Raman scattering from TiNx (0.67 ≤ x ≤ 1.00) single crystals grown on MgO(001)

Epitaxial NaCl-structure δ-TiNx(001) layers, with x ranging across the single-phase compound field from 0.67 to 1.00, are grown on MgO(001) and analyzed by Raman spectroscopy. All samples, including stoichiometric TiN(001), exhibit first-order Raman peaks, which are forbidden by the Oh symmetry of NaCl-structure compounds. Thus, even stoichiometric TiN contains point defects, primarily N and Ti vacancies, consistent with previous electronic transport measurements. However, the presence of a well-resolved second-order longitudinal acoustic line at 615 cm–1 shows that the defect concentration is relatively low. The positions of the first-order acoustic lines are in good agreement with values obtained from calculated phonon density of states. As the N/Ti ratio x in TiNx and, hence, the number n of valence electrons per formula unit (n = 9 for stoichiometric TiN) decreases, the first-order acoustic lines shift to higher frequencies, due to the corresponding decrease in phonon anomalies associated with the acoustic branch. This is in agreement with the observed increase in the intensities of the first-order acoustic phonon peak with decreasing x, characteristic of a higher average N vacancy concentration adjacent to Ti atoms. However, the presence of antisite defects is also required to explain the frequency shift of the optical modes in under-stoichiometric TiNx.