In addition, for each doped cell thus developed and studied, an undoped

bulk Si cell of the same dimensions selleck chemical was constructed to aid in isolating those features primarily due to the doping. Results and discussion Analysis of band structure Once converged charge densities were obtained, band structures were calculated along the M–Γ–X high-symmetry pathway (as shown in Appendix 1), using at least 20 k-points between high-symmetry points. For comparative purposes, the band structures have all been aligned at the valence band maximum (VBM). Figure 3 contrasts the bulk and doped band structures for the 40-layer PW calculation. DZP and SZP results are qualitatively similar on this scale, albeit with different band energies

in the SZP model, and are omitted in the interest of clarity in the diagram. As discussed in Appendix 2, it is evident from the bulk values that the elongated cells have led to the folding of two conduction band minimum valleys towards the Γ selleck chemicals llc point. Also visible is the difference that the doping potential makes to the system; what was the lowest unoccupied orbital (Γ1 band) in the bulk is now dragged down in energy by the extra ionic potential. It is of note that the region near Γ, corresponding to the k z valleys which can be modelled as having different effective masses to the k x,y valleys, [30] is brought lower than the region corresponding to the k x,y valleys and is non-degenerate. The second (Γ2) band behaves in a similar fashion. The third (∆) band appears to maintain Etomidate a minimum away from the Γ point in the ΣTET direction (which is equivalent to the ΔFCC direction; see Appendix 1) but in a less parabolic fashion than the lower two;

its minimum is similar to the value at Γ. This band is non-degenerate along this particular direction in k-space, but due to the supercell symmetry, it is actually fourfold degenerate, in Selleck Ilomastat contrast to the other bands. Figure 3 Full band structure (colour online) of the 40-layer tetragonal system calculated using PW ( vasp ). Bulk band structure (shaded gray background), doped band structure (solid black) and Fermi level (labelled solid red). The Fermi level for the doped system is also shown, clearly being crossed by all three of these bands which are therefore able to act as open channels for conduction. As mentioned above, the band structures are similar across all methods, but upon detailed inspection, important differences come to light. A closer look at the ∆ band shows a qualitative difference between the predictions using SZP (Figure 4c) and the PW and DZP results (Figure 4a,b): the models with a more complete basis predict the band minimum to occur in the ΣTET(∆FCC) direction, below the value at Γ, while the SZP band structure shows the reverse – the minimum at Γ, a similar amount below a secondary minimum in the ΣTET direction, a qualitative difference.