Density functional calculations of Ge(105):: Local basis sets and O(N) methods

The Ge(105) surface has attracted attention recently, both from interest in the reconstruction itself and because the facets of three-dimensional hut clusters which form during heteroepitaxy of Ge on Si(001) are strained Ge(105) surfaces. We present density functional theory (DFT) studies of this surface using local basis sets as a preparation for O(N) DFT studies of full hut clusters on Si(001). Two aspects have been addressed. First, the detailed buckling structure of the dimers forming the surface reconstruction is modeled using DFT and tight binding; two different structures are found to be close in stability, the second of which may be important in building hut-cluster facets [as opposed to perfect Ge(105) surfaces]. Second, the accuracy that can be achieved using local basis sets for DFT calculations is investigated, with O(N) calculations as the target. Two different basis sets are considered: B splines, also known as blips, and pseudoatomic orbitals; B splines are shown to reproduce the result of plane-wave calculations extremely accurately. The accuracy of different modes of calculation (from non-self-consistent ab initio tight binding to full DFT) is investigated, along with the effect of cutoff radius for O(N) operations. These results all show that accurate, linear-scaling DFT calculations are possible for this system and give quantitative information about the errors introduced by different localization criteria.