No abstract

A limiting mean free path was considered in order to better understand the temperature and wire diameter dependence of the resistivity and Seebeck coefficient of bismuth microwire and nanowire samples. The mean free path limited mobility was numerically calculated from experimentally measured mobility in a bulk bismuth sample, and the electron and hole mobilities were dramatically decreased to a 10 μm mean free path. Therefore, the temperature dependence of resistivity in very thin wire was quite different from that of a bulk sample, which had a positive temperature coefficient. The calculations showed that the temperature coefficient decreased gradually with decreasing mean free path, and the coefficient became negative for a mean free path of less than 1 μm at about 150 K. The Seebeck coefficient was also calculated, but showed only a weak dependence on mean free path compared with the resistivity. Experimental comparisons were made to previous measurements of bismuth microwire or nanowire samples, and the temperature and wire diameter dependencies of the resistivity and Seebeck coefficient were qualitatively and quantitatively in very good agreement. Therefore, the temperature dependencies of nanowire samples over 850 nm in diameter were well described using the mean free path limitation.

In this study, the electrical resistivity and Seebeck coefficient of bismuth nanowires, several hundred nanometers in diameter, are calculated using the Boltzmann equation in the relaxation time approximation. The three-dimensional density of states and properties of single-crystalline bulk bismuth, such as carrier density, effective mass, and mobility, are used in the calculation without considering the quantum size effect. The relaxation times of the electrons and holes are calculated using Matthiessen's rule considering the carrier collisions at the wire boundary. The temperature, crystal orientation, and diameter dependence of the electrical resistivity and Seebeck coefficient are investigated. The calculation demonstrates that the electrical resistivity increases gradually with decreasing wire diameter, and the temperature coefficient of the electrical resistivity varies from positive to negative at low temperatures for thin wires with diameters less than approximately 500 nm. The diameter dependence of the electrical resistivity varies with the crystal orientation; the increase along the bisectrix axis is larger than that along the binary and trigonal axes. The temperature dependence of the Seebeck coefficient also strongly depends on the crystal orientation. The absolute value of the negative Seebeck coefficient along the bisectrix axis rapidly decreases with decreasing diameter and even changes sign from negative to positive at low temperatures despite the charge neutrality condition, while the Seebeck coefficients along the binary and trigonal axes do not differ significantly from those of single-crystalline bulk bismuth. We conclude that the thermoelectric properties of bismuth nanowires strongly depend not only on the wire diameter but also on the crystal orientation.