Nanoanalytical quantification of the nitrogen content in $Ga(NAs)∕GaAs$ by using transmission electron microscopy in combination with refined structure factor calculation

We have studied systematically the nitrogen content in $Ga(NAs)∕GaAs$ quantum wells by (002) dark-field transmission electron microscopy (TEM). The nitrogen contents derived from this analysis, when assuming that all the atoms occupy their unperturbed positions in a virtual crystal, deviate significantly from the nitrogen contents we derive for the same samples by other methods; for example, high-resolution x-ray diffraction (XRD) and dynamical simulation of those XRD patterns. The nitrogen causes a significant local strain in the crystal and can accordingly displace the neighboring atoms dramatically. We show that, if the structure factor of the crystals is recalculated, taking these static displacements of the Ga atoms into account, the composition derived from the TEM analysis with that from XRD is in perfect agreement. It is hence necessary for tetragonally distorted crystals that have mixed sublattices containing atoms with different covalent radii to take these static displacements into account when quantification of the composition from dark-field or high-resolution TEM images is aimed for.