Density functional theory is used to quantify the interaction of a pair of 1/4-monolayer phosphorus δ-doped layers in silicon. We investigate changes in the electronic structure as the distance between the two δ-doped layers is altered and identify the onset of interactions between the transverse and longitudinal bands. The calculations show that the valley splitting is insensitive to the separation distance, while the interlayer band splittings are insensitive to the representation used to describe the dopant disorder. These observations are exploited in a hybrid model which enables the calculation of accurate splittings of realistically disordered systems at tractable computational cost
