Theory of the Stark Effect for P donors in Si

We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at high fields, and it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.