Electrical Transport through Single Nanoparticles and Nanoparticle

Article pubs.acs.org/JPCC

Electrical Transport through Single Nanoparticles and Nanoparticle Arrays Marcel Manheller,† Silvia Karthaü ser,*,† Rainer Waser,† Kerstin Blech,‡ and Ulrich Simon‡ †

Peter Grünberg Institut (PGI-7) and JARA-FIT, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany Inorganic Chemistry (IAC) and JARA-FIT, RWTH Aachen University, D-52056 Aachen, Germany

‡

S Supporting Information *

ABSTRACT: In order to achieve the next generation of nanometer-sized electronic devices, a detailed understanding and control of electrical transport is essential. One approach to fabricate nanodevices based on functional components is to assemble a 3D array of nanoparticles on electrode structures, while another method is to bridge the gap between two nanoelectrodes by a single nanoparticle. Here we report on electronic transport measurements of biphenylpropanethiol-capped gold nanoparticles with a diameter of 4 nm used as functional units studied in both setups. The resulting conductance measurements reveal different types of transport mechanisms depending on temperature, such as hopping, superexchange coupling, and tunneling. In addition, Coulomb blockade behavior is shown in the single-nanoparticle device at 4 K and at room temperature. Moreover, a discontinuity in the conductance as a function of temperature is discussed in terms of a possible structural crossover in particle morphologies.

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INTRODUCTION The future generation of nanoscale devices has to deal with phenomena that are not observable in macroscopic devices. In devices based on functional building blocks, which have dimensions of only a few nanometers, such as molecularly functionalized metal nanoparticles, different electrical transport mechanisms have to be considered such as tunneling,1,2 hopping,3,4 Coulomb blockade-dominated transport,5,6 or superexchange coupling.7−9 These electrical transport phenomena appearing at small device sizes can be tailored via compositional and structural parameters of the constituting building blocks. Hence, devices with complex functionalities can be created, such as the functionality of a full adder as a part of a logic circuit10 that can be implemented on a single Coulomb blockade system. In current CMOS technology, 24 transistors are necessary to create such a function. This demonstrates the enormous application potential of such systems in future nanoelectronic circuitry. The electrical properties of three-dimensional nanoparticle systems have extensively been studied via dc and ac measurements.11−15 As a common feature, at high temperatures until several tens of kelvin below room temperature, the temperature-dependent dc and ac conductivities follow a simply activated behavior according to the Arrhenius relation. If the temperature is decreased, the conduction mechanism changes and the conductivity becomes less temperature dependent. This temperature dependence, together with the nonohmic behavior at strong electric fields, can be described by classical hopping transport, in which the nanoparticles act as localization sites embedded into a nonconducting matrix represented by the © 2012 American Chemical Society

capping organic ligands. According to this classical hopping transport, thermally activated nearest-neighbor hops predominate at high temperatures (room temperature and above), while going to lower temperature the transport properties reflect a thermally activated stochastic multiple-site hopping process, i.e., variable range hopping. The characteristic energy associated with this process is a measure of the effective coupling between next nearest neighbors mediated by the molecules. In the language of electron transfer, this mechanism is described as superexchange-coupling.8 Another model, which has been successfully applied to describe the conduction with a small temperature dependence in a heterogeneous system, is the granular metal model.12 It is applicable for disorderdetermined transport in various heterogeneous materials, like cermets or amorphous semiconductors, where localization sites far from being identical have to be considered. At very low temperature, where the hopping transport would be expected to become zero if all particles become electrically neutral, charge transport becomes independent of temperature and is goverened by tunneling between states of similar energy.16 Electrical addressing of individual nanoscale building blocks, such as molecules or nanoparticles, via reliable contacts in device geometry is still a challenge. Several setups are suitable to investigate transport through molecular units, like nanopore devices, STM, conductive AFM, break-junctions, nanogaps, hanging mercury drop junctions, and crossed wires.17,18 Received: February 29, 2012 Revised: August 31, 2012 Published: August 31, 2012 20657

dx.doi.org/10.1021/jp3020029 | J. Phys. Chem. C 2012, 116, 20657−20665

The Journal of Physical Chemistry C

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purified by dialysis within three days and was stored cooled with a concentration of 6.9 × 1017 NP/L. The synthesized gold nanoparticles were characterized by UV/vis spectroscopy, transmission electron microscopy (TEM), dynamic light scattering (DLS), and small-angle Xray scattering (SAXS). The results are available in the Supporting Information section I. Current−Voltage Measurements on Single NPs. The electrical transport properties of single 4 nm BP3-capped AuNPs were investigated after immobilization between gold nanoelectrodes. The nanoelectrodes were fabricated by electron-beam lithography according to a procedure described very recently24 and have a separation of approximately 3−5 nm. The NPs were immobilized in the gap formed by the nanoelectrodes by dc dielectrophoretic trapping (DC-DEPT) as described earlier.25,30 The electrical characterization measurements of the resulting single-NP device were performed in a continuous flow cryostat under He gas atmosphere with varying temperature (RT−4 K). The use of a subfemtoampere sourcemeter (Keithley 6430) with a short wiring to the device and a thorough triaxial shielding allows us to improve the noise and leak resistance so that a resolution in the femtoampere scale is achieved (Supporting Information section II.I). It is worthwhile to note that the resistances measured for empty nanoelectrode gaps are usually larger than 1 TΩ, while nanoelectrode gaps filled with NPs exhibit resistances smaller than 10 GΩ. Impedance Measurements of 3D Nanoparticle Films. Complex impedance measurements were performed on IDE structures (interdigitated electrode structures, Supporting Information section II.II) on which the AuNP solution was drop-casted to form a densely packed film. In these measurements the complex impedance was recorded as a function of frequency (10 mHz−1 MHz) and temperature (340 > T/K > 10) at a constant voltage (USD = 100 mV).

However, even slight changes in the contact geometry on the subnanometer level can significantly influence the transport properties in such devices. Different effects may be responsible for changes in the contact geometry, such as displacement of single metal atoms,19 a temperature-dependent expansion/ contraction of the nanoelectrodes, or structural transitions of the nanoparticle or configurational changes in the molecular structure.20−22 This illustrates some of the main targets that need to be addressed for a successful integration of metal nanoparticles into a CMOS-adapted device geometry. In order to perform a step in this direction, we have recently introduced the fabrication of nanometer-sized devices with electrode gaps of only a few nanometers with current e-beam technology.23,24 Moreover, methods to immobilize nanoparticles into nanogaps were described by Stellacci et al. recently.25 However, Coulomb blockade (CB) behavior observable on a single-nanoparticle (NP) device at room temperature (RT) was so far only achieved in measurements with STM configurations and on Au NPs with a diameter of d < 2.0 nm.26,27 Facing these aspects, device configurations are required in which the nanoelectrode gap and the nanoparticles size including their capping ligand shell are adjusted to each other at the lowest gap size obtainable with present-day e-beam technology. Therefore, we have studied the electrical transport properties of single and 3D arrays of biphenylpropanethiol (BP3)-capped gold nanoparticles (AuNPs) with a diameter of 4 nm. The particle diameter was adjusted to the smallest gaps size we have fabricated so far. BP was chosen as a capping ligand, since it was subjected to our previous STM studies so that its characteristic electrical paramters are known.28 Possible transport mechanisms in such “nanoelectrode−(molecule−NP−molecule)n− nanoelectrode” systems, i.e., in arrays of NPs and single NPs between nanoelectrodes, are explored by temperature-dependent complex impedance or current/voltage measurements. We will show for both systems the change of transport mechanism with temperature and that Coulomb blockade behavior on single particles can be observed at room temperature. Furthermore, we found that the temperature dependence of conductance exhibits a discontinuity that is attributed to a transition in particle morphology.

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RESULTS AND DISCUSSION Analysis of Nanoparticles. The synthesized BP3-AuNPs were characterized by UV/vis, TEM, SAXS, and DLS. From UV/vis spectra (Supporting Information section I.I), an absorbance maximum at 521 nm is observed, which is characteristic for AuNPs in this size range. The TEM analysis (Figure 1) of the BP3-capped NPs under investigation displays almost spherical nanoparticles with a mean diameter of 4.1 ± 0.5 nm. The mean interparticle spacing, based on an analysis of 209 distances, is 1.4 ± 0.4 nm (Supporting Information section I.II). This value corresponds within the limit of error to the calculated length of only one BP3 molecule (lBP3 = 1.49 nm). Accordingly, this can be interpreted either as a strong interdigitating of the ligand shells in the dried state or as back-folding. However, the particles exhibit faceted surfaces, and the ππ interactions between the biphenyl moieties allow for stacking effects stabilizing the molecular monolayer. An analogous behavior has been observed in self-assembled monolayers formed by the same biphenylthiols on Au-surfaces which do not show any backfolding effects.28 Furthermore, it was shown by energy-filtered carbon K-edge TEM that an interdigitation of stabilizing alkanethiolates in silver nanocrystal superlattices is existent.31 Therefore, we assume that an interdigitating of ligand shells is most probable. A hydrodynamic diameter of 6.4 ± 0.4 nm could be obtained from DLS measurements, while SAXS measurements in

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EXPERIMENTAL METHODS Chemical Synthesis. The synthesis of 4′-methyl-1,1′biphenyl-4-propanethiol (BP3)-functionalized gold nanoparticles (AuNPs) follows a modified route according to Murray et al.29 For this synthesis 1.504 g (2.5 mmol) of tetraoctylammonium bromide was dispensed in 80 mL of toluene to which a solution of 0.316 g of tetrachloroauric acid (HAuCl4·3H2O, 0.8 mmol) dissolved in 25 mL of Milli-Q-water was added under stirring. After the gold precursor was transferred into the organic phase, which led to an orange-colored solution, the water phase was separated, and 1/10 mmol (8.35 × 10−5 mol) of the thiol ligand was added. After stirring at room temperature, a solution of 0.382 g (13 mmol) of sodium borohydride in 25 mL of Milli-Q-water was added rapidly. Immediately the color of the solution turned to dark-redbrown. The solution was stirred for 3 h. The organic phase was then separated and the volume reduced by rotary evaporation. Addition of 30 mL of ethanol led to a black precipitate which could be separated from solution by filtration. After redispersing the black precipitate in toluene, the solution was 20658



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we checked every step of the whole procedure, that is, the nanoelectrode fabrication, the dielectrophoretic trapping procedure, and the electrically characterized devices by SEM imaging. However, due to the strong influence of SEM imaging on I(U) measurements, these characterizations were done only on not imaged devices. Anyhow, the proof that also in the conduction measurements shown here only a single AuNP is present in the nanoelectrode gap will be given by the measurements themselves. Temperature-Dependent Transport of Single BP3Capped AuNPs. The temperature-dependent conductance of single BP3-capped NPs, which have a core size of 4.1 nm, was investigated after immobilizing the NPs in a gap formed by a pair of nanoelectrodes (gap size 5 ± 1 nm).30 The electric conductivity (Y) through the nanoelectrode/BP3−NP−BP3/ nanoelectrode device was measured over a wide range of temperature while applying a constant source-drain voltage, USD = 1 V. It is plotted in an Arrhenius-type diagram (Figure 2). Corresponding data of a second device are given in

Figure 1. (a) TEM analysis of BP3-stabilized AuNPs. (b) Mean diameter of BP3-AuNPs was derived from 251 particles and is 4.1 ± 0.5 nm. Additionally the interparticle spacing was calculated to be 1.4 ± 0.4 nm from 209 counted distances. (c) 4′-Methyl-1,1′-biphenyl-4propanethiol (BP3).

Figure 2. Conductance of a single BP3-NP plotted as log(Y) vs T−1. Four different transport regimes can be identified according to their temperature dependence: (I) (Tred = 265−245 K) with an exponential temperature dependence, (II) (Tdis = 245−200 K) intermediate region with significant singularity in conductance, (III) (Tblue = 200−110 K) with a slope indicating a weaker temperature dependence, and (IV) (Tgreen < 110 K) with no significant temperature dependence.

solution lead to a core diameter of 4.8 nm. Hence, the thickness of the ligand shell including solvent molecules is approximately 0.8 nm. This value is smaller than the theoretically determined lengths of the stretched BP3 molecule, probably caused by back-folding of the flexible alkane chain. (c.f. Supporting Information sections I.III and I.IV). A SEM image of a nanoelectrode pair produced in the same way24 as those employed for the measurements of the BPcapped AuNPs is given in the Supporting Information section III. Unfortunately, due to the small gap size of only 3−5 nm between the nanoelectrodes and, in addition, due to their shape, i.e., pronounced apex, it was not possible to detach the leads and take a SEM image of an intact device. Here we had to contend with induced overvoltages destroying the nanoelectrodes, and of course our aim to collect data as long as the device was in good order. However, changing the nanoelectrode shape made it insensible against possible overvoltages due to detaching of leads. Accordingly, a SEM image of a single AuNP trapped in between broader nanoelectrodes separated by a gap of only 3−5 nm is shown in the Supporting Information section III. It is noteworthy that

Supporting Information section IV. We note that a very small vacuum gap in the nanoelectrode/BP3−NP−BP3/nanoelectrode device, i.e., of 0.1 nm, would easily give rise to a change in current of 1 order of magnitude. Thus, currents measured within this range point to reproducible devices. In Figure 2 four different transport regimes are identified clearly and can be attributed in principle, according to their temperature dependence, to different transport mechanisms. In the highest temperature range (I), Tred = 265−245 K, an exponential decrease of the conductivity with decreasing temperature is observed reflecting a thermally activated charge transport. In this temperature range, thermally activated hopping involving molecular moieties, belonging to either one molecule or neighboring molecules, has to be considered so that the activation energy is associated with the relevant molecular motion. Accordingly, in the case of BP3-capped NPs, the mobility of charge carriers is dependent on the dihedral angle between the phenylen rings, being highest for a coplanar 20659



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Figure 3. (a) Conductance of a single BP3-NP device measured at USD = 0.5 V, while sweeping the temperature around the singularity observed in Figure 2 around 235 K. A small hysteresis in transition temperature is observed, Ttrans‑down = 235 K and Ttrans‑up = 252 K. (b) I(U) characteristic obtained at temperatures above (red), equal to (purple), and below (blue) the transition temperature Ttrans = 235 K.

current/voltage measurements, I(U), shown in Figure 3 (see also Supporting Information section IV). The cyclic temperature sweep (Figure 3a) is showing a reproducible hysteresis. The transition to the low-conductance state is achieved by cooling below 235 K, while the transition to the highconductance state is achieved by heating above 253 K. The I(U) characteristics of the NP device (Figure 3b) confirm this result. A significant difference in magnitude of current is observed for I(U) characteristics taken above or below the transition temperature. The high temperature I(U) curve exhibits also a stronger field dependence than the lowtemperature curve. Most interestingly an I(U) curve taken at Ttrans = 235 K reveals a switching between both conductance states. One possible reason for a sudden change of current in the order of one magnitude as observed here might be a geometrical change in the distance between electrodes of about 0.1 nm in vacuum. However, since this change of current is fully reproducible, an accidental geometrical change seems to be rather unlikely. On the contrary a physical reason causing a structural rearrangement is probable. In the third transport regime, identified in Figure 2 for temperatures Tblue = 200−110 K, the conductance becomes less temperature dependent indicating a change in transport mechanism. Possible mechanisms for charge transport in this region are superexchange coupling or electrical transport according to the granular metal model. The superexchange charge transfer process is characterized by the transfer of electrons or holes in one step from a donor to an acceptor unit via bridge orbitals that are used as a medium for electronic coupling. The relevant energy for this process is the reorganization energy, ESE, which is mainly determined by the structural differences between the equilibrium configurations of the respective donor and acceptor units in neutral and ionic states.8,9 Conductivity based on superexchange coupling is described by the following temperature dependence

and lowest for a perpendicular orientation, respectively. However, according to Ratner,9 thermally activated hopping could be observed in polyphenylen units only for temperatures above ∼310 K. Hence it is unlikely that a simple Arrhenius-type conduction mechanism solely based on molecular conduction can be applied here. Furthermore, in our case of conduction measurements through a single nanoelectrode/BP3−NP−BP3/ nanoelectrode device, we have to consider effects induced by the strong electrical field (applied voltage, USD = 1 V) as well. If we assume that no additional vacuum gap exists between the NP and the electrodes, USD drops over the length of twice the BP3 length, i.e., over ltot = 2 × lBP3 × cos 30° = 2.58 nm. The resulting electrical field amounts to ∼0.4 V/nm. Consequently, the observed thermally activated transport through the singleNP device takes place in high electric fields and is described best by Poole−Frenkel-type transport. We have calculated the activation energies according to both models, Arrhenius-type (EA) and Poole−Frenkel-type transport (EPF),32 respectively ⎛ E ⎞ YA = Yo exp⎜ − A ⎟ ⎝ kBT ⎠

⎛ e(E − PF YPF ∝ exp⎜⎜ − ⎝

(1)

eUSD/πεrεoltot ) ⎞ ⎟⎟ kBT ⎠

(2)

where YO is the conductance at T = 0 K, kB Boltzmann’s constant, e the elementary charge, εr the relative dielectric constant of BP3, and εo the vacuum dielectric constant. From the least-squares fits to the data points in Figure 2 in the temperature range I (Tred = 265−245 K), EA = 440 ± 20 meV and EPF = 1135 ± 20 meV are obtained, respectively, using USD = 1 V and εr = 4.5 ± 0.3. The spread in εr results from the reduced order of the BP3-capping layer on AuNPs, as discussed in ref 33 for aromatic sulfides on polycrystalline gold. The activation energies, EA and EPF, respectively, for thermally activated transport are considerably higher than values given for the planarization energy of polyphenyl chains, like EA = 0.19 eV given for a biphenyl unit by Reed.34 Hence, the planarization of the biphenyl unit is not the highest barrier in the hopping process observed in our nanoelectrode/BP3−NP−BP3/nanoelectrode device. In the temperature range II (Tdis = 245−200 K), the conductance reveals a discontinuity, whose origin cannot be explained within this data set. For further characterization we performed additional temperature-dependent conductivity and

1/2 ⎛ E ⎞ ΔE2 ⎛ π ⎞ YSE = ⎜ ⎟ exp⎜ − SE ⎟ ℏ ⎝ ESEkBT ⎠ ⎝ 4kBT ⎠

(3)

where ΔE is the coupling matrix element corresponding to the coupling strength between donor and acceptor unit. On the other side, according to the granular metal model for high fields, the logarithm of YGM should be proportional to T−1/2: 20660



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Figure 4. Conductance of the single BP3-NP device plotted as (a) log(YT1/2) vs T−1 according to superexchange coupling and (b) as log(Y) vs T−1/2 according to the granular metal model.

⎛ C0 YGM = YGM0 exp⎜⎜ − 2 k ⎝ BT

⎞ ⎟⎟ ⎠

Transport Measurements on a Single AuNP Showing Coulomb Blockade Behavior. Besides the temperaturedependent conductance measurements, we performed also cyclic I(U) measurements of single BP3-capped AuNPs . The resulting I(U) curves at room temperature are shown in Figure 5 (average of 250 cycles). A nonlinear and slightly asymmetric

with

⎛ (β l ) ⎞ C0 = 2(βl )EGM⎜1 + ⎟ ⎝ 2 ⎠

(4)

EGM is the activation energy according to the granular metal model. The decay factor, ( βl ) = ∑ni = 1 βili, can be calculated from the decay constants of the respective molecular moieties (βalkane = 7.6 nm−1, βphenyl = 4.6 nm−1) and their corresponding length, li. This approach to determine the decay factor was deduced explicitly for a self-assembled monolayer of biphenylalkanethiols on Au(111) surfaces based on UHVSTM and STS measurements28 and recently generalized for arbitrary molecules.35 In Figure 4 the conductivity in the temperature range III (Tblue = 200−110 K) is plotted as log(YSE T1/2) vs T−1 and as log(YGM) vs T−1/2 according to superexchange coupling and granular metal model, respectively. For this temperature range the experimental data show slightly stronger deviations from the granular metal model, and, thus, superexchange coupling is assumed to be the more likely transport mechanism. From the slope of Figure 4a the characteristic reorganization energy, ESE = 617 meV, is obtained that fits well to the values calculated by Ratner8 ranging from 360 to 1130 meV for 3-methylbiphenyl, depending on the applied theoretical functional, the basis set, and electron or hole transfer. Moreover, a reorganization energy of 580 meV was calculated for electron transport through the biphenyl unit and points to the fact that this mechanism is also relevant in our system. For very low temperatures (Tgreen < 100 K), the temperature dependence of the conductivity measured through the single BP3-NP device vanishes (Figure 2). Therefore it is assumed that tunneling, either direct tunneling or Fowler−Nordheim tunneling, is the main conduction mechanism in this regime. All deduced values for the activation energies in the respective temperature ranges are summarized in Table 1.

Figure 5. (a) Cyclic I(U) measurements of a single BP3-NP in a nanogap at RT (averaged over 250 cycles); (b) normalized first derivative, (dI/dU)/(I/U); (c) flattened first derivative exhibiting periodic peaks with a distance of ΔUCB = 61 mV and a height of ΔG ≈ 8 nS.

Table 1. Activation Energies Obtained for a Single BP3Capped NP in the Temperature Regimes I (Tred = 265−245 K) and III (Tblue = 200−110 K), Assuming Different Transport Mechanisms; See Text

I (265−245K) III (200−110K)

EPF (meV)

EA (meV)

EGM (meV)

ESE (meV)

1135 ± 40 843 ± 15

440 ± 20 148 ± 3

84 ± 19 18 ± 5

1781 ± 90 617 ± 35

behavior can be observed which indicates almost weak asymmetry in the two junctions between the NP and the two nanoelectrodes. Most interestingly, in the normalized first derivative (calculated from the I(U) measurements averaged over 250 cycles), equidistant periodic peaks are found over a large range of applied voltage (Figure 5b). They represent Coulomb blockade peaks and indicate that the electrical current 20661



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flows through a single NP only. To allow stronger visualization, also the flattened first derivative is given in Figure 5c, which reveals Coulomb blockade peaks with a distance of ΔUCB = 61 mV and a height of ΔGCB ≈ 8 nS. The peak distances allow the determination of the charging energy (ΔUCB = 4EC/e; EC = 15 meV) and the total capacitance of the NP (EC = e2/2Ctot; Ctot = 5.2 aF).36,37 Since EC > kBT = 25 meV is a necessary requirement for measurements in the “strong” Coulomb blockade regime, it is not surprising that Coulomb blockade peaks appear here only as small modification of the total conductance, Ytot, of the nanoparticle device at room temperature. In fact, the fwhm of the peaks is 20 meV, and only due to the increased signal-to-noise ratio reached by statistics (average of 250 I(U) curves) are they determined unambiguously. At the same time this proves the high stability of the AuNP device. According to ref 38, it is possible to determine the fraction of conductance corresponding to the Coulomb blockade mechanism (YCB) from the Coulomb blockade peak height (ΔYCB) YCB = ΔYCB

6kBT EC0

temperature is likely correlated to an increased distance of the Au nanoelectrodes. A temperature-dependent contraction of the gold nanoelectrodes of 0.2−0.4 nm can be estimated assuming a temperature change, ΔT ∼ 300 K. An additional vacuum gap (0.2−0.4 nm) in the single BP3-NP device would straightforwardly explain the reduced capacitive coupling and the increased charging energy. Electrical Transport Behavior of 3D Nanoparticle Arrays. Differing from the expected behavior for ligandstabilized gold nanoparticles known from literature,12,15 the Arrhenius plot of BP3-NPs exhibits three different transport regimes (Figure 7). This Arrhenius plot was derived by extrapolating the conductance to log ν → 0 from the admittance spectra and plotting against temperature (Supporting Information section V).

(5)

with EC0 = (Uth+ − Uth−)e/4 and Uth+, Uth− corresponding to the threshold voltages to add or to subtract an electron from the NP. From Figure 5c the first Coulomb blockade peaks (Uth+ = 25 mV and Uth− = −50 mV) can be determined. They are asymmetric around zero bias pointing to a fractional residual charge, Q0 = 0.41 e, on the nanoparticles at USD = 0. A charge Q0 can be induced by polarization effects and stray capacitances located near the NP. In a single-NP device and high applied voltages, polarization effects are likely. Applying eq 5 and T = 300 K results in YCB = 64 nS, while the total conductance for bias voltages around 0 can be determined from Figure 5a to be Ytot = 190 nS. From this follows that the fraction in conductance originated by thermally activated hopping according to Poole−Frenkel-type transport amounts to YPF ∼ 126 nS. At 4 K the electrical transport mechanism through the “nanoelectrode−BP3−NP−BP3−nanoelectrode” system is independent of temperature, and thus a pure tunneling mechanism can be assumed. Furthermore, a stepwise limited transport corresponding to the Coulomb blockade mechanism can be observed from the fine structure of the flattened first derivative of the I(U) curve shown in Figure 6. The curve shows periodic peaks with a distance of 103 mV which corresponds to EC(4 K) = 26 meV and Ctot(4 K) = 3.08 aF. This decreased capacitance at 4 K compared to room

Figure 7. Temperature-dependent conductance of a BP3-NP array plotted according to Arrhenius (log YA vs T−1). The curve shows three different transport regimes: (I) 300−340 K (red fit): linear dependence of the conductance according to Arrhenius; (II) 230− 290 K: discontinuity in the curve, which can be related to a structural crossover in the particles morphology; (III) 100−220 K (blue fit): linear dependence of the conductance according to the Arrhenius equation. Calculated activation energies for the transport regimes I and III assuming different transport mechanisms are summarized in Table 2.

In the first transport regime (300−340 K, red fit in Figure 7), the nanoparticle−ligand system exhibits an almost linear behavior, corresponding to a hopping process between nearest neighbors. In this temperature range, an activation energy of EA = 184 meV is calculated. This value is in good accordance with the planarization energy of biphenyl moieties34 discussed earlier. Consequently, it can be deduced that the thermal activation energy associated with the phenyl rotation is the main energy barrier in this temperature range for BP3-NP arrays. The charge transport according to the Poole−Frenkel model, which describes the field-enhanced electron emission, can be excluded for 3D NP arrays since the voltage drop in this case is negligible (approx. 1 μV/NP) in comparison with the single-nanoparticle experiments. Following the curve to lower temperatures (230−290 K), an atypical charge transport behavior is observed, which is visible as a peak in the Arrhenius diagram. This interesting feature will be discussed in detail in the following section. In the temperature range of 100−230 K (third transport regime), the NP−ligand system exhibits a linear dependence according to the Arrhenius relation, and an activation energy EA of 58 meV can be deduced (Figure 7, blue fit). In this

Figure 6. Flattened first derivative of I(U) measurements performed at 4 K exhibiting periodic peaks with a distance of ΔUCB = 103 mV. 20662



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Figure 8. Temperature-dependent conductance obtained from a 3D BP3-NP array plotted according to the superexchange mechanism (left) and the granular metal model (right). The calculated activation energies obtained from the slopes of the respective linear fits are represented in Table 2.

AuNPs. In order to further scrutinize this unexpected finding, we performed DSC measurements, which reveal in the lowtemperature range the glass transition and melting point of toluene, which was used as solvent for the Au nanoparticles, and an additional endothermal process (Figure 9). This endothermal process appears in the same temperature range, where the peak in the Arrhenius plot was found.

temperature regime, the conductivity is less temperature dependent compared to the first transport regime. Therefore a different transport mechanism can be assumed. The electrical transport behavior in this temperature range is also fitted according to the granular metal and the superexchange coupling model. The resulting linear fits, log(YGMT1/2) vs T−1 and log(YSE) vs T−1/2, are presented in Figure 8, and the activation energies are summarized in Table 2. Table 2. Overview of the Calculated Activation Energies Obtained for the Temperature Regimes I and III Using Different Transport Models: EA (Arrhenius Hopping Processes), EGM, EGM,theo (Granular Metal Model), and ESE (Superexchange Model) I (340−300K) III (220−100K)

EA (meV)

EGM (meV)

EGM,theo (meV)

ESE (meV)

184 ± 20 58 ± 3

70 ± 5 15 ± 2

10 10

792 ± 80 253 ± 20

Furthermore EGM can be predicted according to Abeles38 using a simple electrostatic model based on the radius of the NP (r) and the distance between the nanoparticles (s): (6)

Figure 9. DSC measurements of BP3-functionalized Au nanoparticles; arrows in the low-temperature range indicate the glass transition Tg and melting point Tm of toluene (180, 123 K), which was used as solvent for the Au nanoparticles. In the temperature range 220−290 K endothermal processes occur, which we relate to a possible structural transition of the Au core.

Regarding the linear fits in Figure 8 and the calculated activation energies in Table 2 in the temperature range III, the granular metal model as well as the superexchange coupling mechanism are applicable. The activation energy EGM,theo determined by the electrostatic model is in good agreement with the activation energy EGM derived by the granular metal model. The calculated activation energy ESE according to the superexchange model is 259 meV. It is considerably higher than the calculated activation energy in the first temperature range according to nearest-neighbor hopping, however, smaller than calculated reorganization energies discussed earlier.8 In conclusion, the electrical transport properties of the nanoparticle array can be explained by an Arrhenius-type transport model between nearest neighbors at high temperatures (transport regime I: 300−340 K), while at lower temperatures (transport regime III: 100−220 K) a differentiation between the granular metal model and the superexchange coupling model based on these data is not possible. Morphology Changes of AuNPs. An atypical behavior expressed by a peak in the Arrhenius curve appeared in the temperature range 230−290 K (Figure 7) of the BP3-stabilized

This endothermal process could not be observed in DSC measurements of the pure ligand (Supporting Information section VI). The reason for this atypical behavior is still unclear. A tentative explanation might be a transition in the particle morphologics. This hypothesis is in accordance with the phase map of gold nanoparticles, which was derived from relativistic ab initio thermodynamics published very recently by Barnard et al.20 which is presented in Figure 10. However, the theoretically obtained phase map was experimentally proven by HRTEM during in situ heating experiments on citrate/tannic acid stabilized Au nanoparticles. The diagram predicts the thermodynamically stable size and temperature range for each motif at lower temperatures. We assume that a morphological transition can effect a reorganization of the ligand shell and therefore might cause a change in the electrical conductivity. Furthermore, different work functions of different crystallographic planes may play a role. Recently, Nair and Kimura39 observed a similar phenomenon in the charge transport measurements of 3D superlattices built

EGM,theo =

e2 ⎛ 1 1 ⎞ ⎜ ⎟ − 8πεrε0 ⎝ r r + s⎠

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molecules and thus π−π interaction between neighboring biphenyl moieties is unlikely. Consequently, the molecules forming the “medium” between the single NP and the nanoelectrodes can be regarded as “higher insulating” than in the 3D NP array. Furthermore, the effect of a dielectricum completely surrounding the AuNPs in the 3D NP array will cause also a reduction of the activation energy. However, it is even more interesting to compare both temperature-dependent conductance measurements in more detail. In both measurement setups a thermally activated hopping mechanism can be assumed in the highest temperature range, i.e., region I, whereas in temperature region III a charge transport mechanism with lower temperature dependence becomes apparent. While for the single-NP device superexchange coupling can be assumed, no clear decision for a transport mechanism can be made for the 3D NP array. All considered charge transport mechanisms can be fitted to the experimental curve equally. However, most interestingly in temperature region II a reproducible discontinuity in conductance is measured for both experimental setups. It is not clear why this discontinuity appears in different forms, but it clearly shows up as a sudden change in conductance for a single NP while it is broadened up to 60 K for the NP array. In fact this is an affirmation for the earlier made hypothesis that this discontinuity might be attributed to a transition in the particle morphologics since this the transition temperature is size dependent20 and the NPs have a particle size distribution. Consequently a broadening of the structural transition in a NP array is expected.

Figure 10. From literature20 modified nanogold phase map. The red dot indicates the observed crossover area for the BP3-functionalized gold nanoparticles with the diameter D = 4.1 nm.

up from mercaptosuccinic acid (MSA)-protected AuNPs with different core sizes. They fabricated 3D superlattice crystals from 4.0, 6.2, and 7.5 nm mercaptosuccinic acid (MSA)functionalized AuNPs and characterized these superlattice crystals in a four-probe measurement setup electrically. The I(U) characteristics performed in the temperature range 20− 285 K showed a metallike behavior at low temperatures and a transition to semiconductor behavior with increasing temperature. In the thermally activation range at around 205 K a reversible transition occurred, which the authors attributed to a coherent motion of the MSA ligands causing a large fluctuation in MSA bonding in the superlattice crystals. A similar atypical behavior in electrical resistances of films of AuNPs linked by octanedithiol and hexanedithiol was reported by Müller et al.40 They discussed the temperature-dependent electrical resistances of 300 nm thick films of those dithiol-linked nanoparticles built up from aqueous solution. In the temperature range 220− 285 K a hysteretic behavior occurred, which was attributed to the contraction/expansion of water/ice in the pores of the disordered nanoparticle films and the substrate. However, in our measurements we can exclude this effect, because our nanoparticle films were prepared from dry toluene solutions. Furthermore, other impedance measurements performed using the same experimental setup and analogous drying conditions41 do not show any discontinuities or other effects, which could be related to residual water. Further investigations involving different particle sizes and ligand molecules for a detailed analysis of this interesting effect are ongoing. Comparison of Charge Transport through a Single-NP Device and a 3D NP Array. Besides the fact that charge transport through a 3D NP array is of course considerably higher due to the availability of multiple transport channels, the temperature dependence of the conductance is remarkably smaller as well. This directly points to smaller activation energies in the 3D NP array, which are observed in the whole temperature range under investigation and for all charge transport mechanisms that have been considered. The smaller activation energies in the 3D NP array can be attributed to the array geometry which consists of NPs with strongly interdigitating ligand shells. Thus, the insulating medium consists of close-packed molecules. Furthermore, the determined average interparticle distance of 1.4 ± 0.4 nm probably allows also percolation paths with smaller interparticle distances, i.e., higher conductivity. In contrary, only a few, countable molecules bridge the distance between the single NP and the nanoelectrodes. Here also interdigitation of the

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CONCLUSIONS In conclusion, the charge transport behavior of BP3-NPs has been studied as well in a single-NP device as in a 3D array. The complex temperature dependence of the conductance has been characterized in detail, and different transport mechanisms like thermally activated hopping (Arrhenius, Poole−Frenkel), superexchange coupling, and tunneling were identified. Moreover, Coulomb blockade behavior was observed in the singleNP device at 4 K and room temperature. Finally a discontinuity in the temperature dependence of the conductance in both experimental setups was discussed in terms of a structural transition in the nanoparticle core.

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ASSOCIATED CONTENT

S Supporting Information *

Supplementary methods, supplementary figures for nanoparticle characterization, and the experimental setups for the electrical conductivity measurements. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the DFG program Si609/9-1 and KA 1819/2-1. We thank the EC FET Proactive Project MOLOC for partial support of this work. We thank Jochen Friedrich (PGI-7) for taking the TEM pictures, Peter Kowalzik and Ninet Babajani (PGI-7) for development of broader nanoelectrodes 20664



Article

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and taking the SEM images, Jürgen Nelles (IAC) for calibration of the impedance setup and for performing the impedance measurements, Walter Richtering and Thomas Eckert, Institute of Physical Chemistry for DLS and SAXS measurements, and Klaus Beckerle (IAC) of the RWTH Aachen University for taking the DSC curves.

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