Investigation of the structural, electronic and dynamical properties of a-Sn and its Sn ( 001 )( 2x1 ) surface. SUMMARY Keywords: Phonon, structural properties, electronic properties, dynamical properties, density functional theory, high symmetry directions, lattice dynamics, Sn ( 001 )( 2x1 ) surface. In the first part of thesis, a first-principles study, using a linear-response approach based on the pseudopotential method has been carried out for structural, electronic and dynamical properties of a-Sn. The equilibrium lattice constant for this material compares quite well with an experimental finding. Then, we have presented the electronic band structure of this material along the high symmetry directions. Our results clearly show that a-Sn is a zero band-gap semiconductor. Finally, the phonon spectrum of a-Sn has been calculated. In general, the obtained phonon dispersion curves for this material compare a very well with experimental results. In the second part of this thesis, we have applied an ( ab initio ) pseudopotential density functional theory to study structural and dynamical properties of the a-Sn ( 001 )( 2x1 ) surface. In general, the atomic relaxation parameters and atomic vibrational modes on this surface show a pattern similar to that obtained for the silicon and germanium surfaces. In particular, the calculated dimer bond is characterized by a large tilt of 2 1.9° from the ( 001 ) surface plane, and its length is slightly larger than the bulk bond length. We have presented the full phonon spectrum of this surface along the symmetry directions. The surface sustains phonon modes below the bulk continuum, modes in stomach gaps ( gap regions within the bulk continuum ) and above the bulk continuum. Energy locations and polarization characteristics of ( rocking ) and ( dimer stretch ) phonon modes have been determined. XI
Investigation of the structural, electronic and dynamical properties of a-Sn and its Sn ( 001 )( 2x1 ) surface. SUMMARY Keywords: Phonon, structural properties, electronic properties, dynamical properties, density functional theory, high symmetry directions, lattice dynamics, Sn ( 001 )( 2x1 ) surface. In the first part of thesis, a first-principles study, using a linear-response approach based on the pseudopotential method has been carried out for structural, electronic and dynamical properties of a-Sn. The equilibrium lattice constant for this material compares quite well with an experimental finding. Then, we have presented the electronic band structure of this material along the high symmetry directions. Our results clearly show that a-Sn is a zero band-gap semiconductor. Finally, the phonon spectrum of a-Sn has been calculated. In general, the obtained phonon dispersion curves for this material compare a very well with experimental results. In the second part of this thesis, we have applied an ( ab initio ) pseudopotential density functional theory to study structural and dynamical properties of the a-Sn ( 001 )( 2x1 ) surface. In general, the atomic relaxation parameters and atomic vibrational modes on this surface show a pattern similar to that obtained for the silicon and germanium surfaces. In particular, the calculated dimer bond is characterized by a large tilt of 2 1.9° from the ( 001 ) surface plane, and its length is slightly larger than the bulk bond length. We have presented the full phonon spectrum of this surface along the symmetry directions. The surface sustains phonon modes below the bulk continuum, modes in stomach gaps ( gap regions within the bulk continuum ) and above the bulk continuum. Energy locations and polarization characteristics of ( rocking ) and ( dimer stretch ) phonon modes have been determined. XI
