  We present a complete theoretical treatment of Stark effects in doped
silicon, whose predictions are supported by experimental measurements. A
multi-valley effective mass theory, dealing non-perturbatively with
valley-orbit interactions induced by a donor-dependent central cell potential,
allows us to obtain a very reliable picture of the donor wave function within a
relatively simple framework. Variational optimization of the 1s donor binding
energies calculated with a new trial wave function, in a pseudopotential with
two fitting parameters, allows an accurate match of the experimentally
determined donor energy levels, while the correct limiting behavior for the
electronic density, both close to and far from each impurity nucleus, is
captured by fitting the measured contact hyperfine coupling between the donor
nuclear and electron spin.
  We go on to include an external uniform electric field in order to model
Stark physics: With no extra ad hoc parameters, variational minimization of the
complete donor ground energy allows a quantitative description of the
field-induced reduction of electronic density at each impurity nucleus.
Detailed comparisons with experimental values for the shifts of the contact
hyperfine coupling reveal very close agreement for all the donors measured (P,
As, Sb and Bi). Finally, we estimate field ionization thresholds for the donor
ground states, thus setting upper limits to the gate manipulation times for
single qubit operations in Kane-like architectures: the Si:Bi system is shown
to allow for A gates as fast as around 10 MHz.
