of magnitude smaller. The energy gained in relaxing the cell was less than 37 meV (or 230 $\mu$eV/atom). We therefore regarded any changes to the structure as negligibly small, and proceeded without ionic relaxation.

Single-point energy calculations were carried out with both software programs; for <span style="font-variant:small-caps;">vasp</span> the electronic energy convergence criterion was set to $10^{-6}$ eV, and the tetrahedron method with Blöchl correction [@Blochl94] was used. For <span style="font-variant:small-caps;">siesta</span> 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 1 part in $10^{-4}$; the calculation was then restarted with smearing of 0 K and a new electronic energy tolerance criterion of $10^{-6}$ eV 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). This two-stage process aided convergence as well as ensuring that the energy levels obtained were comparably accurate across methods. In addition, for each doped cell thus developed and studied, an undoped bulk Si cell of the same dimensions was constructed to aid in isolating those features primarily due to the doping.

Results {#sec:blah}
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Analysis of bandstructure 