The peak height is not shown in the work of Carter et al. [32], but the value from another work [31] (1.7 × 1021 e/cm3) is a factor of 0.44 smaller than the peak we observe here. This may be due, to some extent, to the larger width of the SZP model selleck products leading to an associated lowering of

the peak density. Conclusions In this article, we have studied the valley splitting of the monolayer δ-doped Si:P, using a density functional theory model with a plane-wave basis to establish firm grounds for comparison with less computationally intensive localised-basis ab initio methods. We found that the description of these systems (by density functional theory, using SZP basis functions) overestimates the valley splitting by over 50%. We show that

DZP basis sets are complete enough to deliver values within 10% of the plane-wave values and, due to their localised nature, are capable of calculating the properties of models twice as large as is MK-2206 research buy tractable with plane-wave methods. These DZP models are converged with respect to size well before their tractable limit, which approaches that of SZP models. Valley splittings are important in interpreting transport spectroscopy experiment data, where they relate to families of resonances, and in benchmarking other theoretical techniques more capable of actual device modelling. It is therefore pleasing to have an ab initio description A-1210477 of this effect which is fully converged with respect to basis completeness as well as the usual size effects and k-point mesh density. We have also studied the band structures with all three methods, finding that the DZP correctly determines the ∆-band minima away from the Γ point, where the SZP method does not. We show that these minima occur in the Σ direction for the type of cell considered, not the δ direction as has been previously reported. Having established the DZP methodology as sufficient to describe the physics of these systems, we then calculated the electronic density of states and the electronic width of the δ-layer. We found that previous SZP descriptions of these layers underestimate Sunitinib datasheet the width

of the layers by almost 15%. We have shown that the properties of interest of δ-doped Si:P are well converged for 40-layer supercells using a DZP description of the electronic density. We recommend the use of this amount of surrounding silicon, and technique, in any future DFT studies of these and similar systems – especially if inter-layer interactions are to be minimised. Appendix 1 Subtleties of bandstructure Regardless of the type of calculation being undertaken, a band structure diagram is inherently linked to the type (shape and size) of cell being used to represent the system under consideration. For each of the 14 Bravais lattices available for three-dimensional supercells, a particular Brillouin zone (BZ) with its own set of high-symmetry points exists in reciprocal space [54].