Assembly of bismuth clusters into nanowires using etched V-grooves as templates

A. I. Ayesh 1,2, J. G. Partridge1,2, S. A. Brown1,2, R. Reichel1,2, A. D. F. Dunbar1,2

1Nanostructure Engineering Science and Technology (NEST) Group and the MacDiarmid Institute of Advanced Materials and Nanotechnology

2Department of Physics and Astronomy, University of Canterbury, Christchurch, New Zealand

Abstract—The cluster assembly method reported here employs V-grooves as templates for nanowire fabrication. This technique allows the formation of contacted electrically conducting nanowires using simple optical lithography and without painstaking manipulation of the clusters. In–vacuum, temperature dependent I(V) measurements were performed on Bi wires with widths ~1 µm and lengths 50 µm. The temperature dependent resistance of the Bi wires is explained by the variation in the carrier concentration in Bi with temperature.

Keywords: Nanowires; Bismuth; Templated assembly

I. INTRODUCTION

Bi nanoclusters are considered to be a possible model system to study quantum properties in a low dimensional system at room temperature due to the high carrier mobility, the long mean free path and the small effective mass of electrons in Bi [1]. Bulk Bi is a semimetal with a small band overlap (Eg = -38 meV) and an equal number of electrons and holes. If the width of a Bi wire is reduced to the nanoscale, it shows a transition to semiconducting behaviour [2]. Bi nanowires have to date demonstrated useful thermoelectric and magnetoresistive properties [1]. Bi can also be alloyed isoelectronically with other materials (e.g. Sb) to produce high mobility alloys [1]. Bi has a rhombohedral crystal structure [1].

In this work, Bi nanoclusters have been used as building blocks to fabricate wires which have widths in the nano-scale regime. The cluster assembly method provides a practical way of producing supported electrically conducting wires from soft-landed (< 0.001 eV/atom) Bi clusters. This method may be compatible with current Si-based microelectronics processes.

Previous results for Bi and Sb cluster-assembled wires were obtained in a high vacuum deposition system [3-5]. In that system the cluster beam diameter was less than 3mm and non-uniformity of cluster flux across the beam produced significant coverage variation across deposited beam spots. These previous studies focused either on the morphology of the Bi and Sb wires in the V-grooves, or the current-voltage characteristics of Sb nanowires. The focus of this paper is the effect of basic cluster deposition parameters (cluster velocity and the nominal deposited thickness of clusters) for Bi clusters in a new ultra-high vacuum compatible cluster deposition system [6]. This apparatus produces a beam spot exceeding 5cm at the entrance to the deposition chamber, and a

homogenous deposition rate over an area of several square centimetres.

Deposition experiments with a range of source inlet Ar flow-rates were devised in order to understand how the assembly of Bi cluster wires is affected by cluster reflection and motion of clusters on the V-groove walls and the relative contribution of these Bi cluster landing properties. The study also includes I(V) and temperature dependent resistance measurements for Bi wires.

In section II we describe V-groove fabrication, the cluster deposition system and the procedure for forming wires. In section III we discuss the wire morphology, the electrical and cryogenic measurement techniques and present results of electrical measurements on a Bi cluster-assembled wire. In section IV we present our conclusions.

II. EXPERIMENTAL PROCEDURE

An Inert Gas Aggregation (IGA) source was selected to produce the Bi clusters required for this study. Inert Ar gas (99.999% purity) was let in to the source to assist in the aggregation of atomic Bi vapour, produced from a tungsten-filament heated crucible. The crucible contained Bi pellets (purity 99.999%) which were heated to ~ 850oC. A beam of clusters is produced at the source exit. The velocity / kinetic energy of the clusters can be controlled using the source inlet Ar flow-rate [6]. The cluster deposition rate is measured using a quartz crystal Film Thickness Monitor (FTM) mounted in the deposition chamber directly behind a retractable cryostat cold-finger which carries the V-grooved samples. A full description of the deposition system can be found in [6].

V-grooved Si substrates were fabricated using optical lithography and KOH etching [4]. For contacted samples a further lithography stage was used to produce Ti/Au contacts which extended to the apex of the V-grooves. Substrates were passivated with thermally grown oxide prior to deposition of either clusters or the contacts and the separation of these contacts (50μm) defined the length of the cluster-assembled wires.

Both contacted and non-contacted V-grooved samples were mounted on the cryostat cold finger in the deposition chamber. Spring-loaded probes were used to establish contact to planar pads on the contacted sample. The electrical conductivity was measured throughout the contacted V-groove cluster deposition

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experiment. A sharp rise in the conductivity, indicated completion of the wire (the duration of the deposition was ~5-minutes and the deposition rate was 0.4Å/s). The cluster deposition was stopped within 5-seconds of measuring an onset current (manifesting itself as a rise in current flow from ~10pA to ~15nA with a 10mV bias between the contacts). Electrical measurements on the wire formed were subsequently conducted in high vacuum of 10-6–10-7 Torr in the temperature range 4.2–300 K.

III. RESULTS AND DISCUSSION

A. Morphology Bi cluster-assembled wires were produced using source

inlet Ar flow-rates 80–260sccm on non-contacted passivated V-grooves with fixed deposition rates (0.4Å/s) (measured using the FTM) and fixed deposition times of 4-minutes. The morphology of the wires has been studied using Field-Emission Scanning Electron Microscope (FE-SEM) imaging.

Fig. 1 shows FE-SEM images for two wires deposited on 5.5μm V-grooves with source inlet Ar flow-rates of 80sccm (Fig. 1(a)) and 260sccm (Fig. 1(b)). Clusters have assembled at the apex of the V-grooves, whilst the V-groove walls on each sample support relatively few clusters. The wires are similar in width and the density of the packed clusters is similar for the two samples.

The almost complete absence of clusters from the walls of the V-grooves suggests that the vast majority of the Bi clusters incident on the walls tend to move towards the apex. The motion of the clusters is then arrested either by the apex or other stationary clusters. A more detailed discussion of the bouncing of Bi clusters, and a comparison with the behaviour of Sb clusters, is given below.

The dependence of the average diameter of the Bi clusters on the source inlet Ar flow-rate is shown in Fig. 2. Cluster diameters were measured from FE-SEM images of clusters on the plateaus surrounding the V-grooves. The diamonds and squares in the figure represent two different runs. The average diameter is seen to be approximately constant (~35 nm) across the full range of source inlet Ar flow-rates. The uncertainties quoted in Fig 2, and throughout this paper, are two standard deviations of the measured distribution. The constant cluster diameter observed in Fig. 2 is rather remarkable – in many gas aggregation sources, changes in flow rate (which necessarily cause a change in source pressure) result in a change in cluster size due to the different aggregation conditions.

Fig. 3 (a) shows the dependence of the cluster-assembled wire width on the source inlet Ar flow-rate for V-grooves of width 5.5μm and 2.2μm. Samples containing V-grooves with different sizes were placed immediately next to each other in order to eliminate any possibility of different amounts of clusters being deposited. The wires formed in 5.5μm wide V-grooves are clearly wider than those formed in 2.2μm wide V-grooves. In both the 5.5μm and 2.2μm wide V-grooves, the average width of the cluster-assembled wires remained approximately constant over the full range of source inlet Ar flow-rates (80-260sccm).

Fig. 3 (b) shows the dependence of the ratio of the widths of cluster-assembled wires fabricated in 5.5μm and 2.2μm wide V-grooves on source inlet Ar flow-rate. The wire widths were measured using FE-SEM imaging and each data point represents an average taken from 20-25 wires and 3 measurements for each wire. The weak trend to a smaller ratio for larger flow rates is not significant. The ratio of widths strongly reflects the ratio of the V-groove widths i.e. the wire width is proportional to the ‘capture’ area. While this might at first sight seem an obvious result, it implies that the number of Bi clusters that accumulate in a V-groove is not dependent on the number of clusters already in that V-groove. This result allows an important conclusion to be drawn together with the data from Fig. 4 below. Very few clusters are lost from the V-grooves i.e. there are very few clusters which bounce out of the V-grooves (as there were in previous Sb experiments [3-5]).

Figure 2. The average diameter of clusters produced using the IGA source with source inlet Ar flow-rates of 80sccm to 260sccm. The results were

collected from two different runs where 25 clusters were measured for each flow-rate/data point.

Figure 1. Field Emission-SEM images of Bi clusters deposited on passivated Si V-grooves (width 5.5μm) with (a) a source inlet Ar flow-rate

of 80 sccm and (b) with a source inlet Ar flow-rate of 260sccm.

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At lower flow-rates, we would expect the clusters to travel smaller average distances on the inclined walls and therefore higher coverages would be found on the V-groove walls. Using the IGA source and source inlet Ar flow-rates below 80sccm, the deposition rates attainable in the configuration of the new system used here were very low, so deposition using flow rates less than 80sccm was not possible.

Fig. 4 shows the dependence of wire width on the nominal thickness of deposited clusters (measured using the FTM) with constant source inlet Ar flow-rate (100sccm). The linear increase in the wire width shown in Fig. 4 is not the obvious result that might initially be expected. The volume of the clusters trapped in the V-grooves is expected to increase linearly with nominal deposited thickness. If the wire was compact with a triangular cross-section, the wire width would increase as the square root of the nominal deposited thickness. The observed linear dependence is therefore a result of the V-shaped wire cross section and the relatively constant height of clusters in the V-groove i.e. the clusters “back up” the V-groove as they slide down the V-groove walls. This is very different from the wires produced from Sb clusters which had rounded / triangular cross-sections at high flow rates [3-5]. The different behaviour of the Bi clusters can be attributed to their tendency to ‘wet’ the surface more than Sb clusters. The greater degree of wetting means that Bi clusters are “stickier” [3-5].

Fig. 4 also shows the dependence of the cluster surface coverage (psurface) and the corrected coverage (p) on the plateau with the nominal deposited thickness of clusters, for samples prepared with a source inlet Ar flow-rate of 100sccm. The cluster coverage on the SiO2 plateaus surrounding the V-

grooves was calculated from FE-SEM images using image processing software. The corrected coverage was found using the relation:

p = -ln (1-psurface)

[7]. This relationship takes into account the probability that a landing cluster might become a constituent part of the first layer or a constituent part of a higher layer. Fig. 4 shows that, as expected, both the surface plateau coverage and the corrected coverage increase as the total deposited thickness of clusters is increased. However, the apparently linear increase in plateau coverage with the increase of the nominal deposited thickness of clusters is deceptive. After correction, the plateau coverage shows a higher rate of increase. It is believed that this is because incident Bi clusters bounce from clean plateaus more readily than they bounce from the surface when other clusters are attached to the plateaus i.e. deposited clusters serve as soft-landing sites for clusters incident upon them. Bi clusters certainly bounce less easily from plateaus than Sb clusters [3-5], and, for reasons described above, we believe that Bi clusters do not bounce out of the V-grooves: when incident on a V-groove Bi clusters always appear to be trapped, either through a soft landing site on another cluster or by the apex of the V-groove itself.

B. Electrical measurements Fig. 5 shows an example of the dependence of wire

resistance on temperature in the range 4.2–300 K. This wire was produced using source inlet Ar flow-rate of 180sccm. The curve shows an increase in resistance with decreasing temperature (negative temperature coefficient of resistance (TCR)). The inset in fig. 5 shows the linear I(V) curve for the same wire at 300K. Measured wires showed an ohmic conduction characteristic (over the same voltage range -10mV to 10mV).

Figure 4. The surface cluster coverage ( ) and the corrected cluster coverage ( )on the passivated plateaus measured for four nominal

deposited thicknesses of Bi clusters (left hand side scale) and the dependence of cluster-assembled wire width on the nominal deposited

thickness of Bi clusters ( ) (right hand side scale)

Figure 3. Dependence on source inlet Ar flow-rate of (a) the average width of wires fabricated in V-grooves of width 2.2μm ( ) and 5.5μm

( ) and (b) the ratio of the widths of cluster-assembled wires fabricated in V-grooves of width 5.5 (W5) and 2.2μm (W2).

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The negative TCR can be explained in terms of the carrier concentration in the Bi cluster wires. As the temperature decreases from 300K to 4.2K, the decrease in the carrier concentration outweighs any increase in the carrier mobility [2]. This behaviour is different than that of bulk Bi, where there is a positive TCR [8, 9], because in that case the increasing carrier mobility outweighs the decreasing carrier concentration. In the Bi cluster-assembled wires produced to date, it is likely that the dependence of the mobility on temperature is dramatically reduced at temperatures less than 70 K (compared to the bulk) because the dominant scattering mechanism is scattering from the cluster boundaries; phonon scattering which gives rise to the temperature dependent mobility data reported in [2, 10] can be ignored.

IV. CONCLUSION

An Inert Gas Aggregation (IGA) method was used to prepare Bi cluster-assembled nanowires. The average cluster size was found to be independent of source inlet Ar flow-rate. Wire widths were found to increase linearly as the nominal deposited thickness of clusters was increased. Wires formed in 5.5μm wide V-grooves were wider than those formed in 2.2μm wide V-grooves and the ratio of these wire widths was very similar to the ratio of the V-groove widths (i.e. the cluster ‘capture’ widths). Over the range of source inlet Ar flow-rates

used for these experiments the wire widths were approximately equal for a given V-groove width. The corrected cluster coverage on the plateaus surrounding the V-grooves was found to increase with the nominal deposited thickness superlinearly. This property of the cluster film growth was thought to be due to a difference in reflection from a surface covered with other clusters as opposed to clean plateaus. Pre-existing clusters are believed to serve as soft-landing sites for clusters arriving later.

The resistance of Bi wires showed a negative temperature coefficient of resistance (TCR). The negative TCR was explained in terms of the decrease in carrier concentration which outweighed any increase in the carrier mobility as the sample temperature was decreased from 300K to 4.2K.

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Figure 5. Dependence of the resistance of a cluster-assembled Bi wire on temperature. The inset is I(V) plot of the same wire at room

temperature. The contacted wire has the same contact geometry as that shown in Fig. 4 of reference [3].

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