First-principles investigation of the multilayer relaxation of stepped Cu surfaces

Abstract

We performed density-functional theory calculations, employing the all-electron full-potential linearized augmented plane-wave (FLAPW) method, for the multilayer relaxations of the vicinal, high-Miller-index Cu(210), Cu(211), and Cu(331) surfaces, as well as for the flat, low-Miller-index Cu(100), Cu(110), and Cu(111) surfaces. Generally, it is expected that the interlayer relaxation-sequence at stepped metal surfaces with $n$ surface atom rows in the terraces exposed to the vacuum show $n\ensuremath{-}1$ contractions (indicated by $\ensuremath{-}$) followed by one expansion (indicated by $+$). However, recent studies based on low-energy electron diffraction (LEED) intensity analysis and all-electron FLAPW calculations suggested that the multilayer relaxation-sequence of the stepped Cu(331) surface, for which $n=3$, behaves anomalously, i.e., $\ensuremath{-}++\ensuremath{\cdots}$, instead of the expected $\ensuremath{-}\ensuremath{-}+\ensuremath{\cdots}$. From the results presented in this work, we did not find any indication of such anomalous behavior for Cu(331) or for any of the investigated stepped Cu surfaces. For the flat surfaces we obtained the expected contraction of the topmost interlayer distance. In the particular case of the Cu(110) surface, a pronounced alternating oscillatory behavior extending over six interlayer distances was found, i.e., $\ensuremath{-}+\ensuremath{-}+\ensuremath{-}+$. For all studied Cu surfaces in the present work, we found a good quantitative agreement between our interlayer relaxations and those obtained by LEED intensity analysis.