Uniaxial stress dependence of the Orbach spin-lattice relaxation rate of phosphorous and arsenic donors in silicon

Abstract

The ESR absorption and dispersion signals of P and As donors in silicon have been measured as a function of uniaxial stress with an $X$-band spectrometer under saturation conditions in the temperature range between 12 and 20 K, where the spin-lattice relaxation rate $\frac{1}{{T}_{1}}$ is dominated by the Orbach process. The results have confirmed a suggestion by Abragam that uniaxial stress should produce a substantial decrease in the shallow-donor Orbach relaxation rate. These experiments support the hypothesis that the impurity spin-orbit interaction within the $1S\ensuremath{-}{T}_{2}$ manifold is the Orbach spin-flipping mechanism and point to the importance of the $1S\ensuremath{-}{T}_{2}$ level width in the relaxation process for P and As donors. Experiments have been performed for both longitudinal ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$) and transverse ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$) geometries with the compressive force $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}$ applied along the [100], [110], and [111] axes. Qualitative features of the data include: (i) $\frac{1}{{T}_{1}}$ decreases to about 20% of its zero stress value for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}\ensuremath{\parallel}[100]$ axis; (ii) a very small change in $\frac{1}{{T}_{1}}$ is observed for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}\ensuremath{\parallel}[111]$, (iii) a minimum in $\frac{1}{{T}_{1}}$ versus stress, followed by a very gradual rise in $\frac{1}{{T}_{1}}$ versus stress is observed for certain geometries; (iv) a dependence of $\frac{1}{{T}_{1}}$ on magnetic field direction is observed for the transverse case ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$) for a large constant [110] stress. It is demonstrated that all four of these effects are predicted by the valley-repopulation model involving only the $1S\ensuremath{-}{T}_{2}$ states for the Orbach relaxation rate.