Electron Spin Resonance on Interacting Donors in Silicon

The value of the exchange integral $J$ between pairs of donor centers in silicon has been investigated by looking at the endor spectrum of phosphorus-doped silicon in a range of concentration of the order of 8×${10}^{16}$ per cc. The microwave field is saturating the cluster electronic line. The line shape of these endor lines gives an unambiguous determination of the sign of this exchange integral which turns out to be antiferromagnetic. It is also possible to determine an order of magnitude of $J$ and to have an idea about its distribution for two samples. We are able to understand all the features of the endor spectrum at least in a qualitative way by calculating all the energy levels using a second-order perturbation calculation. A line coming from an ionized phosphorus center, weakly coupled to a pair of neutral phosphorus is also identified.