Carrier concentration mediated enhancement in thermoelectric performance of various polymorphs of hafnium oxide: a plausible material for high temperature thermoelectric energy harvesting application

The optimization of figure of merit by tuning carrier concentrations is an effective way to realize efficient thermoelectrics (TEs). Recently, the feasibility of high p -type carrier concentration (order of ∼10 22 cm −3 ) is experimentally demonstrated in various polymorphs of hafnium oxide (HfO 2 ). In light of these studies, using the first-principles calculation combined with the semi-classical Boltzmann transport theory and phonon dynamics, we realized high TE performance in various polymorphs of HfO 2 in a range of carrier concentrations at high temperatures. The phonon dispersion calculations confirm the dynamical stability of all polymorphs. The observed values of the Seebeck coefficient are 945.27 mV K −1 , 922.62 mV K −1 , 867.44 mV K −1 , and 830.81 mV K −1 for tetragonal ( t) , orthorhombic ( o ), monoclinic ( m) , and cubic ( c) phases of HfO 2 , respectively, at 300 K. These values remain positive at all studied temperatures which ensures the p -type behaviour of HfO 2 polymorphs. The highest value of electrical conductivity (2.34 × 10 20 Ω −1 m −1 s −1 ) observed in c -HfO 2 at 1200 K, and the lowest value of electronic thermal conductivity (0.37 × 10 15 W mK s −1 ) observed in o -HfO 2 at 300 K. The lattice thermal conductivities at room temperature are 5.56 W mK −1 , 2.87 W mK −1 , 4.32 W mK −1 , and 1.75 W mK −1 for c-, m-, o - and t - HfO 2 , respectively which decrease to 1.58 W mK −1 , 0.92 W mK −1 , 1.12 W mK −1 , 0.53 W mK −1 at 1200 K for respective phases. The low lattice thermal conductivities lead to the high values of the figure of merit, i.e. 0.97, 0.87, 0.83, and 0.77 at 1200 K for the m-, o-, t -, and c - HfO 2 , respectively, at the optimized carrier concentrations (∼10 21 cm −3 ). The predicted optimized carrier concentrations for various phases are in close agreement with the experimental reports. The estimated high figure of merit can make HfO 2 a potential material for TE energy harvesting applications at elevated temperatures.