Effect of Carrier Concentration on the Raman Frequencies of Si and Ge

Abstract

The first-order Raman spectrum of Ge and Si has been investigated as a function of carrier concentration. In $p$-type materials we observed large broadenings of the Raman line and large shifts to higher frequencies of the Stokes line. We attribute these effects to the splitting of the valence band produced by the $\overrightarrow{\mathrm{k}}\simeq 0$ optical phonon in a manner similar to the effects of doping on the $C_{44}$ elastic constant discussed by Keyes. From these results it is possible to estimate the coupling constant $d_0$ between optical phonons and holes. The $\overrightarrow{\mathrm{k}}\simeq 0$ phonon should also produce a splitting of the conduction band of Ge (but not of Si). However, for a given impurity concentration, the shifts observed in $n$-type materials are much smaller than those for $p$-type materials. The absence of large effects is probably due to the low rate of intervalley scattering. An effect on $n$-type Si related to the splitting of the $X_1$ conduction-band degeneracy by the phonon is also discussed and compared with the analogous effect on the elastic constants. It is shown that the internal stress parameter $\zeta$ is also affected by doping.