DOI: 10.1021/cg1003808
Copper Better than Silver: Electrical Resistivity of the Grain-Free Single-Crystal Copper Wire
2010, Vol. 10 2780–2784
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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 of Cogno-Mechatronics Engineering, Pusan National University, Miryang, Korea, §Department of Materials Science & Engineering, University of California, Los Angeles, California 90095-1595, ^ MCLAB Company Ltd., Pusan National University, Miryang, Korea, Department of Physics, Pusan National 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 grainfree structure of single-crystal copper (SCC) grown by the Czochralski method. The resistivity of grain-free SCC showed a reduction of 9% compared to the international annealed copper standard (IACS) resistivity, with the resulting value smaller than that of silver. We also found that the GBs strongly influenced the resistivity above 70 K, but hardly contributed below 70 K, unlike the impurities. Insights into the GB effects could contribute to our understanding of conducting phenomena and the development of nanoscale analytical models.
Introduction Copper (Cu) is the most widely used electrically and thermally conducting material in the world, as it is cheap and second only to silver (Ag) in its ability to conduct electricity. The resistivity (F) of bulk copper has been reduced by about 3% during the last 100 years since the resistivity of copper was first officially recorded. However, the size effect, a size-related nanoscale phenomenon, has become a key issue in nanoscience and technology because of its application to advanced technology. As the lateral dimension of conductors approaches the nanoscale regime, larger electrical resistivities compared to those of the bulk material are caused by the contributions of surface and grain boundary (GB) scattering to the total electric resistivity. For example, the resistivity of copper film depends on its thickness as the dimensions approach the electron mean free path.1,2 Single-crystal bismuth thin films have been reported to exhibit a larger magnetoresistance effect compared to sputtered polycrystalline bismuth due to a reduction in the number of GBs.3 The size effect was initially thought to be caused by the scattering of electrons from the surface (Fuchs-Sondheimer analytical model) and GBs (Mayadas and Shatzkes analytical model) in thin-metal nanostructured film samples.4-6 Recently, the electrical resistivity in nanoscale materials was reportedly aggravated by increasing the number of GBs, with a particular focus on electron scattering mechanisms.1,7-11 However, compared to the electrical resistivity of the pure metal and mechanical properties, such as the effect of GB dynamics on plastic deformation in crystalline materials,12-19 wire fabrication from bulk single crystals, and the contributions of crystallization to the resistivity of wire, have not been intensively studied. *To whom correspondence should be addressed. E-mail: syjeong@pusan. ac.kr. pubs.acs.org/crystal
Published on Web 04/26/2010
In previous reports, the room temperature resistivity of a copper single-crystal whisker was reported as 1.59 μΩ 3 cm ((5%).20 The whisker had a uniform cross section 1050 μm in diameter and a minimum length of about 15 mm. The measured resistivity was smaller than that of standard high-purity copper. Benard et al. reported that the experimental surface resistance and wave attenuation coefficient for single-crystal copper were reduced from those for highpurity copper.21 To clarify the contributions of GBs, their precise characterization should be performed at the macroscopic scale, eliminating the contributions of thicknessdependent effects, which can then be used as materialconstant parameters in an analytical model. However, it is very difficult to obtain grain-free conducting metal wire by conventional fabrication and thin-film deposition because numerous GBs will be inevitably present. The only way to obtain a grain-free sample is to crystallize the entire sample. Here we developed a novel wire fabrication process that retains the grain-free structure from single-crystal copper (SCC) grown by the Czochralski method. Using single-crystal wire fabricated through a crystal growth process, we reported that the resistivity of pure SCC was 9% lower than the reported value of copper throughout the entire range of temperatures above 100 K, which is less than the resistivity of Ag, and depends strongly on the amount of GBs even in macroscopic wires. We also showed that the GBs strongly influenced the resistivity 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 and high temperatures. We also defined the temperature TI, where the dominant factor in the resistivity changed. The insight gained from measuring grain-free SCC will be invaluable for interpreting experimental results and developing analytical models. r 2010 American Chemical Society
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Figure 1. (a) Schematic of the crystal growth system. (b) Photograph of the grown copper single crystal.
Experimental Section Figure 1a shows the schematic diagram of the crystal growth system. Copper beads with 4 N purity (Sigma-Aldrich) were used as starting material for crystal growth. The SCC was grown by the Czochralski method in a graphite crucible. In order to avoid the oxidation of the graphite crucible and copper, the vacuum chamber was filled with Ar gas of 5 N purity. The crucible and copper were heated through the RF induction method with an RF generator (40 kHz, 20 kW). The pulling speed was 3 mm/h, and the rotation speed was 10 rpm. The grain-free SCC wires were fabricated from a bulk single crystal by a wire electrical discharge machine (wire-EDM, Mitsubishi FA10S, Japan). This uses the rapid series of repetitive electrical discharges to remove small amounts of material, with very thin wire serving as the electrode. The crystallinity of the SCC wire was characterized by highresolution X-ray diffraction (XRD, PANalytical X’pert PRO MRD). The morphology of the surface etched by 50% diluted HNO3 was observed by the scanning electron microscope (SEM, Hitachi, S-4700). The chemical binding states of the SCC wire and oxygenfree copper (OFC) wire of purity 4 N were investigated and compared by X-ray photoelectron spectroscopy (XPS, ESCALAB 250). To investigate the change of chemical composition at the surface of the SCC wire after wire-EDM, we measured the depth profile with a glow discharge spectrometer (GDS, Jobin Yvon 10000 RF). The resistivity was measured in the temperature range from 300 down to 4 K using a 4-He cryostat (PPMS Quantum Design, USA). Electrical contacts were made using pure gold wires 0.0508 mm in diameter and silver epoxy on the sample. For resistivity measurements, we used the fourprobe method and the current-reversal method (delta mode). Generally, the four-probe method can eliminate low-level voltage errors by removing the contact resistance using two extra probes between the current contacts. To minimize the unwanted additional voltages due to the thermoelectric effect, we measured the voltage with the current in one direction, and then repeated the measurement with the reversed current (delta mode). This current-reversal method gave reliable results by removing the temperature difference between the two readings. In the resistivity measurements, we used a nanovoltmeter (Kiethley 2182A) for measurement of the voltage difference and a current source (Kiethley 2425). The resolution of the nanovoltmeter was 1 nV in our measurement. We optimized the DC current between 10 and 80 mA, depending on the temperature range. The accuracy of the current source was 0.1% in our measurement range. Therefore, the resultant standard deviations by equipment (nanovoltmeter and current source) corresponded to 0.1% of the average resistivity value at room temperature. In the experiment, to reduce errors due to sample size uncertainty, the resistivity measurements were performed on OFC and SCC samples fabricated by exactly the same procedure using wire-EDM, with a resultant cross-section deviation of less than 0.1%. We also repeatedly measured the sample dimension using a
Figure 2. XRD patterns of (a) SCC and (b) OFC (the insets show the SEM image for etched surfaces of SCC and OFC, respectively.) (c) Cu 2p peaks of SCC and OFC in XPS spectra. micrometer with a (1 μm resolution limit at room temperature. The resistivity deviations due to the uncertainty of the sample dimension did not exceed 0.1% of resistivity at room temperature. The measurement was carried out after temperature was stabilized by a current flip. No noticeable differences were observed between cooling and warming measurements.
Results and Discussion Figure 1b shows the SCC grown by the Czochralski method in Ar atmosphere. The orientation of the seed crystal was determined by X-ray and neutron scattering experiments (HANARO, Korea Atomic Energy and Research Institute). The grown crystal diameter and body length were 80 and 200 mm, respectively. Figure 2a,b shows the XRD patterns of the SCC disk perpendicular to the growth direction and a polycrystalline OFC, respectively. The X-ray pattern of the SCC showed 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 the OFC was conventional polycrystalline with no distinct symmetry to the etched surface. The average grain size of the OFC was about 200 nm in SEM observation of the etched surface. Figure 2c shows the Cu 2p peaks of SCC and OFC in XPS spectra. As shown in Figure 2c, the chemical binding states of Cu in OFC and SCC were nearly consistent. Only the Cu 2p peaks of the SCC were slightly narrower than those of the polycrystalline OFC. Figure 3a,b shows a schematic of the wire-EDM process for fabrication of the SCC disk and wire. In standard cutting
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Figure 4. Periodic XRD patterns of the SCC wire.
Figure 3. (a) Fabrication of SCC disks by wire-EDM. (b) Fabrication process for SCC wire in a spiral fashion through wire-EDM cutting. (c) Fabricated SCC disk and SCC wire. (d) Straightened SCC wire.
methods, including diamond saw and mechanical wire cutting, the crystal structure of the cut surface is affected due to the excellent ductility and malleability of copper. Mechanical stress during conventional polishing and cutting often introduced additional peaks in the XRD measurements of SCC. As shown in Figure 3a,b, the wire-EDM used a rapid series 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 fed through the material, and the electrical discharges cut the material. We found that the wire-EDM method was suitable for fabricating metallic single-crystal wire. Figure 3c,d shows the fabricated SCC disk and wire. The SCC wire was fabricated from the (200) SCC disk through wire-EDM cutting. It was possible to prepare SCC wafers of arbitrary thickness. From SCC disks of 1 and 2 mm thickness, SCC wires were fabricated in a spiral fashion. The fabricated wire had (200) orientation along the upside direction. After the wire-EDM cutting, the rough and coarse surfaces with depths of about 0.2 μm were easily polished mechanically. The single-crystal wires, 2 mm wide and 0.5 mm thick, were obtained by straightening the spirally processed disks. The XRD patterns obtained from the straightened wires reflected that the wires kept the single-crystal structure and that the strain effect during the straightening process was not serious. As shown in Figure 4, peaks corresponding to the (200) plane periodically appeared along the SCC wire due to the spiral cutting. Generally, in polycrystalline samples, the crystal orientations adjacent to the boundary are supposed to be different. However, in SCC, the entire sample would have the same orientation. Figure 5 shows the result of the GDS depth profile of the SCC wire processed by wire-EDM. At the surface, impurities such as P, Fe, Mg, Co, Ni, and Cr were observed. This contamination mainly came from the material used for wire cutting during wire-EDM cutting. The depth profile showed that the contaminations abruptly decreased underneath the
Figure 5. Result of the GDS depth profile for the SCC wire processed by wire-EDM.
surface. On the basis of the sputtering time, the contaminated layer thickness was estimated to be about 20 nm. Table 1 shows atomic percent of impurities and copper at several depths (10, 20, 200 nm, and 2 μm). As shown Table 1, the SCC wire purity was consistently 99.99% ((0.005%) below 20 nm. Figure 6a,b shows the temperature dependence of the resistivity of the OFC and SCC wires compared with the reported results for copper and silver.19,22,23 For the SCC wires, we performed 12 measurements (four measurements between 4 and 300 K and eight between 90 and 300 K). For the OFC samples, we performed 11 measurements (two between 4 and 300 K and nine between 90 and 300 K). The obtained resistivities of OFC and SCC were 1.67 ( 0.01 and 1.52 ( 0.006 μΩ 3 cm, respectively, at 293 K. The standard deviations of OFC and SCC were approximately (0.6% (OFC) and (0.4% (SCC) of resistivity at 293 K. According to Matthiessen’s rule, the resistivity of the bulk metal was the sum of contributions from the temperature-dependent thermal vibrations of the lattice (i.e., phonon scattering) and the lattice defects (i.e., vacancies, interstitial atoms, dislocations, and GBs), which were independent of temperature.2,12 For nonmagnetic elemental metals, the temperature-dependent resistivity, Fel-ph(T) originated from electron-phonon interactions and followed a power-law function of temperature, the
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Table 1. Atomic Percent of Impurities and Copper at Several Depths depth
Cr(%)
Si(%)
S(%)
Ag(%)
Ni(%)
Co(%)
Mg(%)
Fe(%)
P(%)
Cu(%)
10 nm 20 nm 200 nm 2 μm
1.2013 0.0016 0.0009 0.0007
1.7052 0.0011 0.0007 0.0006
1.0293 0.0014 0.0006 0.0005
0.2014 0.0016 0.0013 0.0012
0.8201 0.0013 0.0011 0.0006
0.8193 0.0010 0.0009 0.0007
2.2708 0.0024 0.0011 0.0008
0.9469 0.0019 0.0017 0.0016
1.2989 0.0015 0.0004 0.0002
89.7068 99.9862 99.9913 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 the Bloch-Gr€ uneisen (BG) formula. The dotted lines represent the resistivities of copper samples with 4 N (FCu(4N)), 6 N (FCu(6N)), and 7 N (FCu(7N)) purity, as given in ref 23. (c) Resistivity reduction rates of OFC and SCC compared to FCu(standard).
Bloch-Gr€ uneisen (BG) formula.24,25 5 Z ΘR =T T x5 dx Fel- ph ðTÞ ¼ Rel- ph ΘR ðex - 1Þð1 - e - x Þ 0 ð1Þ In eq 1, ΘR is the Debye temperature and x is the variable uneisen formula. changing from 0 to ΘR/T in the Bloch-Gr€ The constant Rel-ph is proportional to λtrωD/ωp2, where λtr is the electron-phonon coupling constant and ωD and ωp are the Debye and plasma frequencies, respectively.25 Bid et al. reported that the Bloch-Gr€ uneisen formula was still applicable to the resistivity of nanowires with diameters from 15 to 200 nm.25 The resistivities of the OFC (FOFC) uneisen and SCC (FSCC) well agreed with the Bloch-Gr€ formula from room temperature to about 70 K. In our results, the FOFC was consistent with the standard values (1.67 μΩ 3 cm) at 293 K, corresponding to 103% International Annealed Copper Standard (IACS) of conductivity.19,22 The ICAS reflects a material in which the resistance of 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 the range of measured temperatures. The average value of FSCC obtained from the repeated measurements using 12 different samples was about ∼1.52 μΩ 3 cm (corresponding to ∼113% IACS of conductivity) at 293 K, which was about ∼91% of FOFC, and even less than that of Ag (∼1.59 μΩ 3 cm). Therefore, the FSCC showed a remarkable improvement in the conductivity of the novel metal copper wire. In addition, Rel-ph, a crucial parameter for the temperature dependence of resistivity, could be estimated by fitting the Bloch-Gr€ uneisen to the data in Figure 6a.25 The Rel-ph value obtained for SCC was ∼9% less than the value for OFC; RR is defined as Rel-ph/FΘR, where FΘR is F at the Debye temperature. Its value is 4.225 for copper.25 The values of RR obtained for 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 copper nanowires.25 Figure 6c shows the resistivity reduction rates of OFC (ΔFOFC/FCu(standard)) and SCC (ΔFSCC/FCu(standard)) compared to the resistivity of standard Cu(FCu(standard)), where ΔFOFC = FCu(standard) - FOFC and ΔFSCC= FCu(standard) - FSCC. The resistivity of SCC was more reduced than that of OFC. The fractional change of resistivity, ΔFGB/FOFC, where ΔFGB = FOFC - FSCC, which ideally corresponds to the contribution of GBs to the resistivity, was constant at about ∼9% in the range between room temperature and 100 K (Figure 6c). This means that the electron scattering due to the GBs proportionally decreased with the amount of phonons with the temperature. Consequently, eliminating the GBs could alter the resistivity significantly because the electron scattering due to the GBs is different from the electron-regular phonon scattering in a single crystal. Below 70 K, both FSCC and FOFC with the same grade of purity were similar, but Cu(6N) and Cu(7N) showed much lower values than FSCC (Figure 6b). Hence, below 70 K, where the phonons were strongly suppressed, the amount of impurities was the main determinant of the resistivity, as the reduction in the number of GBs did not contribute to the reduction in resistivity. Therefore, the GBs in OFC added to the resistivity only when they were connected with the phonons. Figure 7 shows the temperature dependence of the temperature coefficients of resistivity (TCR) in SCC and OFC wires. TCR corresponds to (1/F) 3 dF/dT, which was calculated from the temperature derivative of the measured resistivity. For both SCC and OFC, TCR had the same value (0.0039 K-1) at room temperature, which agreed very closely with the standard value for copper. In addition, the TCR showed an anomaly (TI) at about 45 K. The higher purity samples started to deviate from the Bloch-Gr€ uneisen formula at lower temperatures. The temperatures TI were obtained for Cu(6N) at around 30 K and for Cu(7N) at around 20 K, in close agreement with Figure 6b.23 Hence, TI was assumed to
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This study highlights a fundamental phenomenon in one of the most widely used materials in the world. The understanding gained here on the origin of the resistivity should help reduce electric signal losses and distortion at both micro- and nanoscales in situations when the GBs and surface contribute significantly to the resistivity. Acknowledgment. This research was supported by the World Class University program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology, South Korea (Grant No. R31-2008-000-20004-0).
References
Figure 7. Temperature dependence of TCR. The dotted line of TCR is included as a visual guide.
indicate a transition temperature, where the main contributor to the resistivity changed from electron-phonon coupling in the copper lattice to impurities as the temperature decreased. Conclusion To summarize, we showed that the resistivity of copper can be improved below standard values found in the literature by applying a well-known crystallization process. The obtained resistivities 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, the conductivity was found to be nearly 113% IACS. This is higher than that found previously in all kinds of novel metals, including Ag (105-108.4% IACS). The ∼9% reduction in resistivity was seen at temperatures above 100 K, agreeing well with the Bloch-Gr€ uneisen formula. Consequently, our observations suggested that the bulk resistivity of copper has been overestimated by∼9% due to the contributions of GBs (ΔFGB) in pure copper at temperatures above ∼100 K. In addition, GBs are no longer important at temperatures below 70 K, where the contribution of impurities becomes significant. The anomaly TI at the TCR seemed to indicate a transition of the main contributor to the resistivity from electron-phonon coupling to electron impurity scattering as the temperature decreased. For the further verification of TI in metal crystals, further investigations should be carried out.
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