Determination of Shear Deformation Potentials from the Free-Carrier Piezobirefringence in Germanium and Silicon

The present investigations of the free-carrier piezobirefringence phenomenon verify that in $n$-type germanium and silicon as well as in $p$-type silicon this effect can be ascribed to intraband transitions of the carriers. It is demonstrated how a combined investigation of the low-stress and high-stress piezobirefringence in these materials provides a direct and independent method for determining deformation-potential constants. For $n$-type germanium we obtain ${\Xi }_u=18.0\mathrm{}\pm 0.5$ eV, for $n$-type silicon ${\Xi }_u=8.5\mathrm{}\pm 0.4$ eV; for $p$-type silicon a rather crude analytical approximation yields $b=-3.1\mathrm{}$ eV and $d=-8.3\mathrm{}$ eV. Finally, experimental evidence is given to support the assumption, that in $p$-type germanium intraband transitions alone cannot account for the free-carrier piezobirefringence.