pubs.acs.org/crystal Published on Web 04/26/2010 r 2010 American Chemical Society

DOI: 10.1021/cg1003808

2010, Vol. 102780–2784

Copper Better than Silver: Electrical Resistivity of the Grain-Free

Single-Crystal Copper Wire

Yong Chan Cho,† Seunghun Lee,‡ Muhammad Ajmal,† Won-Kyung Kim,‡

Chae Ryong Cho,† Se-Young Jeong,*,‡ Jeung Hun Park,§ Sang Eon Park,^

Sungkyun Park, ) Hyuk-Kyu Pak, ) and Hyoung Chan Kimz

†Department of Nano Fusion Technology, Pusan National University, Miryang, Korea, ‡Department ofCogno-Mechatronics Engineering, Pusan National University, Miryang, Korea, §Department ofMaterials Science & Engineering, University of California, Los Angeles, California 90095-1595,^MCLAB Company Ltd., Pusan National University, Miryang, Korea, )Department of Physics, PusanNational University, Busan, Korea, and zDivision of R&D, National Fusion Research Institute,Daejon, Korea

Received March 22, 2010

ABSTRACT: Using a single-crystal wire fabricated through the crystal growth process, the contribution of grain boundaries(GBs) to electrical resistivity was investigated in copper.We developed a novel wire fabrication process that preserved the grain-free structure of single-crystal copper (SCC) grown by the Czochralski method. The resistivity of grain-free SCC showed areduction of 9% compared to the international annealed copper standard (IACS) resistivity, with the resulting value smallerthan that of silver.We also found that theGBs strongly influenced the resistivity above 70K, but hardly contributed below 70K,unlike the impurities. Insights into the GB effects could contribute to our understanding of conducting phenomena and thedevelopment of nanoscale analytical models.

Introduction

Copper (Cu) is the most widely used electrically andthermally conducting material in the world, as it is cheapand second only to silver (Ag) in its ability to conduct electri-city. The resistivity (F) of bulk copper has been reduced byabout 3% during the last 100 years since the resistivity ofcopper was first officially recorded.However, the size effect, asize-related nanoscale phenomenon, has become a key issue innanoscience and technology because of its application toadvanced technology. As the lateral dimension of conductorsapproaches the nanoscale regime, larger electrical resistivitiescompared to those of the bulk material are caused by thecontributions of surface and grain boundary (GB) scatteringto the total electric resistivity. For example, the resistivityof copper film depends on its thickness as the dimensionsapproach the electron mean free path.1,2 Single-crystal bis-muth thin films have been reported to exhibit a larger magne-toresistance effect compared to sputtered polycrystallinebismuth due to a reduction in the number of GBs.3

The size effect was initially thought to be caused by thescattering of electrons from the surface (Fuchs-Sondheimeranalytical model) andGBs (Mayadas and Shatzkes analyticalmodel) in thin-metal nanostructured film samples.4-6 Recen-tly, the electrical resistivity in nanoscale materials was report-edly aggravated by increasing the number of GBs, with aparticular focus on electron scattering mechanisms.1,7-11

However, compared to the electrical resistivity of the puremetal and mechanical properties, such as the effect of GBdynamics on plastic deformation in crystalline materials,12-19

wire fabrication from bulk single crystals, and the contribu-tions of crystallization to the resistivity of wire, have not beenintensively studied.

In previous reports, the room temperature resistivity of acopper single-crystal whisker was reported as 1.59 μΩ 3 cm((5%).20 The whisker had a uniform cross section 10-50 μm in diameter and a minimum length of about 15 mm.The measured resistivity was smaller than that of standardhigh-purity copper. Benard et al. reported that the experi-mental surface resistance and wave attenuation coefficientfor single-crystal copper were reduced from those for high-purity copper.21 To clarify the contributions of GBs, theirprecise characterization should be performed at the macro-scopic scale, eliminating the contributions of thickness-dependent effects, which can then be used as material-constant parameters in an analytical model. However, it isvery difficult to obtain grain-free conducting metal wire byconventional fabrication and thin-film deposition becausenumerous GBs will be inevitably present. The only wayto obtain a grain-free sample is to crystallize the entiresample.

Here we developed a novel wire fabrication process thatretains the grain-free structure from single-crystal copper(SCC) grown by the Czochralskimethod.Using single-crystalwire fabricated through a crystal growth process, we reportedthat the resistivity of pure SCCwas 9% lower than the repor-ted value of copper throughout the entire range of tempera-tures above 100 K, which is less than the resistivity of Ag, anddepends strongly on the amount of GBs even in macroscopicwires. We also showed that the GBs strongly influenced theresistivity above 70 K, but hardly contributed below 70 K,unlike the impurities. Even though GBs are a kind of defect,like impurities, they show quite different behavior at low andhigh temperatures.We also defined the temperatureTI, wherethe dominant factor in the resistivity changed. The insightgained from measuring grain-free SCC will be invaluable forinterpreting experimental results and developing analyticalmodels.

*Towhom correspondence should be addressed. E-mail: syjeong@pusan.ac.kr.

Article Crystal Growth & Design, Vol. 10, No. 6, 2010 2781

Experimental Section

Figure 1a shows the schematic diagram of the crystal growthsystem. Copper beads with 4 N purity (Sigma-Aldrich) were used asstarting material for crystal growth. The SCC was grown by theCzochralski method in a graphite crucible. In order to avoid theoxidation of the graphite crucible and copper, the vacuum chamberwas filled with Ar gas of 5 N purity. The crucible and copper wereheated through the RF induction method with an RF generator(40 kHz, 20 kW). The pulling speed was 3 mm/h, and the rotationspeed was 10 rpm.

The grain-free SCCwireswere fabricated fromabulk single crystalby a wire electrical discharge machine (wire-EDM, MitsubishiFA10S, Japan). This uses the rapid series of repetitive electricaldischarges to remove small amounts of material, with very thin wireserving as the electrode.

The crystallinity of the SCC wire was characterized by high-resolutionX-raydiffraction (XRD,PANalyticalX’pertPROMRD).The morphology of the surface etched by 50% diluted HNO3 wasobserved by the scanning electron microscope (SEM, Hitachi,S-4700). The chemical binding states of the SCC wire and oxygen-free copper (OFC)wire of purity 4Nwere investigated and comparedby X-ray photoelectron spectroscopy (XPS, ESCALAB 250). Toinvestigate the change of chemical composition at the surface of theSCCwire afterwire-EDM,wemeasured the depth profile with a glowdischarge spectrometer (GDS, JobinYvon 10000RF). The resistivitywasmeasured in the temperature range from300 down to 4Kusing a4-He cryostat (PPMS Quantum Design, USA). Electrical contactswere made using pure gold wires 0.0508 mm in diameter and silverepoxy on the sample. For resistivity measurements, we used the four-probe method and the current-reversal method (delta mode). Gene-rally, the four-probemethod can eliminate low-level voltage errors byremoving the contact resistance using two extra probes between thecurrent contacts. To minimize the unwanted additional voltages dueto the thermoelectric effect, wemeasured the voltage with the currentin one direction, and then repeated the measurement with the rever-sed current (delta mode). This current-reversal method gave reliableresults by removing the temperature difference between the tworeadings. In the resistivity measurements, we used a nanovoltmeter(Kiethley 2182A) for measurement of the voltage difference and acurrent source (Kiethley 2425). The resolution of the nanovoltmeterwas 1 nV in ourmeasurement.We optimized theDCcurrent between10 and 80mA, depending on the temperature range. The accuracy ofthe current source was 0.1% in our measurement range. Therefore,the resultant standard deviations by equipment (nanovoltmeter andcurrent source) corresponded to 0.1%of the average resistivity valueat room temperature. In the experiment, to reduce errors due tosample size uncertainty, the resistivitymeasurements were performedon OFC and SCC samples fabricated by exactly the same procedureusing wire-EDM, with a resultant cross-section deviation of less than0.1%. We also repeatedly measured the sample dimension using a

micrometer with a(1 μm resolution limit at room temperature. Theresistivity deviations due to the uncertainty of the sample dimensiondid not exceed 0.1%of resistivity at room temperature. Themeasure-ment was carried out after temperature was stabilized by a currentflip. No noticeable differences were observed between cooling andwarming measurements.

Results and Discussion

Figure 1b shows the SCCgrownby theCzochralskimethodin Ar atmosphere. The orientation of the seed crystal wasdetermined by X-ray and neutron scattering experiments(HANARO, Korea Atomic Energy and Research Institute).The grown crystal diameter and body length were 80 and200 mm, respectively.

Figure 2a,b shows the XRD patterns of the SCC diskperpendicular to the growth direction and a polycrystal-line OFC, respectively. The X-ray pattern of the SCCshowed only two peaks corresponding to (200) and (400)planes, respectively. As shown in the inset of Figure 2,the etched surface had a distinct four-fold symmetry.However, the XRD pattern of the OFC shows that theOFC was conventional polycrystalline with no distinctsymmetry to the etched surface. The average grain size ofthe OFC was about 200 nm in SEM observation of theetched surface.

Figure 2c shows the Cu 2p peaks of SCC and OFC in XPSspectra. As shown in Figure 2c, the chemical binding states ofCu in OFC and SCC were nearly consistent. Only the Cu 2ppeaks of the SCC were slightly narrower than those of thepolycrystalline OFC.

Figure 3a,b shows a schematic of thewire-EDMprocess forfabrication of the SCC disk and wire. In standard cutting

Figure 1. (a) Schematic of the crystal growth system. (b) Photo-graph of the grown copper single crystal.

Figure 2. XRD patterns of (a) SCC and (b) OFC (the insets showthe SEM image for etched surfaces of SCC and OFC, respectively.)(c) Cu 2p peaks of SCC and OFC in XPS spectra.

2782 Crystal Growth & Design, Vol. 10, No. 6, 2010 Cho et al.

methods, including diamond saw and mechanical wirecutting, the crystal structure of the cut surface is affecteddue to the excellent ductility and malleability of copper.Mechanical stress during conventional polishing and cuttingoften introduced additional peaks in the XRDmeasurementsof SCC. As shown in Figure 3a,b, the wire-EDMused a rapidseries of electrical discharges to cut certain areas of the metal,with very thin wire serving as the electrode. The cutting wire,which did not directly touch the metal sample, was slowly fedthrough the material, and the electrical discharges cut thematerial. We found that the wire-EDM method was suitablefor fabricating metallic single-crystal wire. Figure 3c,d showsthe fabricated SCC disk and wire. The SCC wire was fabri-cated from the (200) SCC disk through wire-EDM cutting. Itwas possible to prepare SCC wafers of arbitrary thickness.From SCC disks of 1 and 2 mm thickness, SCC wires werefabricated in a spiral fashion.

The fabricated wire had (200) orientation along the upsidedirection. After the wire-EDM cutting, the rough and coarsesurfaces with depths of about 0.2 μm were easily polishedmechanically.

The single-crystal wires, 2 mmwide and 0.5 mm thick, wereobtained by straightening the spirally processed disks. TheXRD patterns obtained from the straightened wires reflectedthat the wires kept the single-crystal structure and that thestrain effect during the straightening process was not serious.As shown in Figure 4, peaks corresponding to the (200) planeperiodically appeared along the SCC wire due to the spiralcutting. Generally, in polycrystalline samples, the crystalorientations adjacent to the boundary are supposed to bedifferent. However, in SCC, the entire sample would have thesame orientation.

Figure 5 shows the result of the GDS depth profile of theSCC wire processed by wire-EDM. At the surface, impuritiessuch as P, Fe, Mg, Co, Ni, and Cr were observed. Thiscontamination mainly came from the material used for wirecutting during wire-EDM cutting. The depth profile showedthat the contaminations abruptly decreased underneath the

surface. On the basis of the sputtering time, the contaminatedlayer thickness was estimated to be about 20 nm. Table 1shows atomic percent of impurities and copper at severaldepths (10, 20, 200 nm, and 2 μm). As shown Table 1, theSCC wire purity was consistently 99.99% ((0.005%) below20 nm.

Figure 6a,b shows the temperature dependence of theresistivity of the OFC and SCC wires compared with thereported results for copper and silver.19,22,23 For theSCC wires, we performed 12 measurements (four measure-ments between 4 and 300 K and eight between 90 and300 K). For the OFC samples, we performed 11 measure-ments (two between 4 and 300 K and nine between 90and 300 K). The obtained resistivities of OFC and SCCwere 1.67 ( 0.01 and 1.52 ( 0.006 μΩ 3 cm, respectively, at293 K. The standard deviations of OFC and SCC wereapproximately (0.6% (OFC) and (0.4% (SCC) of resis-tivity at 293 K.

According to Matthiessen’s rule, the resistivity of thebulk metal was the sum of contributions from the tempera-ture-dependent thermal vibrations of the lattice (i.e., pho-non scattering) and the lattice defects (i.e., vacancies,interstitial atoms, dislocations, and GBs), which wereindependent of temperature.2,12 For nonmagnetic ele-mental metals, the temperature-dependent resistivity,Fel-ph(T) originated from electron-phonon interactionsand followed a power-law function of temperature, the

Figure 3. (a) Fabrication of SCC disks by wire-EDM. (b) Fabrica-tion process for SCC wire in a spiral fashion through wire-EDMcutting. (c) Fabricated SCC disk and SCC wire. (d) StraightenedSCC wire.

Figure 4. Periodic XRD patterns of the SCC wire.

Figure 5. Result of the GDS depth profile for the SCC wireprocessed by wire-EDM.

Article Crystal Growth & Design, Vol. 10, No. 6, 2010 2783

Bloch-Gr€uneisen (BG) formula.24,25

Fel- phðTÞ ¼ Rel- phT

ΘR

� �5 Z ΘR=T

0

x5

ðex - 1Þð1- e- xÞ dx

ð1ÞIn eq 1, ΘR is the Debye temperature and x is the variablechanging from 0 toΘR/T in the Bloch-Gr€uneisen formula.The constant Rel-ph is proportional to λtrωD/ωp

2, where λtris the electron-phonon coupling constant and ωD and ωp

are the Debye and plasma frequencies, respectively.25 Bidet al. reported that the Bloch-Gr€uneisen formula was stillapplicable to the resistivity of nanowires with diametersfrom 15 to 200 nm.25 The resistivities of the OFC (FOFC)and SCC (FSCC) well agreed with the Bloch-Gr€uneisenformula from room temperature to about 70 K.

In our results, the FOFC was consistent with the standardvalues (1.67 μΩ 3 cm) at 293 K, corresponding to 103% Inter-national Annealed Copper Standard (IACS) of conducti-vity.19,22 The ICAS reflects a material in which the resistanceof a wire 1 m in length and 1 g in weight is 0.15328Ω at 20 �C.Thus, 100% IACS resistivity was defined as 1.7241 μΩ 3 cm.However, the FSCC was clearly less than FOFC throughout therange of measured temperatures. The average value of FSCCobtained from the repeated measurements using 12 differentsamples was about ∼1.52 μΩ 3 cm (corresponding to ∼113%IACS of conductivity) at 293 K, which was about ∼91% ofFOFC, and even less than that of Ag (∼1.59 μΩ 3 cm). There-fore, the FSCC showed a remarkable improvement in the con-ductivity of the novel metal copper wire.

In addition, Rel-ph, a crucial parameter for the temperaturedependence of resistivity, could be estimated by fitting theBloch-Gr€uneisen to the data in Figure 6a.25 The Rel-ph valueobtained for SCCwas∼9% less than the value forOFC;RR isdefined as Rel-ph/FΘR

, where FΘRis F at the Debye tempera-

ture. Its value is 4.225 for copper.25 The values ofRR obtainedfor both OFC and SCC wires in this study were the same(4.226), in close agreement with the reported value. It was

reported that this value for copper did not change in coppernanowires.25

Figure 6c shows the resistivity reduction rates of OFC(ΔFOFC/FCu(standard)) and SCC (ΔFSCC/FCu(standard)) comparedto the resistivity of standardCu(FCu(standard)), whereΔFOFC=FCu(standard) - FOFC and ΔFSCC= FCu(standard) - FSCC. Theresistivity of SCC was more reduced than that of OFC. Thefractional change of resistivity, ΔFGB/FOFC, where ΔFGB =FOFC-FSCC, which ideally corresponds to the contribution ofGBs to the resistivity, was constant at about∼9% in the rangebetween room temperature and 100K (Figure 6c). Thismeansthat the electron scattering due to the GBs proportionallydecreased with the amount of phonons with the temperature.Consequently, eliminating the GBs could alter the resistivitysignificantly because the electron scattering due to the GBs isdifferent from the electron-regular phonon scattering in asingle crystal. Below 70 K, both FSCC and FOFC with the samegrade of purity were similar, but Cu(6N) and Cu(7N) showedmuch lower values than FSCC (Figure 6b). Hence, below 70K,where the phonons were strongly suppressed, the amount ofimpurities was the main determinant of the resistivity, as thereduction in the number of GBs did not contribute to thereduction in resistivity. Therefore, the GBs in OFC addedto the resistivity only when they were connected with thephonons.

Figure 7 shows the temperature dependence of the tem-perature coefficients of resistivity (TCR) in SCC and OFCwires. TCR corresponds to (1/F) 3 dF/dT, whichwas calculatedfrom the temperature derivative of the measured resistivity.For both SCC and OFC, TCR had the same value (0.0039K-1) at room temperature, which agreed very closely with thestandard value for copper. In addition, the TCR showed ananomaly (TI) at about 45K. The higher purity samples startedto deviate from the Bloch-Gr€uneisen formula at lowertemperatures. The temperatures TI were obtained for Cu(6N)at around 30 K and for Cu(7N) at around 20 K, in closeagreement with Figure 6b.23 Hence, TI was assumed to

Table 1. Atomic Percent of Impurities and Copper at Several Depths

depth Cr(%) Si(%) S(%) Ag(%) Ni(%) Co(%) Mg(%) Fe(%) P(%) Cu(%)

10 nm 1.2013 1.7052 1.0293 0.2014 0.8201 0.8193 2.2708 0.9469 1.2989 89.706820 nm 0.0016 0.0011 0.0014 0.0016 0.0013 0.0010 0.0024 0.0019 0.0015 99.9862200 nm 0.0009 0.0007 0.0006 0.0013 0.0011 0.0009 0.0011 0.0017 0.0004 99.99132 μm 0.0007 0.0006 0.0005 0.0012 0.0006 0.0007 0.0008 0.0016 0.0002 99.9931

Figure 6. Temperature dependences of FOFC and FSCC (a) from 100 to 300 K and (b) from 5 to 100 K; FCu(standard) and FAg(standard)represent the reported value of Cu and Ag, respectively.19 The solid lines show the resistivities calculated for OFC and SCC from theBloch-Gr€uneisen (BG) formula. The dotted lines represent the resistivities of copper sampleswith 4N (FCu(4N)), 6N (FCu(6N)), and 7N (FCu(7N))purity, as given in ref 23. (c) Resistivity reduction rates of OFC and SCC compared to FCu(standard).

2784 Crystal Growth & Design, Vol. 10, No. 6, 2010 Cho et al.

indicate a transition temperature, where the main contributorto the resistivity changed from electron-phonon couplingin the copper lattice to impurities as the temperaturedecreased.

Conclusion

To summarize, we showed that the resistivity of copper canbe improved below standard values found in the literature byapplying a well-known crystallization process. The obtainedresistivities of OFC and SCC were 1.67 ( 0.01 and 1.52 (0.006 μΩ 3 cm, respectively, at 293 K. For the SCC wire, theconductivity was found to be nearly 113% IACS. This ishigher than that found previously in all kinds of novel metals,including Ag (105-108.4% IACS). The ∼9% reduction inresistivitywas seen at temperatures above 100K, agreeingwellwith theBloch-Gr€uneisen formula.Consequently, ourobser-vations suggested that the bulk resistivity of copper has beenoverestimated by∼9% due to the contributions of GBs(ΔFGB) in pure copper at temperatures above ∼100 K. Inaddition, GBs are no longer important at temperatures below70 K, where the contribution of impurities becomes signifi-cant. The anomaly TI at the TCR seemed to indicate atransition of the main contributor to the resistivity fromelectron-phonon coupling to electron impurity scattering asthe temperature decreased.For the further verification ofTI inmetal crystals, further investigations should be carried out.

This study highlights a fundamental phenomenon in one ofthe most widely used materials in the world. The understand-ing gained here on the origin of the resistivity should helpreduce electric signal losses and distortion at both micro- andnanoscales in situations when the GBs and surface contributesignificantly to the resistivity.

Acknowledgment. This research was supported by theWorld Class University program through the NationalResearch Foundation of Korea funded by the Ministry ofEducation, Science andTechnology, SouthKorea (GrantNo.R31-2008-000-20004-0).

References

(1) Rossnagel, S.M.; Kuan, T. S. J. Vac. Sci. Technol., B 2004, 22, 240.(2) Plombon, J. J.; Anddideh, E.; Dubin, V. M.; Maiz, J. Appl. Phys.

Lett. 2006, 89, 113124.(3) Yang, F.Y.; Liu,K.;Hong,K.;Reich,D.H.; Searson, P.C.;Chien,

C. L. Science 1999, 284, 1335.(4) Fuchs, K. Proc. Cambridge Philos. Soc. 1938, 34, 100.(5) Sondheimer, E. H. Adv. Phys. 1952, 1, 1.(6) Mayadas, F.; Shatzkes, M. Phys. Rev. B 1970, 1, 1382.(7) Chiu, P.; Shih, I. Nanotechnology 2004, 15, 1489.(8) Wu, W.; Brongersma, S. H.; Hove, M. V.; Maex, K. App. Phys.

Lett. 2004, 84, 2838.(9) Steinh€ogl, W.; Schindler, G.; Steinlesberger, G.; Traving, M.;

Engelhardt, M. J. Appl. Phys. 2005, 97, 023706.(10) Camacho, J. M.; Oliva, A. I. Thin Solid Films 2006, 515, 1881.(11) Steinh€ogl, W.; Schindler, G.; Steinlesberger, G.; Engelhardt, M.

Phys. Rev. B 2002, 66, 075414.(12) Lu, L.; Shen, Y.; Chen, X.; Qian, L.; Lu, K. Science 2004, 304, 422.(13) Zhao, Y. H.; Bingert, J. F.; Liao, X. Z.; Cui, B. Z.; Han, K.;

Sergueeva, A. V.;Mukherjee, A. K.; Valiev, R. Z.; Langdon, T. G.;Zhu, Y. T. Adv. Mater. 2006, 18, 2949.

(14) Swygenhoven, H. V. Science 2002, 296, 66.(15) Huang, X.; Hansen, N.; Tsuji, N. Science 2006, 312, 249.(16) Shan, Z.; Stach, E. A.; Wiezorek, J. M. K.; Knapp, J. A.;

Follstaedt, D. M.; Mao, S. X. Science 2004, 305, 654.(17) Zhou, S. J.; Preston, D. L.; Lomdahl, P. S.; Beazley, D. M. Science

1998, 279, 1525.(18) Bringa, E. M.; Caro, A.; Wang, Y.; Victoria, M.; McNaney, J. M.;

Remington, B. A.; Smith, R. F.; Torralva, B. R.; Swygenhoven,H. V. Science 2005, 309, 1838.

(19) Matula, R. A. J. Phys. Chem. Ref. Data 1979, 8, 1147.(20) Mende, H. H.; Thummes, G. Appl. Phys. 1975, 6, 93.(21) Benard, J.;Minyawi,N.H.E.;Viet,N.T.Rev.Phys.Appl.1978,13, 483.(22) Lide,D.R.CRCHandbook of Chemistry andPhysics, 81st ed.; CRC

Press: Boca Raton, FL, 2000-2001; pp 12-45.(23) Nakane, H.; Watanabe, T.; Nagata, C.; Fujiwara, S.; Yoshizawa,

S. IEEE Trans. Inst. Meas. 1992, 41, 107.(24) Ziman, J.M.Electrons and Phonons; Clarendon Press: Oxford, 1960.(25) Bid, A.; Bora, A.; Raychaudhuri, A. K. Phys. Rev. B 2006, 74,

035426.

Figure 7. Temperature dependence of TCR. The dotted line ofTCR is included as a visual guide.