J. Phys. Chem. B 2001, 105, 8291-8296
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Temperature-Dependent Electron Transport through Silver Nanocrystal Superlattices R. Christopher Doty,† Hongbin Yu,‡ C. Ken Shih,‡ and Brian A. Korgel*,† Department of Chemical Engineering and Texas Materials Institute, Center for Nano- and Molecular Science and Technology, UniVersity of Texas, Austin, Texas 78712-1062, and Department of Physics and Texas Materials Institute, Center for Nano- and Molecular Science and Technology, UniVersity of Texas, Austin, Texas 78712-1062 ReceiVed: April 2, 2001; In Final Form: June 26, 2001
Temperature-dependent electron transport was measured through three-dimensional close-packed alkanethiolstabilized silver nanocrystal arrays using interdigitated array electrodes. Nanocrystals ranging from 35 to 77 Å in diameter with Coulomb blockade energies well above kT were studied. The nanocrystal superlattices exhibit linear current-voltage behavior for temperatures as low as 70 K. Ordered face-centered cubic (fcc) superlattices exhibit a positive temperature coefficient of resistivity (TCR), characteristic of a metal, at temperatures above approximately 225 to 245 K, depending on the particle size. The values of the conductivity, on the order of 10-6 to 10-7 Ω-1 cm-1, however, are characteristic of semiconductors. Below the transition temperature, the TCR for the size-monodisperse nanocrystal arrays becomes negative, characteristic of an insulator and the conductance G, of the ordered arrays scales exponentially with temperature as G ∝ exp[-(To/T)ν]. The exponent ν, ranges from 0.67 to 1.34 for nanocrystals 77 Å to 35 Å in diameter, respectively, characteristic of a gap in the density of states in the overall electronic structure of the superlattice. We believe that electron transport occurs through a polaron hopping mechanism. In contrast to the organized superlattices, disordered close-packed nanocrystals exhibit insulating behavior at all temperatures studied due to (Andersontype) disorder.
Introduction The fundamental competition between order and disorder lies at the heart of materials science and technology. A finite resistivity in a metal for example occurs only as a result of imperfections in the crystal or lattice vibrations. Sufficiently disruptive crystal imperfections can cause a metal to become insulating with a resistivity that diverges in the limit of zero temperature. The understanding of the disorder-tuned metalinsulator transition has been a major achievement in the theory of condensed matter.1,2 Advances in techniques for the assembly of ordered two- and three-dimensional nanocrystal arrays provide an interesting new context for studies of metal-insulator phase transitions.3-6 Nanocrystal arrays provide the opportunity to tune the energy levels of the lattice sites through size control, the coupling between sites through interparticle spacing and the nature of the chemical spacers, and the symmetry of the array.4,7 In fact, if a metal nanocrystal array was perfectly periodics and all nanoparticles were identicalsit would be expected to have “running wave” solutions to the Schro¨dinger equation just like a natural crystal, with finite resistivity at zero temperature. The regularity requirements, however, are expected to be much more stringent in the nanocrystal array case. The first electron transport measurements for alkanethiolstabilized metal (gold (Au)) nanocrystal arrays were performed by Brust et al.8 The gold nanocrystal arrays exhibited insulating behavior over a wide temperature range. Shortly thereafter, Terrill and co-workers performed an in-depth study of the effect of size and interparticle separation on the electrical conductivity * Author to whom correspondence should be addressed. Phone: (512) 471-5633. Fax: (512) 471-7060. E-mail:
[email protected]. † Department of Chemical Engineering and Texas Materials Institute. ‡ Department of Physics and Texas Materials Institute.
of Au nanocrystal arrays.9 The electrical behavior was found to be insulating over a wide temperature range and the conductivity was modeled equally well by an Arrhenius model (ln σ vs T -1) and a granular metal model (ln σ vs T -1/2) for activated hopping. In both refs 8 and 9, the Au nanocrystals were relatively polydisperse in size and were not organized into close-packed superlattices. Heath et al. reported the first example of a metal-insulator transition in a nanocrystal array. On a Langmuir-Blodgett trough, hydrophobic silver nanocrystals (2.7 nm) were floated on an air-water interface.10 Nanocrystal separations of greater than 12 Å gave insulating arrays. However, compression of the nanocrystal monolayer to interparticle separations less than approximately 5 Å produced metallic behavior as electron wave functions, localized in individual particles at large separations, experienced strong exchange coupling. True metallic behavior in these monolayers has been confirmed using a variety of characterization techniques, including optical spectroscopies and AC electrical measurements.4 In their studies, Heath et al. does not observe metal-insulator transitions for monolayers consisting of particles with large size distributions, which Remacle and Levine11 have attributed to disorder-induced insulating behavior that occurs regardless of the interparticle separation in the array. In 1998, Snow and Wohltjen observed a temperaturedependent metal-insulator transition for condensed alkanethiolcoated gold nanocrystal arrays.12 Their arrays exhibited a positive temperature coefficient of resistivity (TCR)scharacteristic of a metalsat room temperature, and then a negative TCR below a transition temperaturescharacteristic of an insulator. The temperature-dependent metal-insulator transition seen by Snow and Wohltjen for Au nanocrystals was also witnessed for
10.1021/jp011227z CCC: $20.00 © 2001 American Chemical Society Published on Web 08/15/2001
8292 J. Phys. Chem. B, Vol. 105, No. 35, 2001 reasonably size-monodisperse Co nanocrystals produced by a plasma-gas-condensation-type cluster beam deposition technique embedded in a CoO matrix.13,14 In an attempt to explain these results, one group developed a semiclassical predictive model for the metal-insulator transition in metal nanocrystal superlattices that accounts for the size-dependent charging energy and assumes a thermally activated electron transport process.15 Comparison between their predictions and the measurements in ref 12 show reasonable agreement, however both quantitative and qualitative differences between the model and the data exist, such as the inability of the model to predict an abrupt metalinsulator transition. Furthermore, the model does not offer an explanation as to why some of the nanocrystal arrays exhibit only insulating behavior, while some exhibit a metal-insulator transition. In contrast, Remacle and Levine’s first principles quantum mechanical calculations for nanocrystal arrays, that explicitly account for the disorder that can result from the varied charging energies in a collection of size-polydisperse nanocrystals, have compared favorably with experimental measurements.11 Disorder undoubtedly plays a central role in determining the nature of electron transport through nanocrystal superlattices. In this article, we examine the effect of superlattice order on the nature of dc electron transport. At room temperature, structurally disordered silver nanocrystal superlattices exhibit a negative temperature coefficient of resistivity (TCR), characteristic of an insulator; whereas, ordered face-centered cubic silver nanocrystal superlattices with particles that have the same average diameter and interparticle separation exhibit a positive TCR, characteristic of a metal. The TCR of the ordered arrays changes from positive to negative as the temperature decreases, indicative of a metal-insulator transition. The metal-insulator transition in granular metals is typically conceptualized as a crossing over of a percolation threshold, where the metal volume fraction in the insulating matrix is sufficiently high to form a continuous pathway through the insulating material. Here, however, the interparticle separation is controlled to within a few angstroms by the insulating organic capping ligands, and particles are not allowed to touch, even at high particle volume fractions. In this study, we demonstrate the disorder-induced metal-insulator transition in three-dimensional silver nanocrystal arrays. Experimental Section Nanocrystal Preparation and Characterization. All chemicals were bought and used as-is from Sigma-Aldrich. Dodecanethiol-stabilized (C12H25SH) silver nanocrystals were synthesized according to a modified version of the procedure developed by Brust et al.16,17 An aqueous solution of silver ions (0.03 M AgNO3) in the amount of 36 mL was combined with 25 mL of a chloroformic solution of phase transfer catalyst (0.2 M (C8H17)4NBr) and vigorously stirred for 1 h. The organic phase, which contained the silver ions, was isolated by phaseseparation from the aqueous phase and 1 mmol (240 µL) of dodecanethiol was added. After stirring for 15 min, the silver ions were reduced by introduction of 30 mL of an aqueous solution of sodium borohydride (0.44 M NaBH4). This solution was stirred for approximately 12 h to ensure completion of the reaction. The organic phase containing the silver nanocrystals was then isolated from the aqueous phase through phaseseparation. The nanocrystals were washed in excess ethanol (4:1) to remove any phase transfer catalyst and unbound thiol in the organic phase. Upon centrifugation at 10 000 rpm for 5 min, the nanocrystals precipitated out of solution and were
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Figure 1. (A) Optical micrograph of an interdigitated array electrode. (B) The active region of the electrode consists of fingers with 20 µm spacing.
isolated from the supernatant. The nanocrystals were redispersed in chloroform and repeatedly centrifuged to remove any nanocrystals that were not well-capped. Size-selective precipitation was used to reduce the size distribution of the nanocrystals with chloroform/ethanol as the solvent/nonsolvent pair. Size-monodisperse fractions with decreasing average radius were isolated upon addition of increasing amounts of ethanol and centrifugation.6,17 The nanocrystal size and size distribution was determined by transmission electron microscopy (TEM), using either a Phillips 208 at 80 keV or a JEOL 2010 at 200 keV to view the nanocrystals deposited on carbon-coated copper TEM grids. Interdigitated Array Electrode Fabrication. All photolithography chemicals were received and used as-is from the Clariant Corporation. All metal etchants were bought and used as provided from Transene Company, Inc. The conductivity of the nanocrystal superlattices was measured using an interdigitated array electrode consisting of gold contacts on a glass substrate (See Figure 1). Borosilicate glass was cut into sections with a surface area of approximately 1 cm2. The glass substrate was cleaned with isopropyl alcohol, acetone, and deionized water prior to evaporation of an adhesion layer of Cr (50 Å) and 1000 Å of Au. The interdigitated array was lithographically patterned onto the Au film in a cleanroom environment. AZ 5214-E photoresist was spin-coated on the Au film to a thickness of 1 µm and baked at 90 °C for 9 min. Upon UV irradiation for two minutes, the pattern was developed in AZ 425 MIF developer for 45 s. The substrate was then baked at 120 °C for 5 min. The interdigitated array was revealed by wet etching.
Electron Transport through Ag Nanocrystal Superlattices The Cr film was etched in a ceric ammonium nitrate and nitric acid solution, and the Au film was etched in an aqueous potassium iodide solution. The remaining photoresist was removed with AZ 400T photoresist stripper. A voltage was applied across the electrode to ensure that there was no current leakage due to contact between the electrode fingers. Electrode resistance exceeded 1000 MΩ prior to nanocrystal deposition. Conductivity Measurements. A concentrated droplet (0.5 µL of 5-10 mg/mL) of nanocrystals dispersed in chloroform was placed on the interdigitated array. The solvent evaporates to leave a circular film of nanocrystals with a diameter of approximately 3.5 mm. The nanocrystal film fills in the gaps between the interdigitated fingers of the electrode, giving it a thickness of approximately 1000 Å. Profilometer measurements show that there is minimal overflow onto the top of the electrodes, and atomic force microscopy (AFM) showed that the thickness of the superlattice layer varied by less than 10% in all cases. Korgel and Fitzmaurice showed using small-angle X-ray scattering that nanocrystal size distributions with standard deviations less than approximately (12% are required to obtain spatially organized silver nanocrystal superlattices.6 Nanocrystals with size distributions broader than this form arrays with only liquidlike close-range order and lack long-range translational order. TEM images comparing size-monodisperse with -polydisperse nanocrystals are shown in Figure 2. The superlattice conductivity was measured using two current probes and two voltage probes. Low current and low voltage probes were contacted to one pad of the IDA electrode, and high current and high voltage probes were contacted to the other pad. Current was applied with a Kiethley 220 current source, voltage was measured using a Kiethley 200 voltmeter, and temperature was measured using a Lakeshore 330 temperature controller. A current of 100 nA was passed through the nanocrystal superlattice, and the required voltage was measured as a function of temperature. The temperature could be varied from room temperature down to approximately 4.5 K. Scanning Tunneling Spectroscopy. Ag nanocrystals were deposited from dilute dispersions onto freshly cleaved highly oriented pyrolytic graphite (HOPG) surfaces. The sample was then transferred to an ultrahigh vacuum system equipped with a room-temperature scanning tunneling microscope (STM). Base pressure of the chamber is 2 × 10-11 Torr. STM images of Ag nanocrystals were acquired at a sample bias of 2 V and tunneling current of 100 pA, chosen to minimize nanocrystal disturbance. Scanning tunneling spectroscopy (STS), or tunneling currentvoltage curves, were obtained after positioning the STM tip over each point of the scanning area and disabling the feedback controls. The geometry thus formed assumes a double barrier tunneling junction configuration. One barrier is between the STM tip and the nanocrystals due to the organic ligands and vacuum, while the other barrier, also due to the ligands, is between the nanocrystals and the HOPG substrate. Results and Discussion Individually, the nanocrystals used in this study exhibit Coulomb blockade energies much greater than kT (kT ≈ 0.025 eV at room temperature). STS measurements of individual silver nanocrystals exhibit staircase current-voltage (I-V) behavior as shown in Figure 3. As a first approximation, the charging energy Uc, required to add an electron to a nanocrystal is related to the size-dependent capacitance of the nanocrystal, C ) 4πoR, as Uc ) e2/C. Taking typical values for the dielectric constant of the surrounding alkane medium ( ) 2.2), and plugging in the values for the permittivity of vacuum (o )
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Figure 2. TEM images of (A) size-polydisperse (3.8 ( 0.8 nm) dodecanethiol-capped silver nanocrystals and (B) size-monodisperse (3.7 ( 0.3 nm) dodecanethiol-capped silver nanocrystals.
8.85 × 10-12 C2/N•m2) and the fundamental unit of charge (e ) 1.6 × 10-19 C), Uc ranges from 0.17 eV up to 0.37 eV for nanocrystals ranging from 77 to 35 Å in diameter. The threedimensional nanocrystal arrays deposited on interdigitated array electrodes, however, exhibit linear I-V behavior as shown in Figure 4. At room temperature, the nanocrystal array conductivity, σ, is relatively low (10-6 to 10-7 Ω-1 cm-1), with values characteristic of semiconductors. The conductivity of several nanocrystal films is plotted in Figure 5 as a function of temperature. The qualitative difference between the temperature dependence of σ for size-monodisperse and size-polydisperse nanocrystals is striking. In the case of polydisperse nanocrystals, σ drops off rapidly with decreasing temperature and could not be measured below 250 K using the IDA electrodes due to resistances beyond the capabilities of
8294 J. Phys. Chem. B, Vol. 105, No. 35, 2001
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Figure 5. Conductivity versus temperature data for silver nanocrystal films: (a) size-polydisperse sample; size-monodisperse samples with diameters of (b) 7.7 nm; (c) 5.5; (d) 4.8; (e) 4.5; (f) 3.5.
Figure 3. (A) STM image of dodecanethiol-capped silver nanocrystals deposited on a graphite substrate. (B) Scanning tunneling spectroscopy of an individual nanocrystal. The I-V curve shows a nanocrystal charging energy of approximately 300 meV. The scale bar is 5 nm.
Figure 6. Plot of transition temperature (TMI, [) and activation energy (Eg, B) of dodecanethiol-capped silver nanocrystals as a function of particle diameter.
Figure 4. Room-temperature I-V curves of 7.7 nm (B) and 5.5 nm ([) nanocrystals. Resistances are equal to 2.0 × 107 Ω and 5.8 × 106 Ω for the 7.7 and 5.5 nm nanocrystals, respectively.
the experimental setup. In contrast, σ for the size-monodisperse samples increases with decreasing temperature until reaching a critical temperature where the TCR [(1/F)(dF/dT); F is the resistivity] changes sign. This transition temperature can be loosely characterized as a metal-insulator transition (TMI), although the values of the conductivity are several orders of
magnitude lower than those for typical metals. The transition temperatures increase with decreasing particle size, ranging from 225 to 245 K (see Figure 6). Anderson Localization in Polydisperse Nanocrystal Arrays. Heath et al. have demonstrated quite convincingly that the collective electron wave function in individual nanocrystals will overlap and hybridize with the wave functions in neighboring nanocrystals in an array with sufficiently short interparticle separations.4 The critical distance for the metal-insulator transition has been estimated in terms of the parameter, δ ) D/2R, where D is the center-to-center interparticle separation and R is the radius of the metal core.4 Dodecanethiol nanocrystals exhibit an interparticle separation of 16 ( 1 Å and δ ranges from 1.2 to 1.4 in this study. Simulations by Remacle and Levine calculated that a value of 1.3 is needed for exchange coupling to occur in a two-dimensional array.11 The values in ref 11 are slightly above the values reported in ref 4 needed for strong exchange coupling between neighboring nanocrystals. Nonetheless, electronic coupling in the size-monodisperse nanocrystal arrays is sufficient to produce positive TCR values at room temperature. In contrast, the size-polydisperse nanocrystals exhibit a negative TCR. The interparticle spacing is the same in both systems and therefore, in both the size-
Electron Transport through Ag Nanocrystal Superlattices
J. Phys. Chem. B, Vol. 105, No. 35, 2001 8295 TABLE 1: Parameters diameter nanocrystals (nm) polydisperse sample (a) fraction 1 (b) fraction 2 (c) fraction 3 (d) fraction 4 (e) fraction 5 (f)
Figure 7. Offset normalized conductance versus temperature for sizemonodisperse nanocrystals. Curves are normalized to their conductance values at TMI. The model curves represent the best fits to the scaling relationship, G ∝ exp[-(To/T)ν]. Table 1 lists the parameters.
monodisperse and -polydisperse samples electrons must overcome the same energetic barrier due to the capping ligands to transport between nanocrystals. The metal volume fraction φν, in the polydisperse sample (φν ≈ 0.38) is slightly less than in the monodisperse sample (φν ≈ 0.41); however, both of these values are above the percolation threshold for an fcc lattice of particles (φν ≈ 0.25).18 The key difference between the sizemonodisperse nanocrystals and the -polydisperse nanocrystals is the amount of disorder in the system. The “metallic” behavior exhibited by the size-monodisperse nanocrystals reveals that exchange coupling between neighboring nanocrystals occurs to a significant degree. We can think of the interparticle electronic overlap as giving rise to tightbinding bands with width B. Anderson showed that the eigenfunctions of a lattice with a site energy (w) distribution, such as a uniform distribution of width W, P(w) ) 1/W for -1/2W e w e 1/2W, will localize if the strength of the disorder, ∆ ) W/B, exceeds some critical value.2 The site-site fluctuation in Uc in the polydisperse nanocrystal arrays leads to high values of ∆ relative to the monodisperse nanocrystals. Furthermore, the absence of translational order in the polydisperse nanocrystal arrays provides additional inhibition of electron transport. The quantitative effect of the disorder is to give rise to electron transport activation energies of ∼1.5 eV, which are significantly higher than the Coulomb blockade energy of 0.3 eV. The size distribution of the polydisperse nanocrystals leads to insulating behavior at room temperature as a result of an Anderson metalinsulator transition. Polaron Transport in Ordered Nanocrystal Arrays. The size-monodisperse nanocrystal arrays exhibit positive TCR at room temperature. The values of the conductance G, however, are well below the quantum conductance Goo ) e2/2h, indicating that electron transport is localized and occurs by an activated electron hopping mechanism with conductance that is expected to scale with temperature as G ∝ exp[-(To/T)ν].19 Figure 7 shows this relation fit to the size-monodisperse conductance data. (Table 1 lists the parameters.) Below the transition temperature, the scaling exponent ν, ranges from 0.67 for the largest particles up to approximately 1.3 for the smallest particles, indicative of strongly localized electron transport. The activation energies for transport below TMI range from 40 meV
TMI (K)
σ at TMI Tο conductance (10-6 Ω1-) (K) exponent, V
activation energy, Eg (eV) 1.5
7.7 5.5 4.8 4.2 3.5
225 241 244.5 245 245
0.47 1.8 1.1 0.63 0.98
500 300 300 325 350
0.67 1.22 1.34 1.35 1.34
0.038 0.069 0.079 0.080 0.098
up to 100 meV for 77 Å nanocrystals and 35 Å nanocrystals, respectively (see Figure 6). Although these values are much smaller than the Coulomb blockade energies (∼300 meV) of individual nanocrystals, they are still greater than kT at room temperature (25 meV). This could be an indication that exchange coupling between nanocrystals is not sufficient to produce true metallic behavior even though positive TCR are observed at high temperatures. If so, what is the physical explanation for the metal-insulator transition? In the nanocrystal array, the mean free path of the charge carriers approaches the characteristic lattice parameter aH, which is the interparticle spacing in this case. Under these conditions, the carrier polarizes the surrounding environment to create a distortion in the lattice. The potential well created by the polarization cloud tends to localize the carrier, which leads to the formation of Hubbard-type electronic bands. In this situation, localized electron transport with strong electron-phonon coupling and polaron formation is expected. The polaron can be treated as a quasiparticle that transports through the lattice. Polaron interactions affect the width of the polaron bands and the energy “gap.” At a sufficiently high polaron (carrier) density, charge screening can be sufficient to give rise to a degenerate polaron gas. Mott has estimated the carrier density, n, required for degenerate gas formation: n1/3aH = 0.2.19 This carrier concentration roughly equates to the case when 1% of all nanocrystals are occupied by an electron. As an estimate of this possibility, consider a superlattice with one carrier (electron, or polaron) per particle in the ground state. The activation energy for transport Eg, (determined from the slope of the insulating portion of the conductivity versus temperature plots) can provide an estimate of the percentage of “free” carriers relative to the particle concentration no, that are activated at room temperature using the expression, n/no ) exp(-Eg/2kT). At room temperature, approximately 1% of the carriers should be activated and extensive polaron screening is expected. Above TMI, the polarons behave as large effective mass quasiparticles with phonon-inhibited transport. Above TMI, an increase in temperature leads to increased lattice vibrations, which impedes transport and gives rise to positive TCR. Thus, TMI decreases with increasing nanocrystal size, as carriers are more easily promoted in large particles with lower Coulomb blockade energies. Below TMI, the carrier concentration is presumably reduced to values lower than those required for polaron gas formation. Under these conditions, the carrier concentration controls the temperature dependence of the conductivity, which leads to insulating behavior.20 Conclusion Electron transport through the nanocrystal arrays in this study presumably occurred through a polaron hopping mechanism. The size-monodisperse nanocrystal arrays exhibited a positive TCR at room temperature down to a “metal-insulator” transition temperature, TMI. Above TMI, polarons transport as heavy effective mass quasiparticles, whose resistance is dominated by
8296 J. Phys. Chem. B, Vol. 105, No. 35, 2001 phonon scattering. Below TMI, the TCR becomes negative, characteristic of an insulator with activation energies ranging from 40 meV for the largest nanocrystals up to 100 meV for the smallest nanocrystals. Size-monodisperse nanocrystal superlattices exhibit a temperature-dependent metal-insulator transition that shifts to lower temperature as nanocrystal size increases. The size-polydisperse nanocrystal arrays exhibit negative TCR at all temperatures studied due to Anderson-type disorder. Acknowledgment. The authors thank John McDevitt, Dean Neikirk, and John Mendenhall for invaluable technical assistance. R.C.D. thanks Shell for a doctoral fellowship. The authors acknowledge financial support of this work from NSF through a Focused Research Group, Grant Number DMR0071893. References and Notes (1) Mott, N. F. Metal-Insulator Transitions; Taylor & Francis Ltd.: London, 1990. (2) Anderson, P. W. Phys. ReV. 1958, 109, 1492. (3) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Science 1995, 270, 1335. (4) Markovich, G.; Collier, C. P.; Henrichs, S. E.; Remacle, R.; Levine, R. D.; Heath, J. R. Acc. Chem. Res. 1999, 32, 415. (5) Whetten, R. L.; Shafigullin, M. N.; Khoury, J. T.; Schaaff, T. G.; Vezmar, I.; Alvarez, M. M.; Wilkinson, A. Acc. Chem. Res. 1999, 32, 397. (6) Korgel, B. A.; Fitzmaurice, D. Phys. ReV. B 1999, 59, 14191. (7) Alivisatos, A. P. Science 1996, 271, 933. (8) Brust, M.; Bethell, D.; Schiffrin, D. J.; Kiely, C. J. AdV. Mater. 1995, 7, 795. (9) Terrill, R. H.; Postlethwaite, T. A.; Chen, C.-H.; Poon, C.-D.; Terzis, A.; Chen, A.; Hutchison, J. E.; Clark, M. R.; Wignall, G.; Londono, J. D.; Superfine, R.; Falvo, M.; Johnson, C. S., Jr.; Samulski, E. T.; Murray, R. W. J. Am. Chem. Soc. 1995, 117, 12537. (10) Collier, C. P.; Saykally, R. J.; Shiang, J. J.; Henrichs, S. E.; Heath, J. R. Science 1997, 277, 1978.
Doty et al. (11) Remacle, R.; Levine, R. D. J. Am. Chem. Soc. 2000, 122, 4084. (12) Snow, A. W.; Wohltjen, H. Chem. Mater. 1998, 10, 947. (13) Peng, D. L.; Sumiyama, K.; Konno, T. J.; Hihara, T.; Yamamuro, S. Phys. ReV. B 1999, 60, 2093. (14) Peng, D. L.; Sumiyama, K.; Yamamuro, S.; Hihara, T.; Konno, T. J. Appl. Phys. Lett. 1999, 74, 76. (15) Mikrajuddin, F. G. Shi, T. G. Nieh, K. Okuyama, Microelectron. J. 2000, 31, 343. (16) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 801. (17) Korgel, B. A.; Fullam, S.; Connolly, S.; Fitzmaurice, D. J. Phys. Chem. B 1998, 102, 8379. (18) Isichenko, M. B. ReV. Mod. Phys. 1992, 64, 961. (19) Mott, N. F. Conduction in Non-Crystalline Materials; Oxford University Press.: New York, 1987. (20) It is highly unlikely that a structural phase transition of the capping ligands in the superlattice gives rise to the transition in the conductivity. Badia and co-workers21 observed reversible endotherms in differential scanning calorimetry (DSC) scans of alkanethiol-coated gold nanocrystals that depended on the hydrocarbon chain length. They ruled out thiol desorption from the nanocrystal surface as a possible explanation for the endotherms and concluded that the endotherms resulted from an orderdisorder transition in the chain conformation from trans to gauche. The temperature of the peak maxima varied from 3 °C for dodecanethiol-coated gold nanocrystals to 64 °C for C20-coated gold nanocrystals. Since the transitions in the conductivity occur at temperatures ranging from -30 to -40 °C, it is highly unlikely that ligand transformations give rise to the observed transitions in the conductivity. Furthermore, Badia and co-workers gave no indication that the chain packing transition temperatures would be expected to depend on nanocrystal size. Terrill et al. reported similar DSC results on alkanethiol-capped gold nanocrystals.9 We also conducted DSC experiments in the temperature range of -50 °C to 100 °C and did not observe any endotherms. The difference between our results and those reported in refs 9 and 21 could arise from the fact that the previous studies examined polydisperse disordered nanocrystal films; whereas the samples measured in the studies reported here focused on monodisperse, ordered arrays. (21) (a) Badia, A.; Singh, S.; Demers, L.; Cuccia, L.; Brown, G. R.; Lennox, R. B. Chem. Eur. J. 1996, 2, 359; (b) Badia, A.; Gao, W.; Singh, S.; Demers, L.; Cuccia, L.; Reven, L. Langmuir 1996, 12, 1262; (c) Voicu, R.; Badia, A.; Morin, F.; Lennox, R. B.; Ellis, T. H. Chem. Mater. 2000, 12, 2646.
