Evaluation of structural,electronic, thermoelectric,and optical results of C-doped HfO2 by first-principle's investigation

In this work, we report the ab initio numerical simulation investigation on the crystal lattice, electronic structure, optical, and transport properties of pure and C-doped crystalline hafnium dioxide (c-HfO₂) using FP-LAPW method. Different exchange correlation functionals like generalized gradient approximation (GGA) of PBE-sol and Tran and Blaha's modified Becke-Johnson exchange potential (mBJ) within density functional theory have been used. Two kinds of defects in cubic pure HfO₂ have been investigated: one is substitution of Hf atom by C impurity and other substitution of O atom by C impurity in crystalline HfO₂. The computed results indicate that impurity energy bands as a result of 2p states of C are found to present in the band gap of c-HfO₂. Few of these bands are present at the conduction band minimum, which results to a noteworthy band gap contraction, and hence electrons close to Fermi level get transferred in doped c-HfO₂. We have also analysed the dielectric function, absorption coefficient, optical conductivity, optical function, electron energy loss, and reflectivity for both pure HfO₂ and doped with C. Furthermore, the temperature-dependent transport properties of C-doped HfO₂ are also discussed in terms of Seeback coefficient, thermal conductivities, electronic conductivities, power factor, and figure of merit in the temperature range 0 to 1200 K. The calculated value of PF for pure HfO₂ was found to increase from 0.01 × 10¹² WK^?2m^?1s^?1 at 50 K to 1.79 × 10¹² WK^?2m^?1s^?1 at 1200 K and for HfO_{2(1 ? x)}C_x it was found to increase from 0.06 × 10¹² WK^?2m^?1s^?1 at 50 K to 0.25 × 10¹² WK^?2m^?1s^?1 at 1200 K.