Electron paramagnetic resonance properties ofn-type silicon in the intermediate impurity-concentration range

The EPR properties of phosphorus-doped silicon are investigated in detail for impurity concentrations $5\times {10}^{16}\le N_D\le 1.6\times {10}^{18}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$ and temperatures $1.1\le T\le 35$ K. Particular care is taken to ensure that the inhomogeneously broadened spectra obtained correspond to well-defined experimental "passage cases." Rapid-passage and slow-passage spectra are converted into directly comparable "absorption envelope" forms which are convolutions of Lorentzian spin packets and Gaussian envelope functions. Spin-lattice relaxation times, spin-packet widths, and $g$ values are presented for both the hyperfine and broad-center-line (BCL) components of the spectra. The hyperfine-line spin-packet widths exhibit a concentration dependence and have magnitudes which are larger than those expected from spin-echo measurements of $T_2$. A previously unreported concentration dependence is also observed for the hyperfine-line $g$ value. Although similar $g$-value and spin-packet-width concentration dependences are noted for the BCL, the BCL parameters exhibit temperature dependences which are distinct from those observed for the corresponding hyperfine-line quantities. A comparison of the fractional spin susceptibility associated with the BCL and the results of a percolation calculation indicates that the BCL can be attributed to clusters of three or more interacting donor atoms. Evidence is also presented for a hyperfine-line spin-lattice relaxation process which proceeds through cross relaxation with fast relaxing cluster (BCL) centers. This process is shown to be consistent with the experimental temperature dependences of the BCL and hyperfine relaxation rates.