The quantum transport properties of the ultrathin silver nanowires are
investigated. For a perfect crystalline nanowire with four atoms per unit cell,
three conduction channels are found, corresponding to three $s$ bands crossing
the Fermi level. One conductance channel is disrupted by a single-atom defect,
either adding or removing one atom. Quantum interference effect leads to
oscillation of conductance versus the inter-defect distance. In the presence of
multiple-atom defect, one conduction channel remains robust at Fermi level
regardless the details of defect configuration. The histogram of conductance
calculated for a finite nanowire (seven atoms per cross section) with a large
number of random defect configurations agrees well with recent experiment.Comment: 4 pages, 6 figure

Calin, Buia

Han, Jie

Lu, Jian Ping

Zhao, Jijun

English

arXiv

Jijun Zhao

Calin Buia

Jie Han

Jian Ping Lu

Crossref

Quantum transport properties of ultrathin silver nanowires

The quantum transport properties of the ultrathin silver nanowires are investigated. For a perfect crystalline nanowire with four atoms per unit cell, three conduction channels are found, corresponding to three s bands crossing the Fermi level. One conductance channel is disrupted by a single-atom defect, either adding or removing one atom. Quantum interference effect leads to oscillation of conductance versus the inter-defect distance. In the presence of multiple-atom defect, one conduction channel remains robust at Fermi level regardless the details of defect configuration. The histogram of conductance calculated for a finite nanowire (seven atoms per cross section) with a large number of random defect configurations agrees well with recent experiment

Buia, Calin

Carolina Digital Repository

arXiv:cond-mat/0209535v1  [cond-mat.mtrl-sci]  23 Sep 2002Quantum transport properties of ultrathin silver nanowiresJijun Zhao a, Buia Calin a, Jie Han b, Jian Ping Lu a∗a Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599b Eloret Corp., NASA Ames Research Center, MS 229-1, Moffett Field, CA 95051The quantum transport properties of the ultrathin silver nanowires are investigated. For a perfectcrystalline nanowire with four atoms per unit cell, three conduction channels are found, correspond-ing to three s bands crossing the Fermi level. One conductance channel is disrupted by a single-atomdefect, either adding or removing one atom. Quantum interference effect leads to oscillation of con-ductance versus the inter-defect distance. In the presence of multiple-atom defect, one conductionchannel remains robust at Fermi level regardless the details of defect configuration. The histogramof conductance calculated for a finite nanowire (seven atoms per cross section) with a large numberof random defect configurations agrees well with recent experiment.PACS: 73.63.Nm, 73.22.-f, 61.46.+wIn recent years, metallic nanowires are of great interestas building blocks for nanoelectronic devices. Since thedimension of the metallic nanowires is comparable to theelectron Fermi wavelength, the conductance is quantizedin units of G0 = 2e2/h [1,2,3]. The number of conduc-tance channels is determined by the number of electronicbands crossing the Fermi level (EF ) and sensitively de-pends on the nanowire geometry. The effect of conduc-tance quantization and the related high sensitivity leadto potential applications such as single-atom switch [4],conductor [5,6], and chemical sensor [7].Most earlier works on the quantum conductance ofmetallic nanowires are based on the point contactsformed between metal electrodes [1]. With mechanicallycontrollable break junctions [8,9] or tip-surface contact[10,11,12,13] techniques, the statistical histograms of theconductance value for large number of contacts have beenrecorded. However, the metallic nanowires obtained fromnanoscale contact are limited by the short length andstructural instability for practical applications. Otherfabricating methods, such as reduction of metal com-pounds [14], ions irradiation [15], carbon nanotubes capil-lary growth [16,17,18], and template-aid synthesis [19,20]have been introduced to generate much longer nanowireswith well-defined structures. Understanding the trans-port properties of these long and nearly freestandingmetallic nanowires are important for their future appli-cations in nanoelectronics. Recently, Kim’s group hassuccessfully obtained ultrathin single-crystalline silvernanowire arrays [20]. The silver nanowires with 0.4 nmwidth (only four atoms on the cross section) and µm-scalelength are grown inside the pores of organic templates.In this letter, we investigate the transport properties ofthe ultrathin silver nanowires and discussed the effect ofdefects on the conductances.The geometry optimization for the silver nanowires areperformed by using ab initio plane-wave ultrasoft pseu-dopotential method [21]. Both atomic positions and cellparameters for the nanowires (perfect crystalline or withstructural defects) were fully relaxed at level of local den-sity approximation (LDA). We adopt the initial config-urations proposed in Ref.[20], that is, fcc-like crystallinestructure with wire axis along the [110] crystal direction.The equilibrium structures of a perfect silver nanowireare illustrated in Fig.1. The calculated atomic layer spac-ing along the wire axis (2.75 Å) agree well with the ex-perimental result [20]. In this one-dimensional periodicstructure, the four atoms in the unit cell belong to twoinequivalent sites (h and l). Two atoms have lower co-ordination number (l: Z = 6); the other two atoms havehigher coordination (h: Z = 7) (see Fig.1(b)).FIG. 1. Structures of crystalline silver nanowires with wire axis along [110] fcc direction: (a), (b): side and top views ofa thinner wire with four atoms per unit cell (as observed in Ref.[20]). The two inequivalent sites (h, l) with lower or highercoordination are labeled in (b). (a), (c): side and top views of a thicker wire with seven atoms per unit cell, which was suggestedin Ref.[31].It is known that the 4d orbitals in Ag atom act almostlike innershell core orbitals [22]. Our ab initio LDA bandstructure calculations also show that the d bands are low-lying and have little influence on the s electron bandsaround Fermi level. Therefore, the conduction electronsin silver should be reasonably described by a s-orbitaltight-binding (TB) model, which had been used to de-scribe the silver clusters up to Ag68 [23]. The s-orbitalTB Hamiltonian is written asH =∑iǫi +∑<ij>tijwhere the on-site energy ǫi = ǫ0 + αZi depends on thesite coordination number Zi. The hopping integrals tijdepend on the interatomic distance rij between site iand j, tij = t0(d0/rij)2 where d0 is the bulk nearest1neighboring distance (2.89 Å), t0 is the s-orbital hoppingparameter at the bulk distance d0. It was found that pa-rameter set t0=0.89 eV and α=0.26 eV can describe thesilver clusters well [23]. The same parameters are usedin this work. In Fig.2, the electronic band structures ofperfect silver wires near Fermi level by the s-orbital TBmodel are compared with those from accurate LDA cal-culations. Fig.2 clearly shows that the TB model candescribe the electronic structures of silver wire within 1eV of EF reasonably well.-2-1012EFXΓ     LDA TBBand energy (eV)FIG. 2. Band structures of silver nanowires (Fig.1b) along the 1-D wire axis direction (Γ-X). The s-orbital tight-binding(solid lines) calculations reproduce most of the features from LDA (open circles).We use the TB Hamiltonian to study the transportproperties of silver nanowires via the surface Green’sfunction matching method [24,25]. The conductance Gis given by Landauer-Büttiker formula with the trans-mission coefficient T calculated from the surface Green’sfunction. To mimic the nanowire of µm-scale length, thelength of central nanowire section is chosen to be suffi-cient long such that the results are independent of thechoice of length. The perfect crystalline nanowires ofthe same size were used as leads in the two sides. Sim-ilar tight-binding based surface Green’s function meth-ods have been successfully applied to the transportproperties of metallic nanowires and carbon nanotubes[26,27,28,29].The calculated conductance of the perfect crystallinesilver nanowire with four atoms per unit cell is shownin Fig.3. Three conduction channels at the Fermi levelare found, corresponding to the three s electronic bandscrossing the Fermi level as predicted by both TB andLDA calculations (see Fig.2). As the ultrathin silvernanowire has only few atoms on the cross section, it isinevitable that there will be some structural defects onthe wire. Two type of defects, vacancy or adatom areconsidered in present work. In the case of vacancy, themissing atom can be from either the low-coordination (l)sites or high-coordination (h) sites (see Fig.1). Our re-sults (Fig.3) clearly show that one conduction channelis disrupted by a single-atom defect (either vacancy oradatom), independent of the details of defect configura-tions. This effect can be understood by the scatteringof conduction electrons by the defect-induced potential.Similar effect was found in the carbon nanotube [29].-1 0 1123 Energy (eV)Perfecth-vacancyl-vacancy  G (2e2 /h)-1 0 1123    Energy (eV)AdatomPerfectFIG. 3. Conductance of silver nanowires (Fig.1b) with single-atom defect. Solid line: perfect nanowires; dotted line (left):single-atom vacancy at high-coordination site; dashed line (left): single-atom vacancy at low-coordination site; short dashedline (right): adatom single-atom defect. In all the cases, one conduction channel is disrupted by a single-atom defectFIG. 4. (a): 2-D contour plot of the conductance of silver nanowires (Fig.1b) vs. inter-h-vacancy distance and energy. (b)A cut of (a) through Fermi energy. Oscillation of conductance with the defect distance can be seen.In addition to the effect of individual defect, we havealso considered the situation of two separated single-atomdefects. Oscillation of conductance with the defect dis-tance is observed. An example as shown in Fig.4 is the 2-D contour plot of conductance versus defect distance andenergy. The oscillation behavior can be understood byquantum interference of the conduction electronic stateswith oscillation scale related to Fermi wavelength. Fromour ab initio calculations, the density of conduction elec-trons in the silver wire shows similar oscillation with thesame periodicity. Such quantum interference effects werealso found in the carbon nanotubes [28,30].2-1 0 101232 adatomPerfect2 h-vacancy2 l-vacancyG (2e2 /h)Energy (eV)FIG. 5. Conductance of silver nanowires (Fig.1b) with two-atoms defect. Solid line: perfect nanowire; dotted line: defectwith two-atoms vacancy at high-coordination site; dashed line: defect with two-atoms vacancy at low-coordination site; shortdashed line: defect with two adatoms. One to two conduction channels are disrupted by the two-atoms defect at Fermi level.We further investigate the other defect configurationssuch as multiple-atoms vacancies. In the cases of two-atoms vacancy (either both on the h sites or both on thel sites), substantial difference is found between differentdefect configurations (see Fig.5). At Fermi level, one totwo conduction channels are disrupted by the two-atomsvacancy defect, sensitively depending on the local coordi-nation environment of the defect site. It is reasonable tofind that removing two atoms on the high-coordinationsite disrupts two conduction channels, while the absenceof two atoms on the low-coordination site only reduceone conduction channel at Fermi energy. For individualdefect with two adatoms, the result is between the caseof two h and two l vacancy. Further removing one moreatom will create a three-atoms vacancy with one atomlink. Our calculations show that there is still one conduc-tion channel open. In the earlier experimental studies onmetallic contacts, it was usually found that the nanowireretain one conduction channel before breaking [1]. Ourresults indicate that at least one conduction channel inthe silver nanowire is rather robust. Hence, the ultrathinsilver wire might serve as good interconnctor in nanoelec-tronics even with some structural defects formed duringthe fabrication process.So far, there is no direct experimental measurementon the conductance of very long ultrathin silver nanowire.Our current studies can be related to a recent experimenton the quantum conductance of short silver nanowiresgenerate by mechanical elongation [31]. Similar to that inRef.[20], rodlike nanowires along the [110] direction wereobserved. The global histogram recorded for the con-ductance of silver nanowires shows large peaks at 1 G0,∼2.4 G0, and ∼4 G0 [31]. One possible atomic structurefor the nanowire in their experiment is shown in Fig.1(c)with seven atoms per cross section, which can be builtfrom the thinner wire in Fig.1(b). Using the same com-putational scheme, we have calculated the quantum con-ductance of such finite nanowire with seven unit cells inthe central section (∼ 2nm, comparable to experimentallength). Without any defect, the nanowire has five con-duction channels. The conductance drops to 4 G0 withone single-atom defect, similar to that in the case of 4-atoms cross section nanowire discussed above. Our LDAcalculations show four robust s bands crossing the Fermilevel, in consistent with TB results.0 1 2 3 4 50.000.020.040.060.080.100.120.14  Normalized number of countsG (2e2/h)FIG. 6. Histogram of conductance of finite silver nanowire in Fig.1(c) with 500 random defect configurations. Three majorpeaks at 1 G0, 2.6 G0, and 4 G0 are foundTo compare with experimental conductance histogram,we generate a large number (∼ 500) of random defect con-figurations for the finite 7-atom cross section wire andcalculate the conductance at Fermi level. For each con-figuration, the defects are created by randomly select-ing the location of the vacancies. Normalized counts ofconductance are shown in Fig.6. Three major peaks at1 G0, 2.6 G0, and 4 G0 are found, in agreement withthe experimental results. We find that the locations ofthese three peaks are insensitive to the length of finitenanowire length and total number of defect configura-tions. These features can be understood by the abovediscussions on the effects of various defects on crystallinenanowire. The peak at 4 G0 corresponds to the case ofone or few singe-atom defects that disrupt only one con-duction channel from the perfect wire. The dominantpeak at 1 G0 could be associated with the presence ofseveral multi-atoms defects, which disrupt the quantumconductance so dramatically that only one conductionchannel is left. Between the two extreme cases, a peak at∼ 2.5 G0 is found both experimentally and theoretically.In our calculations, four less pronounced peaks around1.5 G0 and 3.4 G0 are also obtained, which were not ob-served experimentally [31]. These peaks may correspondto the energetically less-favorate configurations.In summary, three conduction channels are obtainedfor the crystalline silver nanowire with four atoms percross section, corresponding to three s bands crossingthe Fermi level. One conductance channel is easily dis-rupted by an individual single-atom defect (vacancy oradatom), independent of the defect configurations. Withtwo separated single-atom defects, quantum interferenceleads to oscillation of conductance versus the defect dis-tance. 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Quantum transport properties of ultrathin silver nanowires

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