After many years of study, the polymorphism of group IV elements still remains unresolved. This is due to the existence of metastable phases. On depressurisation of the group IV elements silicon and germanium from their first high pressure metallic phase, they do not return to the initial diamond phase, but form complex 4-fold coordinated high density structures.
This chapter presents complete ab initio total energy calculations on the behaviour of diamond and dense metastable 4-fold coordinated phases (known as BC8 and ST12) carbon, silicon and germanium. The effects of pressure on structure and bonding is also discussed. The calculations incorporate direct relaxation of the atomic positions under the Hellmann-Feynman forces and a search through unit cell parameters for the BC8 structure and, in the case of ST12, a full relaxation of the c/a ratio of the tetragonal unit cell is performed at each volume in order to obtain the complete pressure dependance of the unit cell.
Experiment suggests that similar structures in III-V semiconductors do not exist. For this reason ab initio calculations have been performed to try to explain why these phases are not found.
This chapter is organised as follows. A summary of the total energy calculations discussed in Chapter 2 including the conditions for convergence are given in the next section. A discussion of the BC8 and ST12 structures will be given next followed by the full pressure dependance of these structures. It is possible to extract phonon frequencies from an ab initio molecular dynamics simulation at finite temperature from the ensemble average of the velocity autocorrelation function. This method will be given in Section 4.6 and the method is applied to silicon in the diamond, BC8 and ST12 structures. This can be compared to the phonon calculations in Chapter 4 found using an empirical potential and the harmonic approximation. The electronic structure of carbon, silicon and germanium in these three structures will be discussed in the form of band structures in Section 4.7. It is found that there is a fundamental difference in the nature of the bonding between carbon and silicon or germanium which is presented in Section 4.8. Finally, an investigation into why these metastable structures are not found in III-V semiconductors will be presented in Section 4.10 in terms of a total energy calculations, molecular dynamics and a fully ab initio calculation of ionicities.