Density of states The electronic density of states (eDOS) was calculated for each cell. Figure 6 compares the unscaled eDOS for bulk 80-layer cells to that of doped cells varying from 40 to 80 layers. The bulk bandgap is Wnt inhibitor visible, with the conduction band rising sharply to the right of the figure. The doped eDOS exhibits density in the bulk bandgap, although the features of the spectra differ slightly according to the basis set used. Figure 6 Electronic densities of states for tetragonal systems with 0 and 1/4 ML doping. The DZP (siesta) basis set was used. The Fermi level is indicated by a solid vertical line with label, and 50-meV smearing was applied for visualization

purposes. The Fermi energy exhibits convergence with respect to the amount JNK inhibitor of cladding, as reported above. It is also notable that the eDOS within the bandgap are nearly identical regardless of the cell length (in z). This indicates that layer-layer interactions are negligibly affecting the occupied

states and, therefore, that the applied ‘cladding’ is sufficient to insulate against these effects. Electronic width of the plane In order to quantify the extent of the donor-electron distribution, we have integrated the local density of states between the VBM and Fermi level and have taken the planar average with respect to the z-position. Figure 7 shows the planar average of the donor electrons (a sum of both spin-up and spin-down channels) for the 80-layer cell calculated using the DZP basis set. After removing the small oscillations related to the crystal lattice to focus on the physics of the δ-layer, by Fourier transforming, a Lorentzian function was fitted to the distribution profile. (Initially, a three-parameter Gaussian fit similar to that used in [40] was tested,

but the Lorentzian gave a better fit to the curve.) Figure 7 Planar average of donor-electron density as a function of z -position for 1/4 ML-doped 80-layer cell. The DZP basis set was used. The fitted Lorentzian function is also shown. Table 3 summarises the maximum donor-electron of density and the full width at half maximum (FWHM) for the 1/4 ML-doped cells, each calculated from the Lorentzian fit. Both of these properties are remarkably consistent with respect to the number of layers, indicating that they have converged sufficiently even at 40 layers. Table 3 Calculated maximum donor-electron density, ρ max , and FWHM Number of ρ max FWHM layers (×10−3 e/Å) (Å) 40 3.8 6.2 60 3.9 6.2 80 3.9 6.5 Values are presented as a function of the number of layers in 1/4 ML-doped cells. The DZP basis set was used. Our results differ from a previous DFT calculation [32] which cited an FWHM of 5.62 Å for a 1/4 ML-doped, 80-layer cell calculated using the SZP basis set (and 10 × 10 × 1 k-points).