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We conduct first-principles total-energy density functional calculations to study the band structures in Ge 1Àx Sn x infrared semiconductor alloys. The norm-conserving optimized pseudopotentials of Ge and Sn have been constructed for electronic structure calculations. The composition-bandgap relationships in Ge 1Àx Sn x lattices are evaluated by a detailed comparison of structural models and their electronic band structures. The critical Sn composition related to the transition from indirect-to direct-gap in Ge 1Àx Sn x alloys is estimated to be as low as x $ 0.016 determined from the parametric fit. Our results show that the crossover Sn concentration occurs at a lower critical Sn concentration than the values predicted from the absorption measurements. However, early results indicate that the reliability of the critical Sn concentration from such measurements is hard to establish, since the indirect gap absorption is much weaker than the direct gap absorption. We find that the direct band gap decreases exponentially with the Sn composition over the range 0 < x < 0:375 and the alloys become metallic for x > 0.375, in very good agreement with the theoretical observed behavior [D. W. Jenkins and J. D. Dow, Phys. Rev. B 36, 7994, 1987]. For homonuclear and heteronuclear complexes of Ge 1Àx Sn x alloys, the indirect band gap at L-pointis is found to decrease homonuclear Ge-Ge bonds or increase homonuclear Sn-Sn bonds as a result of the reduced L valley. All findings agree with previously reported experimental and theoretical results. The analysis suggests that the top of valence band exhibits the localization of bond charge and the bottom of the conduction band is composed of the Ge 4s4p and/or Sn 5s5p atomic orbits. V

The first-principles density functional theory is used to study the interaction of atomic hydrogen with ZnO surfaces. We find that atomic-hydrogen environments significantly reduce ZnO surface formation energies with hydrogen adsorption on the surface. The negative surface energy of the O-terminated ZnO(0001) surface is demonstrated in the O- and H-rich limits. The roughening and damage of ZnO surfaces are discussed in the context of the fluctuation of the surface formation energy.

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We conduct first-principles total-energy density functional calculations to study the interaction of H2 on ZnO surfaces. Four surface models of Zn-terminated (0001)-, O-terminated (0001)-, $(10{\bar 1}0)-$, and $(2{\bar 1}{\bar 1}0)-$oriented ZnO planes in the presence of H2 are evaluated. The relative stability of four different surface models is examined as a function of the chemical potentials of oxygen and hydrogen. We find that only surfaces of O-terminated (0001)-oriented ZnO models exhibit active sites for the dissociation of H2, which in turn enables the formation of water from dissociative chemisorption of 2H on the O-terminated ZnO(0001) surface. The surface energy of O-terminated ZnO(0001) surface in the presence of water was found to be negative under the O-rich and H-rich condition. The findings agree with the experimental observations that ZnO epitaxial layers are easily etched by hydrogen at typical growth temperatures.