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Quantum Size Effects in Bismuth Nanowires

Bismuth is a semimetal with unique electronic properties, such as a long electron mean free path and a large Fermi wavelength. FiguresStructures comparable in size to these intrinsic length scales are expected to exhibit finite-size and quantum size effects [1]. Finite-size effects involve additional electron scattering on the surface and at internal grain boundaries. Quantum size effects (QSE) lead to splitting of the energy bands into subbands. A scheme of the band structure of Bi is shown in. Bismuth exhibits an indirect overlap (E0 ~98 meV at 300 K [1]) of the electron conduction band at the L-point with the hole valence band at the T-point of the Brillouin zone. Moreover, it has a direct band gap at the L-point (~36 meV at 300 K [2]). As a consequence of subband splitting, the band edges shift away from each other, i.e., the conduction band at the L-point shifts upward in energy, while the valence bands at both the L- and at the T-points shift downwards in energy. Thus, indirect band overlap decreases, and the direct band gap at the L-point increases with diminishing structural size. For sufficiently small wire diameters, band overlap vanishes and bismuth undergoes a transition from a semimetal to a semiconductor. The plasma frequency, wP, which depends on the charge carrier density, is located at ~ 300 cm-1 for bulk Bi at room temperature. It is affected by dopants and by defects acting as additional charge carriers. In order to investigate both the QSE affecting the band gap at the L- point and the plasma frequency, spectroscopy in the mid as well as the far-infrared regimes was performed.
Our nanowires are fabricated by the so-called template method. For this purpose, polymer membranes are irradiated with heavy ions of several 100 MeV of kinetic energy. Nanometric damage trails are produced along the paths of such energetic projectiles. These tracks can be dissolved selectively by a suitable etchant. One side of the porous membrane is coated with a conductive layer which serves as cathode in the following electrochemical deposition of bismuth into the nanopores. This technique allows controlled growth of nanowires with diameters between 20 nm and several micrometers. To investigate individual nanowires by infrared spectroscopy, the polymer template is dissolved in an organic solvent. A few drops of the dispersion are deposited on a substrate transparent to infrared radiation) which is placed on the optical microscope at the IR beamline. Spectra are recorded for single wires selected employing an aperture 8 µm in diameter.
Fig. 1(a) and (b) show the infrared absorption spectra of single bismuth nanowires with diameters of 200 nm and 80 nm, respectively. The two spectra in each graph were recorded on a single-crystalline and a polycrystalline wire with the same diameters. Within the limits of experimental uncertainty, the absorption edges do not depend on wire crystallinity, but are clearly shifted to bigger wavenumbers for thinner nanowires. We ascribe this blueshift to quantum size effects increasing the band gap, i.e., raising the excitation energy in the vicinity of the L-point.
Far-infrared extinction spectra of Bi nanowires with diameters ranging from 2 µm to 600 nm are presented in Fig. 2. In this energy range, another spectral feature is detected which is also blueshifted with diminishing wire diameter. It is not yet fully understood, but we assume it to be linked to the plasma frequency, wP, because, for the wire 2 µm wide, the extinction increases at 300 cm-1, which is close to the value of wP of bulk Bi. The plasma frequency is proportional to the square root of the charge carrier density, n, i.e., a blueshifting wp involves an increasing n. Since the wires were all grown under the same conditions, conventional doping is excluded. However, defects at boundaries, in particular on the surface of the nanowires, may act as dopants increasing n. During dissolution of the template, the wires are in contact with an organic solvent and, subsequently, exposed to the atmosphere. These preparation steps may create surface defects due to chemical reactions with a solvent or oxidation in air. As the surface-to-volume ratio increases with decreasing diameter, the influence of surface defects become more important for thinner wires and, in turn, wP is blueshifted with diminishing diameter.


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