Stress balance in nano-patterned N/Cu(001) surfaces

TL;DR

This study combines helium atom scattering and density functional theory to analyze how nano-patterned nitrogen on Cu(001) surfaces manages stress, revealing mechanisms like lattice expansion, trench formation, and the ineffectiveness of rumpling displacements.

Contribution

It provides a detailed understanding of stress relief mechanisms in N/Cu(001) surfaces through combined experimental and theoretical approaches, clarifying the role of trenches and dismissing rumpling as a stress relief method.

Findings

Lattice expansion decreases with increasing N coverage.

Stress is relieved by trench formation and stripe development.

Rumpling displacements do not relieve surface stress.

Abstract

We employ helium atom scattering (HAS) and density functional theory (DFT) based on the ultrasoft pseudopotential scheme and the plane-wave basis set to investigate the strain and stress balance in nano-patterned N/Cu(001) surfaces. HAS shows that, with increasing N coverage (and decreasing stripe widths), the stress-relief-driven lateral expansion of the averaged lattice parameter within finite-sized N-containing patches reduces from 3.5% to 1.8% and that, beyond a critical exposure, the lateral expansion of the patches increases again slightly, to 2.4%. The latter implies that in this higher coverage range the compressive stress is partially relieved via another mechanism, which turns out to be nucleation of Cu-vacancy trenches. In full agreement with the above and previous experimental observations, DFT calculations show that an optimized N-induced c(2\times2) structure has a net surface stress level of 4.2 N/m and such stress is effectively relieved when stripes of clean Cu(001) form along the <100> direction or when trench-like steps of Cu atoms form along the <110> direction. Additionally, the calculations demonstrate that (contrary to earlier suggestions) rumpling displacements within the outermost Cu layer do not act to relieve the compressive surface stress levels and that, while clock-like displacements could relieve stress levels, such displacements are energetically unstable.