Improving the reliability of conductive atomic force microscopy-based electrical contact resistance measurements

To determine the extent to which the precautions discussed above (the use of wear-resistant and mechanically strong conductive diamond tips, suppressing fluctuations in environmental humidity and temperature, as well as degassing the sample before the measurements) have improved the reliability and reproducibility of C-AFM-based ECR measurements, we performed comparative experiments, the results of which are summarized in figure 2.

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In particular, figure 2(a) is a histogram of the measured data that demonstrates the spread of ECR values measured on a single location on a flat HOPG terrace under ordinary laboratory conditions (i.e. with no control over humidity and temperature) over a span of 70 min using a Pt tip. As one can clearly observe from the presented data, ECR values recorded in this fashion (extracted from 1157 individual I-V curves) vary dramatically, over more than an order of magnitude, reminiscent of the results presented by Engelkes et al in their detailed study of ECR variations [18]. In addition to the variance in the recorded ECR values, the absolute values (with a mean ECR of 2.45 MΩ and a standard deviation of 2.95 MΩ) are significantly higher than what would be expected from a nanoscopic contact formed between a platinum tip and HOPG (which is on the order of a few kΩ to tens of kΩ [21]), pointing towards the potential presence of contaminant layers on the probe and/or the sample [22–25].

In contrast to figure 2(a), figure 2(b) presents results (extracted from 1200 individual I-V curves recorded over 70 min) that were obtained by taking all the precautions described in section 2, i.e. with a conductive diamond tip, under an N₂ atmosphere and a controlled temperature of 38 °C, with degassing of the HOPG sample performed prior to the I-V spectroscopy experiments. The data obtained in this fashion are in striking contrast to those presented in figure 2(a): ECR values now exhibit a much narrower distribution that can be fit reasonably well with a Gaussian, with a mean of 18.6 MΩ and a standard deviation of only 0.90 MΩ. While the absolute values of the ECR are higher than those obtained via the Pt tip, this can be tentatively attributed to the fact that the resistivity of the conductive diamond is expected to be at least two orders of magnitude higher than the resistivity of platinum [26, 27].

While it is obvious from the comparison of the data in figures 2(a) and (b) that the combined measures of using a hard and wear-resistant tip material and controlling environmental factors have led to a dramatic improvement in reliability and reproducibility, it is not possible to determine which precaution had the most significant impact on the improvement of the data. To address this question, we repeated our C-AFM-based ECR measurements with the Pt tip one more time, but now under an inert N₂ atmosphere, albeit with no control of temperature or sample degassing (figure 2(c)). The data (extracted from 1200 individual I-V curves recorded over 70 min) now exhibit a significantly more narrow distribution (with a mean of 98.0 MΩ and a standard deviation of 12.6 MΩ) than what was achieved under ambient conditions in figure 2(a).

Despite the fact that the variability in ECR measurements observed via the use of Pt tips under the dry N₂ atmosphere (figure 2(c)) is still appreciably higher than what is achievable with the conductive diamond tips (figure 2(b)), the drastic improvement after the switch from ambient conditions to N₂ highlights the major impact that environmental conditions and, in particular, changes in humidity can have on C-AFM-based ECR measurements. On the other hand, at first glance it may be surprising that the mean ECR measured with the Pt tip (98.0 MΩ) is higher than the ECR measured with the conductive diamond tip (18.6 MΩ). This difference, however, can be explained by the fact that (i) a degassing procedure was not used for the measurement with the Pt tip and (ii) the measurements were not taken at the same location on the same terrace and different HOPG terraces can exhibit significantly different conductivities [2].

While experiments reporting on the variability of C-AFM-based ECR measurements and the underlying mechanisms are quite rare in the literature [18, 28, 29], it is still possible to consider our results within the context of these studies. In particular, for C-AFM measurements performed on decanethiol-coated gold substrates, it was reported that the resistance values obtained in a single experimental run with a given AFM tip varied up to three orders of magnitude, depending on the topographical roughness of the gold substrate employed in the experiments [18]. Moreover, switching from measurements in air to those performed under cyclohexane (analogous to the switch from ambient conditions to the dry N₂ atmosphere in our experiments) minimized the issues associated with uncontrolled changes in humidity, leading to a drastic decrease in standard deviation [18]. Another study focusing on a similar material system (self-assembled monolayers of azobenzene thiol molecules on gold) reported results along the same lines, with resistance values varying over more than an order of magnitude [29]. Finally, C-AFM measurements on a granular gold film resulted in resistance values that varied over two orders of magnitude, and the authors attributed the large variability in the results to atomic re-arrangements and mechanical instabilities at the tip-sample junction [28]. The ECR distributions achieved via our improved methodology (see e.g. Figure 2(b)) are significantly more narrow than those reported in the discussed experiments [18, 28, 29], possibly due to the combined use of mechanically strong AFM tips and strictly controlled environmental conditions.

Despite the improvements in reliability reported in section 3.1, we have observed that at least one source of variability remains. In particular, when measurements are continuously performed for durations of a few minutes and longer (with all the precautions described earlier), spontaneous (i.e. sudden) changes in ECR can be observed. Figure 3 presents two experimental runs (performed with conductive diamond tips for ∼30 min and ∼15 min after contact has been established between tip and sample) that comprise spontaneous jumps to different 'branches' of ECR as highlighted by the red arrows. Specifically, in figure 3(a), after an initial gradual drop, the ECR spontaneously jumps to a lower branch, stays stable for about 2 min and then jumps back to the value before the spontaneous drop. The ECR then remains fairly stable for about 12 min, which is then followed by another spontaneous drop. In the second experimental run presented in figure 3(b), there is no initial drop, but the data shows a prominent downward jump in ECR at the ∼3 min mark, followed by a stable region for about 9 min and then another downward jump of smaller magnitude.

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While the initial gradual drop in resistance in figure 3(a) can be tentatively explained by creep [30], the spontaneous jumps in figures 3(a) and (b) appear to be of a different character. During C-AFM measurements, the tip-sample junction is subject to the combined effects of electrically-, thermally-, and mechanically-induced stresses [31]. While, the flow of current through the constricted tip-sample junction leads to Joule heating [32] and consequently thermal stresses, the junction also undergoes electrical stress due to the repeated, cyclic application of bias voltage over an extended period of time to perform I-V spectroscopy [33], in addition to mechanically-induced stresses though the action of adhesive forces acting between the tip and the sample. The potential influence of piezo creep on the contact should also not be ignored. A mechanism that may explain a sudden drop in ECR is the spontaneous breakdown of an insulating contaminant layer [20]. On the other hand, the rapid increase to higher ECR values cannot be explained through a similar mechanism. As such, an alternative explanation that involves spontaneous changes in the atomic-scale structure of the AFM tip apex, perhaps by the re-positioning of a cluster of atoms near the contact in a metastable configuration [34], can result in the experimentally observed jumps between different ECR branches. Support from atomic-scale simulations will be needed to gain more insight into the underlying physical mechanisms.

Regardless of the underlying mechanisms, in order to explore whether the occurrence of spontaneous jumps in ECR can be minimized through experimental means, we recorded a ∼4-hr-long run with a conductive diamond tip in which I-V curves were continuously recorded under an applied normal load of 30 nN, which is on the same order as the typical adhesion force measured between diamond and HOPG. While the results, presented in figure 4, still exhibit an initial gradual drop in ECR, no spontaneous jumps in ECR are recorded subsequently, demonstrating that sudden changes in ECR can be suppressed through the application of normal load at the tip-sample junction. A potential physical mechanism could involve a deepening of potential energy minima for atomic clusters at the tip apex with increasing normal load [35], making it harder for the clusters to jump between different spatial configurations at the apex. The confirmation of this hypothesis would again require input from atomic-scale simulations.

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