Loa, Ingo

Hermann, Andreas

Gregoryanz, Eugene

Mcwilliams, Ryan

Hunt, Jonathan

2024-02-14T10:37:22Z

2024-02-14T10:37:22Z

2024-02-14

Many ab initio approaches for calculating anharmonic phonon dispersion relations have recently been developed, taking advantage of improvements in computational power. In this thesis, anharmonic phonons in the diamond-type semiconductors silicon and diamond are studied using two of these recently developed ab initio techniques to better understand the role of anharmonicity in these materials at elevated temperatures and pressures. The two techniques are the self-consistent phonon method as implemented in the alamode code and the temperature dependent effective potential approach implemented in the TDEP code. Both these approaches rely on density functional theory calculations to compute anharmonic phonon frequencies from first principles. The renormalisation of the zone-centre optical phonon of silicon is calculated using both methods. The TDEP approach accurately reproduces the experimentally observed temperature dependence of the zone-centre phonon, whereas alamode underestimates the renormalisation. This underestimation is determined to originate from the exclusion of certain phonon–phonon interaction processes in a series expansion central to the self-consistent phonon method. In particular, an interaction process involving three phonons is identified to contribute strongly to the anharmonic phonon renormalisation. An attempt was made to extend alamode to include this interaction, which was, regrettably, unsuccessful. The TDEP approach is then applied to diamond in the same manner as silicon. The zone-centre optical phonon is calculated and a comparison to available experimental data is made. The approach is again found to accurately reproduce the experimental data. Consequently, the TDEP approach is used to investigate the so-called quantum isotope effect in diamond. Deviations from the harmonic frequency ratio of the zone-centre phonons are used to investigate the anharmonic nature of the interatomic potential, as well as to search for an experimentally suggested “inversion” of the quantum isotope effect at high pressure. No such inversion of the quantum isotope effect is observed in the calculations made here. A detailed comparison of the effect of different exchange–correlation functionals and pseudopotentials on the density functional theory calculations is made, ultimately recommending local density approximation as the most accurate predictor of phonon frequencies in diamond. Finally, the Raman frequency of natural diamond is calculated at high temperature and pressure using the highly accurate TDEP method. Improvements are made to the stochastic sampling process, eliminating unwanted scatter from misaligned eigenvectors at degenerate points in the Brillouin zone and increasing the precision of the method. The calculated Raman frequency is used to suggest a calibration of the high-frequency edge of the Raman signal from a diamond anvil, which is used as a pressure marker in very-high-pressure experiments. The suggested calibration extends to pressures up to 1 TPa and temperatures up to 2000 K.

https://hdl.handle.net/1842/41444

http://dx.doi.org/10.7488/era/4176

en

The University of Edinburgh

phonon frequencies

harmonic approximation

temperature-dependent effective potential

TDEP method

silicon

anharmonic phonon frequencies

diamond

high pressure

pressure-dependent frequency

First-principles calculations of anharmonic phonons in diamond and silicon at high temperature and pressure

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy