Phase contrast STEM for thin samples: Integrated differential phase contrast

It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR).