Pt-induced nanowires on Ge(001):Ab initiostudy

Abstract

Using ab initio density-functional theory together with a semilocal approximation for exchange and correlation we study structural, energetical, and electronic properties for a variety of reconstruction models of the $\text{Ge}(001)4\ifmmode\times\else\texttimes\fi{}2$ surface with a Pt coverage of 0.25 monolayer. The band-structure calculations are partially performed including spin-orbit interaction. Starting from the idea that the self-organization of the nanowire arrays is driven by the minimization of the total energy of the system, we investigate more than 20 possible overlayer structures, among them dimerized top Pt chains. The comparison of the surface energies, however, shows a clear preference of the formation of Pt-Ge bonds over Pt-Pt bonds. The most favorable surface structure contains fourfold-coordinated Pt atoms embedded in Ge atoms. The seemingly dimerized top chains are formed by edges of Ge tetramers parallel to Ge dimers in trenches two atomic layers below. Incorporation of Pt atoms in the surface Ge layer within the tetramer-dimer-chain model gives rise to the biggest energy gain. Its band structure describes an indirect semiconductor with almost vanishing gap. The role of the Pt $5d$ states and top-ridge Ge orbitals as well as of spin-orbit interaction is emphasized for the wire conductivity. The results are discussed in light of recent experimental scanning-tunneling microscopy studies.