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Monitoring dopants by Raman scattering

in an electrochemically top-gated

graphene transistor

A. DAS1, S. PISANA2, B. CHAKRABORTY1, S. PISCANEC2, S. K. SAHA1, U. V. WAGHMARE3,

K. S. NOVOSELOV4, H. R. KRISHNAMURTHY1, A. K. GEIM4, A. C. FERRARI2*AND A. K. SOOD1*

1Department of Physics, Indian Institute of Science, Bangalore 560012, India

2Department of Engineering, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 OFA, UK

3Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India

4Department of Physics and Astronomy, Manchester University, Manchester M13 9PL, UK

*e-mail: acf26@eng.cam.ac.uk; asood@physics.iisc.ernet.in

Published online: 30 March 2008; doi:10.1038/nnano.2008.67

The recent discovery of graphene1–3has led to many advances in

two-dimensional physics and devices4,5. The graphene devices

fabricatedsofarhave relied

Electrochemical top gating is widely used for polymer

transistors6,7, and has also been successfully applied to carbon

nanotubes8,9. Here we demonstrate a top-gated graphene

transistor that is able to reach doping levels of up to

531013cm22, which is much higher than those previously

reported. Such high doping levels are possible because the

nanometre-thick Debyelayer8,10

electrolyte gate provides a much higher gate capacitance than

the commonly used SiO2back gate, which is usually about

300 nm thick11. In situ Raman measurements monitor the

doping. The G peak stiffens and sharpens for both electron

and hole doping, but the 2D peak shows a different response

to holes and electrons. The ratio of the intensities of the G and

2D peaks shows a strong dependence on doping, making it a

sensitive parameter to monitor the doping.

Figure 1a shows a schematic diagram of our experimental setup

for transport and Raman measurements. (See Supplementary

Information and Methods for details about device fabrication

and measurements.) Figure 1b shows the source–drain current

(ISD) of the top-gated graphene as a function of electrochemical

gate voltage. The gate dependence of the drain current (Fig. 1b)

shows ambipolar behaviour and is almost symmetric for both

electron and hole doping. This is directly related to the band

structure of graphene, where both electron and hole conduction

are accessible by shifting the Fermi level. The ISD2VDS

characteristics at different electrochemical gate voltages (Fig. 1c)

show linear behaviour, indicating the lack of significant Schottky

barriers at the electrode–graphene interface.

In order to compare our top-gating results with the usual back-

gating measurements, it is necessary to convert the top-gate voltage

into an effective doping concentration. In general, the application

of a gate voltage (VG) creates an electrostatic potential difference

f between the graphene and the gate electrode, and the addition

of charge carriers leads to a shift in the Fermi level (EF).

on SiO2

backgating1–3.

inthe solid polymer

Therefore, VGis given by

VG¼EF

eþ fð1Þ

with EF/e being determined by the chemical (quantum)

capacitance of the graphene, and f being determined by the

geometrical capacitance CG. As discussed in the Methods section,

for the back gate, f ? EF/e, whereas for top gating the two

terms in equation (1) are comparable.

The Fermi energy in graphene changes as EF(n) ¼ hjvFj

where jvFj ¼ 1.1?106ms21is the Fermi velocity2,3. For the top

gate, f ¼ ne/CTG, where CTGis the geometric capacitance (TG

denotes ‘top gate’). From equation (1) we get

ffiffiffiffiffiffi

pn

p

,

VTG¼h?jvFj

ffiffiffiffiffiffi

pn

p

e

þne

CTG

ð2Þ

Using the numerical values: CTG¼ 2.2 ? 1026F cm22(as given in

the Methods section) and vF¼ 1.1 ? 106ms21,

VTGðvoltsÞ ¼ 1:16 ? 10?7

ffiffiffi

n

p

þ 0:723 ? 10?13n

ð3Þ

where n is in units of cm22. Equation (3) allows us to estimate the

doping concentration at each top-gate voltage (VTG). Note that, as

in back gating, we also obtain the minimum source–drain current

at finite top-gate voltage (VnTG¼ 0.6 V), as seen in Fig. 1b.

Accordingly, a positive (negative) VTG2VnTGinduces electron

(holes) doping.

Figure 2a plots the resistivity of our graphene layer (extracted

from Fig. 1b knowing the sample’s aspect ratio: W/L ¼ 1.55) as a

function VTG. Figure 2b shows the back-gate response of the same

sample (without electrolyte). There is an increase in resistivity

maximum (?6 kV) after pouring the electrolyte, which may

originate from the creation of more charged impurities on the

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sample. Figure 2a,b also show that, for both top-gate (TG) and back-

gate (BG) experiments, the resistivity does not decay sharply around

the Dirac point. Indeed, it has been suggested that the sharpness of

the resistivity around the Dirac point and the finite offset gate

voltage (VnBG) depend on charged impurities12.

The conductivity minimum (smin) (resistivity maximum) is

obtained when the Fermi level is at the Dirac point. This is

generally around ?4e2/h (ref. 2). In both our back- and top-gate

experiments the conductivity minimum is reduced by the contact

resistance, because measurements are performed in the two-

probe configuration, or possible contaminations at the contact–

graphene interface. Minimum conductivities in the range from

2e2/h to 10e2/h have been reported recently12, with the spread

assigned to charged impurities.

Figure 2c showsthe change in mobility (using the simple Drude

model12m ¼ (enr)21) as a function of doping for our TG/BG

experiments. The Drude model can be safely used here, because

the sample length (?5 mm) is much more than the transport

mean free path (?100 nm)11–13. The mobility is smaller in the

TG case. This is consistent with the reduction in conductivity

minimum and can be attributed to the presence of added charge

impurities from the polymer electrolyte. This reduction in

mobility for TG is consistent with ref. 4.

Despite the limitations in ‘on’ and ‘off’ currents, our large

graphene device shows an on/off ratio of ?5.5. This is higher

than previously reported results4for devices using 20-nm-thick

SiO2as a top gate (on/off ratio ?1.5) and 40-nm-thick PMMA14

as a top gate (on/off ratio ?2). Our demonstration of top gating

with polymer electrolyte paves the way for further research. For

example, by using water as the top gate and extensive graphene

cleaningwe could achievean

Supplementary Information). However, because the water droplet

evaporates in less than one minute, this arrangement is not stable

over long periods of time, unlike the solid polymer electrolyte.

Raman spectroscopy is a powerful non-destructive technique

for identifying the number of layers, structure, doping and

disorder of graphene15–19. The prominent Raman features in

graphene are the G-band at G (?1,584 cm21), and the 2D band

at ?2,700 cm21involving phonons at the K þ Dk points in the

brillouin zone15. The value of Dk depends on the excitation laser

energy, due to a double-resonance Raman process and the linear

dispersion of the phonons around K (refs. 15, 20, 21). The effect

of doping induced by SiO2back gating on the G-band frequency

and full-width at half-maximum (FWHM) has been reported

recently16,17. This results in G peak stiffening and a decrease in

linewidth for both electron and hole doping. The decrease in

linewidth saturates when the doping causes a Fermi-level shift

bigger than half the phonon energy16,17. The strong electron–

phonon coupling in graphene and metallic nanotubes gives rise

to Kohn anomalies in the phonon dispersions21–23, which result

on–offratio of40 (see

VTG

Platinum

Si

SiO2

To spectrometer

From Ar

laser (514 nm)

16

Holes

Electorns

Time (min)

708090

7

6

5

VDS = 50 (mV)

12

8

4

60

–0.5

1.5

0.0

0.3

0.8

0.6

45

30

15

0

0.000.050.10

VDS (V)

0.150.20

–0.8–0.40.00.40.81.21.62.0

×50 objective

VDS

Source

Drain

Graphene

Platinum

Debye

layer

Debye

layer

VTG

VTG (V)

VTG (V)

–––

–

–

–

–

––

–

–

–

+

+

+

+

+

+

+

+

++

+

+

+

++ + +

–––

–

Figure 1 Electrochemically top-gated graphene transistor. a, Schematic diagram of the experimental setup. The black dotted box between the drain and source

indicates the thin layer of polymer electrolyte (PEO þ LiClO4), and the blue stripe between the electrodes represents the graphene sample. The left inset shows the

optical image of a single-layer graphene connected between source and drain gold electrodes. Scale bar: 5 mm. The right inset is a schematic illustration of polymer

electrolyte top gating, with Liþ(magenta) and ClO4

shows the ISDtime dependence at fixed VTG. The dotted line corresponds to the Dirac point (change neutrality point). c, ISDversus VDSat different top-gate voltages.

The black dotted line corresponds to the value of VDSat which the data in Fig. 1b was measured.

2(cyan) ions and the Debye layers near each electrode. b, ISDas a function of top-gate voltages (VTG). The inset

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in phonon softening. The G peak stiffening is due to the non-

adiabatic removal of the Kohn anomaly from the G point16.

The FWHM(G) sharpening occurs because of the blockage of the

decay channel of phonons into electron–hole pairs due to the

Pauli exclusion principle, when the electron–hole gap becomes

higher than the phonon energy16. A similar behaviour is

observed for the longitudinal optic (LO) G2peak of doped

metallic nanotubes8,9,24, for exactly the same reasons.

We now consider the evolution of the Raman spectra. Figure 3a

plots the Raman spectra in the G (left) and 2D (right) region at

different values of the top-gate voltage. Figure 3b,c shows how

the Raman parameters (the positions of the G and 2D peaks, and

the FWHM of the G peak) vary as a function of doping. The

Raman shiftof theG peak

(?1,583.1 cm21) at VTG¼ VnTG?0.6 V, and increases by up to

30 cm21for hole doping and up to 25 cm21for electron doping

(Fig. 3b, top panel). The decrease in the FWHM of the G peak

(Fig. 3b, bottom panel) for both hole and electron doping is

similar to earlier results16,17, even though it extends to a much

wider doping range. Moreover, the 2D and G peak show very

differentdependencies onthe

doping, the position of the 2D peak does not change much

(,1 cm21) until a gate voltage of ?3 V (corresponding to

?3.2?1013cm22). At higher gate voltages, there is a significant

softening of ?20 cm21and for hole doping, the position of the

2D peak increases ?20 cm21(Fig. 3c).

Figure 4 plots the variation of the intensity ratio of the G and

2D peaks (I(2D)/I(G)) as a function of doping. The dependence

of the 2D mode is much stronger than that of the G mode and

hence I(2D)/I(G) is a strong function of the gate voltage.

Therefore, this is a new, important parameter to estimate the

doping density. Figures3 and 4 also show that I(2D)/I(G) and

the position of the G peak should not be used to estimate the

number of graphene layers, contrary to what is suggested in

refs 25 and 26. It is the shape of the 2D peak that is the most

effective way to identify a single layer, as shown in ref. 15.

The theoretical trends in Fig. 3b have been discussed before16.

These confirm previous back-gate experiments, but extend the

data to a much wider electron and hole range16. In this wider

range, the theory still captures the main features, such as the

asymmetry between electron and hole doping27. However, the

quantitative agreement is poor for large doping, and requires us

to reconsider the non-adiabatic calculations of ref. 27. At low

doping, the uncertainty, as estimated by comparing the Raman

data and theory, is at most 25%.

Here we focus on the novel trend of the 2D peak position as a

function of doping. This is experimentally and conceptually

different from the interpretation of the G peak. The 2D peak

originates from a second-order, double-resonant (DR) Raman

scattering mechanism15,20,28. The position of the 2D peak can be

evaluated by computing the energy of the phonons involved in the

second-order, DR scattering process. As shown in ref. 15, because

of the trigonal warping of the p2p* bands and the angular

dependence of the electron–phonon coupling (EPC) matrix

elements, only phonons oriented along the GKM direction and

with q . K give a non-negligible contribution to the 2D peak. The

precise value of q is fixed by the constraint that the energy of the

incoming laser photons (hvL) has to exactly match a real electronic

transition. In particular, only a wavevector q0can be found for

which hvL¼ e(p*, q0)2e(p, q0), where e(n, k) is the energy of an

electron of band index n and wavevector k, and q0is measured

from K and is in the GKM direction. Once q0has been determined,

q ¼ 2q0þ K. Among the six phonons corresponding to the q

vector that satisfy the DR conditions, only the highest optical

branch has an energy compatible with the measured Raman shift.

Therefore, the theoretical position of the 2D peak corresponds to

twice the energy of the Raman active phonon.

In order to be comparable with our experiments performed at

514 nm, we consider hvL¼ 2.5 eV. Assuming the p/p* bandsto be

linear, with a slope of 14.1 eV (ref. 21), this laser energy selects a

phonon with wavevector q of modulus 0.844 in 2p/a0units,

where a0is the lattice parameter of graphene. The dependence of

the position of the 2D peak on doping can be investigated by

calculating, within a density functional theory (DFT) framework,

the effects of the Fermi-level shift on the phonon frequencies.

has itssmallest value

gatevoltage. For electron

20

16

Mobility (cm2 V–1 s–1)

12

8

4

16

14

12

10

8

6

4

–0.50.00.51.0

VTG (V)

1.52.0

–40

105

104

103

102

–20

0

20

VBG (V)

40

6420

n (×1012 cm–2)

–2 –4

Figure 2 Conductivity minimum in graphene. a, Resistivity as a function of

the top-gate voltage. The dots are extracted from Fig. 1b for W/L¼1.55.

b, Resistivity of the same sample as a function of the back-gate voltage.

The dotted black line marks the Dirac point. c, Mobility as a function of doping

for top gating (dashed red line) and back gating (solid blue line).

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In doped graphene, the shift of the Fermi energy induced by

doping has two major effects: (1) a change of the equilibrium

lattice parameter with a consequent stiffening/softening of the

phonons, and (2) the onset of effects beyond the adiabatic

Born–Oppenheimer approximation that modify the phonon

dispersion close to the Kohn anomalies (KAs)16,27. The excess

(defect) charge results in an expansion (contraction) of the

crystal lattice. This has been extensively investigated in order to

understand graphite intercalation compounds29. We model the

shift of the Fermi surface by varying the number of electrons in

the system. Because the total energy of charged systems diverges,

electrical neutrality is achieved by imposing a uniformly charged

background. To avoid electrostatic interactions between the

graphene layer and the background, the equilibrium lattice

parameter of the charged systems is computed in the limit of a

unit cell with an infinite volume. Such a limit is reached by

using a model with periodic boundary conditions where the

graphene layers are spaced by 60 A˚vacuum. Phonon calculations

for charged graphene are carried out with the same unit cells

usedfor the determination

parameter. Interestingly, although we observe that for charged

graphene the frequency of border zone phonons converges only

for layer spacing as large as 60 A˚, the frequency of the E2g

mode is already converged for a 7.5 A˚spacing. This suggests

that border zone phonons are much more sensitive to the

local environment.

Dynamiceffects beyond

approximation play a fundamental role in the description of the

KA in single-walled carbon nanotubes and in graphene16,22,27.

However, for the 2D peak measured at 514 nm, the influence of

dynamic effects is expected to be negligible, because the phonons

giving rise to the 2D peak are far away from the KA at K. Thus,

we can calculate the position of the 2D peak without dynamic

corrections (see Methods).

ofthe correspondinglattice

theBorn–Oppenheimer

4.0

3.5

3.0

2.8

2.6

2.4

2.0

1.6

1.2

1.0

0.6

0 V

–0.1

–0.2

–0.3

–0.4

–0.5

–0.6

–0.7

–0.8

–1

–1.2

–1.6

1,550 1,5751,600 2,600

Raman shift (cm–1)

2,650 2,7002,750

–2.2

Intensity (a.u.)

Fermi energy (meV)

–703

1,610

1,605

Pos(G) (cm–1)

Pos(2D) (cm–1)

FWHM(G) (cm–1)

1,600

1,595

1,590

1,585

1,580

18

16

14

12

10

8

6

4

–3–2–10

Electron concentration (×1013 cm–2)

1234

–3 –2 –10

Electron concentration (×1013 cm–2)

1234

–3–2–10

Electron concentration (×1013 cm–2)

1234

–574 –4060406574703811

Fermi energy (meV)

–703

2,700

2,690

2,670

2,660

2,680

–574 –4060406 574 703811

Figure 3 Raman spectra of graphene as a function of gate voltage. a, Raman spectra at values of VTGbetween 22.2 V and þ4.0 V. The dots are the

experimental data, the black lines are fitted lorentzians, and the red line corresponds to the Dirac point. The G peak is on the left and the 2D peak is on the right.

b, Position of the G peak (Pos(G)); top panel) and its FWHM (FWHM(G); bottom panel) as a function of electron and hole doping. The solid blue lines are the predicted

non-adiabatic trends from ref. 16. c, Position of the 2D peak (Pos(2D)) as a function of doping. The solid line is our adiabatic DFT calculation.

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The comparison between the theoretical and the experimental

position of the 2D peak is shown in Fig. 3c. Our calculations are

in qualitative agreement with experiments, considering the

spectral resolution and the Debye layer estimation. Indeed, as

experimentally determined, the position of the 2D peak is

predicted to decrease for an increasing electron concentration in

the system. This allows the use of the 2D peak to discriminate

between electron and hole doping.

The tradeoff between measured and theoretical data can be

partially explained in terms of the electrostatic difference existing

between the experiments and the model DFT system. In our

simulations, the 2D phonon frequencies are very sensitive to the

charged background used to ensure global electrical neutrality. In

the experiments, the electric charge on the graphene surface is

induced by capacitative coupling. The electrostatic interaction

between graphene and the electrolyte could thus further modify

the 2D phonons. This does not affect the G peak to the same

extent, due to the much lower sensitivity of the G phonon to an

external electrostatic potential. Other effects not captured by

DFT,suchasquasi-particle

considered to fully explain the 2D peak behaviour.

In conclusion, we have demonstrated the first graphene top

gating using a solid polymer electrolyte. We reached much higher

electron and hole doping than standard SiO2back gating. The

Raman measurements show that the G and 2D peaks have

different doping dependence and the 2D/G height ratio changes

significantly with doping, making Raman spectroscopy an ideal

tool for graphene nanoelectronics.

interactions,should alsobe

METHODS

EXPERIMENTAL

Graphene samples were produced by micro-mechanical cleavage of bulk graphite

and deposited on Si covered with 300-nm SiO2(IDB Technologies). Raman

spectroscopy was used to select single layers15. Source and drain Cr/Au

electrodes were then deposited by photolithography as shown in Fig. 1a. Cr was

used instead of Ti to ensure less reactivity with the electrolyte. Top gating was

achieved by using solid polymer electrolyte consisting of LiClO4and PEO in the

ratio 0.12:1, as previously used for nanotubes10. The gate voltage was applied by

placing a platinum electrode in the polymer layer10. Electrical measurements

were carried out using Keithley 2400 source meters. Figure 1 shows a schematic

of the experimental setup for transport and Raman measurements. Raman

spectra of pristine and back-gated samples were measured with a Renishaw

spectrometer. Insitu measurements on top-gated graphenewere recordedusing a

WITEC confocal (?50 objective) spectrometer with 600 lines/mm grating,

514.5 nm excitation and very low power level (?1 mW) to avoid any heating

effect. The spectral resolution of the two instruments was determined by fitting

the Rayleigh line to a gaussian profile and is 1.9 cm21for the Renishaw

spectrometer and 9.4 cm21for the WITEC spectrometer. The Raman spectra

were then fitted with Voigt functions. The FWHM of the lorentzian components

give the relevant information on the phonon lifetime. Note that a very thin layer

of polymer electrolyte does not absorb the incident laser light. Furthermore, the

Raman spectrum of the polymer does not cover the signatures of graphene (see

Supplementary Information). The measured source–drain currents (ISD) and G

and 2D are reversible at different gate voltages. Note that for each point a given

gate voltage is applied for 10 min to stabilize ISD. In transport experiments a

small hysteresis in current (?1 mA) is observed during forward and backward

gate voltage scans (at intervals of 10 min for each gate-voltage step). The Raman

hysteresis, however, is less than 1 cm21.

GATE VOLTAGES AND DOPING LEVELS

We now discuss how the applied gate voltage is converted to the doping in

graphene. Let us first consider back gating. For a back gate, f ¼ ne/CBG,

where n is the carrier concentration and CBGis the geometrical capacitance. For

single-layer graphene, CBG¼ ee0/dBG, where e is the dielectric constant of SiO2

(?4), e0is the permittivity of free space and dBGis 300 nm. This results in a very

low gate capacitance CBG¼ 1.2?1028F cm22. Therefore, for a typical value

of n ¼ 1?1013cm22, the potential drop is f ¼ 100 V, much larger than EF/e.

Hence, VBG? f and the doping concentration becomes n ¼ hVBG, where

h ¼ CBG/e. However, most samples have a zero-bias (VBG¼ 0) doping of,

typically, a few 1011cm22(refs 1, 18, 19). This is reflected in the existence of a

finite gate voltage VnBG, at which the Hall resistance is zero and the longitudinal

resistivity reaches its maximum. This maximum is associated with the Fermi

level positioned between the valence and the conduction bands (the Dirac

point). Accordingly, a positive (negative) VBG2VnBGinduces electron (holes)

doping, with an excess electron surface-concentration of n ¼ h(VBG2VnBG).

Avalue of h ? 7.2?1010cm22V21is found from Hall effect measurements, and

agrees with the estimation from the gate geometry1–3.

We shall nowconsider the present case of top gating. When afield is applied,

free cations tend to accumulate near the negative electrode, creating a positive

charge there and an uncompensated negative charge near the interface. The

accumulation is limited by the concentration gradient, which opposes the

Coulombic forceof theelectric field. When asteadystateis reached,the statistical

space charge distribution resembles that shown in Fig. 1. This layer of

charge around an electrode is called the Debye layer. As shown in Fig. 1, when we

apply a positive potential (VTG) to the platinum top gate (with respect to the

source electrode connected to graphene), the Liþions become dominant in the

Debye layer formed at the interface between the graphene and the electrolyte.

The Debye layer of thickness dTGacts like a parallel-plate capacitor. Therefore,

the geometrical capacitance in this case is CTG¼ ee0/dTG, where e is

the dielectric constant of the PEO matrix. The Debye length is given by

dTG¼ (2ce2/ee0kT)21/2for a monovalent electrolyte, where c is the

concentration of the electrolyte, e is the electric charge and kT is the thermal

energy. In principle, dTGcan be calculated if the electrolyte concentration is

known. However, in the presence of a polymer, the electrolyte ions form

complexes with the polymer chains30. Hence, the exact concentration of ions is

not amenable to measurement. For polymer electrolyte gating the thickness of

the Debye layer is reported to be a few nanometres (?1–5 nm) (ref. 10). The

dielectric constant e of PEO is 5 (ref. 31). Assuming a Debye length of 2 nm, we

obtain a gate capacitance CTG¼ 2.2?1026F cm22, which is much higher than

CBG. Therefore, the first term in equation(1) cannot be neglected.

THEORY

Calculations were performed within the generalized gradient approximation

(GGA)32. We used planewaves (30 Ry cutoff) and pseudopotential approaches.

The semimetallic character of the system was treated by performing

electronic integration with a Fermi–Dirac first-order spreading with a

smearing of 0.01 Ry. Integration over the brillouin zone was covered out with

a uniform 72?72?1 k-points grid. Calculations were carried out using the

Quantum Espresso code (www.quantum-espresso.org).

Received 30 October 2007; accepted 28 February 2008;

published 30 March 2008.

Fermi energy (meV)

–703

3.5

3.0

2.5

2.0

1.5

I (2D)/I(G)

1.0

0.5

–3–2–1

Electron concentration (×1013 cm–2)

0

1234

–574–4060406574703811

Figure 4 The influence of hole and electron doping on the 2D and G peaks.

The ratio of the intensity of the 2D peak in the Raman spectrum to the intensity

of the G peak exhibits a clear dependence on the electron concentration, and

can therefore be used to monitor the level of doping in graphene-based devices.

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Acknowledgements

S.P. acknowledges funding from Pembroke College and the Maudslay Society. A.C.F. acknowledges

funding from the Royal Society and Leverhulme Trust. A.K.S. thanks the Department of Science and

Technology, India, for financial support.

Correspondence and requests for materials should be addressed to A.C.F. and A.K.S.

Supplementary Information accompanies this paper on www.nature.com/naturenanotechnology.

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