Thermoelectric properties for single crystal bismuth nanowires using a mean free path limitation model

Abstract

We present a mean free path limitation model to describe the temperature dependence of both resistivity and Seebeck coefficient for bismuth nanowire. Since the mobility of carriers for bismuth nanowire was limited due to dominant collision at wire boundary, the effective mobility for each carrier was estimated using cyclotron mass, appropriate band structure, and temperature dependence of Fermi energy from 4 to 300 K. Then, the resistivity and the Seebeck coefficient were calculated by using carrier density reported for bulk single crystal. In addition, an individual single-crystal bismuth nanowire sample (725 nm diameter and 2.37 mm length) grown into a quartz template was prepared to estimate the model, and the measurements were also performed. The temperature dependences of not only resistivity, but also Seebeck coefficient were quantitatively and qualitatively in very good agreement in the whole temperature region by using its crystal orientation measured from Laue measurement. We conclude that the mean free path limitation model proposed made us understand the temperature dependences of single-crystal bismuth nanowire without a finite size effect.