Free-induction-decay shape change by defect-induced quadrupole interaction

The change in shape of the free induction decay (FID) in solids is calculated for the case of the point-defect-induced quadrupole interaction. The calculation agrees in form with the result of Fedders and predicts an FID of the form $V\left(t\right)\mathrm{}\exp (-K{t}^{\frac{3}{2}})$, where $V\left(t\right)\mathrm{}$ is the FID with no quadrupole interaction (a perfect crystal), and $K$ is proportional to the defect density. We adapt this theory to analyze FID data taken on the three isotopes in GaAs. The theory gives accurate fits to the data, and defect densities are calculated from the fit parameters for several thermally damaged samples and one doped sample. The principal purpose of this paper was the verification of the $t^{\frac{3}{2}}$ exponential dependence in the FID introduced by the quadrupole effect. The densities found for the damaged samples agree with the prediction of a thermodynamic calculation, for the smaller densities. Significant deviations occur at densities large enough that approximations made in the line-shape theory begin to break down. The magnitude of the deviations is larger than expected from the breakdown of theory alone, and may be evidence for the formation of singly charged vacancy pairs. The defect density measured for the doped sample is an order of magnitude less than the charge carrier concentration. This failure may be due to the breakdown in the theory or to donor clustering on dislocations.