Conductivity of AuCl4-Functionalized Carbon Nanotube Networks

Article pubs.acs.org/JPCC

Conductivity of AuCl4‑Functionalized Carbon Nanotube Networks T. Ketolainen, V. Havu, and M. J. Puska* COMP, Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland ABSTRACT: We have studied the effect of AuCl4 functionalization on the conductivity of carbon nanotube networks by first-principles electronic structure calculations. The functionalization results from treating carbon nanotube networks by dissolved AuCl3. Band structures and electronic transmission functions for single-walled semiconducting carbon nanotubes with physisorbed AuCl4 anions are computed using the density functional theory. The resulting p-type doping of nanotubes accompanied by a downshift of the Fermi level and balanced by negatively charged AuCl4 anions make the nanotubes metallic. Moreover, the influence of AuCl4 functionalization on the conductance of the junction between two semiconducting carbon nanotubes is considered. Increasing the AuCl4 coverage lowers the Fermi level rapidly until it is pinned by a van Hove singularity of the nanotube electronic structure. For these doping levels our calculations based on the density-functional nonequilibrium Green’s function method show a significant increase in the intratube electron transmission. Moreover, our electron transport calculations for crossed nanotubes indicate a simultaneous increase in the intertube conductance. These factors explain the experimentally observed robust conductivity improvement of carbon nanotube networks treated by dissolved AuCl3.

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INTRODUCTION

this case, iodine atoms are believed to form long polyiodine chains inside the nanotubes. CNTs can be doped with acids resulting in observed downshifts of the Fermi level within the occupied nanotube valence band. Doping with sulfuric, nitric, or hydrochloric acids has been studied.16 Downshifts of 0.2 eV (ref 16) and 0.35 eV (ref 17) of the Fermi level have been measured when doping CNTs with the nitric acid. The nitric acid treatment has also been shown to reduce the sheet resistance of CNT thin films.18,19 Measuring the local electrical properties of CNT thin films, the nitric acid has been found to improve the conductivity of both the CNT junctions and individual nanotubes in the film.20,21 A remarkable downshift of the Fermi level has also been observed in experiments in which CNT thin films have been doped with AuCl3 dissolved in nitromethane.22 As a result, the conductivity of the thin film increases significantly. The mechanism of AuCl3 doping has been suggested to be due to chlorine anions.23 However, recent density functional theory (DFT) studies indicate that Cl anions do not result in the systematic p-type doping because with single Cl anions the doping effect depends essentially on the relative positions of the Cl anions on the CNT surface.24,25 In contrast, the recent DFT simulations by Murat et al.24,26 focus on physisorbed AuCl4 anions which are assumed to be formed in treating CNTs by dissolved AuCl3. The formation of AuCl4 anions on πconjugated polymers,27 CNTs,23 and graphene28 has been assumed also previously on the basis of experimental studies. In comparison to the Cl anions, DFT simulations for AuCl4

Modern display technology requires materials that are flexible and transparent and have high conductivity. Currently, indium tin oxide (ITO) is commonly used as a material for transparent electrodes in various applications. However, the rarity of In in the Earth’s crust has boosted the search of substitutes for ITO. Previous studies have shown that carbon nanotube (CNT) thin films, i.e., networks consisting of a large number of CNTs, could also be exploited in transparent-electrode applications.1,2 For instance, transistors,3,4 light-emitting diodes,5 and solar cells6 based on the CNT thin films have already been fabricated. The process of making CNT thin films needs still improvements in order to simultaneously optimize the transparency and the conductivity of the films. For instance, bundling can deteriorate the properties of CNT thin films.7 Moreover, the conductivity of CNT thin films mainly depends on the conductances of junctions between CNTs.8 It can be enhanced, e.g., by linking CNTs in the network with Cr atoms,9 which has also been demonstrated for metallic CNTs by computational transport studies.10,11 To make a CNT network conductive, several aspects need to be addressed simultaneously: (i) the electronic structure of semiconducting CNTs must be modified so that they become conductive, (ii) conductances across CNT junctions must be improved, and (iii) metallic CNTs must not lose their conductivity due to e.g. increased scattering. One way of achieving these goals is doping CNTs with various atoms or molecules that adsorb on the CNT.12 For instance, doping CNTs with bromine or potassium leads to remarkable reduction in the resistivity of the film.13 A less prominent reduction due to O2 and N2 molecules has also been observed.14 Single-walled CNT thin films treated with iodine have also shown a large decrease in the sheet resistance.15 In © 2017 American Chemical Society

Received: November 18, 2016 Revised: January 9, 2017 Published: February 8, 2017 4627

DOI: 10.1021/acs.jpcc.6b11644 J. Phys. Chem. C 2017, 121, 4627−4634

Article

The Journal of Physical Chemistry C

perpendicular (10,0) CNTs. In addition to the electronic structures of individual pristine and doped CNTs, electron transport in these systems is explored. Schematic figures for the used computational unit cell of a doped (10,0) CNT and for a doped intratube transport system are shown in Figures 1a and

anions on semiconducting (10,0) CNTs show a stable doping effect.24,26 The doping mechanism of CNTs by dissolved AuCl 3 presented by Murat et al.24 is based both on earlier experimental findings23 and on their own first-principles calculations. X-ray photoelectron spectroscopy has revealed that after AuCl3 dissolution there are both neutral Au atoms and Au3+ ions in the entire system.23 The neutral Au atoms tend to form clusters that are more common at high temperatures. In order to maintain the 3+ charge state, the Au3+ ions need to coordinate with negative Cl− ions. According to calculations,24 possible stable conformations on a CNT are Au2Cl6 and AuCl4. However, only AuCl4 among the anion candidates leads to a stable p-type doping observed in measurements. In this work, we base our modeling of the AuCl4functionalization of CNT networks on the mechanism proposed by Murat et al.24 and explain how the conductivity of CNT networks improves when they are treated with electronegative dopants. We study the (10,0) CNT as a representative example and determine both the adsorption geometries and the band structures of the AuCl4-functionalized CNT systems. Similarly to the modeling by Murat et al.,24 in our calculations AuCl4 molecules are adsorbed on a CNT and a neutral supercell with periodic boundary conditions is assumed. As a result, charge transfer of about one electron per AuCl4 molecule occurs leading to a negatively charged molecule and a positively charged CNT. When describing our computational results, we therefore use systematically the concepts of the AuCl4 anion and charge transfer from the nanotube to the molecule. Our band structures reveal the amount of charge transfer from the CNTs to the AuCl4 anions and the corresponding downshift of the Fermi level that renders the electronic structure of the doped CNTs into that of a conductor. According to our transport calculations, the physisorbed anions do not affect remarkably the intratube conductance via electron scattering. In the case of CNT networks, it is also important that the junctions between CNTs are highly conductive. Therefore, we study also the electron transport through perpendicular junctions of two doped CNTs and find that in comparison with the junction of two pristine CNTs, doping increases significantly the electron transport. The enhanced intertube conductance is due to the high density of states (DOS) at the van Hove singularity of the CNT electronic structure and the pinning of the downshifted Fermi level at the singularity and hybridized molecule-CNT states. These features do not depend on the details of the doping process or functionalizing species. The structure of the article is as follows. Computational methods and geometries of the CNT systems are described in the Methods and Systems section. The geometries, band structures, and transmission functions of systems comprising semiconducting (10,0) CNTs and AuCl4 anions are presented in the Results section. This section also deals with charge transfer in doped (10,0) CNTs and presents results of transport calculations for CNT junctions in detail. The most important results are summarized in the Conclusions section.

Figure 1. (a) (10,0) CNT doped with one AuCl4 anion per computational unit cell and (b) doped CNT system for intratube transport calculations with the same uniform doping concentration. The borders between the leads and the scattering region are shown by red dashed lines.

1b, respectively. The latter shows the division of the CNT to a scattering region and two leads. To understand the conductivity of CNT networks, electron transport is investigated also in three representative CNT junctions depicted in Figures 2a−c.

Figure 2. Different CNT junctions considered in the present work: (a) junction consisting of two pristine perpendicular (10,0) CNTs, (b) junction where the two (10,0) CNTs are doped with AuCl4 anions, and (c) junction where the two AuCl4-doped CNTs are connected by a AuCl4 linker anion. The ends of the CNTs form the lead regions similarly to Figure 1b.

They are a junction of two pristine (10,0) CNTs, a junction of two doped (10,0) CNTs without a linking molecular anion, and a junction of two doped (10,0) CNTs with a AuCl4 anion between the nanotubes. In the case of a single doped CNT or a junction of two doped CNTs, the leads are also doped so that the dopant concentration is constant along the CNTs of the system. The junctions of two CNTs resemble the pristine14,29 and O2- or N2-doped14 CNT junctions studied previously by electron transport modeling. Electronic Structure Calculations. The calculations are carried out with the electronic structure theory code package FHI-aims based on numeric atom-centered orbitals.30 The initial positions of the atoms in a (10,0) CNT primitive unit cell are calculated with the TubeGen 3.4 nanotube generator.31 Thereafter, both the atom positions in the unit cell and the lattice vectors are relaxed until the maximum force component decreases below 10−2 eV/Å. A 1 × 1 × 8 k-point grid is chosen

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METHODS AND SYSTEMS The systems considered in this work are a pristine semiconducting single-walled (10,0) CNT, a (10,0) CNT doped with AuCl4 anions, and a CNT junction consisting of two 4628


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CNT system or for a four-terminal CNT junction without implicit (self-consistency) effects of a bias voltage. In the transport calculation, the Green’s function Gr for the scattering region connected to the semi-infinite leads is computed by solving the equation29

for the primitive unit cell relaxation and the exchangecorrelation functional used is PBE.32 Spin effects are neglected in all calculations. The doped CNT systems consist of a (10,0) CNT that has either 1, 2, or 4 AuCl4 anions on the outer surface of our computational unit cell which comprises four pristine (10,0) unit cells (see Figure 1a). The length of our computational unit cell is then 17.1 Å, and the dopant concentrations in the systems vary between 0.059 and 0.23 AuCl4 anions per Å. Vacuum between the periodic images in the computational unit cell is 30.0 Å. The size of the computational unit cell including vacuum equals that of ref 24. Figure 1a presents the geometry of the computational unit cell of a (10,0) CNT with one AuCl4 anion. The atomic positions in the doped CNT are relaxed, but the unit cell volume is kept fixed to the value of the pristine cell. We use a Γ-centered 1 × 1 × 27 k-point grid in the relaxation calculations of doped CNTs. The band structures are mainly computed with the HSE06 functional, and the screening parameter ω is set to 0.2 Å−1 (details in ref 33). The value of the mixing parameter α determining the amount of exact exchange is 0.25. The k-point grid is 1 × 1 × 15 in the HSE06 band structure calculations. When the band structures are computed with PBE, it is possible to use the larger, 1 × 1 × 27 grid for the k-point sampling. The electronic structure of a CNT junction is calculated using periodic boundary conditions so that CNT junctions form a periodic structure where the vacuum between the neighboring layers is approximately 50 Å. When relaxing a CNT junction, the coordinates of the atoms in the lead regions are fixed and only atoms in the scattering region are allowed to move. The distance between the two CNTs forming the junction is varied and the CNT junction is relaxed separately for each distance. Then the optimal distance is determined by fitting a second-degree polynomial to the total energy values. The distance between the two CNTs, dCNT−CNT, is given by dCNT − CNT = daxes − 2r

{E − Ĥ 0 −

∑ Σir(E)}Gr (r, r′; E) = δ(r − r′) i

(2)

where E and Ĥ 0 are the single-electron energy and Hamiltonian of the junction region, respectively, and Σri is the so-called selfenergy of the ith lead. The self-energy Σri can be computed with a recursive method under periodic boundary conditions over the lead regions shown in Figure 1b. Since the transport calculation is not self-consistent, it is necessary to align the energy levels of the semi-infinite leads and their counterparts connected to the scattering region (see Figure 1b). A more detailed explanation about the energy level alignment and the computation of the electronic transmission function is given in refs 29 and 35.

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RESULTS AND DISCUSSION Optimized Geometries of CNTs and CNT Junctions. When relaxing the atomic positions in the calculations for doped (10,0) CNTs, we use as the starting points the highly symmetric configurations shown in Figure 3. AuCl4 anions do

(1) Figure 3. Three different configurations for a AuCl4 anion on a (10,0) CNT. The possible positions of the Au atom are denoted by circles. The Cl atoms (shown only in one case) form a cross with bonds along and perpendicular to the CNT axis. The hexagon represents the carbon atoms of the (10,0) CNT.

where the distance between the axes of the CNTs is denoted by daxes and r is the radius of the pristine (10,0) CNT. We use a 1 × 3 × 3 k-point grid in the relaxation and transport calculations. We also take van der Waals interactions into account in CNT junction calculations using the C6/R6 approximation where the C6 coefficients are obtained from the Hirshfeld partitioning of the calculated electron density.34 The carbon atoms in the junction region do not move much during the relaxation. Thus, the junctions with doping in Figures 2b,c are not relaxed completely since the interatomic distances relevant for transport studies are obtained already with the restricted relaxation. Transport Calculations. Electronic transport in doped CNTs and CNT junctions is also studied. The systems of the transport calculations are similar to those that are used to examine the electronic properties of the (10,0) CNTs. In the case of single CNTs, transport in infinitely long pristine and AuCl4-doped (10,0) CNTs is considered by studying the systems similar to that in Figure 1b. The whole system can be divided into three parts that are the two semi-infinite leads and the scattering region. To obtain the electronic structure for the transport calculation, a calculation using periodic boundary conditions including the leads and the scattering region is performed first. The transport module of the FHI-aims code allows us to determine electronic transmission functions for a two-terminal

not move from these positions along the surface but the distance between the molecular anions and the CNT changes in the structure relaxation. After the relaxation, the differences in the total energies between the two configurations are relatively small reflecting physisorption type bonding which is rather position-independent. As the representative configuration for the following calculations, we choose the geometry in which the Au atom is located above a C atom (configuration AuT in Figure 3). The most important results we will find do not depend on the details of atomic positions so that our conclusions about the doping effects will be robust. The CNT−molecular anion distance in the different doped systems vary between 3.47 and 3.50 Å. These values have been determined with the PBE functional and are around one-third of the diameter of the (10,0) CNT. In a previous study without the van der Waals correction,24 the AuCl4 anion has been found to lie approximately 3 Å above the CNT surface. When a AuCl4 anion is placed on a (10,0) CNT, the carbon atoms close to the molecular anion move only a little; i.e., the maximum displacement is less than 4 × 10−2 Å. We calculate the binding 4629


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Figure 4. Band structures computed with the PBE and HSE06 functionals for pristine and AuCl4-doped (10,0) CNTs corresponding to computational unit cells shown in insets: (a, b) A pristine (10,0) CNT, (c, d) (10,0) CNT with one AuCl4 anion per computational unit cell, and (e, f) (10,0) CNT doped with four AuCl4 anions per computational unit cell. The top of the valence band of the pristine CNT and the Fermi level of the AuCl4-doped CNTs are marked with red dashed lines.

Band Structures of Doped CNTs. The effect of doping on semiconducting CNTs can be studied by considering the electronic band structures of doped CNTs. To decrease the self-interaction error, we use the hybrid HSE06 functional in addition to the semilocal PBE functional. The one-dimensional band structures for the pristine (10,0) CNT computed with the PBE and HSE06 functionals are presented in Figures 4a and 4b, respectively. They reveal the semiconducting character with a direct band gap at the Γ point. The width of the band gap is 0.77 (0.97) eV in the case of the PBE (HSE06) functional. The PBE band gap of the present work is close to the value Eg = 0.8 eV that has been obtained in an atomistic self-interaction corrected DFT calculation.24 The degeneracy of the uppermost valence band, including the spin degeneracy, is four. This is a property also predicted by the tight-binding model.36 Adding a AuCl4 anion on the CNT corresponds to a downshift in the Fermi level and a p-type doping effect, which is presented in Figures 4c and 4d for PBE and HSE06 calculations, respectively. Importantly, the downshift is larger in the case of HSE06. In addition, there are several rather dispersionless bands that arise from localized molecular states. In the PBE band structure, they are near the Fermi level whereas they move toward lower energies in the HSE06 calculation. A remarkable downshift of the Fermi level relative to the top of the valence band occurs when the number of AuCl4 anions is increased to four per computational unit cell as it can be seen from Figures 4e,f. We estimate the p-type doping level in the AuCl4-doped CNTs by searching for the point at which the uppermost valence band and the Fermi level cross. Since the one-dimensional uppermost partly occupied valence band could accommodate up to four electrons per computational unit cell,

energy of a single (neutral) AuCl4 molecule using the formula Eb = ECNT−AuCl4 − ECNT − EAuCl4, where ECNT−AuCl4 is the energy of the CNT−AuCl4 system, ECNT the energy of the pristine (10,0) CNT, and EAuCl4 the energy of the AuCl4 molecule. The binding energy for one AuCl4 molecule is Eb = −1.38 eV, which is comparable to the value −1.6 eV found earlier.24 The geometry of the perpendicular junction between the two pristine (10,0) CNTs is optimized and the nanotube distance dCNT−CNT after the relaxation is around 2.63 Å if the van der Waals correction is applied in the calculation. The same distance without the van der Waals correction is approximately 3.68 Å. The physically correct distance is important because it affects strongly the electron tunneling and the conductance of the junction. No significant changes in the relative positions of the atoms within the individual CNTs are found, and the CNTs are not deformed during the formation of the junction. The distance between the AuCl4 anions and the CNTs in the junction between two doped CNTs (see Figure 2b) is the same as in the case of the single (10,0) CNT with four molecular anions (the insets of Figures 4e,f). The distance between two doped CNTs with a linker molecular anion in Figure 2c is around 6.69 Å. The binding energy of two CNTs without a linker molecular anion is around −1.6 eV, and it depends only weakly on the AuCl4 doping concentration of the CNTs. A second CNT is bound to an adsorbed AuCl4 anion with a binding energy of around −1.3 eV. The existence of a linker molecular anion in the junction is justified also by our atomic structure calculations. Namely, when relaxing the atomic positions, the adsorbed AuCl4 anions, which have a net negative charge, have a tendency to move toward the junction of the two CNTs with a net positive charge. 4630


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lowering of the Fermi level and its pinning near the flat and dispersionless bands, however, are expected to be similar (compare especially Figures 4e and 4f). The transmission functions determined with PBE are presented in Figure 5.

the number of holes created by the molecular anions in the CNT per the same volume can be estimated by measuring the distance from the Γ point to the intersection point, dividing the distance by the maximum kz value, and multiplying the ratio by four. The p-type doping level is determined by the doping efficiency of AuCl4 anions, i.e., the number of holes created in the valence band of the (10,0) CNT per adsorbed AuCl4 anion. The doping efficiencies are listed in Table 1 for different AuCl4 Table 1. Doping Efficiency in AuCl4-Doped (10,0) CNTsa NAuCl4

functional

doping efficiency per AuCl4 anion (e)

1 1 2 4 4

PBE HSE06 HSE06 PBE HSE06

0.9 1.1 1.1 0.7 0.7

a

The values are given for the PBE and HSE06 functionals as a function of the number of molecular anions NAuCl4 in the computational unit cell.

Figure 5. Electronic transmission functions for pristine and AuCl4doped (10,0) CNTs for doping concentrations corresponding to one, two, and four AuCl4 anions per computational unit cell (see the insets in Figure 4). In the case of the pristine and doped CNTs, the top of the valence band and the Fermi level determine the energy zero, respectively.

concentrations. Because of the discrete k-point mesh and the smearing of the Fermi level used in the calculations, the accuracy of the estimation is about 0.05−0.1 electrons. A PBE calculation for a (10,0) CNT doped with one AuCl4 anion per computational unit cell gives that 0.9 electrons are transferred from the nanotube to one molecular anion. The doping efficiency estimated for the same system from the HSE06 results is even higher, 1.1 electrons per adsorbed molecular anion. These doping efficiencies indicate physisorption and ionic bonding between the AuCl4 anion and the CNT. The doping level per molecular anion becomes clearly smaller, 0.7 electrons per AuCl4 anion, when there are four AuCl4 anions around the CNT. The decrease of the doping efficiency indicates the hybridization of the molecular and CNT states and appearance of some covalent character in bonding. The hybridization of the AuCl4 and CNT states has been observed also earlier in ref 26 and can be seen also in Figure 9 for a AuCl4 anion linking two (10,0) CNTs. The PBE results of Figures 4c and 4e show that with increasing dopant concentration the Fermi level pushes the hybridized and partly occupied molecular bands down with respect to the valence band maximum. Figures 4e and 4f indicate that for the dopant concentration of four molecular anions per computational unit cell the Fermi level is lowered close to the dispersionless molecular bands and the flat CNT band causing the van Hove singularity. As a result, the Fermi level is pinned in the region of a high DOS due to CNT and molecular states. The Fermi level pinning and the simultaneous hybridization of CNT and molecular states are important for the intertube electronic transport as will be discussed below. Transmission Functions for Doped CNTs. A significant downshift in the Fermi level can be observed in the AuCl4doped (10,0) CNTs as evidenced by the band structure calculations (see Figure 4). To investigate the impact of doping on the conductivity of single nanotubes, we compute electronic transmission functions for the CNT systems shown in the insets in Figures 4a−f. We use here the PBE functional because the computationally much heavier nonlocal HSE06 functional is not feasible for transport calculations. Although the relative positions of the CNT and AuCl4-derived bands differ between the PBE and HSE06 results, the qualitative results with the

The transmission function for a pristine (10,0) CNT shows the characteristic features of a one-dimensional semiconductor, i.e., no transmission within the band gap and a stepwise structure due to opening (or closing) of (sub)bands. When a AuCl4 anion is added on the nanotube, the system becomes metallic. This is seen in Figure 5 as a shift of the transmission curve by around 0.08 eV toward higher energies corresponding to a shift in the band structure plot (Figures 4c and 4d). Increasing the dopant concentration results in an even larger shift of the transmission curve. The upshifts for two and four AuCl4 anions are approximately 0.25 and 0.45 eV, respectively. These values are close to those obtained in the previous band structure calculations of AuCl4-doped (10,0) CNTs.24 The AuCl4 anions also introduce scattering, which is observed as dips in the transmission functions. The dips are common at low energies below the Fermi level. At high energies within the conduction band, AuCl4 anions cause only a few dips in the curves because of the low number of molecular states. A drawback of the doping is the possible shortening of the mean free path of electrons.26 On the other hand, adsorbed AuCl4 anions on CNTs do not influence the mean free path so much as substitutional impurities.37 Electronic Transport through CNT Junctions. Electronic transmission functions for CNT junctions are computed by performing four-terminal transport calculations. Because of the symmetry assumed, intratube transmission functions are presented only for one CNT. Similarly, only one intertube transmission function is required when the transport through the CNT junction is considered. The transmission functions for a CNT junction consisting of two perpendicular pristine (10,0) CNTs (see Figure 2a) are shown in Figure 6. The intratube transmission function for a junction of two pristine (10,0) CNTs without AuCl4 anions is similar to the transmission function of a single (10,0) CNT so that the other CNT in the junction does not affect the intratube transport significantly. In the lower panel in Figure 6, transport through the junction is very low apart from a few peaks appearing close to van Hove singularities where DOS diverges. The peaked character of the interband transmission has been observed also before.14,29 Interestingly, the shape of the intertube transmission function resembles the DOS of the one-dimensional 4631


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Figure 7. Intratube (top panel) and intertube (middle and bottom panels) electronic transmission functions for a junction of two doped (10,0) CNTs without a linking AuCl4 anion between the CNTs. The dopant concentration is four AuCl4 anions per computational unit cell. The Fermi level (blue vertical lines) is chosen as the energy zero.

Figure 6. Intratube (top panel) and intertube (middle and bottom panels) electronic transmission functions for a CNT junction of two pristine (10,0) CNTs. The energy zero corresponds to the top of the valence band of a pristine (10,0) CNT.

electron gas of the CNT. Obviously, at a given energy the number of the electron states or conduction channels perpendicular to the CNTs and participating in the transport is proportional to DOS at that energy. The junctions of doped CNTs with and without a linking AuCl4 anion are depicted in Figures 2b and 2c, respectively. Similarly to the case of the single CNT, placing AuCl4 anions on the CNTs leads to shifts relative to the Fermi level in the intratube transmission functions as shown in the upper panels of Figures 7 and 8. The distance between the Fermi level and the first transmission step above it is 0.3−0.4 eV in the intratube transmission functions. These values are slightly smaller than those obtained in the band structure calculations for CNTs with the same doping level because the band structure calculations have been carried out using the HSE06 hybrid functional. The intertube transmission functions in Figures 7 and 8 suggest that conductances of CNT junctions increase notably when nanotubes are doped with AuCl4 anions. The intertube transmission function for a junction without a linking AuCl4 anion in Figure 7 shows a region with plenty of peaks just below the Fermi level between −0.85 and −0.1 eV. Just a slightly larger concentration of AuCl4 anions would result in the Fermi level pinning on top of the CNT van Hove singularity and in a region of high transmission. Because DOS is large in this energy region, the Fermi level would lower there slowly when the concentration of AuCl4 anions on semiconducting CNTs is further increased. We also notice that transmission peaks just below the Fermi level are broader than the van Hove singularity induced peaks for the junction of pristine CNTs in Figure 6. This reflects the hybridization of the molecular and CNT states.

Figure 8. Intratube (top panel) and intertube (middle and bottom panels) electronic transmission functions for a junction of two doped (10,0) CNTs with a linking AuCl4 anion between the CNTs. The Fermi level (blue vertical lines) is chosen as the energy zero.

The junction of doped CNTs with a linker molecular anion exhibits an intertube transmission function (see the lower panels in Figure 8) where there is a peak at the Fermi level and 4632


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intratube conductance. For intertube electron transmission, it is important that as a function of increased dopant concentration the downshifting Fermi level is pinned at the van Hove singularities of the CNT electronic structure. The downward shift of the Fermi level pushes also the hybridized moleculeCNT states down in energy which further increases the electron transmission at the Fermi level. The intertube electron transmission increases also for CNTs linked by a molecular anion. In this case, the partly occupied CNT and molecular states near the Fermi level hybridize enabling the electron transmission between the two CNTs. The model can be directly generalized to metallic CNTs for which calculations similar to the present ones have predicted only a minute junction transmission.11,29 Similar effects as for AuCl4 are expected also for other dopants such as NO3. Experimental findings are consistent with the model.

many close peaks just below it. All the peaks are quite broad. The most prominent peaks are below the Fermi level, and their intensity decreases toward lower energies in contrast with the junction without the linker molecular anion (Figure 7, lower panels). The intertube transport is suppressed also above the Fermi energy, and only a few very narrow peaks can be seen at higher energies. All these features mean that the electron transmission is due to molecular states which hybridize strongly with the CNT states. Because the Fermi level pushes down the hybridized and partly occupied molecular states (PBE results in Figures 4c and 4e), these states will reside at the Fermi level which will be pinned at a van Hove singularity when the dopant concentration increases. The hybridization of the molecular and CNT states can be clearly seen in Figure 9 which shows the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: martti.puska@aalto.fi (M.J.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to CSC - IT Center for Science Ltd. for providing computational resources. We also thank Prof. Esko I. Kauppinen for suggesting us this project and for many useful discussions as well as Dr. Hannu-Pekka Komsa for helpful discussions. This work was supported by the Academy of Finland through its Centres of Excellence Programme (20122017) under Project No. 251748. The funding for the work was given by the AEF Aalto Energy Efficiency research programme.

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Figure 9. Total electron density of two double-degenerated states near the Fermi level in the junction of two (10,0) CNTs linked with a AuCl4 anion. The hybridization of molecular and CNT states is clearly visible. The density is represented by a blue isosurface. The isosurface extends over the whole CNTs without a significant attenuation.

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total electron density of two double-degenerated states near the Fermi level in a junction of two (10,0) CNTs linked with a AuCl4 dopant. These kinds of states enable the intertube electron transmission when there is a AuCl4 anion in the CNT junction. According to our calculations for the junctions between semiconducting CNTs, the transmission function near the Fermi level attains values of the order of 0.5. Because the unity transmission corresponds to the conductance quantum 2e2/h, in terms of the junction resistance transmission of 0.5 gives an estimate of about 30 kΩ. In recent atomic force microscopy measurements, the best conducting junctions between nitric acid treated CNTs show resistance of this order,20 which supports our model.

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CONCLUSIONS We have created a model that describes the microscopic origin of the conductivity improvement of CNT networks by molecular doping. The model is based on our electronic structure and electron transport calculations for semiconducting (10,0) CNTs with adsorbed AuCl4 anions and junctions formed by them. Electron charge transfer from CNTs to the adsorbed molecular anions results in p-type doping and in increased 4633


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Conductivity of AuCl4-Functionalized Carbon Nanotube Networks

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