Cells used in PW calculations began at 4 layers and ran to 80 layers; larger cells were not computationally tractable with this method. SZP and DZP models began at 40 layers to overlap with PW for the converging region and were then extended to their tractable limit (200 and 160 layers, respectively) to study convergence past the capability

of PW. Figure 2 Ball and stick model of a δ -doped Si:P layer viewed along the [110] STA-9090 direction. Thirty-two layers in the [001] direction are shown. Si atoms (small gray spheres), P atoms (large dark gray spheres), covalent bonds (gray sticks), repeating cell boundary (solid line). For tetragonal cells, the k-point sampling was set as a 9 × 9 × N Γ-centred MP mesh as we have found that failing to include Γ in the mesh can lead to the anomalous placement of the Fermi level on band structure diagrams. N varied from 12 to 1 as the cells became more elongated (see Appendix 1). We note that, as mentioned in the work of Carter et al. [32], the large supercells involved required very gradual (<0.1%) mixing of the new density matrix with the prior step, leading to many hundreds of self-consistent cycles before convergence was achieved. Although it has been previously found Selleck BAY 80-6946 that relaxing the positions of the nuclei gave negligible differences (<0.005 Å) to the geometry [31], this was for a 12-layer

cell and may not have included enough space between periodic repetitions of the doping plane for the full effect to be seen. Whilst a 40-layer model was optimised in the work of Carter et al. [32], this made use of a mixed atom pseudo-potential and is not explicitly comparable to the models presented here. We have performed a test relaxation on a 40-layer cell using the PW basis

(vasp). The maximum subsequent ionic displacement was 0.05 Å, with most being an order of magnitude smaller. The energy gained in relaxing the cell was less than 37 meV (or 230 μeV/atom). We therefore regarded any changes to the structure as negligibly isothipendyl small, confirming the results of Carter et al. [31, 32], and proceeded without ionic relaxation. Single-point energy calculations were carried out with both software programs; for vasp, the electronic energy convergence criterion was set to 10−6eV, and the tetrahedron method with Blöchl correction [52] was used. For siesta, a two-stage process was carried out: Fermi-Dirac electronic smearing of 300 K was applied in order to converge the density matrix within a tolerance of one part in 10−4; the calculation was then restarted with the smearing of 0 K, and a new electronic energy tolerance criterion of 10−6 eV was applied (except for the 120- and 160-layer DZP models for which this was intractable; a tolerance of 10−4 eV was used in these cases).