Comparison and spatial profiling of strain in [001]- and [111]-oriented ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs superlattices from Raman and x-ray experiments

We present spatial area maps of the built-in strain in [001]- and [111]-grown ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs superlattices obtained from Raman studies, and strain depth profiles obtained from x-ray rocking-curve (XRC) studies on the same samples. A theory developed for Raman scattering under applied uniaxial stress has been used to determine the internal strain from the phonon frequency shifts with respect to the unstrained bulk constituents. It is shown that in two-component heterostructures exhibiting single-peak behavior, an overestimation or underestimation of the strain may result if the effects of strain and alloying do not compensate each other completely. For the ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs system, we find that the average strain derived from the LO-phonon data compares well with the XRC results. But if the shift of the TO phonons in [111]-grown samples is used, an underestimate of the strain is found, which is explained by the above mechanism. Information about sample quality and strain variations related to growth are inferred from the strain maps.