Effect of Stress on the Donor Wave Functions in Germanium

The effect of the corrections to the effective-mass approximation on the stress dependence of the donor wave functions has been re-examined. It is found that not only the relative valley contributions to the ground-state wave function are changed by the stress, but also the individual envelope functions $F_j\left(\mathrm{r}\right)$ which originate from the $j$ conduction-band valleys. The stress dependence of the $F_j\left(\mathrm{r}\right)$ depends strongly on the value of the valley-orbit splitting of the donor. This can explain qualitatively the different behavior of the piezoresistance effect in the impurity conduction range of germanium doped with antimony, arsenic, or phosphorus. The stress dependence of the hyperfine splitting of the electron spin resonance is shown to be very insensitive to the stress-induced changes in $F_j\left(\mathrm{r}\right)$ except in the limit of very large stresses.