Focused ion beam processing to fabricate ohmic contact electrodes on a bismuth nanowire for Hall measurements
© Murata and Hasegawa; licensee Springer. 2013
Received: 9 July 2013
Accepted: 21 September 2013
Published: 26 September 2013
Ohmic contact electrodes for four-wire resistance and Hall measurements were fabricated on an individual single-crystal bismuth nanowire encapsulated in a cylindrical quartz template. Focused ion beam processing was utilized to expose the side surfaces of the bismuth nanowire in the template, and carbon and tungsten electrodes were deposited on the bismuth nanowire in situ to achieve electrical contacts. The temperature dependence of the four-wire resistance was successfully measured for the bismuth nanowire, and a difference between the resistivities of the two-wire and four-wire methods was observed. It was concluded that the two-wire method was unsuitable for estimation of the resistivity due to the influence of contact resistance, even if the magnitude of the bismuth nanowire resistance was greater than the kilo-ohm order. Furthermore, Hall measurement of a 4-μm-diameter bismuth microwire was also performed as a trial, and the evaluated temperature dependence of the carrier mobility was in agreement with that for bulk bismuth, which indicates that the carrier mobility was successfully measured using this technique.
Bismuth nanowires are widely known as suitable materials for quantization because bismuth has a very long Fermi wavelength and mean free path length of carriers and phonons [1, 2]. Therefore, it is expected that one-dimensional density of states will be observed on a larger scale than other materials. Furthermore, it is predicted that the thermoelectric performance of bismuth nanowires as a one-dimensional geometry will be enhanced with a diameter of less than 50 nm due to semimetal-semiconductor (SM-SC) transition [3–5]. Many researchers have reported the thermoelectric properties of bismuth nanowires fabricated using various methods [6–14]. Our group has successfully fabricated a quartz template with a hole diameter of several hundred nanometers by applying the fabrication technique for optical fibers. Bismuth nanowires over 1 mm long and with diameters of several hundred nanometers have been fabricated by injecting molten bismuth into the nanohole at a high pressure of almost 100 MPa and then recrystallizing the bismuth by reducing the temperature . The fabricated bismuth nanowires were identified as single crystal from X-ray diffraction measurements  and Shubnikov-de Haas oscillations . To measure the resistivity and Seebeck coefficient of the nanowires, titanium (Ti) and copper (Cu) thin films were deposited on the edges of the bismuth nanowire to obtain appropriate thermal and electrical contacts . The resistivity, Seebeck coefficient, and thermal conductivity of the bismuth nanowires and microwires (300-nm to 50-μm diameter) were successfully measured using this technique [15–25]. The temperature dependence of the Seebeck coefficient and electrical resistivity for bismuth nanowires with diameters smaller than 1 μm are completely different from those of bulk. Size effects in bismuth appear for larger size samples than other materials because the mean free path length of the carriers is very long and in the order of several millimeters at liquid helium temperatures. Furthermore, calculation models with three-dimensional density of states for the thermoelectric properties of bismuth nanowires have also been established [26–30]. The results have suggested that the carrier mobility is decreased with a reduction of the wire diameter due to the limitations placed on the mean free path by narrowing. This was confirmed using an evaluation model for measurement results of the resistivity and Seebeck coefficient [15, 22]; however, direct measurement of the carrier mobility, such as Hall effect measurements, has not yet been performed. There have been very few reports on Hall measurements in the field of nanowire studies due to the difficulty of electrode fabrication on such a small area , and there have been no reports on such with respect to bismuth nanowires. There have been various reports on the temperature dependence of the electrical resistivity and Seebeck coefficient for bismuth nanowires, although it has been unclear why there are inconsistencies in these reports [6–12]. Our previous study revealed that the thermoelectric properties of bismuth nanowire are strongly dependent on the crystal orientation of bismuth, due to its anisotropic carrier mobility . The next step is direct measurement of the carrier mobility by Hall measurement for bismuth nanowires with diameters of several hundred nanometers; however, it is challenging to fabricate electrodes on the surface of a bismuth nanowire that is encased in a template. We have previously reported the successful fabrication of electrodes on a bismuth nanowire encased in a quartz template by utilizing a combination of chemical mechanical polishing (CMP) and focused ion beam (FIB) processing. The resistivity of the bismuth nanowire was thereby successfully measured using the four-wire method . As a next step, a technique for exposure of the bismuth nanowire for Hall measurements was also developed . Many researchers have reported the resistivity of bismuth nanowires measured using the two-wire method due to difficulty of electrode fabrication with the four-wire method; however, the four-wire method is theoretically more suitable for estimation of the resistivity. There have been some results reported for the resistivity measured using the four-wire method; however, the surface of bismuth nanowires is oxidized during the fabrication process, which makes it difficult to fix the boundary conditions for the wire diameter direction [12–14]. Furthermore, it was reported that a majority of the bismuth nanowire becomes amorphous due to irradiation with a high-energy gallium (Ga) ion beam during FIB processing . Therefore, it would be difficult to successfully apply FIB processing to a bare bismuth nanowire. However, the bismuth nanowires prepared in our work were completely encased in a quartz template. Therefore, the influence of Ga ion beam irradiation could be neglected if the exposed area was very small with respect to the entire surface of the bismuth nanowire. The FIB processing technique was applied to fabricate electrodes on a 521-nm-diameter bismuth nanowire for Hall measurements, and the electrodes were evaluated to confirm a suitable contact. Furthermore, the temperature dependence of the resistivity was measured with comparison of the two-wire and four-wire resistance measurements. To confirm the validity of the electrode fabrication technique to estimate the Hall coefficient, Hall measurements were performed using a 4-μm-diameter bismuth microwire. It would be ideal to use a nanometer-order diameter wire to demonstrate the Hall measurement; however, verification with a 4-μm-diameter microwire was performed first, which is predicted to give almost the same Hall coefficient as that of the bulk. We discuss the adequacy of the electrical contacts on the bismuth nanowires for resistivity and Hall measurements.
For experiment 1, both edges of the 0.5-mm-diameter and 2.54-mm-long quartz template were polished to obtain good electrical and thermal contacts with the bismuth nanowire. Metal thin-film layers of Ti (100 nm) and Cu (1,000 nm) were then deposited on both polished end surfaces of the nanowire and template using an ion plating method. The resistance was measured using the two-wire method with an alternating current (AC) and a lock-in amplifier at precisely controlled (<1 mK) temperatures from 4.2 to 300 K achieved using a Gifford-McMahon (GM) cryocooler [34, 35]. In the next step of the experiment, one side surface of the quartz template was removed by polishing until just before the bismuth nanowire was exposed, as shown in Figure 1b. The distance between the surface of the bismuth nanowire and the quartz template was less than 1 μm, as measured with a laser microscope. After removal of the quartz template, the sample was attached with adhesive onto a doped silicon (Si) wafer to prevent charge-up during FIB processing, with the polished surface upward. Ti (100 nm)/Cu (200 nm) thin-film layers were then deposited on the polished surface. The thin-film layers acted as electrodes and helped to prevent charge-up during FIB processing because the majority of the sample was quartz. This sample was installed into a dual-beam FIB-scanning electron microscope (SEM) apparatus (NB5000, Hitachi High-Technologies Ltd., Tokyo, Japan), and six electrical contacts were fabricated by FIB processing.
Results and discussion
Figure 4a,b,c,d,e,f,g shows current–voltage (I-V) characteristics for various combinations of electrodes on the bismuth nanowire measured at 300, 250, 200, 150, 100, 50, and 4.2 K. The measurement was performed with a direct current (DC) from −20 to +20 nA. The electrodes labeled as B and 3 were broken during a decrease in the temperature. The I-V characteristics of all the electrodes are clearly linear over the entire temperature range examined, which indicates that the electrodes fabricated by FIB were ohmic contacts. The resistance values agreed well for pair combinations of A-1 and A-2, A-5 and A-6 because the distances between the electrodes were the same. Figure 4h shows the temperature dependence of the electrical resistance evaluated from these I-V characteristics. The resistance increased in the order of A-1, A-2 < A-4 < A-5, A-6 at 300 K depending on the distance between electrodes. However, the resistance of A-4 became larger than that of A-5 and A-6 at less than 100 K. The increase in the resistance of A-4 with decreasing temperature may be due to the long length of the carbon electrode on the nanowire, although it did not significantly influence the four-wire method.
Resistivity measurement of 521-nm-diameter nanowire
Hall measurement of 4-μm-diameter microwire
We have successfully fabricated ohmic contact electrodes for measurement of the four-wire resistance and Hall voltage in an individual single-crystal bismuth nanowire with a diameter of 521 nm and a length of 2.34 mm covered with a 0.5-mm-diameter quartz template. FIB processing was utilized to expose the side surfaces of the bismuth nanowire, and carbon and tungsten electrodes were deposited on the bismuth nanowire in situ to obtain electrical contact without severe damage to the bismuth nanowire. Oxidation of the bismuth nanowire could be prevented because the bismuth nanowire was covered with the quartz template and all the electrode fabrication procedures were performed under high vacuum. The measured I-V characteristics confirmed that ohmic contacts were obtained over the entire temperature range from 4.2 to 300 K. This result indicates that the electrodes on the bismuth nanowire could be successfully fabricated by FIB processing with suitable contacts for four-wire resistance and Hall measurements. Furthermore, measurement of the temperature dependence of the four-wire resistance was successfully performed for the bismuth nanowire using the fabricated electrodes from 4.2 to 300 K. A difference between the results for the two-wire and four-wire resistances was observed, which indicates that the contact resistance was not negligible, even if the resistance of the nanowire was extremely large and over several kilo-ohms. Although there have been many reports on the resistivity measured using the two-wire method, we must carefully consider whether resistivities measured by the two-wire method are correct. Furthermore, Hall measurements were also conducted on a 4-μm-diameter bismuth microwire, and the evaluated carrier mobility was in good agreement with that for bulk bismuth, which indicates that the carrier mobility of the bismuth microwire in the quartz template could be successfully measured with this technique. Hall measurements were difficult in the low temperature range due to the high contact resistance of the carbon electrodes employed. Therefore, we are planning to fabricate electrodes that consist of only tungsten and to measure the carrier mobilities of bismuth nanowires with diameters of several hundred nanometers.
MM is a Ph.D. candidate under Associate Professor YH in the Department of Engineering, Saitama University, Japan.
The authors would like to thank Dr. Takashi Komine at Ibaraki University for his assistance in this research. This research was supported in part by a Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows, a Grant-in-Aid for Scientific Research (C), and Leading Industrial Technology Development Project Grant Funds of NEDO, TEPCO Memorial Foundation, Inamori Foundation, and Takahashi Industrial and Economic Research Foundation. Part of this research was supported by the Low-Carbon Research Network (Lcnet) and the Nanotechnology Network Program (Center for Nanotechnology Network, National Institute for Material Science) funded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This work was performed under the auspices of the National Institute for Fusion Science (NIFS) Collaborative Research (NIFS13KBAS014).
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