Donor electron wave functions for phosphorus in silicon : Beyond effective-mass theory

We calculate the electronic wave-function for a phosphorus donor in silicon by numerical diagonalisation of the donor Hamiltonian in the basis of the pure crystal Bloch functions. The Hamiltonian is calculated at discrete points localised around the conduction band minima in the reciprocal lattice space. Such a technique goes beyond the approximations inherent in the effective-mass theory, and can be modified to include the effects of altered donor impurity potentials, externally applied electro-static potentials, as well as the effects of lattice strain. Modification of the donor impurity potential allows the experimentally known low-lying energy spectrum to be reproduced with good agreement, as well as the calculation of the donor wavefunction, which can then be used to calculate parameters important to quantum computing applications.