  Adiabatic shuttling of single impurity bound electrons to gate induced
surface states in semiconductors has attracted much attention in recent times,
mostly in the context of solid-state quantum computer architecture. A recent
transport spectroscopy experiment for the first time was able to probe the
Stark shifted spectrum of a single donor in silicon buried close to a gate.
Here we present the full theoretical model involving large-scale quantum
mechanical simulations that was used to compute the Stark shifted donor states
in order to interpret the experimental data. Use of atomistic tight-binding
technique on a domain of over a million atoms helped not only to incorporate
the full band structure of the host, but also to treat realistic device
geometries and donor models, and to use a large enough basis set to capture any
number of donor states. The method yields a quantitative description of the
symmetry transition that the donor electron undergoes from a 3D Coulomb
confined state to a 2D surface state as the electric field is ramped up
adiabatically. In the intermediate field regime, the electron resides in a
superposition between the states of the atomic donor potential and that of the
quantum dot like states at the surface. In addition to determining the effect
of field and donor depth on the electronic structure, the model also provides a
basis to distinguish between a phosphorus and an arsenic donor based on their
Stark signature. The method also captures valley-orbit splitting in both the
donor well and the interface well, a quantity critical to silicon qubits. The
work concludes with a detailed analysis of the effects of screening on the
donor spectrum.
