Theoretical modeling of electrical resistivity and Seebeck coefficient of bismuth nanowires by considering carrier mean free path limitation

Abstract

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.