Mean free path limitation of thermoelectric properties of bismuth nanowire

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.

Spin-orbit interaction and phase coherence in lithographically defined bismuth wires

“…Interest in Bi originates from its highly anisotropic electron Fermi surface, characterized by a low carrier density and a long mean free path, moreover possessing large spin-orbit interaction (SOI), rendering it an excellent platform for observing quantum transport in the strong SOI regime. Quantum transport in Bi films has been extensively studied [2][3][4][5][6][7][8][9] as have been self-assembled wires [10][11][12][13][14][15] . In particular, spin-dependent quantum transport in the form of weak-antilocalization has been observed in Bi films [3][4][5][6][7][8][9] and a nanowire array 14 .…”

Thermoelectric Properties of a 593-nm Individual Bismuth Nanowire Prepared Using a Quartz Template

“…For example, the presence of Sn in bulk bismuth was found to cause the mobility to decrease dramatically in the low-temperature region. 28 However, based on our previous measurements and calculations, 18 the temperature dependence of the resistivity for narrow wire samples does not depend on the mobility of the bulk near 0 K, but instead depends strongly on the wire diameter. Thus, the prepared nanowire sample contains a small amount of contamination, making it possible to change the sign of the Seebeck coefficient in the low-temperature region.…”

“…In a previous report, 18 we introduced a two-carrier model with a limitation placed on the mean free path. The mobility of electrons (l n ) and holes (l p ) in the nanowire sample is then numerically calculated under these conditions.…”

“…To understand these temperature dependences, we introduced a model based on constraints placed on the mean free path of carriers, which affects the mobility, due to the boundary conditions imposed by the template. 18 Comparison between the experimental data and the results of numerical calculations revealed that this model could account for both the reduction of the temperature coefficient of resistivity and the temperature dependence of the Seebeck coefficient.…”

“…[10][11][12][13][14][15][16][17][18][19] The resistivity and the Seebeck coefficient of an 850-nm-diameter bismuth nanowire were measured and found to be approximately 1.31 lX m and À57 lV/K at 300 K, respectively. 17 These values were quite similar to those of a bulk sample at 300 K; however, the temperature dependence of the resistivity was quite different from that of bulk bismuth, which always exhibits a positive temperature coefficient.…”