Model Hamiltonian of donors in indirect-gap materials

We propose a model Hamiltonian for donors in Si and Ge, whose matrix elements can be expressed analytically for Slater-type basis wave functions defined in an ellipsoidal coordinate system. This model Hamiltonian yields results for the energy eigenvalues of the ground state and excited states almost identical to that for the exact Hamiltonian. The simplicity of this model Hamiltonian makes the application to more complicated systems such as donor bound excitons and bound multiexciton complexes possible.