Optical study of the stoichiometry-dependent electronic structure of ${\mathrm{TiC}}_{\mathit{x}}$, ${\mathrm{VC}}_{\mathit{x}}$, and ${\mathrm{NbC}}_{\mathit{x}}$

The stoichiometry-dependent bulk electronic structure has been studied by optical spectroscopy for single crystals of ${\mathrm{TiC}}_{\mathit{x}}$ with x=0.95 and 0.70, ${\mathrm{VC}}_{\mathit{x}}$ with x=0.86 and 0.76, and ${\mathrm{NbC}}_{\mathit{x}}$ with x=0.93, 0.84, and 0.71. The reflectance was measured in the energy range 0.5–40 eV for all of the samples and up to 100 eV for ${\mathrm{TiC}}_{0.95}$, ${\mathrm{VC}}_{0.86}$, and ${\mathrm{NbC}}_{0.93}$. By correcting for the surface-roughness effect using the measured roughness values, the data were Kramers-Kronig analyzed to obtain the dielectric function and related functions. The observed interband transitions have been interpreted on the basis of existing calculations for the energy-band structure and partial density of states. The main peaks above 4 eV were assigned to transitions at and around the X and Q portions in the Brillouin zone. Their shifts to lower energy and reduced intensities with decreasing carbon concentration are discussed in terms of p-d hybridization. Features arising from transitions involving the initial or final states near the Fermi level were observed in the low-energy region.