Z-contrast dependence of quantitative scanning transmission electron microscopy image of Si_1−xGe_x binary crystals

Highlights: • Compositional analysis was performed on Si_1−xGe_x binary crystal using HAADF image. • The intensity obeyed the power law without considering the static displacement. • The Rutherford scattering become dominant as the detector angle increased. - Abstract: A method of quantitative compositional analysis by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was established for Si_1−xGe_x binary crystals at atomic resolution. The relationship between the HAADF intensity I and the scattering cross section was investigated as a function of the Ge concentration. We showed experimentally that the atomic column intensity in a HAADF image of the Si_1−xGe_x binary crystals obeys the power law I ∝ Z^γ without considering the static displacement of the atoms. The exponent γ was quantitatively measured and found to vary from 1.5 to 1.9 as the collection angle increased up to 140 mrad, indicating that Rutherford scattering becomes dominant with increasing collection angle. These experimental results were discussed by comparison with a calculation of the differential cross section of electron scattering