Ab-initio study of Si-Ge alloys and ultra-thin superlattices

This thesis is devoted to the study of SixGe1-x alloys and ultra-thin superlattices, using the state-of-art density functional theory and norm-conserving pseudopotentials. The present work is the only available ab-initio study for Si-Ge alloys. For the alloy phase, we have introduced a model for the microscopic atomic structure based on the tetrahedron approximation. Nine different ordered structures (each corresponding to a different configuration of the tetrahedra) have been studied. These ab-initio calculations allowed us to study the structural properties (lattice parameter, bond length alternation and their variation with x), bond ionicity and its dependence on the chemical environment, stability of the bulk ordered structures and (assuming completely random distribution of atoms at the lattice site) the energy of mixing of SixGe1-x alloys. ·Using our previously calculated formation energies of the tetrahedra configurations, and solid state statistical mechanical methods (cluster variation method and a modified quasi-chemical approximation), the entropy, enthalpy, Gibbs free energy and other thermodynamical functions are calculated from first-principles, as functions of x and temperature. Since bulk ordered structures are found to be unstable, only disordered alloys have been studied. From the calculated free energy of mixing, the phase diagram has been constructed and the critical temperature is deduced. Also, the tendency to clustering in these materials has been studied. Furthermore, the effects of the pressure on the above properties have been studied, by performing similar calculation under hydrostatic pressure. The band structure and its pressure dependence for Si, Ge, And SixGei-x alloys have been studied using the same approach. For the alloys, the calculations are performed within the virtual crystal approximation (VCA) and the supercell approach; the latter is done by performing different supercell calculation at ( x = 0.5), from which we were able to study the effects of ordering, charge density distribution and microscopic structural relaxation on the band . structure. The pressure coefficients of the band gaps at the high symmetry points have been determined for Si and Ge; for the alloys this has been done only at ( x = 0.5), within VCA and Zinc-blend structure. ! Finally, we have studied the stability and the electronic structure along the high symmetry lines of two Si2Ge2 superlattices, having (111) and (001)orientations. The (110)-oriented superlattice has the same crystal structure as the (001)-oriented one. Therefore, the three high symmetry directions are considered in our study of the above superlattice. The total crystal charge densities and that corresponding to the lowest conduction band states are displayed, and the electronic confinement of the conduction band states is studied. The material of this thesis is divided into four chapters, in addition to the introduction. Each of the chapters 2-5 is treated as an indep-endent report having its own introduction, and a summary of the main results and conclusions. The results reported in Ch. 2 are the subject of a paper accepted in final by the Physical Review B, and now in press. Those reported in Ch. 3 are the subject of a paper accepted (subject to a miner revision) by Physical Review B. The results of Ch. 's 4 and. 5 are the subject of further pape.rs, which are presently being written.