Spin Dynamics of Low Phosphorus-doped Silicon in the Low-Temperature and High-Field Limits

Spin dynamics of shallow-trapped donor electron spins in Si:P (phosphorous-doped silicon) has been studied by high frequency ESR. A sample with the donor concentration 6.5 x 10 cm, where the sample is a insulator at low temperatures and the donor is almost isolated, was investigated at 2.87 T (80 GHz) from 48 K to 1.8 K by cw-ESR with field modulation. At low temperatures, where the spin-lattice relaxation time T1 changes in many orders of magnitude, the resonance line shape changed from the usual derivative form of the absorption line at high temperatures to the non-derivative shape caused by the passage effects at low temperatures. These complex behaviors in the resonance line shape have made it possible to estimate the spin-lattice relaxation time T1. We numerically solved the Bloch equations for a given inhomogeneous line shape and obtained the ESR absorption and dispersion signal as a function of the spin lattice relaxation time T1. We analytically solve Bloch equations at the low-temperature limit (eF >>1) to understand spin dynamics. The observed T1 at a high field of 2.87 T is consistent with the reported T1 for samples with the low dopant concentration limit at 0.32 ~ 0.33 T after the theoretical correction for the magnetic field dependence. Possible dynamic nuclear polarization effect on P nuclear spin was observed in asymmetry of ESR intensities between two hyperfine states. 研究報告11