Electron Propagation along CuNanowires Supported on a Cu(111)SurfaceSergio Dıaz-Tendero,*,†,‡ Stefan Folsch,§ Fredrik E. Olsson,| Andrey G. Borisov,†,‡

and Jean-Pierre Gauyacq†,‡

CNRS, Laboratoire des Collisions Atomiques et Moleculaires, UMR 8625, Batiment 351,91405 Orsay Cedex, France, UniVersite Paris-Sud, Laboratoire des Collisions Atomiqueset Moleculaires, UMR 8625, Batiment 351, 91405 Orsay Cedex, France, Paul DrudeInstitut fur Festkorperelektronik, HausVogteiplatz 5-7, 10117 Berlin, Germany, andDepartment of Applied Physics, Chalmers/Goteborg UniVersity, S-41296 Goteborg, Sweden

Received April 11, 2008; Revised Manuscript Received June 12, 2008

ABSTRACTWe present a joint experimental-theoretical study of the one-dimensional band of excited electronic states with sp character localized on Cunanowires supported on a Cu(111) surface. Energy dispersion and lifetime of these states have been obtained, allowing the determination ofthe mean distance traveled by an excited electron along the nanowire before it escapes into the substrate. We show that a Cu nanowiresupported on a Cu(111) surface can guide a one-dimensional electron flux over a short distance and thus can be considered as a possiblecomponent for nanoelectronics devices.

Atomic and molecular nanowires represent an ultimate limitof the miniaturization of electronic devices, where theproperties of the system are governed by quantum mechanics.The central importance of nanowires for nanoscale electron-ics1 as well as the possibility of using them as gas sensors2

has led to a large number of studies over the last few years.3-7

Most of the research so far has been done on free-standingnanowires or nanowires bridging metallic leads, where themajor phenomena controlling the electronic properties andconductivity are quite well understood.8 Recently, manipula-tion of adsorbed atoms and molecules with atomic precisionoffered by scanning tunneling microscopy (STM) allowedthe creation of Pd, Au, and Cu atom chains aligned on ametal surface.9-14 It has been demonstrated that the unoc-cupied electronic states of the chain correspond to a one-dimensional (1D) free-electron-like band quantized on thefinite size object.10,11,13,15 This 1D band describes an electronpropagating along the nanowire. It develops from thehybridization of excited electronic states of sp symmetrystrongly polarized perpendicular to the surface and localizedon the individual adatoms.15,13,16,17 Energetically the 1D bandof nanowire localized states is located inside the surfaceprojected band gap of the substrate.

So far, only the energies and the local density of states(LDOS) distributions of the electronic states of atomic chainssupported on a metal surface have been addressed experi-mentally and theoretically. It has been shown that thedispersion of the 1D sp band can be well-described with atight-binding (TB) modeling only including the electronicstates localized on the chain atoms.13-15 This is a remarkableresult since one could expect an atom in the wire to becoupled in a similar way to its two neighbors in the wireand to its several neighbors in the substrate. It has beenargued that owing to the projected band gap of the substrate,the nanowire-localized states are partly decoupled from thesubstrate leading to a lifetime increase, as already observedin several different systems.18-20 However, the quantitativestudy of the lifetimes of the electronic states of supportednanowires is still missing, despite its central importance: thelifetime determines how far an excited electron can propagatealong the nanowire, i.e., whether an atomic wire on a metalsurface can be considered as an almost independent entityor whether it is simply a protruding part of the substrate.The latter question is crucial for possible applications ofmetal-supported metallic nanowires for nanoscale electronics.

In this Letter, we present a joint experimental-theoreticalstudy of the energies and, most importantly, of the lifetimesof the electronic states of the excited 1D sp band of a Cunanowire on a Cu(111) surface. The two sets of results arein quantitative agreement and we can precisely settle thequestion of electron propagation along the Cu supported wire:

† CNRS, Laboratoire des Collisions Atomiques et Moleculaires, UMR8625.

‡ Universite Paris-Sud, Laboratoire des Collisions Atomiques et Mo-leculaires, UMR 8625.

§ Paul Drude Institut fur Festkorperelektronik.| Department of Applied Physics, Chalmers/Goteborg University.

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10.1021/nl801045b CCC: $40.75 2008 American Chemical SocietyPublished on Web 08/01/2008

the mean distance traveled by an electron along the nanowirebefore its escape into the substrate reaches 12 Å, i.e.,basically five nanowire atoms. It indeed shows a partialdecoupling of the nanowire from the substrate and allowsone to introduce the concept of a short supported Cu wire.

On the experimental side,21 we carried out scanningtunneling spectroscopy (STS) measurements at 7 K tocharacterize the confined states in monatomic Cu/Cu(111)chains assembled by atom manipulation under ultrahighvacuum conditions. The constant-current STM images inFigure 1a illustrate the stepwise Cu chain assembly, starting

with a discrete Cu adatom (left) and finally yielding a nineatomic close-packed chain (right) by the successive attach-ment of single Cu atoms along the ⟨110⟩ in-plane direction22

(N denotes the number of atoms). Figure 1b summarizesheight profiles of the adatom and the assembled chains shownin (a) measured along the ⟨110⟩ chain direction. It is evidentthat with each manipulation event the apparent chain length(represented by the half-width of the along-chain heightprofile) increases by an increment of about 2.5 Å, indicatingthat atoms within the chain reside on nearest-neighbor face-centered cubic (fcc) lattice sites of the substrate surface (theCu-Cu spacing along ⟨110⟩ is a/�2 ) 2.55 Å, with the Culattice constant a ) 3.61 Å). Finally, Figure 1c showsresonance peaks in the bias-dependent differential tunnelingconductance dI/dV (providing a measure of the electronicLDOS) obtained for Cu chains consisting of three to sevenatoms. In each measurement, the STM tip was positioned atconstant height over the chain center (the lateral tip positionsare indicated by the vertical bars in (b), each correspondingto one of the color-coded height profiles). The resonancesreflect the chain-confined lowest lying states characterizedby a single-lobe squared wave function13 and show adownward shift in energy toward the Fermi level withincreasing length. The measured energies are well reproducedwithin a simple tight-binding scheme.14 The insert in Figure1c shows that the peak magnitude scales with 1/N which weinterpret as an indication of the chain-delocalized characterof the 1D state. The peak profiles further indicate a full widthat half-maximum (fwhm) of about half an electronvoltshowing a slight reduction with increasing chain length.

Figure 1. (a) Constant-current STM images of a Cu monomer, adimer, and close-packed monatomic Cu/Cu(111) chains with thenumber N of atoms ranging from three to nine (from left to right).(b) Constant-current height profiles of the adatom and the assembledstructures in (a) measured along the ⟨110⟩ chain direction; eachattachment of a single atom results in a chain length increase byan increment of 2.5 Å. (c) Experimental dI/dV spectra probing theLDOS of close-packed Cu/Cu(111) chains (Cu-Cu spacing 2.55Å) in the regime of unoccupied sample states with the STM tiplocated at constant height over the center of the nanostructure; thecolor-coding of the number N of atoms in the chain is indicated.The resonance peak observed for each chain is associated with thesp-derived chain-confined electronic ground state. The insert showsthat the dI/dV peak magnitude scales with 1/N, consistent with thechain-delocalized character of the 1D state. All data were taken at7 K: set point parameters prior to opening the feedback loop, 1 V,1 nA; peak-to-peak amplitude and frequency of the lock-inmodulation, 30 mV and 640 Hz.

Figure 2. Energy dispersion of the Cu nanowire localized sp band.The energy with respect to the Fermi level is shown as a functionof the electron wave vector parallel to the wire (in atomic units: 1au ) 1 a0

-1). Black solid line with squares: present theoreticalresults for the wire/Cu(111) system. Blue dashed line withdiamonds: present theoretical results with the effect of the STMbias included. Open circles: experimental data by Folsch et al.13

The insert shows schematically the Cu nanowire (red) supportedon a Cu(111) surface (blue).

Nano Lett., Vol. 8, No. 9, 2008 2713

On the theoretical side, we studied a single infinite Cuwire, aligned along the ⟨110⟩ in-plane direction as sketchedin the insert of Figure 2. The distance between the Cunanowire and the topmost layer of surface atoms is 1.92 Åas obtained in the present study. We use a mixed approachwhere ab initio density functional theory (DFT) calculationsof the ground-state properties of the system are followed bythe wave packet propagation (WPP) study of the dynamicsof an excited electron. For detailed descriptions of WPP werefer to refs 20, 23, and 24. The time-dependent Schrodingerequation for the wave function of the excited electronΨ(x,y,z;t) is solved on a 3D mesh in Cartesian coordinates.Periodic Bloch boundary conditions are imposed: Ψ(x,y,z;t)) eikzzψkz(x,y,z;t), where z is the coordinate along the wire(see Figure 2), and kz is the corresponding wave vector. Thex-axis is normal to the surface and goes through the centerof the Cu-wire atom placed at the coordinate origin. Thetime evolution of ψkz(x,y,z;t) is governed by the HamiltonianHkz

Hkz)-1

2[ ∂2

∂x2+ ∂

2

∂y2+ ( ∂

∂z+ ikz)2] +V(x, y, z) (1)

where V(x,y,z) is the total potential (see below). Providedan initial condition ψkz(x,y,z;t ) 0) ) ψ0, the time evolutionis obtained via short time-propagation with the split-operatortechnique.25 The Fourier-grid pseudospectral method26 is usedfor the spatial derivatives entering the Hamiltonian. Thenanowire localized quasi-stationary states appear as expo-nentially decaying resonances of the system. Their energies,

lifetimes and wave functions are extracted from the time-dependence of ψkz.

23

The calculation of the total potential V “seen” by an excitedelectron follows an approach developed in our previousstudies of individual Cu adatoms.16,24 In brief, V consists ofseveral terms

V)Vs(x)+∆Vwire(x, y, z)+Vopt(x, y) (2)

Vs(x) is a one-dimensional representation of the Cu(111)surface potential obtained by Chulkov et al.27 on the basisof ab initio calculations. It is designed to describe theobserved band gap, image states, and surface state energiesat the Γj point. ∆Vwire(x,y,z) is the nanowire-induced potential.An absorbing potential28 Vopt(x,y) is introduced at the x andy mesh boundaries to impose outgoing wave boundaryconditions.

The nanowire-induced potential, ∆Vwire, has been obtainedfrom DFT calculations performed for the clean Cu(111) andCu nanowire/Cu(111) systems (see also refs 16 and 24). Wehave used a plane-wave pseudopotential method within thelocal density approximation as implemented in the Viennaab initio simulation package code.29 The core electrons ofthe Cu atoms were represented by a nonlocal pseudopotentialVPP of Kleinman-Bylander type.30 The supercell geometrywith four Cu layers has been used. For a Cu nanowire casethe 4 × 1 surface unit cell has been used to minimize theinteraction between the nanowire and its periodic images.The calculated nanowire-induced electron density, ∆n, andnanowire-induced one-electron exchange-correlation poten-tial, ∆VXC are thus well localized along the x and ycoordinates inside the calculation supercell. The nanowire-induced Hartree potential, ∆VH, is calculated in entire spaceby solving Poisson’s equation with ∆n as a source. Thisprocedure ensures that the long-range behavior of ∆VH isfree of periodicity effects and corresponds to the case of asingle nanowire on the surface. Finally, ∆Vwire ) ∆VXC +∆VH + VPP.

In Figure 2 we show the calculated energy of the sp bandof the Cu nanowire on the Cu(111) surface together withthe experimental data. Results are presented as a functionof the electron wave vector kz parallel to the wire. Theparabolic shape of the band dispersion corresponds to thefree-particle-like motion of the electron along the wire. Aneffective mass m* ) 0.5me (me is the free electron mass) isobtained from the theoretical WPP results, whereas aneffective mass m* ) 0.68me has been extracted from STSmeasurements.13 The calculated energies of the sp band statesappear systematically lower than the measured ones. Weascribe this discrepancy to the perturbation of the systeminduced by the STM tip. This conclusion is supported bycalculations where an additional term USTM has been addedto the total potential in eq 2 to model the STM junction. Acapacitor model is used here.31 This representation of theapplied voltage in dI/dV simulations gives a good descriptionof the position of the sp resonance of the individual Cuadatom,16 as well as of the shifts of the surface state andimage state thresholds observed in dI/dV data.32,33 To mimicthe experimental STS situation, the bias U of the junctionwas set self-consistently equal to the energy of the nanowire

Figure 3. Width of the quasi-stationary states of the 1D sp bandlocalized on a Cu wire supported on a Cu(111) surface. Resultsare presented as a function of the electron wave vector parallel tothe wire (in atomic units: 1 au ) 1 a0

-1). Black solid line withsquares: present theoretical results for the wire/Cu(111) system.Violet dashed line with diamonds: present theoretical results withthe effect of the STM bias included. Symbols: present experimentalresults. The different colors of the symbols refer to the differentnumbers, N, of atoms in the chain (code given in the insert). Thefull circles present the results for the lowest lying (n ) 1) stateconfined in each chain, whereas the open symbols (squares andtriangles) present higher lying confined states (n ) 2 and 3).

2714 Nano Lett., Vol. 8, No. 9, 2008

localized state (measured from the Fermi level). Since excitedstates above Fermi level are probed, the potential due to theSTM tip is repulsive and lifts the energies of the nanowire-localized states (so-called “Stark shift effect”). Thus, a muchbetter agreement with experiment is reached.

Because of their coupling to the continuum of theelectronic states of the Cu substrate, the nanowire-localizedstates, as studied in the WPP approach, decay via one-electron energy-conserving (resonant) transfer into the metal.Thus, for a given kz, the nanowire-localized state is a quasi-stationary state with a finite width Γ equal to the resonantdecay rate and to the inverse of the lifetime τ: Γ ) 1/τ. Thecalculated and measured widths of the states of the 1D spband are presented in Figure 3 as a function of the electronwave vector kz parallel to the wire. Let us discuss first thetheoretical results obtained for the pure nanowire/surfacesystem (no STM tip-induced electric field included). Anaverage width of the order of 0.36 eV has been obtained,with only a slight dependence on kz for 0 < kz < 0.4 au(1 au ) 1 a0

-1; a0, Bohr radius). The resonant decay ratesobtained here are much larger than the many-body decayrate which is typically of the order of a few tens of meV forvarious excited states at surfaces.19,20 Thus, for the presentsystem the lifetime of the sp band states is dominated bythe one-electron process and is of the order of τ ∼ 2 fs;during this time an excited electron is trapped on the wireand propagates along it.

Figure 3 also presents the sp-level width as extracted fromthe experimental measurements compared to the calculateddecay rate. The color-coded full circles denote the fwhmvalues inferred from the spectra of the lowest lying state inFigure 1, whereas the colored empty symbols indicate fwhmvalues obtained for the second (squares, n ) 2) and thirdstates (triangle, n ) 3) of chains with four (magenta), five(red), and six (orange)34 Cu atoms. With the typical line

widths involved, the peak broadening due to temperature-induced Fermi broadening does not play a role at the presentmeasurement temperature of 7 K. On the other hand, theexperimental data concern finite-size chains, for whichelectron scattering at the end of the chain may lead to anextra decay process. Such an edge-induced broadening effectis consistent with the length-dependent trend in peak widthapparent from the ground-state spectra in Figure 3, docu-menting an increased fwhm value at smaller chain length.

End effects leading to extra decay processes were notaddressed in the present calculations. However, for thecomparison between experimental and theoretical results, thepresence of the STM bias has to be taken into account,similarly to what was done for the energy comparison (Figure2). Two independent effects are present: (i) The electric fieldof the STM junction induces an extra polarization of theelectronic cloud. It pushes the sp electron toward the surface.Thus, the width of the sp-band is increased reflecting anincreased coupling with the substrate. (ii) The experimentalprocedure for the level width measurement involves scanningthe STM bias U and, thus, introduces an apparent increaseof the width. Indeed, due to the Stark shift, the energy ofthe sp-resonance varies roughly linearly with U as has beenobtained here: EU(kz) ∼ E(kz) + RU. E(kz) is the field-freeenergy measured with respect to the Fermi energy. Thecorresponding width can be simply evaluated for a resonantLorentzian profile of the form A/[(U - EU(kz))2 + Γ2(kz)/4].It can be reexpressed as: B/[(U - Eapp(kz))2 + Wapp

2(kz)/4]where the apparent resonance energy and width are givenrespectively by Eapp(kz) ) E(kz)/(1 - R) and Wapp(kz) ) Γ(kz)/(1 - R). Thus when the STM bias is scanned through aresonant profile, the energy position of the resonance changescontinuously, resulting in an apparent change of the reso-nance width. In practice, effect (ii) reduces to defining themeasured width Wapp(kz) from the calculated decay rate Γ(kz)as: Wapp(kz) ) Γ(kz)E′(kz)/E(kz), where E′(kz) is the calculatedenergy of the kz state in the presence of the STM bias (seeFigure 2). Effect (i) turns out to be weaker than effect (ii).As seen in Figure 3, the theoretical prediction, including theSTS bias effect, agrees very well with the experimental data.The agreement between the experimental and theoreticalenergies and widths (Figures 2 and 3) gives confidence inthe present analysis.

Let us now discuss the role played by the surface-projectedband gap of Cu(111) in trapping excited states on thenanowire. Figure 4a illustrates the band gap stabilizationeffect (see also in refs 18-20). The energies of the electronicstates of the system are schematically shown as functionsof the electron momentum ky parallel to the surface andperpendicular to the wire. The band folding effect35 (ex-change of a reciprocal lattice vector in the z-direction) isnot relevant for the kz range considered here. The substratestates disperse parabolically with ky while the sp electron islocalized in the y-direction so that the nanowire-localizedsp-band states do not disperse with ky. The electron escapefrom the nanowire by an energy-conserving (resonant)transition into the substrate requires final electronic statesin the substrate that have finite ky. Two escape pathways are

Figure 4. (a) Energies of different electronic states in the Cu-nanowire/Cu(111) system for kz ) 0. Energies are shown as afunction of the electron momentum perpendicular to the wire ky.Vacuum is at zero energy. The 3D-propagating states are repre-sented by the hatched area. The surface state is shown by the blueparabola. The horizontal line indicates the Cu(111) states degeneratewith the nanowire-localized state. (b) Electron density of the quasi-stationary sp state of the Cu nanowire supported on Cu(111). Thefigure presents the logarithm of the electron density for kz ) 0.Results are shown in the (xy)-plane and the origin of coordinatesis placed at one Cu atom of the wire (see Figure 2). The dark areascorrespond to a large probability of presence of the electron andthe color code is explained in the insert.

Nano Lett., Vol. 8, No. 9, 2008 2715

possible: the intrinsic surface state, with a given ky, and themetal bulk states, with ky above a certain critical value. Decaywith ky ∼ 0, i.e., close to the surface normal, is impossible.The latter is the “easiest” direction of the electron transfer,and so the band gap leads to the stabilization of the nanowire-localized states.

The projected band gap effect is further illustrated inFigure 4b, where the electronic density of the nanowire-localized state is shown for kz ) 0. The spx hybridizationresults in a shift of the maximum of the electron densityabove the nanowire as has been already pointed out bydifferent authors.13,15,16,36 The decay of the nanowire-localizedstate into the surface state continuum of Cu(111) appears asan outgoing flux of electrons along the surface. The decayinto the bulk states is however less pronounced. Since anelectron escape along the surface normal is impossible, theflux of electrons escaping into Cu(111) bulk appears as twosymmetric branches oriented under a certain angle withrespect to the surface normal. The oscillating behavior ofthe wave packet in the bulk reflects the periodicity of theatomic planes of Cu(111). It is noteworthy that electrontransfer into the surface state is the dominating decaychannel. One can stress that, although the electronic structureof the surface is locally perturbed by the atomic chain (thiseffect is introduced via the ∆Vwire term in eq 2), the projectedband gap, i.e., the impossibility for an electron to escapeinto the metal close to the surface normal, is still presentsince it is a bulk property. Thus, the local perturbationinduced by the atomic chain cannot modify the spectrum ofelectronic states available for electron transfer.

We can now turn to the initial question on the nature ofthe wire. Provided the calculated energies and lifetimes ofthe different kz states, we can calculate the distance d traveledby an electron in the 1D sp band of the Cu nanowire. It is

given by the product of the group velocity Vg and the lifetimed(kz) ) Vg(kz)τ(kz) ) Vg(kz)/Γ(kz), where Vg(kz) ) ∂E(kz)/∂kz.Figure 5 shows d as a function of the electron wave vectoralong the wire. The calculated travel distance d increaseswith kz and reaches d ∼ 12 Å, for kz ∼ 0.35 au. This distancecorresponds approximately to five interatomic spacings alongthe wire (2.55 Å); i.e., an excited electron with kz ∼ 0.35 aucovers the equivalent distance of four to five atoms alongthe wire before it escapes into the substrate. Thus, a Cunanowire on the Cu(111) surface can guide a 1D electronflux over a short distance. In this respect it appears as anisolated entity and not as a part of the substrate metal.

In summary, we have presented the results of a jointexperimental-theoretical study of the energy and lifetime ofthe excited 1D sp band localized on an atomic Cu nanowiresupported on Cu(111). By taking the STM bias into account inthe calculation, an energy dispersion and a level width of thesp band are obtained which are in very good agreement withthe STS data. We found that an electron injected into the spband can travel a distance up to 12 Å before it escapes fromthe nanowire into the substrate. Thus, the system can be seenas a short 1D wire with possible applications in nanodevices.The presence of the surface-projected band gap plays anessential role in decoupling the nanowire from the substrate sothat the wire behaves as a separate entity and not as a part ofthe substrate. This suggests that any metal surface with asurface-projected band gap in the relevant energy range is agood candidate for supporting metallic nanowires.

Acknowledgment. S.D.-T. gratefully acknowledges apostdoctoral fellowship from the Spanish Ministerio deEducacion y Ciencia.

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