Phonon Thermodynamics and Elastic Behavior of GaN and GaAs at High Temperatures and Pressures

The work herein studies how high temperatures and pressure impact the properties of four materials: two phases of Gallium Nitride (GaN) and two phases of Gallium Arsenide (GaAs). The particular phases we study are the wurtzite and zinc blende phases of each chemical composition. The properties we study concern (1) the phonon thermodynamics and (2) the elastic behavior. In particular, phonons were calculated at simultaneously elevated temperature and pressure, and elastic constants were calculated as functions of pressure at 0 K. Our studies of phonon thermodynamics included comparing the results of phonon calculations accounting for full temperature effects to the results of a quasiharmonic approximation (QHA) for each material, allowing us to assess the importance of explicitly anharmonic contributions to the phonons with changing temperature and pressure. In GaN, the QHA gave reasonable results for the temperature dependence of the phonon DOS at zero pressure, but unreliably predicted the combined effects of temperature and pressure. Pressure was found to change the explicit anharmonicity, altering the thermal shifts of phonons, and more notably qualitatively changing the evolution of phonon lifetimes with increasing temperature. These effects were largest for the optical modes, and phonon frequencies below approximately 5 THz were adequately predicted with the QHA. In GaAs, the QHA failed to account for temperature-induced phonon frequency shifts at all pressures. As in GaN, the QHA was not able to predict the combined effects of temperature and pressure. In GaAs, the QHA clearly became less reliable with elevated pressure. In particular, the number of three-phonon processes increased with pressure, thereby increasing the temperature-driven broadening of phonon spectral lineshapes. So, why did pressure change the possible three-phonon processes in both GaN and GaAs, but cause them to net increase in GaAs? In all materials, the frequencies of phonon branches were sensitive to pressure to varying degrees. Showing the greatest contrast, transverse acoustic modes in all four materials softened with increasing pressure, whereas all other modes stiffened, albeit at different rates. If the frequencies of all modes scaled uniformly with pressure, we might expect that phonon decay channels consisting of equivalent input and output total phonon frequencies would persist independent of pressure; non-uniform frequency scaling, however, destroys some phonon decay channels and creates others in order to conserve energy. The dissimilar atomic masses of Ga and N create a phonon bandgap in GaN that increased with pressure. The increasing phonon bandgap frequently pushed some of the high frequency optical modes out of range of previously available down-conversion processes, ultimately causing GaN to become more quasiharmonic with pressure. More similar atomic masses in GaAs, however, prevent GaAs from exhibiting a true phonon bandgap; in this case, pressure was not able to drive the acoustic and optical branches away from each other, and instead created more opportunities for conversion. Our understanding of the elastic behavior of each material derived from both calculations of the elastic constants and from additional information we could extract from the phonons. We used elastic constants to study elastic anisotropy and to predict the onset of elastic instability using the Born stability criteria. In GaN, elastic anisotropy increased with pressure until reaching elastic instabilities at 65 GPa (wurtzite) and 40 GPa (zinc blende). In GaAs, elastic anisotropy again increased with pressure through the onset of lattice instability, but the Born stability criteria failed to accurately predict this instability. Instead, pressure caused instabilities of shorter-wavelength transverse acoustic modes in both phases of GaAs that preceded the onset of instability predicted by the Born stability criteria, which depend on elastic constants and thereby only long wavelength phonons. In particular, pressure drove the frequencies of shorter-wavelength transverse acoustic phonon instabilities down until they reached 0 THz, inducing instability at 18 GPa (wurtzite) and 20 GPa (zinc blende). Interestingly, temperature caused a significant stabilization of these phonon modes, however, slowing their softening with pressure.