Structural and electronic properties of the liquid polyvalent elements: The group-IV elements Si, Ge, Sn, and Pb

Abstract

Detailed calculations of the atomic and electronic structure of the molten group-IV elements Si, Ge, Sn, and Pb are presented. The approach is based on interatomic forces derived from pseudopotential and linear-response theories, on molecular-dynamics simulation of the atomic structure, and on self-consistent linear muffin-tin orbitals supercell calculations for the electronic structure. Detailed comparison with existing neutron and x-ray diffraction data for the atomic structure and with recent photoemission spectra demonstrate a very good agreement between theory and experiment. We show that in the two lighter elements Si and Ge the modulation of the random packing of the ions by the Friedel oscillations of the pair potential leads to a complex structure of the liquid with low coordination numbers, only short-range distance correlations, and very weak angular correlations. In the two heavier elements Sn and Pb, nonlocal relativistic effects lead to a damping of the Friedel oscillations and to a return to a hard-sphere-like structure of the melt. The electronic structure of liquid Si, Ge, and Sn is different from that of any of their crystalline phases: the absence of the angular correlation leads to a complete breakdown of the ${\mathrm{sp}}^3$ hybridization and hence to weak covalent bonding effects in liquid Si and Ge. The low coordination numbers lead to an incipient separation of the s and p states in the conduction band of liquid Si and to a deep minimum in the middle of the conduction band of liquid Ge and Sn. This effect is strongly enhanced by relativistic effects in Pb. In liquid Pb the s states are separated from the p states by a gap of about 1.4 eV. The interrelation between the atomic and the electronic structure is discussed in detail.