NANO LETTERS
Fabrication of Highly Stable Configurable Metal Quantum Point Contacts
2008 Vol. 8, No. 11 3922-3927
Naomi Ittah,† Ilan Yutsis,† and Yoram Selzer* School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel Received August 5, 2008; Revised Manuscript Received September 22, 2008
ABSTRACT Metal quantum point contacts (MQPCs), with dimensions comparable to the de Broglie wavelength of conducting electrons, reveal ballistic transport of electrons and quantized conductance in units of G0 ) 2e2/h. While these contacts hold great promise for applications such as coherent controlled devices and atomic switches, their realization is mainly based on the scanning tunneling microscope (STM) and mechanically controlled break junction (MCBJ), which cannot be integrated into electronic circuits. MQPCs produced by these techniques have also limited stability at room temperature. Here we report on a new method to form MQPCs with quantized conductance values in the range of 1-4G0. The contacts appear to be stable at room temperature for hours and can be deterministically switched between conductance values, or reform in case they break, using voltage pulses. The method enables us to integrate MQPCs within nanoscale circuits to fully harness their unique advantages.
If metal quantum point contacts (MQPCs) possess reasonably well-defined quantum modes perpendicular to the direction of electric transport, their conductance can be changed in steps of the quantum unit of conductance, G0 ) 2e2/h. Under such conditions of quantized conductance, these metal contacts form a rich 3D test-bed for concepts from mesoscopic physics such as conductance fluctuations, multiple Andreev reflection, shot noise, and dynamical coulomb blockade.1 Realization of MQPCs has been mainly achieved by three experimental techniques, the scanning tunneling microscope (STM),1 mechanically controlled break junction (MCBJ),1 and electrochemical deposition/dissolution into lithography defined gaps.2 All these techniques, however, are of no significant importance in terms of technological applications such as atomic switches3 or coherent controlled devices,4 as they do not enable us to integrate MQPCs into electronic circuits. It is therefore essential to develop a different method for their realization which would be compatible with current large-scale fabrication technologies. The resulting MQPCs need to be highly stable at room temperature. Contacts based on STM or MCBJs are reported to have only limited mechanical stability at room temperature, degrading in best cases, within tens of seconds.5-9 Complimentary to this high-stability demand, the new fabrication route of MQPCs should also possess fault* Corresponding author. E-mail:
[email protected]. † These authors have contributed equally to this work. 10.1021/nl802372t CCC: $40.75 Published on Web 10/28/2008
2008 American Chemical Society
correcting capabilities, i.e., to be able to “heal” damaged MQPCs when needed. Recent studies suggest that electromigration (EM) could be an alternative fabrication method of MQPCs. EM is the directed migration of atoms caused by a large electric current density. It proceeds by momentum transfer from electrons to atoms and requires sufficient atom mobility to occur.10 Recently, a surge of activity has been focusing on ways to precisely control EM to fabricate very small gaps between metal leads which can then accommodate single molecules to explore their conductance properties.11-20 The mechanical stability of these molecular junctions has been shown to be superior to that of MCBJs.4,20 Is it also possible to control EM to trap individual metal atoms between the leads? A typical process to form an electromigrated gap is based on passing high-current density (typically >108 A/cm2) through a lithography defined metal (typically Au) wire with a constriction (junction) which roughly determines the position of the EM-induced failure. The resistance of the leads to the junction is RL, and the resistance of the junction itself is RJ. Since RL . RJ, the junction is effectively current biased through RL. Consequently, as EM starts shrinking the junction and RJ increases, the power dissipated on the junction grows proportionally to RJ, causing thermal runaway and formation of gaps that are too often larger than a typical length of a molecule. Several feedback-controlled algorithms have been developed to prevent this from happening.12-15 All of them try to dissipate a constant critical power at the junctions while
Figure 1. Conductance (in units of G0) as a function of time for a typical MQPC. Zone I: shows an abrupt decrease in conductance as a gap is formed in a junction (initially at 200G0, not shown). Zone II: tunneling current (∼10-5G0) until a jump-to-contact to 1G0 process occurs. Zone III: the MQPC is shown to be highly stable at 1G0 for minutes. Subsequently, a transition to a higher conductance value is induced by a proper bias. Zone IV: switching between quantize conductance values is demonstrated. Each transition between conductance values occurs by a jump-to-contact process, within a time scale of less than ∼100 ms.
breaking to minimize thermal runaway. With these methods, nanoconstrictions may be narrowed to a target conductance with high reproducibility, often within 10%, provided the target conductance is greater than 2-3G0. Control of conductance below this level is apparently not trivial. Transmission electron microscopy imaging of gap formation reveals a sudden (within less than 50 ms) large deformation of junctions once they become transgranular, suggesting that EM no longer dominates the very last moment of breaking.21 The rate of such a process can be estimated in the following way: the frequency of diffusion steps of metal atoms at temperature T can be written as ν exp(-Ea/kBT), where Ea is an activation energy barrier for a diffusing step and ν is an effective vibrational frequency. For self-diffusion on metal surfaces, the prefactor ν is in the order of 1012 s-1, which implies that a process with an energy barrier of ∼0.5 eV22 occurs within ∼l ms at room temperature. It is clear then that devising a feedback circuit to halt such a (thermally activated) process is very challenging. Thus currently, reproducible and robust fabrication of MQPCs by EM with conductance in the range of 1-4G0 remains a formidable task. We here propose a new method to fabricate MQPCs. The advantages of the approach are depicted in Figure 1, which shows the conductance behavior of a typical MQPC as a function of time. Each of the four zones in this figure reveals a different advantage of the fabrication approach and of the resulting contacts. Zone I shows the formation of a gap in a junction using EM. This step is performed without any feedback control to avoid thermal runaway. Zone II shows a tunneling current across the gap until a “jump to contact” process takes place and a MQPC with conductance of G0 is established. The jump to contact process is induced by an appropriate bias voltage (to be discussed). The fluctuations observed below G0 are discussed later in the text. Zones I Nano Lett., Vol. 8, No. 11, 2008
Figure 2. Optical image of a junction (A), along with a schematic presentation of its structure (B), emphasizing the different thicknesses of the two metal leads. EM results in a gap at the interface between the two leads. (C) An SEM picture showing a typical gap. EM induces changes of structure on the thin side, while the thick electrode appears to be untouched. The signs in this picture depict the bias polarity applied to induce EM. Formation of a MQPC takes place by closing the gap between the thick lead and one of the protrusions of the thin lead: under high enough bias, adatoms on the former electrode are induced to diffuse toward the high-field zone adjacent to the protrusion to nucleate and close the gap (see text for details).
and II show that our approach has the capability to break and make MQPCs. Such a capability is important since conductance quantization is revealed by statistical averaging, i.e., by repeated cycles of breaking and making of MQPCs. With STM and MCBJ, these cycles are induced by mechanical movement of the metal leads. Here it is induced by voltage biases (electric force), allowing gathering of the same statistics from fully anchored junctions. Zone III shows that the formed MQPC is very stable maintaining its conductance over tens of minutes at room temperature. The transition to a higher conductance, in this case to 2G0, which marks the beginning of zone IV, is not arbitrary, and the necessary conditions to deterministically jump between discrete conductance values can be quantitatively rationalized. The stability of the formed contacts in this zone is also very high. The necessary experimental conditions to achieve the above capabilities and advantages and their rationalization are detailed below. All experiments were performed at room temperature under vacuum with a base pressure of 1.0 V/Å is needed for both mechanisms.23-26 While these processes could be effective, perhaps even dominate when the gap is small, it is conceivable that initiation of contact formation is by directed diffusion of Au adatoms toward a zone of high field between a protrusion and the thick lead (see Figure 4). There, as the density of migrating atoms increases, the probability of nucleation and cluster growth also increases, until a growing metal mound is closing the gap.27-30 Such a mechanism has been suggested in the past to explain formation of metal structures induced by STM tips.23,31 Nano Lett., Vol. 8, No. 11, 2008
Exact simulation of this process in our case is beyond the scope of this letter. It is however possible to examine its main attributes by a simple model describing the initiation of gap closing, i.e., when the deformation of the gap is negligible. To a good approximation, the field of a protrusion varies as a Lorentzian function of the form23 E(r) )
(( ) )
1 V d 2r 2 +1 w
(2)
where V is the applied voltage; d is the size of the gap; r is the radius from the center of symmetry; and w is the Lorentzian width parameter (taken here as 100 nm). Without any bias, the diffusion of adatoms on the metals’ surface is a random walk process through small diffusion potential barriers Ud.31 However, since these atoms have nonnegligible atom polarizability, R, in the presence of an inhomogeneous electric field, E, the diffusion barriers are changed according to 1 Ueff ) Ud - RE2 2
(3)
The resulting net drift velocity under these conditions is described by32 υ)
( )
2DE)0 RβLE sinh L 2kBT
(4)
where DE)0 is the surface diffusion constant in the absence of a field; L is the jump length; β is the lateral field gradient; kB is the Boltzmann constant; and T is the temperature. Figure 4 depicts the distribution of field and drift velocity as a function of lateral distance for d ) 50 Å and V ) 3 V. On the surface (of the thick lead) just opposite the protrusion center, the drift velocity decreases sharply to zero, marking the surface area where a metal mound would eventually grow. Importantly, according to the model, the electric field drops to zero within ∼100 nm from the protrusion center. Beyond this radius, the drift velocity nullifies. Assuming adatom surface density of 1012 cm-2, it is evident that within the above radius the number of available adatoms is not sufficient to form a large enough cluster to bridge, in this case, a 50 Å gap. It is therefore argued that the rate of gap closing is determined not by the drift velocity but by the rate of diffusing adatoms on the surface toward the depleted zone adjacent to the protrusion. According to the model, higher fields should enhance the rate of MQPC formation. However, the applied voltage to drive this process cannot be arbitrarily high. To estimate the limit, we recall that under high tunneling flux, e.g., short gaps just prior to contact formation, substantial heating of the leads can take place by coupling of the tunneling electrons to phonons or by excitation of electron-hole pairs.33 The latter mechanism can be shown to be more effective and can be analyzed by assuming that a steady state is reached at the interface, by balancing the energy deposited Nano Lett., Vol. 8, No. 11, 2008
Figure 5. Conductance histograms of two MQPCs, based on breakand-make cycles. The top junction reveals in addition to pronounced conductance peaks at 1G0 and 2G0 also a stable structure with characteristic conductance of 8G0. This demonstrates that deterministic control over the configuration at the end of a jump-tocontact process is difficult. The lower panel reveals a different MQPC with conductance quantization at 1G0, 2G0, and 3G0.
into the leads (in regions of radius r ∼ 5 Å), with the flux of electron-hole pairs that dissipates heat away from the gap. The increase in temperature can then be estimated to be33 ∆T ∼
fP 2πrK
(5)
where f is the fraction of dissipated power P ()IV) and K is the thermal conductivity of the leads (KAu ) 320 W/m/K). It is important to note that the small contact region reduces the bulk thermal conductivity K by a factor of r/λ, λ being the bulk mean free path for electrons (λ ∼ 500 Å). The fraction of energy f can be calculated according to33 f)
V2 ln(2kFd) 4πωPkFφ
(6)
where kF is the wave vector at the Fermi level (∼0.35 Å-1); d is the distance between the leads (∼5 Å); ωp is the plasma frequency (∼12 eV); and φ is in the order of the metal’s work function (∼5 eV). Former studies suggest that the temperature of junctions under EM can be in the order of 450 K.15,18 Assuming that thermal runaway takes place at this temperature, we set ∆T in eq 5 to be 150 K. Assuming G ) 0.1G0 (R ∼ 105) results in a bias limit of ∼3 V, which is set as the limit to the applied bias at this step of the process (see Figure 3). We argued that MQPC formation by the above mechanism is accompanied by negligible EM. This is mainly because of bias polarity. Contact is established while electrons are 3925
Figure 6. Switching between quantized conductance values in two MQPCs (black line), forming in both cases a sequence of 1,2,3,4,3,2,1 in units of G0. The voltage bias applied on the junctions to induce switching is plotted in red. Comparing between the two junctions, it can be seen that in (A) when the absolute value of the applied voltage is higher than the voltage limit calculated by eq 7, more chaotic behavior is observed, with occasion instantaneous jumps of conductance to values of more than 10G0. In (B), the applied bias is not more than ∼|1.2 V|, maintaining ordered switching between quantized conductance values. The polarity of the applied voltage determines if the conductance increases or decreases. Positive bias refers to the thin metal lead as the cathode.
flowing from the thin to the thick lead. This current is accompanied by only negligible accumulation of voids at the contact since the voids are coming from the thick (small flux) lead and dissipate away from it through the thin (high flux) lead. The unique capability of our method to break and make MQPCs enables us to explore conductance quantization, which manifests itself only after statistical averaging.34-40 Averaging is needed mainly because the minimum cross section of the contact is not the only ingredient that controls the conductance but also the geometry of the narrowest part and disorder. In practice, contacts with different radii can have similar values of conductance. Importantly, the statistical averaging presented here is different than previous reported statistics. With MCBJs, quantization is revealed as transient (few tens of data points) conductance plateaus while (mechanically) breaking the contacts. These plateaus result in a higher weight of integer multiplications of G0 in the final histograms. Here, since mechanical manipulation of the contacts is not possible, an open-close sequence is driven by appropriate voltages: few milliseconds (typically 10) of a breaking voltage (∼2 V) followed by a closing-gap-voltage (∼-2 V with the same duration). Each of these voltages is followed by a measurement at 30 mV to establish the conductance. This sequence is repeated many times, and the conductance values of the formed contacts are reported in the histogram. The results of this procedure are demonstrated in Figure 5 which plots conductance histograms (each based on several thousands of break-and-make cycles) from two typical junctions. The first junction has a stable 8G0 contact configuration in addition to peaks at G0, 2G0, and (although less pronounced) also at 3G0. The second junction appears to adopt only 1-3G0 contact configurations. Control over the resulting conductance value after a jumpto-contact process appears to be difficult. However, the formed MQPCs appear to be highly stable. MQPCs with conductance, for example, of 1G0 were found to be stable for many hours. This stability opens the possibility to 3926
deterministically control the conductance of MQPCs by gently manipulating their configurations using controlled EM. The issue of EM in ballistic contacts has previously been discussed.41-43 The driving force for EM has two components: the direct field force and the electron-wind force41-43 that is usually dominating. The wind force acting on the contact can be written as FW ) 2(Ja2 ⁄ e)mνFη
(7)
where J is the current density; a is the atomic distance; m is the electron mass; and νF is the Fermi velocity. A constant η depends on the scattering geometry and takes values between 0 (forward scattering) and 1 (back scattering). The needed breaking force of a single-atom contact of gold is 1.5 nN.44 Taking νF ) 1.4 × 10-6 m/s41 gives Ja2 ) 9.4 × 10-5A. Since when one gold atom bridges the gap between the leads the resistance of the junction is 12.9 KΩ, the needed potential bias to drive electromigration is ∼1.2 V. The importance of this limiting bias value is demonstrated in Figure 6 which depicts switching between quantized conductance values in two different MQPCs. In both cases, a sequence of 1,2,3,4,3,2,1G0 is established. However, Figure 6a shows that when the voltage pulses are not limited in their absolute values some switching can take place to high conductance values leading to chaotic behavior in the needed applied biases to maintain the sequence. In Figure 6b, the applied voltages are ∼1.2 V, leading to switching without abrupt jumps to large (high conductance) contacts. Apparently, the polarity of the pulses is important as well. In general, if for a certain MQPC one polarity increases its conductance, the reverse polarity will decrease it. This is clearly revealed in the two plots of this figure. The reasons for this are currently unclear and will be resolved in future studies. The high stability of the contacts is once again evident, demonstrated in this case for conductance values larger than 1G0. It is informative at this point to reexamine the behavior in zone II of Figure 1, where fluctuations in the conductance are observed until a contact of 1G0 is formed. These Nano Lett., Vol. 8, No. 11, 2008
fluctuations occur since the applied potential needed to close the gap is much higher than the approximate voltage limit calculated above to preserve formed contacts. As a result, rapid (with respect to the sampling rate) processes of MQPCs formation and breakage take place until at some point a stable enough contact is formed which gives enough time for the feedback loop to respond and ramp the bias down to 30 mV. Work to further understand this regime by rapid sampling of current is underway. To conclude, a novel route to fabricate MQPCs has been described. The proposed method enables us to deterministically form MQPCs with integer conductance values between G0 and 4G0. It allows reconfiguration of formed MQPCs to switch between conductance values within this range. The resulting MQPCs appear to be highly stable at room temperature. Since the formed MQPCs are patterned on Si substrates, the fabrication method essentially forms a route to embed MQPCs with deterministic position and conductance within nanoscale circuits and architectures using current mass-production technologies. Additionally, since degraded MQPCs can be reformed, one can envision devices with a fault-correcting algorithm that “heals” damaged MQPCs using the above capability.45 Acknowledgment. Support by the converging technologies program to I.Y. is gratefully acknowledged. References (1) Agraı¨t, N.; Levi Yeyati, A.; van Ruitenbeek, J. M. Phys. Rep. 2003, 377, 8. (2) Meszaros, G.; Kronholz, S.; Kartha¨user, S.; Mayer, D.; Wandlowski, T. Appl. Phys. A: Mater. Sci. Process. 2007, 87, 569. (3) Terabe, K.; Hasegawa, T.; Nakayama, T.; Aono, M. Nature 2005, 433, 47. (4) Sokolov, A.; Zhang, C.; Tysmbal, E. Y.; Redepenning, J.; Doudin, B. Nat. Nanotechnol. 2007, 2, 171. (5) Costa-Kra¨mer, J. L.; Garcia, N.; Garcia-Mochales, P.; Serena, P. A.; Marques, M. I.; Correia, A. Phys. ReV. B 1997, 55, 5416. (6) Abella´n, J.; Chicon, R.; Arenas, A. Surf. Sci. 1998, 418, 493. (7) Abella´n, J.; Arenas, A.; Chicon, R.; Reyes, F. Surf. Sci. Lett. 1997, 372, L315. (8) Smit, R. H. M.; Untiedt, C.; van Ruitenbeek, J. M. Nanotechnology 2004, 15, S472. (9) Tsutsui, M.; Shoji, K.; Taniguchi, M.; Kawai, T. Nano. Lett. 2008, 8, 345. (10) Ho, P. S.; Kwok, T. Rep. Prog. Phys. 1989, 52, 301. (11) Park, H.; Andrew, K.; Lim, L.; Alivisatos, P.; Park, J.; McEuen, P. L. Appl. Phys. Lett. 1999, 75, 301. (12) Wu, Z. M.; Steinacher, M.; Huber, R.; Calame, M.; van der Molen, S. J.; Scho¨nenberger, C. Appl. Phys. Lett. 2007, 91, 53118. (13) Johnston, D. E.; Strachan, D. R.; Charlie Johnson, A. T. Nano Lett. 2007, 7, 2774.
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