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Abstract

The e.p.r. spectrum for relatively dilute samples of phosphorus-doped silicon (<5 x 10(16) donors/cm³) has been calculated in detail for an assumed random distribution of impurities. The system of donor electron spins is treated as a collection of nearest neighbor donor pairs. An expression is derived for the donor pair exchange energy using Kohn-Luttinger wavefunctions and a general exchange energy expression. The resultant relationship contains an adjustable parameter a*, the "effective Bohr radius", which is determined from a comparison of the calculated spectrum and the experimental results obtained for the ratio, C, of the "central pair" and "hyperfine" line intensities. The resulting expression J(R), where J represents the exchange energy and R the separation vector connecting the two pair donors, exhibits an oscillatory spatial dependence due to interference from portions of the wavefunction arising from different conduction band valleys.