Raman spectrometry study of phonon anharmonicity of hafnia at elevated temperatures

Raman spectra of monoclinic hafnium oxide $\left({\text{HfO}}_2\right)$ were measured at temperatures up to 1100 K. Raman peak shifts and broadenings are reported. Phonon dynamics calculations were performed with the shell model to obtain the total and partial phonon density of states, and to identify the individual motions of Hf and O atoms in the Raman modes. Correlating these motions to the thermal peak shifts and broadenings, it was found that modes involving changes in oxygen-oxygen bond length were the most anharmonic. The hafnium-dominated modes were more quasiharmonic and showed less broadening with temperature. Comparatively, the oxygen-dominated modes were more influenced by the cubic term in the interatomic potential than the hafnium-dominated modes. An approximately quadratic correlation was found between phonon-line broadening and softening.

Figure 1

(Color online) (a) Raman spectra of hafnia at temperatures from 300 to 1106 K, with laser power at 200 mW, exposure time of 30 s and at least 10 accumulations of the spectra. Peaks are numbered for reference. The features between peaks 5 and 6 are artifacts. (b) Partial and total phonon density of states of hafnia at room temperature, calculated using GULP. Hafnium contributes much more strongly to the lower-energy modes while oxygen contributes to the higher-energy modes.

Figure 2

(Color online) Temperature-dependent Raman mode softening. At 300 K, modes are evenly spaced in the figure to facilitate comparison of thermal shifts. Blue (dark gray) and red (light gray) represent metal and oxygen-dominated modes, respectively. Lines are linear fits to the data points. Note that second and third modes are decoupled above 700 K, where the line between the 2nd and 3rd modes represent an average peak position. Most error bars are negligibly small. Peaks from the 13th to 18th were not sufficiently distinct to allow fitting at high temperature.

Figure 3

(Color online) Temperature-dependent peak broadening. Blue (dark gray) and red (light gray) represent metal- and oxygen-dominated modes, respectively. Lines are linear fits to the data.

Figure 4

(Color online) (Upper) Two views of the crystal structure of monoclinic hafnia. Red (light gray) and blue (dark gray) spheres denote oxygen and hafnium atoms, respectively. Left: skeletal; right: space-filled model, scaled for ionic radii. Note that the majority of the volume is composed of oxygen while hafnium fits loosely between oxygen planes. (Lower) Representative Raman-active normal modes in one unit cell. Number 3 and 4 modes are hafnium dominated. Number 6 and 12 are oxygen dominated. These modes were well resolved through the whole range of temperatures. Lengths of arrows are proportional to the contribution of vibration from each atom.

Figure 5

(Color online) Broadening vs softening of Raman modes. Blue (dark gray) and red (light gray) squares are metal and oxygen modes, respectively. The dashed line is the boundary separating metal-dominated modes and oxygen-dominated modes. The solid line is a fitting to the points, showing that the relation between absolute linewidth broadening and absolute peak softening is of power 2.1, close to quadratic.