Nanowire transformation and annealing by Joule heatingapachepersonal.miun.se/~hakoli/olinref-filer/Hummelgard...Nanowire transformation and annealing by Joule heating 4 we observed

Nanowire transformation and annealing by Jouleheating

Magnus Hummelgard1, Renyun Zhang1,Torbjorn Carlberg1, Damjan Vengust2, Damjan Dvorsek2,Dragan Mihailovic2 and Hakan Olin1.

E-mail:[email protected],[email protected],[email protected] Department of Natural Sciences, Engineering and Mathematics, Mid SwedenUniversity, SE-851 70 Sundsvall, Sweden2 Jozef Stefan Institute, Jamova 39, SL-1000 Ljubljana, Slovenia

Abstract. Joule heating of bundles of Mo6S3I6 nanowires, in real time, werestudied using in-situ TEM probing. TEM imaging, electron diffraction, andconductivity measurements showed a complete transformation of Mo6S3I6 intoMo via thermal decomposition. The resulting Mo nanowires, had a conductivitythat were 2-3 orders higher than the starting material. The conductivity increasedeven further, up to 1.8·106 Sm−1, when the Mo nanowires went through annealingphases. These results suggest that Joule heating might be a general way totransform or anneal nanowires, pointing to applications such as metal nanowirefabrication, novel memory elements based on material transformation, or in-situimprovement of field emitters.

nanowires, molecular wires, Joule heating, annealing, molybdenum, Mo6S3I6

PACS numbers: 61.46.Km, 68.37.Lp, 68.37.Ef

Submitted to: Nanotechnology

Nanowire transformation and annealing by Joule heating 2

1. Introduction

Driving a high current through a nanowire lead to increased temperature dueto Joule heating. This current induced heating could lead to failure of nanowires,however, heat could also be used to remove imperfections in the wires by annealing.In situ transmission electron microscope (TEM) probing, is one method to studythese phenomena for direct correlation electrical properties with microstructure ofthe nanowires during Joule heating. This method employs a tiny scanning tunnelingmicroscope (STM) inside a TEM. The STM tip is used for contacting the nanowire andapplying the heating current and at the same time monitoring electrical conductivity,while the TEM is used for imaging of the microstructure.

Such real time in situ Joule heating studies have been done on carbon nanotubes,for example, on the transformation of amorphous carbon into crystalline carbonnanotubes [1]. This transformation suggest that the temperature reached is higherthan 1700 C. Joule heating of the carbon nanotubes give rise to recrystallisationwith a resulting increase in electrical conductivity [2], or leading to superplasticdeformation [3]. By further increasing the electric power, the carbon nanotubes willinstead lead to break-down of the wire [4]. The in situ method during Joule heatingare used to study other forms of carbon and graphene sublimation and multi-layeredge reconstruction have been observed [5].

Compound materials are also studied using in situ TEM Joule heating, in the formof GaN nanowires and BN nanotubes. In situ studies show that thermal decompositionof the GaN nanowires and Ga nanoparticles separate to the surface of the wireduring the failure process [6]. This is of importance since GaN are used in laserdiodes operating at high current densities requiring careful consideration of the heatdissipating. Direct in situ TEM studies of BN nanotubes show thermal decompositionof tubular layers leaving spherical nanoparticles behind on the wire surface beforefailure [7, 8]. A problem of Joule heating compound nanowires is a positive feedbackphenomena that quickly lead to nanowire failure, due to decreasing resistance duringheating. One way that may prevent this is to limit the current by a serial resistor,preventing a positive feedback, in a way similar to what have been shown in a studyof welding of nanowires [9].

Here, we describe a study of a compound nanowire, Mo6S3I6, formed as bundles ofnanowires [10, 11]. There are a number of applications of these wires including vapor-and bio-sensors [12] and they can be assembled into more complex structures [13].However, the properties during Joule heating are not well known, which is ofimportance in applications such as field emission [14]. We made two main observations:first a transformation of Mo6S3I6 to metallic Mo via thermal decomposition. Using aserial resistor to limit the current, allowed us to avoid the nanowire failure until onlyMo remained. In the second observation we used these remaining Mo nanowires tostudy the annealing process, in a way similar to the annealing studies of the carbonnanotubes mentioned above, to reveal details about grain growth and the increasedconductivity.

2. Experimental details

The starting material, Mo6S3I6 bundles of nanowires [11], are synthesized in a single-step process and consist of wires with sub-nanometer diameter. During synthesisthe nanowires self-assemble into weakly bounded bundles. These bundles are easily


dispersed in common polar [15] and organic [16] solvents down to individual molecularwires, but here we used the bundles as received (Mo6 company) without furthertreatment. The electrical conductivity, about 10 Sm−1, of these bundles is lowerthan for metal nanowires [17, 18]. The bundles were 20-1000 nm in diameter and oneto several hundred µm in length.

To study the Joule heating process in detail, we made experiments on thebundles. This was done inside a transmission electron microscope (JEOL-2000FX)using an in-situ TEM probing holder [19] (Nanofactory Instruments). In this in-situmethod [20, 21], also called TEM-STM, one electrode is fixed while the other onecan be moved in three dimensions by a piezo-electric actuator with sub-nanometerresolution. We used two 0.25 mm gold wires as electrodes, and to attach the bundlesto one of them, we simply dipped one of the gold wires in conductive glue andthen in the Mo6S3I6 material. The two electrodes were connected to an electricalmeasurement system (figure 1c) allowing a current to be passed through the bundles.Inside the TEM, a bundle was selected and moved into contact by the piezo-element.In real time, the entire process was observed by TEM imaging or electron diffractionwhile controlling the current through the wire-bundle. Movies of the TEM images ordiffraction patterns were recorded together with corresponding electrical data.

It is hard to measure the temperature of small objects such as nanowires. Inthe case of semiconducting nanowires, one may use the temperature dependency ofcurrent transport through the Schottky barriers that form between the wire and thecontacts [7, 8]. Another way is to use a sacrificial material and observe the evaporationof this material during Joule heating. This method has been used on silicon nanowiresto estimate the Joule heating temperature by evaporating a polymer thin film depositon the nanowires [22]. Here, we evaporated gold nanoparticles deposited on thenanowire bundles. We attached the gold nanoparticles to the surfaces of the bundles inone of the experiments (#15) by mixing them with a solution of sodium citrate followedby sonication, boiling and injection of HAuCl4, and separation by centrifugation [23](see also details in the supplementary).

3. Results

The first, most apparent observations were, when increasing the current through theMo6S3I6 bundles, a sudden jump occurred, and the somewhat irregular wires becomestraight, accompanied by an increase in conductivity by several orders (figure 1 a-b andSupplementary, Movie 1). During this transformation, the diameters of the Mo6S3I6bundles were reduced by 30-60% as shown in the histogram in figure 1d). In addition,electron diffraction clearly showed a transformation of Mo6S3I6 to molybdenum(figure 3d,e,f).

TEM imaging before and after the transformation and the correspondingconductivity measurements (figure 2) also showed a change in structure of the wires.The fresh Mo6S3I6 wire (figure 2, type A) was transformed to an amorphous orpolycrystalline wire (type B), with a large increase in conductivity (see the graph infigure 2). After the transformation, by continued heating of the resulting Mo nanowire,the small grains in the type B increased into larger ones (type C and D) while theconductivity increased further by 1-2 orders reaching up to 1.8 · 106 Sm−1, which isabout one order lower than Mo bulk values (see also the supplementary Movie 2 ofelectron diffraction during the annealing phase). The failure current densities were> 8·106 Acm−2 (see table in Supplementary). To estimate the annealing temperature,


we observed the melting of 50 nm gold nanoparticles in one of the experiment (#15)during the slow annealing phase implying a temperature above 1000C (figure 4).

4. Discussion

4.1. Transformation via thermal decomposition

The first step, the transformation from Mo6S3I6 to metallic Mo, was a fast processwhere the structure of the Mo6S3I6 wires collapsed as the sulphur and iodine atomsvaporised. The reduction in diameter of 30-60% (figure 2) is consistent with atransformation to metallic molybdenum since a change in volume will be determinedby the ratio of the densities of the two materials which is 5. If we assume that all threedimensions were reduced equally, this amounts to a 40% reduction in diameter, whileassuming a fixed length will give a 60% diameter reduction. The expected increase inconductivity of several orders (figure 2), the TEM images (figures 2 and 3), and theelectron diffraction (figure 3d,e,f) all clearly showed a transformation to Mo.

The transformation can be understood if, in the lack of the ternary system Mo-S-I, the Mo-S phase diagram is studied and if the Mo2S3 phase is assumed to be similarto the Mo6S3I6 phase with sulphur replacing the iodine atoms. In the temperaturerange from about 660 to 1550C the Mo2S3 phase transforms to Mo if the sulphur isleaving the lattice. The equilibrium diagram is valid for a gas phase at 1 atm, butin a vacuum, where the present experiments were done, it is likely that the volatileconstituents easy can leave the lattice, especially as the single wires in the bundlesare only about 1 nm in diameter. Upon the collapse, an amorphous structure, ora structure with extremely small crystals form. Heating, up to 900 C of Mo6S3I6nanowire bundles in vacuum does not decompose the material, however some signs ofiodine evaporation is present above 700 C [24]. Using the gold melting observation(figure 4) we thus conclude that the transformation temperature was roughly in therange 900-1050C.

4.2. Annealing and grain growth

In the next annealing phase, at a temperature above 1000C, grain growth occurred.Either it started from an amorphous structure with nucleation and growth, or it startedwith small crystallites, which will grow.

Grain growth is often quantitatively treated [25, 26] by the relation

Dn −Dn0 = Kt (1)

where D is the grain size at a certain time and D0 is the initial grain size, t is the timeand K a constant which depends on the metal composition, temperature and surfaceenergy. The exponent n has been found to vary from 2 to 10 for different cases, but forclean materials at high temperatures the value is close to 2. The process is thermallyactivated as it contains the atomic diffusion over the grain boundary, and K can bedescribed by an Arrhenius expression.

In the present case an estimation of the growth rate can be done, as it is possibleto see when the grains have reached the surface. Equation 1 is only valid as long asthe grain growth mainly occurs in the bulk of the wires and as long as only a minorityof the grains have reached the surface. It is reasonable to assume that this holds aslong as the grains are smaller than about half the diameter of the wires, i.e. at astage reached somewhat earlier than what can be seen in figure 2 type C. From the


experiments it can be estimated that the grain size is about 50 nm after about 10min, which means that the constant K becomes 4·10−14 cm2s−1 if the exponent n=2is used.

In the literature one can find investigations of grain growth of nanocrystallinematerials, e.g. [27] and [28] in Co and W, respectively. In [27], at 530 C, it wasfound that the growth deviate from the law represented by equation 1 in such a waythat the exponent n change drastically during the growth from about 1.1 to 4.4, andthe conclusion was that grain growth in the nano range is different from in the microrange. In the present investigation we did not study the grain growth in real timeand therefore it is not possible to evaluate the exponent as we only have start andend data, but in the part of the data in [27] where the exponent was about 2 the rateconstant was about 2·10−14 cm2s−1, which is fairly close to the value found in the Mowires. From the data in [28] rate constants, for grain growth in W can be evaluatedat different temperatures, and at 1200 C, which is a third of the melting point, a Kvalue of 2·10−14 cm2s−1 was obtained. A relatively close agreement can thus be foundbetween the present data and the results in the cited investigations if a temperatureof about a third of the melting point is chosen for the comparison. It can thus beconcluded that grain growth occurs in the Mo wires in a way similar to what has beenobserved in nanocrystalline materials before.

Depending on the energy balances, and thus the orientation of the grains,continuing growth rate will be different on different places along the wires. However,data of the pertinent energies indicate that the growth will slow down or even stop atmany boundaries along the wires as the surface energy of Mo is about 2 J/m2 [29],and the grain boundary energy is probably smaller. No data have been found for Mo,but for several other metals the grain boundary energies are given values between 0.5and 1 J/m2 [30]. Of course they vary strongly with the type of grain boundary, andon certain spots along the wires some grains will shrink and disappear, but the finalappearance of the wires, as illustrated in figure 2 type D, is what can be expected.

4.3. Temperature

The gold melting experiment (circa 1000 C) occurred after the transformation stageand in the beginning of the annealing phase. This gold melting experiment is similarto the carbon nanotube based method of growing carbon cages by gold templating [31],where the gold evaporate away or intercalate with the carbon nanotube. We mightsuspect such a mixing of the gold nanoparticles with the Mo nanowire. However, theeutectic temperature of a mixture of Mo-Au is 1054 C [32], which is close to themelting point of gold, 1064 C. This means that even if the Au mix with the Monanowire, the temperature estimation from Au melting/evaporation experiment stillgive a valid value. We also know that the temperature was below 2600 C, when Momelts. However, the electrical power during the annealing was well below the failurecurrent when Mo melts, it is thus likely that the temperature was closer to 1000 Cthan to the Mo melting point, which is also consistent with the discussion on graingrowth above.

In an attempt to correlate the Joule heating current with the temperature wemade a simple model of the wire, following [33], with the contact electrodes asheat sinks and with radiation cooling (see Supplementary). However, the resultingtemperatures were too high to be realistic. One problem with this approach were theunknown contact resistances. Even if we can calibrate the model using the data from


the gold melting experiment, we could not be sure that the contacts were stable overtime. We also made current-voltage characterisation (see Supplementary) showingnon-linear relations, that we interpreted as suppressed conductivity at high currentsdue to phonon-scattering. However, a simple free electron model of this did alsogave unrealistically high temperatures. One possible source of errors was again theunknown contact resistances.

4.4. Conductivity

It is well known that the conductivities of nanowires often are lower than thecorresponding bulk values due to higher degree of scattering at the surface and at thegrain boundaries [34, 35, 36]. For the smallest, atomic scale nanowires, the electrontransport is ballistic, but there is a transition to diffusive transport for larger ones [37].When the mean free path is longer than the grain size or the diameter of the nanowire,the electron pass before scattering will be shortened. The conductivity is proportionalto the mean free path and a higher degree of scattering will lead to lower conductivity.

In the present case, we directly observed the grain sizes and during the annealingphase, the grains coalescent into larger ones that extended the entire nanowirediameter. However, the growth in the axial direction where much slower and wedid not extended the study to turn the entire (many micrometer long) nanowire intoa single crystal. We thus had a high density of grains, as compared to bulk, withhigh degree of scattering against grain boundaries. It is thus not surprising that theconductivity of the Mo nanowire is one order lower than bulk values.

Another source of scattering might be sulfur or iodine atoms left in the wire.However, the solubility of S or I is limited as can be seen in Mo-S [38] and Mo-I [39] phase diagrams (in lack of the ternary diagram Mo-S-I). For example, sulfurdoes not solve in Mo at room temperature and only at a maximum of 3% at highertemperatures. If there was any S left in the wire at high temperature, it will turn intoMoS2 (with a max of 3% S) when lowering to room temperature. These MoS2 willthen migrate to the surface or to the grain boundaries. We did not specifically studythese possible residues, but at the resolution available in the set-up no such MoS2were visible. EDS, that was not available in the present set-up, might give some moreinformation about S or I residuals.

One source of uncertainty in two-terminal conductance measurements are theunknown contact resistances. It is known that the initial contact resistances arehigh-ohmic (MΩ) for in-situ TEM probing experiments [40], but by driving a highcurrent through the wire the contacts are healed and the resistances decrease. Wealso observed a similar behaviour. In an attempt to model the temperature (seesupplementary information) we discussed the role of contact resistance and if wecalibrate the temperature model with the gold melting experiments (figure 4) wearrived at initial contact resistances of a few tens of kΩ. However, the contactresistances are still uncertain and as the resulting Mo nanowires are low-ohmic ones,the contacts could constitute a significant part of the resistance. Therefor, instead ofsubtracting estimated contact resistances, we consider the measured values as a lowerlimit of the conductivity.

To address this problem of contact resistances, an interesting extension of thepresent study, that might be possible in a carefully designed set-up, would be toprobe the conductivity along the wire and then deduce the nanowire conductivity. Ifa sharp enough tip is used, for example from another nanowire, it might be possible


to directly probe the degree of ballistic transport within each grain and the electronreflection coefficient at the grain boundaries [34].

4.5. Implications for applications

Other molybdenum chalcogenides [41] (Se and Te) have been fabricated in the shapeof nanowires with diameters around 1 nm [42] and also occurring as bundles [43]. Itis likely that Joule heating of these wires could also result in molybdenum wires, andthus be another route for preparation of molybdenum nanowires. Other metals withhigh melting temperature like tungsten, vanadium and niobium, form chalcogenides,which decompose at lower temperature, and these metals should also be obtainedas nanowires in a similar way. Using the same process it might also be possible totransform conducting metal oxides nanowires [41]. One may also compare the insitu Joule heating method with a more standard in situ TEM method that utilize aheating holder. In the standard set-up the temperature is known with a high accuracy.For example, using this kind of heating holders, the thermal decomposition of metaloxides have been studied, such as W18O49 [44] as well as annealing of silver wires [45],however, the conductivity data have to be provided ex situ.

The high differences in conductivity between fresh wires and metal ones suggestapplications as memory elements [46, 47]. A short pulse of high current wouldpermanently transform a high ohmic nanowire to a low ohmic one, and thus providetwo distinct logical states for a kind of nanowire permanent memory. The Joule heatingmethod might also be of general use for improving the crystallinity of nanowires andthus improve conductivity or mechanical properties. For example, field emitters couldbe improved by increasing the current to transform or anneal the wires, and indeedthis kind of sudden increase in conductivity has been observed earlier in field emissionexperiments [14].

5. Conclusion

In conclusion, straight metallic molybdenum nanowires were non-reversibletransformed from Mo6S3I6 bundles by Joule heating via thermal decomposition asconsistently observed by conductivity increase, reduction in diameter, TEM imaging,and electron diffraction. Annealing of the Mo nanowires, with the observed graingrowth as result, seems to prolong in a way that has been observed in nanocrystallinematerials before. Our results suggests that Joule heating might be a general way toanneal or transform nanowires, pointing to applications such as in-situ improvement offield emitters, metal nanowire fabrication, or novel memory elements based on materialtransformation.

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Figure 1. a) In-situ TEM image of the Mo6S3I6 nanowire bundle before, andb) after transformation. c) Diagram of the in-situ TEM probe. The serialresistor limits the current through the wire bundle. d) Histogram of the diameterreduction after transformation of Mo6S3I6 to Mo.


Figure 2. Illustrative TEM images of individual nanowire bundles observedduring different stages of current-treatment. Note that the images are from severaldifferent nanowires. Type A is a fresh sample (scale bar is 100 nm), type B isjust after the transformation into a Mo nanowire (scale 50 nm), and type C (scale50 nm) and D (scale 50 nm) are from the annealing phase. The graph showsthe electrical conductivity and the electrical power during the transformation andannealing phases. The conductivity increases in two steps: first in a fast processduring the first few seconds and then a slow increase during a longer time. (Thedrop in current at 300 s is due to a decrease in bias voltage for diffraction-studies).


Figure 3. TEM images and diffraction patterns before and after current-heat-treatment of the nanowire bundles. The scale-bars in image a) is 700 nm, b) is100 nm, c) 90 nm, d) 0.25/A, e, f) 0.5/A. The black dot in the centre of TEMimages a) and c) is due to an imaging artifact of the TEM. One of the contacts isvisible in the bottom-left corner of a). TEM image a) with corresponding electrondiffraction pattern indexed to Mo6S3I6 structure d) is before current-treatment.TEM image b) with corresponding electron diffraction pattern e) is the type Bstructure observed after the nanowire bundle was transformed. TEM image c)with corresponding electron diffraction pattern indexed to crystalline Mo f) showsthe resulting type D structure after the slow annealing process. Image a,c,d,f) arefrom the same nanowire while b,e) are from another nanowire.


Figure 4. To estimate the temperature, gold nanoparticles (arrowed) wereattached to the surfaces which melted during the slow transformation process, i.e.when wire changed from type B towards type D. This indicate that temperatureis above ∼1000C. TEM images of a) before melting of gold particles and b) after.The scale-bars are in both TEM images 100 nm. The black dot in the centre ofboth TEM images is due to a imaging artifact of the TEM.


6. Supplementary

6.1. Supplementary TEM movies

Movie 1 shows the transformation from a bent and twisted MoSI wire into a straightwire under electric current. Movie 2 shows the diffraction pattern of a Mo nanowireof type B into polycrystalline Mo metal during the slow annealing process.


6.2. Experimental data table

Table 1. A total of fifteen experiments were made. The table is arranged by thetypes defined in figure 2. In some experiments the wire burned off and when itwas possible the remaining part were reconnected and the experiment continued,for example #6 burned off three times. In some of the experiments two types ofnanowire bundles was observed along the same wire; some sections of the wirewas of one type while other parts of another type. In the last experiments #15,gold nanoparticles where attached to the nanowire to estimate the temperatureby melting gold nanoparticles.

#a

Typeb

Φ(nm)c

L(µm)d

I(uA)e

Uw(V)f

P(uW)g σ(Sm

−1)h

G(uS)i

j(Acm−2

)j

Notek

1 B 186 49.0 313 30.0 9390 1.88E+04 1.04E+01 1.15E+06 Burned off

1 C.D 168 27.0 552 52.0 28704 1.29E+04 1.06E+01 2.49E+06 Burned off

2 A 1250 264 – – – – – –

2 B 660 264∗

132 13.5 1782 7.55E+03 9.78E+00 3.86E+04

2 C.D 542 208 217 21.0 4557 9.32E+03 1.03E+01 9.41E+04 Burned off

3 A 1226 239 0.7 30.5 20 4 2.14E-02 5.53E+01

3 B 1174 222 903 82.0 74046 2.26E+03 1.10E+01 8.35E+04 Burned off

4 B 295 242 175 2.51 439 2.47E+05 6.97E+01 2.56E+05 Burned off

5 A 470 34.2 – – – – – –

5 B 245 20.0 1047 0.700 733 6.35E+05 1.50E+03 2.22E+06

5 C.D 216 20.0∗

1017 0.612 622 9.07E+05 1.66E+03 2.78E+06 Burned off

6 A 47.8 11.1 0.347 42.4 15 51 8.18E-03 1.93E+04

6 B.E 44.4 11.5 0.197 18.3 4 80 1.08E-02 1.27E+04 Burned off

6 E 26.1 4.96 3.76 10.5 39 3.32E+03 3.58E-01 7.03E+05 Burned off

6 C.D.E 21.7 4.30 31.3 2.35 74 1.55E+05 1.33E+01 8.47E+06 Burned off

7 A 187 2.18 0.180 10.1 2 1 1.78E-02 6.56E+02

7 A.B 147 2.18 11.4 2.5 28 591 4.60E+00 6.72E+04

8 A 130 1.04 0.989 0.412 0 188 2.40E+00 7.45E+03

8 A 113 1.17 7.10 1.26 9 658 5.63E+00 7.08E+04

8 E 122 1.17 14.8 0.526 8 281 2.81E+01 1.27E+05

9 A 391 45.3 0.674 79.9 54 3 8.44E-03 5.62E+02 Burned off

9 E 221 23.2 1.68 17.4 29 58 9.66E-02 4.38E+03 Burned off

10 A 339 36.5 2.63 87.3 230 12 3.01E-02 2.92E+03 Burned off

11 A 114 5.04 0.797 66.5 53 6 1.20E-02 7.81E+03 Burned off

11 E 113 5.04∗

1.1 52.6 56 10 2.02E-02 1.06E+04 Burned off

12 A 278 100 1.78 46.5 83 63 3.83E-02 2.93E+03

12 B.C.D 348 100 414 0.246 102 1.77E+06 1.68E+03 4.35E+05

13 A 769 102 27.5 2.36 65 2.56E+03 1.17E+01 5.92E+03

13 B 476 102∗

215 5.00 1075 2.46E+04 4.30E+01 1.21E+05 Burned off

14 A 700 45 2.57 37.7 97 8 6.82E-02 6.68E+02

14 B 348 45 25.7 0.300 8 4.05E+04 8.57E+01 2.70E+04

14 C.D 278 45 429 0.271 116 1.17E+06 1.58E+03 7.07E+05 Burned off

15 A 532 33.8 0.319 12.8 4 4 2.49E-02 1.44E+02 Gold exist

15 B 504 33.8∗

18.7 7.39 138 429 2.53E+00 9.38E+03 Gold exist

15 B 362 33.8∗

125 5.66 708 7.23E+03 2.21E+01 1.22E+05 Gold melts

15 C.D 179 33.8∗

456 5.43 2476 1.12E+05 8.40E+01 1.81E+06

aSample number

bVisual appearance of nanowire according to figure 2. Type E, not shown in figure 2, denotes a

damaged wire.cMeasured diameter of nanowire.

dMeasured length of nanowire.

eMeasured electric current through the nanowire.

fMeasured voltage over the nanowire.

gCalculated electrical power in the nanowire.

hCalculated electrical conductivity in the nanowire.

iCalculated conductance of the nanowire.

jCalculated current density in the nanowire.

kIndicates if the wire burned-off.

∗Measurements unavailable, length estimated by previous record.


Figure 5. Temperature modeling. The nanowire is modeled as a cylinder.The generated heat inside the wire by the electric current is dissipated away byconduction through the connected electrodes and by radiation from its surface.

6.3. Model of the nanowire temperature during Joule heating

To estimate the temperature in the nanowire connected to two electrodes one canmodel it as a cylinder with half the length of the nanowire and connect at one ofthe ends to a heat sink and the other end is kept free. The time independent heatequation,

κA∂2T

∂x2dx− 2πrσ(T 4 − T 4

0 )dx+RI2

Ldx = 0, (2)

can then be used to model the heat dissipation [33], where R is the resistance ofthe wire, I the electric current, T the temperature of the wire, T0 the surroundingtemperature, A the cross-section area, L half the nanowire length, κ the thermalconductivity, and σ is the Stefan-Boltzmann constant (we assume an emissivity=1).For a system where both sides are attached to heat sinks to produce a closed electriccircuit, an electric current will heat the nanowire. There are heat loss by conductionand by radiation (figure 5). The thermal conductivity for a metal can be estimatedby using Wiedemann-Franz law, K/σ = LT , that states that for metals the ratio ofthe thermal conductivity and electrical conductivity is proportional to temperatureby the Lorenz-number (2.45 · 10−8 WΩK−2). In the experiments, the measured theelectrical conductivities were below 106 Sm−1 and therefore the thermal conductivityof the nanowire is assumed to have its major contribution from phonons with a thermalconductivity of 10 WK−1m−1, which we used as a fixed value in the model. By solvingequation (2) numerically, using the LSODE-algorithm in the GNU Octave program,and by inserting the diameter 1174 nm, L=222/2 µm and T0=300 K into the equationwe can calculate the temperature along the length of the nanowire and as functionof input electric power. These calculations were made on nanowires from three ofthe experiments (#2, #3 and #15) and the calculated temperatures are presented intable 2.

The measured resistance R value can be described as the sum of contact resistanceand nanowire resistance. If the contact resistance is proportional or higher thanthe nanowire resistance most of the input electric power will be dissipated in thecontact regions giving a lower temperature of the nanowire than the temperaturemodel will predict. Instead if the temperature of the nanowire, by any other meansis known, as in the case when gold nanoparticles melts (T=1064 C) one can do


the reverse calculations and determine the contact resistance. One experiment (#15)was done observing the melting of the gold nanoparticles. Measured total resistancewas 45.3 kOhm, when the gold melted, and the temperature model gives a contactresistance of 37.4 kOhm. Table 2 shows the calculated temperatures with and withoutcorrection of contact resistance for two different samples, assuming the same contactresistance as in the gold melting experiment.

Without contact resistance correction the temperature model gives unrealisticallyto high values. With correction of contact resistance, calculated temperatures showssomewhat lower values but still to high, with values above the melting temperatureof molybdenum (2600 C). The contact resistance are influencing the estimatedtemperatures and as this resistance is unknown (except for experiment #15) andchanging over time, the model does not give reliable temperature estimates.

Table 2. Temperature calculation during the slow annealing process as observedfrom electron diffraction pattern changes. The upper part of the table is datataken from sample no 2: L=264 µm, φ=660 nm and the lower part is from sampleno 3: L=222 µm, φ=1174 nm. The start of the slow annealing phase was detectedby studying the electron diffraction pattern change during increase of bias voltage.Before annealing the patterns were static and at the beginning and during theannealing the diffraction pattern rotated.I(uA)

a R(kΩ)b Rc(kΩ)

c j(Acm−2

)d σ(Sm

−1)e σc(Sm

−1)f

∆T (C)

g∆Tc(

C)

hAnnealing

i

33 106 68.6 9.6E+03 7280 11200 1210 960 Before

122 102 64.6 3.6E+04 7570 11900 2930 2530 Beginning

154 101 63.6 4.5E+04 7640 12100 3330 2880 During

34 104 66.6 3.2E+03 1990 3100 600 409 Before

163 92.6 55.2 1.5E+04 2220 3740 2930 2520 Beginning

289 93.1 55.7 2.7E+04 2220 3710 4030 3520 During

871 91.8 54.4 8.1E+04 2240 3790 7220 6280 Burn off

aMeasured electric current.

bMeasured electrical resistance.

cCalculated electrical resistance after correction for contact resistances.

dCurrent density.

eElectrical conductivity.

fElectrical conductivity, after correction.

gCalculated temperature in nanowire from model.

hCalculated temperature after correction of contact resistance.

iObserved change in electron diffraction pattern i.e. when the slow annealing phase begins.

6.4. Procedure for depositing gold nanoparticles to the Mo6S3I6 nanowire bundles

Briefly, 1 mg Mo6S3I6 nanowire bundles were mixed with 4 ml sodium citrate (1 wt %in doubly distilled water) and sonicated for 5 min, then the mixture was diluted to 100ml using doubly distilled water and heated to the boiling point. Then, 1 ml HAuCl4(1 wt % in doubly distilled water) was injected into the solution during continuedheating for 5 min. The sample was separated using a centrifuge at a speed of 5000rpm.

6.5. Temperature estimation from non-linear IV-curves

IV-curves before transformation of the Mo6S3I6 bundle and after annealing to type Dstructure is shown in figure 6a,b.

If one consider that the current I is depending on the electrical conductivity σ aswell as the temperature T (u) due to phononic interactions and that the temperatureitself to be depending on the bias voltage u to the second order, because the electricinput power into the wire is P = u2/R we get

I =u

lA ( 1σ + cT (u))

(3)


Figure 6. IV characteristic of sample #14 a) before Mo6S3I6 bundletransformation and b) at the end of the annealing phase when the nanowirehas reach type D structure state. The non-linear shape may be due to phononscattering that limits the current. Both raising voltage and dropping voltagecurves are presented in both figures.

where l and A is the length respective the cross-section area of the nanowire, and thetemperature will be

T (u) = Tmaxu2 + T0. (4)

By applying a free-electron-model we can then calculate the constant c inequation 3 if we insert the material data for metallic molybdenum; two conductingelectron per unit cell and speed of sound V = 5400m/s:

c =kBme(2F kF )2

πρvFn(me3hV )2≈ 3 · 10−11Ωm/K, (5)

kF = (3π2n)1/3, (6)

vF = hkF /me, (7)

and

F =h2

2me(3π2n)2/3 ≈ 5.8eV. (8)

If we then fit equations 3 and 4 to the measurement data via Tmax we getTmax = 27000K which is an unrealistically high temperature (figure 7). The calculatedconstant c is a factor of ten too small to give reasonable temperatures. The freeelectron model might be too simple and it could be, for example, corrected for aneffective electron mass, but again the unknown contact resistances are making themodeling problematic.


Figure 7. Current-voltage data and model of the temperature usingequations 3 and 4. Fitting of experimental data (crosses and diamonds) to themodel gives unrealistically high temperatures.

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Nanowire transformation and annealing by Joule heatingapachepersonal.miun.se/~hakoli/olinref-filer/Hummelgard...Nanowire transformation and annealing by Joule heating 4 we observed