Fourier transform imaging of impurities in the unit cells of crystals: Mn in GaAs

The lattice sites of Mn in ferromagnetic (Ga,Mn)As thin films were imaged using the x-ray standing wave technique. The model-free images, obtained straightforwardly by Fourier inversion, disclose immediately that the Mn mostly substitutes the Ga with a small fraction residing on minority sites. The images further reveal variations in the Mn concentrations of the different sites upon post-growth treatments. Subsequent model refinement based on the directly reconstructed images resolves with high precision the complete Mn site distributions. It is found that post-growth annealing increases the fraction of substitutional Mn at the expense of interstitial Mn whereas hydrogenation has little influence on the Mn site distribution. Our study offers an element-specific high-resolution imaging approach for accurately determining the detailed site distributions of dilute concentrations of atoms in crystals.