IOP PUBLISHING NANOTECHNOLOGY

Nanotechnology 19 (2008) 415302 (7pp) doi:10.1088/0957-4484/19/41/415302

Exploring the conduction in atomic-sizedmetallic constrictions created bycontrolled ion etchingA Fernandez-Pacheco1,2, J M De Teresa2,3, R Cordoba1 andM R Ibarra1,2

1 Instituto de Nanociencia de Aragon, Universidad de Zaragoza, Zaragoza, 50009, Spain2 Instituto de Ciencia de Materiales de Aragon, Universidad de Zaragoza-CSIC, Facultad deCiencias, Zaragoza, 50009, Spain

E-mail: deteresa@unizar.es

Received 21 April 2008, in final form 22 July 2008Published 3 September 2008Online at stacks.iop.org/Nano/19/415302

AbstractA novel technique to establish atomic-sized contacts in metallic materials is shown. It is basedon etching a (sub)micrometric electrode via a low-energy focused ion beam. The in situmeasurements of the nanoconstriction resistance during the etching process permit control ofthe formation of atomic-sized constrictions with milling time, observing steps in theconductance in the range of the conductance quantum (G0 = 2e2/h), just before entering thetunnelling regime. These constrictions are highly stable with time due to the adherence to asubstrate, which allows further studies such as the detailed current–voltage transportinvestigation reported here. Scanning electron microscopy images are used to correlate theetching process and the constriction microstructure. The high control achieved in the processmakes us suggest this technique as a promising route to study physical phenomena in the vergeof the metal–tunnel conduction crossover.

S Supplementary data are available from stacks.iop.org/Nano/19/415302

M This article features online multimedia enhancements

(Some figures in this article are in colour only in the electronic version)

1. Introduction

As the roadmap of micro/nano-electronics is developed, thecritical dimensions of electrodes, barriers, gates, etc isseen to shrink to nanometric values, which has requiredthe development of advanced nanofabrication tools such assteppers for optical lithography, dual beam systems (combiningan electron and an ion column) for inspection and repairof optical masks and integrated circuits, etc [1]. Suchcomplex equipment, in principle sophisticated at the laboratorylevel, are standard in the semiconductor industry, and thecurrent level of development of micro/nano-electronics couldnot be understood without them. Thus, past experience

3 Address for correspondence: Instituto de Ciencia de Materiales de Aragon,Universidad de Zaragoza-CSIC, Calle Pedro Cerbuna 12, 50009 Zaragoza,Spain.

says that complex procedures at the laboratory level canbe implemented in industry using well-known approachessuch as automatization, fabrication in parallel, etc. that leadto cost-effective production. One of the paradigms ofthis phenomenon is the use of magnetoresistive sensors inmagnetic read heads, which require sophisticated fabricationand patterning technology, but are standard in computers andother electronic devices [2]. As dimensions become more andmore demanding, these magnetoresistive sensors have evolvedfrom anisotropic magnetoresistance sensors to current-in-planegiant magnetoresistance sensors to tunnel magnetoresistancesensors [3]. In the near future, it is expected that current-perpendicular-to-plane giant magnetoresistance sensors willreplace them because the very small lateral size required(below 50 nm) calls for the use of sensors with metallicconduction [4]. Eventually, advanced technology in this field

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

could use metallic devices approaching just a few nanometresacross (called nanoconstrictions), which requires not only highcontrol of the fabrication process but also the understanding ofthe physical phenomena at that scale. This is why it is highlydesirable to apply advanced tools for the controlled creation ofsuch small constrictions and the investigation of the physicalphenomena involved.

Previous research indicates that when the electricalconduction is restricted through an atomic-sized constriction,the classical Ohm’s law gives way to new effects such asthe quantization of conductance [5, 6]. This phenomenon,described by the theory developed by Landauer [5], wasexperimentally discovered in 1988 by Van Wees et al [6]when a two-dimensional electron gas of a GaAs–AlGaAsheterostructure was modulated in width by means of a gatevoltage, detecting steps in the conductance of value G0. Formetals, several experimental methods have been used to createpoint contacts. Scanning tunnel microscopy (STM) as wellas the mechanically controllable break junctions (MCBJs) arethe most used techniques, based on the progressive stretchingof a created constriction [7]. The use of STM as well asMCBJs has paved the way for the observation of ballisticconduction (without scattering), as well as quantum effects,such as the quantization of conductance in metals and thequantization of the supercurrent in superconductors. Theseexperiments have led to huge advances in the understandingof electron conduction in atomic-sized metal structures.It was soon realized that the large number of possibleatomic configurations at the constriction made necessarystatistical studies, most of the measurements requiring liquidhelium temperature. Nanolithography techniques have beenused, aiming to create stable nanoconstrictions at roomtemperature, which could lead to immense applications. Wecan cite approximations such as anodic oxidation by atomicforce microscopy [8, 9], deposition from an electrolyticsolution [10, 11], some hybrid formulae [12] and the use oftransmission electron microscopy [13–15].

In the present work, we show a novel technique toestablish nanoconstrictions and atomic-sized contacts at roomtemperature in metallic materials, based on the potentialitiesthat dual-beam equipment offers. In order to illustratethe procedure, the creation of a controlled atomic-sizedconstriction based on chromium/aluminium electrodes as wellas on iron electrodes is described. We expect that thistechnique will be applicable to many types of material. Startingfrom a micrometric electrode, previously patterned by opticallithography, we create a progressive decrease of conductanceby means of focused Ga-ion etching. The in situ monitoring ofthe resistance using electrical microprobes during the etchingprocess allows the observation of a step-wise structure inthe electrical resistance, with steps in the range of G0, justprior to an abrupt jump, which occurs at the crossover tothe tunnelling regime. The simultaneous scanning electronmicroscopy (SEM) imaging during the process enables us toestablish the correlation between the transport measurementsand the microstructure of the etched material. We have alsoperformed current versus voltage (I –V ) curve measurementsat determined stages of the milling process, which allow one to

clearly distinguish between the metallic (ohmic) and tunnelling(non-ohmic) regimes. First, we chose a Cr metallic layerto demonstrate the feasibility of this novel technique for thefabrication of constrictions due to its good adhesion to thesubstrate. Afterwards, we applied the same technique toFe metallic layers due to their potential applications in spinelectronics. The procedure is expected to be applicable to manydifferent metallic materials, being of general interest.

2. Experimental details

The experiments were made at room temperature incommercial dual-beam equipment (Nova 200 NanoLab fromFEI) that integrates a 30 kV field-emission electron columnand a Ga-based 30 kV ion column placed forming 52◦ withcoincidence point at 5 mm away from the electron columnpole. This configuration allows obtaining images generatedby the SEM column during the ion etching under a basepressure of 10−6 mbar. A well-defined geometry for reliableand feasible experiments was obtained by conventional opticallithography. This allowed patterning the microelectrodes. Thesubstrate was either a Si3N4 layer (300 nm thick) depositedby plasma-enhanced chemical vapour deposition on a Si waferor a thermally oxidized Si wafer (300 nm SiO2 on top ofthe Si substrate). In both cases good electrical insulationbetween the electrode and the Si wafer was found. Afurther optical lithography lift-off process was carried out,via an image reversal photoresist and Cr (20 nm) and Al(400 nm) deposition by electron-beam evaporation in thefirst type of electrode and Fe (20 nm) in the second typeof electrode. After the lithographic process, large metallicpads were connected via 4 μm wide electrodes. On theseelectrodes an ion etching pattern (with dimensions 2 μm ×6 μm) was performed. In the first type of electrode, the Alwas deposited on top of the chromium due to its granularstructure, assuring a highly anisotropic etching which favoursthe formation of nanoconstrictions. In fact, the formationof narrow constrictions with a few conduction channels wasidentified in the SEM imaging. In the second type of electrode,the Fe layer was not covered by Al. Even though the etchingwas more isotropic than in the previous case, nanoconstrictionswere also formed as identified by SEM imaging. Twoelectrical microprobes (Kleindiek) were contacted on the pads(see figure 1). These conductive microprobes are connectedvia a feedthrough to a 6220 DC current source–2182Ananovoltmeter combined Keithley system, located out of thechamber. The lead resistance is about 15 �, which guaranteesno significant influence on the measured resistance at thestages where the conductance steps occur, which correspondsto approximately 13 k�.

3. Results and discussion

We first draw attention to the results obtained on the Cr-based electrodes. The Ga-ion etching process was done intwo consecutive steps. The first started from 15 �, with theion column set at 5 kV and 0.12 nA, aiming to shorten thetime of the experiment. The etching was stopped when the

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

B

A

Figure 1. (A) SEM image of the electrical aluminium pads patterned by optical lithography. The two microprobes are contacted for real-timecontrol of the electrode resistance. The inset is an SEM image of the Al/Cr electrode prior to the Ga etching. The SEM images in the electronicversion have been coloured for better visualization. (B) Schematic diagram of the etching process. Electrical transport measurements aresimultaneously measured. The inhomogeneous Al etching favours clear images of the formed Cr nanoconstrictions when Al is fully removed.

resistance reached 500 �, still far from the metallic quantumlimit. In the second step, the ion column was set at 5 kVand 2 pA, for about 12 min. During this period we monitoredthe variation of the resistance and simultaneously 10 kV SEMimages were collected. This allowed us to examine thecorrelation between resistance and microstructure. In otherexperiments, the milling was stopped at determined resistancevalues, at which current versus voltage curves were measured.The maximum bias current was selected in order to avoid thedeterioration of the device due to heating effects.

In figure 2 we show a typical resistance versus etching-time result at a starting value of 500 �. The resistanceincreases continuously for about 10 min, up to a point, in whicha three orders of magnitude jump is seen. Just before thisabrupt change, the resistance shows a discrete number of steps.

We can see in figure 3 that for this particular case, plateauswith a small negative slope for the conductance are roughlylocated near integer multiples of G0. This step-wise structureis a clear indication of the formation of point contacts in themetal electrode before the complete breaking of the formednanowires. This is similar to what it is seen in experimentsdone with other techniques [7]. The long experimental timeto create one of these constrictions (hundreds of seconds)compared to other techniques such as STM or MCBJs (tens ofmicroseconds) does not favour the building of histograms withenough statistics to assign the observed step-wise behaviourto conductance quantization. From tens of experiments,we can conclude the reproducible existence of steps in theconductance in the verge of the metal–tunnelling crossover andcertain dispersion in the specific values of the conductance

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

Figure 2. Resistance versus time in a typical ion etching process ofthe Al/Cr electrode, where discrete jumps are observed. The insetsshow I–V curves measured at fixed resistance values. A lineardependence, as expected for metallic conduction, is observed exceptfor the last stages of milling, where the tunnelling regime has beenreached.

plateaus, which we always observe below 4G0. Previousstudies indicate that conductance histograms are more irregularin transition metals nanoconstrictions [7, 16] than in the caseof monovalent metals like Au [17]. This is due to the fact thatthe number of conducting channels in a single-atom contact isdetermined by the number of valence electrons and their orbitalstate. Theoretical works show that the conductance in non-monovalent metals strongly depends on the specific atomicconfigurations of the constriction [18, 19], which suggests thatstrong dispersions in the specific values of the conductanceplateaus are expected in a reduced number of experiments.To determine the values where steps in conductance occur,numerical differentiation of the G(t) curve was done. Peakswith approximately zero maximum value are observed whereplateaus in G occur. In the particular case of figure 3, the fitof these peaks to a Gaussian curve gives the maximum at thevalues (1.02 ± 0.01)G0, (1.72 ± 0.01)G0, (2.17 ± 0.01)G0,and (3.24 ± 0.02)G0. The broadness of the found steps is atypical feature of room temperature measurements [7, 15, 16].However, we would like to remark that, from one experimentto another one, the positions of the plateaus are observed tochange.

In figure 4, SEM images taken during the etchingprocess are shown. In addition, in the supplementarymaterial (available at stacks.iop.org/Nano/19/415302), a video(available at stacks.iop.org/Nano/19/415302) of this processis shown. The etching by Ga ions in the first stages ofmilling is highly inhomogeneous due to the presence of anAl layer deposited on purpose on top of the Cr layer. Thegranular morphology presented by the evaporated aluminiumfavours this phenomenon, known as ‘channelling’, in whichpreferential sputtering of some grains with respect to otherswith different crystalline orientation occurs [20]. At thismilling time, numerous micrometric channels conduct the

Figure 3. Conductance (in G0 = 2e2/h units) versus etching time ofthe nanoconstriction whose results are shown in figure 2. In thisstage of milling, steps of the order of G0 are seen, corresponding todiscrete thinning of the contact area of the order of one atom. Thelast step is followed by a sharp decrease of conductance,corresponding to the crossover to the tunnelling regime.

current. The progressive thinning during the process as wellas the fracture of some of them involves a progressive andcontinuous increase of resistance. Around 1 k�, one canclearly distinguish how the Al layer has been fully removedfrom the constriction zone. The chromium is now the onlyelement responsible for conduction. The Cr grain size issmaller than in Al, and a more homogeneous etching processtakes place from that moment on. The plateaus found for theconductance correspond with images where only one metalnanowire is not fractured, reaching atomic-sized contacts justbefore the final breaking and the crossover to the tunnellingregime. When this finally occurs, an abrupt jump occurs in theresistance, reaching values in the M� range, associated witha tunnelling conduction mechanism. In some constrictions,the etching was stopped at different moments, for measuringthe I –V curves. As can be seen in the insets of figure 2,the linear I –V behaviour indicates metallic conduction, andconsequently that the constriction is not broken. Once theconstriction breaks, a non-linear I –V behaviour is found, asexpected in tunnelling conduction. Fitting the I –V curves fortunnelling conduction to the Simmons model for a rectangulartunnel barrier [21] gives as a result a barrier height of theorder of 4.5 V, a junction effective area of 300 nm2, and abarrier width of the order of 0.65 nm. The barrier height foundcorresponds with the work function for chromium [22], and theother parameters seem reasonable, evidencing the adequacy ofthe fit in spite of the simplified assumptions of the model. Eventhough re-sputtering of some Al atoms towards the contact areacould be possible, the value found for the barrier height in thetunnelling regime seems to indicate that the electronic transportthrough the nanocontact is governed by the Cr atoms.

We have not observed degradation during the measure-ment time (tens of seconds) since the substrate under theformed metal constriction guarantees a robust and stablestructure. We have found that when the constriction shows

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

Figure 4. SEM images (view at 52◦ tilt angle) at different stages of a typical milling process performed on an Al/Cr electrode, showing thechange of the electrode microstructure as a function of time. The high magnification used in the images allows the visualization of theevolution of the material under ion bombardment at a sub-micrometric scale. The SEM images in the electronic version have been colouredfor better visualization. The original figures are included in the supplementary material (available at stacks.iop.org/Nano/19/415302). Theresistance value in each case is shown. In the verge of the metal–tunnel crossover (image corresponding to R = 4 k�) the current flowsthrough a single nanoconstriction and atomic-sized conduction features are observed. When the last nanoconstriction gets fractured (imagecorresponding to R = 15 M�), the resistance jumps to M� range values. The arrow signals the breaking point of the constriction.

resistance values of the order of the conductance quantum,a limiting maximum power of 0.3 nW is required to avoiddegradation, which constrains the maximum applied voltageto values below ∼6 mV. Considering a contact area of0.3 × 0.3 nm2, a 5.5 × 107 A cm−2 current density is obtained,which is around three orders of magnitude larger than themaximum current bearable by a macroscopic metallic wire.This huge current density is understood in terms of ballistictransport through the contact [7].

With the available data, it is not possible to discardthat, due to the moderate vacuum level (10−6 Torr) and theGa-assisted etching process, some impurity could be in thesurroundings of the nanoconstriction and could exert someinfluence in the conduction properties. However, the obtained

linearity in the I –V curves in the metallic regime seemsto confirm the presence of clean contacts, because only thepresence of adsorbates and contaminants produces non-linearcurves in the low-voltage regime [23, 24]. In our case, theuse of low ion energy (5 kV) and current (2 pA) is expectedto minimize the role of Ga damage and implantation. Wehave carried out a chemical analysis of the surroundings ofthe created nanoconstrictions by means of EDX measurements.The results give a typical composition for Si/O/Cr/Ga/C(in atomic percentage) of 30/45/23/1/1 (see supplementarymaterial (available at stacks.iop.org/Nano/19/415302)). If thesubstrate elements (Si and O in this case) are discarded, theCr and Ga atomic percentages are found to be around 96%and 4%, respectively. However, one should be aware that this

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

Figure 5. Resistance versus time in a typical ion etching process ofan Fe electrode, where discrete jumps are observed before thetunnelling regime is reached. The inset shows the correspondingconductance (in G0 = 2e2/h units) versus etching time. In this stageof milling, steps of the order of some fraction of G0 are seen,corresponding to discrete thinning of the contact area of the order ofone atom. The last step is followed by a sharp decrease ofconductance, corresponding to the crossover to the tunnellingregime.

technique has a very limited resolution in depth and lateralsize. Further experiments are required to deeply investigatethis point, which is beyond the scope of the present paper,focusing on the description of this novel approach to createatomic-sized constrictions. We would like to remark that ionetching processes are commonly used in micro/nanofabricationsteps in laboratory and industrial processes without affectingthe device properties. Thus, it is reasonable to assume that formany types of device the use of suitable ion energy and dosewould not affect the device properties.

The second type of nanoconstriction, performed on Fe-based electrodes, will be presented hereafter. Such a materialhas been chosen due to its magnetic character and itspotential application in spin electronics. In fact, one excitingresearch line nowadays is that of atomic-sized constrictionsbased on magnetic materials [25–30], where sizeable effectssuch as ballistic anisotropic magnetoresistance or tunnellinganisotropic magnetoresistance have been found. In theparticular case of Fe, experiments by Viret et al with the MCBJtechnique performed at 4.2 K indicate that in the vicinityof the conductance quantum the magnetoresistive effects canapproach giant values [28]. Aiming at the creation of stableFe-based atomic-size constrictions at room temperature, weapplied the described Ga etching technique to Fe electrodes.One typical experiment is shown in figure 5. During the first2 min, the Ga etching process is performed using 5 kV and70 pA, the resistance approaching 2 k� at the end. Then, wecontinue the Ga etching process using 5 kV and 0.15 pA. Theprocess is slower and allows the detection of step-wise changesin the resistance before the jump to the tunnelling regime,similar to the observed behaviour in the case of the Cr-basedelectrodes. The inset shows a close-up of the same resultsrepresenting the conductance (in units of the conductance

quantum) versus time. Clear steps are observed which are alsointerpreted as evidence of the formation of atomic-size metalliccontacts just before entering the tunnelling regime. Thisopens a fascinating route to create stable nanoconstrictionsat room temperature which could have functional use. Ifthese nanoconstrictions were stable out of the chamber atroom temperature, they could eventually be used for magneticsensing. Our first attempts to measure the magnetoresistanceof these nanoconstrictions out of the chamber are promising,but more experiments are necessary to build the requiredsystematization.

4. Conclusions and outlook

The reported results reveal that this new approach based onfocused ion beam techniques to obtain stable atomic-sizedmetallic contacts at room temperature under high vacuum isvery promising for nanotechnology applications. We haveshown that this behaviour is exhibited by metallic electrodessuch as Cr and Fe. The steps in the conductance just priorto the crossover to the tunnelling regime can be interpretedin terms of atomic reconstructions, where the contact sizechanges discretely by, approximately, the area of one or a fewatoms. The last step before losing the contact could correspondto a single-atom contact. The plateaus at different conductancevalues are associated with different atomic configurationsin the constriction. We remark that the contact has astable geometrical configuration due to the attachment of theconstriction to the substrate. The geometrical changes in theconstriction are due to the continuous removal of atoms bymeans of ion etching. We must point out the importance of thechosen parameters, crucial to see the transition from the ohmicto the tunnelling regime in a detailed way (this is not the casein other conditions—see supplementary material (available atstacks.iop.org/Nano/19/415302)). The simultaneous imagingof the etching process via the electron column allows followingthe formed structure in real time.

The high stability found at room temperature for thecontacts around the conductance quantum is a great advantage,although some drawbacks can be anticipated, such as thedifficulties in building histograms with a large number ofcounts and the lack of ultra-high vacuum in the processchamber. The possibility of establishing point contacts in awide variety of materials under similar conditions is expectedwith the exposed methodology. This is not the case forother techniques, which are less flexible with respect to thematerials and protocols used. In our case, the sputteringrate of the material under etching at the ion energy usedseems to be the most relevant factor, together with theion column current, which influences the ion beam widthand the etching rate. In addition, it seems feasible toincorporate heaters/coolers in the chamber in order to extendthe range of temperatures for the study of the properties ofthe nanoconstriction. One exciting research line nowadaysis that of atomic-sized constrictions based on magneticmaterials [25–30]. Such kind of studies could in principlebe performed in an analysis chamber attached to the processchamber without breaking the vacuum. It is also interesting

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Nanotechnology 19 (2008) 415302 A Fernandez-Pacheco et al

to investigate the stability and magnetotransport properties ofthese atomic-sized constrictions when taken out of the processchamber. One advantage of dual-beam systems is that theconstriction could be locally covered by an insulating material,giving stability and protection. Thus, the technique describedhere could be useful for the creation of nanoconstrictionsbased on many different materials and with several types ofapplication.

In conclusion, a new approach to create controlledconstrictions reaching atomic-sized contacts is described.The proposed method uses Ga-based focused ion etching,in situ electrical measurements, and SEM imaging. Thisapproach could be relevant as critical dimensions in somenanoelectronic devices progress towards the true nanometricrange. Besides, many physical phenomena are drasticallychanged when the system dimensions become comparable toits fundamental physical lengths. One of these phenomena isthe electrical conduction through atomic-sized constrictions,where quantum effects have been observed in the past. Thehigh control achieved with the shown methodology to realizenanoconstrictions is a promising route to explore some of theseexciting phenomena.

Acknowledgments

Financial support by the Spanish Ministry of Science (throughprojects MAT2005-05565-C02 and MAT2008-06567-C02),and the Aragon Regional Government are acknowledged.

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