Characterization of contact resistances in ceramic-coated vertically aligned carbon nanotube arrays

Despite the technological significance of carbon nanotube (CNT) arrays and metal-oxide coated CNTs for electronic and electrochemical devices such as supercapacitors, lithium-ion batteries, and solar-chemical cells, sub-optimal device performance often results due to large contact resistance between the CNTs and the metallic current collectors or between the CNTs and their ceramic coatings. While contact resistance measurements are regularly carried out on individually contacted CNTs, contact resistance measurements on vertically aligned (VA) CNT arrays are not routine. Here, we demonstrate that two-probe electrical current–voltage measurements and electrochemical impedance spectroscopy can be used to probe the end contact resistance and side contact resistances of coated and uncoated VACNT arrays in order to optimize material deposition and selection.


Introduction
With highly directional transport and a large graphitic surface area for functionalization, vertically aligned carbon nanotube (CNT) arrays have outstanding electrical and physical properties 1-3 for a number of different types of devices. 4 For instance, it has been predicted that a densely packed forest of vertically aligned CNTs (VACNTs) could outperform Cu as microelectronic interconnects. 5 CNTs decorated with conductive polymers or inorganic oxides have applications in electrochemical devices such as supercapacitors, 6,7 dye-sensitized solar cells, 8 and water splitting cells. 9 Used as a conductive additive, CNTs help lower electrode resistance to enhance capacitive deionization performance for salt water desalination, 10 or increase the rate performance and cyclability in lithium-ion batteries. 11 Given the low bulk resistance of the CNTs, the contact resistance they form at the interface with charge collectors or surface coatings play a critical role in the overall device performance.
In order to minimize ohmic losses, it is necessary for the CNTs to be electrically connected with minimal resistance to the charge collectors and for coatings to be electrically connected with minimal resistance to the CNTs. Although a theoretical quantum contact resistance of a single-walled carbon nanotube (SWCNT) is $6.45 kU, 12 experimentally measured contact resistances span many orders of magnitude. 13,14 For multiwalled CNTs (MWCNTs), contact resistance variations can be even greater. For example, a MWCNT ($100 nm in diameter) semi-spherically coated with Ti/Au over a large contact area, contact resistance (R c ) has been reported to be 1.56 kU. 15 However, a resistance value of $1 GU has been reported for the case where the tube is placed directly on small, pre-deposited Au nger electrodes without any further treatment. 16 Reasons for these large discrepancies (in addition to differences in the CNTs themselves) include differences in contact area and conguration (side-or end contact), physio-chemical parameters of the contact (e.g., work function and wettability), 17 and the type of interfacial contact (e.g., quantum mechanical tunneling [18][19][20] vs. classical Schottky junction 21,22 ).
Most reports [13][14][15][16][23][24][25][26][27][28][29][30] measure the R c of a suspended CNT, which involves use of advanced nanofabrication and characterization such as in situ transmission electron microscopy (TEM) or conductive atomic force microscopy (AFM). Although quite precise, these methods are usually costly and timeconsuming. On a device scale, the ensemble-averaged, endcontact resistance per nanotube can be obtained from a polished VACNT forest less than a micrometer in height. 17,31,32 This approach loses accuracy the taller the CNT forest (tall CNT forests offer higher mass loading in electrochemical devices 33 ) because their lengths become the more heterogeneous. 34,35 Here, we establish characterization methods for both sideand end-contact resistances of VACNT forests (Fig. 1). We show that two-probe electrical measurements can be used to determine contact resistances between the end of the CNTs and the current collector. It is further possible to determine the effective spacing between the metallic current collector and the CNTs, which relates to the electronic structure of the substrate and the wetting of the metal and the CNTs. To determine side contact resistances between a coating and a CNT sample, we show that electrochemical techniques (cyclic voltammetry and electrochemical impedance spectroscopy) enable the decoupling of impedance contributions from different origins. Combined with knowledge of the average length and number of CNTs in the array, the resistivity of the coating itself can also be determined.

Material synthesis
To grow a VACNT array, a catalyst layer consisting of a (nominal) 3 nm-thick Fe layer atop a 20 nm-thick Al barrier lm was deposited via e-beam evaporation on Si chips (0.5 mm in thickness) or on Ni foils (Alfa Aesar, 99% metal basis, 0.025 mm in thickness). Prior to the catalyst deposition, the Ni foil surface was physically etched away with mild Ar + beam milling in order to remove contaminants. The catalyst samples were loaded into a quartz tube furnace, heated up to 750 C at 30 C min À1 at ambient pressure with a ow of 600 sccm of H 2 and 400 sccm of Ar, and annealing for 20 min at these conditions. Aer annealing, C 2 H 4 (250 sccm) was added to the gas ambient to grow VACNT forests. TiO 2 was coated on the as-grown VACNTs via plasma-enhanced atomic layer deposition (ALD) at 120 C in an Oxford Instrument AL1 FlexAL system. Each cycle consisted of a 1.5 s dose (at 200 sccm) of Tetrakis(dimethylamino)titanium as a Ti precursor and a 10 s dose (at 20 sccm) of ozone plasma as an oxygen source.

VACNT transplantation
VACNT transplantation was done via a poly(methyl methacrylate) (PMMA) assisted stamping procedure described previously. 8 The as-grown CNT samples were pressed into a coating ($1 mm in thickness) of PMMA on different conductive substrates, i.e. FTO glass, W coated glass or Ni foil, before curing and peeling off. The PMMA layer was then pyrolized by annealing in 900 sccm H 2 /100 sccm Ar at 400 C for 2 h. The pyrolysis process removes most of the PMMA, 36 and thus does not interfere with the electrical or weight measurements. The transferred CNTs were weighed on a new substrate with a Mettler Toledo XP2U ultra-micro balance (1 mg in resolution) before and aer transplantation.

Characterizations
The height and alignment of the VACNTs were characterized using scanning electron microscopes (SEM, FEI Nova 450 and Hitachi SU 8200). TEM was used to obtain CNT diameter statistics (Philips CM12). Catalyst particle density was probed with a Bruker Fastscan AFM. The as-grown CNT quality and the phase information of the as-deposited TiO 2 layer were determined by use of a Renishaw InVia Raman spectroscope (785 nm excitation) and NTMDT NTEGRA Raman spectroscope (571 nm excitation).

VACNTs characterization
To perform macroscopic measurement on a VACNT array and then extract information about the average properties of individual tubes, we rst need to know the properties of the CNTs, including their areal number density (n CNT ), length (l), and linear resistivity (r 00 ). Literature has shown that the linear resistivity relies heavily on the CNT quality, such as wall number (n), diameter and defect density, 37,38 and is usually described by a charge mean-free-path theory. 14,39 Fig. 2 provides information about the VACNT forests investigated in this work. As can be seen from Fig. 2c and d, the VACNTs near the top of the forest are more aligned, while they are less dense and more entangled near the bottom, consistent with a density decay regime. 40,41 Aer transplantation (where the "top" and "bottom" end of the CNTs are reversed), both the forest height (L) and alignment are well preserved with minimal bending at the top likely caused by decreased CNT number density or small pressures applied during the transfer process. Statistics over 300 tubes grown in different batches reveal that the MWCNTs possess an average outer diameter (d out ) of 10.2 AE 0.42 nm and inner diameter (d in ) of 6.0 AE 0.47 nm (more details can be found in Fig. S1 †). With $0.34 nm as the interlayer spacing between CNT walls, 42 an averaged n of each CNT is estimated as $6. Raman spectra at the top and bottom of a CNT forest are similar with unchanged Raman D-to-G intensity ratio ($1.35) along the thickness, suggesting an invariant defect density as well as r 00 along the CNTs. 37 We note that the bottom end switches with the top aer transplantation. Regardless of the growth time (t) or forest height, CNTs remain of similar characteristics in terms of tube diameter and quality (information about VACNTs of other thicknesses can be found in Fig. S1 †).
Counting the number of CNTs from cross-sectional SEM images alone may not provide an accurate effective n CNT because an SEM of a porous structure like a CNT forest contains depth information. A more accurate and reliable way is the weight-gain method, 43 which allows us to describe n CNT and model its dependency on L. Assuming the tube growth is self-terminated 44 with a catalyst deactivation probability constant a, one can relate areal density n CNT to growth time t: Neglecting the initial CNT self-organization period, n CNT roughly equals to the catalyst number density (N 0 ¼ 4 Â 10 10 cm À2 from AFM data, Fig. S2 †) at t ¼ 0. Integration over eqn (1) gives: The mass of the entire VACNT forest (M) over area (A) can then be written as the summation of all the nanotubes grown until t: In this equation, m (in g) and l (in nm) are the mass and length of an individual tube at t. To proceed, two maneuvers can be applied. One is to set l ¼ vt, where v is the steady-state growth rate of the VACNT forest (10 mm min À1 in this study). Another is to consider the specic surface area of a MWCNT referring to the literature 43 (eqn (4)), where D is the aggregate diameter of all the carbon walls summed up (53 AE 2.5 nm from our TEM analysis): Combining eqn (1)-(4) and replacing the nal t with L/v, we nally reach: Fitting Fig. 2h with eqn (5) (black line) yields a ¼ 0.40 min À1 . Plugging this value to eqn (2), we can see that n CNT drops by a factor of $20 when L becomes longer than $80 mm. The relatively short length (submillimeter) and low density (O(#10 10 ) cm À2 ) agree with previous ndings in the literature that the growth of the VACNT forest is limited by catalyst poisoning. 45 Extrapolation of eqn (5) predicts saturation of the CNT forest growth if L exceeds 150 mm (M/A reaching a plateau, and entering the termination stage 40 ), which is in good agreement with our experimental data.

Measuring end contact resistance of VACNTs
To determine the end contact resistance, we use the two-probe electrical current-voltage measurements shown in Fig. 3a. The measurements are carried out with a probe station (Cascade) connected to a semiconductor device analyzer (Agilent B1500A). A pair of W probes (19 mm in diameter, giving A probe ¼ 2.83 Â 10 À6 cm 2 ) is aligned horizontally with a separation distance of $100-200 mm and then carefully placed atop the CNT forest (approaching in 2 mm steps) to make direct electrical contact. Measurements are repeated at a minimum of 6 distinct positions on each sample.
When using this setup, electrons are injected from one W probe into multiple CNTs (about $ 10 4 ) in parallel. CNTs much shorter than the average are not probed. As reported previously, 32 the lateral resistance between CNTs in the VACNT forest is large enough to neglect. Most injected electrons thus travel across the bottom conductive substrate and exit from CNTs that contact another probe (Fig. 3b). Therefore, one can write the resistance (R) per individual CNT as: R c,tip-CNT and R c,CNT-sub represent the contact resistances between the W tip and a CNT and between a CNT and the bottom substrate, respectively. The rst term ideally remains a constant, and the latter depends solely on the nature of the interface between the CNT end and substrate. The sum of these two terms renders total contact resistance, R c . Fig. 3c-e shows the I-V curves of as-transplanted VACNTs on various substrates. For any given VACNT height and bottom contact, a linear I-V curve is observed so R tot is the inverse slope. Plotting R tot vs. the VACNT height shows a non-linear behavior (Fig. 3f). As discussed previously, while CNT quality (mainly r 00 and n) does not vary over l or L, n CNT changes signicantly. Therefore, to extract the contact resistance R c , we combine eqn (2) and (6): and t this to the data in Fig. 3f. The tting results (Table 1) indicate a r 00 ($1.15 MU mm À1 ) and a that are invariant with substrate material. This highlights the reliability of the t since r 00 and a should indeed be intrinsic properties of the CNTs. The tted values of a match reasonably well with the one from our modied weight-gain approach. At a small electric eld, it is very unlikely that optical phonons and zone-boundary phonons play any signicant role in electron transport, 39 and therefore r 00 is dominated by acoustic phonons from scattering at the defects. The r 00 value of our MWCNTs is higher than the values measured by dipping a freestanding nanotube into liquid metals 2,25,48 (200 U mm À1 ) or in a FET conguration (41 kU mm À1 ), 49 but it is quite close to the values measured where the tube is curved by an AFM tip (1.93 MU mm À1 ) 50 or under direct probing (1.39 MU mm À1 ). 51 This nding suggests that in addition to the CNT quality, r 00 might also be sensitive to slight bending (Fig. 2b). In fact, theoretical modelling has shown that the resistance of CNT under mechanical deformation can change. 52 However, R c varies by orders of magnitudes for the different substrates (Ni, W, and FTO). On Ni, the contact resistance is the lowest with R c ¼ 0.4 MU. Metals with unlled d-orbitals (Ni has   17 In such a case, the weak bonding is partially van der Waals in nature and can be thought of as an average bonding length (or vacuum gap) of s (in A) through which electron tunneling occurs. 19 At small electrical bias (in our case V # 0.1 V), Simmons 55 has derived eqn (8) for electron tunneling between two dissimilar electrodes, in which 4 (in eV) is the averaged work function, and J the current density (in A cm À2 ): Here, J is linearly proportional to V. Given the end-contact area of an individual CNT (A CNT $ 5 Â 10 À13 cm 2 ), one can rearrange eqn (8) into (9): Since both 4 and s appear in the exponent, the resistance can differ substantially by the choice of metal leads, consistent with our ndings (Table 1). Fitting by eqn (9) gives a tunneling gap of $3.7Å in W and $5.9Å in FTO. In Fig. S3, † we see that astransplanted CNTs on the FTO substrate detach easily aer soaking into water, in contrast to their stability on Ni. This observation supports the fact that CNT bond less strongly to FTO. In short, in order to minimize R c , it is crucial to have good wetting and to shorten the tunneling gap spacing with metals such as Ti, 15,26,56,57 Ni, 49,58 and Pd. 30

Measuring side contact resistance of coated VACNTs
To probe the side-contact resistance between a CNT and a coating, we propose electrochemical characterization. We are faced with the geometry shown in Fig. 4a and wish to extract the interface resistance R i and normalize it with the areal coverage of the coating A coat to obtain the 2D resistance R 2D . To do so, we use electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV). By performing these measurements on a series of coated VACNT samples, where the thickness of the coating varies, we are also able to extract the resistance of the coated layer, R s , and its resistivity, r coating .
To carry out the electrochemical characterization, we use the setup sketched in Fig. 4b. The working electrode consists of either coated or uncoated VACNT samples, which are grown on Ni foil. The samples are partially taped with Kapton, leaving an effective area (A electrode ) of approximately 0.8 cm Â 0.8 cm exposed (see Fig. 1a). This working electrode (WE) is immersed in 1 M Na 2 SO 4 aqueous electrolyte with Pt and Ag/AgCl as counter (CE) and reference electrodes (RE), respectively. We use an electrochemical workstation (CH Instruments, CHI 660E). All measurements are conducted at room temperature.
To demonstrate our approach, we perform electrochemical characterization on three VACNT samples, coated with different thickness layers of TiO 2 (35, 50 and 75 cycles) using atomic layer deposition (ALD). The EIS data is acquired at open circuit potential with an oscillation amplitude of 5 mV and shown in Fig. 4c. Previous work has shown that this ALD-based, TiO 2 coating bonds covalently onto the MWCNT exterior (L z 100 mm over d out z 10 nm) and forms a side contact as shown schematically in Fig. 4a. 59,60 In the rst 20 ALD cycles, it is seen that the TiO 2 coating grows at a slower rate than at a later stage, which likely comes from inhomogeneous nucleation and growth (Fig. S4 †). Therefore, for the relative low numbers of ALD cycles here, we assume that we will not have complete coverage of the TiO 2 coating, and include a leakage capacitance C l (associated with ion adsorption directly onto and off of the CNTs) in the equivalent circuit model used to t the EIS data (inset of Fig. 4c).
We note that this equivalent circuit model is similar to that of a ref. 61 for a suspended SWCNT coated with MnO 2 . We assume that the resistance of the CNT is negligible and that we do not observe strong ionic diffusion limitations within the electrolyte (Fig. S5 †). In addition to the leakage capacitance C l , the other parameters in the equivalent circuit model include: the series resistance of the electrode and electrolyte, R 0 ; the leakage resistance to the Ni foil substrate, R l ; the electrical resistance of the TiO 2 , R s ; the surface capacitance of the TiO 2 coating C s (associated with ion adsorption directly onto and off of the TiO 2 ); the bulk faradaic contribution Q (with non-ideality factor n close to 1), and the Warburg diffusion resistance, W (associated with ionic diffusion into the TiO 2 ); and nally, the key parameter of interest, the interfacial resistance between the CNT and TiO 2 coating, R i .
Values for all ts are provided and trends with number of ALD layers are discussed in the ESI. † To further conrm that the values extracted from the equivalent circuit model tting to EIS are sensible, we show in Fig. 4d that the sum of all the capacitances (C l , C s , and Q) extracted from the equivalent circuit model tting to EIS are within 8% of the values of the capacitance C extracted from CV measurements (at 100 mV s À1 scanning rate) on the three coated VACNT samples within a 0-0.8 V voltage window.
To determine the 2D interfacial contact resistance R 2D from the interfacial resistance R i , we need to know how much of the CNT surface is coated (A coat ): We use the CV scan to quantify the surface coverage of the coating A coat . The ratio of the leakage capacitance of the coated-VACNTs (extracted from the EIS measurements) to the capacitance of the uncoated-VACNTs (measured with CV to be C 0 z 2.47 mF) enables us to quantify the surface coverage of the coating A coat using the expression: where the total side surface area (A 0 z 5.2 Â 10 2 cm 2 ) is known from n CNT z 3 Â 10 10 cm À2 and the weight-gain method. The area of TiO 2 coating (A coat ) increases with the number of ALD cycles; however, even aer 75 ALD cycles of ALD, surface coverage is only $82%. The normalized 2-dimensional contact resistance (R 2D ) can be dened by normalizing R i with the total contact area (eqn (10)). We nd a thickness independent R 2D of $85 U cm 2 (Fig. 4e). Such a value is orders-of-magnitude greater than the typical contact resistance between metal (such as Ni) and graphene 62 (similar to unfolded SWCNT surface) as 5 Â 10 À6 U cm 2 , which suggests a possible Schottky barrier at the interface between the CNT and the TiO 2 . Additionally, we show that the resistivity of the coating, r TiO 2 , can be obtained from R s , extracted from the EIS tting. This value is important to know because of the type and quality (i.e., crystal phase and morphology) of the coating grown on a high aspect ratio may differ from that grown using the same conditions on a at 2D substrate. Indeed, here, we show from Raman spectroscopy, that the asdeposited TiO 2 is a mixture of anatase and rutile phases (Fig. S4e †). We take the coated CNT to be analogous to a coaxial cable (eqn (12)), where the resistivity of the coating layer takes the form: with the term in the latter bracket accounting for an effective number of coated CNTs. With the length (L) and diameter of TiO 2 coated CNT (d TiO 2 ) obtained from SEM (Fig. S4 †), and n CNT determined via the weight-gain method, we nd r TiO 2 from the slope of normalized R s vs. ln(d TiO 2 /d out ) plotted in Fig. 4e to be 2.6 Â 10 10 U cm. The value is of the same order of magnitude as an anatase TiO 2 thin lm calcined at 600 C in air (10 10 to 8 Â 10 10 U cm). 63 In contrast a thin lm with oxygen vacancies (e.g., that has undergone hydrogen doping 64 or thermal annealing in vacuum) is less resistive with 10 À2 to 10 1 U cm, independent of whether it is rutile or anatase phase. 65 This hints that the TiO 2 coating prepared by our ALD process likely has high crystallinity and few defects.

Conclusion
In order to systematically design lower resistance electrical and electrochemical devices using CNTs, we present approaches to measure the end contact resistance of CNTs in a VACNT array and the side contact resistances of ceramic coated CNTs in a VACNT array. These approaches can be performed on asfabricated VACNT arrays or also on arrays that have been transplanted to different substrates. The approaches enable us to determine additional information such as the tunnel distance between the CNTs and the substrate as well as the quality of the coating (i.e., its resistivity). Our study highlights that contact resistances depend on the contact quality, which will be determined by the electronic structure of the substrate or coating material and its wettability with carbon (dening the tunneling barrier). While it is widely known that low-resistance end contacts are found between CNTs and metallic catalysts 17,32,34,35,51,[66][67][68][69] (e.g., a bond as strong as 7.6 eV per bond could be formed between Co catalyst and SWCNT 70 ), our results show that transplantation of CNTs (e.g., on Ni at 400 C) can still enable low resistively end contacts much below the typical CVD temperature (750 C). These ndings highlight that VACNT arrays can be transferred to substrates and devices on which direct CVD growth of the CNTs is not possible (e.g. exible substrates, glass) such that their good electrical properties are maintained. However, even a substrate or coating that itself has high quality (e.g., our ALDcoated TiO 2 exhibits a low number of defects) may exhibit high contact resistance with the CNTs due, for example, to suboptimal wetting.

Conflicts of interests
There are no conicts to declare.