Classical and quantum transport in focused-ion-beam-deposited Pt ...

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Feb 3, 2003 - Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287-1504. Received 2 October 2002; accepted 5 ...
APPLIED PHYSICS LETTERS

VOLUME 82, NUMBER 5

3 FEBRUARY 2003

Classical and quantum transport in focused-ion-beam-deposited Pt nanointerconnects J.-F. Lin and J. P. Birda) Nanostructures Research Group, Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287-5706

L. Rotkina Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Ave., Urbana, Illinois 61801

P. A. Bennett Department of Physics and Astronomy, Arizona State University, Tempe, Arizona 85287-1504

共Received 2 October 2002; accepted 5 December 2002兲 We study the electrical properties of Pt nanointerconnects, formed on SiO2 substrates by focused-ion-beam deposition. Studies of their temperature-dependent resistivity reveal a small residual-resistivity ratio, and a Debye temperature that differs significantly from that of pure Pt, indicative of the disordered nature of the nanowires. Their magnetoresistance 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. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1541940兴

Focused-ion-beam 共FIB兲 deposition of nanointerconnects 共NIs兲 is an attractive approach to the formation of electrical contacts1–3 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 defined 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-defined NIs. A knowledge of the electrical characteristics of these nanowires is vital to their use as interconnects in complicated circuits. In this letter, we describe the results of studies of electron transport in Pt NIs, formed on insulating SiO2 substrates by FIB deposition. Studies of their temperature-dependent resistivity reveal a small residual-resistivity ratio, and a Debye temperature that differs significantly from that of pure Pt, indicative of the disordered nature of the nanowires. Their magnetoresistance 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. In light of the above, we discuss the advantages of using the FIB-deposited wires as interconnects to smaller, nanoscale, structures. FIB techniques have grown in popularity in recent years, finding applications in transmission-electron microscope sample preparation, micro-machining, and lithographic-mask and circuit modification. For FIB deposition of the Pt NIs, we have used a dual-beam system, manufactured by FEI Company™ 共Dual-Beam 235 FIB兲. Prior to the FIB step, Ti/Au contacts were formed on SiO2 substrates by photolithography, using a bilayer resist 共LOR™ and M.S1813™兲 that yields good re-entrant profiles for lift-off. The thickness of deposited gold in these contacts was 1900 Å, giving a a兲

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resistance of a few tens 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 共1– 4 pA兲, this gives rise to milling of the surface and introduces disorder. To avoid such undesirable effects, we therefore perform all focus and alignment on neighboring pads. The coupled beams are then moved to the area of interest to deposit the fine wires 共Fig. 1兲, using the ion beam. For electrical studies, the NIs were used to bridge twoterminal contact structures, similar to those shown in Fig. 1. The results of studies of the electrical properties of three different NIs are presented in this letter, and in Table I we define 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 for resistivity measurements in either a dilution refrigerator 共0.01–10

FIG. 1. Scanning-electron micrographs of a FIB-deposited NI, similar to those investigated here, taken at a glancing angle of 45°.

0003-6951/2003/82(5)/802/3/$20.00 802 © 2003 American Institute of Physics Downloaded 19 Jan 2005 to 149.169.53.99. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

Lin et al.

Appl. Phys. Lett., Vol. 82, No. 5, 3 February 2003

803

TABLE I. Parameters of the different NIs studied here.

Wire

Length 共␮m兲

Width 共nm兲

␳ 300 K 共␮⍀ cm兲

␳ 77 K 共␮⍀ cm兲

␳4 K 共␮⍀ cm兲

␳ 300 K / ␳ 4 K

⌰D 共K兲

␳⬘ 共␮⍀ cm兲

S M L

5.9 13 20

56⫾14 60⫾7 45⫾8

61.5 482 545

47.3 377 417

44.4 360 393

1.39 1.34 1.39

168 209 181

0.18 1.4 1.7

K兲 or a variable-temperature insert 共4 –100 K兲. Small constant currents 共⬃7 nA兲 and low-frequency 共11 Hz兲 lock-in 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 temperature dependence of the resistivity of wires L and S. The behavior is fairly typical of classical metals, and the solid lines through the data represent the results of fits to the well known Bloch–Gruneisen form:4

␳共 T 兲⫽ ␳ o⫹ ␳ ⬘T

冋 册冕 T ⌰D

4

⌰ D /T

0

5

x dx x 共 e ⫺1 兲共 1⫺e ⫺x 兲

共1兲

Here, ␳ (T) is the resistivity at a temperature T, ␳ 0 is the residual resistivity, and ⌰ D is the Debye temperature. Since ␳ 0 is determined directly by experiment, two-parameter ( ␳ ⬘ and ⌰ D ) fits to the data have been used in Fig. 2. It is clear from Fig. 2 共and from the data in Table I兲 that there are large variations in the magnitude of the resistivity of the different NIs. The residual-resistivity ratio of all three NIs is also very small 共Table I兲, indicating the presence of significant disorder. This is consistent with previous studies of the resistivity of two-dimensional Pt films, formed by FIB deposition.5–7 We also note that the values of ⌰ D , inferred from the fits to Eq. 共1兲, differ appreciably from that reported for pure Pt8,9 (⌰ D ⫽215– 240 K). This is not altogether surprising, since the FIB lithography involves the use of a precursor gas, and can lead to the deposition of disordered Pt, contaminated with Ga from the ion beam and C from the precursor gas, as well as with O if the pressure is not optimal. In fact, Auger

analysis of our NIs has shown them to consist of approximately 30% Pt, with the remaining 70% largely comprised of codeposited C. In Fig. 3, we show the results of magnetoresistance measurements of wire L at several different temperatures. A positive magnetoresistance 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.10 In onedimensional 共1D兲 wires, this magnetoresistance is predicted to take the form:11,12



d ⌬R 1 e 2 Rl ␸ ⫽ Ai 共 x 兲 关 Ai 共 x 兲兴 R ␲ ប L dx &



⫺1

.

共2兲

Here, A i (x) denotes the Airy function, L is the wire length, and x⫽2(l ␸ /l ␸ o ) 2 •l ␸ ⫽(D ␶ ␸ ) 0.5 is the phase-breaking length due to quasi-elastic Nyquist scattering,11 ␶ ␸ is the Nyquist dephasing time, and D is the diffusion constant. l ␸ o ⫽(D ␶ ␸ o ) 0.5, where 1/␶ ␸ o (B)⫽1/␶ ␸ o (B⫽0)⫹1/␶ B , and 1/␶ ␸ o (B⫽0) is the inelastic electron–electron scattering rate.10 1/␶ B is the effective dephasing rate introduced by the magnetic field (B), and is given by 1/␶ B ⫽DW 2 /12l B4 , where W is the width of the wire and l B ⫽(ប/2eB) 0.5. The lines through the experimental data of Fig. 3 are two-parameter 共W and l ␸ ) fits to the form of Eq. 共2兲. The values of W inferred from the fits are in good agreement with the physical width, as we show in Table I. We have also attempted to fit the magnetoresistance using the theoretical forms for weak antilocalization in two 共2D兲 and three dimensions 共3D兲. The 3D form gives a poor fit to the data, while the 2D form gives a reasonable fit, but only with W⬎200 nm, nearly four times

FIG. 3. Temperature-dependent magnetoresistance of wire L. The solid lines represent fits to Eq. 共2兲, using W⫽46 nm and l ␸ ⫽53 nm at 0.1 K; W FIG. 2. Temperature dependence of the resistivity for the long and short NIs. The solid lines through the experimental data points represent two⫽58 nm and l ␸ ⫽43 nm at 0.7 K; W⫽50 nm and l ␸ ⫽33 nm at 1.6 K, and parameter fits to Eq. 共1兲. W⫽60 nm and l ␸ ⫽19 nm at 4.2 K. Downloaded 19 Jan 2005 to 149.169.53.99. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

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Appl. Phys. Lett., Vol. 82, No. 5, 3 February 2003

FIG. 4. Temperature dependence of l ␸ , measured in the three different wires 共L: filled circles, M: open circles, S: filled squares兲. 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 共see Ref. 11兲.

larger than the physical value. For these reasons, we consider the 1D fits to give the best agreement with experiment. Figure 4 shows the temperature dependence of l ␸ in the three different wires. The dotted line in this figure indicates the T 1/3 slope of l ␸ , predicted for the Nyquist dephasing mechanism in one dimension.11 The source of this dephasing is quasielastic electron–electron scattering, due to timedependent variations in the self-consistent electric field, generated by the random thermal motion of the electrons. At temperatures around 1 K, the variation of l ␸ in the wires appears to be consistent with the T 1/3 dependence, but a steeper variation can be seen at higher temperatures in some of the data 共see the filled and open circles兲. This deviation could possibly be due to the emergence of other dephasing mechanisms at higher temperatures, such as inelastic electron–electron, and/or electron–phonon, scattering, both of which are known to show a stronger variation than T 1/3. 10 Another feature of the data to note is that the values of l ␸ in this range are comparable to, or even slightly smaller than, the width of the wire 共indicated by the dashed line in Fig. 4兲. Strictly speaking, the transport should therefore be intermediate between the quasi-2D and quasi-1D regimes. At temperatures below 1 K, l ␸ becomes temperature independent, similar to the behavior found in other studies of metallic nanowires.10,13,14 We are confident that this behavior is not due to a loss of thermal contact to the electrons in the wires, since their zero-field resistance continued to increase as the temperature was lowered below the saturation onset 共not shown here兲. The source of the saturation remains the subject of debate, and we do not speculate further on its microscopic origin here. Rather, we simply note that the behavior shown in Fig. 4 appears quite typical of disordered metals. While we have measured two-terminal transport in the NIs, we do not believe that our results are significantly influenced by the contact resistance between the Ti/Au pads and the NIs. Firstly, we have made separate measurements of the resistivity of the Ti/Au pads, and find this to be at least two orders of magnitude smaller than the measured resistivity of the NIs. Secondly, we note that the scaling of the resistivity with wire length in Table I is not consistent with a

contact-limited measurement. Finally, we point out that the presence of a significant contact resistance would disrupt the weak localization analysis, which we actually have found to yield fitted wire widths in good agreement with the fabricated values 共Table I兲. While FIB deposition allows the realization of NIs with excellent structural uniformity, this work reveals that the transport in these wires is highly disordered, a conclusion that seems consistent with the results of our Auger analysis. In terms of their use as interconnects to smaller nanostructures, it is clear that the NIs provide a convenient means for the definition of complex multi-probe structures, with robust mechanical characteristics. While there might be some concern about the high resistivity of these wires, this may often be obviated in experiment by the use of a four-probe geometry. Our magnetotransport studies indicate a short phasecoherence length at low temperatures. This is actually a positive attribute for the use of these wires as interconnects, since it is undesirable in transport studies of nanostructures that the measurement should be influenced by the coherent extension of the wave function, over long distances in the leads. In conclusion, we have studied the electrical properties of Pt nanointerconnects, formed on SiO2 substrates by focused-ion-beam deposition. Studies of their temperaturedependent resistivity were found to reveal a small residualresistivity ratio, and a Debye temperature that differs significantly from that of pure Pt, indicative of the disordered nature of the NIs. Their magnetoresistance 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-1D electron interference. Work at Arizona State University was sponsored by the Department of Energy 共DE-FG03-01ER45920, JPB兲 and the Office of Naval Research 共N00014-98-0594兲. Work at Illinois was carried out in the Center for Microanalysis of Materials, University of Illinois, which is partially supported by the Department of Energy 共DEFG02-91-ER45439兲 and by a Critical-Research Initiative grant.

1

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