The elastic constants c 11 and c 44 of single-crystal NaCl-structure ␦-TiN x ͑001͒ layers, with x ranging from 0.67 to 1.0, were determined using sound velocity measurements. Picosecond ultrasonic optical pump/probe techniques were employed to generate and detect longitudinal sound waves and surface acoustic waves ͑SAW͒ in order to obtain c 11 ͑x͒ and c 44 ͑x͒, respectively. SAW generation was achieved by depositing a periodic series of Al bars on the TiN x ͑001͒ layers to spatially modulate the surface reflectivity. c 11 and c 44 were found to decrease continuously from 626 and 156 GPa with x = 1 to 439 and 92 GPa with x = 0.67. The Voit-Reuss-Hill average aggregate elastic moduli E VRH ͑x͒ obtained from our measured c 11 ͑x͒ and c 44 ͑x͒ values are in good agreement with previous TiN x ͑001͒ nanoindentation results.

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The effects of lanthanum incorporation into HfO2 dielectrics were studied using first-principles total energy calculations. The author’s computational result clearly showed that the formation energy of a neutral oxygen vacancy (VO0) in the vicinity of substitutional La atoms at Hf sites is 0.7eV larger than that in pure HfO2, indicating that the concentration of VO0’s is drastically reduced by La incorporation. This effect is understood to be caused by the decrease in the local dielectric constant κL around La atoms due to the strong ionic character of the La–O bond compared to the Hf–O bond.

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