External field control of donor electrons at the Si-SiO$_2$ interface

Prospects for the quantum control of electrons in the silicon quantum computer architecture are considered theoretically. In particular, we investigate the feasibility of shuttling donor-bound electrons forth and back between the impurity in the bulk and the Si-SiO$_2$ interface by tuning an external electric field. We calculate the shuttling time to range from sub-picoseconds to nanoseconds depending on the distance ($\sim$ 10-50 nm) of the donor from the interface. For a certain range of parameters, the state at the interface is localized in all three dimensions, which allows to take the electron back to the donor. The size of the wave-function at the interface can be manipulated by applying a perpendicular magnetic field. Our results establish that quantum control in such nanostructure architectures should be achievable.