Ultrasonic Wave Propagation in Dopedn-Germanium andp-Silicon

The effect of doping germanium with $n$-type material and silicon with $p$-type material is to increase the attenuation and decrease the elastic moduli. The decrease in the $c_{44}$ elastic modulus for $n$-type germanium agrees fairly well with theoretical predictions. However, the modulus decrease in $p$-type silicon is much larger and varies with temperature much faster than predicted by any present theory. It is suggested that there is a temperature-induced change in hole population along the energy surfaces. The intervalley relaxation time, which determines the added attenuation, becomes independent of the doping for high dopings with the antimony time being about 100 times that for arsenic. This result indicates that the relative values are determined by the square of the triplet singlet separation which occurs near the impurity atoms. For $p$-type silicon the relaxation time at low temperatures increases very markedly indicating an activation-energy effect. The energies agree well with the energies measured by infrared techniques for the largest excited state orbits around the impurity atoms. The relaxation times measured at high temperatures indicate that the hole is transported $\frac{1}{3}$ cycle from one $〈111〉$ position to the next.