STEM moiré analysis for 2D strain measurements

A moiré pattern is created in a scanning transmission electron microscope (STEM) when the scan step is close to a crystalline periodicity. Usually, fringes are visible in only one direction, corresponding to a single set of lattice planes, but fringes can be formed in two directions or more. Using an accurate independent calibration, the strains in silicon devices have been determined from the spacing and orientation of one-directional STEM moiré fringes. In this report, we first discuss the origin of the STEM moiré, and then we show how an accurate calibration of the scan step can be obtained from the STEM moiré pattern itself, providing that we know initially only an approximate scan step and the planar spacing. The new calibration scheme also makes the STEM moiré experiments easier, since it can be applied for the moiré where the scan direction is not precisely aligned with the crystalline lattice. Finally, we show how the two-dimensional strain information will be readily extracted from two one-directional moiré patterns using the concept of geometric phase.