Theory of one and two donors in silicon

We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D(0), D(-), D(+)(2) and D(0)(2) centers. The impact of different levels of approximation is discussed. The most accurate instances--for which we provide quantitative results--are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations--in particular, for a donor pair, we discuss the single orbital LCAO method, the Hückel approximation and the Hubbard model. Finally, we connect these results with recent experiments on devices with few dopants.