## Abstract

In analyzing zT improvements due to lattice thermal conductivity (κ_{L}) reduction, electrical conductivity (σ) and total thermal conductivity (κ_{Total}) are often used to estimate the electronic component of the thermal conductivity (κ_{E}) and in turn κ_{L} from κ_{L} = ∼ κ_{Total} - LσT. The Wiedemann-Franz law, κ_{E} = LσT, where L is Lorenz number, is widely used to estimate κ_{E} from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10^{-8} WΩK^{-2} (degenerate limit). However, significant deviations from the degenerate limit (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10^{-8} WΩK^{-2} for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: L = 1. 5 + exp - | S | 116 (where L is in 10^{-8} WΩK^{-2} and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si_{0.8}Ge_{0.2} where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity.

Original language | English |
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Article number | 041506 |

Journal | APL Materials |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2015 |