Understanding Charge Transport in Mixed Networks of Semiconducting Carbon Nanotubes.

The ability to select and enrich semiconducting single-walled carbon nanotubes (SWNT) with high purity has led to a fast rise of solution-processed nanotube network field-effect transistors (FETs) with high carrier mobilities and on/off current ratios. However, it remains an open question whether it is best to use a network of only one nanotube species (monochiral) or whether a mix of purely semiconducting nanotubes but with different bandgaps is sufficient for high performance FETs. For a range of different polymer-sorted semiconducting SWNT networks, we demonstrate that a very small amount of narrow bandgap nanotubes within a dense network of large bandgap nanotubes can dominate the transport and thus severely limit on-currents and effective carrier mobility. Using gate-voltage-dependent electroluminescence, we spatially and spectrally reveal preferential charge transport that does not depend on nominal network density but on the energy level distribution within the network and carrier density. On the basis of these results, we outline rational guidelines for the use of mixed SWNT networks to obtain high performance FETs while reducing the cost for purification.

Introduction

With the tremendous progress of separation techniques of semiconducting from metallic single-walled carbon nanotubes (SWNTs), one of the major obstacles for the application of SWNT dispersions as inks for printed, flexible, and stretchable electronics has been overcome. By using polymer-wrapping,[1−3] gel-chromatography,[4−6] or density gradient ultracentrifugation,[7] it is nowadays possible to produce dispersions of semiconducting SWNTs with purities of more than 99.5%[8,9] and to reproducibly fabricate field-effect transistors (FETs) based on dense random or aligned networks. These FETs show effective carrier mobilities of tens to hundreds of cm2 V–1 s–1,[3,10,11] or on-conductivities of more than 200 μS/μm in submicrometer channel length devices[12,13] while maintaining on/off current ratios of 106. This progress has already led to the demonstration of highly integrated nanotube network circuits based on solution-processed SWNTs, such as backplanes for tactile sensors or X-ray imager arrays,[14,15] ring-oscillators,[16−18] SRAM,[19] etc.

While in the past the experimental investigation and theoretical modeling of transport in random networks of SWNTs focused on the impact of the number of metallic nanotubes and their percolation threshold on device performance,[20−22] their absence enables new questions. How does the polydispersity of the semiconducting nanotubes and thus their different energy levels and bandgaps affect charge injection and transport in random or semialigned networks? Is it necessary or advantageous to aim for single-chirality networks for maximum performance? Which chiralities offer the best mobility versus on/off current ratio values? Answering these questions requires control over the exact composition and density of semiconducting SWNT networks. Further, analytical tools are necessary that allow us to directly investigate charge transport beyond simple current–voltage measurements and give insight into current pathways within a network and the distribution of charge carriers among the various nanotubes. Here, we employ near-infrared electroluminescence of semiconducting SWNTs that originates from electron–hole recombination in ambipolar field-effect transistors based on such networks as a highly sensitive and quantitative measure for charge accumulation and current paths. We show that charge transport predominantly takes place through the nanotubes with the smallest bandgaps even if they constitute just a small minority within the network. The nanotubes with the largest bandgaps only start to participate in the transport at higher gate voltages. By tailoring the composition of the SWNT networks, we demonstrate that a small fraction of small-bandgap SWNTs can dominate charge transport over a wide gate voltage range while larger bandgap nanotubes barely contribute to the current. This behavior has severe impact on the overall device characteristics and must be considered for future SWNT network transistors.

Experimental Section

Preparation of SWNT Dispersions

CoMoCat single-walled carbon nanotubes (Aldrich, diameter 0.7–0.9 nm), HipCO single-walled carbon nanotubes (Unidym Inc., batch P2172, diameter 0.8–1.2 nm, <11 wt % iron), poly(9,9-dioctylfluorene) (PFO, Aldrich, Mw > 20 kg·mol–1), and poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT, American Dye Source, Mw = 164 kg·mol–1, PD = 3.4) were used as purchased. All dispersions were prepared as described previously.[23,24] Briefly, 2 mg/mL polymer was dissolved in toluene at 80 °C for 15 min. After cooling to room temperature, 1.5 mg/mL SWNTs were added and dispersed by bath sonication for 90 min. After centrifugation at 60 000g for 45 min, the supernatant was collected and underwent an additional centrifugation step at 268 000g for 60 min to remove bundled SWNTs. The dispersed SWNTs were pelletized via ultracentrifugation at 268 000g for 20 h and washed with toluene three times. After solvent removal, the pellet was stored until redispersion in toluene by ultrasonication for immediate use.

FET Fabrication

Interdigitated bottom electrodes (channel width W = 20 mm, channel length L = 20 μm) were patterned on AF32eco Thin Glass (SCHOTT AG) using standard photolithography in combination with electron-beam evaporation of 2 nm of chromium and 30 nm of gold. The redispersed SWNT pellet was immediately used for deposition by DC-electrophoresis: 10 μL of SWNT dispersion was drop-cast onto a heated substrate (100 °C) while a bias of 80 V was applied to the source-drain electrodes. This step was repeated twice with opposite voltage polarity. Substrates were subsequently washed with THF to remove residual polymer. Alignment of the SWNTs was confirmed by field-emission scanning electron microscopy (Carl Zeiss Auriga, 1 kV). Atomic force microscopy (tapping mode, Bruker Dimension Icon) was used to determine the average SWNT density for all networks: 9–10 μm–1 for HipCO/PFO, 8–9 μm–1 for CoMoCat/PFO, and 3–6 μm–1 for tailored (7,5)/(10,5) network. Residual solvent and moisture were removed by baking in dry nitrogen at 300 °C for 30 min. Spin coating of 6 mg/mL PMMA (Polymer Source, syndiotactic, Mw = 350 kg mol–1) in n-butyl acetate at 6000 rpm for 60 s resulted in a smooth 10 nm layer on which 61 nm of hafnium oxide was grown by atomic layer deposition (ALD) using tetrakis(dimethylamino)hafnium precursor (Strem Chemicals Inc.) and water at 100 °C. Thermal evaporation of a 30 nm silver top gate electrode using shadow masks completed the device.

Characterization

All measurements were carried out at room-temperature and in air. Current–voltage characteristics were measured with an Agilent 4155C semiconductor parameter analyzer or a Keithley 2612A source-meter. Absorbance spectra of dispersions were recorded with a Cary 6000i spectrometer (Varian Inc.). PLE maps of the dispersions were obtained with a Fluorolog 3 with iHR320 spectrometer (Horiba Jobin-Yvon GmbH). For the PLE maps of the SWNT networks within the final device, the spectrally separated output of a WhiteLase SC400 supercontinuum laser source (Fianium Ltd.) was used for excitation and a Cornerstone 260 monochromator with a InGaAs/InP single-photon avalanche diode (Micro Photon Devices) for spectrally resolved emission detection. Photo- and electroluminescence images were recorded with a Xenics XEVA-CL-TE3 InGaAs camera. PL and EL spectra were obtained with an Acton SpectraPro SP2358 (grating 150 lines/mm) spectrometer with an OMA-V InGaAs line camera (Princeton Instruments) and corrected for background and wavelength-dependent sensitivity.

Results and Discussion

We investigated three different types of semiconducting SWNT networks that can be obtained by selective dispersion of nanotubes with conjugated polymers as shown in Figure . A very common SWNT mix of five different semiconducting species can be extracted by dispersion of HipCO nanotubes with poly(9,9-dioctylfluorene) (PFO) as originally shown by Nish et al.[1] After removal of excess polymer, the dispersion contains mostly (8,7), (8,6), and (7,6) nanotubes but also small amounts of (9,7) nanotubes (7%) with the smallest bandgap and about 19% of (7,5) nanotubes with the largest bandgap as indicated in the absorption spectrum (Figure a) and the corresponding photoluminescence excitation–emission (PLE) map (Supporting Information Figure S1a) of the dispersion. After deposition of these nanotubes by DC-electrophoresis between source-drain electrodes on a glass substrate and removal of most of the residual polymer by washing with THF, a very uniform and semialigned thin film is formed (see Figures a and 2b). The PLE maps of such dense films (Figure d) already show strong energy transfer from the large bandgap nanotubes to the small bandgap nanotubes as indicated by the cross peaks that are not or barely visible in the PLE maps of the dispersion. This energy transfer was shown to be extremely fast (1–3 ps) by Mehlenbacher et al.[25,26] Because the origin of an exciton (by optical excitation or electron–hole recombination) should not affect its subsequent energy transfer and decay we can assume that any steady-state photo- or electroluminescence spectrum already includes exciton transfer as well as chirality-dependent photoluminescence efficiencies.[27] Hence, in the following we will always directly compare photoluminescence and electroluminescence images and spectra from the same network and sample area to take exciton transfer within the network and different emission efficiencies into account.

Figure 1

(a–c) Absorbance spectra of polymer-sorted and enriched semiconducting SWNT dispersions in toluene with different distributions and nanotube species. (d–f) Photoluminescence excitation–emission maps of SWNT thin films deposited from these dispersions within an FET structure. Energy transfer is visible as cross peaks between different nanotube species.

Figure 2

(a) Scanning electron micrograph of semialigned SWNT network. (b) Tapping-mode atomic force microscopy image of semialigned SWNT network. (c) Schematic structure of SWNT-FET on glass substrate with gold source-drain electrodes, dense SWNT network, hybrid dielectric (PMMA/HfO2), and silver top gate. (d) Typical ambipolar transfer characteristics at low source-drain bias for all mixed SWNT networks. (e) Schematic illustration of hole and electron injection and transport in the ambipolar regime leading to recombination and light emission. (f–h) Three examples of normalized photoluminescence (PL) images of channel area and corresponding normalized composite electroluminescence (EL) images for a gate voltage sweep at constant current (0.5 mA (f), 0.1 mA (g), and 0.5 mA (h)) for different SWNT networks (scale bar 10 μm).

The second network is based on CoMoCat nanotubes, which predominantly contain (6,5), (7,5), and (7,6) nanotubes. After dispersion in PFO/toluene solution, mostly (7,5) nanotubes with a large bandgap of 1.211 eV[28] and a minority of (7,6) nanotubes (only 4%) (bandgap 1.107 eV) with traces of (8,6) SWNTs remain in dispersion (Figures b and S1b). Again energy transfer from the (7,5) to the (7,6) nanotubes can be observed in the PLE maps of the semialigned films (Figure e).

Finally, we created a network that was specifically tailored to contain a large majority of (7,5) nanotubes and a minority of (10,5) nanotubes with a significantly smaller bandgap (0.993 eV), so that the difference between the first van-Hove singularities of the valence or conduction band was about 109 meV and thus much larger than the thermal energy kT at room temperature. For this, a dispersion of CoMoCat SWNTs in PFO was mixed with a dispersion of HipCO SWNTs with poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) in toluene. The latter is highly selective for (10,5) nanotubes.[29] After co-sedimentation, removal of most of the polymer, and redispersion, a nanotube ink with about 18 times as many (7,5) nanotubes as (10,5) nanotubes was obtained (Figure c). The PLE map of the deposited network shows a cross peak between the two species (Figure f). The observed energy transfer confirms good mixing and close contact between the nanotubes.

All of these networks were used to fabricate bottom contact, top-gate field-effect transistors with a hybrid dielectric of 10 nm of PMMA and 61 nm of atomic layer deposition HfO2 (see device geometry in Figure c). This hybrid dielectric with a very high capacitance enables low-voltage and air-stable operation with very low leakage currents and negligible hysteresis.[10,30] Transfer characteristics (see Figure d and Supporting Information Figure S2) at low source-drain voltages (Vds) show hysteresis-free and balanced ambipolar transport with excellent on/off ratios of 106 (limited mainly by the gate leakage current as shown in Figure S2) and mobilities of 5–10 cm2 V–1 s–1 (calculated with linear SWNT density-corrected capacitances[31]) for HipCO/PFO and CoMoCat/PFO nanotube networks. These excellent device characteristics reflect the intrinsic properties of the SWNT networks rather than trap-dominated behavior that can occur in devices with, for example, back-gated SiO2 as a dielectric and without encapsulation.[32] The low onset voltages, sharp subthreshold swings, and balanced hole and electron mobilities also corroborate the fact that any remaining polymer wrapping does not act as a hole or electron trap. The large band gap and position of the HOMO/LUMO levels of the polymers PFO (−2.6 eV/–5.7 eV) and F8BT (−3.3 eV/–5.9 eV)[33] compared to the nanotubes with even the largest bandgap, i.e., the (7,5) SWNTs (−3.97 eV/–4.98 eV[34]), preclude this possibility. Further, the output characteristics (see Supporting Information Figure S3) show ohmic behavior at low source-drain voltages (Vds), which indicates good charge injection that is not limited by Schottky barriers.

However, as evident from the transfer and output characteristics, the tailored (7,5)/(10,5) nanotube network shows about 20–25 times lower on-currents and also lower effective mobilities (0.1–1.0 cm2 V–1 s–1) than the other two networks. Such large differences cannot be explained by the minor differences between the SWNT network densities of 9–10 μm–1 for HipCO/PFO, 8–9 μm–1 for CoMoCat/PFO, and 3–6 μm–1 for the tailored (7,5)/(10,5) network. All of the investigated semialigned networks were well above the percolation limit, and thus no superlinear scaling of the on-currents or mobility with network density was expected. Note that simple current–voltage characteristics are not suitable to reveal any underlying transport differences between these networks, and thus other methods are necessary.

All of the fabricated SWNT network transistors exhibit the typical behavior of ambipolar FETs at higher source-drain voltages with a V-shaped transfer curve that shifts with Vds (see Supporting Information Figure S2).[35] For a certain range of voltage conditions, a hole and an electron accumulation zone are formed in series within the channel, thus creating an induced and movable pn-junction (ambipolar regime, Figure e). Exciton formation and near-infrared light emission take place where the hole accumulation layer and the electron accumulation layer meet.[23] This recombination and emission zone is visible as a narrow line with a width of about 1 μm. The position of the emission zone depends on the precise gate and source-drain bias and can be moved arbitrarily through the entire channel (see video and D in Supporting Information). Note that we do not observe any light emission from the network or the electrode edges when the transistors operate in the unipolar regime (only hole or only electron accumulation) even at high drain currents and voltages. We can thus exclude impact excitation[36] as a source of electroluminescence, which was previously observed for unipolar and short-channel SWNT network FETs.[37,38]

Importantly, in the ambipolar regime, when the emission zone is positioned within the channel and several micrometers away from the electrodes, the electron and hole currents are perfectly balanced because all injected charges must recombine either radiatively or nonradiatively, and thus a given drain current always results in a corresponding number of excitons. Recording near-infrared (800–1600 nm) electroluminescence images for a gate voltage sweep at a constant drain current (see Supporting Information Figure S4) and assigning to each pixel the maximum intensity value during this sweep produces an electroluminescence map as previously shown for light-emitting polymer FETs[39] and can be directly compared to photoluminescence images from the same area (see Figure f–h).

Here and in the following we will make the assumption that the spatial and spectral distribution of electroluminescence compared to photoluminescence reflects the density of mobile charge carriers and thus those nanotubes that contribute to the current. The idea of using electroluminescence to study charge transport was recently applied to blends of regiorandom and regioregular poly(3-hexylthiophene) in light-emitting diodes.[40] Electroluminescence is also commonly used to investigate transport and shunts in inorganic (e.g., silicon) solar cells.[41] Regarding the electroluminescence from ambipolar FETs, it is important to again emphasize that all injected charge carriers have to recombine when the recombination zone is positioned away from the electrodes. The mean free path of a minority carrier (e.g., electron) in an accumulation layer of majority carriers (e.g., holes) in a network of carbon nanotubes, which requires hopping from nanotube to nanotube, must be negligible compared to the channel length (20 μm) of the transistor. This becomes clear when considering the width of the emission zone (∼1 μm). As the emission zone is moved through the channel, its intensity is directly correlated to the number of recombining holes and electrons and thus current density in that region. Trap-assisted recombination of carriers (Shockley–Read–Hall mechanism) might play a role but will not contribute to the electroluminescence, as it is nonradiative.[42] Hence, the composite EL map essentially shows areas of preferential charge transport and EL spectra should correlate with the distribution of charges among the different nanotube species.

The only other experimental technique that could provide similar spatial and spectral information for a thin film transistor is charge modulation spectroscopy or microscopy,[43,44] which has been used for polymer semiconductors but to the best of our knowledge has not yet been applied to any nanotube network. Other techniques that can spatially map charge carrier density (e.g., Kelvin probe microscopy[45] and Raman microscopy[46]) or transport paths (conductive AFM[47]) cannot readily distinguish between different semiconducting species of nanotubes.

The obtained composite EL maps must be compared to the PL maps of the same area that show the spatial distribution of SWNTs (including differences in emission efficiency and excitation transfer). This was done for three different networks in Figure f–h. As can clearly be seen, the PL and EL maps are not identical but can differ significantly. Figures f and 2g show relatively uniform PL intensity and therefore more or less evenly distributed SWNTs throughout the channel, but the corresponding EL maps show some hotspots at the electrodes and streak-like features (see Figure g). There is only a partial correlation between areas of strong photoluminescence and those with bright electroluminescence. It seems likely that points of higher charge injection at the electrodes, visible as hot spots on the right, influence the subsequent transport paths. The difference between PL and EL maps is especially striking in Figure h where an area with a very nonuniform SWNT distribution was chosen. The PL image appears very patchy, but the EL map shows many bright emission paths. Even areas that appear very dark in the PL image light up during the gate voltage sweep. Clearly, charge transport is not simply correlated with the absolute density of the SWNT network but must follow certain pathways that start with efficient charge injection followed by good interconnectivity, most effective gating, and lowest resistance along the length of the channel. Unfortunately, the spatial resolution of these images is restricted to about 1 μm due to the wavelength of the emitted light and the limitations of the optical setup. Hence, it is not possible to resolve pathways on the single nanotube level with this imaging method.

To determine which species of nanotubes carry most of the current and hence also emit preferentially, we recorded EL spectra for different applied voltages and for a wide range of current densities, but with the emission zone always positioned at the center of the channel, and compared them to PL spectra from the exact same spot. The PL spectrum (excitation at 640 nm) and selected EL spectra at low and high gate voltages for the HipCO/PFO mix network (all normalized to the integrated total emission intensity) are presented in Figure a. The PL spectrum shows the expected distribution of emission from the five different nanotube species with narrow peak widths of 25–45 nm. Due to the fast energy transfer, strong emission from the (8,6), (8,7) and (9,7) nanotubes is observed although they cannot be excited directly by the 640 nm laser. The EL spectra show the same peaks without any broadening or shifts but with a very different intensity distribution. Most obviously, emission from the (7,5) nanotubes is completely absent. The EL spectra are dominated by emission from the two nanotubes with the smallest bandgaps, i.e., the (9,7) and (8,7) nanotubes. Especially the share of EL from the (9,7) nanotubes is substantially larger than what would be expected according to their fraction in the network (6%), even after energy transfer.

Figure 3

(a) Normalized PL spectrum (excitation at 640 nm) and EL spectra at different gate voltages (normalized to total emission). (b) Share of emission from each SWNT species (determined from peak fits) depending on applied gate voltage compared to photoluminescence. (c) Linear density of states (DOS) for each species according to abundance of SWNTs in the network. (d) Simulation of electroluminescence distribution depending on charge carrier density.

With increasing gate voltage and thus current density, the overall intensity and all individual peak intensities increase (see Supporting Information Figure S5). However, the fraction of emission from the (8,6) and (7,6) nanotubes grows at the expense of the (9,7) and (8,7) contribution. Weak emission from the (7,5) SWNTs can be observed only at very high gate voltages and current densities close to the breakdown of the dielectric. Figure b shows the contribution of each SWNT species (after peak fit) to the total emission intensity depending on the applied gate voltage. While the total intensity increases, the fraction of EL from the two nanotube species with the smallest bandgaps and lowest conduction band levels (correspondingly highest valence band levels) decreases continuously with gate voltage and thus carrier density, while the fraction of EL from all other nanotubes grows.

In a first approximation, this can be understood with the equilibrium distribution of accumulated charges within a SWNT network with different energy levels depending on the position of the Fermi level. We used a simple one-dimensional semiconductor model[48] in steady-state condition that takes into account the linear density of states (DOS, see Figure c) weighted by the abundance of each nanotube species in the network (obtained from fitted absorbance spectra of the dispersion and known chirality-dependent absorption cross sections[49]), the Fermi–Dirac distribution for carriers at room temperature, energy transfer, and experimentally determined chirality-dependent PL efficiencies[27] (for details, see Supporting Information G and H). This model can qualitatively reproduce the observed trends of the EL distribution depending on gate voltage (i.e., total charge density) as shown in Figure d for the HipCO/PFO mix network.

Another indication for the chirality-dependent accumulation of charges within the network is the successive quenching of photoluminescence with increasing gate voltage and thus charge carrier density that results in nonradiative three-carrier Auger recombination.[50,51] As shown in Figure a, the PL (normalized to the (7,5) peak) of the SWNTs with the smallest bandgap is quenched first at low carrier accumulation and the large bandgap nanotubes follow at higher gate voltages/carrier densities. Note that at high carrier densities, red-shifted trion emission starts to become visible.[24] The distribution of PL intensity among the nanotube species varies with gate voltage as shown quantitatively in Figure b by introducing a gate-voltage-dependent photoluminescence quenching factor (QF), that is the PL intensity at zero gate voltage (no additional charge carriers) divided by the PL intensity at a given positive or negative gate voltages (electron or hole accumulation). The increase of the quenching factor with gate voltage for the different nanotube species can be reproduced well by the simple analytical model as introduced above and shown in Figure c. This quenching experiment also corroborates that the variations in EL intensities among the nanotubes with increasing gate voltage in Figure are not due to Auger quenching at higher charge carrier densities as this would lead to the opposite trend for the EL spectra, i.e., larger contribution by the (7,5) nanotubes at low gate voltages. Note also that, within the applied gate voltage range, the second subbands of these small-diameter nanotubes are not yet reached and can be neglected in contrast to, for example, electrolyte-gated large diameter nanotubes.[52]

Figure 4

(a) Photoluminescence spectra of a HipCO/PFO SWNT network (normalized to the (7,5) peak) depending on applied positive gate voltage, i.e., electron accumulation. Note that at high electron densities, trion emission starts to become visible.[24] (b) Gate-voltage-dependent photoluminescence quenching factor QF. (c) Calculated charge carrier density on individual nanotubes for increasing overall charge density leading to Auger quenching.

The demonstrated simple one-dimensional semiconductor model assumes a steady-state accumulation of charges and does not take into account chirality-dependent variations in charge injection, junction resistance, or random network pathways that are likely to be important for the actual current flow in the device. Nevertheless, the good agreement of experimental data and analytical model implies that electroluminescence and photoluminescence can be used as sensitive and even quantitative measures for the distribution of carriers within a mixed nanotube network. It also shows clearly that the effective network density that is available for transport varies with charge carrier density. The apparent carrier mobility should thus be gate voltage-dependent similar to other energetically disordered semiconductors such as amorphous polymers[53] or quantum dot solids.[54]

To test this approach further, we investigated electroluminescence spectra of the less complex network based on CoMoCat/PFO nanotube dispersions. The most abundant species are the (7,5) and the (7,6) nanotubes whose first van Hove singularities (i.e., conduction/valence band levels) are separated by only 52 meV (see Figure a). Again the PL spectrum (excitation wavelength 640 nm close to resonance with both nanotubes) shows some energy transfer from the (7,5) to the (7,6) nanotubes. However, the EL spectrum exhibits a distinctly different distribution of emission between the two species (see Figure b). The emission from the (7,6) nanotubes is much stronger than expected. Its contribution to the EL decreases with increasing gate voltage and current density, eventually approaching the PL values (Figure c). Note that the increasing shoulder at 1220 nm is due to trion emission by the (7,5) nanotubes.[24,55] Although it is clear from the previous experiment that especially at low gate voltages a substantial amount of current must go through the (7,6) nanotubes that constitute only 4% of the network, the (7,5) nanotubes also contribute significantly. At higher gate voltages, when the EL resembles the PL spectrum, the carrier distribution should reflect the respective network proportions and the emission is only affected by energy transfer. This is understandable as the energy difference between the two nanotube species is not very large compared to kT at room temperature. EL measurements at low temperatures and thus lower kT should lead to a more pronounced effect with more transport through and thus more emission from the (7,6) nanotubes.

Figure 5

(a) Linear DOS of conduction band for a SWNT network with a majority (96%) of (7,5) SWNTs and 4% (7,6) nanotubes. Note that the DOS for the (7,5) nanotubes was divided by 10 for clarity. (b) PL spectra (black line, excitation at 640 nm) and EL spectra at different gate voltages from network transistor with (7,5) and (7,6) SWNTs. (c) EL shares of each nanotube species depending on applied gate voltage and in comparison to PL. (d) Linear DOS of conduction band for a SWNT network with a majority (91%) of (7,5) SWNTs, traces of (7,6), (8,6), and 5% (10,5) nanotubes. (e) PL spectra (black line, excitation at 640 nm) and EL spectra at different gate voltages from network transistor with (7,5) and (10,5) SWNTs. (f) EL shares of each nanotube species depending on applied gate voltage and in comparison to PL. Note that trion emission appears at high carrier densities.

Finally, the tailored network of mostly (7,5) nanotubes (91%) with about 5% (10,5) nanotubes is tested. Here the energy difference between the conduction/valence band levels is about 109 meV and thus substantially larger than in the previous case (see Figure d). The PL spectrum of the network (excitation wavelength 640 nm in resonance only with (7,5) nanotubes) already shows some emission from the (10,5) nanotubes at 1300 nm, and additional peaks are observed that can be assigned to small amounts of (7,6) and (8,6) nanotubes (see Figures e). For this network, the EL spectrum shows mostly emission from the (10,5) nanotubes at low gate voltages and electroluminescence from the (7,5) nanotubes is low. In agreement with our previous observations, this EL spectrum strongly suggests that the majority of charges is accumulated in and transported through the (10,5) nanotubes despite the fact that they make up only 5% of the entire network. The effective network density is thus much lower than assumed. This difference may also explain the significantly lower on-currents and apparent mobilities for the tailored (7,5)/(10,5) network transistor. At higher gate voltages and current densities, the emission from the (8,6) nanotubes (only 2% of the network) increases and the (7,5) nanotubes also start to participate in the transport and thus emit, while the contribution by the (10,5) nanotubes decreases again. Note that (7,5) trion emission at 1224 nm[24] also contributes to the EL spectrum at very high gate voltages. This exaggerated example of a mixed SWNT network shows how different bandgaps affect transport and how electroluminescence spectra can be used to directly and quantitatively reveal the differences of transport at different gate voltages that cannot be easily extracted from simple current–voltage characteristics.

The abundance of each nanotube species according to absorbance and the PL and EL distributions of all networks are summarized in Supporting Information Figure S6 and Table S1. The data show clearly that energy transfer between the different chiralities in the network that is quantified by PL spectra cannot be neglected for interpretation of EL spectra, as it is one of the major contributions to the final spectrum, besides chirality-dependent charge distribution and PL efficiencies. A previous EL/PL study by Engel et al.[56] on large diameter (1.3–1.7 nm) nanotube networks found a general red-shift and narrowing of the PL and EL emission (width >200 nm) compared to the expected distribution (width >500 nm) but did not find any difference between EL and PL. This might be due to the much smaller energy differences between nanotubes in this diameter range (<50 meV)[28] compared to nanotubes with small diameters (0.8–1.1 nm) that were used here. For polydisperse large diameter SWNT networks, the small energy differences should only become important at low temperatures.

Finally, the presence of small amounts of residual metallic nanotubes should be considered. Their contribution to charge transport would not be visible in the electroluminescence spectra. They would act as efficient quenchers, and significant amounts of metallic SWNTs would lead to strongly reduced PL and EL. If their concentration is well below the percolation limit, they could possibly also act as unwanted charge traps similar to metallic nanoparticles in semiconducting layers.

Clearly, the specific diameter/bandgap/energy level distribution within a network of semiconducting carbon nanotubes has a large impact on its transport properties and should be taken into account for practical device fabrication. While single-chirality networks might be theoretically ideal, the cost of creating those is very high. Additional nanotube species can be tolerated if their bandgaps are very similar to or larger than those of the majority species. Mixtures of nanotube chiralities with very different bandgaps should be strictly avoided, as the transport will ultimately be determined by the nanotubes with the smallest bandgap. The other nanotubes will not significantly contribute to the on-current and are thus wasted. They might even impede charge transport through the network as effective trap sites if their density is below the percolation limit. Such a scenario would be similar to host/guest systems in disordered organic semiconductors.[57] With increasing gate voltage, the number of SWNTs that contribute to the transport increases and thus the effective network density changes. This effect further complicates field-effect mobility calculations for mixed SWNT networks.

Conclusions

In summary, we have demonstrated the large impact of the diameter distribution on charge transport in polydisperse but purely semiconducting SWNT networks by using near-infrared electroluminescence as a sensitive and quantitative measure. Despite the absence of metallic nanotubes, the transport paths are far from uniform and depend strongly on injection, on interconnectivity of the nanotubes, and, most importantly, on their energy level distribution. By increasing the applied gate voltage and thus carrier density, the contribution of each nanotube species to the overall transport changes and the participation of larger bandgap nanotubes increase gradually as expected from the Fermi–Dirac distribution. Importantly, the presence of small bandgap nanotubes leads to preferential transport through these even if they constitute only a minority within the network, thus rendering the other nanotubes almost worthless. Narrow diameter distributions are thus much better suited to obtain maximum on-currents in FETs with a given network density. In addition, the availability of pure semiconducting and even monochiral dispersions paves the way to specifically tailored SWNT networks, in which transport can be studied depending on network density, energy level distribution, etc. Understanding and designing these networks will lead to optimized device performances with a minimum of purification and thus cost.