Electron/phonon coupling in group-IV transition-metal and rare-earth nitrides
Transport electron/phonon coupling parameters and Eliashberg spectral functions α{sub tr}{sup 2}F(ℏω) are determined for group-IV transition-metal (TM) nitrides TiN, ZrN, and HfN, and the rare-earth (RE) nitride CeN using an inversion procedure based upon temperature-dependent (4 < T < 300 K) resistivity measurements of high-crystalline-quality stoichiometric epitaxial films grown on MgO(001) by magnetically-unbalanced reactive magnetron sputtering. Transport electron/phonon coupling parameters λ{sub tr} vary from 1.11 for ZrN to 0.82 for HfN, 0.73 for TiN, and 0.44 for CeN. The small variation in λ{sub tr} among the TM nitrides and the weak coupling in CeN are consistent with measured superconducting transition temperatures 10.4 (ZrN), 9.18 (HfN), 5.35 (TiN), and <4 K for CeN. The Eliashberg spectral function describes the strength and energy spectrum of electron/phonon coupling in conventional superconductors. Spectral peaks in α{sup 2}F(ℏω), corresponding to regions in energy-space for which electrons couple to acoustic ℏω{sub ac} and optical ℏω{sub op} phonon modes, are centered at ℏω{sub ac} = 33 and ℏω{sub op} = 57 meV for TiN, 25 and 60 meV for ZrN, 18 and 64 meV for HfN, and 21 and 39 meV for CeN. The acoustic modes soften with increasing cation mass; optical mode energies remain approximately constant for the TM nitrides, but are significantly lower for the RE nitride due to a lower interatomic force constant. Optical/acoustic peak-intensity ratios are 1.15 ± 0.1 for all four nitrides, indicating similar electron/phonon coupling strengths α{sub tr}(ℏω) for both modes.