Conductivity-limiting bipolar thermal conductivity in semiconductors

Abstract

Intriguing experimental results raised the question about the fundamental mechanisms governing the electron-hole coupling induced bipolar thermal conduction in semiconductors. Our combined theoretical analysis and experimental measurements show that in semiconductors bipolar thermal transport is in general a "conductivity-limiting" phenomenon, and it is thus controlled by the carrier mobility ratio and by the minority carrier partial electrical conductivity for the intrinsic and extrinsic cases, respectively. Our numerical method quantifies the role of electronic band structure and carrier scattering mechanisms. We have successfully demonstrated bipolar thermal conductivity reduction in doped semiconductors via electronic band structure modulation and/or preferential minority carrier scatterings. We expect this study to be beneficial to the current interests in optimizing thermoelectric properties of narrow gap semiconductors.

Figure 1

(a) Numerically calculated total reduced kinetic energy for holes and electrons, hole (majority carrier) concentration, and electron (minority carrier) partial electrical conductivity as a function of the reduced Fermi level (ξ_p); (b) calculated κ_b as a function of minority carrier partial electrical conductivity σ_n. The dashed line is a guide for eye. The calculations were carried out for p-type skutterudites (R_xFe₃NiSb₁₂) with E_g = 0.2 eV, m_p^* = 5m₀, m_n^* = 2m₀, at 800 K.

Figure 2

Room temperature carrier mobility as a function of carrier concentration for (a) p-type and (b) n-type R_x(Fe,Co,Ni)₄Sb₁₂ skutterudites. The solid lines are least squares fits to the data using Eq. (5). Data used here are taken from Refs. , , , , , , , , , , , , , and , , , , , , , , , , , , .

Figure 3

(a) Experimental (symbols) and fitted (solid lines) bipolar thermal conductivity of intrinsic Si single crystal and degenerate Yb_0.7Fe₃NiSb₁₂ vs. T. (b) Experimental (κ_b^Exp) and calculated (κ_b^Cal) bipolar thermal conductivity for intrinsic Si and Ge single crystals, and degenerate Bi₂Te₃-based zone melted (ZM) compounds and p-type skutterudites at various temperatures. The dashed line represents κ_b^Cal = κ_b^Exp.

Figure 4

(a) The density of states around the CBM for BaCo₂Fe₂Sb₁₂ and BaCo₃FeSb₁₂. (b) Bipolar thermal conductivity at 800 K as a function of hole (majority carrier) concentration for Ba_xCo₂Fe₂Sb₁₂ and Ba_yCo₃FeSb₁₂. The lines in (b) are fits to the data using different minority carrier effective mass values.

Figure 5

(a) The calculated electron wavelength, and the product of the Fermi-Dirac distribution function and electronic density of states f(E) g(E) vs. energy with the zero point corresponding to the conduction band minimum (E_c). (b) The experimental and modeled bipolar thermal conductivity vs. temperature, for p-type zone melted (ZM) and nanostructured (MS-SPS) Bi_0.5Sb_1.5Te₃. The inset is a TEM picture of the MS-SPS bulk sample which shows 10–50 nm nanoprecipitates. (The room temperature minority carrier mobilities of ZM and Nano samples are μ_n = 4095 and 1115 cm²/V-s, respectively).