Multiexciton Engineering in SeededCore/Shell Nanorods: Transfer fromType-I to Quasi-type-II RegimesAmit Sitt,† Fabio Della Sala,‡ Gabi Menagen,† and Uri Banin*,†

The Institute of Chemistry and the Center for Nanoscience and Nanotechnology,The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel, and NNL-NationalNanotechnology Laboratory of CNR-INFM, UniVersita del Salento, Via per Arnesano,73100 Lecce, Italy

Received May 27, 2009; Revised Manuscript Received July 24, 2009

ABSTRACT

Multiple excitations in core/shell CdSe/CdS-seeded nanorods of different core diameters are studied by quasi-cw multiexciton spectroscopyand envelope function theoretical calculations. For core diameters below 2.8 nm, a transfer from binding to repulsive behavior is detected forthe biexciton, accompanied by significant reduction of the triexciton oscillator strength. These characteristics indicate a transition of theelectronic excited states from type-I localization in the core to a quasi-type-II delocalization along the entire rod as the core diameter decreases,in agreement with theoretical calculations.

Colloidal core/shell semiconductor nanocrystals (NCs) haveattracted considerable interest in the past few years owingto their unique optical and electrical properties, which aregoverned by the composition, dimensions, and shape of eachof their components.1-6 By controlling the NCs’ potentialprofile through material choice and particle size, the spatialdistribution of the electrons’ and holes’ excited state wavefunctions can be confined either to the core or to the shell.Consequently, the overlap between the wave functions canbe controlled, affecting the band gap photoluminescence (PL)energy, the quantum yield, the lifetime, and the multiexciton(MX) properties. For example, NCs with a type-I enclosedpotential profile, where both electrons and holes are confinedto the same region of the NC, exhibit bright and stablefluorescence and are used for biological tagging7-9 and asemitters in light-emitting diodes,10-12 while NCs with a type-II staggered potential profile, where electrons and holes areconfined to the different regions of the NC, exhibit intrinsiccharge separation, which is beneficial for photovoltaicapplications.5,6,13 The MX states in such systems also exhibitremarkably different behaviors and reveal intriguing many-body interactions.5,6,14,15 The biexciton (BX) state in a type-II system is characterized by a repulsive interaction leadingto a blue-shifted emission peak with respect to the exciton(X), which was shown to provide advantageous lasingproperties,6 while in a type-I system, the BX state is

characterized by an attractive interaction leading to a red-shifted emission peak with respect to the X peak.

Recently, several types of high-quality seeded rod quantumdots (QDs), in which a CdS rod-like shell was grown ontoa spherical NC, were developed.16-19 Of particular interestis the system of a CdSe core embedded in a CdS rod, whichyields highly uniform NCs with very high quantum yields(reaching 70%)16,17,19 and linearly polarized photolumines-cence that can be tuned by an external electric field.20,21 Thesehigh-quality heterostructures provide a benchmark for fun-damental studies of optical and electronic properties in asystem of mixed dimensionality where the core is a 0D dot,while the rod-shaped shell imposes a 1D confinement.Elegant optical studies on these systems, utilizing lifetimemeasurements accompanied by model calculations, yieldeda conclusion of a flat band offset for the conduction band,resulting in a quasi-type-II system, where the electron isdelocalized over the CdS nanorod while the hole is localizedto the core.17,20-22 However, more direct scanning tunnelingspectroscopy (STS) studies accompanied by model calcula-tions on such NCs indicate a type-I band offset of 0.3 eVfor the conduction band potential.23 To date, this differenceregarding the band offsets of the system in the literature wasnot explained.

Here, we investigate multiexciton (MX) behavior of CdSe/CdS-seeded rods and explore its dependence on the dimen-sions of the system using quasi-continuous-wave MX spec-troscopy24 along with theoretical modeling. On the basis ofthe X-BX emission spectral shifts, we analyze the nature

* To whom correspondence should be addressed. E-mail: banin@chem.ch.huji.ac.il.

† The Hebrew University of Jerusalem.‡ CNR-INFM.

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10.1021/nl901679q CCC: $40.75 2009 American Chemical SocietyPublished on Web 08/05/2009

of the system, showing its shift from a type-I to a quasi-type-II behavior while changing the CdSe core’s diameter, andshow that this behavior can be explained by considering a type-Ipotential band offset. We also demonstrate that the quasi-type-II system MX behavior can be tuned and that the MX peakpositions can be red shifted just by increasing the rod’s width.This study resolves the previous differences between opticalstudies and the STS work discussed above.

CdSe cores of several diameters, ranging from 2.2 to 4nm, were synthesized and encapsulated within CdS rods withdiameters of ∼5 nm and lengths ranging from 45 to 100nm, based on literature procedures (see Table S1 of theSupporting Information for the dimensions of the samples).17

In addition, for a core size of 2.2 nm, CdS rods of severalwidths and lengths were attained by halting the synthesis atdifferent times after the injection of cadmium and sulfurprecursors through rapid cooling of the system to roomtemperature using a water bath (see Table S2 of theSupporting Information for the dimensions of this set ofsamples). The samples were cleaned and purified throughprecipitation and redissolved in hexane for spectroscopicmeasurements. The effective dimensions of the NCs weremeasured by transmission electron microscopy (TEM)analysis of at least 100 particles per sample (see Figure S1of the Supporting Information for characteristic TEM im-ages).

MX experiments were performed using the quasi-continu-ous-wave (qcw) excitation method,24 in which a nanosecondoptical excitation pulse, long compared to the Augerlifetimes, was used. The average number of excitons per QD,⟨n⟩, was determined in this regime by a steady-state ladderclimbing process, where higher MX states are sequentiallygenerated upon increasing the excitation fluence via statefilling. As the MX emissions occur at different wavelengthsthan that of the X, it is possible to separate the instantaneousemission spectrum temporally overlapping the excitationpulse into the different components which are related to eachMX state. The laser source used in our experiments is afrequency-tripled Q-switched Nd:YAG laser (355 nm)providing 5 ns pulses at 10 Hz. Pulses were weakly focused,at room temperature, to an area of 5 mm2 in a cuvettecontaining QDs in hexane solution with an optical densityof 0.1 at the excitation wavelength. Fluorescence emissionwas collected by a 0.5 numerical aperture lens and directedthrough a monochromator onto a photomultiplier tube. Thesignal was detected on a digital oscilloscope triggered by afast Si p-i-n photodiode. Transient emission spectra wereobtained by scanning the monochromator wavelength overthe entire emission spectral range.

The absorption (Figure 1) and PL spectra (Figure 1, inset)of the CdSe/CdS dot/rod NCs show, from bottom to top,the change in the linear absorption and PL as the corediameter is increased (consecutive traces are shifted verticallyfor clarity). The significant increase in the absorption atwavelengths lower than 500 nm is attributed to the onset ofabsorption into the CdS rod transitions. The position of theCdS absorption peak is nearly the same for all measuredsystems, indicating a weak size dependence of the CdS

electronic states, as expected for this system in the range ofrod dimensions between 4.7 and 6 nm. The weak absorptionpeak at higher wavelengths (Figure 1, inset) is associatedwith the first electronic transition related to the CdSe core,which is of significantly smaller volume compared to theCdS rod. Band edge PL assigned to the X emission can beobserved. Both the emission and CdSe absorption peak arered shifted as the core size is increased due to the quantumsize effect.

Three examples of MX emission spectra, at intensitiesvarying from 10 nJ to 1 mJ per pulse, measured at the peakof the excitation pulse, are shown in Figure 2. Briefly, theX emission is obtained from the lowest-energy data, where,on average, less than one photon is absorbed per dot. Theset of spectra measured at higher illumination intensities isfitted using three additional peaks (each with an arbitraryspectral location and spectral width), accounting for BX (inblue), a triexciton (TX) (in green), and a third peak whichwe shall label as CdS rod emission (in magenta). Theassignment of the peaks is obtained both from their order ofappearance and from the peak amplitude dependence onpump intensity. A detailed description of the fitting procedureappears elsewhere.24

Figure 2a portrays the spectra obtained for CdSe/CdS-seeded rods (core diameter of 4.0 nm; rod dimensions of 45nm × 6 nm). The amplitude of the first appearing peak at612 nm (shown in red) is linearly dependent on the excitationintensity (inset), indicating that it involves the absorption ofone photon, and thus can be assigned to the X. The secondpeak, which appears at a wavelength of 622 nm, (blue)follows a quadratic power law with respect to the excitationintensity, attesting that it involves the sequential absorptionof two photons, and thus can be assigned to the BX. TheBX peak appears significantly red shifted with respect to theX peak. This shift is attributed to the binding interaction inthe BX state, which is typical for type-I systems.

The third appearing peak, at 564 nm, is blue shifted withrespect to the X and can be easily distinguished at high

Figure 1. Absorption spectra of colloidal CdSe/CdS-seeded rodswith different cores sizes (the core diameter, rod length, and roddiameter for each system are listed above). Consecutive spectraare shifted vertically for clarity. The inset shows a magnificationof the absorption in the band gap regions (solid) and band edgeemission (dashed).

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excitation fluences. Due to its low intensity at low excitationfluences, it is difficult to obtain its initial growth from thedata, but it is apparent that once the systems have reachedan absorbance level of a single photon per dot, it shows aquadratic dependence. This implies that a sequential three-photon absorption process is required in order to obtain thisstate, indicating that it is the TX state emission. The lastappearing peak, at 480 nm, also shows a quadratic growth.This peak, whose position is in the vicinity of the CdSabsorption (Figure 1), can be attributed to states in the CdSrod, as will be discussed below.

Figure 2c shows similar spectra obtained from ZnSe/CdS-seeded rods (core diameter of 3.9 nm; rod dimensions of 50nm × 5 nm). In this case, the BX peak, at 563 nm, is blueshifted with respect to the X peak, at 585 nm. This blueshift is typical to type-II systems and is attributed to therepulsive interaction in the BX state. This result agrees withthe bulk band offsets and with STS experiments that wereperformed on this system.23 In addition, the TX peak, at 541nm, is considerably less pronounced than that in the type-Icase above. This behavior is typical to type-II systemsbecause of the reduction in TX oscillator strength due tospatial charge separation and thus can be used as anadditional signature for such systems. Again, there is abuildup of another peak at 475 nm, at the gap of the CdS

absorption, which can be attributed to emission from the CdSrod states.

Figure 2b shows the spectra obtained for CdSe/CdS-seededrods with small cores (core diameter of 2.2 nm; roddimensions of 114 nm × 4.7 nm). In this case, the BX peak,at 556 nm, is blue shifted with respect to the X peak, at 568nm. The TX peak, at 524 nm, has a relatively low intensityand is hard to distinguish. As mentioned above, these areindicators for a type-II system, in contrast to the type-Icharacteristics that were obtained for the first case, for asystem with the same composition but larger core size.

Similar experiments and analyses were performed for aseries of seeded rods of various dimensions. The measuredpositions of the MXs peaks as a function of the core diameter,extracted from the qcw spectra, are plotted in Figure 3a, andthe extracted MX shifts with respect to the X are plotted inFigure 3c. Upon increase of the core diameter, we observea transition of ∆BX-X (Figure 3c) from positive (repulsivebinding interactions, maximal value of +43 meV), whichindicates a type-II behavior, to negative (attractive bindinginteractions, minimal value of -33 meV), which is charac-teristic of a type-I system. The crossover between theattractive and repulsive BX behavior is seen for a corediameter of ∼2.75 nm.

Figure 2. Transient emission spectra (solid black line) measured at the peak of the excitation pulse at increasing pulse energies rangingfrom 0.01 to 150 photon per dot (ppd) (a) for 4 nm diameter CdSe cores embedded in 45 nm × 6 nm CdS rods, (b) for 2.2 nm diameterCdSe cores embedded in 114 nm × 4.7 nm CdS rods, and (c) for 3.9 nm diameter ZnSe cores embedded in 50 nm × 5 nm CdS rods.Spectra sets were fitted using four peaks featuring the X (red), BX (blue), TX (green), and CdS emission (magenta). The red shift betweenX and BX peaks in (a) indicates an attractive interaction, while the blue shift between the peaks in (b) and (c) indicates a repulsive interaction.The insets present the pump intensity dependence of the X (red circles), BX (blue squares), TX (green triangles), and CdS (magentadiamonds) peak amplitudes compared to a linear and a quadratic fitting curve (dashed red and blue line, respectively).

3472 Nano Lett., Vol. 9, No. 10, 2009

Figure 3d shows the ratio between the TX peak and theX peak intensities for different core diameters at an excitationflux of ∼100 photons per dot. For systems with corediameters lower than 2.9 nm, there is a significant drop inTX intensity under the same excitation fluence, with highcorrelation to the BX behavior crossover. The results showthat as the core diameter increases, there is a transfer fromtype-II to type-I behavior. Systems with core diameters lowerthan ∼2.8 nm exhibit a distinctive type-II behavior, whichis characterized by BX positive binding energies and lowintensity of the TX emission due to small overlap betweenthe electron and hole wave functions. For core diameterslarger than ∼2.8 nm, negative BX binding energies and highintensity of the TX emission are seen, all indicative for highoverlap between the excited electron and hole wave functionstypical for a type-I system.

The effect of the CdS rod diameter was examined for fixedcore sizes of 2.2 and 4.0 nm (see Supporting Informationfor further details). In the large, 4 nm, core system, increasingthe CdS shell width affected only the position of the CdS-related peak but did not affect the peak positions of the Xand BX. This explicitly indicates that in this system, the Xand BX involve core states and therefore are not affectedby the change in the rod’s dimensions. In contrast, the CdS-related emission peak is shifted to the red as the rod diameterincreases, indicating that it is related to transition from statesin the CdS rod. On the other hand, for the small core system,increasing the rod’s width shifted all of the peaks to the red(see Figure S3, Supporting Information), indicating that allof them involve rod states.

The experimental study was accompanied by theoreticalinvestigations using the envelope function approximation(EFA).27 The dot/rod NC was modeled as a sphere of CdSewith diameter Dc inside of a hexagonal prism of CdS oflength L and diameter Ds. The center of the CdSe spherewas located at a distance D ) L/4 from the hexagonalbasis.17,25,26 The experimental results were modeled by aseries of simulations, with a variable core diameter (Dc). Roddimensions were kept constant, with diameter Ds ) 6 nmand length L ) 40 nm (resembling the experimentaldimensions; see Table S1, Supporting Information).

The electronic and optical properties of the NCs wereobtained by solving the variable effective mass Hamilto-nian27,28 on a three-dimensional Cartesian grid. The effectivemass parameters which were used are me ) 0.13 and mh )0.45 for CdSe and me ) 0.2 and mh ) 0.70 for CdS.17,25,26

The energy gaps at room temperature were taken as 1.75eV for CdSe and 2.5 eV for CdS.29 A uniform dielectricconstant of ε ) 8 was used for the entire rod. Dielectricmismatch effects15,30 will be considered elsewhere. The CdSe/CdS conduction band offset (∆c) has been fixed to 0.3 eV,as found recently in our combined STS-theory study, whichdirectly measures this value.23 A smaller band offset (∆c )0.2 eV) was also considered in order to estimated thesensitivity of this parameter. The band offset with respectto the vacuum level is fixed to 1.25 eV for both electronsand holes.31 Previous calculations have shown that thisapproach can correctly describe the energy levels23 and thewhole absorption spectra of the seeded rods.17,26

Figure 3. (a) Multiexciton peak positions as a function of core diameter. Measured X (blue circles), BX (red squares), TX (green downward-pointing triangle), and CdS (magenta upward-pointing triangle) peak positions in CdSe/CdS-seeded rods. Dashed lines are a guide to theeye. (b) MX transition scheme. (c) Extracted ∆BX-X shifts; a crossover from repulsive (type-II) to attractive (type-I) BX binding energy isseen at a core diameter of ∼2.75 nm. (d) Measured intensity ratio of TX/X at an excitation flux of 100 photons per dot.

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The MX emission energies, EMX (see Figure 3b) can beobtained from perturbation theory32-36 as follows

where εi is the ith single particle eigenvalue of the electronor hole, J indicates the coulomb integral, and K is theexchange integral. The coulomb and exchange integral arecomputed as Jab ) ⟨φa|Vbb|φa⟩ and Kab ) ⟨φa|Vab|φb⟩,respectively, where Vab(r) is the electrostatic potential of theproduct density φa(r)φb(r), obtained by solving the Poissonequation.25 The emission intensity of the X transition isapproximated as fX ∝ |⟨φe1|φh1⟩|2, that is, proportional to thesquare of the electron-hole overlap.

We note that in atomistic or multiband calculations theground-state triexciton configuration has a non-Aufbauoccupation sequence (see Figure 3b) where one hole alwaysoccupies the low-lying p-state due to reduced hole-holecoulomb interaction.37 This suggests that the single-bandeffective mass approximation, where the crystal field splits-type hole state is not present, can correctly describetriexcitons. In eq 1, we consider the TX emission energiesoriginating from a p-p recombination channel.37 The s-srecombination channel will have emission energies close toexcitons,37,38 in contrast with the data in Figure 3a (see alsoin the following).

Figure 4a shows the lowest seven conduction bandeigenvalues, εej, calculated for different core diameters. Forthe smallest cores, the first conduction state wave functionφ1e(r) is not localized in the core (Figure 4a, inset); notethat the eigenvalues are higher than the bottom of the CdSconduction band due to the rod quantization energy. As thecore diameter increases, the first eigenvalue energy decreases.

For the largest core, the φ1e(r) is localized in the core. Highereigenvalues are already fully delocalized along the rod andthus do not present significant variation for different CdSecores size.

To better quantify the localization of the wave function,we report in Figure 4b the core localizations defined as lX )∫CdSe |φX(r)|2 d3r for X ) e1, h1, e2, and h2. Figure 4b showsthat le1 continuously changes from 0.11 to 0.80, while lh1 isin the range of 0.68-0.96. As a consequence, the excitonemission intensity, that is, the square of the e1-h1 overlap,changes by a factor of 2.20.

Figure 4b also reports the core localization for the secondelectron (e2) and second hole (h2) states. The e2 state iscompletely delocalized in the rod for Dc < 4 nm. For a largercore, it is localized in the core and assumes a p-type character(see the corresponding wave functions in Figure S5 andenergies in Figure S6, Supporting Information). The h2 stateis a p-type orbital with increased localization in the core forlarge Dc. For the smallest core radius (Dc ) 2 nm), this statedelocalizes into the rod.

Figure 5 reports the computed MX properties. In Figure5a, we report the difference between the BX peak (EBX) andthe X peak (EX), which corresponds to the negative of thebiexction binding energy. Note that the expression in eq 1for the biexciton energies does not include correlationcontributions, yields always positive values for EBX - EX,and hence is only approximation for type-I systems.35,39 Thecomputation of the correlation can be performed as described,for example, in refs 35 and 39, but it will be very expensivefor the systems considered in this work due to the contribu-tion of several electronic rod states. However, eq 1 shouldcorrectly describe the trends between our systems becausethe electronic rod states are not changing with the corediameter (see Figure 4a), and thus, the correlation contribu-tions can be expected to be almost a constant.35,39 Figure 5ashows that for ∆c ) 0.3 eV, the biexciton binding energies

Figure 4. Computed electronic properties for CdSe/CdS core/shell NCs with different CdSe core diameters (Dc) and with L ) 40 nm andDs ) 6 nm (∆c ) 0.3 eV). (a) Lowest seven electron eigenvalues. The CdS and CdSe conduction band edges (2.05 and 1.75 eV, respectively)are also shown. Inset: First electronic wave function along the main axis of the rod for Dc ) 2.0 and 4.8 nm. (b) Core localization for thee1, h1, e2, and h2 states and the exciton emission intensity (fX).

EX ) εe1 - εh1 - Je1,h1

EBX ) EX + Je1,e1 + Jh1,h1 - 2Je1,h1

ETXp ) εe2 - εh2 + 2Jh1,h2 - Kh1,h2 + 2Je1,e2 -

Ke1,e2 - (2Je2,h1 + 2Je1,h2 + Je2,h2)

(1)

3474 Nano Lett., Vol. 9, No. 10, 2009

vary by about 50 meV for the core diameters considered inthe experiments, in close agreement with the measured valuesin Figure 3c.

In Figure 5b, we report the computed TX/X intensity. TheTX emission intensity is approximated as fTX ∝ |⟨φe2|φh2⟩|2.39

The TX energies mainly depend on the single-particle energygap εe2 - εh2 (see Figure S7, Supporting Information) andin particular on εh2 as εe2 does not change with Dc (see Figure4a). For the smallest core size (Dc e 2 nm), the TX/Xintensity is high because the second hole state is not localizedin the CdSe core, but it is spread along the rod (see FigureS5, Supporting Information). For a Dc > 2 nm, the secondhole state rapidly assumes a p-type shape and becomeslocalized in the CdSe (see Figure S5, Supporting Information,and Figure 4b). For a larger core size, the p-hole state doesnot change its shape considerably (see Figure S5, Sup-porting Information), while the second electronic wavefunction becomes more localized inside of the CdSe,increasing the overlap with the hole p-state and thus theTX/X intensity. Note that the graph in Figure 5b is on a logscale. Thus, the TX intensity can hardly be observed for smallcore size (i.e., quasi-type-II confinement). This is in qualita-tive agreement with the experimental results, showing onlya very weak TX emission peak for small core diameters,and confirms that the measured triexcitons are due to a p-precombination.

From both the computational and the experimental results,it can be seen that the behavior of the CdSe/CdS system isshifted from a type-I to a quasi-type-II behavior by tuningthe system dimensions. This is achieved due to the special

potential profile of this system and its mixed dimensionality.The bulk potential structure of the system exerts a type-Istructure, where both excited electrons and holes shouldoccupy the core. However, the conduction band offset ofCdS and CdSe is relatively small (0.3 eV), thus the barrierfor the electrons is relatively low, and as a result, the abilityto confine the electronic states in the core is highly influencedby its diameter. For larger CdSe core diameters, the lowestconduction band state of the CdSe resides within the core.In this case, a type-I behavior is seen. For smaller corediameters, the lowest conduction band state of the CdSe risesin energy and eventually goes above the barrier, forming aCdSe-CdS mixed state, which is delocalized along the rod,forming a quasi-type-II structure.

These results resolve the differences in the literatureregarding the CdSe/CdS-seeded rod band structure. The STSmeasurements, which were done on CdSe cores with adiameter of 4 nm, indicated a type-I behavior and yielded,along with the theoretical analysis, a CB offset of 0.3 eV.23

The present results are well explained using this band offset,where the observed clear transfer from type-I to quasi-type-II was a direct consequence of reducing the core size. Theprevious optical spectroscopic measurements of the seededrods reported a quasi-type-II behavior, and these indeedfocused on the range of relatively small cores,17,26 for whichsuch behavior was also observed in the MX propertiesmeasured here.

We have thus demonstrated the transfer of CdSe/CdS-seeded rod NCs from type-I to quasi-type-II behaviors bydirect engineering of the lowest electronic state wave functionand its distribution along the particle through controlling thecore size and rod width. These results provide new insightsinto the electronic structure of these heterostructures withmixed 0D-1D dimensionality and demonstrate the utilizationof the multiexciton properties as a sensitive indicator for theband structure of such systems.

Supporting Information Available: (I) TEM images anddimension measurements. (II) Measured system dimensionsand spectroscopic information for systems with different corediameters. (III) Measured system dimensions and spectro-scopic information for systems with a fixed core diameterof 2.2 nm and varying rod dimensions. (IV) Effect of roddimensions in the quasi-type-II regime for a fixed 2.2 nmcore size. (V) Lifetime measurements for type-I and quasi-type-II CdSe/CdS-seeded rods. (VI) Calculated secondelectronic state and second hole state wave functions alongthe main axis of the rod. (VII) Calculated eigenvalues ofthe first and second valence levels for a CdS/CdSe dot/rodwith different core diameters. (VIII) Calculated TX emissionenergy for different core diameters. This material is availablefree of charge via the Internet at http://pubs.acs.org.

Acknowledgment. This work was supported in part bythe Israel Science Foundation Converging Technologiesprogram (Grant No. 1704/07) and by the NanoSci-ERAnetSingle Nanohybrid project. U.B. acknowledges supportof the Alfred and Erica Larisch Memorial Chair in solarenergy.

Figure 5. MX properties of CdSe/CdS core/shell NCs for differentCdSe core diameters and with L ) 40 nm and Ds ) 6 nm with ∆c

) 0.2 eV (red circles) and ∆c ) 0.3 eV (black squares). (a)Difference between BX and X emission energies. (b) Ratio betweenTX and X intensities.

Nano Lett., Vol. 9, No. 10, 2009 3475

We thank Dr. Dan Oron for helpful discussions.This work is partially funded by the ERC-Starting Grant FP7-

Project “DEDOM”, Grant agreement no. 207441 (F.D.S.).

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