Improving the depth resolution of STEM-ADF sectioning by 3D deconvolution

Although the possibility of locating single atom in three dimensions using the scanning transmission electron microscope (STEM) has been discussed with the advent of aberration correction technology, it is still a big challenge. In this report we have developed deconvolution routines based on maximum entropy method (MEM) and Richardson-Lucy algorithm (RLA), which are applicable to the STEM-annular dark-field (ADF) though-focus images to improve the depth resolution. The new three-dimensional (3D) deconvolution routines require a limited defocus-range of STEM-ADF images that covers a whole sample and some vacuum regions. Since the STEM-ADF probe is infinitely elongated along the optical axis, a 3D convolution is performed with a two-dimensional (2D) convolution over xy-plane using the 2D fast Fourier transform in reciprocal space, and a one-dimensional convolution along the z-direction in real space. Using our new deconvolution routines, we have processed simulated focal series of STEM-ADF images for single Ce dopants embedded in wurtzite-type AlN. Applying the MEM, the Ce peaks are clearly localized along the depth, and the peak width is reduced down to almost one half. We also applied the new deconvolution routines to experimental focal series of STEM-ADF images of a monolayer graphene. The RLA gives smooth and high-P/B ratio scattering distribution, and the graphene layer can be easily detected. Using our deconvolution algorithms, we can determine the depth locations of the heavy dopants and the graphene layer within the precision of 0.1 and 0.2 nm, respectively. Thus, the deconvolution must be extremely useful for the optical sectioning with 3D STEM-ADF images.