In the framework of the envelope function approximation, the wave functions of electrons localized at shallow donors P, As, Sb in Ge are calculated taking into account the valley-orbit coupling caused by the donor short-range potential. It is proposed an approach that makes it possible to include inter-valley mixing in the equation for a multi-component envelope function. The calculation of the effects of the valley-orbit interaction was carried out according to the perturbation theory, while the "bare" single-valley functions were found using the Ritz method. The parameters of the short-range part of the potential and the coefficient of inter-valley mixing were found individually for each donor, making it possible to obtain the best agreement with the results of experimental measurements of the energies of the singlet and triplet states. The envelope functions of the 1s(A1) and 1s(T2) states are calculated. The parameters of the valley-orbit interaction are found for each donor. It is also shown how the functions of the excited 2s, 2p0, 2p±, 3p0 states should be modified in order to remain orthogonal to the singlet and triplet functions within the framework of a more rigorous multivalley model.

In the framework of the envelope function approximation, the wave functions of low-lying 1s(A1), 2s, 2p0, 2p±, 3p0 states of shallow donor centers P, As, Sb in germanium are calculated considering the short-range part of the impurity potential. The latter is constructed individually for each impurity, taking into account the spatial dispersion of the dielectric function and the difference between the ionic cores of germanium and the impurity center. The envelope function equation was solved using the Ritz variational method, and selected trial wave functions of the orbitally non-degenerate s-states are characterized by two spatial scales: the first one is of the order of the donor effective Bohr radius and corresponds to the long-range part of the potential, and the second one, which is an order of magnitude less, simulates the electron response to the short-range part of the donor potential. The electron density in the donor ground state is shifted to the nucleus due to the attractive “central cell” correction. The envelope functions of p-states, in turn, are constructed in such a way they are orthogonal to the ground state envelope functions for each impurity center, and, unlike previous works, are different for various donors.