High-Frequency Characterization of Contact Resistance ... - IEEE Xplore

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 59, NO. 10, OCTOBER 2011

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High-Frequency Characterization of Contact Resistance and Conductivity of Platinum Nanowires Kichul Kim, Member, IEEE, T. Mitch Wallis, Paul Rice, Dazhen Gu, Sang-Hyun Lim, Atif Imtiaz, Pavel Kabos, Fellow, IEEE, and Dejan S. Filipovic, Senior Member, IEEE

Abstract—Contact resistance and conductivity of individual platinum (Pt) nanowires (NWs) embedded in coplanar waveguide structures are investigated at high frequencies. Two approaches to extract the NW conductivity and contact resistance from two-port -parameters are developed. The first approach is based on transmission-line theory, while the second approach is based on a lumped-element physics-based model. Full-wave and circuit simulations are used to aid validation and the systematic analysis of both methods. Simulations are compared to calibrated on-wafer measurements of individual Pt NWs. The studies of the transmission-line-based approach reveal that the contact resistance can be determined accurately, but the obtained conductivity is inaccurate. By contrast, the lumped-element approach produces accurate results for both the contact resistance and conductivity of Pt NWs. The lumped-element method is used to determine the and conductivity of 0.013 times contact resistance of about 50 the bulk conductivity of Pt for fabricated Pt NWs with 300-nm diameter.

Index Terms—Conductivity, contact resistance, high-frequency characterization, platinum (Pt) nanowires (NWs).

Fig. 1. Conductivity and contact resistance boundaries for Pt NWs. When one of the two parameters is determined, the other is obtained from the plotted relation. D is the diameter of the NWs. Literature A: [4], Literature B: [5], and Literature C: [6].

I. INTRODUCTION EMANDS FOR small electronic devices with many integrated functionalities are growing at a rapid pace. To address this, advanced manufacturing technologies for smaller feature size, as well as denser integrated circuits, interconnects, and nanoscale systems, are needed. However, reducing interconnect feature size down to the nanometer scale leads to the variation of current behavior in metallic wires [1], causes reduction of conductivity, and magnifies the influence of contact impedance. It has been observed previously that the conductivities of Au [2] and Cu [3] nanowires (NWs) are lower than their bulk values. For platinum (Pt) NWs, conductivity in the range ( S/m) [4]–[6] and contact resistances of about 100–138 [5], [6] or 700–800 k [7] were

D

Manuscript received June 09, 2011; revised June 30, 2011; accepted July 21, 2011. Date of publication August 22, 2011; date of current version October 12, 2011. The work of K. Kim, P. Rice, and D. S. Filipovic was supported by the Defense Advanced Research Projects Agency (DARPA) Center on Nanoscale Science and Technology for Integrated Micro/Nano-Electromechanical Transducers (iMINT) funded by DARPA N/MEMS S&T Fundamentals Program (HR0011- 06-1-0048). K. Kim and D. S. Filipovic are with the Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Boulder, CO 80309 USA (e-mail: [email protected]; [email protected]). T. M. Wallis, D. Gu, S.-H. Lim, A. Imtiaz, and P. Kabos are with the National Institute of Standards and Technology, Boulder, CO 80305 USA (e-mail: [email protected]). P. Rice is with the Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 80309 USA. Digital Object Identifier 10.1109/TMTT.2011.2163417

reported. These results were obtained with dc or low-frequency measurements. High-frequency characterization of Pt NWs with 100- and 250-nm diameters was performed by combining a full-wave finite-element method (FEM) modeling and calibrated two-port measurements in [8]. Coplanar waveguide (CPW) structures incorporating individual Pt NWs were modeled first and their simulated -parameters were fitted to the measured -parameters and conductivity in order to determine contact resistance of the NWs. From the results presented in [8], it followed that the two parameters could not be determined simultaneously from two-port measurements of a single device. For example, and an simulated -parameters with a fixed value matched the measured -parameters just as well optimized as simulated -parameters with a fixed value and optimized . To augment findings from [8], Fig. 1 shows ranges of the two parameters for the considered diameter NWs. All combinations of the two parameters along the curve produce the same simulated -parameter results. Obtained results are consistent with relevant findings reported in [4]–[6], as well as the circuit-based modeling reported in [9]. This paper follows up on previous work [8] and discusses two algorithms developed to extract contact resistance and conductivity of individual Pt NWs from measurements of multiple Pt NWs with different lengths. The first algorithm is based on a conventional transmission-line theory [10]. The algorithm and its circuit-element-based validation were originally presented

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in [9]. Here, the development and evaluation of the algorithm is completed using full-wave modeling based on direct solution of wave equation as implemented in the FEM code ANSYS HFSS v.11.1 Circuit-based modeling within AWR Microwave Office 20091 is also provided for completeness. As seen, the transmission line approach is found to have limitations with respect to the accurate characterization of highly resistive NW-based devices. The second algorithm is based on equivalent physics-based lumped-element models, which are fully validated using both full-wave FEM and circuit-based modeling. It is seen that this approach yielded more accurate results than the transmission-line-based approach. Initial experimental validation of the second algorithm is conducted with CPW devices incorporating micrometer-size monolithic Au bridges whose contact resistance and conductivity are 0 and about 4.1 10 S/m (the bulk value for Au), respectively. Pt NWs with lengths of 4 and 8 m are also measured and their measured -parameters are analyzed via the lumped-element algorithm. Results show that the contact resistance and conductivity of and , 300-nm-diameter Pt NWs are about 50 respectively. Note that the developed algorithms can be extended to other metallic NWs provided that the wires do not exhibit quantum effects such as quantized resistance. Note that the contact resistance discussed herein deals mainly with the resistance of metal–metal junctions consisting of Pt NWs with diameters of hundreds of nanometers and CPW signal lines. Within the measured frequency range, the quantum effects may be neglected for metallic NWs of such large diameters. II. FABRICATION, MEASUREMENT, AND MODELING A. Fabrication CPW devices incorporating individual Pt NWs are fabricated in a two-stage process. In the first fabrication stage, the CPW structures are fabricated using conventional photolithography on a polished quartz substrate. Each device includes a 1150- m-long CPW line with a gap of 4 or 8 m across the signal line. 75 m of the signal line to either side of the gap are tapered to constrain the area where Pt NWs will bridge the gap and to reduce electrical discontinuity between the CPW signal lines and the Pt NWs. The slot width between the signal lines and ground is kept at 5 m. The nontapered portions of the CPW lines are designed to have a characteristic impedance of about 50 . 20-nm-thick Ti and 200-nm-thick Au layers are sequentially deposited to create the CPW host device. CPW devices with 4- and 8- m-long Au bridges are also fabricated on the same wafer, as shown in Fig. 2(a). Each Au bridge is 2- m wide. In the second fabrication stage, supporting SiO dielectric and Pt NWs are deposited on the CPW devices by use of a dual beam focused ion beam (FIB) system (NOVA 600i DualBeam).1 The deposition mechanism is the same for both materials, except their precursors: Tetraethyl orthosilicate is utilized for the SiO layer, while Methylcyclopentadienyl Pt trimethyl is used for Pt NWs [10]. During the deposition, the fabrication process 1Trade names are provided for technical clarity and do not imply endorsement by the National Institute of Standards and Technology (NIST). Products from other manufacturers may perform as well or better.

Fig. 2. SEM of the fabricated devices. (a) Au bridge in 4-m gap. (b) Pt NW in 4-m gap. (c) Pt NW in 8-m gap.

is monitored with a scanning electron microscope (SEM). The ion beam accelerating voltage is kept at 30 kV, and beam current is set at 20 pA. The vacuum in the specimen chamber is 6.66 10 Pa (5 10 torr) and deposition duration is approximately 30 s. Fabricated Pt NWs in the gap of 4 and 8 m are shown in Fig. 2(b) and (c), respectively. To be able to characterize the devices over a wideband frequency range, CPW calibration lines, which are necessary for on-wafer multiline thru-reflect-line (TRL) calibration [11], [12], are also fabricated on the same wafer. The calibration devices include lines with lengths 1.80, 2.60, 3.83, and 6.10 mm. The thru is 0.50-mm long and the reflect is 0.20-mm long. B. Measurement Two-port -parameter measurements are carried out with a vector network analyzer (VNA) and an on-wafer measurement system. The system consists of two ground–signal–ground (GSG) microwave probes, probe manipulators, and an optical microscope. The measured frequency range is from 0.1 to 40 GHz. Multiline TRL calibration is performed with NISTcal software, and reference planes are translated to planes 500 m away from the probe contacts, i.e., at the beginning of the CPW taper. DC resistance from port 1 to port 2 is measured during each measurement. Multiple devices for each length NW are measured and the measurement process has been repeated several times to confirm the repeatability of the measurements. The measurement setup and a full-wave model of CPW device-under-test (DUT) are shown in Fig. 3(a). C. Modeling Full-wave modeling is carried out with an FEM code implemented within ANSYS HFSS. To reduce the computational overhead associated with volumetric meshing, two GSG probes, shown in Fig. 3(a), are replaced by ideal wave ports, as explained in [8]. Note that the same full-wave modeling is used for approaches discussed in Sections III and IV. In the full-wave modeling, the distance between the NW and . substrate is assumed to be equal to the radius of the NW, To assess the sensitivity of the device’s -parameters on this height, the simulations for low- and high-resistivity NWs and to 5 are conducted. It is seen heights varying from that the effect of height variation is relatively small. Specifidecreases by no more than 1 dB cally, the transmission throughout the measured frequency range when the height is to 5 . It is important to note that the changed from observed changes do not significantly alter the conclusions presented below.

KIM et al.: HIGH-FREQUENCY CHARACTERIZATION OF CONTACT RESISTANCE AND CONDUCTIVITY OF Pt NWs

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Fig. 4. SEM image of Pt NW and its equivalent transmission-line model with characteristic impedance Z and propagation constant . Contact resistance R is connected at both ends of the NW.

from the previous work [8], [9], the contact reactance has a negligible effect. III. TRANSMISSION-LINE-BASED METHODS

Fig. 3. Schematic of two-port measurement setup and full-wave and circuit-based models. (a) Measurement setup with full-wave FEM model of CPW device. (b) Circuit-based model for the transmission line model-based approach. (c) Circuit-based model for the lumped-element model-based ap,” “Wire ,” “R ,” and “C ” are circuit-based elements, proach. “CPW while “CPW ” and “Taper” are modeling elements obtained with the MoM. CPW and Wire is for a section of Au bridge or Pt NW, R is contact is the coupling capacitance. resistance, and C

Fig. 3(b) and (c) shows circuit-based models developed within AWR Microwave Office for the transmission-line and lumped-element-model-based approaches, respectively. The models are actually hybrid in that CPW elements designated ” and “Taper” are obtained by method of moment as “ (MoM) simulations, while “ ,” “Wire ,” “ ,” and ” are circuit-based elements from the AWR’s library. “ is considered as a CPW element, the signal line of is modwhich can be either an Au bridge or a Pt NW. Wire eled with a “round wire” element from AWR’s library, which can be defined with its dimensions (wire length and diameter) ” and and conductivity. Note that the modeling “ “Taper” using the MoM yield more accurate results, as shown in [9]. The circuit-based elements serve as parameters (i.e., and of or Wire ) to be determined for each NW. is included to take into account the A contact resistance represents the stray coupling capacitance contact effects. between the two tapered CPW lines. The value of is determined by fitting the circuit model to the measurements of an “empty” device without an NW, and it is found to be 0.30 fF for the 4- m gap and 0.23 fF for the 8- m gap. Note that in both circuit-based models, the and Wire elements take into account both resistive and reactive components of the NW impedance. Also note that the contact effects may be represented by complex impedance [13]; however, as follows

In order to simultaneously determine both contact resistance and conductivity for Pt NWs from two-port measurements, at least two devices with Pt NWs of different lengths are needed. The Pt NWs in both devices are assumed to have the same conductivities and contact resistances on both sides. During the fabrication, the FIB moves back and forth several times from one CPW signal line to the other to deposit the Pt NW across the gap. Thus, the two contact resistances in one device may be assumed to be the same, on average. Although in practice the contact resistance of a device may be different from that of the other devices because of uncertainties in structural parameters and fabrication processes, the developed algorithms are applicable only for the above assumptions. This section demonstrates a transmission-line-based approach. Limitations of the approach are addressed based on careful validation procedures with circuit and full-wave FEM simulations. A. Algorithm Description The intuitive approach is to consider the NW as a signal line of a CPW structure modeled by a simple transmission line. The transmission line between two contacts is characterized with characteristic impedance and propagation constant , as shown in Fig. 4. Assuming that the two contact resistances is constant for a particular diameter of are identical and that and in this approach are maintained independent Pt NWs, of the length of the NWs. In other words, one seeks the solution for the NW under the condition that and of and are equal to and for two different lengths and of the lines, respectively. To solve this problem, we start by converting two-port -parameter matrices into corresponding matrices [14]. -parameter matrices for the device with a Pt NW, , and , are obtained by moving for the device without the NW, the reference planes to the start of the taper by use of NISTcal. Next, each -parameter matrix is converted to an admittance and , by use of the equations given in ( ) matrix, for the combination of the NW and [14]. The matrix the contact resistance (shown in Fig. 4) is then obtained from (1)

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The resulting matrix is then converted to an matrix, , to find the characteristic and propagation constant for the NW section, impedance and contact resistance . Since the two contact resistances can be and the NW are connected in series, represented as

can be used with terms up to the second order in (5). The quantity is assumed to be small for the 4- and 8- m Pt NWs. Then, from (4), (5), and (9),

(10) Therefore, the resulting propagation constant is (2) (11) and the

matrix for the NW is given by and the condition for propagation constant

results in (12)

(3) is obtained from measurements, and (3) can be rewritten as

from either (8) or (12). The characteristic One can determine impedance and propagation constant for the NW sections in the two devices are found from (6) and (7). To compute the conductivity of the Pt NW, the characteristic impedance and propagation constant of the NW section can be used. Since the NW section is modeled as a transmission line, it can be represented with resistance , inductance , conducper unit length [14]. and are tance , and capacitance rewritten as

(4) (13) Since the NW section is represented as a transmission line, matrix can also be written as [15] its

and (14)

(5) From (4) and (5), the characteristic impedance and propagation constant for the NW can be found to be

(6) (7) where lengths

. By the use of (6) and two different line and , the contact resistance that satisfies condition is found to be

From (13) and (14), the resistance per unit length for the NW section is m

(15)

takes into account resistances of the Pt NW and ground metallization. The resistance of the ground layer is difficult to calculate since its effective dimensions are unknown. The ground layer is made from Au with bulk conductivity of 4.1 10 S/m, which is about 4.4 times the bulk conductivity of Pt ( S/m). Since the conductivity of the Pt NW is smaller , is than its bulk conductivity, the resistance of the Pt NW, can be approximated the dominant contribution to . Thus, and represented as to (16)

(8) where subscripts 1 and 2 denote the line lengths and , respectively. Note that contact impedance can also be obtained matrix contains complex numbers. from (8) since the For the other condition, , the propagation constant in (7) is a complex logarithmic function, which cannot be solved analytically. Instead, the Taylor-series expansion (9)

Formula (16) corresponds to the dc resistance of a 1-m-long round wire with a radius and conductivity [16]. Even though this paper characterizes Pt NWs at high frequencies, (16) is valid because the skin depth of Pt at 10 GHz is about 1.6 m, and it , the curis much larger than the NW’s radius. If rent distribution is almost constant throughout the cross section of the round wire [17]. For the Pt NW with 250-nm diameter at is 0.107, thus, the current distribution 10 GHz, the factor in Pt NWs can be considered uniform. Therefore, the conductivity of the Pt NW in this approach is obtained from (16) as


Fig. 5. Computed R and of Pt NWs from the transmission-line-based aland gorithm. Preset contact resistance and conductivity are R S/m, respectively. :

9 3 2 10

= 100

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Fig. 6. Simulated electric field distribution around Pt NW obtained with HFSS. The gap distance is 4 m. Note that the field distribution in the gap is not that of a TEM mode.

=

(17)

B. Validation Validation of this approach is conducted with the 250-nm-diameter Pt NW by use of circuit [see Fig. 3(b)] and full-wave FEM-based test-beds, as described in Section II. The lengths of the NWs are 4 and 8 m. Validation procedures are: 1) conand tact resistance and conductivity are fixed at S/m (this selection is essentially arbitrary); 2) these values are used to calculate -parameters of the structure by use of either the circuit or full-wave model; and 3) obtained -parameters serve as the input of the algorithm that reand as de-embedded from (8) or (12) and (17). This sults in and are plotted in Fig. 5. As way, the obtained results for seen, the contact resistance obtained from -parameters generated from circuit model agrees very well with the preset value . However, the extracted conductivity has about a 17% error, which is likely caused due to the approximation in (16). On the other hand, the contact resistance and conductivity obtained from the full-wave FEM simulations are very different from their preset values. The reason for discrepancy is the non-TEM mode in the gap, as shown in Fig. 6, which, in the transmission-line model, is assumed to be of a TEM nature. However, electric fields normal to the metal surface in the gap are parallel to the NW for a few micrometers of the NW’s length, as shown in the figure. These electric fields induce on axis currents in the NW so that some amount of the , is included into the contact resistance, NW’s resistance, and not into the resistance per unit length of the NW CPW resulting from this approach line. Therefore, the values of , while resistance per unit in fact corresponds to . length of the NW CPW line corresponds to may be about 2.5 m since The effective length for (2.5 m)/ . When longer NWs are used, e.g.,

Fig. 7. SEM image of Pt NW and its equivalent two-port T-network. Z and Z represent series impedance of the Pt NW. Z is shunt impedance between the Pt NW and ground.

16 and 20 m, increases to about 80 , indicating that . Note that use of longer NWs cannot remove the effect of a higher conductivity can mitigate this effect. For example, if decreases to ten times higher (9.3 10 S/m) is used, one-tenth of the above values. In fact, this phenomenon can happen in conventional transmission lines with a “stepped” discontinuity along the line. However, those lines are typically made from good conductors such as Cu or Au, and their is negligible. In summary, the computational studies for the line-based approach show that the contact resistance can be determined accurately with circuit models, but the obtained conductivity is inaccurate. The full-wave errors are much larger, thus indicating that this approach is not very accurate for lossy devices. Note that the HFSS simulations with preset high conductivities have shown good accuracy. IV. LUMPED-ELEMENT-BASED METHOD In this section, a lumped-element-based approach is developed and theoretically validated through circuit and full-wave FEM simulations. A. Algorithm Description The Pt NW is modeled as an equivalent two-port T network to represent the symmetric nature of the device and appropriate loss mechanism, as shown in Fig. 7. Series impedances and arising from conduction currents are one-half of the NW’s for the length of . Shunt impedance impedance is included due to displacement currents between the NW and ground. For the length of , the series impedances and

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and shunt impedance can be used. The relationships between impedances for the two lengths are as follows:

(18) and (19) The T-network in Fig. 7 is represented by an [14]

matrix

(20)

Fig. 8. Computed R and of Pt NWs from the lumped-element physicalmodel-based algorithm using full-wave FEM and circuit models. Preset contact and S/m, respec: resistance and conductivity are R tively.

= 100

= 9 3 2 10

Since (1)–(4) can also be used for this approach, impedances associated with the model are found from (4) and (20) as (21) and (22) and for the NW with length can be obtained the same way with (22) and (21), respectively. The contact resistance can be determined by substituting (22) for the two lengths and (with subscript 2 instead of 1 for ) into (18) as (23) Note that contact impedance (not only resistance) can also be found from (23) because the matrix is complex, similar or to (8) and (12). Since NW’s resistance is a real part of , the conductivity of the Pt NW can be determined with the formula for the dc resistance of a round wire (16) as or The factor of 1/2 is used due to the fact that impedance of the NW with a half length of

of the CPW taper, the obtained values of and include the taper resistance, which is 1 . Note that the obtained and show slight dispersion of less than 2% for frequencies above 20 GHz. This is likely due to several reasons; the distributed effects of the tapered lines, which are part of the device as verified by the results obtained after the tapers, are de-embedded before the algorithm is applied (see Fig. 8) and/or the not investigated yet influence of the applied calibration procedure for extreme impedances at higher frequencies. As seen, once the taper is reand are consistent and equal moved from the device both to their preset values. In general, this approach, for investigated devices, is more accurate than the approach discussed in Section III. Therefore, the lumped-element physics-based algorithm is applied to the measurements of the fabricated Pt NW test sets and results are discussed below. Even though the lumped-element approach may seem to be intuitively correct if one uses only the wavelength to device size relation, nevertheless it is necessary to examine the potential distributed effects that may be important for other types of NW-based devices.

(24) (or (or ).

) is the

B. Validation Validation is carried out by using the circuit in Fig. 3(c) and full-wave simulations. The computational setup and validation methodology for the lumped-element-based approach are the same as in Section III-B. Note that the contact resistance and NW’s conductivity are set at and S/m. Extracted contact resistance and conductivity of the Pt NW from the lumped-element physics model-based algorithm are shown in Fig. 8. and values are well correlated with their The obtained preset values for both full-wave and circuit simulations even when the tapers are not de-embedded from the algorithm. Since the reference planes for the -parameters are placed at the start

V. EXPERIMENTAL RESULTS To experimentally validate the lumped-element-based algorithm, the devices with Au bridges are first measured, and the measured -parameters are analyzed with the lumped-element algorithm (in MATLAB). Since the CPW signal lines are made from a uniform Au layer, the contact impedance is estimated . In addition, one expects from the de-embedto be ding procedure to get the conductivity of the Au bridges close to the bulk value of 4.1 10 S/m. Three sets of devices with Au bridges and two sets of empty devices with the 4- and 8- m gap distances are measured, resulting in a total of 36 combinaand tions. Measured mean values and standard deviations of for devices with 4- and 8- m-long Au bridges are shown in is smaller than 1 . The nonzero Fig. 9. As seen, the obtained is attributed to the resistance of the tapered CPW lines. The de-embedded conductivities for the Au bridge at around 3 GHz


Fig. 9. Measured mean values and standard deviations for R and of Au bridge devices. Values are obtained with a lumped-element algorithm. 36 different sets of the devices are used to obtain the statistical error bars.

TABLE I MEASURED LENGTHS OF THE Pt NWs

are close to the expected value of 4.1 10 S/m. The differences may be due to calibration. The results (specifically, standard deviations) at higher frequencies ( 20 GHz) are contaminated by the measurement noise, but overall, the extracted values in the measured frequency range document the feasibility of the developed approach giving the confidence for the extraction of these parameters for an arbitrary NW. Devices with Pt NWs are measured and analyzed next. Ten Pt NWs are deposited in the CPWs with 4- and 8- m gaps. The widths of the deposited Pt NWs are measured to be about 300 nm. Careful measurement of NW lengths is critical since is strongly dependent on the two lengths [see the extracted (23)]. Even though the NW and signal lines are overlapping for about 3 m, NW lengths do not include this overlapping distance. Since the NWs are highly resistive, this overlapping distance is shunted by Au signal lines. Measured lengths are listed in Table I. Measured mean values and standard deviations for de-emand for Pt NWs under test are shown in Fig. 10. bedded The statistical data are obtained by processing 100 combinations of five devices with Pt NWs and the two empty devices for each is measured to be about 50 , length (4 and 8 m). As seen, . Note that the obtained is lower and is about than the reported values [5]–[7]. The difference is attributed to depends sensitively on fabrication methods. The the fact that cm, which is close to the measured resistivity is about 827 cm, of [6]. The low conductivity is due results, 860–3078 to effects of contaminants and the NW’s small size. Elemental analysis shows that the Pt NWs in this study have approximately 60% Pt, 34% C, and 6% Ga. In [6], Pt NWs were fabricated with 31% Pt, 10% C, and 50% Ga, in reasonable agreement

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Fig. 10. Measured mean values and standard deviations for R and of 300-nm-diameter Pt NWs. Results are obtained with lumped-element-based algorithm. 100 different sets of the devices are used to obtain this statistics.

with the obtained results in this study, since the Pt NWs in [6] have fewer Pt atoms, and higher resistivity is thus expected. The conductivity is computed assuming a circular 300-nm-diameter cross section of the NWs. Based on the results in Fig. 10, the total resistances of the NWs for 4- and 8- m lengths including two contact resistances are calculated to be 568 and 1036 , respectively. An upturn observed at low frequencies (less than 2.5 GHz) is due to poorly calibrated -parameter measurements in the frequency range. It is expected that errors in this range can be reduced by recalibration with longer calibration standards. VI. CONCLUSION Comprehensive methodology for simultaneous characterization of contact resistance and conductivity of individual Pt NWs over a broadband frequency range have been discussed. In order to separate the contact resistance from NW’s properties, two algorithms using transmission-line and lumped-element models for Pt NWs are developed. Both algorithms rely on measurements of two NWs with different lengths. It is shown that an algorithm based on transmission-line models is not suitable for highly resistive devices with nonzero contact resistance. It is seen that the lumped-element algorithm provides accurate results for both contact resistance and conductivity. This algorithm is thoroughly validated with full-wave and circuit simulations, as well as measurements. Measurements of several sets of devices with 300-nm-diameter Pt NWs have obtained contact . resistance of about 50 and conductivity of about The proposed metrology is suitable for extension to a variety of NW structures. REFERENCES [1] C. Durkan, Current at the Nanoscale: An Introduction to Nanoelectronics. London, U.K.: Imperial College Press, 2007. [2] P. A. Smith, C. D. Nordquist, T. N. Jackson, T. S. Mayer, B. R. Martin, J. Mbindyo, and T. E. Mallouk, “Electric-field assisted assembly and alignment of metallic nanowires,” Appl. Phys. Lett., vol. 77, pp. 1399–1401, 2000. [3] M. E. T. Molares, E. M. Hohberger, C. Schaeflein, R. H. Blick, R. Neumann, and C. Trautmann, “Electrical characterization of electrochemically grown single copper nanowires,” Appl. Phys. Lett., vol. 82, pp. 2139–2141, 2003.

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[4] J.-F. Lin, J. P. Bird, L. Rotkina, and P. A. Bennett, “Classical and quantum transport in focused-ion-beam-deposited Pt nanointerconnects,” Appl. Phys. Lett., vol. 82, pp. 802–804, 2003. [5] G. D. Marzi, D. Iacopino, A. J. Quinn, and G. Redmond, “Probing intrinsic transport properties of single metal nanowires: Direct-write contact formation using a focused ion beam,” J. Appl. Phys., vol. 96, pp. 3458–3462, 2004. [6] L. Penate-Quesada, J. Mitra, and P. Dawson, “Non-linear electronic transport in Pt nanowires deposited by focused ion beam,” Nanotechnology, vol. 18, pp. 215203-1–215203-5, 2007. [7] T. Schwamb, B. R. Burg, N. C. Schirmer, and D. Poulikakos, “On the effect of the electrical contact resistance in nanodevices,” Appl. Phys. Lett., vol. 92, pp. 243106-1–243106-3, 2008. [8] K. Kim, T. M. Wallis, P. Rice, C. J. Chiang, A. Imtiaz, P. Kabos, and D. S. Filipovic, “A framework for broadband characterization of individual nanowires,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 3, pp. 178–180, Mar. 2010. [9] K. Kim, T. M. Wallis, P. Rice, C. J. Chiang, A. Imtiaz, P. Kabos, and D. S. Filipovic, “Modeling and metrology of metallic nanowires with application to microwave interconnects,” in IEEE MTT-S Int. Microw. Symp. Dig., 2010, pp. 1292–1295. [10] K. Kim, P. Rice, T. M. Wallis, S.-H. Lim, D. Gu, A. Imtiaz, P. Kabos, and D. S. Filipovic, “Contactless approaches for RF characterization of metallic nanowires,” in Eur Microw. Conf., 2010, pp. 691–694. [11] R. B. Marks, “A multiline method of network analyzer calibration,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 7, pp. 1205–1215, Aug. 1991. [12] P. Kabos, H. C. Reader, U. Arz, and D. F. Williams, “Calibrated waveform measurement with high-impedance probes,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 2, pp. 530–535, Feb. 2003. [13] S. C. Jun, X. M. H. Huang, S. Moon, H. J. Kim, J. Hone, Y. W. Jin, and J. M. Kim, “Passive electrical properties of multi-walled carbon nanotubes up to 0.1 THz,” New J. Phys., vol. 9, pp. 265-1–265-9, 2007. [14] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005. [15] P. L. D. Peres, C. R. de Souza, and I. S. Bonatti, “ABCD matrix: A unique tool for linear two-wire transmission line modelling,” Int. J. Elect. Eng. Educ., vol. 40, pp. 220–229, 2003. [16] D. K. Cheng, Field and Wave Electromagnetics, 2nd ed. Reading, MA: Addison-Wesley, 1989.

[17] R. E. Matick, Transmission Lines and Communication Networks: An Introduction to Transmission Lines, High-Frequency and High-Speed Pulse Characteristics and Applications. Piscataway, NJ: IEEE Press, 1995. Kichul Kim (S’07–M’10), photograph and biography not available at time of publication.

T. Mitch Wallis, photograph and biography not available at time of publication.

Paul Rice, photograph and biography not available at time of publication.

Dazhen Gu, photograph and biography not available at time of publication.

Sang-Hyun Lim, photograph and biography not available at time of publication.

Atif Imtiaz, photograph and biography not available at time of publication.

Pavel Kabos (SM’93–F’05), photograph and biography not available at time of publication.

Dejan S. Filipovic (S’99–M’02–SM’08), photograph and biography not available at time of publication.