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.

Electronic Properties of Bi-Sn Diluted Alloys

“…Fermi level goes down with increase of dopant concentration. This leads to dominance of holes at low temperatures and explains shift of Hall and Seebeck coefficient to positive values [12]. The increase of electron concentration with temperature determines the fact that the Hall coefficient of doped samples decrease by absolute value at room temperature (Fig.5).…”

Frequency dependent figure-of-merit in cylindrical thermoelectric nanodevices

“…(11) we assume that both the heat flux, and the electrical current may only flow longitudinally through the system. Moreover, in the present case, we assume that the bulk profiles for the different diffusive fluxes are given by…”

“…[3] (see Eqs. (11) therein) in the spirit of the Maxwell-Cattaneo equation (3), wherein a relaxational term (including the time derivative of the heat flux) is added to the usual Fourier heat-transport equation. Though in the usual applications the term τ ðpÞ w D t q ðpÞ w is vanishingly small, for high frequencies it may be obviously important, and therefore its incorporation in Eq.…”

“…For instance, whenever the characteristic size of the system is comparable to the mean-free path (mfp) ℓ of the different heat carriers (phonons, electrons, holes, etc.) it is known that a thermal conductivity reduction can be realized over Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physb a wide temperature range, or the power factor can be increased at the same time by increasing ϵ more than σ e is decreased [10,11].…”

Polycrystalline bismuth films: Correlation between grain structure and electron transport

“…To take into account a nonparabolicity of the electron energy dispersion law, the Lax model was used for describing the partial Seebeck coefficient for electrons [5,15] …”