Low-temperature decoherence in disordered Pt nanowires

Low-temperature decoherence in disordered Pt nanowires

Available online at www.sciencedirect.com Physica E 19 (2003) 112 – 116 www.elsevier.com/locate/physe Low-temperature decoherence in disordered Pt n...

436KB Sizes 0 Downloads 67 Views

Available online at www.sciencedirect.com

Physica E 19 (2003) 112 – 116 www.elsevier.com/locate/physe

Low-temperature decoherence in disordered Pt nanowires J.-F. Lina , J.P. Birda;∗ , L. Rotkinab a Nanostructures b Beckman

Research Group, Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, USA Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, IL 61801, USA

Abstract We study the electrical properties of Pt nanowires, formed on SiO2 substrates by focused-ion-beam deposition. Their magneto-resistance shows evidence for weak-antilocalization at temperatures below 10 K, with a phase-breaking length of ∼ 100 nm, and a temperature dependence suggestive of quasi-one-dimensional interference. Studies of their temperature-dependent resistance at low temperatures reveal a signicant contribution due to electron-electron interaction as well as weak anti-localization. A switching behavior in the temporal resistance signals suggests two metastable states exist in local lattice congurations of the systems, which might be the source of saturation of phase-breaking length at low temperatures. ? 2003 Elsevier B.V. All rights reserved. PACS: 72.80.Ng Keywords: Decoherence; Nanowires

FIB techniques have grown in popularity in recent years, nding applications in transmission-electron microscope (TEM) sample preparation, micromachining, and lithographic-mask and circuit modication. Focused-ion-beam (FIB) deposition of nano-interconnects (NIs) is an attractive approach to the formation of electrical contacts [1–3], to structures such as carbon nanotubes and single molecules. This approach allows for the formation of complex interconnects, in just a single processing step, with resolution comparable to structures dened by electron-beam lithography. In spite of these advantages, however, there have been few, if any, reports to date of the electrical properties of the FIB-dened NIs. A knowledge of the electrical characteristics of ∗ Corresponding author. Tel.: +1-480-965-7421; fax: +1-480965-8058. E-mail address: [email protected] (J.P. Bird).

these nanowires is vital to their use as interconnects in complicated circuits. In this paper, we describe the results of studies of electron transport in Pt NIs, formed on insulating SiO2 substrates by FIB deposition. Their magneto-resistance shows evidence for weak antilocalization at temperatures below 10 K, with a phase-breaking length of ∼ 100 nm, and a temperature dependence suggestive of quasi-one-dimensional interference. Studies of their temperature-dependent resistance at low temperatures reveal a signicant contribution due to electron-electron interactions, in addition to the weak antilocalization. Switching behavior in the temporal resistance signals suggests that metastable states exist in the local lattice congurations of the systems, which might be the source of the saturated phase-breaking length at low temperatures. For FIB deposition of the Pt NIs, we have used a dual-beam system, manufactured by FEI CompanyTM

1386-9477/03/$ - see front matter ? 2003 Elsevier B.V. All rights reserved. doi:10.1016/S1386-9477(03)00317-5

J.-F. Lin et al. / Physica E 19 (2003) 112 – 116

113

0.025 0.1 K

0.020

[R(B) -R(0)]/R(0)

0.7 K

0.015

0.010

1.6 K

0.005 4.2 K

0.000 -1.2 Fig. 1. Scanning-electron micrograph of FIB-deposited NIs, similar to those investigated here, taken at a glancing angle of 45◦ .

(Dual-Beam 235 FIB). Prior to the FIB step, Ti/Au contacts were formed on SiO2 substrates by photolithography, using a bilayer resist (LOR TM & M:S1813TM ) that yields good re-entrant proles for lifto. The thickness of deposited gold in these  giving a resistance of a few tens contacts was 1900 A, of ohms for each of these structures. Prior to deposition of the NIs, a crucial step that must be performed is imaging of the substrate surface with the ion beam. We have found, however, that, even with the lowest measurement currents (1–4 pA), this gives rise to milling of the surface and introduces disorder. To avoid such undesirable eects, we therefore perform all focus and alignment on neighboring pads. The coupled beams are then moved to the area of interest to deposit the ne wires (Fig. 1), using the ion beam. For electrical studies, the NIs were used to bridge two-terminal contact structures, similar to those shown in Fig. 1. The results of studies of the electrical properties of three dierent NIs are presented in this Letter, and in Table 1 we dene the symbols used hereafter to refer to these. Inspection of similar wires by atomic-force microscopy reveals an approximately square cross section, with a deposited thickness of 60 nm. The three wires studied here were formed on the same chip, and were bonded into a ceramic carrier

-0.6 0 0.6 1.2 MAGNETIC FIELD (TESLA)

Fig. 2. Temperature-dependent magneto-resistance of wire L. The solid lines represent two-parameter ts to Eq. (2).

for resistivity measurements in either a dilution refrigerator (0.01–10 K) or a variable-temperature insert (4 –100 K). Small constant currents (∼ 7 nA) and low frequency (11 Hz) lockin detection were used for these measurements, and the resistance between pairs of contacts, unbridged by the NIs, was found to be in excess of 10 M. Such values are several orders of magnitude larger than the measured resistance of the NIs, indicating that substrate conduction is negligible. In Fig. 2, we show the results of magneto-resistance measurements of wire L at several dierent temperatures. A positive magneto-resistance is visible in the traces, and increases in magnitude with decreasing temperature. Such behavior is a well-known signature of weak antilocalization, and occurs in systems with strong spin-orbit scattering (for a recent review, see Ref. [4]). In one-dimensional (1D) wires, this magneto-resistance is predicted to take the form [5,6]:  −1 Rloc d 1 e2 Rl’ Ai(x) : (1) =√ (Ai(x)) R dx 2 ˝ L Here, Ai (x) denotes the Airy function, L is the wire length, and x = 2(l’ =l’0 )2 · l’ = (D’ )0:5 is the phase-breaking length due to quasi-elastic Nyquist scattering [5], ’ is the Nyquist dephasing time, and

J.-F. Lin et al. / Physica E 19 (2003) 112 – 116

114

T -1/3

φ

l (nm)

100

10 0.1 1 10 TEMPERATURE (KELVIN) Fig. 3. Temperature dependence of l’ , measured in the three dierent wires (L: lled circles, M : open circles, S: lled squares). The long-dashed line indicates the approximate width of the NIs, while the dotted line is a guide to the eye that indicates a power-law variation of T 1=3 .

D is the diusion constant. l’0 = (D’0 )0:5 , where 1=’0 (B) = 1=’0 (B = 0) + 1=B , and 1=’0 (B = 0) is the inelastic electron–electron scattering rate [4]. 1=B is the eective dephasing rate introduced by the magnetic eld (B), and is given by 1=B = DW 2 =12l4B , where W is the width of the wire and lB = (˝=2eB)0:5 . The lines through the experimental data of Fig. 3 are two-parameter (W and l’ ) ts to the form of Eq. (1). The values of W inferred from the ts are in good agreement with the physical width, as we show in Table 1. We have also attempted to t the magneto-resistance using the theoretical forms for weak-antilocalization in two- (2D) and

three-dimensions (3D). The 3D form gives a poor t to the data, while the 2D form gives a reasonable t, but only with W ¿ 200 nm, nearly four times larger than the physical value. For these reasons, we consider the 1D ts to give the best agreement with experiment. Fig. 3 shows the temperature dependence of l’ in the three dierent wires. The dotted line in this gure indicates the T 1=3 slope of l’ , predicted for the Nyquist dephasing mechanism in one dimension [5]. At temperatures above 1 K, the variation of l’ in all three wires appears to be consistent with this prediction. We point out, however, that the values of l’ in this range are comparable to, or even slightly smaller than, the width of the wire (indicated by the dashed line in Fig. 4). Strictly speaking, the transport should therefore be intermediate between the quasi-twodimensional and quasi-one-dimensional regimes. At temperatures below 1 K, l’ becomes temperature independent, similar to the behavior found in other studies of metallic nanowires [4,7,8]. In the main panel of Fig. 4, we show the measured variation of the zero-eld resistance of wire, relative to its value at 4:2 K. In principle, this measured variation should be determined by separate contributions from weak antilocalization and electron–electron interactions (EEI). To determine the contribution from weak antilocalization, we use the result of Eq. (1), while for our analysis of the EEI we use the usual one-dimensional expression [9,10]: Rint (T ) e2 R = LT : R 2˝ L

(2)

This expression is valid at temperatures where W is less than the thermal length LT = (˝D=kB T )0:5 . For a comparison with our experimental results, we rst use the value of l’ , inferred from the weak antilocalization magneto-resistance (Fig. 2), and substitute this into Eq. (1) to determine the localization

Table 1 Parameters of the dierent NIs studied here

Wire

Length (m)

Width (nm)

300 K ( cm)

77 K ( cm)

4 K ( cm)

300 K = 4 K

D (cm2 = s)

S M L

5.9 13 20

45 49 56

61.5 482 545

47.3 377 417

44.4 360 393

1.39 1.34 1.39

4.80 13.3 9.34

J.-F. Lin et al. / Physica E 19 (2003) 112 – 116 400

1.06 10

4

1.04 10

4

115 2.25 10

4

2.20 10

4

2.15 10

4

RESISTANCE (OHMS)

0.010

0.005

loc

[R(T) - R(4.2 K) ] (OHMS)

int

∆R /R & ∆R /R

0.015

0.000

200 0.1 1 10 TEMPERATURE (KELVIN)

0

1.02 10

4

1.00 10

4

0

0.1

1

10

TEMPERATURE (KELVIN)

Fig. 4. Temperature dependence of the zero-eld resistance of wire L (“+” symbols). The open symbols represent one-parameter ts (D) to the sum of Eqs. (1) and (2). The inset shows the temperature dependence of the relative contributions to the resistance from localization (Rloc =R, lled symbols) and interactions (Rint =R, lled symbols).

contribution to the resistance at zero magnetic eld. After subtracting this term from the total resistance variation (plotted in Fig. 4 with the “+” symbols), we then use Eq. (2), with an optimized t for the diusion constant, to calculate the interaction term. To indicate the quality of this t, in the main panel of Fig. 4 we show as open symbols the total resistance correction obtained by summing the localization and interaction terms. The agreement with experiment is good and the values of D used to t each of the wires (see Table 1) are seen to be consistent with expectations for disordered metals. In the inset to Fig. 4, we show the separate contributions to the resistance from localization (Rloc ) and interactions (Rint ). The data here reveals that, while the weak antilocalization provides the dominant contribution to the magneto-resistance, the leading quantum correction to the conductance is provided by EEI. This is quite typical for disordered metals [11]. A common feature of many experimental studies of quantum wires, which is also found in this study here, is a saturation of the phase-breaking length at low temperatures. One suggestion that has been made

100

200

300

400

500

TIME (MINUTES)

Fig. 5. Time-dependence of the zero-eld resistance in wire L at 0:9 K (upper curve) and wire M at 4:2 K (lower curve).

in the literature is that the saturation, in metal wires at least, may be due to uctuations in the occupation of two-level systems [12]. In connection with this possibility, it is interesting to note that the resistance of these wires was found to exhibit switching characteristics over long time intervals (Fig. 5). The long time scale associated with the switch in this gure is of order minutes (in the lower curve) to an hour (in the upper curve). Such variations are much longer than those associated with typical switching noise in mesoscopic structures, but are similar to the behavior that is found in amorphous systems at low temperatures. This activity in the resistance was found to decrease strongly over time, while the sample was maintained at liquid-Helium temperatures or lower. Typically, after the sample had been kept cold for several days, variations such as those shown in Fig. 5 were no longer observed. This may suggest a slow decay of the evolution of the physical structure of the wire, towards a less amorphous state. In conclusion, we have studied the electrical properties of Pt NIs, formed on SiO2 substrates by focused-ion-beam deposition. Their magneto-resistance showed evidence for weak antilocalization at temperatures below 10 K, with a phase-breaking length of ∼ 100 nm, and a temperature dependence suggestive of quasi-one-dimensional electron interference. Analysis of the temperature

116

J.-F. Lin et al. / Physica E 19 (2003) 112 – 116

dependence of the zero-eld resistance allowed the interaction and localization terms to be separated, and the former was found to be larger than the latter by a factor of ∼4 –5. Work at ASU is sponsored by the Oce of Naval Research (N00014-98-0594, JPB) and the Department of Energy NSET program (DE-FG03-01ER45920, JPB). Work at Illinois was carried out in the Center for Microanalysis of Materials, University of Illinois, which is partially supported by the U.S. Department of Energy under grant DEFG02-91-ER45439 and under UIUC Critical Research Initiative grant. References [1] T.W. Ebbesen, H.J. Lezec, H. Hiura, J.W. Bennett, H.F. Ghaemi, T. Thio, Nature 382 (1996) 4.

[2] B. Wei, R. Spolenak, P. Kohler-Redlich, M. Ruhle, E. Arzt, Appl. Phys. Lett. 74 (1999) 3149. [3] J.-F. Lin, J.P. Bird, L. Rotkina, P.A. Bennett, Appl. Phys. Lett. 82 (2003) 802. [4] J.J. Lin, J.P. Bird, J. Phys.: Condens. Matter 14 (2002) R501. [5] B.L. Altshuler, A.G. Aronov, D.E. Khmelnitskii, J. Phys. C 15 (1982) 7367. [6] P.M. Echternach, M.E. Gershenson, H.M. Bozler, A.L. Bogdanov, B. Nilsson, Phys. Rev. B 48 (1993) 11516. [7] P. Mohanty, E.M.Q. Jariwala, R.A. Webb, Phys. Rev. Lett. 78 (1997) 3366. [8] D. Natelson, R.L. Willet, K.W. West, L.N. Pfeier, Phys. Rev. Lett. 86 (2001) 1821. [9] B.L. Altshuler, A.G. Aronov, M.E. Gershenson, Yu.V. Sharvin, Sov. Sci. Rev. A 9 (1987) 223. [10] B.L. Altshuler, A.G. Aronov, in: M. Pollack, A.L. Efros (Eds.), Electron-Electron Interactions in Disordered Systems, North-Holland, Amsterdam, 1985, p. 1. [11] P.M. Echternach, M.E. Gershenson, H.M. Bozler, A.L. Bogdanov, B. Nilsson, Phys. Rev. B 50 (1994) 5748–5751. [12] A. Zawadowski, J. von Delft, D.C. Ralph, Phys. Rev. Lett. 83 (1999) 2632.