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Charge Transport in Mixed Semiconducting Carbon Nanotube Networks with Tailored Mixing Ratios Maximilian Brohmann,† Felix J. Berger,† Maik Matthiesen,† Stefan P. Schießl,† Severin Schneider,† and Jana Zaumseil*,†,‡ Downloaded via 193.9.158.122 on July 24, 2019 at 11:18:43 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
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Institute for Physical Chemistry, Universität Heidelberg, D-69120 Heidelberg, Germany Centre for Advanced Materials, Universität Heidelberg, D-69120 Heidelberg, Germany
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S Supporting Information *
ABSTRACT: The ability to prepare uniform and dense networks of purely semiconducting single-walled carbon nanotubes (SWNTs) has enabled the design of various (opto-)electronic devices, especially field-effect transistors (FETs) with high carrier mobilities. Further optimization of these SWNT networks is desired to surpass established solution-processable semiconductors. The average diameter and diameter distribution of nanotubes in a dense network were found to influence the overall charge carrier mobility; e.g., networks with a broad range of SWNT diameters show inferior transport properties. Here, we investigate charge transport in FETs with nanotube networks comprising polymer-sorted small diameter (6,5) SWNTs (0.76 nm) and large diameter plasma torch SWNTs (1.17−1.55 nm) in defined mixing ratios. All transistors show balanced ambipolar transport with high on/off current ratios and negligible hysteresis. While the range of bandgaps in these networks creates a highly uneven energy landscape for charge carrier hopping, the extracted hole and electron mobilities vary nonlinearly with the network composition from the lowest mobility (15 cm2 V−1 s−1) for only (6,5) SWNT to the highest mobility (30 cm2 V−1 s−1) for only plasma torch SWNTs. A comparison to numerically simulated network mobilities shows that a superposition of thermally activated hopping across SWNT−SWNT junctions and diameter-dependent intratube transport is required to reproduce the experimental data. These results also emphasize the need for monochiral large diameter nanotubes for maximum carrier mobilities in random networks. KEYWORDS: single-walled carbon nanotubes, network, polymer-wrapping, field-effect transistors, charge transport, random resistor network model
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limitations arises. Due to variations of network density, average SWNT length, and extrinsic effects such as contact resistance, dipolar disorder of the dielectric, interfacial trapping, or different wrapping polymers in various studies, it remains unclear if and how the overall device performance of SWNT FETs is intrinsically determined by the nanotube network composition, which would have implications for further purification efforts. The junction resistances between intersecting semiconducting nanotubes were found to be orders of magnitude higher than the resistances along individual SWNTs as shown by conductive atomic force microscopy measurements19,20 and, hence, junctions are often considered to be the bottleneck for charge transport in nanotube networks. However, there is
andom networks consisting of semiconducting singlewalled carbon nanotubes (SWNTs) have become a competitive material for solution-processed thin-film electronics. The well-established polymer-wrapping technique enables the efficient separation of semiconducting from metallic nanotubes with both high selectivity (>99.9%) and yield.1−6 It facilitates the application of purely semiconducting and even monochiral SWNT networks as active layers in highperformance field-effect transistors7−11 (FETs) and circuits.12−17 So far, various semiconducting nanotube samples with different diameters and, thus, bandgaps and with different diameter distributions (from monochiral to very broad) were used in network transistors, their composition being mainly determined by the available carbon nanotube raw material and the conjugated wrapping polymer. While the achieved effective charge carrier mobilities were generally high (e.g., up to 50 cm2 V−1 s−1)18 and the overall performance parameters very good, the question of further optimization and possible intrinsic © 2019 American Chemical Society
Received: May 13, 2019 Accepted: June 6, 2019 Published: June 7, 2019 7323
DOI: 10.1021/acsnano.9b03699 ACS Nano 2019, 13, 7323−7332
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Cite This: ACS Nano 2019, 13, 7323−7332
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ACS Nano evidence that thermally activated hopping between adjacent nanotubes is not the only determining factor for the overall carrier mobility in a network.21,22 Large diameter SWNTs exhibit substantially higher charge carrier mobilities than small diameter nanotubes, not only in single SWNT devices23,24 but importantly also in networks. In FETs with networks of semiconducting SWNTs with a range of diameters the source− drain current seems to predominantly pass through the nanotubes with the largest diameter and thus the smallest bandgap. Due to the energy difference between the conduction bands of the various nanotube species, this current distribution also depends on the charge carrier density (i.e., applied gate voltage) as shown by spectrally resolved electroluminescence measurements and simulations based on a random resistor network model.22,25 As a result, parts of the semiconducting network may remain inactive (large bandgap nanotubes), while others may act as trap sites (small bandgap nanotubes). Overall, the distribution of bandgaps is expected to create an uneven energy landscape for charge transport, which in the worst case may limit the overall transistor performance.26 Previous studies relied on directly available polymer-sorted dispersions with fixed ratios of semiconducting nanotubes with different diameters.22 However, now that highly pure SWNT dispersions with defined nanotube species are available, it is possible to create networks with controlled mixing ratios of large and small bandgap nanotubes and reveal their impact on charge transport in FETs under identical and optimized conditions. Such tailored networks of different semiconducting nanotubes could also act as a model system for a wider range of spatially and energetically disordered semiconductors, e.g., colloidal quantum dot solids27,28 or amorphous organic semiconductors.29−31 The special advantage of nanotube networks relies on the perfect miscibility of different SWNT species without any phase segregation or changes in film morphology that complicates data analysis in other systems. Here, we use small- and large-diameter, polymer-sorted SWNTs extracted from two different nanotube raw materials but with the same wrapping polymer and blend them in different ratios to create dense nanotube networks of controlled composition by spin-coating. Top-gate field-effect transistors based on these networks show ambipolar transport, high on/off current ratios, negligible hysteresis, and high carrier mobilities for all mixing ratios. We systematically investigate the impact of the SWNT network composition on hole and electron transport and compare the results to a model that simulates the charge transport in mixed SWNT networks based on nanotube−nanotube junctions only. In combination with temperature-dependent transport measurements, we find that both thermally activated charge hopping between SWNTs, which is limited by energetic disorder, and the diameterdependent band transport within individual nanotubes determine the overall transport properties and effective carrier mobilities in network FETs.
Figure 1. Molecular structure of the wrapping polymer PFO-BPy and UV−vis−nIR absorbance spectra of the mixed (6,5)/plasma torch SWNT dispersions in toluene (mixing ratios in 10% steps from 100% to 0% and vice versa, only every other mixing ratio shown here). Circles next to color gradient illustrate mean nanotube radii for plasma torch and (6,5) SWNTs.
monochiral dispersion of (6,5) SWNTs with a relatively large bandgap of 1.27 eV and small diameter of 0.76 nm, a range of narrow bandgap SWNTs (0.70−0.88 eV) with diameters between 1.17 and 1.55 nm was achieved for the plasma torch nanotubes.2,21 The same solvent and polymer were used for both dispersions, but the CoMoCAT nanotubes were dispersed by shear-force-mixing and the plasma torch SWNT dispersion was prepared by bath sonication to avoid crosscontamination (see Methods for further details). The average length of the dispersed SWNTs depends on the source material and exfoliation method employed for the polymer wrapping process,2 thus the average nanotube lengths of both stock dispersions were analyzed (see the Supporting Information, Figure S1). The purified plasma torch SWNTs were slightly shorter (0.8 ± 0.3 μm) than the (6,5) SWNTs (1.2 ± 0.4 μm). Mixed (6,5) SWNT/plasma torch SWNT dispersions with a controlled composition were realized by volumetric mixing of the two stock dispersions in 10% steps from 100% (6,5) SWNTs to 100% plasma torch SWNTs. To ensure a representative mixing ratio and a comparable total SWNT concentration in both stock dispersions, the integrated and baseline corrected absorbances of the E22 transitions of (6,5) and plasma torch SWNTs were equalized before mixing. Figure 1 shows the absorption spectra of pure (6,5) and plasma torch SWNTs, the mixed dispersions as well as an illustration of the different SWNT radii. In addition to the expected E11 and E22 transitions of the (6,5) and plasma torch SWNTs, the spectra exhibit a rather small and almost unchanging absorption peak of the wrapping polymer PFO-BPy for all mixing ratios, implying a negligible and constant amount of polymer (wrapped and/or free) in the dispersions. For the deposition of SWNTs from all pure and mixed nanotube dispersions to form networks of corresponding composition and comparable network density, all SWNT dispersions were spin-coated onto glass substrates with photolithographically structured bottom electrodes under the same conditions. A homogeneous and high network density (≥40 SWNT/μm) without the presence of a considerable
RESULTS AND DISCUSSION To prepare mixed but purely semiconducting SWNT networks with tailored mixing ratios and thus network compositions, selective nanotube dispersion in toluene by polymer-wrapping was applied using the copolymer poly[(9,9-di-n-octylfluorene2,7-diyl)-alt-(2,2′-bipyridine-6,6′-diyl)] (PFO-BPy, see Figure 1 for molecular structure) together with CoMoCAT and plasma torch SWNT raw material, respectively.32,33 While the combination with CoMoCAT SWNTs yielded a quasi 7324
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Figure 2. (a) Atomic force micrographs of three representative SWNT films with different network compositions. (b) Modeled 2D-stick networks (linear network density 7 μm−1) illustrating the respective (6,5) SWNTs (purple) versus plasma torch SWNTs (orange) ratio.
All nanotube networks were integrated in bottom-contact/ top-gate field-effect transistors (FETs) with a gated four-point probe (gFPP) layout (see device geometry in Figure 3a). This device structure enables direct measurement of the contact resistance, extraction of the contact resistance-corrected linear carrier mobility, and their gate voltage dependence.21 The hybrid dielectric consisted of a 61 nm layer of high-k HfOx on top of 11 nm PMMA. This bilayer combines the advantages of
amount of nanotube bundles throughout all mixing ratios was revealed by atomic force microscopy images of the networks. Figure 2a shows three representative networks. The network densities of the two pure networks and the mixed network closely resemble each other, which confirms the nearly equal SWNT concentrations of the (6,5) and plasma torch SWNT stock dispersions. Dense SWNT networks are important for meaningful comparative transport studies as they reduce current hysteresis in bottom-contact/top-gate transistor geometries8 and minimize the impact of minor density variations. Given the difference in average nanotube length of plasma torch vs (6,5) SWNTs, the high network density also enables a reliable analysis of the carrier mobility. In contrast to that, nanotube length variations in sparse SWNT networks are likely to affect the number of nanotube−nanotube junctions and thus the effective mobility.21,34 To ensure that the nanotube composition within the different networks matches the initial SWNT distribution in the dispersions, all pure and mixed networks were characterized by Raman spectroscopy. More than 1600 Raman spectra were averaged over a large area for each SWNT network with two different excitation wavelengths (see Methods for further details). The G+-mode shifts characteristically to higher wavenumbers for larger nanotube diameters,35−38 and we observed the same for increasing plasma torch to (6,5) SWNT mixing ratio in the respective networks (Supporting Information, Figure S2). In addition, the relative radial breathing mode (RBM) peak area of the (6,5) and the plasma torch SWNTs (Supporting Information, Figures S3 and S4) changed gradually with the assumed volumetric mixing ratio. These measurements confirmed a representative SWNT composition that matched the initial SWNT species distributions of the corresponding dispersions. Nearly constant Raman signals over areas of 100 × 100 μm2 further indicated homogeneous SWNT networks for all samples. We can thus assume that the actual network compositions resembled the volumetric mixing ratios for the (6,5) and plasma torch SWNT stock dispersions. These network compositions were later simulated as 2D-stick networksalthough with a lower density to keep the computation cost manageableand are illustrated schematically with different colors in Figure 2b.
Figure 3. (a) Schematic device structure of a nanotube network FET with Cr/Au bottom contacts (S, source; D, drain) in a fourpoint probe layout with voltage probes (VP1, VP2), spin-coated SWNT network, PMMA/HfOx hybrid dielectric and silver top gate electrode (G). Layers are laterally shifted for better visibility. (b) Transfer characteristics (forward and reverse gate voltage sweeps at VDS = −0.1 V; ID, drain current; IG, gate leakage) of a pure (6,5) SWNT network, a pure plasma torch SWNT network, and a mixed network (plasma torch/(6,5) SWNT ratio 1:1). 7325
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Figure 4. (a) SWNT network composition-dependent onset voltages (forward sweep only), (b) hysteresis (quantified as onset voltage difference between forward and reverse sweep), and (c) width-normalized contact resistances (RC, extracted at maximum gate voltage) for electron and hole transport (VDS = −0.1 V). Error bars represent standard deviations.
both dielectric materials in SWNT network FETs, i.e., lowvoltage and air-stable operation with reduced dipolar disorder, current hysteresis and low gate leakage.39 Transfer characteristics of all pure and mixed SWNT network transistors at small source-drain bias (VDS = −0.1 V) showed ambipolar transport with low hysteresis and high on/off current ratio of 106 for all network compositions as shown in Figure 3b (for clarity, the current−voltage curves for only three networks are shown; a complete plot can be found in the Supporting Information, Figure S5). The near-ideal ambipolar device characteristics indicate the absence of significant external transport limitations (e.g., trap states) that may complicate the analysis. The maximum on-currents for both charge carriers varied significantly with the nanotube network composition. The drain currents increased monotonously with increasing contents of the large diameter plasma torch SWNTs, culminating in four times higher on-currents for the pure plasma torch SWNTs compared to the monochiral small diameter (6,5) nanotube network. Given the larger average nanotube length of the (6,5) SWNTs compared to the plasma torch nanotubes and considering the similar nanotube network densities for all mixing ratios, the opposite trend might be expected. However, the intratube charge carrier mobility of SWNTs scales with the square of the diameter and even in networks a consistently higher mobility for large diameter nanotubes is found,21,23,24 which is in agreement with the current data. Furthermore, for all SWNT networks the hole currents were about twice as high as the electron currents. An explanation for this slight imbalance might be the UV/ozone treatment of the gold electrodes prior to SWNT deposition, leading to larger charge carrier injection barriers for electrons. Although the output characteristics imply nearly ohmic contacts for electrons and holes for all nanotube network compositions (see the Supporting Information, Figure S6), this may also be attributed to the relatively long channel length (L = 40 μm) of all devices, resulting in low contact resistance compared to the channel resistance. The output curves further corroborate the much higher on-currents in FETs with large diameter plasma torch nanotubes compared to (6,5) SWNTs reaching one order of magnitude higher values in the saturation regime. The onset voltages (defined as the lowest gate voltage for which the drain current significantly exceeds the gate leakage) for both electron and hole transport (forward sweeps, respectively) shifted characteristically with the nanotube network composition as shown in Figure 4a. As suggested recently, in the absence of dopants the onset voltages depend on the mean SWNT bandgap of a nanotube network, causing
higher onset voltages and larger gaps between hole and electron onset for larger bandgap and thus smaller diameter SWNTs as in case of (6,5) nanotubes.21 Interestingly, these onset voltages dropped significantly for a plasma torch nanotube content of only 10% and approached the pure plasma torch SWNT onset values at 30%. Facilitated by the overall high network density, this indicates the presence of percolation pathways through the transistor channel consisting of mainly plasma torch SWNTs, switching on at lower gate voltages than the (6,5) SWNT network. A similar effect was observed via electroluminescence from network FETs, in which a large part of the current appeared to be conducted by a small amount of narrow bandgap nanotubes within a network of larger bandgap SWNTs.22 A slight current hysteresis (here defined as onset voltage difference between forward and reverse sweep) with a characteristic network composition dependence is observable for both electrons and holes in Figure 4b. While there is effectively no hysteresis for a pure (6,5) SWNT network, it increases significantly with a growing share of plasma torch nanotubes starting already at low amounts of 10% until a maximum is reached for networks with a (6,5):plasma torch SWNT ratio of 1:1. As soon as the plasma torch nanotubes represent the majority of the network, the hysteresis decreases again with decreasing (6,5) nanotube content until it approaches 0 V for the pure plasma torch network. This hysteresis behavior may imply charge trapping within the mixed SWNT networks presumably caused by the large energy level offset (∼220 meV) between (6,5) and plasma torch SWNT band edges compared to kT at room temperature (25 meV, k − Boltzmann constant and T − temperature). Within all mixed networks, individually distributed large diameter and thus narrow bandgap plasma torch nanotubes could act as trapping sites when located within a percolation path mainly consisting of (6,5) SWNTs. This scenario is most likely for networks with parity mixing of plasma torch and (6,5) nanotubes. Considering the slightly imbalanced electron and hole currents for all network compositions and the known charge injection differences between plasma torch and (6,5) SWNTs, a thorough contact resistance (RC) analysis is required for a meaningful transport study.21 Figure 4c shows the widthnormalized contact resistances for all network compositions, revealing again a pronounced network composition dependence. The RC values monotonously increase with decreasing plasma torch SWNT content reaching about one order of magnitude higher contact resistances for pure (6,5) SWNTs than for pure plasma torch SWNTs, which is in good 7326
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ACS Nano agreement with previous studies.18,21 The lowest contact resistance values for the pure (6,5) SWNT network were 210 Ω·cm for holes and 820 Ω·cm for electrons whereas the pure plasma torch nanotube network FETs exhibited minimum contact resistances of 20 Ω·cm for holes and 100 Ω·cm for electrons (see the Supporting Information, Figure S7, for VGdependent contact resistances). For all mixing ratios, the contact resistances for electron injection were about four times higher than for hole injection which explains the overall higher hole currents in the transfer and output characteristics. Given the significant contact resistance differences between the (6,5) and plasma torch nanotubes, a correction of the apparent linear carrier mobilities (μeff) is necessary for a meaningful, undistorted analysis of the network compositiondependent charge transport.21 A comparison of μeff and the contact resistance corrected carrier mobilities (μRC) resulted in up to 80% higher values for the corrected mobilities as shown in the Supporting Information, Figure S8. Thus, all charge carrier mobilities presented here are contact resistancecorrected. Within the gate voltage range of ±10 V, the field-effect mobilities of electrons and holes reach their first maximum for both pure (6,5) SWNT, plasma torch SWNT, and mixed nanotube networks as shown by the gate voltage-dependent carrier mobilities in the Supporting Information, Figure S8. This characteristic behavior is commonly observed for both individual semiconducting SWNTs and in nanotube networks. It can be explained by filling of the first one-dimensional SWNT sub-band and interband phonon scattering, which leads to a lower carrier mobility at higher gate voltages.23,24,40 Figure 5a shows the extracted linear peak mobilities for all pure and
soon as the plasma torch nanotubes dominate the network composition. For a better understanding of this behavior, we simulated the charge transport in mixed SWNT networks based on random resistor networks of nanotube−nanotube junctions as introduced by Schießl et al.21,25 These networks were formed by the random distribution of one-dimensional sticks within a twodimensional box. Each stick represents an individual SWNT of defined length and with a certain energy level. By including the first conduction sub-band of the selected SWNT species corresponding to the experimental nanotube films, various network compositions (illustrated by different colors in Figure 2b) were created (see the Supporting Information, Table S1 for input parameters). Based on a conventional approach for disordered systems, the conductance of each junction resistor is solved to extract the charge carrier mobility for a given network composition and carrier concentration. Although the model neglects any intratube contribution to the overall network charge transport by treating the individual SWNTs as zero-resistance segments, it was recently shown to describe charge transport in both monochiral and mixed SWNT networks in good agreement with experimental data.22,34 Here, we assumed an overall Gaussian energetic disorder of 45 meV to take the dipolar disorder at the interface between the nanotube network and the dielectric into account and simulated the charge carrier density dependent network mobilities for all network compositions (see the Supporting Information, Figure S9, for normalized network mobilities of three different SWNT networks). The extracted mobilities for all simulated nanotube networks (each averaged over five equivalent networks) reach a maximum value for carrier densities between 2 × 1011 and 1 × 1012 cm−2, which is in good agreement with the gate voltagedependent experimental mobilities, and again can be ascribed to the filling of the first conduction sub-band (van Hove singularity). The peak mobility of the simulated networks (normalized to the maximum mobility of the monochiral (6,5) SWNT network) drops with increasing plasma torch nanotube content until it reaches a minimum for equal amounts of large and small diameter SWNTs (see Figure 5b). For plasma torch SWNT concentrations above 50%, the peak mobility increases again up to the value of the pure plasma torch nanotube network. The observed asymmetric shape of the compositiondependent mobility dip is in agreement with the changes of conductivity in disordered organic semiconductor host−guest systems. In these systems (experimental and in simulations), small bandgap guest species act as charge traps within a matrix of large bandgap host molecules. This leads to a decrease in mobility with increasing guest molecule concentration until their concentration is high enough so that they form their own charge transport pathways; i.e., they become the host system.29−31 At first glance, the simulated network mobilities and their network composition dependence in Figure 5b do not correlate well with the trends for the experimental SWNT network in Figure 5a. The simulated mobility of the pure plasma torch SWNT network is lower than that of the pure (6,5) nanotube network in stark contrast to the experiment. The underlying Miller−Abrahams hopping mechanism in the model results in less efficient charge transport between adjacent SWNTs with different band edge energies.21 Consequently, the narrow but existent energy level distribution within the different plasma torch nanotubes of about 80 meV
Figure 5. (a) Network composition-dependent contact resistancecorrected peak mobilities for electrons and holes. Error bars represent standard deviations. (b) Normalized compositiondependent carrier mobilities for simulated SWNT networks with compositions equal to the experimental networks without any intratube transport contribution (black) and composition-dependent and weighted (weighting factor for plasma torch vs (6,5) SWNT = 50:15 cm2 V−1 s−1) carrier mobility (red). Error bars indicate standard deviation for five simulated networks. Solid lines are guides to the eye.
mixed networks. Owing to the contact resistance correction, the hole and electron mobilities are now quite balanced and increase with growing plasma torch SWNT content. However, this mobility increase does not follow a linear “rule of mixtures” dependence. Instead, the mobilities remain rather constant for networks composed of more than 50% of (6,5) SWNTs and exhibit a pronounced, monotonous increase as 7327
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Figure 6. (a) Schematic illustration of intra- and intertube electron transport in SWNT networks with different compositions. Arrow widths scale with carrier mobility within the nanotubes depending on SWNT diameter. (b) Energetic differences between the first van Hove singularities (first conduction sub-bands) affect the charge transport across the illustrated SWNT−SWNT junctions.
Figure 7. (a) Temperature-dependent transfer characteristics (forward and reverse gate voltage sweeps at VDS = −0.1 V) at temperatures from 60 to 300 K (measured in steps of 20 K, only every other transfer curve shown here) for three selected SWNT network compositions. (b) Normalized temperature-dependent carrier mobilities extracted at ±5 V gate overdrive for hole and electron transport.
diameter of both pure networks (plasma torch SWNTs: 1.36 nm and (6,5) SWNTs: 0.76 nm) and their experimental network mobility values. This weighting factor gives the modified mobilities (red squares) shown in Figure 5b. These weighted mobilities result in a much better qualitative fit to the composition dependent changes of the experimental mobility data. Nevertheless, a mismatch between experiment and model remains for networks from 100% to 50% (6,5) SWNTs. The employed random resistor model is based on several assumptions, e.g., a constant hopping prefactor for all SWNT species, which is not very realistic, and the inclusion of only the first conduction sub-band.25 These simplifications were necessary but inevitably lead to quantitative mobility
(including 45 meV extrinsic disorder) results in lower simulated peak mobilities compared to the monochiral (6,5) SWNTs. The random resistor model also excludes all contributions of the carrier mobility within each individual semiconducting nanotube, which scales with the square of the SWNT diameter.23,24 In contrast to that, a simple “rule of mixture” dependence, that is, a linear increase from the lower effective carrier mobility of a pure (6,5) SWNT network (∼15 cm2 V−1 s−1) to that of a pure plasma torch network (∼30 cm2 V−1 s−1), would neglect the contribution of charges hopping through a highly uneven energetic landscape. Consequently, we aim to combine the two extremes and introduce a mobility weighting factor of 50:15 cm2 V−1 s−1 for plasma torch versus (6,5) SWNTs based on the square of the mean nanotube 7328
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all SWNT compositions, while not following the trends for variable range hopping (VRH). In contrast to previous studies on temperature-dependent charge transport in polymer-sorted SWNT networks, we do not report activation energies based on the conventional VRH or the fluctuation induced tunneling (FIT) model.21,41−44 The VRH model does not deliver a suitable fit especially for low temperatures where the decreasing carrier mobilities level off, while the FIT model lacks a profound physical relation to the characteristic properties of semiconducting SWNT networks. In addition, both models would reduce the temperaturedependent charge carrier mobilities across the nanotube network to only the SWNT−SWNT junctions, while charge transport along the individual nanotubes exhibits an opposite temperature dependence (mobility proportional to 1/T).23,24 Thus, we qualitatively compare the temperature-dependent carrier mobilities of the selected SWNT networks by normalization to their respective maximum value at 300 K as shown in Figure 7b. The relative decrease of the hole mobilities upon cooling exhibits a significant network composition dependence, namely a much more pronounced temperature dependence for the small diameter (6,5) SWNT network than for the mixed and the pure plasma torch nanotube network. For electron transport, this difference in temperature dependence is considerably smaller, possibly caused by residual contact resistance effects or electron trap states, although the qualitative trends persist. Given the abovementioned quadratic diameter dependence of the intrananotube carrier mobilities together with their reciprocal temperature dependence, the significantly smaller mobility drop of the larger diameter plasma torch SWNTs compared to the small diameter (6,5) SWNTs with decreasing temperature is reasonable. It further highlights the obvious impact of the intrananotube charge transport on the overall network properties of polymer-sorted SWNT films, which makes them a complex and intriguing semiconducting material.
deviations. Indeed, the weighted mobility curve approaches the experimental data when the mobility weight of the (6,5) SWNTs is further decreased (see the Supporting Information, Figure S10). The overall similarity between the weighted mobilities and the experimental mobility values suggests that the charge carrier mobility in mixed SWNT networks should be described as a superposition of inter- and intratube transport processes and is not only limited by the junctions. This interplay of intra- and internanotube transport is illustrated in Figure 6a and can explain the almost constant experimental carrier mobilities for mixing ratios with ≤50% plasma torch SWNTs shown in Figure 5a. In this composition range, an increasing plasma torch nanotube content leads to additional energy barriers at the SWNT−SWNT junctions, whereas the share of SWNTs with large diameters and thus higher intratube carrier mobility increases. Figure 6b shows the energy differences between the first conduction sub-bands of adjacent nanotubes for different SWNT network compositions excluding extrinsic disorder. For plasma torch SWNTs contents of more than 50%, the effective energetic disorder is reduced again as large diameter nanotubes form percolation paths, leading to a monotonous increase of the experimental network mobilities with increasing plasma torch SWNT concentration. Finally, to further examine the impact of inter- and intratube contributions to the overall SWNT network carrier mobilities, we performed temperature-dependent transport measurements of selected SWNT network transistors. Figure 7a shows transfer characteristics at temperatures from 60 to 300 K for pure (6,5) SWNT, pure plasma torch SWNT, and 50%/50% mixed nanotube network transistors. The ambipolar transport behavior with high on/off current ratio and low hysteresis is retained over the whole temperature range for all three network compositions. All devices show the characteristic monotonous decrease in on-current and increase in onset voltage with decreasing temperature, indicating overall thermally activated transport as shown before albeit to a different extent.21,41,42 The monochiral (6,5) SWNT network exhibits a much more pronounced drop in on-current and steeper increase in onset voltage (shown in the Supporting Information, Figure S11) upon cooling, whereas the mixed and the pure plasma torch network exhibit a much smaller dependence on temperature. A similar trend is observed for the temperature dependence of the width-normalized contact resistances (see the Supporting Information, Figure S12), namely a larger rise in resistance for the pure (6,5) SWNT network. The similarity between the current−voltage characteristics of the mixed and the pure plasma torch SWNT networks over the full temperature range further implies that a large number of percolation pathways with only plasma torch nanotubes exist in the mixed network with 50% (6,5) SWNTs. As pointed out above, the differences between the three networks with respect to their onset voltage and its shift with temperature, require a mobility extraction at a comparable charge carrier concentration.21 Thus, we extracted the contact resistance corrected linear carrier mobilities at ±5 V gate overdrive, i.e., the difference between the gate voltage and the onset voltage for a given network and temperature, which roughly corresponds to a carrier concentration of 3 × 1012 cm−2. The temperature-dependent electron and hole mobilities of the selected SWNT networks are shown in the Supporting Information, Figure S13. They emphasize the thermally activated nature of the overall network charge transport for
CONCLUSION We have revealed the unexpectedly large impact of the network composition on hole and electron transport in networks containing large- and small-diameter nanotubes with tailored mixing ratios. The initially almost constant and then linearly increasing carrier mobilities with growing share of large diameter nanotubes cannot be explained by only considering SWNT−SWNT junctions and energetic disorder. As also supported by temperature-dependent measurements, the contribution of charge transport along each individual SWNT within the network and its dependence on the nanotube diameter is substantial. While the junctions are important, they only partially determine the overall charge carrier mobilities in pure and mixed SWNT networks. Their characteristic dependence on composition should be interpreted as a superposition of thermally activated intertube hopping transport within a disordered energy landscape and the diameter-dependent intratube band transport with an inverse temperature dependence. Given the much higher intratube carrier mobility of large diameter SWNTs and the observed detrimental impact of energetic disorder due to different bandgaps, networks of a single nanotube species with a large diameter (>1.2 nm) would be the optimum for high mobility network transistors. An upper limit of the ideal diameter is given by on/off current ratio requirements that are partially dictated by the bandgap.45 However, while there are a 7329
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objective (Leica, N.A. 0.75). Maps consisting of approximately 1600 spectra over an area of 100 × 100 μm2 were collected in StreamLine mode with two different lasers (532 and 785 nm). For each sample, the spectra were averaged and baseline corrected. Atomic force microscopy images were recorded in ScanAsyst mode using a Dimension Icon (Bruker Corp.) atomic force microscope. Current− voltage characteristics of all transistors were recorded in dry nitrogen atmosphere using a semiconductor parameter analyzer (4155C, Agilent Technologies Inc.). Gate dielectric capacitances were measured with an LCR meter (E4980A, Agilent Technologies Inc.) directly on each transistor. The maximum effective areal capacitance was extracted at a frequency of 1 kHz while the transistor was in the on-state. Temperature-dependent transport measurements were performed under vacuum (≤10−6 mbar) in a cryogenic probe station with a closed cooling-cycle (CRX-6.5K, Lake Shore Cryotronics, Inc.) starting always from base temperature (10 K). Before each measurement, thermal equilibration was ensured by a 20 min hold time after each temperature step (20 K).
number of options to purify monochiral dispersions of various small diameter nanotubes (
