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May 02, 2013

C 2013 American Chemical Society

Room-Temperature Single-ElectronCharging Detected by ElectrostaticForce MicroscopyAntoni Tekiel,* Yoichi Miyahara, Jessica M. Topple, and Peter Grutter

Physics Department, McGill University, 3600 University Street, Montreal, QC H3A 2T8, Canada

In nanoelectronic devices where compo-nents are connected by tunnel barriersand capacitively coupled to external

electrodes, the transport can be dominatedby single electron effects. Among such phe-nomena, Coulomb charging plays a key rolein many systems, including single electrontransistors and single electron memory de-vices. Measurement of the capacitance be-tween the components of nanoscale circuitsand understanding its origin is of greatimportance for the effort of improving suchdevices in order to work reliably at roomtemperature.1,2 However, characterizationof local electronic properties becomes in-creasingly challenging as structures are re-duced to nanoscale dimensions. Methodsbased on transport measurements and con-ventional charge sensing are limited in flex-ibility since they require lithographic techni-ques to fabricate nanoscale electrodes. Inthis work, we use electrostatic force micro-scopy with single-electron sensitivity (e-EFM)to characterize charging of individual Aunanoparticles (NP), including measurementof electron addition spectra and tunnelingrates. The nanoparticles are separated froman Fe(001) back electrode by an ultra-thinNaCl film and due to their small size exhibitCoulomb blockade at room temperature.

Because the e-EFM technique can both im-age the topography of the studied deviceand measure electronic properties of indi-vidual nanoparticles, it allows for exploringstructure�property relationships. Given thesimple design of the studied system, we usefinite element electrostatic simulation toexamine the relevant contributions to thetotal nanoparticle capacitance, which is de-termined experimentally from themeasure-ment of electron addition energy. The resultspoint toward a total capacitance dominatedby themutual capacitance between the nano-particle and the back electrode. A comparisonof the experimentally determined capacitancewith numerical simulations indicates that thenanoparticles should bemodeled as truncatedspheres in order to reduce the mutual capaci-tance to the substrate.The e-EFM technique is a new and extre-

mely versatile method that is based on non-contact atomic force microscopy (NC-AFM)and suited for characterization of nano-structures supported on thin insulating films.In e-EFM an oscillating AFM tip is used bothas a gate to charge individual nanoparticleswith single electrons from a conductingback electrode, and a charge-sensitive probeto detect the tunneling through a change incantilever energy dissipation. As a scanning

* Address correspondence toantoni.tekiel@mail.mcgill.ca.

Received for review April 14, 2013and accepted May 2, 2013.

Published online10.1021/nn401840n

ABSTRACT We use atomic force microscopy to measure electron

addition spectra of individual Au nanoparticles that exhibit Coulomb

blockade at room temperature. The cantilever tip charges individual

nanoparticles supported on an ultra-thin NaCl film via single-electron

tunneling from the metal back electrode. The tunneling is detected by

measuring frequency shift and damping of the oscillating cantilever. Finite

element electrostatic calculations indicate that the total nanoparticle

capacitance is dominated by mutual capacitance to the back electrode.

KEYWORDS: Coulomb blockade . capacitance . single-electron tunneling . room-temperature charge stability . Au nanoparticles .atomic force microscopy . finite element method

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probe technique, e-EFM can routinely access nano-meter length scale and offers an alternative approachthat overcomes the difficulty in attaching the electro-des. The e-EFM technique has been successfully used atcryogenic temperatures3�9 to measure energy spectra(ground8 and excited states9), electron tunneling rates,as well as shell structures8 of various nanoscale struc-tures and entities. It is clear that in principle thistechnique, which has been used at temperatures ashigh as 95 K,8 could alsowork at room temperature andlead to wide-ranging applications.6 So far, however,the only e-EFM experiment conducted at room tem-perature reported a relatively weak signal,10 makingcharacterization of individual nanostructures difficult.In this work, we extend the e-EFM technique to roomtemperature by carefully tuning the sample design andfabrication relative to the cantilever response toachieve maximum sensitivity.The essential part of the e-EFMmethod is an insulat-

ing film that separates the nanostructures under in-vestigation from a back electrode, which is shownschematically in Figure 1a. The rate of tunnelingthrough the thin insulating film largely decides thesensitivity of the method by affecting the relativestrength of the cantilever dissipation and frequencyshift signals,6 which are measured in e-EFM. Figure 1bshows that the dissipation of the cantilever, Δγ, ismaximal when the tunneling rate is matched withthe oscillation frequency of the cantilever, while the

frequency shift, Δω = 2πΔf, increases with increasingtunneling rate (see also the Supporting Information).Although the signal could be optimized by a properchoice of the cantilever, this imposes a potentiallimitation due to the range of resonance frequencies(10�1000 kHz) of commercially available AFM probes.Alternatively, the e-EFM technique can be made sensi-tive at room temperature by achieving full control overthe tunnel barrier thickness and adjusting the tunnel-ing rate to the cantilever resonance frequency. Weutilize an ultra-thin epitaxial NaCl film as the tunnelbarrier, grown under ultra-high vacuum (UHV) on theFe(001)-p(1� 1)O surface of the Fe back electrode. Ourgroup has recently developed a method to grow suchfilms layer by layer with a small number of defects.11

Metal nanoparticles, formed by thermally evaporatingAu onto the NaCl surface, are used as electron confin-ing nanostructures.

RESULTS AND DISCUSSION

Figure 1c shows an NaCl film at a nominal thicknessof 7 atomic monolayers (ML) with a submonolayercoverage of Au. The epitaxial NaCl film has a (001)orientation and a (4� 4) symmetrywith charge-neutralstep edges oriented along the Æ110æ directions of theFe(001) substrate. It grows in a near perfect layer-by-layer mode, allowing for precise control of the tunnelbarrier thickness.11 Although the underlying step edgesof Fe slightly disturb the nearby growth of NaCl, on flat

Figure 1. (a) Schematic of the studied system. The AFM tip is used as a local gate to charge individual nanoparticles withelectrons from the back electrode. (b) Plot of the dissipation and resonance frequency shift response (in normalized units)versus the normalized tunneling rate (in units of the cantilever resonance frequency,ω0 = 2πf0). (c) Topography of anNaCl thinfilmwith a submonolayer coverageof Au that self-assembled into homogeneous nanoparticles. (d) Topography of studiedAunanoparticles (the width of the nanoparticles derived from AFMmeasurements is overestimated). (e) Energy diagram of thesystem for positive sample bias allowing for sequential unloading of electrons.

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substrate areas the film is characterized by an almostcomplete sixthML, and a far from complete seventhML.On the NaCl film, as shown in Figure 1c, Au reveals astrong affinity for substrate steps, similarly to alkalihalide bulk surfaces,12�15 To meet the requirementfor the electron addition energy, Eadd, to be largerthan kBT at room temperature, a small amount of Au(approximately 0.02ML) was deposited that resulted ina formation of isolated nanoparticles (with an averagenumber density of 1.3� 1011 NP/cm2). The nanoparticlesare anchored symmetrically above NaCl step edges andare homogeneous in size. In Figure 1d, the size of thestudied nanoparticles is characterized by a height of3.5 nm when measured from the lower NaCl terrace anda diameter of approximately 10 nm. In topography char-acterization, the AFM tip usually leads to increased lateraldimensions due to tip convolution effects.12,13,15 For thisreason, the width of the nanoparticles derived from theAFMtopographymeasurement is certainly overestimated.To induce tunneling between a supported Au nano-

particle and the back electrode, the AFM tip is placedwithin several nanometers above the nanoparticle (seeFigure 1a). A DC bias voltage, VB, is applied to the backelectrode, while the oscillating cantilever is electricallygrounded. Tunneling between the tip and the nano-particle is negligible because of the large barrier heightand width (∼5 nm) of the vacuum gap. The potentialdropbetween theAunanoparticle and thebackelectrode,i.e., across the NaCl tunnel barrier, is a fraction of theapplied bias voltage, RVB (R < 1). The R(x,y,z) parameter(commonly called the lever-arm) depends on the lateraland vertical position of the tip. Consequently, even smalltip oscillations modulate R, leading to an effective mod-ulation of the voltage across the barrier. Tunneling of anelectron between the back electrode and the Au nano-particle only takes place if the Coulomb blockade is liftedby selecting a proper value of VB and tuning eRVB to oneof the electrochemical potential levels of the nanoparticle(Figure 1e). Under this condition, the oscillation of R leadsto an oscillation of the number of electrons on thenanoparticle, N, between two neighboring ground statescharacterized by N = n and N = n þ 1 electrons. Theoscillating charge on the nanoparticle causes both aresonance frequency shift, Δf, and damping of the

cantilever, Δγ.7,8 Although tunneling of electrons is astochastic event, the average charge, ÆN(t)æ, follows theoscillating motion of the tip. As a result, the oscillatingelectrostatic force has not only an in-phase, but also a 90�out-of-phase component that leads to energy dissipation(which is a similar effect to theQ-factor degradation in theQ-control system used in amplitude modulation AFM16).A detailed quantummechanical treatment of the coupledcantilever-quantum dot system is needed to understandtheexperimentallyobserved frequencyanddissipation lineshapes, which has been explored in detail elsewhere.7,8

We first focus on qualitative observation of thetunneling process by scanning the tip in the area withthe three nanoparticles shown in Figure 1d in constantheight mode with fixed VB. Figure 2 shows a setof dissipation (γ) images recorded at a tip heightof ≈8 nm (measured from the level of NaCl surfacetopography characterization) with a fixed bias voltagein the range of 11�13 V. In this situation, although thetip height remains constant (it is only slightly modu-lated due to the cantilever oscillation amplitude), thelevel arm R depends on the relative position withrespect to the nanoparticle and decreases monotoni-cally as a function of the tip�nanoparticle distance. Ifthe bias voltage is high enough to induce Coulomboscillations, dissipation features are visible in the γimages as concentric rings centered above nanoparti-cles. The circular shape is a consequence of the factthat R, to a good approximation, does not depend onthe radial direction with respect to a nanoparticle.Considering a single nanoparticle, during the tip scaneRVB takes its maximal value at closest approachdirectly above the nanoparticle. If this maximal valuematches exactly one of the electrochemical potentiallevels, which lifts the Coulomb blockade, a disk-likefeature will form in the γ image. When the VB voltage isfurther increased, the disk transforms into a ring. Thewidth of this disk (and rings) is well understood anddepends among other parameters on the oscillationamplitude of the cantilever.7,8 Each ring originates froma single peak and indicates the spatial positions of the tipwhere eRVB is equal to a particular value that lifts theblockade (the largest ring corresponds to the smallestvalue of eRVB). As shown clearly in Figure 2, the size of the

Figure 2. Dissipation (γ) images taken at room temperature showing the same three Au nanoparticles as Figure 1d, tip heightz≈ 8.3 nm and cantilever oscillation amplitude A = 0.5 nm. The bias voltage across the tunnel barrier, equal to R(x,y,z)VB, wasgradually increased by changing VB from 11 to 13 V, allowing for tunneling of a larger number of electrons.

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nanoparticles is small enough to make the electronaddition energy exceed the thermal energy, kBT, sincethe rings are clearly resolved at room temperature.The potential drop across the tunnel barrier can also

be controlled by changing the tip height while the biasvoltage is kept constant. Decreasing the tip heightincreases all R(x,y) values and leads to a higher poten-tial drop across the tunnel barrier at all lateral tippositions (x,y). If this change is sufficiently large toaccess further electrochemical potential levels of thenanoparticle, which are separated by Eadd, more ringsare observed in the γ images. This is demonstrated inFigure 3a�d, where the tip is brought progressivelycloser to the sample, staring from 10.0 nm and endingup at 7.5 nm, while VB is fixed at 10 V and the cantileveroscillation amplitude is maintained at 1 nm. Each ringemerges first as a disk above the nanoparticle centerand next grows in diameter with decreasing the tipheight. As the ring diameter gets larger, the intensity ofthe ring decreases due to the weaker electrostaticdamping force at larger tip-nanoparticle distances.Figure 3e shows an electron addition spectrum for

the upper nanoparticle imaged in Figure 1c (the tipposition is also marked with a cross in Figure 3d). Theγ-VB spectrum reveals three distinct peaks which cor-respond to the concentric rings imaged in Coulombblockage images in Figures 2 and 3. The dissipationsignal is recorded for positive values of VB, where singleelectrons sequentially tunnel out of the nanoparticlewith increasing VB (see Figure 1e). If the modulation ofeRVB caused by the cantilever oscillation is smaller thanthe thermal energy, which is easily met at room tem-perature, the changes in Δω and Δγ are described bya linear response.8,17,18 In this case, the shape of the

Coulomb blockade peak is given by:

Δγ(VB) ¼ γ0f (ΔE)[1 � f (ΔE)]

¼ γ0 cosh�2 eR(VB � V0)2kBT

(1)

where f(ΔE) is the Fermi functionevaluatedat thepointofcharge degeneracy,V0, withΔE= μNP� μBE = eR(VB� V0)(μNP and μBE are the electrochemical potentials of thenanoparticle and the back electrode, respectively). γ0 is aconstant determined by the measurement temperature,parameters of the cantilever and the coupling strengthbetween the tip and the nanoparticle.8 In the e-EFMmethod, eq 1 can be used to extract the R parameterwithout any knowledge about the tip and sample. Thesolid fitted lines in Figure 3e were obtained by a simulta-neous optimization of ∑i=1

3 Δγi(γi0, Vi

0, Ri), yielding onaverage R = 0.040 (see the Supporting Information fordetails). Once the R parameter is known, Eadd can beobtained from the separation of consecutive peaks in theγ-VB spectrum being Eadd = eRΔi,iþ1 = eR(Viþ1

0 � Vi0). For

the nanoparticle under characterization, the measure-ment gives the addition energy of Eadd = (137( 27) meV,confirming Eadd. kBT requirement. Although in thisworkwe focus on the dissipation signal, a similar additionspectrum was also recorded using the frequency shift,allowing for extraction of tunneling rates, which arewithin 1 order of magnitude of the resonance frequencyof the cantilever (see the Supporting Information).Before we can relate the measurement of the addi-

tion energy to the capacitance of the nanoparticleand draw an equivalent circuit diagram, we performelectrostatic finite element method (FEM) modelingof the studied system using commercially available

Figure 3. (a�d) Dissipation images showing sequential unloadingof electrons fromAunanoparticles throughdecreasing thetip height, and thus increasing R. (e) γ-VB spectrum taken at room temperature over the upper nanoparticle with oscillationamplitude A = 1.0 nm and tip height z = 7.5 nm. Similarly to panel (a), where after entering each ring the number ofelectrons on the nanoparticle reduces by one, the electrons are sequentially unloaded after increasing VB and passingeach peak in the γ-VB spectrum in panel (e). The level arm, R, is determined by a simultaneous fit describing all threepeaks using eq 1. The separation of consecutive peaks, Δ, is given by Eadd/eR, allowing for calculation of nanoparticleaddition energy.

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COMSOL Multiphysics software (version 4.3a). Theconsidered geometry is depicted in Figure 4a, wherethe nanoparticle is supported on a 6 ML thick NaCl film(with 5.9 relative permittivity) and its shape is approxi-mated by a solid hemisphere with a radius of 3.5 nm.Above the nanoparticle, at a distance of 8 nm from theNaCl film, there is a metallic tip with a curvature radiusof 10 nm (at room temperature heavily doped Si can beapproximated by a metal). In total, there are fourelectrodes: (1) the nanoparticle, (2) the back electrode,(3) the tip, and (4) the system boundary. Figure 4bshows three relevant mutual capacitances in this sys-tem. We obtain the following calculated capacitances:C12 = CBE = 2.028 aF, C13 = CTIP = 0.107 aF, C14 = CENV <0.0002 aF, and the total capacitance of the hemisphe-rical nanoparticle CΣ = CBEþ CTIPþ CENV = 2.135 aF. Thecapacitance between the nanoparticle and the systemboundary, i.e., the environment, CENV, which representsthe capacitance to a grounded plane at infinity (oftencalled “self-capacitance”), is negligible. Consequently,the circuit diagram can be reduced to a single electronbox, as shown in Figure 4c. In this case, R = CTIP/CΣ, andCΣ = CTIP þ CBE is the total capacitance of the nano-particle, where the CENV component is neglected. Thecalculated values of the capacitances CTIP and CBE yieldR ≈ 0.050, which is in very good agreement with thevalue obtained experimentally, although the actualnanoparticle and tip shape may be different. Thegeometry shown in Figure 4a can also be used tocalculate the R parameter by applying a voltage bias,e.g., 1 V, to the tip, grounding the back electrode andkeeping the nanoparticle charge-neutral at a floatingvoltage. Still assuming a hemispherical shape, thecalculated voltage at the nanoparticle gives in this situa-tion an indistinguishable value from the previously cal-culated result using the ratio of capacitances.Numerical simulation of the hemispherical nanopar-

ticle suggests a very dominant role of CBE, i.e., themutual capacitance between the nanoparticle and theback electrode in the total capacitance. Most impor-tantly, calculations performed for different tip�sampledistances indicate that CBE does not depend stronglyon the exact position of the tip that is used in theexperiment (see the Supporting Information). An FEMsimulation of the capacitance performed for this nano-particle shape but without the tip leads to a compar-able total capacitance of CΣ = CBE þ CENV = 2.118 aF. Inthis case, the capacitance component due to thesystem boundary is increased, but is still very smallCENV < 0.007 aF, C∑. We found also that CENV dependsweakly on the size of the system in the 100�1000 nmrange used in the FEM modeling. CBE can be stillaccurately calculated in a geometry that is furthersimplified by neglecting the tip and assuming CΣ ≈CBE. The discrepancy is on the order of CTIP, and sinceR = CBE/CΣ, the percentage discrepancy is approximatelyequal to R, which in this experiment is about 5%.

Given the equivalent circuit diagram of a singleelectron box, the total capacitance of the nanoparticlecan be simply obtained from the experimental value ofEadd using the relation Eadd = e2/CΣ, which leads to anexperimental (EXP) total capacitance value of CΣ

EXP =(1.16 ( 0.26) aF with CTIP

EXP = (0.046 ( 0.015) aF andCBEEXP = (1.11 ( 0.26) aF. Clearly, this is much smaller

than CBEFEM ≈ 2.14 aF, i.e., the capacitance calculated for

a hemispherical nanoparticle used in the initial approx-imation above. Increasing the NaCl film thickness from6 to 7 ML reduces CBE

FEM only to 1.95 aF, which does notaccount for the discrepancy between the experimentaland calculated capacitances. What turns out to be highly

Figure 4. (a) FEM geometry for calculating the capacitancecomponents of the nanoparticle (1). (b) Relevant capaci-tances to the three electrodes: back electrode (2), tip (3), andsystem boundary (4). (c) Equivalent circuit diagram for anindividual nanoparticle.

Figure 5. (a) Variously shapednanoparticles supportedon a6 ML thick NaCl film used in capacitance calculations basedon FEM. The shape of truncated spheres of constant height(3.5 nm) is parametrized by a describing the diameter of thecircular contact area (marked schematically in red). (b)Change in the total capacitance for different a parametersshowing that the characterized nanoparticle can be bestmodeled by a truncated sphere with a = 4.2 nm leading toCBEFEM = 1.11 aF. (c) For a similarly shapednanoparticle anchored

symmetrically above an NaCl step edge (between the sixthand seventh ML), the capacitance is only slightly altered(CBE

FEM = 1.13 aF).

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relevant, however, is the contact area between the nano-particle and the back electrode. Because the height of thenanoparticle is precisely known from the experiment(contrary to the lateral size), we can estimate CBE

FEM fornanoparticles with different contact areas. We assume atruncated sphere as the shape of the nanoparticles andcalculateCBE

FEM for different contact areas keeping the sameheight as shown in Figure 5a. The exact shape is parame-trizedby only oneparameter,a, describing thediameter ofthe circular contact area between the nanoparticle and theNaCl film. The a parameter can take values from 0 to 7 nmand describe intermediate shapes spanning from a sphereto a hemisphere. The values calculated from the FEMmodeling are shown in Figure 5b and indicate a specificshape of the nanoparticle that describes correctly theexperimental results. Compared to the hemisphericalnanoparticle, the computationally determined truncatedsphere has both a smaller radius, r= (2.4( 0.3) nm, and asmaller contact areawith adiameter ofa= (4.2( 0.9) nm.To take into account the preferential formation of the Aunanoparticles on the step edges on the NaCl film, acorresponding geometry is alsomodeled (see Figure 5c).For a nanoparticle anchored symmetrically above anNaCl step edge, CBE

FEM is only slightly altered and takes avalue of 1.13 aF (the radius is fixed at r = 2.4 nm). Thedeterminedmorphologyof thenanoparticle correspondsto a volume of 49 nm3 containing ≈2900 atoms, andis very similar to the equilibrium shape of Au nano-and microstructures on a weakly interacting graphitesurface.19,20 Interestingly, it also resembles the shape ofAu nanoparticles on a more complex, rutile TiO2(110)surface, which has been characterized experimentallyby atomic-resolution scanning transmission electronmicroscopy21 and grazing incidence X-ray scatteringtechniques.22

The relatively large number of atoms in the nano-particle justifies the validity of classical electrody-namics equations used in the FEM calculation, as thenumber of electrons on the nanoparticle is large enoughto consider a continuous distribution of the electricalcharge. Similarly, the electron energy level spacing ismuch smaller than the thermal energy at room tempera-ture, thus corresponding to the classical regime of theCoulomb blockade. In this situation, Eadd is mostly due tothe charging energy of the nanoparticle that is deter-mined by the total capacitance. It is worth mentioningthat the self-capacitance of a solid hemisphere with r =3.5 nm in free space calculated analytically23 is 0.329 aF.This value is significantly larger than the CENV component(CENV < 0.0002 aF) calculated above where the hemi-spherical nanoparticle is supported on an NaCl film. Thisclearly suggests that the concept of self-capacitancedefined as the capacitance with reference to a groundedplane at infinity cannot be used to estimate the totalcapacitance of the system with nanoparticles coupled tonearbyelectrodes. It shouldbenoted that theeffectof theself-capacitanceon single-electron charginghasnotbeen

sufficiently emphasized in the literature, and its subtleaspectswere only discussedbyOhgi et al.24 Especially, wefound that the total capacitance cannot be divided into afixed self-capacitance component, which is given by theshapeof thenanoparticle, andmutual capacitances to theelectrodes. Even though this can be still conceptuallydone, such defined capacitances are not additive and donot sum up to the total capacitance of the nanoparticle.This observation has a fundamental impact on the designof nanoelectronic circuits, where the components have tomeet desired requirements for capacitances that deter-mine coupling and charging effects. For instance, in ourstudy the total capacitance of the nanoparticle is domi-nated by the mutual capacitance to the back electrode,which can be primarily controlled by adjusting the con-tact area between the nanoparticle and thedielectricfilm.Given the fabrication flexibility and the fact that all

measurements were performed in situ on samplesprepared under ultraclean conditions, the presentedmethod can be easily extended to other areas. Thewell-definedmorphologymakes the system approach-able by various theoretical methods, including densityfunctional theory and molecular dynamics. A variety ofnanoscale processes on alkali halide surfaces have beenwell characterized, such as the self-assembly of metalclusters and large organic molecules.25 Such detailedunderstanding makes the fabricated system attractivefor further studies. For instance, organic molecules canbe used to interconnect two Au nanoparticles26,27 andcontrol their mutual capacitance and quantum mechan-ical interactions. In this way, coherent tunneling in coup-led quantum dots28 could be systematically studiedin situ. Our approach is also applicable to studies ofmodelcatalysis on various insulating oxide films at temperaturesas high as room temperature, as there is a close analo-gy with the widely studied system of Au nanoparticlessupported onMgO films.29 Au nanoparticles are known tobe a very efficient catalyst that can be active over a widerange of temperatures.30 The chemical functionality ofsuch metal nanostructures depends crucially on their sizeand shape, as well as the charge state,31 which can becharacterized by e-EFM. The size of nanoparticles used inthis study is very close to the regime in which Au revealsmaximal chemical activity.31 By shortening the evapora-tion time this size can be reduced leading to enhancedelectronic quantum size effects that play a significant rolein oxidation of CO molecules by Au nanoclusters.32 Thee-EFMmethod couldbeusednot only to sense the chargestateof individualAuclusters, but also to resolveelectronicquantum energy levels and observe changes in frontierorbitals upon interaction with reactants.

CONCLUSIONS

We have demonstrated that by exercising precisecontrol over sample design and growth the e-EFMtechnique can be used to characterize single-electroncharging at room temperature. The electron addition

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energy of a 3.5 nm tall Au nanoparticle supported on a6 ML thick NaCl film is measured as Eadd = (137 ( 27)meV, which substantially exceeds the thermal energyand allows for observation of the Coulomb blockade atroom temperature. Electrostatic FEM calculations in-dicate that the total nanoparticle capacitance is domi-nated by themutual capacitance to the back electrode.The nanoparticle shape modeled that best matchedour experimental data was a truncated sphere, in

which the mutual capacitance to the substrate canbe reduced. Flexible in situ fabrication based on well-characterized UHV processing techniques of alkalihalide surfaces can extend the e-EFM technique toroom temperature characterization of other systemson thin insulating films. In particular, this approach canbe used to study quantum mechanically coupledquantumdots and the catalytic activity of Au nanoclus-ters at room temperature.

METHODSThe experiment, including sample preparation and charac-

terization, was performed in a modified commercial JEOL JSPM4500a UHV AFM system. The detailed preparation procedure ofthe NaCl film, whichwas grown on an Fe(001)-p(1� 1)O surface,is described elsewhere.11 A submonolayer of Au was depositedby an electron-beam evaporator (Oxford Applied ResearchEGN4, fitted with a charge-retarding grid) onto the sample keptat room temperature. For data acquisition and cantilever oscil-lation, a scanning probe microscope (SPM) control systemfrom SPECS-Nanonis was used. A highly doped Si cantilever(Nanosensors PPP-QNCHR) with a resonance frequency ofapproximately 286 kHz, Q-factor of 33 000 and nominal springconstant of 42 N/m was oscillated with a phase-locked looposcillation controller (OC4 fromNanonis). The amplitude controllerwas used to regulate the driving signal amplitude in order to keepthe oscillation amplitude constant while tracking the resonancefrequency of the cantilever with a phase-locked loop. The topo-graphy images were taken in constant frequency shift mode,where the frequency shift of the cantilever was maintainedconstant by the SPM feedback loop controlling the z-piezo posi-tion. The dissipation of the cantilever can be extracted bymeasur-ing theQ-factor degradation, which corresponds to the amplitudeof the cantilever drive signal needed to keep the amplitude of theoscillation constant.8 The dissipation images were recorded inconstant-height mode with linear z-drift compensation.33 Thecorrection for the vertical drift improved the stability of the tipheight at room temperature by reducing its change to only afraction of a nanometer over the time needed to scan one frame,which typically was 15 min. During the experiment, the vacuumpressure was maintained in the low 10�8 Pa range.

Conflict of Interest: The authors declare no competingfinancial interest.

Acknowledgment. We acknowledge helpful discussionswith Antoine Roy-Gobeil from McGill University. This work waspartly supported by Natural Sciences and Engineering ResearchCouncil (NSERC), Canadian Institute for Advanced Research(CIfAR), Canadian Microelectronics Corporation (CMC) and Re-groupementQuébécois sur lesMatériaux de Pointe (RQMP). A.T.gratefully acknowledges NSERC for financial support as a VanierCanada Graduate Scholar.

Supporting Information Available: Additional details aboutthe e-EFM method, best-fit parameters, estimation of tunnelingrates and finite element electrostatic simulations. This materialis available free of charge via the Internet at http://pubs.acs.org.

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