Science_2004.pdf

R EPORTS

that are based on increasing the optical

thickness of atomic samples (16), as well as

elimination of transmission losses, could pro-

vide several orders of magnitude increase in

R 2 . Our results also demonstrate the possi-

bility of realizing quantum nodes consisting

of multiple atomic qubits by using multiple

beams of light. This approach shows prom-

ise for implementation of distributed quan-

tum computation (20, 21).

2. S. Haroche, J. M. Raimond, M. Brune, in Experimental

Quantum Computation and Information,F.deMartini,

C. Monroe, Eds. (Proceedings of the International

School of Physics Enrico Fermi, course CXLVIII, IOS

Press, Amsterdam, 2002), pp. 37–66.

3. C. A. Sackett et al., Nature 404, 256 (2000).

4. M. D. Barrett et al., Nature 429, 737 (2004).

5. M. Riebe et al., Nature 429, 734 (2004).

6. B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe,

Nature 428, 153 (2004).

7. S. Bose, P. L. Knight, M. B. Plenio, V. Vedral, Phys. Rev.

Lett. 83, 5158 (1999).

8. H. J. Kimble, Phys. Scr. 76, 127 (1998).

9. A. Kuzmich, E. S. Polzik, in Quantum Information with

Continuous Variables, S. L. Braunstein, A. K. Pati, Eds.

(Kluwer, Dordrecht, 2003).

10. M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).

11. L.-M. Duan, M. D. Lukin, I. J. Cirac, P. Zoller, Nature

414, 413 (2001).

12. A. Kuzmich et al., Nature 423, 731 (2003).

13. C. H. van der Wal et al., Science 301, 196 (2003).

14. W. Jiang, C. Han, P. Xue, L.-M. Duan, G. C. Guo, Phys.

Rev. A. 69, 043819 (2004).

15. C. W. Chou, S. V. Polyakov, A. Kuzmich, H. J. Kimble,

Phys. Rev. Lett. 92, 213601 (2004).

16. L.-M. Duan, J. I. Cirac, P. Zoller, Phys. Rev. A. 66,

023818 (2002).

17. A. Kuzmich, T. A. B. Kennedy, Phys. Rev. Lett. 92,

030407 (2004).

18. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev.

A. 60, 1888 (1994).

19. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K.

Wooters, Phys. Rev. A. 54, 3824 (1996).

20. Y. L. Lim, A. Beige, L. C. Kwek, www.arXiv.org/quant-ph/

0408043.

21. S. D. Barrett, P. Kok, www.arXiv.org/quant-ph/0408040.

22. We acknowledge fruitful conversations with T. A. B.

Kennedy, J. A. Sauer, L. You, A. Zangwill and, par-

ticularly, M. S. Chapman and thank R. Smith and E. T.

Neumann for experimental assistance. This work was

supported by NASA and the Research Corporation.

tection efficiency for the read beam is $ ;

0.04, so we infer the efficiency of quantum

state transfer from the atoms onto the pho-

ton, O ; 0.03.

We have realized a quantum node by

combining the entanglement of atomic and

References and Notes

1. I. Chuang, M. Nielsen, Quantum Computation and

Quantum Information (Cambridge Univ. Press, Cam-

bridge, 2000).

28 July 2004; accepted 16 September 2004

Electric Field Effect in Atomically

Thin Carbon Films

K. S. Novoselov, 1 A. K. Geim, 1 * S. V. Morozov, 2 D. Jiang, 1

Y. Zhang, 1 S. V. Dubonos, 2 I. V. Grigorieva, 1 A. A. Firsov 2

than traditional semiconducting devices (3)^.

However, this would require atomically thin

metal films, because the electric field is

screened at extremely short distances (G1nm)

and bulk carrier concentrations in metals are

large compared to the surface charge that can

be induced by the field effect. Films so thin

tend to be thermodynamically unstable, be-

coming discontinuous at thicknesses of sev-

eral nanometers; so far, this has proved to be

an insurmountable obstacle to metallic elec-

tronics, and no metal or semimetal has been

shown to exhibit any notable (91%) field ef-

fect (4).

We report the observation of the electric

field effect in a naturally occurring two-

dimensional (2D) material referred to as

few-layer graphene (FLG). Graphene is the

name given to a single layer of carbon atoms

densely packed into a benzene-ring struc-

ture, and is widely used to describe proper-

ties of many carbon-based materials, including

graphite, large fullerenes, nanotubes, etc. (e.g.,

carbon nanotubes are usually thought of as

graphene sheets rolled up into nanometer-sized

cylinders) (5–7). Planar graphene itself has

been presumed not to exist in the free state,

being unstable with respect to the formation of

curved structures such as soot, fullerenes, and

nanotubes (5–14).

We describe monocrystalline graphitic films, which are a few atoms thick but are

nonetheless stable under ambient conditions, metallic, and of remarkably high

quality. The films are found to be a two-dimensional semimetal with a tiny overlap

between valence and conductance bands, and they exhibit a strong ambipolar

electric field effect such that electrons and holes in concentrations up to 10 13 per

square centimeter and with room-temperature mobilities of

The ability to control electronic properties of

a material by externally applied voltage is at

the heart of modern electronics. In many

cases, it is the electric field effect that allows

one to vary the carrier concentration in a

semiconductor device and, consequently,

change an electric current through it. As the

semiconductor industry is nearing the limits

of performance improvements for the current

technologies dominated by silicon, there is a

constant search for new, nontraditional mate-

rials whose properties can be controlled by

the electric field. The most notable recent

examples of such materials are organic

conductors (1) and carbon nanotubes (2). It

haslongbeentemptingtoextendtheuseof

the field effect to metals Ee.g., to develop all-

metallic transistors that could be scaled down

to much smaller sizes and would consume

less energy and operate at higher frequencies

1 Department of Physics, University of Manchester,

Manchester M13 9PL, UK. 2 Institute for Microelec-

tronics Technology, 142432 Chernogolovka, Russia.

*To whom correspondence should be addressed.

E-mail: geim@man.ac.uk

666

22 OCTOBER 2004 VOL 306 SCIENCE www.sciencemag.org

photonic qubits with the atom-photon quan-

tum state transfer. By implementing the

second node at a different location and

performing a joint detection of the signal

photons from the two nodes, the quantum

repeater protocol (11), as well as distant te-

leportation of an atomic qubit, may be real-

ized. Based on this work, we estimate the

rate for these protocols to be R 2 ; ($O"n s ) 2 R ;

10 j7 s j1 . However, improvements in

10,000 square

centimeters per volt-second can be induced by applying gate voltage.

R EPORTS

We have been able to prepare graphitic

sheets of thicknesses down to a few atomic

layers (including single-layer graphene), to

fabricate devices from them, and to study

their electronic properties. Despite being

atomically thin, the films remain of high

quality, so that 2D electronic transport is

ballistic at submicrometer distances. No

other film of similar thickness is known to

be even poorly metallic or continuous under

ambient conditions. Using FLG, we demon-

strate a metallic field-effect transistor in

which the conducting channel can be

switched between 2D electron and hole gases

by changing the gate voltage.

Our graphene films were prepared by

mechanical exfoliation (repeated peeling) of

small mesas of highly oriented pyrolytic

graphite (15). This approach was found to

be highly reliable and allowed us to prepare

FLG films up to 10 6minsize.Thickerfilms

(d Q 3 nm) were up to 100 6m across and

visible by the naked eye. Figure 1 shows

examples of the prepared films, including

single-layer graphene Esee also (15)^.To

study their electronic properties, we pro-

cessed the films into multiterminal Hall bar

devices placed on top of an oxidized Si

substrate so that a gate voltage V g could be

applied. We have studied more than 60

devices with d G

typical V g 0 100 V, the formula yields n ,

7.2 10 12 cm j2 . The electric field doping

transforms the shallow-overlap semimetal

into either completely electron or completely

hole conductor through a mixed state where

both electrons and holes are present (Fig. 2).

The three regions of electric field doping are

clearly seen on both experimental and

theoretical curves. For the regions with only

electrons or holes left, R H decreases with

increasing carrier concentration in the usual

way, as 1/ne. The resistivity also follows the

standard dependence D j1

0 G 0 ne6 (where

changes little with V g , indicating the substi-

tution of one type of carrier with another,

while the Hall coefficient reverses its sign,

reflecting the fact that R H is proportional to

is carrier mobility). In the mixed state,

10 nm. We focus on the

electronic properties of our thinnest (FLG)

devices, which contained just one, two, or

three atomic layers (15). All FLG devices

exhibited essentially identical electronic

properties characteristic for a 2D semimetal,

which differed from a more complex (2D

plus 3D) behavior observed for thicker,

multilayer graphene (15) as well as from

the properties of 3D graphite.

In FLG, the typical dependence of its sheet

resistivity D on gate voltage V g (Fig. 2)

exhibits a sharp peak to a value of several

kilohms and decays to

Fig. 1. Graphene films. (A) Photograph (in normal white light) of a relatively large multilayer

graphene flake with thickness

3 nm on top of an oxidized Si wafer. (B) Atomic force microscope

m area of this flake near its edge. Colors: dark brown, SiO 2 surface;

orange, 3 nm height above the SiO 2 surface. (C) AFM image of single-layer graphene. Colors: dark

brown, SiO 2 surface; brown-red (central area), 0.8 nm height; yellow-brown (bottom left), 1.2 nm;

orange (top left), 2.5 nm. Notice the folded part of the film near the bottom, which exhibits a

differential height of

mby2

0.4 nm. For details of AFM imaging of single-layer graphene, see (15). (D)

Scanning electron microscope image of one of our experimental devices prepared from FLG. (E)

Schematic view of the device in (D).

n 0 ( T ) /n 0 (4K)

( m Ω

-1

)

gate voltage for different temperatures

(T 0

5, 70, and 300 K for top to bottom

curves, respectively). (B) Example of

changes in the film’s conductivity

100 ohms at high V g

(note that 2D resistivity is given in units of

ohms rather than ohms cm as in the 3D

case). Its conductivity G 0 1/D increases

linearly with V g on both sides of the resistivity

peak (Fig. 2B). At the same V g where D has its

peak, the Hall coefficient R H exhibits a sharp

reversal of its sign (Fig. 2C). The observed

behavior resembles the ambipolar field effect

in semiconductors, but there is no zero-

conductanceregionassociatedwiththeFermi

level being pinned inside the band gap.

Our measurements can be explained

quantitatively by a model of a 2D metal

with a small overlap & ( between conductance

and valence bands (15). The gate voltage

induces a surface charge density n 0 ( 0 ( V g /te

and, accordingly, shifts the position of the

Fermi energy ( F . Here, ( 0 and ( are the

permittivities of free space and SiO 2 , respec-

tively; e is the electron charge; and t is the

thickness of our SiO 2

G 0

(V g ) obtained by inverting the 70 K

curve (dots). (C) Hall coefficient R H

versus V g for the same film; T 0

5K.(D)

Temperature dependence of carrier

concentration n 0 in the mixed state

for the film in (A) (open circles), a

thicker FLG film (squares), and multi-

layer graphene (d ,

-100 0 100

V g (V)

100

300

5 nm; solid circles).

Red curves in (B) to (D) are the

dependences calculated from our mod-

el of a 2D semimetal illustrated by

insets in (C).

T (K)

δε

ε F

0.5

ε F

-100

-50

100

layer (300 nm). For

V g (V)

www.sciencemag.org SCIENCE VOL 306 22 OCTOBER 2004

667

(AFM) image of 2

Fig. 2. Field effect in FLG. (A) Typical

dependences of FLG’s resistivity

R EPORTS

to large

positive V g . However, this shift is attributed

to an unintentional doping of the films by

absorbed water (16, 17). Indeed, we found

that it was possible to change the position of

the peak by annealing our devices in

vacuum, which usually resulted in shifting

of the peak close to zero voltages. Exposure

of the annealed films to either water vapor or

NH 3 led to their p- and n-doping, respec-

tively (15). Therefore, we believe that intrin-

sic FLG is a mixed-carrier material.

Carrier mobilities in FLG were deter-

mined from field-effect and magnetoresist-

ance measurements as 6 0 G(V g )/en(V g ) and

6 0 R H /

Shubnikov–de Haas (ShdH) oscillations in

both longitudinal resistivity D xx and Hall re-

sistivity D xy (Fig. 3A), serving as another

indicator of the quality and homogeneity of

the experimental system. Studies of ShdH os-

cillations confirmed that electronic transport

in FLG was strictly 2D, as one could reason-

ably expect, and allowed us to fully charac-

terize its charge carriers. First, we carried out

the standard test and measured ShdH oscil-

lations for various angles K between the

magnetic field and the graphene films. The

oscillations depended only on the perpendic-

ular component of the magnetic field BIcos K,

as expected for a 2D system. More impor-

tant, however, we found a linear dependence

of ShdH oscillations_ frequencies B F on V g

(Fig. 3B), indicating that the Fermi energies

( F of holes and electrons were proportional

to their concentrations n. This dependence is

qualitatively different from the 3D dependence

( F º n 2/3 and proves the 2D nature of charge

carriers in FLG. Further analysis (15) of ShdH

oscillations showed that only a single spa-

tially quantized 2D subband was occupied up

to the maximum concentrations achieved in

our experiments (È3 10 13 cm j2 ). It could

be populated either by electrons with mass

m e , 0.06m 0 (where m 0 is the free electron

mass) located in two equivalent valleys, or

by light and heavy holes with masses of

È0.03m 0 and È0.1m 0 and the double-valley

degeneracy. These properties were found to

be the same for all FLG films studied and are

notably different from the electronic struc-

ture of both multilayer graphene (15) and

bulk graphite (5–7). Note that graphene is

expected (5–7) to have the linear energy

dispersion and carriers with zero mass, and

the reason why the observed behavior is so

well described by the simplest free-electron

model remains to be understood (15).

We also determined the band overlap & (

in FLG, which varied from 4 to 20 meV for

different samples, presumably indicating a

different number of graphene layers involved

(18). To this end, we first used a peak value

D m of resistivity to calculate typical carrier

concentrations in the mixed state, n 0 (e.g., at

low T for the sample in Fig. 2, A to C, with

6 , 4000 cm 2 /V and D m , 8 kilohms, n 0 was

È2 10 11 cm j2 ). Then, & ( can be estimated

as n 0 /D, where D 0

2 is the 2D

density of electron states and I is Planck_s

constant divided by 2>. For the discussed

sample, this yields & ( , 4 meV Ei.e., much

smaller than the overlap in 3D graphite

(È40 meV)^. Alternatively, & ( could be

calculated from the temperature dependence

of n 0 , which characterizes relative contribu-

tions of intrinsic and thermally excited car-

riers. For a 2D semimetal, n 0 (T) varies as

n 0 (0 K)IfIlnE1 þ exp(1/f )^, where f 0 2k B T/& (

and k B is Boltzmann_s constant; Fig. 2D

shows the best fit to this dependence, which

yields & ( , 6 meV. Different FLG devices

were found to exhibit a ratio of n 0 (300 K)/

n 0 (0) between 2.5 and 7, whereas for

multilayer graphene it was only È1.5 (Fig.

2D). This clearly shows that & ( decreases

with decreasing number of graphene layers.

The observed major reduction of & ( is in

agreement with the fact that single-layer

graphene is in theory a zero-gap semicon-

ductor (5, 18).

Graphene may be the best possible metal for

metallic transistor applications. In addition to

the scalability to true nanometer sizes envis-

aged for metallic transistors, graphene also

offers ballistic transport, linear current-voltage

(I-V) characteristics, and huge sustainable

currents (910 8 A/cm 2 )(15). Graphene tran-

sistors show a rather modest on-off resistance

ratio (less than È30 at 300 K; limited because

2m e /> I

, respectively. In both cases, we

obtained the same values of 6, which varied

from sample to sample between 3000 and

10,000 cm 2 /VIs. The mobilities were practi-

cally independent of absolute temperature T,

indicating that they were still limited by

scattering on defects. For 6 , 10,000 cm 2 /VIs

and our typical n , 5 10 12 cm j2 , the mean

free path is È0.4 6m, which is surprising

given that the 2D gas is at most a few )

away from the interfaces. However, our

findings are in agreement with equally high

6 observed for intercalated graphite (5),

where charged dopants are located next to

graphene sheets. Carbon nanotubes also exhib-

it very high 6, but this is commonly attributed

to the suppression of scattering in the 1D case.

Note that for multilayer graphene, we observed

mobilities up to È15,000 cm 2 /VIs at 300 K

and È60,000 cm 2 /VIsat4K.

Despite being essentially gigantic fuller-

ene molecules and unprotected from the

environment, FLG films exhibit pronounced

Fig. 3. (A)ExamplesofShdH

oscillations for one of our FLG

devices for different gate volt-

ages; T 0

1.5

-100V @ 9T

3K,andB is the mag-

netic field. As the black curve shows,

we often observed pronounced

plateau-like features in

+80V

D xy at val-

1.0

+80V

(in this case,

( F matches the Landau level with

filling factor

100

T (K)

2ataround9T).

Such not-fully-developed Hall

plateaus are usually viewed as an

early indication of the quantum

Hall effect in the situations where

D xx does not yet reach the zero-

resistance state. (B) Dependence

of the frequency of ShdH oscilla-

tions B F on gate voltage. Solid and

open symbols are for samples with

& ( ,

8 0

+100V

0.5

-25V

-100V

-100

-50

100

B (T)

V g (V)

6 meV and 20 meV, respec-

tively. Solid lines are guides to the eye. The linear dependence B F º

V g indicates a constant (2D) density of states (15). The observed

slopes (solid lines) account for the entire external charge n induced

by gate voltage, confirming that there are no other types of carriers

and yielding the double-valley degeneracy for both electrons and

holes (15). The inset shows an example of the temperature

dependence of amplitude

< c is

their cyclotron frequency. The fit (solid curve) yields light holes’ mass

of 0.03m 0 .

k B T/

I < c )where

668

22 OCTOBER 2004 VOL 306 SCIENCE www.sciencemag.org

the difference between electron and hole

concentrations.

Without electric field doping (at zero V g ),

FLG was found to be a hole metal, which is

seen as a shift of the peak in

ues close to (h/4e 2 )/

of ShdH oscillations (circles), which is

fitted by the standard dependence T/sinh(2

R EPORTS

of thermally excited carriers), but this is a

fundamental limitation for any material with-

out a band gap exceeding k B T. Nonetheless,

such on-off ratios are considered sufficient for

logic circuits (19), and it is feasible to increase

the ratio further by, for example, using p-n

junctions, local gates (3), or the point contact

geometry. However, by analogy to carbon

nanotubes (2), other, nontransistor applications

of this atomically thin material ultimately may

prove to be the most exciting.

5. M. S. Dresselhaus, G. Dresselhaus, Adv. Phys. 51,1

(2002).

6. I. L. Spain, in Chemistry and Physics of Carbon,P.L.

Walker, P. A. Thrower, Eds. (Dekker, New York,

1981), pp. 119–304.

7. O. A. Shenderova, V. V. Zhirnov, D. W. Brenner, Crit.

Rev. Solid State Mater. Sci. 27, 227 (2002).

8. A. Krishnan et al., Nature 388, 451 (1997).

9. E. Dujardin, T. Thio, H. Lezec, T. W. Ebbesen, Appl.

Phys. Lett. 79, 2474 (2001).

10. H. Shioyama, J. Mat. Sci. Lett. 20, 499 (2001).

11. Other methods of preparing thin graphitic layers

exist. The closest analogs of FLG are nanometer-sized

patches of graphene on top of pyrolytic graphite (12,

13), carbon films grown on single-crystal metal

substrates (14), and mesoscopic graphitic disks with

thickness down to

17. M. Kru¨ger,I.Widner,T.Nussbaumer,M.Buitelaar,

C. Sch¨nenberger, N. J. Phys. 5, 138 (2003).

18. We believe that our thinnest FLG samples (as in

Fig. 2A) are in fact zero-gap semiconductors,

because small nonzero values of & ( found exper-

imentally can be attributed to inhomogeneous

doping, which smears the zero-gap state over a

small range of V g and leads to finite apparent & ( .

19. M. R. Stan, P. D. Franzon, S. C. Goldstein, J. C. Lach,

M. M. Zeigler, Proc. IEEE 91, 1940 (2003).

20. Supported by the UK Engineering and Physical

Sciences Research Council and the Russian Acad-

emy of Sciences (S.V.M., S.V.D.). We thank L. Eaves,

E. Hill, and O. Shklyarevskii for discussions and

interest.

Supporting Online Material

www.sciencemag.org/cgi/content/full/306/5696/666/

DC1

Materials and Methods

SOM Text

Figs. S1 to S11

References and Notes

1. C. D. Dimitrakopoulos, D. J. Mascaro, IBM J. Res. Dev.

45, 11 (2001).

2. R. H. Baughman, A. A. Zakhidov, W. A. de Heer,

Science 297, 787 (2002).

3. S. V. Rotkin, K. Hess, Appl. Phys. Lett. 84, 3139

(2004).

4. A. V. Butenko, D. Shvarts, V. Sandomirsky, Y.

Schlesinger, J. Appl. Phys. 88, 2634 (2000).

60 graphene layers (8, 9).

12. A. M. Affoune et al., Chem. Phys. Lett. 348,17

(2001).

13. K. Harigaya, Y. Kobayashi, K. Takai, J. Ravier, T. Enoki,

J. Phys. Cond. Matter 14, L605 (2002).

14. T. A. Land, T. Michely, R. J. Behm, J. C. Hemminger,

G. Comsa, Surf. Sci. 264, 261 (1992).

15. See supporting data on Science Online.

16. J. Kong et al., Science 287, 622 (2000).

19 July 2004; accepted 15 September 2004

Hydrated Electron Dynamics:

From Clusters to Bulk

A. E. Bragg, 1 J. R. R. Verlet, 1 A. Kammrath, 1 O. Cheshnovsky, 2

D. M. Neumark 1,3 *

Transient absorption measurements made

with femtosecond (fs) laser pulses as short as 5

fs (12) show a near infrared (NIR) absorption

band beyond 900 nm developing on a 40- to

50-fs time scale after e a – ( p) @ e a – (s)

excitation. This broad feature shifts back to

shorter wavelengths on a time scale of several

hundred fs, with recovery of the original e a – (s)

absorption spectrum largely complete within

The electronic relaxation dynamics of size-selected (H 2 O) n

– /(D 2 O) n

–

[25 e

50] clusters have been studied with time-resolved photoelectron imaging.

The excess electron ( e c

1 picosecond (ps). Deuteration of the

solvent (8, 12) appears only to affect the

fastest measured time scale (i.e., the buildup

time of the transient NIR absorption), with

C D 2 O / C H 2 O 0 1.4 to 1.6. As described by

Yokoyama et al.(8), two rather different

energy relaxation mechanisms have been

proposed to account for these observations.

In the Badiabatic solvation[ scheme (13, 14),

the infrared transient at the earliest times is

attributed to absorption of the e a – ( p)electron,

which is solvated on the upper state within 50

fs (process x in Fig. 1A). The excited electron

then undergoes internal conversion (IC) to the

ground state (y) on a 400-fs time scale,

generating ground-state electrons that further

relaxontheÈ1-ps time scale by dissipating

energy to the solvent. In contrast, the

Bnonadiabatic relaxation[ mechanism (7, 9,

12) invokes much more rapid IC, on a 50-fs

time scale, and attributes the transient NIR

band at early times to absorption of the

ground-state electron in a vibrationally excited

solvent environment. In this model, subsequent

dynamics are assigned to reorganization of the

local (È400 fs) and extended (È1 ps) solvent

network following the electronic decay.

We present an alternative and comple-

mentary approach to assessing the relaxation

dynamics of the hydrated electron through

time-resolved photoelectron imaging (TRPEI)

studies (15) of electron dynamics in size-

selected water cluster anions, (H 2 O) n –

– ( s ) transition with

an ultrafast laser pulse, with subsequent evolution of the excited state

monitored with photodetachment and photoelectron imaging. All clusters

exhibited p-state population decay with concomitant s-state repopulation

(internal conversion) on time scales ranging from 180 to 130 femtoseconds

for (H 2 O) n

– ) was excited through the e c

– ( p ) @ e c

– ; the lifetimes decrease

with increasing cluster sizes. Our results support the ‘‘nonadiabatic relaxa-

tion’’ mechanism for the bulk hydrated electron ( e aq

– and 400 to 225 femtoseconds for (D 2 O) n

–

), which invokes a 50-

femtosecond

e aq

(

Y e aq

(

s . ) internal conversion lifetime.

A free electron introduced into a polar sol-

vent, such as water (1)orammonia(2), may

be trapped by locally oriented solvent mole-

cules. In water, an Bequilibrated[ hydrated

electron Ee a – (s)^ can be transiently confined

within a roughly spherical cavity defined by

six OH bonds oriented toward the negative

charge distribution in the so-called Kevan

geometry (3–5). The hydrated electron is an

important reagent in condensed-phase chem-

istry and molecular biology, as it participates

in radiation chemistry, electron transfer, and

charge-induced reactivity. Thus, research in-

vestigating the dynamics of this species,

whether in the presence or absence of other

reagents, has attracted considerable attention

in the theoretical and experimental physical

chemistry communities. Here, we present

time-resolved results on the electronic relax-

ation dynamics of anionic clusters of water

that lend profound insight to the elucidation of

hydrated electron dynamics in the bulk.

The electronic energetics of a hydrated

electron are characterized by three types of

states (Fig. 1A): a localized e a – (s) ground

state; three localized, near-degenerate e a – ( p)

excited states; and a delocalized conduction

band (CB) characterized by a charge distri-

bution spread across hundreds of molecules

in the solvent Bnetwork.[ The visible ab-

sorption spectrum of the equilibrium hy-

drated electron, a broad band peaking at

720 nm (1), is well understood as an ex-

citation from the occupied e a – (s) state to the

vacant e a – ( p) states (4, 5). The electron-

solvent dynamics subsequent to e a – ( p) @

e a – (s) excitation are more controversial, how-

ever, in spite of considerable experimental

(6–12) and theoretical (13, 14) effort devoted

to this problem.

1 Department of Chemistry, University of California,

Berkeley, CA 94720, USA. 2 School of Chemistry, The

Sackler Faculty of Exact Sciences, Tel-Aviv University,

69978 Israel. 3 Chemical Sciences Division, Lawrence

Berkeley National Laboratory, Berkeley, CA 94720,

USA.

*To whom correspondence should be addressed.

E-mail: dan@radon.cchem.berkeley.edu

and

– , with 25 e n e 50. Water cluster

anions were first detected mass spectromet-

www.sciencemag.org SCIENCE VOL 306 22 OCTOBER 2004

669

n e

–

)

–

(D 2 O) n

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