- Email: [email protected]
Break conductance of Al nanocontacts
ARTICLE IN PRESS
Physica E 29 (2005) 495–499 www.elsevier.com/locate/physe
Break conductance of Al nanocontacts T. Minowaa, S. Kurokawab, A. Sakaia, a
Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan b International Innovation Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Available online 26 July 2005
Abstract We measured a break conductance, the last conductance of a contact before its complete break, for Al nanocontacts of 0–200G0 ðG 0 2e2 =h is the quantum unit of conductance) in ultrahigh vacuum at room temperature. We found that the distribution of the break conductance shows a broad single peak, the position of which shifts with the contact current. From the observed current dependence of the break conductance peak, it is suggested that Al nanocontacts break up most likely when the contact current density reaches a critical value 5 1010 A/cm2. r 2005 Elsevier B.V. All rights reserved. PACS: 73.63.Rt; 81.07.Lk; 66.30.Qa; 73.40Jn Keywords: Conductance; Contact break; Nanocontacts; Al
1. Introduction Nano- or atom-sized metal contacts and wires have been a subject of intensive theoretical and experimental studies in the past decade because of their unique mechanical and electronic properties [1]. One characteristic which is of practical importance, in applications of metal nanowires and nanocontacts as interconnects in nano-scale devices, is their capability of carrying high current Corresponding author at: International Innovation Center,
Mesoscopic Materials Research Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan. Tel.: +81 75 753 4833; fax: +81 75 753 4841. E-mail address: [email protected] (A. Sakai).
densities. For example, Yanson et al. [2] have shown that a monatomic chain of Au can sustain current density as high as 8 1010 A/cm2. For other metal nanocontacts, however, there have been few experimental studies about a maximum current density beyond which a metal nanocontact becomes unstable and breaks up. To estimate such a current density, two experimental methods can be employed. One is a current-disruption experiment [3] where a nanocontact of specific conductance (typically 1G0 or 2G0) is first produced and then the contact bias is increased to find a critical value at which the contact ruptures. Another method is to break a macroscopic metal contact under high biases and monitor the break conductance at which the contact completely breaks
1386-9477/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.06.013
ARTICLE IN PRESS 496
T. Minowa et al. / Physica E 29 (2005) 495–499
up. It is well known that even a macroscopic contact shrinks to the size of atoms just prior to its contact break [1]. Therefore, experimental data of the break conductance provide us some information on the critical current density of nano- or atom-sized metal contacts. We previously applied the latter method to noble metal nanocontacts and found that the critical current density for their contact break is (6–9) 1010 A/cm2 [4]. In this paper, we extend our study to Al nanocontacts and present experimental data of their break conductance.
2. Experiment Details of our experimental setup and conductance measurements have been described in Refs. [4–6]. A contact is formed between a fixed Al disk and a movable Al wire (both 99.999% pure) attached to a piezo actuator. We repeated contact break at 1 Hz and measured the transient conductance at each contact break by monitoring a voltage drop Vm across a 1 kO resistor connected in series with the contact. The bias Va is applied to the (contact+resistor) and divided between them. The contact conductance G is thus nonlinearly related to Vm as G ¼ V m =ðV a V m ÞR0 , where R0 ¼ 1 kO. Also, the contact current I can be expressed as I ¼ GV a =ð1 þ GR0 Þ. Note that in a high-conductance regime where GR0 b1, changing Va is effectively equivalent to changing the contact current I. Fig. 1 shows an example of the transient conductance trace observed at V a ¼ 1:2 V. This is actually a trace of Vm with a vertical scale converted to conductance, resulting in a strongly nonlinear conductance scale in Fig. 1. In the plot, the conductance suddenly exhibits a rapid fluctuation prior to the complete contact break, just as we observed in contact breaks of noble metals under high bias/current [5,6]. Each transient conductance was digitally measured with a time interval of 20 ms, and the last data point before the conductance drops below 0.5G0 was recorded as the break conductance Gb. An arrow in Fig. 1 indicates the Gb of the trace shown in the figure. All measurements were carried out at room
Fig. 1. Example of a transient conductance trace observed in a breaking Al contact at V a ¼ 1:2 V.
temperature in ultrahigh vacuum better than 5 108 Pa.
3. Results and discussion Fig. 2 summarizes break conductance histograms of Al contacts obtained at different values of Va from 0.4 to 3.2 V. Each histogram was constructed from 6000 conductance traces. The histograms were first built as Vm histograms and then converted to Gb histograms. As a result, the bin width in Fig. 2 is non-uniform and depends on both Va and Gb. For VaX0.8 V, the histogram shows a broad but well-defined peak. This peak in the distribution of Gb clearly indicates that the break of Al contacts takes place preferably at a specific contact size corresponding to the peak position. We denote this peak position by G^ b . Since G^ b is in a range 50–150G0, we are able to use the following Sharvin formula (for circular constrictions) [7] to estimate the contact size corresponding to G^ b : G ¼ G0
Ak2F k 2 R2 ¼ G0 F , 4p 4
(1)
where kF is the Fermi wavevector, and A and R are the contact cross-sectional area and radius,
ARTICLE IN PRESS T. Minowa et al. / Physica E 29 (2005) 495–499
497
Fig. 2. Histograms of the break conductance of Al contacts obtained at different values of Va.
respectively. Since G^ b 502150G 0 , Eq. (1) shows that Al contacts break at R 0.8–1.4 nm. It can be seen in Fig. 2 that the broad G^ b peak shifts to the lower conductance side as Va is reduced, i.e. G^ b decreases with Va (the peak height also decreases with Va, but this is an apparent effect due to the smaller bin width in histograms at lower Va). This shift of G^ b is just the same as we previously observed for G^ b of noble metal nanocontacts [4] and can thus be analyzed in the same manner. First, we note G^ b R0 b1 for G^ b 502150G 0 , so that it is the contact current I that varies with Va, as we pointed out in Section 2. Thus, the decrease in G^ b is actually a currentinduced phenomenon. Next, we estimate how high the current density is at the contact break. The current density j^b corresponding to the peak position G^ b can be easily obtained from the ratio I=G^ b , since G^ b is linearly proportional to the contact area A according to Eq. (1). We plot in Fig. 3 the resulting j^b as a function of the contact current I. Although j^b slightly increases with I, it stays nearly constant over the entire current range covered in this experiment. This result suggests that Al nanocontacts make a current-induced break, which takes place most likely when the
Fig. 3. Current density j^b at which the contact breaks with maximum likelihood is plotted as a function of the contact current I . Arrows indicate levels of j^b for the break of Au, Ag and Cu nanocontacts [4].
contact current density reaches the constant value of j^b . From the average of j^b data shown in Fig. 3, we estimate that the critical current density is hj^b i5 1010 A=cm2 for the break of Al nanocontacts. For comparison, we indicate in Fig. 3 experimental critical current densities for the break of noble metal nanocontacts [4]. It can be seen in Fig. 3 that the hj^b i of Al is roughly half that of Cu and 20% lower than that of Au.
ARTICLE IN PRESS 498
T. Minowa et al. / Physica E 29 (2005) 495–499
Our experimental results on Gb and j^b show that the break of Al nanocontacts under high biases/currents has the same characteristics as those of noble metal nanocontacts [4]. Thus, a common break mechanism is likely to work in these metals. It is, however, not well understood at this time what makes Al and noble metal nanocontacts unstable and broken at their hj^b i. Considering a high level of hj^b i, electromigration would be a possible source of such a contact instability which generates the conductance fluctuations [4–6] and eventually leads to the contact break. In fact, the magnitude order of hj^b i of noble metal nanocontacts follows that of the activation energy of electromigration. Since Al has lower activation energy than that of noble metals, the observed low hj^b i of Al is consistent with the electromigration-induced contact break. However, other mechanisms, e.g. local melting, cannot be ruled out since the melting point of metals also positively correlates with the activation energy of electromigration [8] and hence with hj^b i as well. Further experiments on other metals will be needed to clarify the relation between hj^b i and electromigration parameters of metals [9]. When Va decreases below 0.5 V, we found that the Gb histogram of Al becomes almost featureless, and the first bin for Gbo0.5G0 rapidly grows up with decreasing Va. This result is in contrast to low-Va histograms of noble metal nanocontacts, where a couple of sharp peaks arising from certain stable contact geometries appear at 1–7.5G0 [4]. No such sharp peaks were observed in our histograms of Al obtained at 0.1–0.5 V. However, this result may not necessarily indicate the absence of preferred geometries at the break of Al nanocontacts, since previous experiments and MD simulations [10–12] demonstrate the existence of stable contact geometries with conductance 1–50G0. It is thus more likely that some contact geometries are actually preferred at the contact break, but their stability is still insufficient at VaX0.1 V for producing sharp peaks in the Gb histogram. For example, the 0.8G0 contacts of Al, which make a large peak in a conventional conductance histogram [13–15], have an average lifetime of 4 ms [15] compared to the time
resolution 20 ms of this experiment. Thus, the 0.8G0 contacts would make little contribution to the Gb histogram even if they appear at the contact break [16].
4. Summary We have measured the break conductance Gb of Al nanocontacts and investigated how its distribution changes with the contact bias/current. For VaX0.8 V, it is found that the break characteristics of Al nanocontacts are essentially the same as those of noble metal nanocontacts under high bias/current: the contact break is current-induced and takes place at a critical current density hj^b i5 1010 A=cm2 . This hj^b i of Al nanocontacts is 20–50% lower than that of noble metals. Different from low-Va Gb histograms of noble metal nanocontacts, those of Al at 0.1–0.5 V show no sharp peaks of stable contact geometries. This implies that geometries of Al nanocontacts preferred at their break have lower stability than those of noble metals.
References [1] N. Agraı¨ t, A.L. Yeyati, J.M. van Ruitenbeek, Phys. Rep. 377 (2003) 81. [2] A.I. Yanson, G. Rubio-Bollinger, H.E. van den Brom, N. Agraı¨ t, J.M. van Ruitenbeek, Nature 395 (1998) 783. [3] R.H.M. Smit, C. Untiedt, J.M. van Ruitenbeek, Nanotechnology 15 (2004) S472. [4] A. Fujii, M. Tsutsui, S. Kurokawa, A. Sakai, Phys. Rev. B 72 (2005) 045407. [5] A. Fujii, J. Mizobata, S. Kurokawa, A. Sakai, e-J. Surf. Sci. Nanotechnol. 2 (2004) 125. [6] A. Fujii, S. Kurokawa, A. Sakai, e-J. Surf. Sci. Nanotech. 2 (2004) 155. [7] A. Garcı¨ a-Martı¨ n, J.A. Torres, J.J. Sa´enz, Phys. Rev. B 54 (1996) 13448. [8] A. Mogro-Campero, J. Appl. Phys. 53 (1982) 1224. [9] Break conductance data of Pt nanocontacts are reported in T. Minowa, M. Tsutsui, S. Kurokawa, and A Sakai, to be published in Jpn. J. Appl. Phys. [10] H. Hasmy, E. Medina, P.A. Serena, Phys. Rev. Lett. 86 (2001) 5574. [11] M. Dı´ az, J.L. Costa-Kra¨mer, P.A. Serena, E. Medina, H. Hasmy, Nanotechnology 12 (2001) 118.
ARTICLE IN PRESS T. Minowa et al. / Physica E 29 (2005) 495–499 [12] E. Medina, M. Dı´ az, N. Leo´n, C. Guerrero, H. Hasmy, P.A. Serena, J.L. Costa-Kra¨mer, Phys. Rev. Lett. 91 (2003) 026802. [13] A.I. Yanson, J.M. van Ruitenbeek, Phys. Rev. Lett. 79 (1997) 2157. [14] A. Halbritter, Sz. Csonka, O. Yu. Kolesnychenko, G. Miha´ly, O.I. Shklyarevskii, H. van Kempen, Phys. Rev. B 65 (2002) 045413.
499
[15] J. Mizobata, A. Fujii, S. Kurokawa, A. Sakai, Phys. Rev. B 68 (2003) 155428. [16] Measurements with finer resolution for Go1 G0 yielded a peak around 0.8 G0. The peak is nearly buried within the background and appears much reduced compared to sharp peaks in low-bias Gb histograms of noble metal nanocontacts.
Physica E 29 (2005) 495–499 www.elsevier.com/locate/physe
Break conductance of Al nanocontacts T. Minowaa, S. Kurokawab, A. Sakaia, a
Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan b International Innovation Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Available online 26 July 2005
Abstract We measured a break conductance, the last conductance of a contact before its complete break, for Al nanocontacts of 0–200G0 ðG 0 2e2 =h is the quantum unit of conductance) in ultrahigh vacuum at room temperature. We found that the distribution of the break conductance shows a broad single peak, the position of which shifts with the contact current. From the observed current dependence of the break conductance peak, it is suggested that Al nanocontacts break up most likely when the contact current density reaches a critical value 5 1010 A/cm2. r 2005 Elsevier B.V. All rights reserved. PACS: 73.63.Rt; 81.07.Lk; 66.30.Qa; 73.40Jn Keywords: Conductance; Contact break; Nanocontacts; Al
1. Introduction Nano- or atom-sized metal contacts and wires have been a subject of intensive theoretical and experimental studies in the past decade because of their unique mechanical and electronic properties [1]. One characteristic which is of practical importance, in applications of metal nanowires and nanocontacts as interconnects in nano-scale devices, is their capability of carrying high current Corresponding author at: International Innovation Center,
Mesoscopic Materials Research Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan. Tel.: +81 75 753 4833; fax: +81 75 753 4841. E-mail address: [email protected] (A. Sakai).
densities. For example, Yanson et al. [2] have shown that a monatomic chain of Au can sustain current density as high as 8 1010 A/cm2. For other metal nanocontacts, however, there have been few experimental studies about a maximum current density beyond which a metal nanocontact becomes unstable and breaks up. To estimate such a current density, two experimental methods can be employed. One is a current-disruption experiment [3] where a nanocontact of specific conductance (typically 1G0 or 2G0) is first produced and then the contact bias is increased to find a critical value at which the contact ruptures. Another method is to break a macroscopic metal contact under high biases and monitor the break conductance at which the contact completely breaks
1386-9477/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.06.013
ARTICLE IN PRESS 496
T. Minowa et al. / Physica E 29 (2005) 495–499
up. It is well known that even a macroscopic contact shrinks to the size of atoms just prior to its contact break [1]. Therefore, experimental data of the break conductance provide us some information on the critical current density of nano- or atom-sized metal contacts. We previously applied the latter method to noble metal nanocontacts and found that the critical current density for their contact break is (6–9) 1010 A/cm2 [4]. In this paper, we extend our study to Al nanocontacts and present experimental data of their break conductance.
2. Experiment Details of our experimental setup and conductance measurements have been described in Refs. [4–6]. A contact is formed between a fixed Al disk and a movable Al wire (both 99.999% pure) attached to a piezo actuator. We repeated contact break at 1 Hz and measured the transient conductance at each contact break by monitoring a voltage drop Vm across a 1 kO resistor connected in series with the contact. The bias Va is applied to the (contact+resistor) and divided between them. The contact conductance G is thus nonlinearly related to Vm as G ¼ V m =ðV a V m ÞR0 , where R0 ¼ 1 kO. Also, the contact current I can be expressed as I ¼ GV a =ð1 þ GR0 Þ. Note that in a high-conductance regime where GR0 b1, changing Va is effectively equivalent to changing the contact current I. Fig. 1 shows an example of the transient conductance trace observed at V a ¼ 1:2 V. This is actually a trace of Vm with a vertical scale converted to conductance, resulting in a strongly nonlinear conductance scale in Fig. 1. In the plot, the conductance suddenly exhibits a rapid fluctuation prior to the complete contact break, just as we observed in contact breaks of noble metals under high bias/current [5,6]. Each transient conductance was digitally measured with a time interval of 20 ms, and the last data point before the conductance drops below 0.5G0 was recorded as the break conductance Gb. An arrow in Fig. 1 indicates the Gb of the trace shown in the figure. All measurements were carried out at room
Fig. 1. Example of a transient conductance trace observed in a breaking Al contact at V a ¼ 1:2 V.
temperature in ultrahigh vacuum better than 5 108 Pa.
3. Results and discussion Fig. 2 summarizes break conductance histograms of Al contacts obtained at different values of Va from 0.4 to 3.2 V. Each histogram was constructed from 6000 conductance traces. The histograms were first built as Vm histograms and then converted to Gb histograms. As a result, the bin width in Fig. 2 is non-uniform and depends on both Va and Gb. For VaX0.8 V, the histogram shows a broad but well-defined peak. This peak in the distribution of Gb clearly indicates that the break of Al contacts takes place preferably at a specific contact size corresponding to the peak position. We denote this peak position by G^ b . Since G^ b is in a range 50–150G0, we are able to use the following Sharvin formula (for circular constrictions) [7] to estimate the contact size corresponding to G^ b : G ¼ G0
Ak2F k 2 R2 ¼ G0 F , 4p 4
(1)
where kF is the Fermi wavevector, and A and R are the contact cross-sectional area and radius,
ARTICLE IN PRESS T. Minowa et al. / Physica E 29 (2005) 495–499
497
Fig. 2. Histograms of the break conductance of Al contacts obtained at different values of Va.
respectively. Since G^ b 502150G 0 , Eq. (1) shows that Al contacts break at R 0.8–1.4 nm. It can be seen in Fig. 2 that the broad G^ b peak shifts to the lower conductance side as Va is reduced, i.e. G^ b decreases with Va (the peak height also decreases with Va, but this is an apparent effect due to the smaller bin width in histograms at lower Va). This shift of G^ b is just the same as we previously observed for G^ b of noble metal nanocontacts [4] and can thus be analyzed in the same manner. First, we note G^ b R0 b1 for G^ b 502150G 0 , so that it is the contact current I that varies with Va, as we pointed out in Section 2. Thus, the decrease in G^ b is actually a currentinduced phenomenon. Next, we estimate how high the current density is at the contact break. The current density j^b corresponding to the peak position G^ b can be easily obtained from the ratio I=G^ b , since G^ b is linearly proportional to the contact area A according to Eq. (1). We plot in Fig. 3 the resulting j^b as a function of the contact current I. Although j^b slightly increases with I, it stays nearly constant over the entire current range covered in this experiment. This result suggests that Al nanocontacts make a current-induced break, which takes place most likely when the
Fig. 3. Current density j^b at which the contact breaks with maximum likelihood is plotted as a function of the contact current I . Arrows indicate levels of j^b for the break of Au, Ag and Cu nanocontacts [4].
contact current density reaches the constant value of j^b . From the average of j^b data shown in Fig. 3, we estimate that the critical current density is hj^b i5 1010 A=cm2 for the break of Al nanocontacts. For comparison, we indicate in Fig. 3 experimental critical current densities for the break of noble metal nanocontacts [4]. It can be seen in Fig. 3 that the hj^b i of Al is roughly half that of Cu and 20% lower than that of Au.
ARTICLE IN PRESS 498
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Our experimental results on Gb and j^b show that the break of Al nanocontacts under high biases/currents has the same characteristics as those of noble metal nanocontacts [4]. Thus, a common break mechanism is likely to work in these metals. It is, however, not well understood at this time what makes Al and noble metal nanocontacts unstable and broken at their hj^b i. Considering a high level of hj^b i, electromigration would be a possible source of such a contact instability which generates the conductance fluctuations [4–6] and eventually leads to the contact break. In fact, the magnitude order of hj^b i of noble metal nanocontacts follows that of the activation energy of electromigration. Since Al has lower activation energy than that of noble metals, the observed low hj^b i of Al is consistent with the electromigration-induced contact break. However, other mechanisms, e.g. local melting, cannot be ruled out since the melting point of metals also positively correlates with the activation energy of electromigration [8] and hence with hj^b i as well. Further experiments on other metals will be needed to clarify the relation between hj^b i and electromigration parameters of metals [9]. When Va decreases below 0.5 V, we found that the Gb histogram of Al becomes almost featureless, and the first bin for Gbo0.5G0 rapidly grows up with decreasing Va. This result is in contrast to low-Va histograms of noble metal nanocontacts, where a couple of sharp peaks arising from certain stable contact geometries appear at 1–7.5G0 [4]. No such sharp peaks were observed in our histograms of Al obtained at 0.1–0.5 V. However, this result may not necessarily indicate the absence of preferred geometries at the break of Al nanocontacts, since previous experiments and MD simulations [10–12] demonstrate the existence of stable contact geometries with conductance 1–50G0. It is thus more likely that some contact geometries are actually preferred at the contact break, but their stability is still insufficient at VaX0.1 V for producing sharp peaks in the Gb histogram. For example, the 0.8G0 contacts of Al, which make a large peak in a conventional conductance histogram [13–15], have an average lifetime of 4 ms [15] compared to the time
resolution 20 ms of this experiment. Thus, the 0.8G0 contacts would make little contribution to the Gb histogram even if they appear at the contact break [16].
4. Summary We have measured the break conductance Gb of Al nanocontacts and investigated how its distribution changes with the contact bias/current. For VaX0.8 V, it is found that the break characteristics of Al nanocontacts are essentially the same as those of noble metal nanocontacts under high bias/current: the contact break is current-induced and takes place at a critical current density hj^b i5 1010 A=cm2 . This hj^b i of Al nanocontacts is 20–50% lower than that of noble metals. Different from low-Va Gb histograms of noble metal nanocontacts, those of Al at 0.1–0.5 V show no sharp peaks of stable contact geometries. This implies that geometries of Al nanocontacts preferred at their break have lower stability than those of noble metals.
References [1] N. Agraı¨ t, A.L. Yeyati, J.M. van Ruitenbeek, Phys. Rep. 377 (2003) 81. [2] A.I. Yanson, G. Rubio-Bollinger, H.E. van den Brom, N. Agraı¨ t, J.M. van Ruitenbeek, Nature 395 (1998) 783. [3] R.H.M. Smit, C. Untiedt, J.M. van Ruitenbeek, Nanotechnology 15 (2004) S472. [4] A. Fujii, M. Tsutsui, S. Kurokawa, A. Sakai, Phys. Rev. B 72 (2005) 045407. [5] A. Fujii, J. Mizobata, S. Kurokawa, A. Sakai, e-J. Surf. Sci. Nanotechnol. 2 (2004) 125. [6] A. Fujii, S. Kurokawa, A. Sakai, e-J. Surf. Sci. Nanotech. 2 (2004) 155. [7] A. Garcı¨ a-Martı¨ n, J.A. Torres, J.J. Sa´enz, Phys. Rev. B 54 (1996) 13448. [8] A. Mogro-Campero, J. Appl. Phys. 53 (1982) 1224. [9] Break conductance data of Pt nanocontacts are reported in T. Minowa, M. Tsutsui, S. Kurokawa, and A Sakai, to be published in Jpn. J. Appl. Phys. [10] H. Hasmy, E. Medina, P.A. Serena, Phys. Rev. Lett. 86 (2001) 5574. [11] M. Dı´ az, J.L. Costa-Kra¨mer, P.A. Serena, E. Medina, H. Hasmy, Nanotechnology 12 (2001) 118.
ARTICLE IN PRESS T. Minowa et al. / Physica E 29 (2005) 495–499 [12] E. Medina, M. Dı´ az, N. Leo´n, C. Guerrero, H. Hasmy, P.A. Serena, J.L. Costa-Kra¨mer, Phys. Rev. Lett. 91 (2003) 026802. [13] A.I. Yanson, J.M. van Ruitenbeek, Phys. Rev. Lett. 79 (1997) 2157. [14] A. Halbritter, Sz. Csonka, O. Yu. Kolesnychenko, G. Miha´ly, O.I. Shklyarevskii, H. van Kempen, Phys. Rev. B 65 (2002) 045413.
499
[15] J. Mizobata, A. Fujii, S. Kurokawa, A. Sakai, Phys. Rev. B 68 (2003) 155428. [16] Measurements with finer resolution for Go1 G0 yielded a peak around 0.8 G0. The peak is nearly buried within the background and appears much reduced compared to sharp peaks in low-bias Gb histograms of noble metal nanocontacts.