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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. [ABSTRACT FROM AUTHOR]

Wire-diameter dependencies were investigated using microwire sample arrays with diameters from 2 to 25 ¿m and polycrystalline bulk bismuth. Seebeck coefficient and resistivity were measured from 50 to 300 K. Although the temperature dependence of the Seebeck coefficients of all samples were similar to that of the bulk, the resistivity dependence of the 2-¿m-diameter microwire array sample had a small positive temperature coefficient, and was quite different from the other samples. Mobility was estimated using a simple model to identify the dependences on temperature and wire diameter. The ratio of electron mobility divided by hole mobility gradually decreased with decreasing temperature for samples with wire diameters below 6 ¿m, and electron mobility was suppressed at low temperatures, explaining the promotion of the boundary scattering. Therefore, small positive temperature coefficients of resistivity were obtained for very small diameter microwire array samples. To compare with the temperature dependence of the nanowire array samples that typically have negative temperature coefficient reported, a model for mobility was developed to represent the temperature dependence of resistivity. [ABSTRACT FROM AUTHOR]