Optimum Carrier Concentration in n-Type PbTe Thermoelectrics

Taking La‐ and I‐doped PbTe as an example, the current work shows the effects of optimizing the thermoelectric figure of merit, zT, by controlling the doping level. The high doping effectiveness allows the carrier concentration to be precisely designed and prepared to control the Fermi level. In addition to the Fermi energy tuning, La‐doping modifies the conduction band, leading to an increase in the density of states effective mass that is confirmed by transport, infrared reflectance and hard X‐ray photoelectron spectroscopy measurements. Taking such a band structure modification effect into account, the electrical transport properties can then be well‐described by a self‐consistent single non‐parabolic Kane band model that yields an approximate (m*T)1.5 dependence of the optimal carrier concentration for a peak power factor in both doping cases. Such a simple temperature dependence also provides an effective approximation of carrier concentration for a peak zT and helps to explain, the effects of other strategies such as lowering the lattice thermal conductivity by nanostructuring or alloying in n‐PbTe, which demonstrates a practical guide for fully optimizing thermoelectric materials in the entire temperature range. The principles used here should be equally applicable to other thermoelectric materials. Optimum carrier concentration (n*) in thermoelectric n‐PbTe is found to be dependent on both temperature (T) and density of state effective mass (m*) through n* ∼ (m*T)1.5. The validity of this model is confirmed in materials with and without band structure modification by doping, enabling a general guiding principle for designing thermoelectrics throughout the working temperature range.