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

Abstract

The different relaxation processes that connect the four energy levels in phosphorus doped silicon have been investigated experimentally. The relaxation time ${T}_{s}$ ($\ensuremath{\Delta}{m}_{s}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{I}=0$) was found to be independent of phosphorus concentration below \ensuremath{\sim}${10}^{16}$ P/${\mathrm{cm}}^{3}$. Its value at 3200 oersteds and 1.25\ifmmode^\circ\else\textdegree\fi{}K was \ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{+3}$ seconds and varied as $\frac{1}{T}$ for $1.3\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<2\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$ and as $\frac{1}{{T}^{7}}$ for $2.5\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<4.2\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. 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 ${10}^{\ensuremath{-}4}$ seconds at 3\ifmmode\times\else\texttimes\fi{}${10}^{17}$ 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 ${T}_{x}$ ($\ensuremath{\Delta}{m}_{s}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{I}=\ensuremath{\mp}1$) was \ensuremath{\sim}30 hours at 3000 oersteds and \ensuremath{\sim}5 hours at 8000 oersteds in fair agreement with the theory of PBS. The relaxation time ${T}_{N}$ ($\ensuremath{\Delta}{m}_{I}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{s}=0$) at 1.25\ifmmode^\circ\else\textdegree\fi{}K exceeded 10 hours.The effect of light was investigated with a monochromator for $0.5 \mathrm{ev}<h\ensuremath{\nu}<2 \mathrm{ev}$. The number of carriers introduced by light was obtained from the Hall coefficient. In a sample with 7\ifmmode\times\else\texttimes\fi{}${10}^{15}$ P/${\mathrm{cm}}^{3}$, ${T}_{s}$ was reduced to 25 seconds by 2\ifmmode\times\else\texttimes\fi{}${10}^{6}$ electrons/${\mathrm{cm}}^{3}$. Under the same conditions the spin-spin time ${T}_{\mathrm{ss}}$ was reduced to 1 second. The bottleneck in the ${T}_{s}$-spin exchange mechanism suggested by PBS is the spin-lattice relaxation time of the free carriers. This bottleneck is absent in a double spin exchange mechanism suggested by Anderson and is responsible for the observed ${T}_{\mathrm{ss}}$ process.A resonant spin-spin interaction was observed between the electron bound to an iron impurity and the phosphorus donor electron when the magnetic field at which the two resonance lines overlap was traversed. The application of this "mixing" effect to a nuclear polarization scheme is discussed. A complete mixing of two levels was also observed in phosphorus doped silicon at a magnetic field of 40 oersteds.A spin diffusion process capable of transmitting a spin excitation to different parts of the resonance line was observed in arsenic doped silicon. This process proceeds in discrete steps with frequencies determined by the different Larmor frequencies of the ${\mathrm{Si}}^{29}$ nuclei situated at various lattice sites relative to the donor atom.