Coulomb blockade phenomena observed in supported metallic nanoislands I-Po Hong, Christophe Brun, Marina Pivetta, François Patthey, Wolf-Dieter Schneider

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I-Po Hong, Christophe Brun, Marina Pivetta, François Patthey, Wolf-Dieter Schneider. Coulomb blockade phenomena observed in supported metallic nanoislands. Frontiers in Physics, Frontiers, 2013, 1, pp.13. ￿10.3389/fphy.2013.00013￿. ￿hal-01233578￿

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Distributed under a Creative Commons Attribution| 4.0 International License ORIGINAL RESEARCH ARTICLE published: 27 September 2013 PHYSICS doi: 10.3389/fphy.2013.00013 Coulomb blockade phenomena observed in supported metallic nanoislands

I-Po Hong 1,2, Christophe Brun 1,3, Marina Pivetta 1, François Patthey 1 and Wolf-Dieter Schneider 1,4*

1 Faculté des Sciences de Base, Ecole Polytechnique Fédérale de Lausanne, Institut de Physique de la Matière Condensée, Lausanne, Switzerland 2 Key Laboratory for Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing, China 3 Institut des Nanosciences de Paris, Université Pierre et Marie Curie and CNRS-UMR 7588, Paris, France 4 Department of Chemical Physics, Fritz-Haber-Institute of the Max-Planck-Society, Berlin, Germany

Edited by: The transport properties of single crystalline metallic nanostructures in the Peter Fischer, Lawrence Berkeley Coulomb blockade (CB) regime have been investigated by low-temperature scanning National Laboratory, USA tunneling spectroscopy. To this end, nanoscale flat-top Pb islands with well-defined Reviewed by: geometries are grown on NaCl-covered Ag(111) substrates. The tunneling spectra acquired Aidan Hindmarch, Durham University, UK at 4.6 K on the Pb nanoislands reflect the presence of single electron tunneling processes Shuji Hasegawa, University of across the double-barrier (DBTJ). By a controlled change of the tip-island Tokyo, Japan tunnel distance, the spectra display the characteristic evolution from CB to Coulomb Sebastian Loth, Max Planck Institute staircase (CS) regime. Simulations within the semi-classical orthodox theory allow us for Solid State Research, Germany Richard Berndt, IEAP,CAU Kiel, to extract quantitatively the parameters characterizing the DBTJ, i.e., the resistances, Germany , and the residual charge Q0. Manipulation of Q0 is achieved by controlled *Correspondence: application of pulses on the Pb islands. Moreover, under specific tunneling Wolf-Dieter Schneider, Ecole conditions, the influence of the tip-island junction on Q0 is revealed in topographic images Polytechnique Fédérale de of the Pb islands. Lausanne, Institut de Physique de la Matière Condensée, Cubotron 421, CH-1015 Lausanne, Switzerland Keywords: coulomb blockade, STM, STS, Pb-nanoislands, support e-mail: wolf-dieter.schneider@epfl.ch

1. INTRODUCTION conditions imply that extremely small metal clusters have to be The study of Coulomb blockade (CB) phenomena in nanos- probed, or that the measurements have to be performed at low tructures is a very attractive area of condensed matter physics, temperature. because single electron electronics is considered to have a high Previous studies of nanostructures in the CB regime by STM potential for basic research and for technological applications were performed on amorphous particles (11, 13, 17, 18), on (1–5).Thefieldstartedmorethan40yearsagowiththeinves- particles covered by shells consisting of specific ligands and/or tigation of small metal particles embedded in an oxide layer molecules (19–22), and to a lesser extent on supported clus- between two planar metal electrodes (6, 7). Subsequently, in ters and metal islands (18, 23–26). The vast majority of the CB order to avoid ensemble effects and to study single double- spectroscopy results have been successfully described within the barrier tunnel junctions (DBTJ), CB phenomena have been orthodox theory of the DBTJ (2), which allowed the authors investigated in small-area tunnel junctions prepared by litho- to determine quantitatively the tip-particle and the particle- graphic methods developed for microelectronics (8, 9). More substrate junction parameters (see Figure 1B). Within the context recently, junctions using a scanning tunneling microscope (STM) of single electron tunneling, the “orthodox theory,” a semi- tip as one adjustable electrode came into the focus of research classical theory, is based on the following three assumptions (3). (10–13). (1) The electron energy quantization inside the conductors is Consider single electron transport in the system shown in ignored, i.e., the electron energy spectrum is continuous. (2) Figure 1: the two barriers constitute a DBTJ. For each junction Coherent quantum processes consisting of several simultaneous the barriers are modeled by an ohmic Ri in parallel with a tunneling events (“cotunneling”) are ignored. This assumption Ci, i = 1 for the substrate-island junction and i = 2for is valid if the resistance of all tunneling barriers of the system the island-tip junction, as shown in the equivalent electronic cir- is much higher than the quantum unit of resistance. Only under cuit in Figure 1B. In order to transfer a single electron through this condition the quantum-mechanical uncertainty of the DBTJ, the electron must overcome the Coulomb charging is suppressed because of the high tunneling resistance (i.e., less 2 energy Ec = e /C,whereC = Ci. If the charging energy Ec tunneling events). Thus one can neglect the concurrent tunneling is much larger than the thermal energy kBT, the tunneling of an events and treat one electron at a time, which makes control- electron is blocked for bias smaller than Uc = e/C.This lable single-electron manipulation possible. (3) The tunneling phenomenon has been termed CB (CB) (2, 3, 14–16). Moreover, time τt of an electron tunneling through the barrier is assumed in order to keep charge fluctuations sufficiently small, the cou- to be negligible compared to other time scales (including the pling resistance of each junction has to be significantly larger than interval between subsequent tunneling events). For a typical tun- 2 τ −15 the quantum resistance: Ri RQ = h/(2e ) ≈ 12.9k.These neling event in a practical junction (3), t is around 10 s. For

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influence of the adjustable tip-island junction on Q0 is revealed in topographic images of the Pb islands. In an STM measurement of a DBTJ, in general the tip-island junction resistance R2 is always much larger than the quantum resistance RQ. Then the electron transport through such a DBTJ can be separated into three different regimes (16): if the island- substrate resistance R1  RQ, the whole system corresponds to a single junction; if R1 is of the order of RQ, the dynamical Coulomb blockade (DCB) regime is reached; if R1 RQ,the CB and CS regime is entered. These different conditions can be FIGURE 1 | (A) Schematic diagram of the Coulomb blockade system. The selectively and controllably fulfilled in our experimental setup Pb nanoisland is embedded between the vacuum barrier and a few NaCl by choosing the appropriate size of the islands (by changing the dielectric layers on Ag(111). (B) Equivalent double-barrier tunnel junction growth parameters) and the pertinent tunnel parameters, includ- (DBTJ) circuit where each junction is represented by a set of and ing an adjustable tip-island distance (by changing the tip-island , connected in parallel. resistance R2). In this way island-size-dependent CB gaps and CS have been unambiguously identified in the tunneling spectra obtained on the Pb quantum dots on NaCl/Ag(111). a typical STM tunneling junction with 1 nA tunneling current, on average one electron tunnels per 10−10 s. Considering that the 2. EXPERIMENTAL + electronic lifetime of an electron in the states of the islands is The Ag(111) single crystal substrate was cleaned by Ar sputter- around 10−13–10−15 s, electrons tunnel one at a time and con- ing and subsequent annealing cycles. NaCl powder was thermally ◦ sequently under these conditions cotunneling processes can be evaporated from a crucible at a temperature of T = 620 Conto neglected. the Ag substrate held at room temperature or heated to ≈ 420 K. Recently, in a low-temperature scanning tunneling spec- Subsequently, Pb islands were grown by evaporation of Pb from troscopy (STS) study, we reported (27) on the observation of a W filament onto the NaCl-covered Ag substrate cooled to 130 K the dynamical Coulomb blockade (DCB) (28–30) in nanosized to obtain Pb islands of the desired size. electrical contacts consisting of small Pb islands on various con- The experiments were conducted in a homebuilt STM oper- ducting, semiconducting, and partially insulating substrates. We ated at 4.6 K (31). Differential conductance (dI/dV)measure- observed a suppression of the differential tunnel conductance ments were performed with an open feedback loop using a lock-in at small bias voltages due to DCB effects. The differential con- technique with modulation voltage from 2 to 10 mVpp at 300– ductance spectra allowed us to determine the capacitances and 400 Hz frequency with tunneling current ranging from 100 pA to resistances of the electrical contact which depend systematically afewnA. on the island-substrate contact area. Calculations based on the theory of environmentally assisted tunneling agree well with the 3. RESULTS AND DISCUSSION measurements. 3.1. GROWTH OF Pb NANOISLANDS ON NaCL/Ag(111) Here, we extend the previous observations from the DCB to A bulk NaCl crystal is a dielectric material with a wide band gap the orthodox CB and Coulomb staircase (CS) regime. We report in the range of 8.5 − 9eV(32–34).ForthinNaClfilms,theband on the observation of CB phenomena in Pb nanoislands, rang- gapisreportedtobeclosetothebulkvalue(35)For1− 3MLof ingfromalateralsizeofafewnanometerstotensofnanometers NaCl on Ag(100), recent STS measurements of the energy posi- and a thickness of a few monolayers, grown on ultrathin dielec- tions of field emission resonances propose a work function of tric films of NaCl deposited on Ag(111). For selected Pb islands 3.2eV(36), while ultraviolet photoemission spectroscopy (UPS) of well-defined area, the local tunneling spectra reflect CB and CS yields 3.5eV(36, 37). From dI/dV spectra measured on top of phenomena in the DBTJ (see Figure 1) characteristic for single a 2 ML NaCl film, we deduce that the gap lies within the voltage electron tunneling: Every additional electron tunneling to or from range of ±2 eV around EF,whichistheenergyrangeselectedfor the Pb nanoisland is counted one by one. Using a model based on the measurement of the dI/dV spectra of the Pb nanoislands on the orthodox theory of single electron tunneling (12, 16), we are NaCl. able to simulate the experimental tunneling spectra and to extract Studies of NaCl layers on other substrates abound, e.g., on the relevant parameters of the DBTJ, i.e., the resistances of island- Al(111) (35, 38), on Cu(111) (39), on Ag(100) (36, 40, 41), substrate and tip-island junctions (R1 and R2), the capacitances and on Au(111) (42–44). NaCl(100) layers are very versatile as of island-substrate and tip-island junctions (C1 and C2), and a dielectric ultrathin film for the electronic decoupling of sup- theresidualcharge(Q0)ontheisland.TheextractedC1 capaci- ported molecules (39, 42, 43) or other nanostructures (27)from tances fit well with the values corresponding to a planar capacitor, a metallic substrate. C1 = ε0εrAisland/d, the island area Aisland being measured from Here, NaCl was deposited on the substrate held at two different the STM topography and the insulator thickness determined by temperatures, 300 K, and ≈ 420 K, the latter favoring the forma- field emission resonances (FERs) analysis. Manipulation of Q0 tion of more extended, flatter, and defect-free layers. Figures 2A,B is achieved by controlled application of voltage pulses on the show STM images corresponding to these two different sample Pb islands. Moreover, under specific tunneling conditions, the preparations, yielding Pb islands of different average size. This

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behavior is mainly due to the higher density of nucleation points to 1 nm), the NaCl dielectric constant plays an important role, on the NaCl layer in (b) with respect to (a). The NaCl layer leading to capacitances C1 ten times larger than typical values has different characteristics in the two cases: the layer is flat and for C2. By varying the set-point current, the tip-island distance is presents very few defect in (a), while it shows the coexistence of modified and consequently also R2 and C2. The resistance, how- various thicknesses and a higher density of edges in (b). In (a) ever, decreases exponentially with decreasing distance, while the the side length of the equilateral triangular Pb islands is in the increases only weakly. range of 25 to 60 nm, while in (b) it is ≤ 10nm.FortheSTS Figure 3 shows dI/dV spectra acquired on four different Pb measurements, triangular islands of various sizes were selected. islands. The spectra present the typical signature of CB, i.e., a The Pb islands expose (111) crystal faces. A determination of zero-conductance gap around the Fermi energy (EF). Notice that the thickness of NaCl layers at a given location is not straight- bulk Pb is superconducting at the measurement temperature of forward. Moreover, the apparent height of NaCl layers varies T = 4.6 K. We neglect here the possible existence of the super- depending on tunneling conditions, such as bias voltage and tip conducting gap in the Pb islands because the energy scale of the conditions. Coulombgapismuchlargerthantheoneofthesuperconduct- ing gap of ≤ 1meV(45). Consequently, we treat the tunneling 3.2. COULOMB BLOCKADE AND COULOMB STAIRCASE ON Pb junctions as if they are in the normal state. The width of the NANOISLANDS gap is inversely proportional to the island area Aisland:thegap 2 In a STM double junction geometry, there are some intrinsic is ≈ 120 mV wide for the smallest island (Aisland ≈ 20 nm ), and 2 limitations in the relations between resistances and capacitances ≈ 18 mV for the largest one (Aisland ≈ 220 nm ). This is the of the two junctions. As discussed in the introduction, in order expected behavior, since for C2 < C1 the gap width is governed to observe CB phenomena, the condition Ri RQ has to be by the tip-substrate capacitance C1. Therefore, as C1 increases for satisfied. In the tunneling regime, this condition is easily sat- increasing island area, it leads to narrower gaps. The 220 nm2- isfied for junction 2 (tip-vacuum-island), for which resistances island (a triangle with 22 nm side) represents the upper limit for R2 of 1 M to 1 G are usual. For junction 1, this condition an unambiguous observation of a zero-conductance gap at this requires the presence of an insulating layer of sufficient thick- temperature. From the measured gap, we estimate C1 to approxi- 2 ness, leading in our case to resistances R1 of the order of 1 M mately 10 aF. For the 20 nm -island, C1 is ten times smaller. These to 100 M. Concerning the capacitance, although the tip-island values are in agreement with values calculated using the expres- distance is of the same order as the insulating layer thickness (0.5 sion for a parallel plate capacitor C1 = ε0εrAisland/dNaCl,with the island supported on a 3 ML NaCl film of thickness dNaCl = 0.8 nm and dielectric constant of bulk NaCl εr = 5.5(46)The small features in Figure 3A just below ±0.1 eV are related to the capacitance C2 (see discussion of Figure 5). Figure 4 displays the typical evolution of the tunneling spec- tra from the CB to the CS regime for a selected Pb triangular

FIGURE 2 | STM topographies acquired on two different samples with Pb islands grown on NaCl/Ag(111). Pb islands are visible in both images, most of them with triangular shape and a few with rounded shape. The FIGURE 3 | dI/dV spectra labeled (A to D) acquired on four Pb islands smaller island size in (B) as compared to (A) is obtained on a NaCl film with different area Aisland. A Coulomb gap of decreasing size is visible in exhibiting more defects. (A): +1V,20pA;(B): +4V,20pA. going from spectrum (A to D) reflecting a Coulomb blockade process.

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island with a side length of 14 nm. The dI/dV spectrum A shows the tunnel spectra with increasing initial current, corresponding a simple Coulomb gap while spectra B to E display a series of to decreasing tip sample separation and decreasing resistance R2, equidistant peaks (steps in the I − V characteristics, a CS) with in going from spectrum A to E. Our simulation within the ortho- increasing intensity. This progression is achieved by measuring dox theory reproduces the general features of the measured spec- tra revealing CB and CS characteristics. The simulation of these spectra within orthodox theory allows us to extract the pertinent parameters of the double barrier system, i.e., the capacitances and resistances of both junctions, as well as the residual non-integer charge Q0 on the Pb island, see figure caption. Notice that, with decreasing tip-sample distance, R2 decays exponentially, whereas C2 increases linearly (13, 18). As this latter variation is small, C2 is assumed to be constant throughout this series of simulations. To summarize, tunneling spectra on such nanoislands may display a simple CB gap or a CS depending on the parameters of the DBTJ. Well-developed CS’s are observed with an asymmetric resistance ratio R2 < R1. Concerning the robustness of the simulations and the preci- sion of the derived parameters we note that Q0 is always deter- mined with an error of < 10%, as it corresponds to an energy shift of the tunneling spectra with respect to zero bias voltage. The capacitances C1 and C2 are also reasonably well determined, especially in situations like those depicted in Figure 5 or Figure 6 where two well separated energies are well-defined. The errors of the determined values are thus also < 10%. The sum of R1 and R2 is fixed by the experimentally determined I(V) characteristics. FIGURE 4 | Evolution from Coulomb blockade to Coulomb staircase: experimental STS data acquired on a Pb island with 14 nm side Their ratio is most favorably evaluated in the CS regime, as the 2 (Aisland ≈ 85 nm ) (dots) and simulation (black line) based on the height and the width of the various peaks are linked directly to orthodox theory. The spectra are offset for clarity. Parameters of the their ratio. In this situation a precision of the order of 10% is = = . = . = simulation: R1 39 M , C1 7 46 aF,and C2 0 7aF;(A): R2 300 M obtained (see Figure 4). In the simple CB case, the precision of =− . = =− . = and Q0 0 15 e, (B): R2 105 M and Q0 0 2 e, (C): R2 26 M and the resistance ratio is ≥ 10%. Q0 =−0.26 e, (D): R2 = 13 M and Q0 =−0.26 e, (E): R2 = 4.5M and Q0 =−0.28 e.

FIGURE 5 | Spectra (A to D): increase of the tip-island capacitance C2 FIGURE 6 | Manipulation of the residual charge Q0. dI/dV spectra with decreasing tip-island distance (increasing tunnel current). The measured on the same island with 7.9 nm side, showing features related to spectra, offset for clarity as dI/dV (0V ) = 0, have been acquired on a Pb both, C1 and C2,withvaryingQ0, and corresponding simulations. The island of 14 nm side. Parameters of the simulation, performed for spectra residual charge (Q0) of the island is changed by a bias voltage pulse (A) and (D) curve: C1 = 5.0aF,C2 = 0.77 aF, R1 = 5M, R2 = 1700 M, (duration: 50 μs, current: 1 nA). Parameters of the simulation: C1 = 3.8aF, Q0 = 0.062 e; (D) curve: C1 = 5.0aF,C2 = 0.86 aF, R1 = 5M, C2 = 0.335 aF, R1 = 25 M, R2 = 2300 M; (A): Q0 = 0.03 e, R2 = 145 M, Q0 = 0.07 e. (B): Q0 = 0.33 e, (C): Q0 =−0.41 e.

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A closer comparison of calculations and data in Figure 4 shows values of the fractional residual charge Q0,obtainedfromour that there are some deviations in the intensity of the structures. simulation, on the Pb island. For the present island of a thickness of 11 ML, a quantum well It has been proposed that the residual charge Q0 is related to state, reflecting the vertical confinement, located at +0.2eVabove the difference in work function of the various metals constituting EF contributes a considerable background to the spectra (47). the junctions (12): Therefore, a quantitative fitting of the tunnel spectra within the orthodox theory should consider the density of states (DOS) of Q = [C (φ ) − C (φ )] /e (1) the sample (48). 0 2 2 1 1 If the parameters of the DBTJ are appropriately chosen, spec- tral features reflecting both, tip-island (C2) and island-substrate where φ1 is the difference between substrate and island work (C1) capacitance can be observed simultaneously. Note that the functions, and φ2 the difference between tip and island work electrostatic energy of the island is given by the Coulomb charging functions. As a result of voltage pulses, charge can be trapped in 2 energy Ec = e /C,whereC = Ci.However,thethreshold defects or impurities in the NaCl layer beneath the Pb nanoisland, voltage necessary for the transfer of an electron across the tip- leading to a permanent modification of the residual charge Q0. island (island-substrate) junction is inversely proportional to the In the following section we demonstrate the influence of the capacitance C2 (C1)(12, 13). Spectra of Figure 5 were acquired tip-island junction on the residual charge Q0 via the variation on a Pb island of ≈ 14 nm side length. Spectrum A shows a of C2, variation due to the displacement of the tip with respect Coulomb gap around EF as well as two peaks at ≈±0.1V,which tothePbislandduringscanning.InFigures 7A,B two differ- are related to the C2 capacitance. For decreasing tip-island dis- ent Pb islands are displayed. In the closeup-view topographic tance (increasing tunnel current), the tip-island capacitance C2 images of Figures 7C,D, very striking concentric lines follow- is expected to increase slightly. This behavior is observed in ing the contours of the island are visible. Figures 7E,F shows Figure 5B: by approaching the tip to the island from A to D, the typical dI/dV spectra obtained on these islands. Our measure- value of C2 increases leading to a decreased separation between ments show that, by scanning laterally across the surface, an the two C2 peaks, as indicated by the vertical lines. In addition, energy shift of the spectrum is observed which corresponds to if the island area Aisland becomescomparabletotheeffectivetip a maximum fluctuation of the residual charge Q0 =±e/2. We area Atip, there will be also a contribution to C2 due to the tip- deduced the Q0 values by simulating each local STS spectrum substrate capacitance. In the present measurement Aisland turns in the CS regime. For the Pb island shown in Figures 7A,C, out to be smaller than Atip. C2 is then evaluated using the simple we obtain a value of Q0 ≈+0.35e for the spectrum acquired at parallel-plate capacitance formula. In addition to the capacitance the center of the island, and Q0 ≈−0.15e fortheoneacquired between the metallic island and the tip, the capacitance between in the surrounding region. For the system of Figures 7B,D, the tip and the substrate, including the vacuum and the NaCl up to six regions of alternating negative and positive Q0 are layers, is considered in the model. detected. The present measurements and their analysis allow us to In order to explain this surprising effect we have to consider obtain the dielectric constant of the ultrathin NaCl film within that the parameters of junction 2 depend on the tip position with a parallel plate capacitor model, if we take the island substrate respect to the island. As already mentioned, the residual charge capacitance C1 from the simulation of the spectra, the area Q0 is related to the difference in work function of the various Aisland of the capacitor plate from the STM topographies, and the metals constituting the junctions, see Equation 1. For a given thickness dNaCl of the NaCl film as deduced from STS of FERs set of measurements C1 is fixed by the Pb island and the NaCl 2 (36) With a typical island size of Aisland = 100 nm and dNaCl = layer characteristics and the work functions are well defined. In 0.8 nm (3 ML), we obtain εr = 4, a reasonable value compared to these conditions, Equation 1 shows that a variation of Q0 can the one of ε = 5.5 for bulk NaCl (46), and the one extracted from only originate from a variation of C2.Asdiscussedabove,thelat- FERs measurements, ε = 3.5(36). eral extension of the tip can exceed the island area. Therefore, to In contrast to the situation in a planar tunnel junction (49), evaluate C2, not only the capacitance between tip and island, but our setup has no gate electrode. However, by externally applying also the one between tip and substrate has to be included. When a bias voltage pulse to the junction (12), a gate voltage change scanning over a Pb island, the ratio between these two contribu- is mimicked. In Figure 6 we present three tunneling spectra, tions changes continuously, leading to variations of the residual obtained on the same position on a triangular island of 7.9 nm charge within the island. Now, considering the CS spectra shown side, where subsequently a bias voltage pulse of ±5V hasbeen in Figures 7E,F, we recall that with increasing bias voltage every applied to the junction. The spectra clearly show the result of this additional CS peak in the differential conductance spectrum indi- action, a pulse-bias-dependent shift of the central Coulomb gap cates the hopping of an additional electron to/from the island. away from the symmetric zero-voltage position, accompanied by In an STM scan at a bias voltage close to a CS peak, e.g., at ashiftoftheC2-related spectral features. The background above 0.075 eV in Figure 7E, a small change in Q0 (due to the changing +0.2 V originates from the tail of a quantum well state at higher tip-island capacitance) will lead to a situation where the measure- energy (47).Thisbackgroundcontributesalsototheobserved ment will be performed above or below the respective CS peak, intensity variations of the spectral features. The asymmetric dis- corresponding to one more (above the peak) or one less elec- placement of the central Coulomb gap and of the C2-related peaks tron (below the peak) tunneling to the island. This effect leads under the action of an external voltage pulse reflects the different to the observed symmetric triangular step patterns in the STM

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FIGURE 7 | (A,B) Topographic images of Pb islands on NaCl; (A): −1V,20pA,(B):2.5V,20pA;(C,D) Close-up view; (C): −0.15 V, 200 pA; (D): −0.01 V, 20 pA); (E,F) dI/dV spectra acquired on the locations represented by the corresponding symbol, showing different values of Q0 (see text). topographies shown in Figures 7A,B. Evidently, the sharp appar- 4. CONCLUSIONS AND OUTLOOK ent height steps visible in the STM images reflect the hopping We investigated the transport properties of single crystalline of one additional electron on/off the Pb island, while the tran- metallic nanostructures in the CB regime. To this end, small Pb sition regions correspond to a continuous variation of Q0. Notice islands with well-defined geometries, ranging from a diameter of that, contrary to the first impression gained from the images, at a few to tens of nanometers and a thickness of a few monolayers each instant the value of the charge Q0 is the same over the entire are grown on crystalline NaCl layers on Ag(111) substrate. The island, as expected for a conducting object. These features are visi- tunneling spectra obtained at 4.6 K on the metallic quantum dots ble when C1φ1 ≈ C2φ2, a condition which can be fulfilled for show clearly the presence of CB phenomena. By reducing the tip- φ1 ten times smaller than φ2, since C1 is typically ten times island distance, the tunneling spectra reflect the evolution from larger than C2. This implies that φ1 has to be small in order CB to CS. Our simulations employing the semi-classical orthodox to observe these features. Moreover, φ2 strongly depends on theory describe well the observed spectra in both regimes allow- the specific tip conditions, explaining the fact that these effects ing us to extract quantitatively the parameters of the DBTJ, i.e., were not systematically observed. In this situation, a C2 variation the resistances, capacitances, and the residual charges. of the order of 10% can induce a modification of Q0 as large as The present STM/STS studies have shown that not only the ±e/2. size and shape of the metallic nanoislands can be well determined Finally, we note that the observation of Coulomb charge but that, importantly, also their local electronic structure and rings with scanning probe methods has been made before their transport properties can be quantitatively elucidated. In the for quantum dots inside carbon nanotubes (50), for quan- past, e.g., the superconducting properties of small particles have tum dots of a two-dimensional electron gas inside semicon- been investigated (56) revealing a number parity property. STS ductor heterostructures (51), and for quantum dots inside InAs experiments of isolated superconducting islands would allow us nanowires (52). Controlled charge switching has been performed to observe simultaneously the pairing correlation on islands with for single Au atoms on NaCl (53), for a single Si donor in different parity. Moreover, in small metallic particles containing Si doped GaAs (54), and for a small conductive grain on an magnetic impurities, the Kondo resonance was predicted to be InAs surface (55). The present measurements on Pb nanois- strongly affected in a parity-dependent way (4), another excit- lands show that these intriguing CB phenomena and the related ing phenomenon to look at with local probes. We believe that charging effects are also observed in metallic quantum dots. STM/STS will continue to be a decisive player for the elucidation While the observed phenomena are similar they are not iden- of the of nanostructures. tical. The essential difference between the present measure- ments and the SPM investigations on the quantum dots before ACKNOWLEDGMENTS is that in our case the STM tip is in the tunneling mode We would like to thank K.-H. Müller and C. Flindt for stimulat- measuring the conductance through the Pb island without a ing discussions. We are also indebted to V. S. Stepanyuk, N. N. gate electrode, while the former investigations use a standard Negulyaev, P. Ignatiev, K. Horn and D. Roditchev for their very conductance measurement of the nanowires (quantum dots) valuable input. Wolf-Dieter Schneider would like to thank H.-J. andtheretheSPMtiprepresentsanexternalelectrodethe Freund for stimulating discussions and for his generous hospi- field of which shifts the CS spectra of the observed quantum tality. We acknowledge financial support of the Swiss National dots. Science Foundation.

Frontiers in Physics | Condensed Matter Physics September 2013 | Volume 1 | Article 13 | 6 Hong et al. Coulomb blockade phenomena

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www.frontiersin.org September 2013 | Volume 1 | Article 13 | 7 Hong et al. Coulomb blockade phenomena

44. Cañas Ventura ME, Xiao W, conductor nanocrystals. Annu state of individual gold atoms. that could be construed as a potential Ruffieux P, Rieger R, Müllen K, Rev Phys Chem. (2003) 54:465. Science. (2004) 305:493. doi: conflict of interest. et al. Stabilization of bimolecular doi: 10.1146/annurev.physchem. 10.1126/science.1099557 islands on ultrathin NaCl films by 54.011002.103838 54. Teichmann K, Wenderoth M, Received: 23 July 2013; paper pending a vicinal substrate. Surf Sci. (2009) 49. Ralph DC, Black CT, Tinkham Loth S, Ulbrich RG, Garleff JK, published: 11 August 2013; accepted: 603:2294. M. Gate-voltage studies of Wijnheijmer AP, et al. IControlled 06 September 2013; published online: 45. Brun C, Hong IP, Patthey F, discrete electronic states in charge switching on a single 27 September 2013. Sklyadneva IY, Heid R, Echenique aluminum nanoparticles. Phys donor with a scanning tun- Citation: Hong I-P, Brun C, Pivetta PM, et al. Reduction of the super- Rev Lett. (1997) 78:4087. doi: neling microscope. Phys Rev M, Patthey F and Schneider W-D conducting gap of ultrathin Pb 10.1103/PhysRevLett.78.4087 Lett. (2008) 101:076103. doi: (2013) Coulomb blockade phenom- islands grown on Si(111). Phys 50. Woodside MT, McEuen PI. 10.1103/PhysRevLett.101.076103 ena observed in supported metallic Rev Lett. (2009) 102:207002. doi: Scanned probe imaging of 55. Wildoer JWG, van Roij AJA, nanoislands. Front. Physics 1:13. doi: 10.1103/PhysRevLett.102.207002 single-electron charge states Harmans CJPM, van Kempen 10.3389/fphy.2013.00013 46. Robinson MC, Hallett ACH. Static in nanotube quantum dots. H. band This article was submitted to dielectric constant of NaCl, KCl, Science (2002) 296:1098. doi: switching by charging a small Condensed Matter Physics, a section of and KBr at temperature between 10.1126/science.1069923 grain with a single electron. the journal Frontiers in Physics. 4.2 degrees K and 300 degrees K. 51. Fallahi P, Bleszynski AC, Phys Rev B. (1996) 53:10695. Copyright © 2013 Hong, Brun, Can J Phys. (1966) 44:2211. doi: Westervelt RM, Huang J, Walls doi: 10.1103/PhysRevB.53.10695 Pivetta, Patthey and Schneider. 10.1139/p66-179 JD, Heller EJ, et al. Imaging a 56. Black CT, Ralph DC, Tinkham This is an open-access article dis- 47. Hong IP, Brun C, Patthey F, single-electron . M. Spectroscopy of the super- tributed under the terms of the Sklyadneva IY, Zubizarreta X, Nano Lett. (2005) 5:223. doi: conducting gap in individual Creative Commons Attribution License Heid R, et al. Decay mechanisms 10.1021/nl048405v nanometer-scale aluminum (CC BY). The use, distribution or of excited electrons in quantum- 52. Bleszynski AC, Zwanenburg FA, particles. Phys Rev Lett. (1996) reproduction in other forums is per- well states of ultrathin Pb islands Westervelt RM, Roest AL, Bakkers 76:688. doi: 10.1103/PhysRevLett. mitted, provided the original author(s) grown on Si(111): scanning tun- EPAM, et al. Scanned probe 76.688 or licensor are credited and that the neling spectroscopy and theory. imaging of quantum dots inside original publication in this journal Phys Rev B. (2009) 80:081409. doi: InAs nanowires. Nano Lett. (2007) Conflict of Interest Statement: The is cited, in accordance with accepted 10.1103/PhysRevB.80.081409 7:2559. authors declare that the research academic practice. No use, distribution 48. Banin U, Millo O. Tunneling and 53. Repp J, Meyer G, Olsson FE, was conducted in the absence of any or reproduction is permitted which optical spectroscopy of semi- Persson M. Controlling the charge commercial or financial relationships does not comply with these terms.

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