi level of graphene, and indeed succeed in ac-counting for the observed kinetics by the analysis basedon the Butler–Volmer theory. We also found that thechemisorbed molecules decrease the mobility of graphene,and interestingly, the mobility change is dependent onthe gate voltage applied during the adsorption, indicat-ing that the adsorption state, e.g., transferred charge ordistance between a molecule and graphene, can be mod-ified electrically. Graphene, offering a continuously tun-able platform for study of chemisorptions on it, realizesthe electrical control of the adsorption by gate electricfield, a novel and versatile method in which we wouldexplore extensively a wider variety of host–guest interac-tions between graphene and foreign molecules.

Supporting Information. Additional descrip-tions about (i) the experimental method, (ii) theelectrochemistry-based kinetics model and the mathe-matical derivation for it, and (iii) an expanded discussionabout the gap-opening effects.

Acknowledgments

The authors acknowledge support from Grant-in-Aidfor Scientific Research No. 20001006 from the Ministryof Education, Culture, Sports, Science and Technology,Japan. The authors thank M. Kiguchi, T. Kawakami, K.Yokota, and Y. Kudo for useful discussion.

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