Classical topography vs. current map AFM images are displayed in Figure
. They can be simultaneously recorded in c-AFM configuration operating in contact mode. Trench-like CNT arrays are separated via SiO2
as marked in Figure
. When a sample bias of 500 mV is applied, a current flow is generated between the bottom metal line and the metallic tip via the vertically aligned MWCNTs. While a strong signal from the CNT arrays can be identified in the current map, there is no current detected at the SiO2
side. At a first view, the system seems to exhibit a perfect homogeneous conductivity within the MWCNT arrays. However, the observation is misleading since the measured current exceeds the maximum 10 nA detectable with our system.
Topography (left column) vs. current map (right column).
Therefore, the current map is recorded within the saturation regime which can be avoided using much lower sample biases as it will be shown later on. However, at this point, it is sufficient to emphasize a successful electric connectivity of the CNTs to the bottom metal line. High resolution down to single MWCNT is accessible via AFM. The corresponding electric response can be addressed as well, which earns AFM superiority over the classical electric measurements where the entire MWCNT array is contacted using top electrodes. Determining the CNT density and taking into consideration the AFM tip radius, it was obtained that the AFM tip gets in contact with (1.1 ± 0.1) CNTs
]. What can be seen in the highly resolved AFM image is only the top end of the MWCNTs. The CNTs are well embedded in a SiO2
matrix to ensure stabilization during chemical–mechanical planarization. It can be observed from the corresponding current map that the current flows exclusively at the CNT site and drops immediately to zero at the SiO2
site, indicating the lack of lateral leakage currents.
The lateral resolution is well known to be tip-convoluted, and therefore, a reliable CNT diameter estimation is not possible from these measurements. Especially, in c-AFM where the AFM tip is rastering in contact mode at the sample surface, the tip convolution is greater since the metal coating leads to an enlarged tip radius. There exist some reports where this issue is carefully addressed and solutions are proposed.
For example, in lying CNTs, the tip diameter estimation is done according to the height appearance which however was shown to become problematic for larger diameters due to the tip-induced deformation which results into a non-circular cross section of the CNT
]. To reduce the tip convolution and to further increase the lateral resolution in c-AFM down to 1 nm, Hong et al.
] have manufactured an atomic-size metallic filament on a commercial AFM probe. In our case, using the conventional tapping mode, the tip convolution can be considerably reduced. Here, uncoated pure silicon tips allow for recording high-resolution AFM images with much better improved lateral resolution. Furthermore, phase imaging provides a better contrast where the edges of individual CNTs can be distinguished more easily. The top end of individual CNTs appears as a disc-like shape with a shallow depression in the middle (see Figure
). According to the grain size statistics, a mean value of 20 nm was obtained with a filling percentage of 43%. A highly resolved AFM phase image of an individual CNT is displayed in Figure
. A corresponding transmission electron microscopy (TEM) image of a single MWCNT grown under the same conditions is shown in Figure
. There can be observed a very good agreement between the AFM and TEM images concerning the tube diameter.
High-resolution AFM phase images and TEM image of MWCNT. High-resolution AFM phase images inside the MWCNT array (a) and of a single MWCNT (b); TEM image of a single MWCNT (c).
If the current map is recorded using a much lower sample bias of only 25 mV, variations in the electric response between distinct CNT arrays can be observed despite the good inside homogeneity (see Figure
). A detailed insight into the electric behaviour can be addressed by I
spectroscopy. Here, two types of experiments were performed. On one hand, different initial sample biases were used to check if there is any influence on the I
spectroscopy of presumably different initial loading forces induced by slight variations in the electric field between the metallic tip and the MWCNTs expected to be metallic. On the other hand, I
spectroscopy was performed on distinct locations to get an insight into the MWCNT array homogeneity. The average spectra for the selected MWCNT arrays I and II are displayed in Figure
Current map and the corresponding I-V characteristics. Current map (a); the corresponding I-V characteristics for the indicated MWCNT arrays in (a) recorded under different initial sample voltages (b) on different locations (c).
Figure 4 Average I-V characteristics of MWCNT arrays, voltage-dependent current map and corresponding profile lines. The average I-V characteristics of the MWCNT arrays I (a) and II (b); the voltage-dependent current map (c); the corresponding profile lines ( (more ...)
The outcome proves that none of both experiments influences somehow the electric response and sustains a very good reproducibility of the IV
spectroscopy. The estimated average error bar approaches 2% and 4% relative to the average resistance determined for the selected I and II MWCNT arrays, respectively. Similar conductivity obtained on distinct locations supports the current mapping in what concerns the good homogeneity inside individual MWCNT arrays. The obtained linear IV
spectra indicate that the metallic character of the MWCNTs is in good agreement with the results obtained from Raman spectroscopy and TEM studies
]. It is more important to highlight that the formation of the MWCNT/metal contact preserves the metallic behaviour which however is not always necessarily the case. Furthermore, voltage-dependent current mapping allows probing the electric response upon a couple of sample biases at one glance (see Figure
). This type of study is mostly recommended and helpful for very small objects like, for example, lying CNTs, where the tip positioning and consequently a reproducible tip-CNT contact geometry becomes problematic. However, in this case, it can be furthermore used to check the correlation with the IV
spectroscopy. In Figure
, two profile lines are depicted for two different sample biases, namely 50 mV (red line) and 25 mV (blue line) (refer to Figure
as well). The pointing-up arrows (refer to Figure
,b) obeying the same colour code indicate the current values obtained via IV
spectroscopy for the previously mentioned sample biases. A very good agreement between the IV
spectroscopy and the voltage-dependent current mapping can be clearly observed. The outcome looks very promising in investigating long and narrow nano-objects. As, for example, a lying single-walled CNT (with a length in the micron range but a diameter of only 1 nm) can presumably be very accurately sectioned via the voltage-dependent current mapping rather than performing uncertain IV
spectroscopy with random tip-CNT contact geometry. The few obtained IV
points will be sufficient to get a trend and therefore an insight into the electric behaviour (linear or non-linear).
A similar study can be successfully extended at larger scale as can be observed from Figure
. The same good analogy can be made between the voltage-dependent current mapping and the I
spectroscopy. In both cases, variations in the electric response could be emphasized from array to array.
Topography (a) vs. voltage-dependent current map (b); corresponding I-V characteristics of indicated MWCNT arrays (c).
The estimated resistances of the investigated MWCNT arrays are included in Table
. As shown previously, an error bar up to 4% might occur. Despite the relative high magnitude, the resistance values will however be considerably reduced (some orders of magnitude) for the overall highly dense vias where vertically aligned CNTs will be integrated in parallel. For example, using a rough estimation, within a 2-μm-diameter via, there can be ideally integrated (100% filling percentage) up to 10,000 MWCNTs with a diameter of 20 nm. However, if a similar filling percentage can be assumed as the one previously estimated, a correction factor of slightly larger than 2 should be included. Still, a reduced resistance of up to 3 orders of magnitude is expected to characterize the entire via. In our setup, it must be mentioned that the estimated resistances contain, besides the internal CNT resistance, inputs from metal contacts, namely metallic tip/CNT and CNT/bottom metal line. Whilst the first-mentioned top contact resistance is constant (due to the same loading force) and the CNT quality is presumably the same (Raman spectroscopy confirmed this issue on a similar sample
]), the observed variation in the electric response from network to network is due to the bottom contact resistance. At the moment, it can be concluded that the electric behaviour of the bottom contact layer is inhomogeneous. The reason behind is mostly due to the formation of tantalum oxide and tantalum carbides as could be emphasized by energy-filtered TEM
] which however requires for ultimate sample damage. In this regard, it was shown that c-AFM gives the extra possibility to electrically investigate buried interfaces to a very low scale being superior in this regard to the standard IV
measurements which exhibit a strong average character.
The estimated resistance values of the indicated MWCNT arrays