Effects of strain gradients on strain measurements using geometrical phase analysis in the transmission electron microscope

An analysis of the effects of lens aberrations on the phase contrast images used for strain measurement by geometric phase analysis (GPA) in the TEM shows that errors may result when strain gradients are present and when ∇χ≠0 at the reciprocal lattice spacing used for the analysis. This conclusion is demonstrated experimentally using a model specimen consisting of a strained Si layer grown epitaxially on a Si–Ge alloy substrate. Image simulations for this model specimen show that strain gradients can introduce oscillations in strain maps when the defocus is not optimized for GPA. This work also makes it possible to identify other potential sources of error in GPA.