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Nanoscale mapping of the full strain tensor, rotation and composition in partially relaxed In$_x$Ga$_{1-x}$N layers by scanning X-ray diffraction microscopy

Strain and composition play a fundamental role in semiconductor physics, since they are means to tune the electronic and optical properties of a material and hence develop new devices. Today it is still a challenge to measure strain in epitaxial systems in a non-destructive manner which becomes especially important in strain-engineered devices that often are subjected to intense stress. In this work, we demonstrate a microscopic mapping of the full tensors of strain and lattice orientation by means of scanning X-ray diffraction microscopy. We develope a formalism to extract all components of strain and orientation from a set of scanning diffraction measurements and apply the technique to a patterned In$_x$Ga$_{1-x}$N double layer to study strain relaxation and indium incorporation phenomena. The contributions due to varying indium content and threading dislocations are separated and analyzed.