A carrier scattering process in polycrystalline bismuth at 300 K has been investigated by measuring its Seebeck coefficient, electrical resistivity, magneto-resistivity, Hall coefficient, and Nernst coefficient and solving the Boltzmann equation under the relaxation time and low magnetic field approximations. All measurements were performed using identical bulk bismuth samples; as a result, the scattering process, carrier density, carrier mobility, and Fermi energy were estimated. It was found that acoustic deformation potential scattering was a dominant process even at a temperature of 300 K. In addition, a new measurement method (called a quasi-AC method) was proposed to determine the Nernst coefficient more quickly as compared to the conventional method. It was also shown that the difference in the Nernst coefficients estimated by the two methods affected other material parameters (such as carrier density, mobility, and Fermi energy) only slightly; however, the accurate determination of the Nernst coefficient was required for elucidating the scattering mechanism and estimating the Fermi energy of the studied material.

Temperature dependence of dimensionless figure of merit zT of a Π-shaped thermoelectric module using bismuth-telluride materials was estimated on the basis of a theory of impedance spectroscopy, which is able to ascertain zT directly using only electrometric measurements from the frequency dependence of the impedance without any calorific measurement. The dependence of the module was measured from 5 mHz to 10 kHz with precise temperature control. From the analysis, the ohmic resistance, the impedance due to the Peltier effect, and the characteristic heat frequency at 300 K were determined under two different boundary conditions (the suspended and fixed conditions of a heat bath). A comparison between these boundary conditions revealed that their difference led to a slight change in the frequency dependence of the measured impedance due to the variation in the heat capacity of the module, and the estimated dimensionless figure of merit was identical for the two boundary conditions (zT ≈ 0.839 at 300 K). The temperature dependence of the dimensionless figure of merit of the module was successfully measured from 20 K to 300 K. The dependence of the thermal conductivity was also estimated with an assumed Seebeck coefficient from the definition of zT. In addition, a new method using only two impedances with repeatability was proposed and demonstrated to estimate the dimensionless figure of merit precisely (zT ≈ 0.845 at 300 K).

The dependence of the scattering process on temperatures ranging from 50 to 300 K was comprehensively investigated by measuring five transport coefficients (resistivity, magnetoresistivity, Seebeck coefficient, Hall coefficient, and Nernst coefficient) using polycrystalline bulk bismuth. The values of five physical properties (carrier density, electron and hole mobilities, and electron and hole Fermi energies) were calculated assuming that carrier scattering ranged from acoustic deformation potential scattering to ionized impurity scattering. The accompanying mean-free paths of carriers were also evaluated using the calculated Fermi energy and the effective mass tensor. The mean-free path and grain size (typically several micrometers) obtained from electron backscattered diffraction helped narrow the distribution range of the different scattering processes. Thus, the physical properties, including temperature dependence of the scattering processes, were recalculated, and realistic temperature dependence of the electron mobility was assumed. Quantitative and qualitative analyses showed that near room temperature, acoustic deformation potential scattering dominated, which changed to ionized impurity scattering when the estimated mean-free path exceeded 1 μm. This indicated that the scattering process of polycrystalline bulk bismuth depends on the grain size when the measurement results of the Nernst coefficient related to the scattering process are directly used. The bandgap energy of bismuth was also calculated, and the temperature dependence of the scattering process was estimated. The results showed that the temperature dependence tendency of bandgap energy is similar to that described in the literature. Finally, this study provides the temperature dependence of the physical properties of polycrystalline bismuth.

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The thermal conductivity (κ) and specific heat (Cp) of a thermoelectric element consisting of Bi2Te3 (SRM 3451) were obtained by impedance spectroscopy and using only electrometric measurements. The dimensionless figure of merit (zT) was successfully estimated by the four-probe method from the frequency dependence of the impedance, and the result was compared with that obtained using the two-probe method. The calculated values of zT and resistivity were 0.577 and 13.4 µΩ m, respectively, at 300 K, which allowed us to obtain κ = 2.11 W/(m K) and Cp = 165 J/(kg K) by using a Seebeck coefficient of −233 µV/K, a thermal diffusivity of 1.68 mm2/s, and a mass density of 7.60 g/cm3 from our earlier electrometric measurements. The calculated κ and Cp are quite reasonable when compared to reported values. We thus conclude that, without relying on calorimetric measurements, impedance spectroscopy is a powerful technique for determining not only zT but also the thermal properties of thermoelectric materials via the Peltier effect.