title: Quantitative analysis of ultrathin doping layers in semiconductors using high-angle annular dark field images.
abstract: It is well known that the high-angle annular dark field (HAADF) technique in scanning transmission electron microscopy is an incoherent imaging process in the lateral (xy) plane. However, as a consequence of the existence of partial coherence in the z direction, accurate quantitative interpretation of image intensity is difficult. The effects of coherence in the z direction can be reduced by increasing the inner collector angle of the annular detector so that the scattering from atoms in the z direction is essentially incoherent. We thus show that it is feasible to quantify the total As concentration of ultrathin InAsxP1-x layers in InP in a simple but accurate way using a thickness integrated Bloch wave calculation including phonon scattering with a large inner collector angle of the annular detector of around 150 mrad. We compare the As composition derived from this approach with that from the Fresnel method and high resolution imaging. We also show that the non-linear variation of the HAADF intensity with thickness is consistent with our simpler simulations for such conditions. Therefore, this approach enables us easily and quickly to quantify compositions using HAADF images. The tetragonal distortion due to lattice mismatch is also shown to influence the contrast and has been included in the calculations.