Temperature dependent exchange narrowing of line width in EPR on interacting donors in germanium and silicon

An expression has been derived for the temperature dependent exchange integral for a pair of interacting shallow donors substituted in a dielectric material. This has been achieved by taking into account the phonon induced mixing of excited orbital states with the ground orbital states of the impurity centres. The results have been used to explain the temperature narrowing of the EPR line width observed by some workers in phosphorus doped germanium at low temperatures. Good agreement between theory and experimental results seems to favour the proposed mechanism in preference to one of motional narrowing due to hopping.