Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study

With a motivation to understand microscopic aspects of ScN, ZrN, and HfN relevant to the thermoelectric properties of nitride metal/semiconductor superlattices, we determine their electronic structure, vibrational spectra and thermal properties using first-principles calculations based on density functional theory with a generalized gradient approximation of the exchange correlation energy. We find a large energy gap in the phonon dispersions of metallic ZrN and HfN, but a gapless phonon spectrum for ScN spanning the same energy range, this suggests that a reduced thermal conductivity, suitable for thermoelectric applications, should arise in superlattices made with ScN and ZrN or ScN and HfN. To obtain an electronic energy band gap of ScN comparable to experiment, we use a Hubbard correction with a parameter U (=3.5 eV). Anomalies in the acoustic branches of the phonon dispersion of ZrN and HfN, manifested as dips in the bands, can be understood through the nesting of Fermi surface determined from our calculations. To connect with transport properties, we have determined effective masses of ScN and determined their dependence on the U parameter. Using the relaxation time approximation in the Boltzmann transport theory, we estimate the temperature dependence of the lattice thermal conductivity and discuss the chemical trends among these nitrides.