Temperature-Dependent Hall and Field-Effect Mobility in Strongly

Jan 27, 2014 - ... Franck Institute, University of Chicago, Illinois 60637, United States ...... (63) Beverly, K. C.; Sample, J. L.; Sampaio, J. F.; R...
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Letter pubs.acs.org/NanoLett

Temperature-Dependent Hall and Field-Effect Mobility in Strongly Coupled All-Inorganic Nanocrystal Arrays Jaeyoung Jang,† Wenyong Liu,† Jae Sung Son,† and Dmitri V. Talapin*,†,‡ †

Department of Chemistry and James Franck Institute, University of Chicago, Illinois 60637, United States Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States

‡

S Supporting Information *

ABSTRACT: We report on the temperature-dependent Hall effect characteristics of nanocrystal (NC) arrays prepared from colloidal InAs NCs capped with metal chalcogenide complex (MCC) ligands (In2Se42− and Cu7S4−). Our study demonstrates that Hall effect measurements are a powerful way of exploring the fundamental properties of NC solids. We found that solution-cast 5.3 nm InAs NC films capped with copper sulfide MCC ligands exhibited high Hall mobility values over 16 cm2/(V s). We also showed that the nature of MCC ligands can control doping in NC solids. The comparative study of the temperature-dependent Hall and field-effect mobility values provides valuable insights concerning the charge transport mechanism and points to the transition from a weak to a strong coupling regime in all-inorganic InAs NC solids. KEYWORDS: Hall effect, InAs nanocrystals, inorganic ligands, charge transport, doping, electron mobility, carrier trapping

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transport regime has been associated with the adiabatic diffusion of polarons, despite significant structural and electronic disorder. At the present time, it is still unclear how diffusive transport can coexist with the multiple sources of disorder present in NC-based materials.25 Furthermore, how these materials behave in the vicinity of anticipated crossover from hopping to diffusive band transport remains to be elucidated. So far, all temperature-dependent charge transport measurements in NC solids have been carried out using two-terminal FET devices.13−15 This technique has many advantages, but it focuses on electron transport in a very thin, two-dimensional accumulation layer formed at the interface between the NC layer and the gate dielectric. This interface can trap charge carriers26 or somehow alter NC properties. Other mobility measurement techniques should be used to crosscheck the FET data and better understand electronic transport in strongly coupled NC arrays. The recent development of NC solids with high electron mobility relies on inorganic surface ligands that do not introduce insulating barriers between adjacent NCs. As the field progresses, it is important to understand how inorganic ligands affect the properties of individual NCs and NC arrays. For example, capping ligands can lead to the remote doping of the NC core,15,18 which affects carrier concentration and trap distribution in NC arrays.27 Therefore, charge transport studies that can provide information of carrier concentrations are

olloidal semiconductor nanocrystals (NCs) have attracted considerable interest as building blocks for optoelectronic1−4 and electronic5 devices due to their solution processability and size-tunable optical and electronic properties.6,7 Because the operation of these devices mainly depends on electronic conduction in NC arrays, control over and proper understanding of the type, concentration, and mobility of charge carriers are key factors for successful device performance. The weak coupling model can explain charge transport in arrays of NCs capped with organic ligands.7−10 There, electrons nonadiabatically hop between strongly localized states.7−10 The recent development of inorganic ligands for colloidal NCs11,12 has enabled very high electron mobility (μ > 15 cm2/(V s)) in NC thin films13−15 and has led to high-performance NC-based integrated devices.16,17 Our group13,15 and the Kagan group14 have reported bandlike charge transport (i.e., transport with a negative temperature coefficient for mobility, dμ/dT < 0, and high μ > 1 cm2/(V s)) in the arrays of inorganically capped NCs, which serve as active layers in n-type field-effect transistors (FETs). The Law group recently reported all-inorganic, high-mobility ambipolar PbSe NC FETs with dμ/dT ≤ 0 over a broad temperature range.18 Band-like transport in PbSe NC solids was also reported by Siebbeles et al. based on THz spectroscopy studies.19 Very recently, Johnson et al. reported coherent delocalization of excitons in all-inorganic NC arrays.20 All of these results suggest the possible emergence of strong coupling in quantum-confined NC arrays. A theoretical framework for band transport in NC arrays can be found in the recent work by Shabaev et al.21 There are numerous examples of band-like transport in highmobility organic semiconductors.22−24 In many cases this © 2014 American Chemical Society

Received: October 17, 2013 Revised: January 22, 2014 Published: January 27, 2014 653

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Figure 1. (a) X-ray diffraction patterns for thin films of In2Se42− capped (upper panel) and Cu7S4− capped (lower panel) InAs NCs before (black lines) and after (red lines) RTA treatment at 350 °C for 5 s. The vertical blue lines on the bottom are the corresponding positions and intensities of X-ray reflections for bulk InAs. (b) Absorption spectra measured using an integrating sphere for thin films of In2Se42− capped (upper panel) and Cu7S4− capped (lower panel) InAs NCs before (black lines) and after (red lines) RTA treatment at 350 °C for 5 s. Inset: Schematic illustrations of InAs NCs capped with each MCC ligand.

ligands, recently introduced by our group,11 are appropriate materials for these studies due to their high conductivity and mobility in solid-state thin films. Here we report the temperature-dependent Hall effect measurements of In2Se42− and Cu7S4− capped InAs NC arrays. These NCs have shown the highest conductivity and field-effect mobility among a series of MCC-capped NCs, respectively, while preserving optical absorption spectra of strongly quantum confined semiconductor NCs.15 MCC-capped III−V NCs can provide a low-cost alternative to traditional III−V technologies that rely on highly expensive single crystals. The solution-based route to III−V semiconductors can be particularly useful for printable electronic and optoelectronic devices where III−V materials can be more attractive than II−VI and IV−VI analogues owing to their superior carrier mobility, relatively lower toxicity,33−37 and higher thermal stability.15 We found that In2Se42− ligands induced a stable n-type doping in InAs NC arrays as confirmed by almost Tindependent carrier concentrations above 1018 cm−3 from room temperature (RT) down to 10 K. In contrast, Cu7S4− capped InAs NC arrays showed a very low doping level that resulted in a strong T-dependence of carrier concentrations with values less than 2 orders of magnitude higher than intrinsic carrier concentrations in bulk InAs. Moreover, Cu7S4− capped InAs NCs exhibited a Hall mobility (μH) as high as 16.8 cm2/ (V s) with a negative T-dependence near RT (260−340 K). In2Se42− capped NCs exhibited a lower RT Hall mobility (∼1.3 cm2/(V s)) with monotonic positive T-dependence and a surprisingly low activation energy (Ea ∼ 2 meV) below 50 K. Finally, we studied temperature-dependent FET mobility (μFET) for these NC arrays, where carrier transport takes place in a thin charge accumulation channel induced by the gate field. μFET was then compared with μH to better understand the transport in MCC-capped NC arrays. Tri-n-octylphosphine (TOP)-capped InAs NCs with the first excitonic transition at ∼1240 nm in the absorption spectrum (Figure S1) were synthesized by a previously reported

necessary to better understand transport properties in allinorganic NC arrays and to further exploit NC-based devices. Hall measurements provide a convenient way to study charge transport in electronic materials. When combined with longitudinal resistance measurements, Hall measurements allow for the independent measurement of carrier mobility and concentration.28 Furthermore, Hall measurements offer a possibility to explore intrinsic charge transport (i.e., the transport that is not affected by carrier trapping at the dielectric/semiconductor or metal/semiconductor interfaces, which are crucial for conventional FET measurements). However, the Hall effect in solution-processed NC arrays has not been systematically explored probably due to insufficient carrier mobility that prevented the generation of detectable Hall voltages. Also, it is well-known that the Hall effect is strongly suppressed in the hopping transport regime.29,30 In materials with hopping conductivity, the Hall coefficient can even show a sign opposite to the sign of the majority carriers, which is known as the double sign anomaly observed, for example, in amorphous Si.30,31 Such complexity originates from the fact that the generation of Hall voltage requires thermally assisted electron (or hole) hopping between three different sites, but FET-type measurements reflect the probability of hopping between two sites.29,30 In fact, if Hall mobility is comparable to the mobility extracted from FET transfer characteristics, it is strong evidence for the departure from hopping toward the band transport.32 Recently, the Kagan group reported the first observation of the Hall effect with a mobility of 2.8 cm2/(V s) in solutiondeposited films made of thiocyanate (SCN−) capped PbTe NCs.12 These measurements were performed at room temperature and were not compared to FET mobility. Considering that temperature-dependent measurements are widely used for understanding transport properties of semiconductors, a temperature-dependent Hall coefficient is necessary to clarify the physics behind electronic transport in strongly coupled NC arrays. NCs capped with metal chalcogenide complex (MCC) 654

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Figure 2. (a) Schematic illustration of the device structure for Hall effect and van der Pauw measurements. The black arrow represents the positive direction of the applied magnetic field. A current applied between contacts 1 and 3 generated voltage between contacts 2 and 4 under an applied magnetic field. (b,c) The voltage (black solid line) recorded under a different sign and magnitude of the applied magnetic field (red dashed line) for devices made of (b) Cu7S4− capped and (c) In2Se42− capped 5.3 nm InAs NCs (T = 300 K). (d) Magnified plot of b for showing extraction of the Hall voltage, VH. (e) The dependence of the VH on the magnetic field B for devices of Cu7S4− capped (upper panel) and In2Se42− capped InAs NCs (lower panel) (T = 300 K). (f) The VH measured using different contact configurations for devices of Cu7S4− capped (gray) and In2Se42− capped (red) InAs NCs (T = 300 K and B = 1 T).

analyses of the NC films revealed that the XRD patterns were almost identical before and after the RTA treatment, as shown in Figure 1a. These results suggest the absence of NC grain growth and phase separation between NCs and MCC ligands in both In2Se42− and Cu7S4− capped InAs NC films.11,13,15 Figure 1b shows the absorption spectra for the films of In2Se42− and Cu7S4− MCC-capped InAs NCs before and after the RTA treatment. Both NC films maintained their excitonic features in the absorption spectra with some minor red shifts and broadening of excitonic peaks, implying that RTA at 350 °C for 5 s did not induce sintering of the MCC-capped InAs NCs. Small red shifts of the excitonic peaks indicated the polarization changes of the dielectric environment.41 The broadening of the first excitonic peak could be due to the strengthened electronic coupling between NCs after annealing as well as by other factors related to NC size distribution and dielectric environment as will be discussed below.14,41,42 The devices used for the Hall measurements were made using van der Pauw (VDP) geometry, as shown schematically in Figure 2a. Three to four successive spin coating cycles of colloidal solutions of In2Se42− and Cu7S4− capped InAs NCs in hydrazine were performed on oxygen plasma-treated glass substrates. A high solution concentration (>100 mg/mL) and low spin rate (∼800 r.p.m.) were necessary to make thick (>200 nm) and dense films. Finally, an RTA treatment was performed on the NC films before patterning and electrode deposition. An atomic force microscope (Multimode, Digital Instruments) was used to measure the thickness of the films, which was found to be ∼250 nm for both In2Se42− and Cu7S4− capped InAs NC films. The NC films were manually patterned using a sharp tungsten scriber, leading to a square pattern having an approximate area of 0, VH(0) − VH(B) when B < 0. As shown in Figure 2e, the VH is linearly proportional to the applied magnetic field, as expected from the expression:

Al top-contact electrodes, a shadow mask was aligned with the patterned NC film under an optical microscope. Al with a thickness of 150 nm was deposited onto the four corners of the NC film through the shadow mask by thermal evaporation, resulting in four electrodes, each with an approximate area of ∼120 × 120 μm2. The optical microscopy image of the topview of Hall devices and typical VDP I−V characteristics are shown in Figure S2. All fabrication processes were performed in an N2filled glovebox. All electrical measurements were performed in a Physical Property Measurement System (PPMS-9, Quantum Design) under He-filled inert atmosphere using a Keithley multimeter controlled by a LabVIEW interface. The electric bias applied to the NC samples to pass current during Hall measurements did not generate significant electric fields (E < 20 V/cm or 103 at 300 K (it increased to ∼105 below 150 K) and small Vth G ∼ −10V, which is typical for a channel with moderate n-type doping. This difference in output characteristics and on/ off ratios between FETs using In2Se42− capped and Cu7S4− capped NCs clearly supports the difference in doping levels observed in the Hall measurements. As shown in Figure 4c, overall trends of field-effect mobilities (μFET) with T, measured with a drain voltage of 8 V applied across a 150 μm long channel, were found to be similar to the trends seen in μH. In other words, μFET of Cu7S4− capped NC arrays showed a positive slope at higher temperatures (300 to 200 K) and a negative slope at lower temperatures (200 to 20 K) over 1/T.

core, it is expected that both the diffusion and doping could be facilitated by a more favorable interface between the NC and the ligand shell. All of these aspects strongly suggest the possibility of higher doping by In2Se42− ligands than by Cu7S4− ligands. The use of different MCC ligands could lead to a qualitatively different doping behavior. This is an important finding that provides potential for systematic control of n in NC solids (e.g., via using mixed MCC ligands). Although tremendous efforts have been devoted to controlling n in NC solids through doping using metal evaporation,14,51,52 electrochemistry,51 remote doping via hydrazine exposure5 or halide binding,53 and incorporation of impurity atoms,44,54,55 simultaneously controlling doping and producing strongly coupled NC solids still remains a challenge. In this sense, it is noteworthy that the use of In2Se42− MCC ligands provides stable doping even at very low temperatures down to 10 K. At 300 K, a much higher μH of 16.2 cm2/(V s) was observed from Cu7S4− capped NC arrays compared to that of In2Se42− capped NCs (1.3 cm2/(V s)). The plot of log(μH) versus 1/kBT revealed that the μH of Cu7S4− capped NC arrays showed a positive slope from 340 to 260 K and a negative slope from 260 to 140 K (Figure 3b). These results imply that the conduction mechanism switched from band-like (i.e., dμ/dT < 0 with μ > 10 cm2/(V s)) to thermally activated transport with an activation energy of 35.2 meV as the temperature decreased. For the In2Se42− capped InAs NC arrays, the μH (and also electrical conduction considering their similar T-dependences) showed a gradual decrease over 1/T, with effective activation energy gradually changing from ∼14 meV (300 to 180 K) 658

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In2Se42− capped NC FETs showed a consistent decrease of μFET over 1/T. Figure 5a and b displays μH and μFET on the same plot, together with other important parameters, e−/NC and Ea for each device. In FET, transport occurred in a thin accumulation layer with a high carrier density (∼1.0 e−/NC) defined by the gate voltage. The high doping level in In2Se42− capped NC arrays resulted in a similar density of carriers in the FET channel and Hall devices. This implies that the charge transport in Hall and FET devices occurred in nearly the same environment. Interestingly, Hall and FET devices of In2Se42− capped NCs showed very similar μ values in a temperature range from 300 to 100 K (Figure 5a). Such accurate coincidence over a broad temperature range would be hard to explain within accepted models of hopping transport.29 As the temperature decreased below 100 K, a decoupling between μH and μFET was observed. For the hopping transport, it is very common to observe μH < μFET,32 but we observed the opposite trend with μH > μFET. It might come from the difference in the operating mechanism of Hall and FET devices. As shown in Figure 3a, the nH starts decreasing gradually from ∼100 K, from ∼1.0 e−/NC at 100 K down to ∼0.55 at 10 K. The reduction of nH implies that some charge carriers were trapped and the carriers spent a longer time trapped as the temperature decreased. In the heart of FET operation, there is a change of channel conductance caused by additional carriers induced by applying voltage to the gate electrode: Δ(σ) = eμFETΔ(n). During the gate voltage sweep, some carriers injected from the source electrode into the FET channel were being trapped in the shallow trap states present in NC arrays. In FET devices, electron transport occurs near the interface between the NC film and the SiO2; additional trapping can occur at this interface containing a large density of trapping sites associated with surface hydroxyl groups.26 According to the multiple trap-and-release model, the effect of trapping on the channel conductivity can be accounted for in two different ways:22,28,58 σ τ = μ0 μeff ≡ en τ + τtr (2) or, alternatively τ neff = n τ + τtr

could be due to partial trapping of charge carriers on shallow traps, as explained by eqs 2 and 3. The observation of band-like transport at a higher T does not mean the complete elimination of trapping.22,28 At the same time, the crossover from dμ/dT < 0 to dμ/dT > 0 occurred at a higher T for μH and was followed by a mobility drop with a larger value of Ea as compared to μFET. To understand this trend, we need to take into account the important difference between n in Hall devices and FETs for semiconductors in which doping is initially low. In an FET, n is determined by the gate voltage and is similar at all temperatures, while in our Hall devices, carrier freezeout resulted in an exponential drop of n as T decreased (Figure 3b). As a result, the Fermi level in the FET device was close to the 1Se states of NCs at all temperatures, while μH(T) was measured as the Fermi level was moving toward the tail in the density of the electronic states with decreasing temperatures (Figure 5c and d). These tail states are highly localized and can participate only in the hopping transport, which requires significant activation energy approximately experimentally observed as 35 meV. It should be noted that both the μH and μFET of In2Se42− capped NC arrays are about 1 order of magnitude lower than those of Cu7S4− capped NC arrays. This is most likely due to more efficient tunneling of electrons through the Cu2S barriers as compared to In2Se3. The lower mobility can be also caused by a higher density of ionized dopant impurities in In2Se42− capped NC arrays, which contribute to electron scattering. The negative T-dependence of μH near room temperature with high absolute mobility values above 10 cm2/(V s) observed in Cu7S4− capped InAs NCs and very low Ea values observed in In2Se42− capped InAs NC arrays down to 10 K suggest that the classical hopping conduction mechanism does not apply to these systems. There is a growing body of experimental data suggesting that all-inorganic NC solids are somewhere beyond the weak-coupling limit.13−15,18,20 First of all, it is not clear how μ > 10 cm2/(V s) could be achieved within hopping formalism. According to ref 25 the hopping mobility in three dimensions for an array with one conductance channel per NC (this case should apply to InAs quantum dots) can be expressed as μ hop =

(3)

where τ and τtr are the average times that the charge carrier spends traveling between shallow traps and being trapped on shallow traps, respectively. In an FET, all charges injected by the gate are treated as mobile carriers (neff = n) which is an overestimate since some carriers end up trapped. Such trapping is accounted in mobility: μeff ≈ μFET. The μFET is therefore reduced compared to the intrinsic trap-free value μ0.28 On the contrary, because the nH calculated from Hall measurement is the concentration of moving carriers at a given moment of time, the temporarily trapped charges in shallow traps are not taken into account in Hall voltage, namely, nH = neff.28 These considerations suggest the possibility that μH is closer to the intrinsic trap-free mobility μ0 and therefore μH is higher than the μFET when trap-and-release processes play an important role. For Cu7S4− capped InAs NC arrays, more differences were observed between μH and μFET as shown in Figure 5b. It is remarkable that both μH in thick NC films and μFET in twodimensional NC channels show the band-like temperature dependence near RT. μH was even higher than μFET around RT (16.2 cm2/(V s) vs 7.5 cm2/(V s)). The μH > μFET above 180 K

⎛ ea 2Ea E ⎞ exp⎜ −χl − a ⎟ 3hkBT kBT ⎠ ⎝

(4)

where a is the center-to-center distance between adjacent NCs, h is the Planck constant, and χ defines the attenuation of the wave function probability in the inter-NC barrier with width l. Within this model, NCs with a = 6.5 nm corresponding to our 5.3 nm InAs cores with a ∼0.6 nm upper estimate for the MCC ligand shell11 gives the maximum hopping mobility μmax hop ≈ 12 exp(−χl) cm2/(V s) that is significantly smaller than the experimentally observed μH for Cu7S4− capped InAs NCs. To the best of our knowledge, there are no precedents of hopping transport with μ > 10 cm2/(V s) in other material systems. In addition, for hopping transport it should be μH < μFET which is opposite to our experimental data. An alternative to the diffusive transport through the 1Se states could be sintering of NCs. We view this scenario as improbable on the basis of the following arguments. No grain growth was observed in the XRD patterns (Figure 1a). NC necking without grain growth would require the formation of a continuous percolation cluster. The site percolation threshold for randomly packed equal-sized spheres is 0.31.59 It would be 659

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solids studied in this work can be close to the metal−insulator transition. In our previous report,15 we employed the concept of “domain localization” in granular electronic systems62 to explain nonmonotonic T-dependence of field-effect mobility in all-inorganic NC films. We proposed that the NC solid consists of regions with stronger and weaker coupling and that intradomain transport occurs through extended states of strongly coupled NCs and interdomain transport occurs via hopping.63 Then, it can be explained that, at a high T, intradomain diffusive transport dominates conduction and dμ/ dT < 0 is caused by electron−phonon scattering. As the temperature decreased, the hopping between strongly coupled domains becomes a transport bottleneck, which is governed by trap states near the edges of the extended states. At these temperatures, τ ≫ τtr is no longer valid, and the effective mobility in the thermally activated transport regime should be described as: μeff = μ0(τ/τtr) ∝ exp(Ea/kBT).22 The crossover from dμ/dT < 0 to dμ/dT > 0 has been previously observed not only in NC arrays14,15 but also in organic semiconductors including single crystals22 and thin films.24 Our results are also qualitatively comparable with reported data on time-of-flight measurements of lightly doped bulk organic single crystals.64,65 In summary, we studied for the first time the temperaturedependent characteristics of the Hall effect of strongly coupled all-inorganic NC arrays prepared from colloidal InAs NCs capped with In2Se42− and Cu7S4− MCC ligands. The In2Se42− ligands were found to induce a stable n-type doping of InAs NC arrays at temperatures as low as 10 K, leading to a nearly Tindependent nH of around 3.0−5.8 × 1018 cm−3. We also found that the μH of Cu7S4− capped InAs NC arrays showed a negative temperature coefficient with high values of 14.9−16.8 cm2/(V s) at 340 to 260 K, which we attribute to an emergence of strongly coupled domains within the NC array. A comparative study of temperature dependences between μH and μFET revealed that the applied gate field in FETs plays more evident roles in the charge transport of a low doping system, namely, Cu7S4− capped InAs NC arrays, by providing a charge accumulation in a semiconducting channel. On the other hand, μH and μFET were found to be very similar for highly doped In2Se42− capped InAs NC arrays from 300 K down to a certain temperature near 100 K. Below this temperature, μH was higher than μFET presumably due to less influence from the dielectric/ semiconductor interfaces in Hall devices. We believe that our study offers a foundation for a more thorough understanding of the charge transport in strongly coupled all-inorganic NC arrays and the role of inorganic ligands in charge transport.

necessary to neck >31% NCs together to form a continuous current path in a NC solid. Such massive necking should cause dramatic changes in the absorption spectra of NC films, which is obviously not the case (Figure 1b). It is generally accepted that switching from hopping to diffusive transport requires that the bandwidth (Δ) originated from the exchange coupling between the NCs should exceed the Coulomb charging energy (Ec) and inhomogeneous broadening disorder.29 We can put rough estimates on these parameters. The bandwidth and exchange coupling energy can be estimated from the broadening of the 1S−1S transition in the absorption spectra of separated NCs and conductive NC films.14 In solution, the full width at half-maximum (fwhm) of the 1S−1S transition was about 162 meV for both In2Se42− and Cu7S4− capped InAs NCs (Figure S1). Deposition of closepacked films resulted in broadening of the absorption peak by ∼31 meV for In2Se42− and ∼38 meV for Cu7S4− capped InAs NCs, respectively. This broadening could not be caused by sintering or necking of NCs because they did not lose colloidal solubility. According to Johnson et al., as-deposited films of MCC-capped CdSe NCs already showed the coherent delocalization of excitons beyond individual NCs.20 Shortterm annealing at 350 °C results in further broadening of the excitonic transitions that finally approach 45 meV for In2Se42− and ∼67 meV for Cu7S4− capped InAs NCs, respectively. Because of a huge difference in effective mass for electrons and holes in the electronically active Γ-valley of InAs (m*e = 0.023m0 vs mh* = 0.41m0), we expect that the absorption broadening is caused primarily by delocalization of electron states. Taking into account that other factors can also contribute to absorption peak broadening, we consider it an optimistic upper limit for Δe. For a close-packed NC layer, the exchange coupling energy (β) is related to the bandwidth as β = Δ/16 = ∼2.8 meV for In2Se42− capped and ∼4.2 meV for Cu7S4− capped InAs NCs. Then, the lower limit for the effective mass (m*sb) in the first sub-band can be estimated as: * = ℏ2/(2βa2), where ℏ is the reduced Planck constant and a msb is the NC center-to-center distance.21 This relation yields m*sb of ∼0.3m0 for In2Se42− capped InAs NC and ∼0.23 m0 for Cu7S4− capped InAs NC arrays. Our estimate for the bandwidth significantly exceeds the Coulomb charging energy estimated as Ec = e2/(4εmε0d) where εm is the dielectric constant of the surrounding medium and d is the NC diameter. Generally, the dielectric constant of MCCs is much higher than that of organic ligands. We used the Maxwell−Garnett approach to roughly estimate the effective dielectric constant of the NC array (see the Supporting Information for details) and obtained Ec ∼ 17−26 meV for In2Se42− capped InAs NC and 18−26 meV for Cu7S4− capped InAs NCs. Other estimates yield even smaller values for Ec (see the Supporting Information for details). In fact, when the interNC coupling increases, Ec can further decrease due to virtual electron tunneling processes.60 We can evaluate inhomogeneous broadening from the width of the first excitonic peak of the absorption spectra of noninteracting colloidal NCs. According to Efros and Rosen, strong band coupling in InAs and InSb QDs results in similar size dependence for both electron and hole levels, despite a large difference in m* for electrons and holes.61 In that case, the 162 meV fwhm of the absorption peak can reflect ∼80 meV spread in the energies of 1Se states of InAs NCs (disorder). This value is close to our estimated upper limit for Δe, and it seems to be reasonable to expect that MCC-capped InAs NC

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* Supporting Information S

Additional experimental details and figures. 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]. Phone: +1-773-834-2607. Fax: +1-773-832-5863. Notes

The authors declare no competing financial interest. 660

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ACKNOWLEDGMENTS We thank Matthew Panthani and James Kurley for help with LabVIEW programs. The work on synthesis and characterization of MCC-capped NCs was supported by NSF under Award Number DMR-1310398; the work on charge transport in NC solids was supported by DOD ONR Award Number N00014-13-1-0490. D.V.T. also thanks the David and Lucile Packard Foundation and Keck Foundation for their generous support. This work used facilities supported by NSF MRSEC Program under Award Number DMR-0213745. The work at the Center for Nanoscale Materials (ANL) was supported by the US Department of Energy under Contract No. DE-AC0206CH11357.

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