Computational techniques are key predictive tools in the drive to engineer semiconductive materials. Diamond, intrinsically a wide band-gap insulator, can be made to semiconduct $n$-type by doping with phosphorus. However, the relatively deep level at $E_c-0.6\mathrm{eV}$ forces us to search for shallower donors. Theory predicts among other candidates both substitutional arsenic and a complex made up from silicon and nitrogen to introduce shallow donor levels. We show in this study that the location of the calculated donor level may be qualitatively affected by supercell size. We conclude that large supercells must be used to obtain converged values for donor levels of highly strained systems in “stiff” materials such as diamond: In the current study using supercells of up to 1000 host sites the donor levels of ${\mathrm{Si}}_4\mathrm{N}$ and ${\mathrm{As}}_s$ are calculated to lie deeper and shallower than ${\mathrm{P}}_s$, respectively.

• Received 24 May 2006

DOI:https://doi.org/10.1103/PhysRevB.74.245217