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. 2021 Oct 15;21(20):8794–8799. doi: 10.1021/acs.nanolett.1c03073

Current-Induced One-Dimensional Diffusion of Co Adatoms on Graphene Nanoribbons

Tobias Preis †, Sasha Vrbica ‡, Jonathan Eroms †, Jascha Repp †, Jan M van Ruitenbeek ‡,*
PMCID: PMC8554795  PMID: 34652923

Abstract

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One-dimensional diffusion of Co adatoms on graphene nanoribbons has been induced and investigated by means of scanning tunnelling microscopy (STM). To this end, the nanoribbons and the Co adatoms have been imaged before and after injecting current pulses into the nanoribbons, with the STM tip in direct contact with the ribbon. We observe current-induced motion of the Co atoms along the nanoribbons, which is approximately described by a distribution expected for a thermally activated one-dimensional random walk. This indicates that the nanoribbons reach temperatures far beyond 100 K, which is well above the temperature of the underlying Au substrate. This model system can be developed further for the study of electromigration at the single-atom level.

Keywords: adatom diffusion, graphene nanoribbons, scanning tunneling microscopy, electromigration

Graphene nanoribbons (GNR) can be engineered with atomic perfection by on-surface synthesis from molecular precursors,1 offering a rich variety of fascinating electronic properties.2−6 Their band gap can be tuned by the physical width of the ribbon, such that they represent nearly ideal model systems for investigating one-dimensional (1D) electron transport.7,8 GNR can be intrinsically doped by adsorption onto a surface with a different work function9−12 or by substituting carbon atoms in the lattice.13,14 Alternatively, dopants can be deposited onto the GNR,15,16 but little is known of how a current flow through GNR may affect adsorbed dopants.17 Here, we demonstrate that high current densities will drive dopant atoms to diffuse, at bath temperatures for which thermal diffusion is inhibited. Interestingly, the diffusion is confined to the GNR, rendering GNR unique for studies of atomic diffusion in one dimension. We anticipate that the system can be further developed as a model system for studying electromigration at the atomic scale and testing fascinating predictions.18,19 STM experiments were carried out under ultrahigh vacuum at low temperatures T of 7–10 K, unless specified otherwise. Images were acquired at constant current of I = 2 pA at a bias voltage V = ± 100 mV, referring to the sample voltage with respect to the tip. The tip was made from a 20 μm thick PtIr wire, conditioned by controlled indentations into the clean gold surface, producing atomically sharp gold-coated tips. A Au(111) single-crystal surface was cleaned by Ne+ ion sputtering, followed by thermal annealing at 550 °C. GNR on Au(111) were synthesized following ref (1), resulting in 7-carbon-dimers-wide ribbons with armchair edges (7-aGNR). Subsequently, Co atoms were coadsorbed onto the cold (≃ 15 K) surface. A significant fraction of them is adsorbed on top of the GNR, see Figure 1a.

Figure 1.

Figure 1

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Overview of GNR and coadsorbed Co adatoms on Au(111). (a) Large-area STM image of the sample after cobalt adatom deposition. Some GNR are not fully flattened out from dehydrogenation (black arrow), and a few GNR are kinked (red arrow) or deviate otherwise from their ideal 1D structure. Most Co adatoms are located on clean areas of Au (white arrow), while a few are located on top of GNR (blue arrow). The inset shows the geometric structure of the GNR along with the five possible ring-centered adsorption sites per unit cell. (b) STM image of a GNR decorated by two Co adatoms. (c) Line profile along one arm of the kinked GNR, indicated by the black line in (b).

GNR fabricated by this method1,20 have a uniform width but vary in length. Whereas Co on Au(111) has an apparent height of 0.1 nm in the STM images, Co adatoms on a GNR show an apparent height of 0.23 nm. A similar increase in apparent height is also observed on ultrathin insulating layers.21 Occasionally, some Co-atom-related protrusions on GNR appear even larger—about 0.35 nm high (Figure 1b,c). They may be due to dimers, hydrogen attachment, or different adsorption,22 and are disregarded here.

At T ∼ 7 K, the Co atoms and the GNR remain stationary. To determine the preferred adsorption site, the center position of Co adatoms as well as the central axis of a GNR were extracted from suitable fitting procedures of the images. From this analysis, we find only adsorption at positions A, B, D, and E (see inset in Figure 1a), consistent with Co preferentially adsorbing at the centers of the outer carbon rings of the GNR, in agreement with ref (23).

The current injection with the STM tip into GNRs to induce motion of the adatoms is performed as follows. The STM tip is positioned above a suitable GNR at a lateral distance s from a Co atom, indicated by the green dot in Figure 2c.

Figure 2.

Figure 2

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Procedure of current-pulse injection. (a) The blue curve indicates the tip approach toward the GNR. A voltage pulse is applied in contact, here 0.8 V for a duration of 0.5 s (green curve). (b) Tunneling current recorded during the pulse. An abrupt increase indicates the jump to contact, as shown on a 3.7× magnified scale in the inset. The current is seen to rise nearly linearly with the voltage (right inset). The curves shown here are representative for all the data, at both voltage polarities. (c) STM images of a GNR before (top) and after (bottom) the voltage pulse for Vmax = 0.8 V. The green dot on the GNR marks the tip position for the applied voltage pulse, at a distance s from the adatom’s initial position. After the pulse, the Co adatom has moved away from the tip over a distance d, as observed in the lower image.

Next, the feedback is switched off and the tip is lowered (z decreases; blue curve in Figure 2a). The tunneling current, Figure 2b, rises exponentially with decreasing tip–sample distance until a kink (observed in most traces) indicates a jump to contact.24,25 The tip approach is continued for another 0.02–0.03 nm to ensure stable contact. In contact, the sample voltage is ramped up, briefly maintained at Vmax and then ramped down to its initial value, over a total duration of 1 s (see Figure 2a). Afterward, the tip is retracted and another STM image is taken; an example is shown in Figure 2c. By comparing the images before and after the pulse the displacement d of the Co atom is determined. d > 0 indicates a displacement away from the tip. The high-bias resistance of the junction in contact does not depend systematically on voltage polarity, nor on the distance to a Co adatom.

We applied over 900 pulses on GNRs and recorded a total of 1430 events (a single pulse may affect multiple Co adatoms). Remarkably, after application of a pulse, roughly half of the Co atoms investigated are displaced to a new position on the same GNR (see Table 1). Atoms can be displaced toward or away from the tip, for either voltage polarity, and the average displacement is quite significant, averaging at 3–4 graphene hollow sites. Only in very few cases were Co atoms found to be moved from the GNR to the bare Au surface. Finally, roughly 7% of the atoms disappeared from the image after the pulse. We assume that they must have been picked up by the tip. We restrict the analysis to experiments for voltage pulses |V| ≥ 600 mV. We also exclude data for which the tip–sample resistance remained larger than 330 kΩ upon contact. Atoms located at the end points of the GNR or at kink sites are disregarded.

Table 1. Statistics for Co Motion after a Voltage Pulse.

response to voltage pulses of Co adatoms on GNRs number % of total
total number of Co atoms traced 1430 100%
number of Co atoms that did not move 736 51.5%
number of displaced Co atoms (including events below) 694 48.5%
Co moved along GNR 536 37.5%
Co dropped to Au surface 6 0.4%
Co moved to other edge (between sites A and E) 54 3.8%
Co atom disappeared (pick up by STM tip) 98 6.8%
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Figure 3a shows the escape probability of Co adatoms on GNRs after a voltage pulse, as a function of the initial tip–adatom distance s. We define the escape probability as the ratio of the atoms that are displaced (excluding those that have presumably been picked up by the tip), to the total number of Co atoms traced. The data are grouped in intervals of s, and a data point at s combines data for the interval from s – 1 nm to s + 1 nm. Clearly, atoms closer to the tip are more likely to be displaced.

Figure 3.

Figure 3

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Escape probability (a) as a function of initial tip-adatom separation and (b) as a function of pulsing voltage, for pulses with s < 10 nm. Error bars show the standard deviation.

Figure 3b shows the escape probability as a function of Vmax, extracted from all data for s < 10 nm, since the dependence on s in this range is small. Each data point represents an interval of 0.1 V. Despite some scatter, we can recognize a trend of increasing escape probability for increasing bias voltage.

Figure 4 shows a histogram of the distance d by which adatoms are displaced as a result of a pulse, extracted from all data with |V| ≥ 0.6 V. The red curve is a fit of the histogram, excluding the anomalous bin at d = 0, to Inline graphic. The center of the distribution lies at zero, to within the statistical accuracy, d0 = 0.1 ± 0.8 nm, as expected for a random-walk probability distribution. The width w2 = 1.0 nm2 suggests an average number of hopping events per pulse of 13. Although the fit appears to match the data reasonably well on a linear scale, a semilog plot (see inset) reveals deviations at larger distances. The events with d > 3 nm appear orders of magnitude more frequently than expected from the simple 1D random walk. We return to these long tails and the anomalously large peak at d = 0 below.

Figure 4.

Figure 4

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Histogram of the distance d traveled by Co adatoms along the GNR after a voltage pulse, with tp ≃ 0.5 s. Positive (negative) d indicates motion away from (toward) the tip, while d = 0 nm indicates Co adatoms that did not move. The red curve shows a fit of the data to a 1D random walk probability distribution, eq 1 with N ≈ 13, excluding the data points for d = 0. The inset shows the data on a semilog scale, emphasizing the deviations to the fit for large displacements d.

The Co atoms on the Au substrate in the vicinity of the GNR occasionally are also displaced after a voltage pulse. We performed additional experiments for Co atom migration resulting from voltage pulses applied on the bare Au surface,26,27 which turned out to be useful for better understanding the origin of atom migration on the GNR, by comparison. By using the same pulsing scheme as for GNR and restricting this comparison to s ≤ 7 nm, we observe that adatoms are much less frequently displaced for pulses directly on gold, namely only 3% (16 of 519 atoms).

To compare the effect of voltage-pulse-induced atom migration to thermal activation, we performed a series of experiments at elevated temperatures T (raised in steps of ∼15 K) by heating the STM head. At each temperature, from drift-corrected sequences of STM images of the same surface area, we analyzed the diffusion of the adatoms.28

Thermally activated displacement of Co atoms on the bare gold surface was first detected at T ∼ 34 K. At even higher temperatures, the high mobility complicates quantitative analysis of the images. However, up to T = 79 K, motion of Co on GNRs was not observed. Hence, the diffusion barrier for Co adatoms on GNRs is much higher than that for Co on Au(111). On the basis of the observed diffusion rate of Co/Au(111) at 34 K and assuming a common attempt frequency of ν0 = 1013 s–1, we estimate the diffusion barrier of Co on Au(111) to be EDAu = 0.10 eV in agreement with a theoretical study.29 As mentioned above, for current injection, we observed a rather low escape rate for Co atoms directly adsorbed on Au, indicating that current-induced heating keeps the temperature of the gold surface well below 40 K, in agreement with the large thermal conductivity of bulk Au.

We now turn to a discussion of the observed adatom hopping on GNRs. Remarkably, upon activation by a voltage pulse, the Co atoms diffuse along the GNR and only drop to the Au surface in exceptional cases. This suggests the presence of an Ehrlich–Schwoebel barrier at the GNR edges. The absence of a preferential direction of motion suggests that the motion is activated by current-induced heating of the GNR.30−35 Adopting a theoretical value of about EDGNR ≈ 0.5 eV for the diffusion barrier for Co on single layer graphene from theory (see ref (36) and references therein), we can use the observed hopping rate ν during a pulse, ν ∼ 25 s–1, for estimating the effective temperature on the GNR. Here, we have calculated ν from the average number of hopping events, N = 13 (see above), and the typical pulse duration of 0.5 s. Through the Arrhenius law ν = ν0exp(−ED/(kBT)), we obtain a pulse-induced effective temperature Teff ≃ 200 K (with an uncertainty ±20 K), which is indeed much higher than the temperatures that we were able to explore by direct heating of the STM.

Provided that the current-induced diffusion can be regarded as analogous to thermally driven diffusion,37 our observations can be interpreted as follows. The escape probability, Figure 3a, being nearly constant up to ∼8 nm, and only dropping by a factor of ∼4 at 20 nm, suggests that the effective temperature of the GNR during a pulse is raised above that of the substrate, and is nearly homogeneous over long distances. The exponential dependence of hopping rate with temperature permits a drop of Teff by only about 10 K at the largest distance s = 20 nm–small compared to the estimated Teff of 200 K. This picture is consistent with known thermal transport properties: if we simplify and assume that the Au substrate remains uniformly at the base temperature, the balance between thermal transport along the GNR and heat transport into the substrate leads to a decay of temperature with distance s as, T(s) = Tm  exp(− s/λ) + T0, for an infinitely long GNR. Here, Tm is the maximum temperature at the tip position, and the decay length is Inline graphic. For the thermal conductivity of graphene we use κ = 200 W/Km,38,39 appropriate for 200  K and for the typical length of 10–20 nm of our GNRs. For the thickness b = 0.144 nm of graphene, this is equivalent to a two-dimensional thermal conductivity of κ□ = 30 nW/K. For the Kapitza interface conductivity we take the value for the interface between graphite and Au,40G = 30 · 106 W/m2K. From these two competing thermal conductivities we find a decay length of λ = 31 nm for the temperature along the ribbons, supporting the assessment that Teff is nearly constant along the GNR, consistent with experiments for Co metal islands on Cu.41

Turning back to the distribution of hopping distances in Figure 4, in case of thermal activation we expect the distribution to be closely approximated by that for a 1D random walk, for which the probability for an atom to move by n lattice sites, P(n), in the limit of large numbers of jumps, N, takes the form,42

graphic file with name nl1c03073_m003.jpg 1

The histogram in Figure 4 agrees with such a description for short hopping distances, but the large peak at d = 0 and the large displacements up to d = 8 nm are clearly incompatible. Likely, these deviations result from the variations in effective temperatures between pulses. The currents resulting from a voltage pulse vary because of variations in the contact resistance between tip and GNR. In addition, the total length of the GNR determines the interface area with the Au substrate for thermal relaxation and is expected to influence Teff. The diffusion rate is exponentially sensitive to variations in Teff. For example, a reduction of Teff by only 20 K yields an average number of hops during a pulse below 1, which would explain the large peak at d = 0. Similarly, a deviation from Teff ≃ 200 K by only 20 K to higher temperatures is compatible with hopping to distances as large as 8 nm. Despite these uncertainties, the global behavior is in agreement with thermally activated 1D diffusion.

We find no polarity dependence in adatom diffusion along the GNR. Directional asymmetry could result from electromigration forces. Electromigration has been widely studied, notably for current-carrying carbon nanotubes.43 However, it is difficult to obtain access to the effects truely at the atomic scale. Here, we conventionally distinguish a direct force and a wind force.44 The direct force arises from the effective charge of the Co adatom in the electric field at the surface. The horizontal component of the field should be very small, because of the large effective tip radius, on the order of 50 nm, and the boundary conditions imposed by the Au surface. (Note that the effective tip radius relevant for tunneling is different from the tip radius for electrostatics.) For an adatom sitting 0.3 nm above the image plane, at a distance s = 10 nm from the point of tunneling, and for a tip–sample potential difference of 1 V, the horizontal component of the electric field can be estimated as 2 × 106 V/m. For a charge of 0.5 e on the adatom,36 the force would be 0.16 pN. The resulting difference in left and right barrier heights would be ΔE = 0.2 meV, and at Teff ∼ 200 K, the ratio of left and right jumps would be 0.988. With N = 13 this would lead to an expected average displacement of d̅ = 0.16 nm. Although this shows that we cannot resolve the effect from our data, it suggests that the directional component should be detectable by improving the statistics. The wind force is expected to be very small in our experiment because the 7-aGNR has a band gap of about 2.5 eV.

In summary, we have shown that 7-aGNR on Au(111) serve as nearly perfect 1D channels for Co adatom diffusion. Current pulses injected from an STM tip can be used to heat the GNR, and the statistics of adatom diffusion suggests that this leads to a nearly homogeneous temperature of the GNR. This temperature is remarkably high and far from equilibrium with the underlying Au substrate. The GNR may serve as a model system for single organic molecules connected between metallic leads, for which previous experiments indicated similar high temperatures excited by the transport current,45 where this temperature cannot be directly measured. Further elaboration of this platform of STM observation of adatom diffusion on GNRs can serve as a nearly ideal model system for the study of electromigration at the atomic scale. Parameters obtained from computational studies for adatoms on graphene suggest that the experiment can be set up to achieve the required current densities.46 Relevant adjustements would include replacing our 7-aGNR by nanoribbons with a small band gap, such as 5-aGNR47,48 or 9-aGNR,49 and arranging the GNR over the edge of thin insulating islands.8

Acknowledgments

This work is part of the research program of the Netherland’s Organization for Scientific Research, NWO. Funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 689, project A07 and 314695032/CRC 1277, projects A09 and B01 is gratefully acknowledged.

The authors declare no competing financial interest.

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