Electronic Properties of Bismuth Nanowires
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Electronic Properties of Bismuth Nanowires Stephen B. Cronina, Yu-Ming Linb, Oded Rabinc, Marcie R. Blackb, Gene Dresselhausd, and Mildred S. Dresselhausa,b a Department of Physics, bDepartment of Electrical Engineering and Computer Science, c Department of Chemistry, and dFrancis Bitter Magnet Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139
ABSTRACT The pressure filling of anodic alumina templates with molten bismuth has been used to synthesize single crystalline bismuth nanowires with diameters ranging from 7 to 200nm and lengths of 50µm. The nanowires are separated by dissolving the template, and electrodes are affixed to single Bi nanowires on Si substrates. A focused ion beam (FIB) technique is used first to sputter off the oxide from the nanowires with a Ga ion beam and then to deposit Pt without breaking vacuum. The resistivity of a 200nm diameter Bi nanowire is found to be only slightly greater than the bulk value, while preliminary measurements indicate that the resistivity of a 100nm diameter nanowire is significantly larger than bulk. The temperature dependence of the resistivity of a 100nm nanowire is modeled by considering the temperature dependent band parameters and the quantized band structure of the nanowires. This theoretical model is consistent with the experimental results.
INTRODUCTION Bismuth is an interesting material to study on the nanoscale because bulk Bi has very small effective mass carriers (mass components as small as 0.001me), highly anisotropic carrier pockets (ml/mt ~ 200) and a very long mean free path (~0.4mm at 4K and ~100nm at 300K). These bulk properties lead to a very pronounced quantum behavior that can be observed in nanowires of relatively large diameter. The electronic band structure of Bi is shown in Figure 1. The dashed curves represent the electronic bands in bulk Bi, where the T-point valence band overlaps with the L-point conduction band by ∆0=38meV at 77K, making Bi a semimetal. The solid curves represent the quantized subbands in a Bi nanowire, where the spacing between the subbands is approximately 2h 2π m * d 2 , where m* and d are the effective mass and wire diameter, respectively. As the diameter of the nanowire gets smaller, the spacing between the subbands increases. Thus for small enough wire diameters, the L-point conduction band no longer overlaps with the T-point valence band, and the material becomes a semiconductor with a bandgap. This is known as the semimetal-to-semiconductor transition. Detailed calculations of these subband energies have been carried out by solving Schrödinger’s equation numerically for a circular wire cross-section [1]. Since the energies of the subband separations go as 1/m*, the small effective masses in Bi yield very large quantized subband energy separations, even for relatively large wire diameters. In a detailed calculation [1], the critical diameter for the semimetal-to-semiconductor transition was found to be 49nm (at 77K) B2.4.1
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