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 Tₛ (Δmₛ=±1, ΔmI=0) was found to be independent of phosphorus concentration below {~}10¹⁶ P/cm³. Its value at 3200 oersteds and 1.25^∘{}K was {~}3×{}10⁺³ seconds and varied as 1/T for 1.3^∘K<T<2^∘K and as 1T⁷ for 2.5^∘K<T<4.2^∘K. The magnetic field dependence in the 1/T region suggests a direct phonon process. In the 1T⁷ region Tₛ was independent of the magnetic field between 3000 and 8000 oersteds. Above a concentration of 10¹⁶ P/cm³ Tₛ varied rapidly with donor concentration, dropping to 10^-4 seconds at 3×{}10¹⁷ P/cm³. In this concentration dependent region Tₛ was independent of the magnetic field but depended on the number of acceptors present. None of the Tₛ mechanisms can at present be accounted for by the theories of Pines, Bardeen, and Slichter, and Abrahams. The relaxation time Tₓ (Δmₛ=±1, ΔmI=∓1) was {~}30 hours at 3000 oersteds and {~}5 hours at 8000 oersteds in fair agreement with the theory of PBS. The relaxation time TN (ΔmI=±1, Δmₛ=0) at 1.25^∘{}K exceeded 10 hours.The effect of light was investigated with a monochromator for 0.5 ev<hν<2 ev. The number of carriers introduced by light was obtained from the Hall coefficient. In a sample with 7×{}10¹⁵ P/cm³, Tₛ was reduced to 25 seconds by 2×{}10⁶ electrons/cm³. Under the same conditions the spin-spin time Tₛₛ was reduced to 1 second. The bottleneck in the Tₛ-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 Tₛₛ 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 Si²⁹ nuclei situated at various lattice sites relative to the donor atom.