Control of dopants in silicon remains the most important approach to tailoring the properties of electronic materials for integrated circuits, with Group V impurities the most important n-type dopants. At the same time, silicon is finding new applications in coherent quantum devices, thanks to the magnetically quiet environment it provides for the impurity orbitals. The ionization energies and the shape of the dopant orbitals depend on the surfaces and interfaces with which they interact. The location of the dopant and local environment effects will therefore determine the functionality of both future quantum information processors and next-generation semiconductor devices. Here we match observed dopant wavefunctions from low-temperature scanning tunnelling microscopy (STM) to images simulated from first-principles density functional theory (DFT) calculations. By this combination of experiment and theory we precisely determine the substitutional sites of neutral As dopants between 5 and 15A below the Si(001):H surface. In the process we gain a full understanding of the interaction of the donor-electron state with the surface, and hence of the transition between the bulk dopant (with its delocalised hydrogenic orbital) and the previously studied dopants in the surface layer.