High-Stress Optical Birefringence in Pure and Degeneraten-Type Germanium

The stress birefringence in degenerate As- and Sb-doped Ge containing between $N=1.2\mathrm{}\times {10}^{18} \mathrm{and} 7.2\times {10}^{18}$ impurities per cc was measured as a function of uniaxial [111] compression at 1.4°K. Wavelengths in the range 1.8-2.5 μ and stresses up to 8×${10}^9$ dyn/${\mathrm{cm}}^2$ were used. These stresses were high enough to cause a transfer of all electrons to a single conduction-band valley, and thus effect a saturation in the birefringence of the free carriers. Deviations of the results from the simple degenerate model are ascribed to tail states below the conduction-band edge and a possible increase of effective mass with $N$. The birefringence due to interband transitions in As-doped Ge was found to differ by an amount proportional to $N$ from that of pure Ge and also from Sb-doped Ge. The cause for this difference is attributed to the large central-cell potential of As impurities. The stress optical constants of pure Ge were also measured in the above-mentioned wavelength range. Agreement with the data of Schmidt-Tiedemann was found. The stress optical constant for [111] stress $Q_{44}$ shows a linear dependence on the photon energy $E$ at 4.2° and 90°K, while the stress optical constant for [100] stress, $Q_{11}-Q_{12}$, deviates strongly from a linear dependence on $E$. In addition, the birefringence for [100] stress exhibits a nonlinear stress dependence. The stress birefringence of pure Ge is interpreted in terms of the effect of stress on the electronic transitions in the neighborhood of critical points in the interband density of states.