Surface and interface properties in germanium/silicon heteroepitaxy from first-principles

First-principles calculations based on density functional theory (DFT) are a powerful tool for elucidating thermodynamic properties of materials from the atomic scale and are widely used to study complex surface and interface structures. The Ge/Si (001) system is well studied and serves as a model system for investigations into heteroepitaxial growth and the self-assembly of three-dimensional nanostructures. Surface and interface excess energies are key parameters in thermodynamic models of nanoscale structure self-assembly. In this dissertation, fundamental materials parameters for various surfaces and interfaces in the Ge/Si system are calculated from first principles. Bulk materials parameters, including equilibrium lattice constant and total cohesive energy per atom are first determined for Ge and Si. With these parameters as input, slab supercells are constructed for various surface and interface geometries, and surface and interface excess energies are extracted from the calculated total cohesive energy of these slabs. In this manner the uniaxial and biaxial strain-dependence of the surface excess energy of Si and Ge dimer reconstructed (001) surfaces is calculated. The biaxial and uniaxial strain-dependence and dimer vacancy line spacing-dependence of the surface excess energy of Ge dimer vacancy line reconstructed (001) surfaces is also calculated. The details of the dimer vacancy line rebonds on Ge (001) surfaces are examined as a function of biaxial and uniaxial strain. Finally, the biaxial and uniaxial strain-dependence of the surface excess energy of the Ge (105) rebonded-step reconstruction is calculated. The implications of these strain-dependent surface energies on the formation energy of experimentally observed Ge (105) but pyramids on Si (001) are discussed.