Electrical stress effect on Josephson tunneling
through ultrathin AlO barrier in Nb/Al/AlO/Nb junctions
The effect of dc electrical stress and breakdown on Josephson and quasiparticle tunneling in Nb/Al/AlO/Nb junctions with ultrathin AlO barriers typical for applications in superconductor digital electronics has been investigated. The junctions’ conductance at room temperature and current-voltage (-) characteristics at 4.2 K have been measured after the consecutive stressing of the tunnel barrier at room temperature. Electrical stress was applied using current ramps with increasing amplitude ranging from 0 to corresponding to voltages across the barrier up to V, where is the Josephson critical current. A very soft breakdown has been observed with polarity-dependent breakdown current (voltage). As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. The observed changes in superconducting tunneling suggest a model in which a progressively increasing number of defects and associated additional conduction channels (superconducting quantum point contacts (SQPCs)) are induced by electric field in the tunnel barrier. By comparing the - characteristics of these conduction channels with the nonstationary theory of current transport in SQPCs based on multiple Andreev reflections by Averin and Bardas, the typical transparency of the induced SQPCs was estimated as . The number of induced SQPCs was found to grow with voltage across the barrier as with V, in good agreement with the proposed model of defect formation by ion electromigration. The observed polarity dependence of the breakdown current (voltage) is also consistent with the model. Based on the observed magnitude of breakdown currents, electric breakdown of AlObarrier during plasma processing was considered to be an unlikely cause of fabrication-induced, circuit pattern-dependent nonuniformities of Josephson junctions’ critical currents in superconductor integrated circuits.
Aluminum oxide (AlO) is widely used as a barrier material in various applications involving tunnel junctions. It was also considered as a potential gate oxide in advanced memory devices and metal-oxide-semiconductor (MOS) transistors. Dielectric reliability issues such as oxide barrier stability, leakage currents, and electric breakdown are very important for electronics applications, especially for magnetic tunnel junctions (MTJs) used for magnetic random access memories and superconducting tunnel junctions (STJs) used for superconductor digital circuits requiring ultrathin ( nm) tunnel barriers. The physics of dielectric breakdown in ultrathin barriers is of great interest in its own right. Oxide breakdowns are usually classified into two modes: intrinsic and extrinsic. Though the difference is somewhat blurry, extrinsic breakdowns are those caused by defects introduced or created during oxide growth, whereas intrinsic ones are the property of a perfect dielectric. In relatively thick oxide layers such as those used as gate dielectric in MOS transistors, electric breakdown usually proceeds by the accumulation of defects (traps) inside the dielectric until a percolation pass is formed, at which point the resistivity suddenly decreases from a very high value to a very low value, and a hard breakdown occurs.Degraeve et al. (1998); Chang et al. (2001) In thinner oxide layers the breakdown often has a soft character which is characterized by small gradual changes in resistance.Alam et al. (Feb 2002a, Feb 2002b) The thickness of ultrathin tunnel barriers used in superconductor electronics is a couple of oxide monolayers, only a few interatomic distances. Therefore, any defects formed in the oxide as a result of electrical stress (e.g., displaced ions, oxygen vacancies, etc.) should create additional conduction channels with significantly increased transmission probability and consequently dramatically alter the quasiparticle and Cooper-pair tunneling. In other words, the percolation path forming at breakdown may consist of just a single defect (trap) and hence the breakdown may be very soft.
There have been several publications on the reliability and breakdown of aluminum oxide layers with thicknesses above nm as a new gate oxide and nm in MTJs.Shimazawa et al. (2000); Das et al. (2001); Oliver et al. (2004); Kim and Cho (2005); Akerman et al. (Oct. 2006) The existence of both intrinsic and extrinsic breakdown modes was suggested.Oliver et al. (2004) The intrinsic mode was associated with a hard breakdown, and was suggested to be related to the chemical bond breaking in applied electric field.Hill and Dissado (1983a, b); McPherson and Mogul (1998) The extrinsic mode was associated with a soft, gradual breakdown. It was suggested to be related to pre-existing pinholes in the barrier which grow in area as breakdown progresses due to Joule heating and/or electric field effect.Oliver et al. (2004)
Superconductor-insulator-superconductor (SIS) junctions offer unique opportunities in studying breakdown mechanisms in ultrathin oxides because both the quasiparticle and Josephson tunneling in STJs are extremely sensitive to the barrier properties and boundary conditions at the metal-oxide interfaces. In contrast to MTJs, pre-existing pinholes in SIS junctions are easily identifiable because they carry supercurrent thus creating nonuniform Josephson current distribution and dramatically increasing subgap conductance. Whereas a microshort in MTJs was associated with a junction having the resistance-area product of 0.8 m, and no tunneling magnetoresistance,Oliver et al. (2004) STJs with even lower values of product exist and display interesting Josephson tunneling properties.Kleinsasser et al. (1993); Miller et al. (1993); Patel and Lukens (1999)
Superconductor digital electronics utilizing SIS junctions has a potential for sub-THz clock frequencies and ultra-low power dissipation for digital signal processing, high-performance communications and computing.Likharev and Semenov (1991) Recently, complex superconducting circuits based on Rapid Single Flux Quantum (RSFQ) logic such as analog-to-digital converters and digital RF receivers containing thousands of logic gates with clock frequencies 30 GHz have been demonstrated, operating not only in liquid He but also on commercial closed-cycle cryocoolers.Vernik et al. (2007) Increasing the clock frequencies of superconductor integrated circuits to 100 GHz would require employing high- junctions with products below 1 m, perhaps the thinnest tunnel barriers among all known devices.Chen et al. (1998); Tolpygo et al. (2007a)
Dielectric reliability may not appear to be important for superconducting digital circuits because they operate at very low temperatures and at very low voltages (1 mV). Its significance however arises from the possibility that tunnel barrier degradation may occur during integrated circuit fabrication. For instance, the current state of the art in RSFQ circuits has been plagued by limited circuit yield brought about to a large extent by fabrication-induced variations on the Josephson critical current () of the tunnel junctions.Tolpygo et al. (2007a, b) These variations may be related to dielectric barrier degradation and electrical breakdown. It has been observed, for example, that the of Josephson tunnel junctions may depend on how the junction is wired to other circuit elements, and in particular, at which step in the fabrication process the junction makes electrical contact with the circuit’s ground plane.Tolpygo et al. (2007b) For series arrays of nominally identical tunnel junctions, it was frequently observed that the Josephson critical current of a few junctions (usually of the first and the last junction in the array) is significantly larger than for the rest of the junctions. This cannot be simply explained by a variation in the area of that one junction coming from the lithography and etch processes of junction definition. Neither can it be explained by a random fluctuation in the tunnel barrier transparency in that particular junction, considering that the effect reproduces in different arrays and the junctions in the array are just 10 m apart. Instead, it was suggested that the above phenomena are brought about by electrical currents flowing through the tunnel barriers, a result of plasma processing steps which follow the SIS trilayer deposition. Recent experiments involving tunnel junctions protected from plasma process-induced electric stress by current-limiting resistors support this suggestion.Tolpygo and Amparo (2008)
Surprisingly, there has been almost no research on the reliability of ultrathin AlO barriers in STJs, except for early works on Al/AlO/Pb junctions which studied the effects of electric annealing on the barrier thickness, height and asymmetry of AlO barriers formed by plasma oxidation.Konkin and Adler (1980) These junctions, however, have no practical application, and the changes in superconducting and Josephson properties were not studied.
In this paper the effect of applied dc electrical stress on quasiparticle and Josephson tunneling in Nb/Al/AlO/Nb junctions was investigated. The study focused on this type of junctions because of their dominant use in superconductor digital and analog electronics.
The Nb/Al/AlO/Nb junctions used in this study were fabricated at HYPRES, Inc. using an 11-level process for superconductor integrated circuits.Tolpygo et al. (2007a); Hyp (2008) The fabrication was performed on 150-mm Si wafers. The process is based on in-situ Nb/Al/AlO/Nb trilayer deposition.Gurvitch et al. (1983) Specifically, Nb/Al bilayer (150 nm and 8 nm, respectively) deposition is followed by AlO formation by room temperature oxidation of Al. The AlO layer is then topped off by the deposition of the Nb counter-electrode (50 nm). All metal layers are deposited by dc magnetron sputtering in a cryopumped vacuum system with base pressure of Torr. Two Josephson critical current densities, (1 kA/cm and 4.5 kA/cm), were targeted, obtained by Al oxidation for 15 min at oxygen pressure of 170 mTorr and 18 mTorr, respectively. After the counter-electrode etch process that defines the junctions, their interior was sealed along the perimeter and sidewalls by an anodization layer composed of AlO and NbO in order to protect the barrier from reacting with process chemicals used in subsequent fabrication steps.
Circular JJs with design radii of 2.00 m ( m) and 0.95 m ( m) for wafers with kA/cm and 4.5 kA/cm were arranged on -mm chips referenced according to wafer number and the coordinates (in units of 5 mm) of the chip location on the wafer. For example, a chip from wafer KL1004 with location (-5,7) is to be called KL1004N5P7.
Each chip was mounted inside a magnetically shielded cryoprobe. The junctions were measured using a low-pass filtered four-probe setup with a Keithley 2000 voltmeter and a Keithley 6220 current source. Electrical stress was applied at room temperature by ramping current through the junction up to a preselected value and back down to zero. The stress application was preceded and followed by a measurement of the junction’s room-temperature resistance, using a low current of 500 A. The tunneling - characteristics were then measured in the superconducting state at K with the cryoprobe submerged in a liquid He. The next stress/measurement cycles were then performed using progressively higher values of .
The effect of stress polarity was also investigated. Here we define positive stress as current flowing from the counter electrode (positive potential on the top Nb layer) to the base electrode (Nb/Al bilayer), while negative stress is current flowing in the opposite direction. At room temperature, there is a resistance in series with the tunnel barrier associated with the normal resistance of interconnects to the junction. This series resistance was estimated from the interconnects’ geometry using a separately measured sheet resistance of the layers involved. This resistance was assumed to remain unchanged by stress applications and was simply subtracted from the total measured resistance, thus allowing us to estimate the potential difference that develops across the tunnel barrier during stressing. Parameters of some of the studied junctions are given in Table 1.
Iv Experimental Results
Fig. 1 shows the resistance at low currents ( A) of four Nb/Al/AlO/Nb junctions after each subsequent stress application. The junction resistance remains roughly constant after stressing with low currents until a threshold stress current for breakdown is reached, above which the resistance starts to decrease indicating irreversible changes in the barrier. Each succeeding decrease in resistance is apparently a cumulative effect of all previous stress applications. The threshold current varies among nominally identical junctions on the wafer and from wafer to wafer, suggesting some statistical nature of the barrier breakdown. Despite these variations, the observed threshold current for the positive stress (current from Nb counter-electrode to Al) is consistently higher than for negative stress as listed in Table 1. If the resistance after stressing is scaled with the resistance in the initial junction and the stress current is scaled with the threshold current, all the curves in Fig. 1 collapse onto a single curve (see Fig. 1 inset) suggesting a universal breakdown mechanism and a universal character of resistance changes due to electrical stress.
The irreversible decrease of the tunnel barrier resistance may be due to (a) a decrease in the average barrier height and/or thickness; (b) the barrier becoming nonuniform due to formation of additional conduction channels (regions with increased barrier transparency which are often called micro- or nano-shorts); and (c) a combination of the above. However, room temperature measurements alone are insufficient to distinguish between these possibilities and measurements in the superconducting state of the junction electrodes are needed.
The electric stress-induced changes in the tunnel barrier properties are clearly seen in the Josephson - characteristics at K shown in Fig. 2(a). Five main features are worth mentioning. First, the Josephson critical current, (defined here as the switching current) increases with the stress current. Second, the normal-state resistance, of the junction decreases with the stress current. Third, the so-called knee structure in the quasiparticle tunneling just above the gap voltage of the junction also shifts to higher currents as the stress increases. Fourth, the junction conductance in the subgap region of voltages increases with the stress current. The retrapping current also increases with the increase in subgap conductance. Finally, the gap voltage is nearly independent of the stress current and decreases only slightly at very high stress currents. The increase in the subgap conductance is by far the most pronounced change in the - curves of the stressed junctions. For instance, after applying a stress current of 96 mA, the Josephson critical current of the junction increases by a factor of whereas the subgap conductance at 2 mV increases by a factor of .
|Target||Stress||at 300 K||at 4.2 K||at 4.2 K|
The experimental results presented in the previous section show that there is a broad range of electric stress currents through Nb/Al/AlO/Nb junctions (and corresponding voltages across the AlO tunnel barrier) where a gradual change of the barrier properties occurs. This can be interpreted as a soft breakdown of the oxide barrier in contrast to the sudden changes (hard breakdown) usually observed in thicker oxide layers of SiO and AlO. For the junctions with kA/cm, this range spans from the typical threshold current mA (corresponding to a stress current density A/cm) to mA ( A/cm) above which the stressed devices lose all the signatures of superconducting tunnel junctions. For the positive stress polarity, the threshold current in Table 1, mA corresponds to the voltage across the barrier 0.519 V. For the negative stress polarity, mA corresponds to V. The typical barrier thickness for the Josephson current densities used in this work is nm or less.Tolpygo et al. (June 2003); Cimpoiasu et al. (2004) Hence, the typical electric fields across the AlO barrier at which the irreversible changes start are V/m and V/m for the negative and positive stress polarities, respectively.
The difference between and was also observed in AlO breakdown measurements in magnetic tunnel junctionsKim and Cho (2005); Akerman et al. (Oct. 2006) where it was speculated to be a result of different surface roughness of the two metal/oxide interfaces. We suggest that the difference between and is more fundamental and is a result of difference in work functions of the junction electrodes. Indeed, from the contact potential difference measurements, the work functions in the electrodes are eV and eV for Al and Nb, respectively. Therefore, in a Nb/Al/AlO/Nb junction the potential barrier becomes asymmetric and there is an internal electric field across the barrier V/m directed from the Nb/Al base electrode towards the Nb counter electrode and arising from the difference in work function eV. This barrier asymmetry agrees well with the result obtained from the asymmetry of conductance vs. voltage characteristics of Nb/Al/AlO/Nb junctions with low tunnel barrier transparency.Tolpygo et al. (June 2003); Cimpoiasu et al. (2004) For the negative stress polarity (higher potential on Nb counter-electrode), the external field adds up to the internal field in the same direction, whereas for the positive stress polarity the external field is opposite to the internal one , where is the total field in the dielectric and is the externally applied electric field. If defects in the barrier start to form when the net internal field reaches some critical level (e.g., as a result of ion electromigration), from the onset of irreversible resistance changes (soft breakdown), we estimate the critical voltage to be V, corresponding to V/m. The barrier asymmetry in this model corresponds to V, in excellent agreement with the 0.18 V difference between work functions.
Let us see what can be inferred about the nature of stress-induced changes to the barrier from the data presented in Sec. IV. Clearly the increase of the critical current and decrease in the normal resistance in stressed junctions indicate that the critical current density and the average barrier transmission increase. The question is whether the tunnel barrier remains uniform or not. If the barrier remains uniform and only its height and/or thickness is changing with the applied stress, one would expect the junction product to remain constant because in the limit of low barrier transmission probability, it is given by the Ambegaokar-Baratoff (AB) relationship for ,Ambegaokar and Baratoff (1963) and the gap voltage was found to remain nearly constant after barrier stressing. Contrary to this, the measured product increases significantly in the stressed junctions as can be seen in Fig. 3. This may indicate a transition from tunnel junction to point contact behavior because for point contacts between two superconductors at the product is greater than in the tunnel junction by a factor of 1.32 in the dirty limit and by a factor of 2 in the clean limit, as was shown by Kulik and Omel’yanchuk (KO).Kulik and Omel’yanchuk (1975, 1978) It was also found by ArnoldArnold (1985, 1987) that, for an insulating and structureless barrier of arbitrary thickness, the product in general depends on the barrier transmission probability , and reduces to the AB result at and to the KO result for the clean point contact at .
It is easy to show, however, that the barrier does not remain uniform and structureless after stressing. For this, we compare the - curves of a stressed junction and an as-prepared, unstressed junction with the same average Josephson critical current density. The as-prepared junction is presumably as uniform as possible for the given fabrication method. The - curves are shown in Fig. 4. The stressed junction with kA/cm clearly has different - characteristics (especially at ) than the as-prepared junction with an even higher kA/cm. This comparison indicates that the changes in the - curves and the increase in the product brought about by electric stress cannot be explained by a gradual increase in transparency of a uniform and structureless barrier. A dramatic increase in the subgap conduction in the stressed junctions, the appearance of pronounced features at subharmonics of the gap voltage, at shown in Fig. 5 along with the increase in strongly indicate that additional conduction channels with increased transparency are gradually formed as a result of electric stress. These conduction channels can be viewed as point contacts between the junction electrodes, pinholes, or nanoshorts in the barrier, contributing to both the quasiparticle and Cooper-pair transport in parallel to the main tunnel barrier which remains largely unmodified by the stress.
Subgap features similar to those appearing in electrically stressed junctions (Fig. 2(b) and Fig. 5) have long been observed in Nb/Al/AlO/Nb and other types of junctions Kleinsasser et al. (1993); Miller et al. (1993); Patel and Lukens (1999) with high critical current densities and attributed to MAR. Two models were proposed to explain the appearance of MAR in high- junctions. Kleinsasser et al. Kleinsasser et al. (1994) suggested that, as oxygen exposure during Al oxidation decreases, the barrier becomes nonuniform, consisting of regions with low transparency (good tunnel barrier) and regions with high transparency (pin holes). That is, the transparency distribution has two sharp peaks, one at a low value and another one at . As oxygen exposure decreases, the relative contribution of the second peak increases, and so does the . Naveh et al. Naveh et al. (2000) argued that the defects in the ultrathin tunnel barrier are naturally occurring and, therefore, the transparency distribution in high- junctions is universal and given by the Schep-Bauer (SB) distributionNaveh et al. (2000)
They found that SB distribution gives a better fit to experimental - curves than averaging over the Dorokhov distribution describing the transparency distribution in long disordered conductors—not a surprise though because the Dorokhov distribution should not be applicable to short channels by definition. There is ample experimental evidence however that the behavior of high- junctions is not universal. For instance, the value of at which MAR steps become visible strongly depends on the junction fabrication procedure and varies between different experimental groups.Miller et al. (1993); Patel and Lukens (1999) Our experimental results show that MAR steps can be created at will in tunnel barriers with any initial transparency as a result of electrical stress. Therefore, what were perceived as natural and universal defects appearing in the oxide barrier as a result of a short oxidation process Mallison et al. (1995) could be simply a result of damage to the very thin tunnel barrier induced during the junction (wafer) fabrication processes. This could explain why improvements in the junction fabrication process usually shift the level at which MAR steps begin to appear towards higher values.
Although no microstructural characterization of the barrier changes was undertaken in this work, a plausible scenario of how the additional conduction channels are induced by electric stress can be proposed. It is known that AlO formed by room temperature oxidation is amorphous and nonstoichiometric, i.e. contains a large amount of oxygen vacancies.Tan et al. (2005) At the oxidation conditions used in our work, the barrier thickness is only nm, i.e. just about two to three nearest-neighbor distances. Therefore, a displacement of even a single atom from the barrier can significantly increase local transparency. If a dc electric field is applied to the oxide barrier, electromigration of cations (Al) and anions (O, O) in opposite directions may occur. From anodic oxidation of Al in electrolytes it is known that the anodizing ratio for Al is nm/V, i.e., 1.3 nm of AlO is formed for each volt applied to the Al/electrolyte interface.Diggle et al. (1969) That is, on average, oxygen ions are transported inside the aluminum electrode by nm per 1 volt of applied voltage. Ionic current density in the oxide is a strong function of the electric field strength .Diggle et al. (1969); Dignam and Ryan (1968) In our case, there is no electrolyte providing a constant supply of oxygen atoms for the oxide to grow. However, some oxygen ions from AlO barrier will electromigrate into Al underlayer of the Nb/Al/AlO structure if the Nb/Al base electrode is at a positive potential (negative stress polarity in our nomenclature) while Al cations should migrate towards the interface with Nb counter electrode. At a positive potential on Nb counter electrode (positive stress), oxygen ions from the AlO barrier will move into Nb counter electrode, depleting the barrier. The average oxygen displacement at the onset of breakdown can be estimated using the typical threshold voltage V and nm/V, giving nm. This closely corresponds with O-O nearest-neighbor distance of 2.8 Å in amorphous alumina.Lamparter and Knieper (1997)
Any ion displacement in the barrier under the effect of an applied electric field creates a defect and alters the barrier transparency. The length of the newly created conduction channel is about the same as the barrier thickness which is much less than the coherence length and the magnetic field penetration depth . The cross-section of such a channel is also on the atomic scale, much less than and . The theory of current transport through such short and narrow channels, often called quantum point contacts (QPCs), is well developed. For the single mode QPC, the Josephson current is given by
where is the channel transparency and is the phase difference.Beenakker (1991)
The theory of nonstationary properties in SQPCs was developed by Averin and Bardas.Averin and Bardas (1995) It is based on the idea of multiple Andreev reflections (MAR) Andreev (1964) which reveal themselves as current steps at subharmonics of the gap voltage , at . They found that - characteristics strongly depend on the SQPC transparency and demonstrate the most pronounced subharmonic steps at intermediate values of to 0.5. The theoretical - curves reduce to a pure tunneling characteristics at and to a featureless curve typical for an - of a clean S-N interface at .Averin and Bardas (1995)
Let us see what properties of conduction channels created in the AlObarrier by electrical stressing can be inferred from the measured - curves shown in Fig. 2. Because of space constraints we will restrict our analysis to the positive stress polarity only. The case of the negative stress polarity is completely analogous and will be presented elsewhere. First, we note that the amplitude of the current step at practically does not change in stressed junctions although the subgap conductance dramatically increases. (In the first approximation we will neglect some broadening of the current step at and a small decrease in at extremely high stress currents which could result from the smearing of the metal-insulator interfaces.) In the microscopic theory of tunneling in superconductors, the size of the current step is proportional to the area of the tunnel barrier and is given by
where is the specific normal-state tunneling conductance.
It is easy to verify that the experimentally observed in Fig. 2 is very close to the value given by Eq. (3). The independence of of electric stress indicates that the area of the tunnel barrier and its conductance does not change noticeably. It means that the total area of additional conduction channels formed by stressing is much smaller than the junction area. Therefore, a stressed junction can, in the first approximation, be represented by a parallel combination of the initial (unstressed) junction and some number of SQPCs (see Fig. 7): . To obtain the -characteristics of these SQPCs, we can subtract the - curve of the tunnel (unstressed) junction from the experimental in the stressed junction. The result of this procedure is shown in Fig. 6, along with the theoretical - curves calculated for a SQPC with different transparencies.Averin and Bardas (1995)
Although the subtraction procedure is not very accurate near the gap voltage because of the gap smearing in the highly stressed junction, it is clear that the - curve of the SQPCs has no significant current step at . This is true for any stress current (any number of SQPCs) because in all the - curves in Fig. 2 the current step at is the same as in the initial junction. In the microscopic theory of nonstationary properties of a single SQPC,Averin and Bardas (1995) the size and broadening of the current step at in the -curve as well as the size and broadening of subharmonic current steps strongly depends on the channel transparency. The step at basically disappears at while subharmonic steps basically disappear at . Therefore, in the theory, the range of channel transparencies where the - curves would look like in Fig. 2(b) and Fig. 6 is very narrow . Hence, it would not make a significant error if, for simplicity, we assume that all the channels have the same transparency. A better approach would only be a full fitting of the - curves to the theory, which will be done elsewhere. It can be seen from Fig. 6 that all the - curves of SQPCs formed in the stress current range from the breakdown to 2 lie between the theoretical curves with and . Therefore, the average channel transparency formed at electric stressing can be taken as .
From the linear part of the - curves at , the normal-state conductance of the channels is simply , where is the normal-state tunnel resistance in the initial junction measured before stressing. Since the normal-state conductance of a single QPC is given by , we can estimate the number of created SQPCs using = . Its dependence on the stress voltage is shown in Fig. 9. At , the number of channels formed at the maximum stress currents studied is , corresponding to an average channel density of channels/cm and an average channel spacing of nm. In our model each channel is associated with a displaced ion in the barrier, so the estimates above give the surface density and the average distance between displaced ions in the barrier at the maximum stress currents mA. The obtained estimates are self-consistent with the initial supposition that the number of additional conduction channels is small and that the area occupied by the channel is negligible with respect to the area of the tunnel barrier.
Since each SQPC carriers a supercurrent, the increase of the critical current in the stressed junctions should be proportional to the number of conducting channels. This is shown in Fig. 8. Using the assumption of equal channel transparency and , we can estimate the average contribution of each created channel from Fig. 9 to be about A/channel. Using the experimental value of mV and , from Eq. (2) we obtain the theoretical value of A/channel, a very close value.
The theory Averin and Bardas (1995) also explains the existence of the excess current in the - curves as a nonzero average of the Josephson ac current at finite voltages. It can be seen in Fig. 6 that the part of experimental - curves at (region of the excess current) agrees very well with the theory. The excess current defined as is shown in Fig. 8, where was determined by fitting the - curves at to and index 0 identifies the initial, unstressed junction. The straight-line fit yields A/channel, or in very good agreement with the theory,Averin and Bardas (1995) giving at .
So, by analyzing the additional subgap conductance, additional normal state conductance, and additional Josephson currents induced by electric stressing of the junction’s barrier we obtained a self-consistent picture. In this picture, after a point of soft breakdown has been reached, atomic-size conduction channels with similar transparencies are being formed in the barrier as the stressing progresses. We also proposed a scenario in which the formation of these channels is a result of electric-field-stimulated ion migration away from the barrier. Let us see if this scenario also agrees with the available experimental data.
The treatment of ion transport in an electric field (electromigration) is very well known and goes back to the original Frenkel defect theory and works by Mott,Mott (1947) and Cabrera and Mott.Cabrera and Mott (1949) Following Cabrera and Mott (1949), the ionic current density can be written as
where is the concentration of the mobile ions, is the attempt frequency, is the activation energy, is the ion charge and is the activation or half-jump distance. Ionic (atomic) transport in solids is usually proceeds via vacancy exchange mechanism (in which case is the height of the energy barrier the ion needs to overcome) or via formation of Frenkel defects (vacancy-interstitial pairs) in which case is the activation energy for formation of a Frenkel defect. The total number of displaced ions in the barrier can be hence presented as
where is the stress duration, is the voltage across the barrier, , and is the barrier thickness.
Since in our model each displaced ion represents a new conduction channel, in Fig. 9 we plotted the “effective” number of conduction channels determined from the increase in the junction conductance = as a function of maximum voltage across the junction which develops during each stressing at room temperature. The dependence given by Eq. (5) is also shown and fits the data very well, giving V. Assuming that oxygen ions are the mobile species, we can take , Å (nearest-neighbor distance), nm, and K, and get from Eq. (5) V in excellent agreement with the experimental data in Fig. 9. If instead we use the value Å determined from direct measurements of ionic current in alumina films,Dignam and Ryan (1968) the fit to the experimental data in Fig. 9 gives a tunnel barrier thickness nm which is in a better agreement with the barrier thickness data Tolpygo et al. (June 2003); Cimpoiasu et al. (2004) obtained from differential conductance vs voltage dependences.
A secondary objective of this study was to relate the studied above effect of dc electrical stress with anomalous - characteristics of Josephson junction arrays frequently observed for many fabrication processes Tolpygo et al. (2007b); Tolpygo and Amparo (2008); Hidaka et al. (2008). As was described in Sec. I, usually one or two junctions at the ends of the array demonstrate an that is significantly larger than the average of the other junctions in the array, see Fig. 10. Clearly two junctions have an that is significantly larger than the average of the rest of the junctions. Usually, the junction with the highest deviation from the average is the last junction in the array, the one which has the base electrode directly connected to the ground plane layer.Tolpygo et al. (2007b); Tolpygo and Amparo (2008) The second deviating junction is the first junctions in the array, the one which is connected by the wiring layer to the chip contact pads.Tolpygo et al. (2007b) These usually large deviations in are also reflected in the so-called knee region of the - curve where the knee current of the junctions in question is much higher and can be distinctly seen in the normal branch of the curve. Also the subgap conductance corresponding to these two junctions is significantly higher than the average. MAR steps in the subgap region of these junctions have also been observed.Tolpygo and Amparo (2008)
Qualitatively, these anomalous junctions look like the junctions subjected to electric stress as described above. Electric currents can flow through some of the Josephson junctions during their fabrication, e.g., during reactive ion etching. The question is whether the amplitude of the current is high enough to cause degradation of the barrier in many junctions on the wafer. From the results of dc electric stressing, we have found that the typical breakdown current in the smallest junctions used in superconductor integrated circuits is mA at which a critical voltage develops across the barrier, i.e., . The typical 0.25-cm test chip contains Josephson junction arrays. Therefore, to cause breakdown of all 20 grounded junctions in these arrays, it would need a current density of A/cm because for plasma-induced current the grounded junctions are connected in parallel. There are also several test chips spread out on the 150-mm wafers. So the total current through the wafer should be huge. The typical rf power used for etching in our process is from 40 to 150 W and peak-to-peak voltage is from 305 V to 900 V depending on the circuit layer, corresponding to power density from 88 mW/cm to 332 mW/cm. Although, rf power is coupled capacitively to the wafer and to the circuits’ ground plane, the rf current can flow directly through the junctions which are galvanically coupled to the ground plane. Estimating the amplitude of electric current supplied by the rf source, we find it to be in the range of 0.5 A to 0.7 A, corresponding to the current density from 1 mA/cm to 1.55 mA/cm. This is clearly too small a current to cause significant damage to oxide barriers in Josephson junctions. Therefore, we conclude that, although exposure to processing plasma has a potential in creating voltage differences on the wafer surface which are large in comparison with the typical breakdown voltages in ultrathin oxide barriers,Cheung (2000) the typical etching plasmas used in superconductor integrated circuits fabrication do not supply enough current to electrically break down the tunnel barriers of Josephson junctions due to their high tunneling conductance. The same conclusion was also reached in Tolpygo and Amparo (2008).
Because of these results, it is likely that the damage to junctions galvanically coupled to the ground plane or other circuit layers observed in Tolpygo et al. (2007b) is chemical or electrochemical in nature. For instance, it can be due to diffusion or electromigration of impurity atoms from the layers in direct contact with the junction to the junction’s electrodes and to the barrier, e.g., hydrogen atoms dissolved in Nb. In many respects the features of oxide barrier damage by H electromigration should be similar to that of electron current damage. However, the required currents can be substantially lower because hydrogen is known to be highly mobile in Nb. Therefore, it should be much easier to cause diffusion of hydrogen atoms in Nb than to displace oxygen atoms from the AlO oxide barrier. This damage mechanism will be considered separately.
We have studied the effect of dc electric stress (current) applied at room temperature to Nb/Al/AlO/Nb junctions with = 1.0 and 4.5 kA/cm on their Josephson and quasiparticle tunneling properties. We have observed a very soft breakdown: above a certain threshold stress current the changes in - characteristics indicate formation in the barrier of additional conduction channels with increased transparency. These channels reveal themselves in dramatic increase in the subgap conduction, appearance of subharmonic current steps (multiple Andreev reflections), an increase in the critical current, a decrease in the normal state resistance, and an increase in the product. The range of the stress currents where these gradual changes occur is quite broad, from to , corresponding to to . The threshold (breakdown) current depends on the stress current polarity and is larger when the Nb counter electrode is at a positive potential.
We have suggested that the soft breakdown proceeds via formation of defects in the barrier as a result of ion migration in the applied electric field. The stress polarity dependence was explained as due to internal electric field caused by the difference in the work functions of the junction electrodes. The observed breakdown fields V/m ( V across the barrier) correspond to the magnitude required for near-neighbor displacement of oxygen ions.
From the changes in the tunneling characteristics in the superconducting state we concluded that the total area of the additional conduction channels is much smaller than the area of the initial tunnel barrier, and that they can be considered as connected in parallel to the initial tunnel junction whose properties remain virtually unchanged by electric stressing. Using this parallel connection model, we estimated the transparency of the additional conduction channels by comparing their - characteristics to the nonstationary theory of current transport in superconducting quantum point contacts by Averin and Bardas. We found that all the channels have similar transparencies in the range from to . We found an excellent agreement of the shape of - characteristics of the conduction channels created by electric stressing with the Averin-Bardas theory for SQPCs.Averin and Bardas (1995) From the change in the normal-state resistance we calculated the effective number of the additional conduction channels . The observed changes in the junction critical current per channel and the excess current per channel were found to be consistent with the predictions of the microscopic theory for SQPCs.
We also found an exponential dependence of the number of additional conduction channels created by electric stressing on the stress voltage, . The characteristic voltage was found to be in excellent agreement with the proposed model of defect formation by ion electromigration out of the barrier.
Due to the high tunneling conductance of oxide barriers used in superconductor digital electronics it is unlikely that breakdown currents can be reached during plasma processing steps of junction fabrication. However, it is possible that electromigration and diffusion of impurity atoms in Nb layers is responsible for pattern-dependent tunnel barrier degradation frequently observed in superconductor integrated circuits.
Acknowledgements.We would like to thank Daniel Yohannes, Richard Hunt, and John Vivalda for their part in wafer processing. Many discussions with Alex Kirichenko, Timur Filippov, Vasili Semenov and Dmitri Averin are highly appreciated. We would also like to thank D. Averin for providing the program for calculating the theoretical curves shown in Fig. 6. We are also grateful to Deborah Van Vechten for her interest and support of this research. This work was supported by ONR Grants N000140810224 and N000140710093.
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