Letter pubs.acs.org/NanoLett
Experimental and Theoretical Evaluations of the Galvanomagnetic Effect in an Individual Bismuth Nanowire Masayuki Murata* and Atsushi Yamamoto iECO, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
Yasuhiro Hasegawa Faculty of Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama 338-8570, Japan
Takashi Komine Faculty of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan S Supporting Information *
ABSTRACT: The galvanomagnetic effect is evaluated experimentally and theoretically in an individual bismuth nanowire encapsulated within a quartz template. A small section of the side surface of the encapsulated bismuth nanowire is exposed using focused ion beam processing, and a total of six carbon film electrodes are fabricated on the exposed nanowire surface by in situ deposition in order to be able to perform electrical measurements on the nanowire. The results show that the galvanomagnetic effect in the nanowire is affected by carrier collisions at the nanowire boundary; this is particularly the case at low temperatures. The Hall mobilities of electrons and holes are determined based on the measured Hall coefficient and magnetoresistivity values. It is found that the carrier mobility in the bismuth nanowire is lower than that in bulk bismuth and that it plateaus at low temperatures, as predicted by the calculation model used in the study, which takes into account the carrier mean free path limitation imposed by the small diameter of the nanowire. KEYWORDS: Bismuth nanowire, galvanomagnetic effect, Hall effect, magnetoresistance, focused ion beam anoscale structures such as thin films, nanowires, and nanodots are being studied intensively because they are expected to exhibit novel functionalities and phenomena. In the field of thermoelectrics, it is predicted that the dimensionless figure of merit, ZT, would be enhanced in nanostructured materials owing to a decrease in the thermal conductivity and an increase in the Seebeck coefficient.1 Therefore, nanostructured materials have come to be regarded as a strategic area of study in thermoelectrics ever since these theoretical predictions were first made. Nanowires are especially amenable to ZT enhancement because they exhibit significantly different densities of state and because it has been predicted that the quantum confinement effect can be induced in them without hindering carrier conduction.2 It is known that both the classical and quantum size effects are enhanced in bismuth nanowires,3,4 because bismuth has a long carrier mean free path and Fermi wavelength owing to its small effective mass.5,6 A number of researchers have studied the thermoelectric properties of bismuth nanowires.7−14 However, accurate measurements have been lacking, even those of its electrical resistivity, owing to the difficulty of performing measurements on such small wires. The fabrication of suitable ohmic contact
N
© 2016 American Chemical Society
electrodes on bismuth nanowires is a major challenge because bismuth is oxidized readily, is sensitive to impurities, and exhibits low resistances with respect to chemical reactions and mechanical stress.15 In a previous study, we had successfully fabricated bismuth nanowires more than 1 mm in length, having a diameter of several hundred nanometers, using a quartz template and had successfully measured their Seebeck coefficients and electrical resistivities.16 These nanowires were fabricated by injecting molten bismuth into a nanosized cylindrical hole at the center of a quartz template at 370 °C under a pressure of approximately 100 MPa and then allowing it to recrystallize by gradually cooling it. The thus-fabricated bismuth nanowires were confirmed to be single crystalline based on single-crystal X-ray diffraction (SC-XRD) analysis17 and also because they exhibited Shubnikov-de Haas oscillations.18 However, some aspects of the crystallinity and crystal orientation of the Received: August 25, 2016 Revised: November 4, 2016 Published: December 15, 2016 110
DOI: 10.1021/acs.nanolett.6b03592 Nano Lett. 2017, 17, 110−119
Letter
Nano Letters
Figure 1. Setup used for performing Hall measurements on a 700 nm diameter bismuth nanowire. (a) Schematic showing the configuration used for performing the Hall measurements on the bismuth nanowire. (b) SEM image of the FIB-processed area where the electrodes were fabricated. The inset shows an SEM image of one of the facets of the 700 nm diameter bismuth nanowire. (c) Schematic diagram showing the overall view and dimensions of the fabricated sample. (d) Optical micrograph of the sample used for the Hall measurements after Au wires had been attached on the Ti/Cu thin films deposited on the quartz template.
not possible.26 In a previous study, we had developed an electrode fabrication procedure that employs FIB processing and allows for Hall measurements to be performed on bismuth wires encapsulated within quartz templates.27 Using this system, the Hall coefficient of a 4 μm diameter bismuth microwire was measured successfully; the measured value agreed with that of bulk bismuth for temperatures of 150−300 K.28 However, the Hall coefficient could not be measured at temperatures lower than 150 K because the signal-to-noise (S/ N) ratio was too low because of the high electrical resistance of the carbon electrodes that were fabricated by FIB processing. Thus, the next step would be to fabricate electrodes that allow for Hall measurements to be performed on individual bismuth nanowires over a wide range of temperatures. Hence, in this study the Hall resistivity of a 700 nm diameter bismuth nanowire and the electrical resistivity along the wire’s longitudinal direction, which is called the diagonal resistivity, were measured using suitable electrodes at temperatures of 4.2−300 K. Further, the Hall mobility was determined from the measured Hall coefficient and diagonal resistivity values. Experimental Section. Figure 1a illustrates the setup used for the Hall coefficient and diagonal resistivity measurements performed on an individual bismuth nanowire, which was encapsulated in a quartz template. Electrodes must be fabricated on the side surface of the bismuth nanowire when determining the Hall voltage, which is measured transversely along the longitudinal direction of the nanowire. Thus, six carbon film electrodes were fabricated on the bismuth nanowire using FIB-scanning electron microscopy (SEM) processing. A bismuth nanowire with a diameter of 700 nm and length of 2.69 mm and encapsulated within a 0.53 mm diameter cylindrical quartz template was used for the Hall coefficient and electrical resistivity measurements. The inset of Figure 1b shows an SEM
fabricated bismuth nanowires have still not been identified because some nanowires are not perfectly single crystalline and also because crystallographic orientations cannot be controlled. The large length of the nanowires (>1 mm) allowed for accurate measurements of the Seebeck coefficient as well as electrical resistivity in the same sample using the two-wire method.19 Furthermore, we developed a procedure for fabricating ohmic contact electrodes on the side surfaces of the bismuth nanowires, which were encapsulated in a quartz template, by nanoscale processing while employing focused ion beam (FIB) milling and polishing. As a result, the electrical resistivity of an individual bismuth nanowire could be measured successfully by the four-wire method.20 The measured Seebeck coefficient and electrical resistivity of the bismuth nanowire were completely different from those of bulk bismuth, pointing to a decrease in the carrier mobility with a decrease in the wire diameter.21,22 Thus, it became necessary to determine the carrier mobility experimentally through galvanomagnetic effectrelated measurements, for example, Hall effect and magnetoresistance effect measurements, in order to elucidate the effect of the carrier mean free path limitation imposed by collisions at the wire boundary. However, performing Hall effect measurements on a single bismuth nanowire is challenging because it is difficult to fabricate nanosized electrodes on the sides of the wire. Only a few groups have been able to successfully perform Hall measurements on nanowires. For instance, such measurements have been made previously on InP23 and InAs nanowires24 at room temperature, FeS2 nanowires25 at 240− 300 K, and MnSi nanowires25 at 10−100 K. Although the nanoprocessing of InP, InAs, FeS2, and MnSi has been achieved, that of bismuth remains difficult because of its high fragility and oxidizability. It is for this reason that Cronin suggested that Hall measurements on bismuth nanowires were 111
DOI: 10.1021/acs.nanolett.6b03592 Nano Lett. 2017, 17, 110−119
Letter
Nano Letters micrograph of a facet of the 700 nm diameter bismuth nanowire as viewed along the center of the quartz template. The surface of the nanowire facet was cleaned after the SEM observations, in order to remove the platinum−palladium alloy coating deposited for the observations, as well as any stains present. The crystal orientation for the longitudinal direction of the bismuth nanowire was [0.22152, −0.19080, −0.95630] in the Brillouin zone of bismuth [binary, bisectrix, trigonal] that was measured by the SC-XRD measurement as shown in the Supporting Information, Figure S1. To prepare the nanowire for FIB processing, one side surface of the cylindrical quartz template was first removed by polishing it to the point where the bismuth nanowire was almost exposed. The distance between the surface of the quartz template and the bismuth nanowire was less than 1 μm, as measured by a laser microscope. To facilitate sample handling, an adhesive was used to fix the polished quartz template onto a Si wafer; the polished surface was made to face up. A 100 nm thick Ti layer and a 200 nm thick Cu layer were then deposited on the quartz template to prevent charging during FIB processing; these were also used later as the electrode pads. The prepared sample was then placed in a dual-beam FIB-SEM system (Hitachi HighTech Science Corp., Xvision200DB). The electrode fabrication procedure used in this study was slightly different from the one used previously;28 the procedure used in the present study is described in Supporting Information. Figure 1b shows an SEM image of the FIB-processed area used for fabricating the electrodes on the bismuth nanowire. The pink line in Figure 1b indicates the approximate position of the bismuth nanowire embedded within the quartz template, while the blue areas indicate the deposited tungsten, which connects the bismuth nanowire and the Ti/Cu thin films on the quartz template. That the Ti/Cu thin films were separated by 2 μm wide grooves was confirmed from the SEM micrograph shown in Figure 1b. The oxidation of the bismuth nanowire was prevented because the entire electrode fabrication process, starting from the exposure of the nanowire to the attachment of the carbon electrodes, was performed under a high vacuum (of the order of 10−5 Pa). As a result, current−voltage (I−V) measurements confirmed that an ohmic contact was formed at every electrode (Figure S5). Figure 1c shows the sample prepared for the Hall coefficient and diagonal resistivity measurements, presenting an overall schematic of the process as well as the sample dimensions. The Ti/Cu thin films were connected directly to both ends of the bismuth nanowire, because both ends had been exposed by the polishing process. As determined using an optical micrograph, the distances between the left and middle and the right and middle electrodes were 0.532, and 0.557 mm, respectively. Figure 1d shows an optical micrograph of the sample fabricated for measuring the Hall coefficient and diagonal resistivity. Au wires of 25 μm diameter were electrically attached to the Ti/Cu thin films using Ag epoxy (Diemat DM6030Hk), as shown in Figure 1d. This setup was used to measure the electrical properties of the 700 nm diameter bismuth nanowire under a magnetic field. The Hall resistivity, ρxy, and the diagonal resistivity, ρxx, were measured at precisely controlled temperatures (
