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Dielectric breakdown in AlOx 

tunnelling barriers

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 44 (2011) 135403 (5pp) doi:10.1088/0022-3727/44/13/135403

Dielectric breakdown in AlOx tunnellingbarriers

D M Schaefer1,2, P F P Fichtner2, M Carara1, L F Schelp1 andL S Dorneles1

1 Universidade Federal de Santa Maria, Departamento de Fısica, Av. Roraima, 1000, Santa Maria97105-900, RS, Brazil2 Universidade Federal do Rio Grande do Sul, Instituto de Fısica, Av. Bento Goncalves, 9500,Caixa Postal 15051, Porto Alegre 91501-970, RS, Brazil

E-mail: lsdorneles@gmail.com

Received 22 September 2010, in final form 24 January 2011Published 16 March 2011Online at stacks.iop.org/JPhysD/44/135403

Abstract

We studied the dielectric breakdown in tunnelling barriers produced by plasma-assistedoxidation of an aluminium surface. The barrier mean height, thickness and the effectivetunnelling area were extracted from current versus voltage curves measured at roomtemperature. The effective tunnelling area ranged from 10−10 to 10−5 cm2, corresponding toless than 1% of the geometrical surface of the samples. The estimated electrical field tobreakdown agreed with predictions from thermochemical models, and decreased exponentiallywith the effective tunnelling area.

1. Introduction

Thedestructionofthininsulatorsbydielectricbreakdown(BD)has been a key issue in microelectronics for decades, where itsstatistical occurrence determines the lifetime of metal–oxide–semiconductor components. As a result, several relationsbetween the chemical quality/morphology of barriers and thebreakdown mechanisms were established, specially for SiO2

layers [1–5].More recently, the interest in developing non-volatile

random access memories has attracted considerable attentionto the study of magnetic tunnel junctions. These devicesconsist of two magnetic electrodes connected by a very thintunnelling barrier, usually amorphous Al2O3 or crystallineMgO [6–16]. Although presenting quite similar breakdownphenomena, gate capacitors and tunnel junctions have someintrinsic differences that make unclear, up to now, to whatextent the knowledge accumulated in the first system can beapplied to the second one.

In several nanometre thick SiO2 layers, the leak currentsare relatively small and just in part due to hole/electrontunnelling. In contrast, in magnetic junctionsa high tunnellingprobability is mandatory to allow large magnetoresistance andto maintain the device resistance inside practical limits. As aconsequence, the insulating barrier should not be more than a

few nanometres thick,meaning electrical fields up to 1 GV m−1

with 2 V applied to the electrodes. As shown by scanning

tunnelling microscopy and transport measurements in Al2O3[17–22] and more recently in MgO [23, 24], fluctuations in theinsulator thickness concentrate the tunnelling current in ‘hotspots’. In these small portions of the insulating barrier, thehigh current densitiescertainly alterparametersrelevant for thebreakdown, e.g. charge to breakdown and local temperature.

Another parameter sensible to inhomogeneous currentdistributions is the stress variable, either the time or theelectrical field to breakdown. As long as thedensity of intrinsicdefects (dueto thicknessfluctuations, barrier structuraldefects,impurities, etc) is constant over the junction surface andextrinsic defects (such as dust inclusions) are absent, thestress variable is expected to decrease as the junction areaincreases [25–27]. But when the current is not homogeneouslydistributed over the insulating barrier surface, we have a lesspredictable situation and the stress variable can, for example,scale with the junction perimeter [27].

Aswillbeshownhereforagroupofsampleswiththesamegeometrical area, but presenting ‘hot spots’, the electrical fieldto breakdown scales with the effective tunnelling area.

2. Experimental details

Al/AlOx /Al tunnel junctions were deposited by magnetronsputtering with a typical base pressure of 10−7 mbar (or lower)

using masks to define 200 µm wide electrodes in the crossedstripe geometry, producing samples with a 4 × 10−4 cm2

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J. Phys. D: Appl. Phys. 44 (2011) 135403 D M Schaefer et al

Figure 1. I  versus V  curves, measured at room temperature in the

current drive mode (symbols), and calculated (line). Inset shows themeasurement up to higher currents, past the breakdown voltage.

 junction area. This system has symmetric interfaces, andno over/under oxidation of the insulating barrier is possible.Typically 14 out of 16 samples survive the deposition process,and more than half survive the connection to the measurementsystem.

In a first group of samples the insulating barrier wascreated by plasma-assisted oxidation of the freshly depositedbottom Al electrode, in a 100 mTorr O2 atmosphere with timeof plasma discharge (T ox) ranging from 10 to 50s. In a secondgroup, the insulating barrier was created by exposing the Albottom electrode to the same oxygen atmosphere for 12h, butwith no discharge (T ox = 0).

I  versusV  curves were measured at room temperature, andfor each sample Simmons’ equation [28, 29] was fitted to theexperimental data in a voltage window below 0.8 V, followingthe modifications introduced in [22]. In the non-linear leastsquare fitting algorithm, the barrier mean height (), thebarrier thickness (t AlOx

) and also the effective tunnellingarea (Aeff ) have been left as free parameters. The iterationprocedure was made until a predetermined chi-square is notfurther reduced. Local minima were dismissed by testingdifferent sets of initial values. The breakdown process was

followed using current ramps and as the breakdown voltage(V BD) criterion, the first drop in voltage was considered.

3. Results and discussion

Figure 1 presents a typical I  versus V  curve obtained with aconstant dI  /dt . A linear dependence in the low voltage regionis followed by an exponential growth of I  with V , as expectedfrom tunnelling models [28–31]. As exemplified in the insetof figure 1, as V BD is reached there is a drastic reduction inthe voltage, followed by a linear I  versus V  behaviour. Formost of the studied samples the breakdown was a one-stepprocess, characterized by a sudden drop in the voltage neededto maintain the set current.

Figure 2. Weibull plot for a group of Al/AlOx /Al samples subject tothe same stress.

Figure 3. Breakdown voltage V BD as a function of stress ramp speeddV  /dt . Oxidation times (T ox) are indicated.

Figure 2 presents the Weibull plot for a group of samplesprepared with T ox > 0, where F  is the fraction of samples thatfailed in V < V BD. It follows reasonably well a straight line,indicating that intrinsic defects drive the breakdown process.

It is expected that V BD increases with the stress speed [32, 33],which is observed in figure 3. But, this behaviour is notobserved in thesamples prepared with T ox = 0, suggesting thatthe chemical quality or the density of defects is significantlyaltered when natural oxidation is used.

It is important to note the values observed for samplesprepared with T ox > 0. They range from 1.4 to 1.9 V, andare not consistent if the geometrical area of the junctions isrelevant to the breakdown description. From extrapolations of the reported behaviour of  V BD versus area [25–27] obtainedfrom devices with much smaller areas, the studied samplesshould have V BD values smaller than 0.5 V, even if we admitdifferences in density of defects due to sample production

particularities. An open possibility is to admit that theinsulating barrier is not flat and thickness fluctuations are

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J. Phys. D: Appl. Phys. 44 (2011) 135403 D M Schaefer et al

Figure 4. RAeff  versus t AlOxfor the studied samples. Oxidation

times (T ox) are indicated.

present, as is the case for our samples [22, 34] and also for

samples from other groups [35] and other materials, such asMgO [23, 24, 36] or MgB2 native oxide [37]. In this caseelectronic transport would be restricted to a smaller area of the sample, as the tunnelling current would be concentrated inregions less thick.

To include this effective area in the analysis, we considerthe area as an additional free parameter while fitting thecalculated I  versus V  curves to the experimental data. Asdiscussed below, we have independent evidence that thisapproach is justified andgives meaningful figures to thebarrierparameters.

First, if we consider that the current flows through thewhole geometrical junction area, there is no clear exponential

increase in the junction’s resistance and the extracted t AlOx ,which is true not only here but also in most of the worksfound in the literature. Exceptions are found for samples withextremely high structural quality and/or small lateral size. If we consider the effective tunnelling area Aeff  obtained fromthe fitting process, a clear exponential dependence of R versusAeff  is observed, as shown in figure 4 for more than 20 samplesstudied, prepared under different conditions. The samplesprepared using T ox = 0 (without plasma-assisted oxidation)are in the lower thickness range as should be expected. Thevalues of  for all the samples show a trend to increase witht AlOx

(figure not shown) and lie within the range from 1.1 to

1.6 eV, smaller than the reported values for massive Al2O3probably due to imperfections in the oxide layer. The valuesof Aeff  are within the range from 10−10 to 10−5 cm2, around1% of the geometrical area, due to thickness fluctuationsof the insulating barrier [1, 5, 16–22]. These values areconsistent with those obtained by direct measurement, wheresimultaneous topographic and tunnelling current images wereobtained from an Al2O3 insulating barrier [19, 38, 39]. Aswill be discussed below we were able to test this procedure insamples where oneof thebarrier parameters, thebarrier height,was known.

Second, if the breakdown occurs at voltages higher thanthe barrier height, a plot of the logarithmic derivative of 

conductivity versus V  will present a maximum at a voltage of about 1.2 times the barrier height [40, 41]. In other words, it is

Figure 5. I  versus V  curve measured at room temperature(symbols). Lines are fittings of Simmons’ equation to the data using

the parameters presented in table 1. Solid black line is from routine(a), dashed red line is from routine (b) and dotted blue line is fromroutine (c), as explained in the text. Inset: the arrow indicates themaximum in the logarithmic derivative of conductivity versus V curve.

(This figure is in colour only in the electronic version)

Table 1. Parameters obtained by fitting Simmons’ equation to theexperimental data from figure 5. (a), (b) and (c) are the parametersused to generate the solid, dashed and dotted lines in the figure,respectively.

Fitting routine Aeff  (×10−7 cm2) t AlOx(Å) (eV)

(a) 3± 1 18± 2 1.4± 0.2

(b) 5± 0.3 18.3± 0.1 1.485 (fixed)(c) 4000 (fixed) 25.6± 0.9 1.43± 0.06

possible to obtain one of the barrier parameters independentlyby direct measurement. This plot, for a representative sample,is shown in the inset of figure 5.

In order to compare the results from our fitting procedure(three fitting parameters) with the results from the traditionalprocedures (two fitting parameters), figure 5 also shows ameasurement of I  versus V  extracted from this sample (opencircles), and three curves obtained fitting Simmons’ equationto the experimental data using three different routines (in avoltage window below 1.5 V). In routine (a) (solid line) fittingwas performed with , t AlOx

and Aeff  as free parameters; inroutine (b) (dashed line) t AlOx

and Aeff  were free parameters,and the measured value for was used; in routine (c) (dottedline) and t AlOx

were free parameters. As can be seen in thefigure, both solid and dashed lines fit very well the measuredcurve, as the dotted line hardly matches it.

In table 1 the values obtained for the barrier parametersextracted from one representative sample, using the threedifferent fitting routines, are given. The values for t AlOx

obtained from routine (b) is much smaller than that fromroutine (c). This result is also observed in other works where

fittings to STM I  versus V  curves, where the probe size isknown with nanometre resolution, are compared with fittings

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J. Phys. D: Appl. Phys. 44 (2011) 135403 D M Schaefer et al

Figure 6. Breakdown field EBD as a function of the effective areaAeff . The vertical dashed line indicates the geometrical area(4× 10−4 cm2). Oxidation times (T ox) are indicated.

to curves extracted from the tunnelling junction with the sameoxide barrier [19]. The values for t AlOx, and Aeff  (for this

particular sample Aeff  is less than 1% of the geometrical area)obtained from routine (a) are in very good agreement with thevalues obtained from routine (b). This was observed for all thesamples where it was possible to measure directly.

At the stress speed used BD occurs for V BD above , inthe Fowler–Nordheim regime [4] and in contrast with someof the reported results [33]. The transport measurements donot allow us to observe the exact geometrical location of thebreakdown; however, as the time to breakdown is shorter whenthe current density is larger [3], one can infer that the BDoccurs within the area determined by Aeff . Considering that

the breakdown occurs within Aeff  where the thickness is t AlOx ,in a first approximation the breakdown field can be defined asEBD = V BD/t AlOx

.A very clear behaviour of  EBD versus Aeff  can be seen

in figure 6, where the values obtained from all samples (thefittingroutine isused to obtainfits ofthe samequality asthe onepresentedinfigure 5(a))areplotted. Thisplotincludessampleswith Aeff  within a range of five orders of magnitude from10−10 to 10−5 cm2, indicating that EBD behaves as indicatedby the solid line independent of T ox or stress speed. This canbe explained by the Poisson model for randomly distributeddefects (see, e.g., [42]), and we can estimate the defect density

in the barrier by the slope of the EBD versus ln(Aeff ) plot.Using the data presented in figure 6 we obtain a defect densityσ = 2.5×107 cm−2. This value is very close to that estimatedby other authors such as Stathis [43] andDiMaria[44] for SiO2

barriers within the same thickness range. This percolationmodel applied to these SiO2 barriers states that insulatingbarriersintheverysmallthicknessrange(<3nm)needaminorbut almost constant σ ∼ 0.5× 107 cm−2 to break down.

For the samples with a smaller effective area, EBD

approaches1.3GVm−1, a valuethat is largerthanthoseusuallyreported in the literature. But this value is closer to theprediction based in the thermochemical model for crystallineAl2O3 [45, 46].

Another important result is the fact that by themeasurement of an I  versus V  curve, associated with the

proper fitting of Simmons’ equation to it, one can estimatethe breakdown field or the time to breakdown.

4. Conclusions

We have analysed the breakdown process in tunnelling barriers

where, due to thickness fluctuations in the insulator, thecurrent concentrates in ‘hot spots’. The barrier parameters,particularly the barrier thickness and the tunnelling effectivearea, were obtained for each sample from fittings of Simmons’equation to the measured I  versus V  curves. For samplesprepared with the same geometrical area, the expectedbehaviour of thebreakdown field with thearea is only observedif the effective tunnelling area and thickness are taken intoaccount.

Acknowledgments

This work was partially supported by the Brazilian agencies,CNPq (Conselho Nacional de Desenvolvimento Cientıficoe Tecnologico), CAPES (Coodenacao de Aperfeicoamentode Pessoal de Nıvel Superior) and FAPERGS (Fundacao deAmparo a Pesquisa do Estado do Rio Grande do Sul).

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