Electron Spin Resonance Experiments on Donors in Silicon. II. Electron Spin Relaxation Effects

The different relaxation processes that connect the four energy levels in phosphorus doped silicon have been investigated experimentally. The relaxation time $T_s$ ($\Delta m_s=\pm 1$, $\Delta m_I=0\mathrm{}$) was found to be independent of phosphorus concentration below ∼${10}^{16}$ P/${\mathrm{cm}}^3$. Its value at 3200 oersteds and 1.25°K was ∼3×${10}^{+3\mathrm{}}$ seconds and varied as $\frac{1}{T}$ for $1.3°\mathrm{K}<T<\mathrm{}2\mathrm{}°\mathrm{K}$ and as $\frac{1}{T^7}$ for $2.5°\mathrm{K}<T<\mathrm{}4.2\mathrm{}°\mathrm{K}$. The magnetic field dependence in the $\frac{1}{T}$ region suggests a direct phonon process. In the $\frac{1}{T^7}$ region $T_s$ was independent of the magnetic field between 3000 and 8000 oersteds. Above a concentration of ${10}^{16}$ P/${\mathrm{cm}}^3$ $T_s$ varied rapidly with donor concentration, dropping to ${10}^{-4\mathrm{}}$ seconds at 3×${10}^{17}$ P/${\mathrm{cm}}^3$. In this concentration dependent region $T_s$ was independent of the magnetic field but depended on the number of acceptors present. None of the $T_s$ mechanisms can at present be accounted for by the theories of Pines, Bardeen, and Slichter, and Abrahams. The relaxation time $T_x$ ($\Delta m_s=\pm 1$, $\Delta m_I=\mp 1$) was ∼30 hours at 3000 oersteds and ∼5 hours at 8000 oersteds in fair agreement with the theory of PBS. The relaxation time $T_N$ ($\Delta m_I=\pm 1$, $\Delta m_s=0\mathrm{}$) at 1.25°K exceeded 10 hours.