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Combinatorial Evaluation for Field Emission Properties of Carbon Nanotubes Part II: High Growth Rate System Yosuke Shiratori*,† and Suguru Noda†,‡ Department of Chemical System Engineering, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan ReceiVed: April 15, 2010; ReVised Manuscript ReceiVed: June 21, 2010
Carbon nanotube (CNT) emitters are of interest for inclusion in cold cathodes and field emission displays. CNT field electron emitters self-organized on substrates with an Fe/Al2O3 catalytic/supporting layer, which accelerates CNT growth, are characterized using combinatorial libraries. A variety of morphologies are formed on single substrates by C2H2 thermal chemical vapor deposition for 10 s at ambient pressure. Degradation of field emission decreases upon prolonged operation. Raman signals from thinner single-walled CNTs predominantly degrade during operation. Controlling the number of protruding thin CNTs is crucial to extracting current and ensuring sustainability. Thin CNTs protruding from CNT ensembles formed on a substrate with a multimodal distribution of catalyst particles show good field emission (FE) properties with practical sustainability. A potential design for self-organized thin CNTs fabricated by the current process is discussed on the basis of the combinatorial evaluation for field emission and 3D electric field simulations. 1. Introduction Carbon nanotubes (CNTs) are high value-added elements, for example, to be incorporated as cold cathodes in lighting devices and field emission displays (FEDs), including flat panel displays and battery-powered character displays.1,2 Notable attempts to implement single- and multiwalled carbon nanotubes (SWCNTs and MWCNTs) in triode-type microcathodes3-6 have been reported, and the potential of color-SWCNT-3 and -MWCNTFEDs6 was noted in the early 2000s. We have been optimizing growth conditions such as feedstock species and composition, thicknesses of catalyst/supporting materials, reaction temperature, and pressure and time in thermal chemical vapor deposition (CVD) processes for device applications.7-11 Recently, a very low driving voltage for a CNT cold cathode, a current density contrast of 1:10 000 at a driving voltage of 9 V, was demonstrated by our original triode-type 1D arrays of CNT emitters.9 Self-organization of CNTs with small diameters such as SWCNTs, double-walled carbon nanotubes (DWCNTs), and thin-walled CNTs (TWCNTs) is a process potentially capable of producing (1) a large number of emitters simultaneously with (2) a field enhancement factor that is high enough for practical uses. The optimal balance of these two parameters can be investigated by using libraries of CNTs that are prepared by the combinatorial masked deposition (CMD) of a catalyst material. This allows the reproduction of a large number of significant catalyst compositions on a single substrate12 and subsequent temperature-, gas pressure-, and reaction time-tuned thermal CVD. The universal application of CNT emitters and the use of soft-electron beam sourced from these emitters are limited by the following issues: (1) the scale-up problems with CVD reactors, (2) glass tolerability in CVD processes, (3) throughput * To whom correspondence should be addressed. E-mail: y-shiratori@ chemsys.t.u-tokyo.ac.jp. Phone: +81-3-5841-7330. Fax: +81-3-5841-7332. † The Univeristy of Tokyo. ‡ PRESTO.
(direct and rapid implementation without post-treatments), (4) practical field emission (FE) properties, and (5) controllability of emitter morphologies. The synthesis of micrometer-tall CNTs in one second through pulse-current C2H2-CVD under ambient pressure,10 and the fabrication/evaluation of line-patterned triodetype emitter arrays showing efficient FE9 provides prospects for addressing issues 1-4. CMD of catalysts11 and FE evaluation of the obtained CNT libraries8 accelerate the search for CNT types (SWCNTs or MWCNTs) and morphologies with the number densities of emitters desired for end uses. This approach augments 5 controllability of emitter morphologies (sharpness, height, interspace). Here, we demonstrate the self-organization of CNT emitters and investigate their FE properties by using combinatorial CNTlibraries with an Fe/Al2O3 catalytic/supporting layer, which promotes growth of CNTs.13 Control over emitter formation using this route is discussed on the basis of the physicochemical and practical perspectives built up through the studies on growth mechanisms13-16 and device fabrication.7-10 A variety of CNTs are formed on two different single substrates with a uniform cathode surface and with line-patterned growth areas, respectively. The effects of CNT types and morphologies and a macroscopic texturing on FE properties are efficiently studied. The insights obtained in the present study will contribute to extracting growth conditions that allow a short CVD time and that will expand the FE properties with sufficient sustainability of the fabricated cold cathodes leading to the development of practicable devices for end uses. 2. Experimental Methods Two types of combinatorial catalyst libraries (Figure 1) were prepared not only to form a variety of CNT morphologies but also to show the effect of a macroscopic texturing of cathodes. The first (Figure 1a) is a simple library that was built on an Al2O3(15 nm)/p-type Si substrate with a thickness gradient of Fe (20-0.2 nm). After the top Si layer was washed with hydrofluoric acid, an Al2O3 supporting layer (15 nm) was
10.1021/jp103378c 2010 American Chemical Society Published on Web 07/12/2010
Field Emission Properties of Carbon Nanotubes II
Figure 1. Illustrations of combinatorial catalyst libraries with an exponential thickness profile of Fe: (a) Library 1 and (b) Library 2. x is the distance from the position at the substrate level just below the CMD slit.
deposited on the substrate using conventional radio frequency (RF)-magnetron sputtering. A catalyst library was then formed by CMD11,12 with an Fe layer with an exponential thickness profile (Library 1). The second library (Figure 1b) contains linepatterned Al2O3 layers on Mo(30 nm)/SiO2. A resist layer coated on the Mo layer (30 nm) was exposed to UV light through a photomask containing microwindows (2 µm width, 50 µm pitch, and 10 mm × 12 mm patterned area). An Al2O3 layer was deposited next on the developed substrate. After lifting off the Al2O3 layer on the resist layer, an Fe layer with an exponential thickness profile was subsequently formed on the substrate by CMD (Library 2). The catalyst layer on the supporting layer was reduced by heating the sample up to 800 °C under H2 (5 vol%)/Ar gas flow at ambient pressure. The reduced combinatorial catalyst libraries were finally processed at 800 °C and ambient pressure for 10 s by introducing C2H2 (3.6 vol%)/H2 (6.6 vol%)/Ar (balance) into the hot-wall CVD chamber. Linepatterned samples with uniform nominal Fe thicknesses (5, 1, and 0.3 nm) were also prepared using the above-mentioned patterning procedure and without using CMD. The surfaces of the obtained samples were observed using a Hitachi S-4700 FE scanning electron microscope (SEM). The quality of the CNTs at the molecular level was evaluated on the basis of Raman scattering profiles recorded by a HORIBA Jobin Yvon LabRAM HR-800 spectrometer equipped with a Synapse CCD system using a backscattering configuration. The prepared CNTs were excited with a MELLES GRIOT 543 Ar+ laser (488.0 nm radiation) focused by an OLYMPUS BX41 microscope unit equipped with a 100× objective with a numerical aperture of 0.90. FE currents extracted from the obtained CNTs were measured at about 1 × 10-5 Pa under a diode configuration. The p-type Si or Mo layer beneath the Al2O3 layer was grounded. An Al2O3 layer with a nominal thickness of 15 nm is still conductive in a vertical direction and works as a resistant layer to stabilize FE operation. Indium tin oxide (ITO) glass and 150 µm thick glass slides were used as an anode and as spacers, respectively. DC voltages (to obtain current-voltage (I-V) curves) or pulsed voltages (in the case of cathode luminescence tests: 100 Hz, 1/2 duty) applied to the anode (Va) were swept by a KEITHLEY 2410 high-voltage source meter, which is simultaneously an ammeter. Phosphor layers on ITO/glass substrates were prepared by screen-printing ZnO:Zn powders on the anodes. 3D electric field analysis based on the integral element method was executed around the CNT emitters using the ELFIN software package and an ELF/EGmap PrePost processor (ELF Co., Osaka).
J. Phys. Chem. C, Vol. 114, No. 30, 2010 12939 3. Results and Discussion 3.1. Characterization and FE Evaluation of CNT Libraries. Growth of CNTs is accelerated by using an Fe/Al2O3 layer as a catalyst/supporting layer.11,13,14 A CVD time of 1 s or less is not only tolerated by glass10 but also assures the quality of the CNTs.16 Two types of combinatorial libraries were prepared as described in section 2. Figure 2 shows the characteristics of the CNTs in Library 1. The morphology of the CNTs (Figure 2b) is random and spaghetti-like except for the vertically aligned (VA) CNTs at x ) 7.5 mm corresponding to an Fe thickness (tFe) of 1.0 nm. The CNTs at x ) 3.5 mm (tFe ) 4.6 nm) exist sparsely because of the multimodal catalyst distribution including active and inactive catalysts.8 CNTs were not observed at x > 10.5 mm (tFe < 0.4 nm). Raman spectra recorded at the specific positions in Library 1 are shown in Figure 2c. According to essential contributions about the Raman spectroscopy of CNTs,17 radial breathing modes (RBMs) at low wavenumber are assigned to symmetric in-phase displacements of carbon atoms in SWCNTs in the radial direction. Strong peaks at around 1600 cm-1 are the so-called G bands, which are assigned to the tangential phonons appearing in Raman spectra of graphite. A weak band at around 1350 cm-1 is a disorder-induced feature, called the D band, which is observed when there is a symmetry-breaking perturbation on the hexagonal sp2 bonded lattices of graphite and CNTs. Raman scattering profiles with an intensity ratio of the G band to the D band (G/D ratio) of over 10, splitting of the G band, and RBMs recorded for the CNTs in Library 1 (Figure 2c) indicate the presence of SWCNTs. The CNTs at x ) 3.5 mm consist of CNTs with small and large tube diameters (Figure 2b left). We will use the terms “thin” and “thick” CNTs for CNTs with small and large tube diameters, respectively. Because the intensity of resonant Raman scattering peaks assigned to SWCNTs is much larger than the intensity from MWCNTs, the obtained scattering profile is SWCNT-type (Figure 2c left). According to the appearance of a sharp intense RBM at 170 cm-1 (Figure 2c right), the sparse growth of CNTs at x ) 9.5 mm (tFe ) 0.5 nm) may originate from a unimodal distribution of the catalytic particles. Results of combinatorial FE evaluation at Va of 450 and 600 V are shown in Figure 2d. The area at x > 10 mm (tFe < 0.4 nm) without CNTs does not show any emission. At x ) 7.5 mm (tFe ) 1.0 nm) with VACNTs, a narrow dark area is found. This result may be caused by field screening effect because of the VA morphology combined with dense packing of the CNTs. Another dark area is shown at x < 2.5 mm (tFe > 7.3 nm) of which MWCNTs are a major component. In Library 1, the FE is highest at x ) 5.5 mm (tFe ) 2.0 nm). Highly protruding CNTs (Figure 2b second from left) effectively concentrate the electric field. Figure 3 shows the characteristics of Library 2. CNTs grow selectively on the lines (Figure 3b). Even at x ) 12.5 mm (tFe ) 0.2 nm), randomly oriented grass-type SWCNTs are formed. Because the CNT-grown area is limited to the lines, effective incorporation of carbon during CVD is confined to the microlines. Such localized incorporation may modulate the incorporation-precipitation balance of carbon in the nonpatterned sample with the Al2O3 layer covering the whole substrate surface (Library 1). Line width/pitch- and reaction time-tuned experiments are in progress. The active emission area of Library 2 (Figure 3d) is wider than that of Library 1 (Figure 2d), which is consistent with a wider growth range in Library 2. Library 2 is visually brighter than Library 1 because of the increased field enhancement introduced by the line-patterned macroscopic structure. The most active area occurs around x ) 5.5 mm,
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Figure 2. (a) Photograph of Library 1 showing the nominal Fe thickness (tFe) profile, (b) SEM images of the top surfaces and cross sections of the substrates, (c) Raman spectra in the regions of RBM and D and G bands recorded for the representative positions in Library 1, and (d) results of combinatorial FE evaluation. x is the distance from the position at the substrate level just below the CMD slit. Photographic images of luminescence from the rear surface of the anode at Va of 450 and 600 V are superimposed with a photograph of Library 1 and an exponential profile of the nominal Fe thickness (tFe) as a function of the distance from the CMD slit (x).
where emitters protrude from the matrix of randomly entangled thick CNTs as observed for Library 1. A dark area at x < 2.5 mm in Library 1 (Figure 2d right) shifts to x < 3.5 mm in Library 2 (Figure 3d right) corresponding to the finding that the Raman scattering profile of CNTs at x ) 3.5 mm (tFe ) 4.6 nm) in Library 2 (Figure 3c left) is more MWCNT-like than that recorded at the same position in Library 1 (Figure 2c left). 3.2. Prolonged FE Operation and the Transformation of CNT Characteristics. Figure 4 shows the evolution of (a) the applied electric field to maintain the FE currents at the time of onset (t ) 0 min) and luminescence images from the rear surface of the anode obtained over time for (b) Library 1 and (c) Library 2. Initial FE current densities (J) of 74 µA/cm2 (Library 1) and 69 µA/cm2 (Library 2) at 4.3 V/µm were maintained over the total operation time (420 min). The J standardized by the line area in Library 2 is 1.4 mA/cm2 [69 [µA/cm2] × (50 [µm]/2.5 [µm])]. Bright spots in Library 1 at t ) 0 min gradually diminish, and the brightness spreads out in the first 120 min (Figure 4b). Plausible morphological changes during FE are (1) shortening
of highly protrusive emitters because of current-induced evaporation18,19 and (2) raising of entangled CNTs by the applied electric field.19 Increasing the applied field to give a constant FE current indicates that there is a decrease in the field enhancement or number of emission sites. Even after the applied field stabilizes at 330 min (Figure 4a), delocalization of the emission sites still proceeds (Figure 4b). In Library 2, the applied field and distribution of bright spots do not stabilize during the measurement period (Figure 4a, c). As already described, the J standardized by the CNT grown area in Library 2 is 20 times as large as that in Library 1. Therefore, both phenomena 1 and 2 will occur more intensively with increasing the applied field. Modulation of cathode luminescence occurs at every area with an SWCNT-type Raman profile even for those with different types of morphologies (2.5 mm < x < 10.5 mm for Library 1 and 3.5 mm < x < 13.5 mm for Library 2). Characteristics of CNTs before and after FE operation at the specific x positions in Library 1 and Library 2 are shown in Figures 5 and 6, respectively. At x ) 3.5 mm in Library 1 (Figure 5a left), thin and thick CNTs are mixed, and therefore,
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Figure 3. (a) Photograph of Library 2 showing the nominal Fe thickness (tFe) profile, (b) SEM images of the top surfaces (at low magnification to demonstrate the line shape and at high magnification to show the CNTs) and cross sections of the substrates, (c) Raman spectra in the regions of RBM and D and G bands recorded for the representative positions in Library 2, and (d) results of combinatorial FE evaluation. x is the distance from the position at the substrate level just below the CMD slit. Photographic images of luminescence from the rear surface of the anode at Va of 450 and 600 V are superimposed with a photograph of Library 2 and an exponential profile of the nominal Fe thickness (tFe) as a function of the distance from the CMD slit (x).
an SWCNT-type Raman scattering profile (Figure 5a right) appears. After the operation for 420 min, the thick CNTs are not raised but thin CNTs tend to protrude (see inset of Figure 5a middle). In the Raman spectra, RBMs disappear and the G/D ratio declines after FE (Figure 5a right). The applied electric field effectively concentrates on the highly protruding as-grown SWCNTs, and they may be degraded by current-induced evaporation.18,19 At the same position in Library 2 (Figure 6a left), thin CNTs protruding from the matrix of thin CNTs could not be seen. However, according to the Raman spectrum with RBMs for the as-grown sample, thin CNTs exist, but their number is less than in the case of Library 1 (Figure 5a left). Many of the thin CNTs may be buried and entangled in CNT ensembles resulting in a smaller G/D ratio (Figure 6a right) than at the same position in Library 1 (Figure 5a right). After FE operation for 420 min, the RBMs disappear and the G/D ratio decreases. Nanosized particles are observed on the surface of the thick CNTs after operation (see inset of Figure 6a middle). Because the FE current per single emitter is much larger than in Library 1, a current induced transformation of the emitter surface is likely.
At x ) 5.5 and 7.5 mm, raised CNTs are found in both libraries after FE operation (Figures 5b, c and 6b, c). RBMs at around 250 cm-1 disappear after operation. This result suggests that the thinner SWCNTs are selectively degraded during FE. As shown in the insets of Figure 5c (middle) and 6c (middle), protruding emitters do not disappear after operation (even in Library 2, which has a larger FE current per single emitter than that in Library 1), but nanoparticles attach on their surfaces. Deterioration of the G/D ratio is pronounced at x ) 5.5 mm (Figures 5b, 6b right), which gives the brightest cathode luminescence. At x ) 9.5 mm (Figure 5d) and x ) 12.5 mm (Figure 6d) in Library 1 and Library 2, respectively, stand-alone bundles tend to disappear during FE. The tendencies for the RBMs assigned to thinner SWCNTs to decrease and the G/D ratio to deteriorate are also found. 3.3. Individual Uniform Emitters. Figure 7 shows (a) SEM micrographs of CNTs (samples A-C) prepared on the substrates with an Fe (5, 1, and 0.3 nm)/Al2O3 (15 nm, line-patterned) layer on Mo (30 nm) and (b) Raman spectra recorded for these samples (solid line) and Library 2 at the same tFe (dotted line). The Raman scattering profiles of the individual samples and
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Shiratori and Noda operation. For samples A-C, J is defined as the current divided by the area of the anode (not by the area containing CNTs on the lines). According to the F-N theory for electron emission from a metal surface at an applied voltage V, the current I(A) is given by
I)
{
1.54 × 10-6(Elocal)2S 6.83 × 107φ1.5 exp φ Elocal
}
(1)
where Elocal is a local field at an emission site given in V cm-1, S is the effective emission area in cm2 and φ is the work function of an emitter material in eV.20 We assume that the φ of the CNTs is 5 eV, which is a typical value for graphite.21 The field enhancement factor β (in cm-1) is defined in terms of Elocal ) βV. The equation 1 is transformed into
ln(I/V2) ) -
6.83 × 107 × φ1.5 × (1/V) + β 1.54 × 10-6 × Sβ2 ln φ
(
Figure 4. Time evolutions of (a) the applied electric field to maintain FE current densities (J) at t ) 0 min (Library 1: solid line, Library 2: dotted line) and luminescence images from the rear surface of the anode obtained for (b) Library 1 and (c) Library 2.
the corresponding positions in Library 2 agree closely. Randomly entangled thick CNTs containing SWCNTs (A), VACNTs containing SWCNTs (B), and random grass-type SWCNTs with stand-alone bundles (C) are implanted on the substrates with tFe ) 5, 1, and 0.3 nm. Thin CNTs protruding from the matrix of thick CNTs cannot be seen for the line-patterned sample with a uniform tFe ) 5 nm (sample A) as is observed for the thick tFe region in Library 2 (Figure 6a left). However, according to the Raman spectrum of the RBMs of sample A (Figure 7b left), thin CNTs exist in the ensembles of thick CNTs, but these are difficult to detect by SEM observation (Figure 7a left). The field emission characteristics of samples A (black: tFe ) 5 nm), B (red: tFe ) 1 nm), and C (blue: tFe ) 0.3 nm)s(a) current density-electric field (J-E) curves, (b) Fowler-Nordheim (F-N) plots before (closed circles) and after (open circles) prolonged operation, and (c) evolution of the applied electric field to maintain the initial current densities at 4.3 V/µm over timesare shown in Figure 8. The FE characteristics before prolonged operation (pristine characteristics) were obtained after several I-V sweeps of the as-grown samples. Figure 9 shows (a) luminescence images from the rear surface of the anode obtained for samples A-C at t ) 0 and 420 min and (b) Raman spectra before (solid lines) and after (dotted lines) prolonged
)
(2)
Because the coefficient of 1/V and the last term in eq 2 are uniquely determined for each emitter structure, the relationship between 1/V and ln(I/V2) should be linear if the current detected at the anode originates from field electron emission. β values are estimated from the slopes of the plot. The FE parameters obtained before (pristine) and after (aged) prolonged operation of samples A-C are listed in Table 1. The relationships between the pristine FE parameters, βA,pri > βB,pri > βC,pri and SA,pri ≈ SB,pri > SC,pri, were revealed. Samples A and B with protruding CNTs on macroscopic platforms, entangled CNT ensembles (Figure 7a left) and VA-CNT forests (Figure 7a middle), show much better pristine FE properties than sample C with sparsely dispersed protruding bundles from thin grasses of CNTs. In a diode configuration, macroscopic structuring is crucial to penetrate equipotential planes among macrostructures and to enhance local fields at protruding CNTs.7 The efficient FE from CNT-nanohorn hybrids,22 in which nanohorns are platforms of SWCNT emitters, also shows the importance of such cathode texturing. Time evolutions of the electric field applied to maintain the initial current densities at 4.3 V/µm (Figure 8c) show that sample A (black) stabilizes at around 240 min, degradation of the FE for sample B (red) is the most pronounced, and the evolution of sample C (blue) is stepwise increased during operation. Thin CNTs protruding from entangled matrixes of thick CNTs in sample A (Figure 7a left) are more sustainable compared with protruding CNTs on VA-CNT forests in sample B (Figure 7a middle). According to the pristine and aged FE properties (Table 1), β increases for samples A and C and is nearly constant for sample B, and the S values for all of the samples decrease significantly (decrease rate: B ≈ C > A) after prolonged operation. These results also support the degradation of FE particularly for sample B. Outstanding bright spots in the pristine states (t ) 0 min in Figure 9a) originate from locally existing but a large number of highly protruding CNTs after only several I-V sweeps for initial aging applied for the as-grown samples. After prolonged FE operation, such a local outstanding brightness diminishes, but the spots apparently spread out. Taking the S values obtained for the pristine and aged samples (Table 1) and the evolutions of the cathode luminescence together, it is believed that the number of emission sites for the aged
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Figure 5. SEM micrographs and Raman spectra of CNTs at specific x positions in Library 1 before (as-grown) and after FE operation for 420 min. Scale bars in SEM images and insets correspond to 1 µm and 100 nm, respectively.
samples decreases from the pristine states but that active emitters exist with larger intervals in the aged states than in the pristine states. The FE properties of the samples are modulated by (1) line-patterning of emitters preventing the edge emitters from being screened; (2) decreasing the intrinsic β for single emitters because of current-induced shortening, defects, or C-migration; and (3) increase/decrease of β originating from increase/decrease of the interspaces between active emitters in each line (reduction of field screening in each line). It is hard to picture such dynamics from the present experiments; however, texturing of the cathode (line patterns in the present study) prevents the reduction of β even when the microscopic emitter modulations occur at the cathode lines. As described in section 3.2, thin emitters on ensembles of thick CNTs are mechanically more static under electric field compared with emitters on VA-CNT forests and the CNT grasses. Such mobility, which induces repeated raising and damaging of protruding CNTs, will transiently enhance field but will reduce the overall number of emission sites. The uniformity of brightness is poorer for sample
A (Figure 9a left) than for sample B (Figure 9a middle) because the FE of each emission site in sample A is more static. Precise control of CNT growth with uniform morphology over a large area is a plausible way to improve emission homogeneity. Raman spectra recorded for samples A and B before and after prolonged operation (Figure 9b) reveal again that the signals from the thin SWCNTs degrade through FE operation as seen for Libraries 1 and 2 (Figures 5 and 6). Emission sites in sample C are very sparse (Figure 9a right). S is 1 order smaller, but β is comparable with those for samples A and B (Table 1), and it increases after prolonged operation. The number of sites with large FE currents is small initially but increases over time to maintain J. FE-induced degradation of the Raman signals from SWCNTs is less apparent in sample C than in samples A and B (Figure 9b) because the dark area, in which CNTs are not transformed by current, dominates sample C during FE operation. 3.4. Design of SWCNT Cold Cathode. There is concern that the sustainability of SWCNT cold cathodes is not sufficient
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Figure 6. SEM micrographs and Raman spectra of CNTs at specific x positions in Library 2 before (as-grown) and after FE operation for 420 min. Scale bars in SEM images and insets correspond to 1 µm and 100 nm, respectively.
for prolonged operation in lighting devices.23,24 We suggest that one can harness SWCNTs not only if their qualities are guaranteed to be resistant to an FE current of 1 nA per single emitter but also if their morphologies are well-controlled to provide 108 emitters per 1 cm2 (isotropic interspace of emitters: 1 µm).9 According to the combinatorial study in Library 1, an Fe nominal thickness (tFe) over the range 2.0-0.5 nm (5.5 mm < x < 9.5 mm) (see Figure 5b-d) gives interspaces between protruding CNTs of
