Preparation of bismuth nanowire encased in quartz template for Hall measurements using focused ion beam processing
© Murata et al.; licensee Springer. 2012
Received: 13 August 2012
Accepted: 2 September 2012
Published: 7 September 2012
Forming electrodes on opposite sides of an individual bismuth nanowire was attempted to prepare for Hall measurements. Although a 1-mm-long bismuth nanowire which is completely covered with a quartz template has been successfully fabricated to prevent oxidation, it is very difficult to attach Hall electrodes on the opposite sides of the nanowire due to the quartz covering. One side of the cylindrical quartz template was removed by polishing without exposure of the nanowire to the atmosphere; the thickness between the polished template surface and the nanowire was estimated to be several micrometers. Focused ion beam processing was successfully employed to expose both surfaces of the nanowire under high vacuum by removing part of the quartz template. A carbon thin film was then deposited in situ on the wire surface to fabricate an electrical contact on the bismuth nanowire sample. Furthermore, the energy dispersive X-ray analysis was performed to the area processed by focused ion beam, and the bismuth component of the nanowire was successfully detected. It was confirmed that the focused ion beam processing was applicable to attach electrodes to bismuth nanowire for Hall measurement.
Nanoscale structures such as superlattices and nanowires attract research interest due to their electrical transport properties. It has been expected that nanostructured thermoelectric materials would exhibit enhanced performance [1–5]. In particular, one-dimensional bismuth nanowires have been expected to show an enhanced figure of merit as thermoelectric materials [2, 3]. Bismuth, as a semimetal, has interesting electrical properties such as small effective mass, low carrier density, and a long mean free path; and the properties of bismuth, such as its Fermi surface and effective mass, have been well studied [6, 7]. Bismuth nanowires have been fabricated using several methods for the study of the thermoelectric properties of one-dimensional systems [8–13]. Our group has fabricated a bismuth microwire array using a glass template and individual nanowires using a quartz template by application of a liquid-phase high pressure injection method [14–24]. The quartz template possesses an individual hole of several-hundred-nanometer diameter and over 1 mm long and is fabricated by identical procedure of an optical fiber for us to make the nanowire . The simultaneous measurement of the Seebeck coefficient and resistivity was successfully achieved using the bismuth nanowire. The results implied that the carrier mobility of a nanowire less than 1 μm in diameter was significantly reduced compared with that for a bulk bismuth sample due to the collision at the quartz template surface, which functioned as a boundary condition, as a result of the classical size effect [25, 26]. Although we have considered variations in the mobility of each carrier in the nanowire sample using a mean free path limitation model, direct measurement results have not yet been reported. Discussions have been based only on the model and temperature dependence measurement results of Seebeck coefficient and resistivity. Therefore, the carrier density and mobility should be evaluated by Hall measurement.
Bismuth nanowires are usually fabricated by using alumina templates [8–11]. Since bismuth nanowires are covered with the alumina template, the template must be removed so that the electrodes can be attached at the opposite sides of the nanowire for Hall measurements. Even if the alumina template component was completely removed using acid, it has been reported that the bare surface of the bismuth nanowire is likely to be oxidized in the atmosphere. Therefore, removal of the oxide layer covering the nanowire surface is a very important process to achieve ohmic contact with the electrodes [27–29]. Recently, a new fabrication process for bismuth nanowires called on-film formation of nanowires was reported , where the oxidized surface was removed by ion beam sputtering, and electrodes were deposited in situ on the bismuth nanowire without breaking the vacuum. However, a majority of the bismuth nanowire area was oxidized.
In the current research, however, the bismuth nanowires were covered with a quartz template; therefore, oxidation of the wire surface is prevented. Although such nanowire has apparent advantages, it was not considered to be suitable for the four-wire and Hall measurements because it is very difficult to remove the quartz component locally. However, in the previous study, we had successfully fabricated electrodes on the surface of the bismuth nanowire with ohmic contact using polishing and focused ion beam (FIB) processing and performed four-wire resistance measurement . A local area of the bismuth wire was successfully exposed, and a carbon electrode was deposited on the bismuth wire in situ. In this paper, this method was applied for the preparation of a Hall measurement sample and discussed for a nanowire covered with a quartz template. The quartz template was cut using FIB processing to successfully expose the opposite side surfaces of a bismuth nanowire under high vacuum, and a carbon electrode was then immediately deposited on the surface of the bismuth nanowire.
Results and discussion
The magnitudes of the Hall voltage measured for the nanowire are now discussed. The Hall coefficient (RH) for a two-carrier model is expressed by , where rH is the Hall factor, n and p are the electron and hole carrier densities, respectively, and b is the mobility ratio between electrons μ n and holes μ p . The value of rH is almost 1, even if carrier scattering processes are assumed. The values of n and p are taken from  for that of bulk Bi. The b value was estimated to be from 3 to 10, depending on the crystal orientation , and a value of b = 3 was selected as a severe assumption. The Hall resistance RHall is approximately expressed as , where d and B are the wire diameter and the magnitude of the magnetic field, respectively. Here the cross section of the nanowire (S) and the gap between metal electrodes for the Hall measurement (l) are approximated by and , respectively. Conditions of d = 100 to 1,000 nm were considered in B = 0.12 T, which satisfy the low magnetic field approximation at 300 K . Therefore, the calculated |RHall| is estimated to be from 0.19 Ω at 1,000 nm to 1.9 Ω at 100 nm. The electric current introduced into the bismuth nanowire for the measurement should ideally be less than 1 μA due to the small heat capacity of the narrow wire and the high resistance, so that an increase in temperature and burn out can be avoided. The absolute value of the measured Hall voltage was estimated to be 190 nV to 1.9 μV under the same conditions. Nanovolt-order voltage can be measured using a lock-in amplifier with modulation of the introduced current and magnetic field, which confirms that the configuration (Figure 6) enables the experimental measurement of the Hall coefficient. The Hall coefficient of the bismuth nanowire enables us to evaluate carrier density and mobility experimentally. Therefore, the temperature dependence of resistivity of bismuth nanowires less than 1 μm can be described by the measurement of carrier density and mobility more directly than the calculation model of our previous study. In ition, it will be possible to measure not only Hall coefficient but also Nernst coefficient using the configuration; then, various electrical properties of bismuth nanowires can be evaluated.
A method to attach Hall electrodes on opposite sides of an individual bismuth nanowire encased in a quartz template was demonstrated using polishing, FIB processing, and carbon deposition. An accelerated Ga ion beam was used to detect the position of the nanowire in the quartz template without exposure. The quartz component covering the nanowire was then successfully removed with the Ga ion beam to locally expose the opposite side surfaces of the nanowire. Carbon thin films were then deposited in situ on the exposed wire surfaces to form electrical contacts, while avoiding oxidation of the nanowire. EDX analysis of the processed area indicated that the bismuth component remained after FIB processing.
The mobility reduction of bismuth nanowires less than 1 μm in diameter due to mean free path limitation at wire boundary will be evaluated experimentally by Hall measurement. Moreover, further investigations are planned using the configuration to examine the temperature and wire diameter dependence of the thermoelectric properties of bismuth nanowires, and the influence of the quantum effect using much smaller diameter of bismuth nanowires will be also estimated.
MM is a PhD candidate under associate professor YH in the department of engineering, Saitama University, Japan.
This research was supported in part by Grant-in-Aid for JSPS Fellows, Grant-in-Aid for Scientific Research (B) and (C), leading industrial technology development project grant funds of NEDO, Asahi Glass Foundation, Japan Aluminum Association, and TEPCO Memorial Foundation. This work was performed under the auspices of the National Institute for Fusion Science (NIFS) collaborative research (NIFS11KECA012) and NINS's Creating innovative research fields project (number NIFS08KEIN0091). This research was supported by the Nanotechnology network program (Center for Nanotechnology Network, National Institute for Material Science) of the Ministry of Education, Culture, Sports, Science and Technology.
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