Experimental determination of lattice thermal conductivity and Lorenz number as functions of temperature for n-type PbTe

Abstract

The thermal conductivity of materials, κ, consists of two components, i.e. the lattice contribution from phonon transport, κL, and the electrical contribution from electron/hole transport, κE, and κ = κL + κE. The Lorenz number (L) relates κE to electrical conductivity, σ, and temperature, T, as L = κE/σT. In the analyses of thermoelectric properties on non-degenerate semiconductors, L has commonly been adopted as 2.44 × 10−8 W/S-K2 to derive the lattice thermal conductivity from the measured thermal and electrical conductivity. However, this value was obtained using a model of free electron gas and, thus, is only valid for metals or degenerate semiconductors. In this study, the thermal conductivity and electrical conductivity have been measured at 13 different temperatures between 37 and 615°C on about 100 n-type doped PbTe samples processed by melt growth of directional solidification, which resulted in the wide ranges of data values. By analyzing the plot of thermal conductivity vs. electrical conductivity with linear regression, the lattice thermal conductivity and Lorenz number have been experimentally determined from the intercept and slope at each temperature for n-type PbTe. The former values represent the intrinsic case for the lattice thermal conductivity, i.e. the heat conduction of an ideal PbTe lattice without any extrinsic electrical contribution, and the latter values give the relationship between electrical conductivity and its contribution to thermal conductivity for the n-type PbTe material.