Conductance of Atom-Sized Contacts of Indium

Conductance of atom-sized contacts of In has been measured in ultrahigh vacuum at room temperature. The conductance histogram shows a peak at 0.83G0 (G0 ≡ 2e/h is the conductance quantum) and a broad structure spanning from 1.5G0 to 4G0 with small peaks at ∼ 1.8G0, ∼ 2.5G0, and ∼ 3.3G0. The observed histogram is in overall agreement with the one obtained at 4 K (Makk et al., Phys. Rev. B 78, 045414 (2008)) but markedly differs from the histogram of Ga (Lewis et al., Solid State Commun. 109, 525 (1999)) which reveals no peak features at room temperature. Because the crystal structure of In is nearly FCC, our results support the conjecture suggested by Lewis et al. that the absence of peaks in the room-temperature histogram of Ga might be related to complexities in the crystal structure of Ga and its deformation characteristics. We also found that the same conductance trace sometimes appears repetitively in successive contact breaks. Such replication of the conductance trace is often observed at cryogenic temperatures but unexpected at room temperature particularly for soft metals such as In. [DOI: 10.1380/ejssnt.2011.85]


I. INTRODUCTION
Conductance of atom-sized contacts of metals has been a subject of many theoretical and experimental studies over the past decade [1].For single-atom contacts (SACs) of metals, it has been theoretically [2] and experimentally [3,4] demonstrated that their conductance critically depends on the transmission of the electronic states or channels formed by the valence electrons of the atom occupying the contact site.Monovalent metals such as Au, Ag, and Cu, for example, have one valence electron in the s orbital that forms a highly transparent conductance channel.As a result, the SAC of these metals exhibits a conductance in good agreement with G 0 = 2e 2 /h, the quantum unit of conductance, as manifested by a sharp peak at 1G 0 in the conductance histogram.On the other hand, trivalent metals Al, Ga, and In have three valance electrons in the s and p orbitals.In the Al SAC, these valence orbitals hybridize to form one high-and two lowtransmission channels [5].Experimentally, it is found that the contributions from these three channels sum up to yield the SAC conductance of ∼ 0.8G 0 and produce a pronounced SAC peak slightly below 1G 0 in conductance histograms obtained at 4 K [6,7] and at room temperature [8].Because Ga and In have the same valency as Al, similar SAC conductance close to 1G 0 can also be expected for these metals.This is, however, not the case for Ga as shown by Lewis et al. [9] They measured the conductance of Ga atom-sized contacts at different temperatures and found at room temperature that the conductance histogram is featureless and reveals no peak structures.With reducing the temperature, the SAC peak gradually grows up around 1G 0 , and becomes a well defined peak at 4 K. Thus, the agreement of the SAC conductance between Al and Ga can be found only at liquid helium temperature.Lewis et al. suggest that a non-FCC (orthorhombic) crystal structure of Ga complicates the necking deformation of Ga nanocontacts, and this might be the reason why they obtained the flat histogram at room temperature.
Indium is another metal that has the same valency as that of Al and Ga.In contrast to the wide use of In to make Ohmic contacts of various materials, only a few experiments have been carried out on the atom-sized contacts of In.This is probably due to the extreme softness of In, which makes this metal quite unsuitable for the break-junction technique widely used for fabricating atomic and molecular junctions [1].Makk et al. [10] measured the conductance of In atom-sized contacts at 4 K, and this would be the only one experimental work made so far on In.They carried out the conductance measurements with and without hydrogen atmosphere and found for clean In contacts a well-defined conductance peak at 1G 0 , followed by a broad intensity distribution extending over (2 − 6)G 0 with peaks at 2.4G 0 , 3.7G 0 and ∼ 6G 0 , respectively.No such broad feature has been observed in the histogram of Al and Ga.However, the first peak, which is certainly the SAC peak of In, appears at 1G 0 and is in good agreement with the SAC peak of Al and that of Ga at 4 K. Therefore, again at 4 K, the SAC conductance of three trivalent metals agrees with each other.This agreement, however, breaks down at room temperature where Ga shows no SAC peak in its histogram as we mentioned before.Then, a next step should naturally be to investigate whether or not the room temperature histogram of In shows the SAC peak as it does at 4 K. Like Ga, In is a non-FCC metal.If the flat histogram of Ga at room temperature arises from its non-cubic crystal structure, then the room-temperature histogram of In might be featureless as well.However, the tetragonal structure of In is nearly identical with FCC.It is thus also likely that the conductance histogram might be temperature independent as is the case with FCC Al and exhibits the SAC peak at room temperature.To decide this issue, we measured in this work the conductance of In atom-sized contacts at room temperature.We previously carried out conductance measurements on In wire-wire contacts at room temperature employing an apparatus described in Ref. 11 and found a sharp peak at 2.3G 0 in the conductance histogram.This result was, however, obtained in ambient air and must certainly be affected by various con- taminants, the influence of which on the conductance is quite unknown for In.In this work, we, therefore, carried out all our measurements under an ultrahigh vacuum condition.

II. EXPERIMENT
The apparatus used in this experiment is the same as that described in Ref. 8. Instead of the wire-disk contact used in Ref. 8, we employed in this experiment a wirewire junction where two pieces of In wire make a contact with each other in a cross-wire configuration.First, a short (∼ 5 mm) piece of In wire (0.5 mm in diameter and 99.99% pure) is placed on an aluminum substrate and fixed there by a silver paste.One such In-wire/Alsubstrate assembly is mounted on a sample holder, and another one is fixed onto a tube-scanner/Inchworm STM module (Burleigh ARIS-10-0.5).These two assemblies are placed such that the In wires are facing each other and their directions are nearly orthogonal.The distance between In wires is reduced with the Inchworm, while stretching and retracting the tube scanner at a rate of 1.74 Hz.When two wires come close to each other, their separation is finely adjusted so that the wire-wire contact makes ON-OFF synchronously with the stretching oscillation of the tube scanner.In the case of usual metals, a couple of gap adjustments are sufficient to make the contact continue ON-OFF many times before it becomes necessary to readjust the wire-wire separation.On the contrary, In contacts typically repeat ON-OFF a few times and then remain open even at the largest stretching of the tube scanner.This is clearly due to the flattening of the touching point of the contact.Frequent adjustment of the wire-wire separation was therefore needed.Softness of In posed another problem.We usually employ the "hardindentation" method where a contact is strongly pressed at its "ON" state to crack contamination layers and establish a clean metal-metal contact.For In contacts, such a hard indentation only enlarges the contact flattening and cannot be used in the contact formation.At the same time, we found that a gentle touching between In wires results in the replication of the same conductance trace as will be mentioned in the next section.We, therefore, had to make additional adjustments of the "ON" state conductance to ensure that each ON-OFF cycle yields different conductance traces.These adjustments had to be made manually and considerably consumed the measuring time.As a result, accumulation of a large number of conductance traces was practically unattainable, and the total number of traces used to construct the histogram is around 1200.
The conductance was measured by monitoring the voltage drop V m across a R = 1 kΩ current-sensing resistor connected in series with the contact.An external bias V a = 0.1 V is applied to (contact) + R, and the conductance G can be obtained from and lower than V a .This difference between V a and V b changes with the conductance and is 7% when G = 1G 0 .All measurements were carried out at room temperature in ultrahigh vacuum better than 5 × 10 −8 Pa.

A. Replication of the conductance trace
When the "ON" state conductance is (5 − 8)G 0 , we often found that each contact opening yields the same conductance trace.An example of such repetitive traces is displayed in Fig. 1.All traces show the same waveform and display plateaus at the same positions.In many cases, one waveform continues several times and then switches to another one which again repeats several times.Such a trace replication is often observed at liquid helium temperature when a contact is formed under weak pressing.In such a soft touching of electrodes at 4 K, it is believed that the atomic arrangement at and around the contact remains unshuffled at the contact formation and, in the subsequent contact opening, evolves along the same deformation path as the previous one.Thus, each contact opening yields the same conductance trace.Such a freezing of the atomistic configuration of the contact seems plausible at 4 K but unlikely at room temperature, particularly for a soft metal such as In.It is thus quite unexpected that we could observe such repetitive traces as shown in Fig. 1.Presumably, in the case of In, not the immobility but the mobility of contact atoms might be responsible for the observed trace replication.At each soft touching of two wires, the contact may relax into a specific geometry which has a fixed deformation path inherent to it.Then, the contact would always undergo the same thinning deformation and repeat the same conductance trace.If this is actually the case, it would be interesting that both the rigidity and the fluidity of the contact-atom arrangement lead to the same phenomenon.We note in connection to this that the conductance trace of liquid metals is completely repetitive and provides an ideal example of the trace replication [12].
Whatever the mechanism of the trace replication is, the positions of the plateaus appearing in repetitive traces indicate the conductance of certain preferred atomic geometries and are thus worth examining.To locate the plateau positions quantitatively, we divided repetitive conductance traces into three groups of different waveforms and http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology constructed the histogram for each group.Figure 2 shows the resulting histograms.Because traces in each group have nearly the same waveform, the bin height in each histogram has no statistical significance.However, the conductance plateaus produce a couple of sharp peaks in each histogram, the position of which indicates the conductance of the preferred contact geometry.In Fig. 2, a peak around 1G 0 is commonly observed in three histograms, showing the higher preference of this ∼ 1G 0 state.As we will show in the next section, a similar peak also appears in the conventional conductance histogram, and this ∼ 1G 0 state is likely to represent the SAC of In.Two histograms show peaks at ∼ 0.5G 0 , ∼ 1.8G 0 , and ∼ 2.5G 0 .These peaks correspond to some metastable contact geometries, but their origins are yet unidentified.The ∼ 0.5G 0 peak appears in the subquantum regime and is likely due to some contaminations.Because Makk et al. [10] found no hydrogen-induced peaks below 1G 0 , the possible contaminant would not be residual hydrogen but might be some oxides left unremoved in the soft contact formation described in the previous section.

B. Conductance histogram
Figure 3 shows examples of non-repetitive conductance traces obtained in this experiment.Conductance plateaus can be seen at ∼ 0.5G 0 , ∼ 1G 0 , and ∼ 1.8G 0 , in good correspondence with the preferred contact geometries discussed in the previous section.These and other plateaus of In are flat or slightly decreasing with time but exhibit no positive slopes.Because the plateaus of Ga also share the same features [9], the distinct positive slope of Al plateaus [8] would be a characteristic reflecting unique properties of the Al conductance channels [13].
Despite our finely adjusting the "ON" state conductance, repetitive traces sometimes appeared between nonrepetitive ones.In order not to deteriorate the statistical significance of the histogram, we excluded those repetitive traces and constructed the conductance histogram from 1197 non-repetitive traces measured on two samples.The result is shown in Fig. 4. Though the number of accumulated traces is relatively small, the histogram shows clear peak features.The first peak can be well identified and appears slightly below 1G 0 .A broad feature follows after the first peak and spans from 1.5G 0 to 4G 0 .A couple of peaks are superimposed on the broad feature and can be located at ∼ 1.8G 0 , ∼ 2.5G 0 , and ∼ 3.3G 0 .Among these peaks, those at ∼ 1G 0 , ∼ 1.8G 0 , and ∼ 2.5G 0 agree with the peaks observed in the histograms of repetitive traces shown in Fig. 3 and certainly correspond to the preferred contact geometries of In.The accurate position of the first peak is 0.83G 0 , which is slightly lower than that of the SAC peak of In and Ga at 4 K, that is 1.0G 0 [10] and 1.1G 0 [9], respectively.However, the observed peak position is in good agreement with that of the Al SAC peak found at (0.79 − 0.83)G 0 [6][7][8].Considering a relatively large width of the SAC peak of In and Ga at 4 K, the small discrepancy in the peak position might be unimportant, and the observed first peak can be identified with the SAC peak of In.This allows us to conclude that, like Al and unlike Ga, the SAC peak of In can be observed at room temperature.
Concerning the higher-conductance peaks, the peaks at 2.5G 0 and 3.3G 0 roughly agree with the maxima found by Makk et al. [10] at 2.3G 0 and 3.7G 0 .On the other hand, no peak corresponding to the 1.8G 0 peak can be found in the histogram at 4 K.In the 4 K histogram, the broad feature above 1.5G 0 shows higher intensity than the SAC peak and dominates the histogram.Presumably, the 1.8G 0 peak, which appears as a shoulder-like structure in http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) the histogram in Fig. 4, might be buried in the predominant broad feature and becomes unrecognizable at 4 K.
Except for this minor difference on the 1.8G 0 peak, there can be seen an overall agreement between the observed room-temperature histogram and the 4 K histogram reported by Makk et al. [10] As is the case with Al, the histogram features of In exhibit no substantial changes between room and low temperatures.We note that the histogram shown in Fig. 4 reveals no peak features around 0.5G 0 , even though the 0.5G 0 peak and the 0.5G 0 plateau can be found in the histograms in Fig. 2 and the trace in Fig. 3, respectively.This absence of the 0.5G 0 peak indicates that the 0.5G 0 state has a small chance of formation but mainly appears in the repetitive traces.Such a contact state would possibly not be an intrinsic state of In but a contaminated one.Contaminated contacts form when residual foreign atoms on the electrode surface happen to be included into a contact, and such an atomic incorporation may not be a frequent process under the ultrahigh vacuum condition when the atomic geometry is entirely shuffled at each contact formation.Thus, the contaminated contacts should have relatively small formation probability, and the absence of the 0.5G 0 peak in the conventional conductance histogram is in consistent with our assumption that the 0.5G 0 state represents a contaminated contact.

IV. DISCUSSION
Table I summarizes the position of the first peak in the conductance histogram of trivalent metals at low and room temperatures.This comparison clearly illustrates the similarity between Al and In and indicates that the missing of the SAC peak in the room temperature histogram is an exceptional phenomenon specific to Ga.As mentioned in Sec.I, the crystal structure of In is tetragonal but deviates only slightly from FCC.Our results, therefore, support the conjecture proposed by Lewis et al. [9] that the non-cubic crystal structure of Ga and the resulting complexity in its necking deformation might lead to the SAC peak missing at room temperature.In a crystal having lower symmetry like Ga, the critical shear stress for activating its slip systems quickly increases with decreasing temperature.At cryogenic temperatures, Ga be- comes brittle and its plastic deformation mostly proceeds via twinning [14], in contrast to FCC metals such as Al which primarily undergo glide deformations even at low temperatures.In the case of In, the twinning deformation becomes dominant at low temperatures but the (111)-slip system remains operative [15].If the peculiar temperature dependence of the Ga SAC peak really comes from the deformation characteristics of Ga, the above comparison about the plastic deformation of three metals implies that the number of active slip systems at low temperatures would make difference between Al/In and Ga concerning the appearance of the SAC peak.We point out that the missing of the SAC peak at room temperature, similar to the one observed on Ga, has also been observed on Mg [16] and Zn [17].These are HCP metals which also have a small number of restrictive slip systems and tend to make twinning deformations at low temperatures.It appears quite counter-intuitive that these non-FCC metals reveal their SAC peak not at room temperature but at low temperatures where they become more brittle and less deformable.Presumably, the contact thinning (and the SAC formation) of non-FCC metals would be accomplished through entirely different processes from those of FCC metals which have been well clarified by direct electron-microscopy observations [18,19].Some peculiar schemes have been proposed for the thinning deformation of atom-sized contacts of W [20] and Bi [21], but details are yet unclarified.For non-FCC metals, further studies would be needed for elucidating the correlation between their deformation characteristics and the SAC formation.

V. CONCLUSION
Indium is the same trivalent metals as Al, but its atomsized contacts have been far less studied than those of Al, probably because of the softness of In that makes this metal quite unsuitable for experiments exploiting the break-junction method.In this work, we have successfully fabricated atom-sized contacts of In by carefully making and breaking wire-wire junctions at room temperature.The observed conductance histogram of In reproduces the peak features reported by Makk et al. [10] at 4 K and hence makes no substantial changes between 4 K and room temperature.Different from the featureless roomtemperature histogram of Ga, our In histogram shows a clear SAC peak at 0.83G 0 in good agreement with the SAC peak of Al.This observation, combined with the nearly FCC structure of In, indicates that the missing of the SAC peak at room-temperature is a phenomenon specific to Ga and might be related to its highly non-cubic http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology Volume 9 (2011) crystal structure and complex deformations as suggested by Lewis et al. [9] The conductance histograms of trivalent metals provide us illustrative examples which reveal the complex origin of the histogram features.The peak structures reflect not only the contact electronic properties but also the contact deformation characteristics.

6 FIG. 1 :
FIG. 1: Repetitive conductance traces observed at room temperature in the contact breaks of In.Successive trace reproduces the same conductance features.

FIG. 2 :
FIG.2: Conductance histograms constructed from the repetitive conductance traces like those shown in Fig.1.We found three types of the repetitive trace and grouped them to obtain three histograms shown in (a) through (c).Because each histogram accumulates nearly identical traces, the intensity of the peak features in each histogram has no physical significance.Their positions, however, indicate us the conductance of some preferred contact geometries.

FIG. 3 :
FIG.3: Examples of the non-repetitive conductance trace observed at room temperature in the contact breaks of In.

FIG. 4 :
FIG. 4: A conventional conductance histogram of In obtained at room temperature.The histogram is constructed from 1197 non-repetitive traces measured on two samples.The first peak is clearly distinguished and located at 0.83G0.

TABLE I :
First peak position in the conductance histogram of trivalent metals at liquid helium and room temperatures.
a Refs.7, 8 b Ref. 9 c Ref. 10 and this work